Finite Group Databasebeta

← #35197174

Subgroups — #35197174

Order 20224.

7900 conjugacy classes of subgroups.

The subgroup lattice has 2008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777917C214yesmaximal, complemented
2#23777915C214yesmaximal, complemented
3#23777801C212yesmaximal, complemented
4#23777799C212yesmaximal, complemented
5#23777775C212yesmaximal, complemented
6#23777773C212yesmaximal, complemented
7#23777769C214yesmaximal, complemented
8#23777636C214yesmaximal, complemented
9#23777435C212yesmaximal, complemented
10#23777433C212yesmaximal, complemented
11#23777428C214yesmaximal, complemented
12#23777313C211yesmaximal, characteristic, complemented
13#23777312C212yesmaximal, complemented
14#23777277C212yesmaximal, complemented
15#23777269C212yesmaximal, complemented
16#23777253C212yesmaximal, complemented
17#23777245C212yesmaximal, complemented
18#23777178C211yesmaximal, characteristic, complemented
19#23777173C212yesmaximal, complemented
20#23777173C211yesmaximal, characteristic, complemented
21#23777163C212yesmaximal, complemented
22#23777158C212yesmaximal, complemented
23#23777070C212yesmaximal, complemented
24#23777066C214yesmaximal, complemented
25#23777064C212yesmaximal, complemented
26#23776693C211yesmaximal, characteristic, complemented
27C2×#19099114C211yesmaximal, characteristic, complemented
28#532×D79C211yesmaximal, characteristic, complemented
29C79×#3511C211yesmaximal, characteristic, complemented
30C2×#14579207C2212yescomplemented
31C2×#14579207C2214yescomplemented
32C2×#14579207C2212yescomplemented
33C22×#11929625C2212yescomplemented
34C2×#41×D79C2212yescomplemented
35#19099309C2218yescomplemented
36#19099305C2218yescomplemented
37#19099304C2218yescomplemented
38#19099303C2218yescomplemented
39#19099298C2214yescomplemented
40#19099298C2214yescomplemented
41#19099296C2214yescomplemented
42#19099295C2214yescomplemented
43#19099287C2212yescomplemented
44#19099285C2214yescomplemented
45#19099279C2212yescomplemented
46#19099276C2214yescomplemented
47#19099276C2214yescomplemented
48#19099274C2212yescomplemented
49#19099269C2214yescomplemented
50#19099266C2214yescomplemented
51#19099264C2218yescomplemented
52#19099261C2214yescomplemented
53#19099261C2214yescomplemented
54#19099257C2214yescomplemented
55#19099257C2214yescomplemented
56#19099235C2212yescomplemented
57#19099235C2214yescomplemented
58#19099235C2214yescomplemented
59#19099235C2212yescomplemented
60#19099234C2214yescomplemented
61#19099234C2212yescomplemented
62#19099234C2214yescomplemented
63#19099234C2212yescomplemented
64#19099232C2214yescomplemented
65#19099231C2214yescomplemented
66#19099225C2214yescomplemented
67#19099224C2214yescomplemented
68#19099223C2214yescomplemented
69#19099216C2212yescomplemented
70#19099215C2214yescomplemented
71#19099215C2214yescomplemented
72#19099214C2214yescomplemented
73#19099210C2214yescomplemented
74#19099210C2214yescomplemented
75#19099208C2218yescomplemented
76#19099208C2214yescomplemented
77#19099206C2218yescomplemented
78#19099206C2214yescomplemented
79#19099205C2218yescomplemented
80#19099204C2214yescomplemented
81#19099204C2218yescomplemented
82#19099204C2214yescomplemented
83#19099204C2214yescomplemented
84#19099204C2214yescomplemented
85#19099204C2214yescomplemented
86#19099202C2218yescomplemented
87#19099201C2214yescomplemented
88D4×D316C2212yescomplemented
89D4×D316C2212yescomplemented
90D4×D316C2218yescomplemented
91D4×D316C2214yescomplemented
92D4×D316C2214yescomplemented
93D4×D316C2214yescomplemented
94D4×D316C2214yescomplemented
95D4×D316C2212yescomplemented
96D4×D316C2212yescomplemented
97#19099197C2214yescomplemented
98#19099197C2214yescomplemented
99#19099197C2218yescomplemented
100#19099197C2214yescomplemented
101#19099197C2214yescomplemented
102#19099197C2214yescomplemented
103#19099197C2214yescomplemented
104#19099197C2214yescomplemented
105#19099187C2214yescomplemented
106#19099186C2214yescomplemented
107#19099185C2214yescomplemented
108#19099169C2214yescomplemented
109#19099169C2214yescomplemented
110#19099166C2214yescomplemented
111#19099164C2214yescomplemented
112#19099153C2218yescomplemented
113#19099152C2218yescomplemented
114#19099152C2218yescomplemented
115#19099149C2218yescomplemented
116#19099147C2218yescomplemented
117#19099146C2218yescomplemented
118#19099144C2214yescomplemented
119#19099144C2212yescomplemented
120#19099143C2214yescomplemented
121#19099143C2218yescomplemented
122#19099143C2214yescomplemented
123#19099132C2214yescomplemented
124#19099132C2214yescomplemented
125#19099132C2212yescomplemented
126#19099132C2214yescomplemented
127#19099131C2218yescomplemented
128#19099131C2214yescomplemented
129#19099131C2214yescomplemented
130#19099131C2214yescomplemented
131#19099129C2214yescomplemented
132#19099129C2214yescomplemented
133#19099127C2212yescomplemented
134#19099127C2214yescomplemented
135#19099124C2218yescomplemented
136#19099121C2218yescomplemented
137#19099118C2212yescomplemented
138#19099117C2211yescharacteristic, complemented
139#19099117C2211yescharacteristic, complemented
140#19099116C2211yescharacteristic, complemented
141#19099114C2212yescomplemented
142#19099114C2212yescomplemented
143#19099114C2212yescomplemented
144#19099114C2212yescomplemented
145#19099114C2212yescomplemented
146#19099114C2212yescomplemented
147#19099114C2212yescomplemented
148#19099114C2211yescharacteristic, complemented
149#19099114C2212yescomplemented
150#19099114C2212yescomplemented
151#19099114C2212yescomplemented
152#19099113C2212yescomplemented
153#19099113C2211yescharacteristic, complemented
154#19099112C2212yescomplemented
155#19099111C2211yescharacteristic, complemented
156#19099110C2212yescomplemented
157#19099110C2211yescharacteristic, complemented
158#19099110C2211yescharacteristic, complemented
159#19099110C2212yescomplemented
160#19099109C2211yescharacteristic, complemented
161#19099109C2212yescomplemented
162#19099108C2212yescomplemented
163#19099108C2212yescomplemented
164C4⋊Q8×D79C2211yescharacteristic, complemented
165C2×#14579158C2211yescharacteristic, complemented
166C2×#14579158C2212yescomplemented
167#127×D79C2211yescharacteristic, complemented
168#127×D79C2212yescomplemented
169#19099100C2211yescharacteristic, complemented
170#19099100C2211yescharacteristic, complemented
171#19099095C2211yescharacteristic, complemented
172#19099095C2211yescharacteristic, complemented
173#19099093C2212yescomplemented
174#19099093C2212yescomplemented
175#19099091C2212yescomplemented
176#19099091C2212yescomplemented
177C2×#14579150C2212yescomplemented
178#124×D79C2212yescomplemented
179#19099076C2214yescomplemented
180#19099075C2211yescharacteristic, complemented
181#19099075C2214yescomplemented
182#19099072C2212yescomplemented
183#19099072C2218yescomplemented
184#19099072C2212yescomplemented
185#19099070C2211yescharacteristic, complemented
186C2×#14579136C2212yescomplemented
187C2×#14579136C2214yescomplemented
188C2×#14579136C2212yescomplemented
189#121×D79C2214yescomplemented
190#121×D79C2212yescomplemented
191#121×D79C2218yescomplemented
192#121×D79C2212yescomplemented
193#19099045C2214yescomplemented
194#19099044C2212yescomplemented
195#19099037C2214yescomplemented
196#19099035C2214yescomplemented
197C4×#11929624C2212yescomplemented
198C4×#11929624C2211yescharacteristic, complemented
199C4×#11929624C2212yescomplemented
200C2×#14579123C2212yescomplemented
201C2×#14579123C2212yescomplemented
202C4×D4×D79C2212yescomplemented
203C4×D4×D79C2212yescomplemented
204C2×C42×D79C2211yescharacteristic, complemented
205#556×C79C2212yescomplemented
206#555×C79C2212yescomplemented
207#554×C79C2212yescomplemented
208#553×C79C2214yescomplemented
209#548×C79C2214yescomplemented
210#547×C79C2212yescomplemented
211#542×C79C2214yescomplemented
212#537×C79C2212yescomplemented
213#533×C79C2212yescomplemented
214#532×C79C2211yescharacteristic, complemented
215#532×C79C2212yescomplemented
216C2×C4⋊Q8×C79C2211yescharacteristic, complemented
217#520×C79C2212yescomplemented
218C4×#41×C79C2211yescharacteristic, complemented
219#14579207—416no—
220#14579207—48no—
221#14579207—48no—
222C2×#11929625—48no—
223C2×#11929625C2314yes—
224C2×#11929625C2314yes—
225C2×#11929625C2314yes—
226C2×#11929625C2314yes—
227C2×#11929625C2314yes—
228C2×#11929625C2314yes—
229C2×#11929625C2312yes—
230C2×#11929625C2314yes—
231C2×#11929624C2312yes—
232C2×#11929624C2311yescharacteristic
233C2×#11929624C2312yes—
234C2×#11929624C2318yes—
235C2×#11929624C2314yes—
236C2×#11929624C2314yes—
237C2×#11929624C2314yes—
238C2×#11929624C2312yes—
239C2×#11929623C2314yes—
240C2×#11929623C2312yes—
241#41×D79—48no—
242C2×Q8×D79C2312yes—
243C22×D316C2312yes—
244C22×D316C2314yes—
245C22×D316C2314yes—
246C22×D316C2318yes—
247C22×D316C2314yes—
248C22×D316C2312yes—
249C22×D316C2314yes—
250C22×D316C2314yes—
251C22×D316C2312yes—
252C2×D4×D79C2312yes—
253C2×D4×D79C2318yes—
254C2×D4×D79C2318yes—
255C2×D4×D79C2318yes—
256C2×D4×D79C2318yes—
257C2×D4×D79C2314yes—
258C2×D4×D79C2314yes—
259C2×D4×D79C2314yes—
260C2×D4×D79C2312yes—
261C2×D4×D79C2314yes—
262C2×D4×D79C2314yes—
263C2×D4×D79C2312yes—
264C22×C4×D79C2311yescharacteristic
265C22×C4×D79C2311yescharacteristic
266C22×C4×D79C2311yescharacteristic
267C22×C4×D79C2314yes—
268C22×C4×D79C2314yes—
269#14579161C2311yescharacteristic
270#14579160C2312yes—
271#14579160C2311yescharacteristic
272#14579160C2312yes—
273#14579160C2311yescharacteristic
274#14579159C2311yescharacteristic
275#14579159C2312yes—
276#14579158C2314yes—
277#14579158C2312yes—
278#14579158C2312yes—
279#14579158C2314yes—
280#14579158C2314yes—
281#14579158C2318yes—
282#14579158C2311yescharacteristic
283#14579158C2312yes—
284#14579158C2312yes—
285#14579157C2314yes—
286#14579157C2311yescharacteristic
287#14579157C2312yes—
288#14579157C2312yes—
289#14579157C2318yes—
290#14579157C2314yes—
291#14579157C2314yes—
292#14579157C2312yes—
293#14579156C2318yes—
294#14579156C2318yes—
295#14579156C2312yes—
296#14579156C2312yes—
297#14579155C2318yes—
298#14579154C2312yes—
299#14579154C2312yes—
300#14579152C2314yes—
301#14579152C2311yescharacteristic
302#14579152C2311yescharacteristic
303#14579151C2312yes—
304#14579151C2312yes—
305#14579150C2314yes—
306#14579150C2318yes—
307#14579150C2314yes—
308#14579150C2314yes—
309#14579150C2311yescharacteristic
310#14579150C2312yes—
311#14579150C2314yes—
312#14579150C2314yes—
313#14579150C2314yes—
314#14579149C2318yes—
315#14579149C2318yes—
316#14579149C2312yes—
317#14579149C2314yes—
318#14579148C2311yescharacteristic
319#14579148C2312yes—
320#14579147C2318yes—
321#14579147C2314yes—
322#14579147C2318yes—
323#14579147C2312yes—
324#14579147C2312yes—
325#14579147C2314yes—
326#14579146C2318yes—
327#14579146C2318yes—
328#14579146C2318yes—
329#14579146C2318yes—
330#14579146C2318yes—
331#14579146C2318yes—
332#14579146C2312yes—
333#14579146C2312yes—
334#14579145C2318yes—
335#14579145C2312yes—
336#14579144C2318yes—
337#14579143C2318yes—
338#14579143C2318yes—
339#14579143C2318yes—
340#14579143C2312yes—
341#14579143C2312yes—
342#14579142C2312yes—
343#14579141C2311yescharacteristic
344#14579141C2314yes—
345#14579141C2318yes—
346#14579141C2314yes—
347#14579141C2311yescharacteristic
348#14579139C2312yes—
349#14579139C2318yes—
350#14579139C2318yes—
351#14579139C2312yes—
352#14579138C2312yes—
353#14579138C2312yes—
354#14579137C2311yescharacteristic
355#14579137C2318yes—
356#14579137C2314yes—
357#14579137C2311yescharacteristic
358#14579136C2318yes—
359#14579136C2318yes—
360#14579136C2314yes—
361#14579136C2318yes—
362#14579136C2314yes—
363#14579136C2318yes—
364#14579136C2314yes—
365#14579136C2314yes—
366#14579136C2314yes—
367#14579136C2318yes—
368#14579136C2314yes—
369#14579136C2318yes—
370#14579136C2318yes—
371#14579136C2314yes—
372#14579136C2312yes—
373#14579136C2314yes—
374#14579136C2314yes—
375#14579136C2314yes—
376#14579136C2314yes—
377#14579136C2314yes—
378#14579136C2312yes—
379#14579136C2314yes—
380#14579136C2314yes—
381#14579136C2314yes—
382#14579136C2311yescharacteristic
383#14579136C2311yescharacteristic
384#14579135C2318yes—
385#14579135C2314yes—
386#14579135C2314yes—
387#14579135C2318yes—
388#14579135C2318yes—
389#14579135C2318yes—
390#14579135C2314yes—
391#14579135C2312yes—
392#14579135C2312yes—
393#14579135C2314yes—
394#14579134C2318yes—
395#14579134C2314yes—
396#14579134C2318yes—
397#14579134C2318yes—
398#14579134C2318yes—
399#14579134C2318yes—
400#14579134C2318yes—
401#14579134C2318yes—
402#14579134C2318yes—
403#14579134C2318yes—
404#14579134C2314yes—
405#14579134C2312yes—
406#14579134C2312yes—
407#14579133C2314yes—
408#14579133C2318yes—
409#14579133C2312yes—
410#14579133C2314yes—
411#14579133C2312yes—
412#14579132C2318yes—
413#14579132C2312yes—
414#14579132C2312yes—
415#14579132C2311yescharacteristic
416#14579132C2311yescharacteristic
417#14579131C2318yes—
418#14579131C2318yes—
419#14579131C2318yes—
420#14579131C2318yes—
421#14579131C2318yes—
422#14579131C2318yes—
423#14579131C2318yes—
424#14579131C2318yes—
425#14579131C2318yes—
426#14579131C2318yes—
427#14579131C2318yes—
428#14579131C2312yes—
429#14579131C2318yes—
430#14579129C2318yes—
431#14579129C2318yes—
432#14579129C2318yes—
433#14579129C2312yes—
434#14579129C2318yes—
435Q8×Dic79C2314yes—
436C4×Dic158C2312yes—
437C4×Dic158C2311yescharacteristic
438C4×Dic158C2312yes—
439C4×Dic158C2311yescharacteristic
440C4×Dic158C2312yes—
441C4×Dic158C2312yes—
442#14579126C2314yes—
443C4×D316C2318yes—
444C4×D316C2318yes—
445C4×D316C2318yes—
446C4×D316C2314yes—
447C4×D316C2314yes—
448C4×D316C2311yescharacteristic
449C4×D316C2312yes—
450C4×D316C2312yes—
451C4×D316C2311yescharacteristic
452C4×D316C2312yes—
453C4×D316C2312yes—
454C4×D316C2312yes—
455C4×D316C2312yes—
456D4×Dic79C2312yes—
457D4×Dic79C2312yes—
458#14579123C2314yes—
459#14579123C2318yes—
460#14579123C2314yes—
461#14579123C2312yes—
462#14579123C2314yes—
463#14579123C2314yes—
464#14579123C2314yes—
465#14579123C2314yes—
466#14579123C2314yes—
467#14579123C2314yes—
468#14579123C2314yes—
469#14579123C2312yes—
470#14579123C2314yes—
471#14579123C2314yes—
472#14579123C2314yes—
473C4×C22⋊D79C2318yes—
474C4×C22⋊D79C2318yes—
475C4×C22⋊D79C2312yes—
476C4×C22⋊D79C2312yes—
477C4×C22⋊D79C2312yes—
478C4×C22⋊D79C2312yes—
479C4×C22⋊D79C2312yes—
480C4×C22⋊D79C2312yes—
481C4×C22⋊D79C2314yes—
482C4×C22⋊D79C2312yes—
483C4×C22⋊D79C2312yes—
484C4×C22⋊D79C2312yes—
485C4×C22⋊D79C2312yes—
486C4×C22⋊D79C2314yes—
487(C22⋊D79)⋊C4C2314yes—
488(C22⋊D79)⋊C4C2318yes—
489(C22⋊D79)⋊C4C2314yes—
490#14579120C2312yes—
491#14579120C2312yes—
492#14579120C2311yescharacteristic
493#14579119C2314yes—
494#14579119C2314yes—
495#14579118C2312yes—
496#14579118C2312yes—
497#14579118C2312yes—
498#14579118C2312yes—
499#14579118C2318yes—
500#14579118C2312yes—
501C4⋊C4×D79C2312yes—
502C4⋊C4×D79C2314yes—
503C4⋊C4×D79C2318yes—
504C4⋊C4×D79C2312yes—
505C2×(C2×D79)⋊C4C2314yes—
506C2×(C2×D79)⋊C4C2318yes—
507C2×(C2×D79)⋊C4C2314yes—
508C22⋊C4×D79C2318yes—
509C22⋊C4×D79C2318yes—
510C22⋊C4×D79C2314yes—
511C22⋊C4×D79C2318yes—
512C22⋊C4×D79C2314yes—
513C2×C4×Dic79C2311yescharacteristic
514C2×C4×Dic79C2311yescharacteristic
515C2×C4×Dic79C2311yescharacteristic
516C42×D79C2311yescharacteristic
517C42×D79C2311yescharacteristic
518C42×D79C2311yescharacteristic
519C42×D79C2311yescharacteristic
520C42×D79C2311yescharacteristic
521C42×D79C2311yescharacteristic
522C42×D79C2311yescharacteristic
523C42×D79C2311yescharacteristic
524C42×D79C2312yes—
525C2×#41×C79C2311yescharacteristic
526C2×#41×C79C2312yes—
527C2×#41×C79C2314yes—
528C22×Q8×C79C2312yes—
529C4⋊Q8×C79C2312yes—
530C4⋊Q8×C79C2312yes—
531C4⋊Q8×C79C2312yes—
532C4⋊Q8×C79C2312yes—
533C4⋊Q8×C79C2311yescharacteristic
534#127×C79C2311yescharacteristic
535#126×C79C2318yes—
536#125×C79C2314yes—
537#124×C79C2318yes—
538#124×C79C2314yes—
539#124×C79C2312yes—
540#123×C79C2318yes—
541C22⋊Q8×C79C2318yes—
542C22⋊Q8×C79C2314yes—
543C22⋊Q8×C79C2314yes—
544C22⋊Q8×C79C2314yes—
545#121×C79C2314yes—
546#121×C79C2314yes—
547#121×C79C2312yes—
548#121×C79C2312yes—
549#121×C79C2318yes—
550#121×C79C2314yes—
551C4×Q8×C79C2314yes—
552C4×Q8×C79C2314yes—
553C4×Q8×C79C2311yescharacteristic
554C4×Q8×C79C2311yescharacteristic
555C4×D4×C79C2318yes—
556C4×D4×C79C2314yes—
557C4×D4×C79C2311yescharacteristic
558C4×D4×C79C2312yes—
559C4×D4×C79C2312yes—
560C4×D4×C79C2311yescharacteristic
561C4×D4×C79C2314yes—
562C4×D4×C79C2312yes—
563C4×D4×C79C2312yes—
564#117×C79C2311yescharacteristic
565#117×C79C2312yes—
566#117×C79C2314yes—
567#117×C79C2314yes—
568C2×C4⋊C4×C79C2314yes—
569C2×C4⋊C4×C79C2312yes—
570C2×C4⋊C4×C79C2312yes—
571C2×C42×C79C2311yescharacteristic
572C2×C42×C79C2312yes—
573C23×D79C2411yescharacteristic
574C23×D79C2414yes—
575C23×D79C2414yes—
576C23×D79C2418yes—
577C23×D79C2418yes—
578#11929625—216no—
579#11929625—44no—
580#11929625—48no—
581#11929625—48no—
582#11929625—48no—
583#11929625—48no—
584#11929625—48no—
585#11929625—48no—
586#11929624—28no—
587#11929624—28no—
588#11929624—24no—
589#11929624—416no—
590#11929624—48no—
591#11929624—48no—
592#11929624—48no—
593#11929624—44no—
594#11929623—48no—
595#11929623—44no—
596C2×Dic158C2412yes—
597C2×Dic158C2412yes—
598C2×Dic158C2411yescharacteristic
599C2×Dic158C2414yes—
600C2×Dic158C2412yes—
601Q8×D79—44no—
602C2×D316—28no—
603C2×D316—44no—
604C2×D316—48no—
605C2×D316—48no—
606C2×D316—48no—
607C2×D316—44no—
608C2×D316—48no—
609C2×D316—48no—
610C2×D316—416no—
611C2×D316C2414yes—
612C2×D316C2414yes—
613C2×D316C2412yes—
614C2×D316C2412yes—
615C2×D316C2411yescharacteristic
616C2×D316C2418yes—
617C2×D316C2412yes—
618C2×D316C2414yes—
619C2×D316C2414yes—
620C2×D316C2412yes—
621C2×D316C2414yes—
622C2×D316C2412yes—
623C2×D316C2418yes—
624C2×D316C2414yes—
625C2×D316C2418yes—
626C2×D316C2418yes—
627C2×D316C2418yes—
628C2×D316C2418yes—
629C2×D316C2414yes—
630C2×D316C2418yes—
631C2×C22⋊D79C2414yes—
632C2×C22⋊D79C2414yes—
633C2×C22⋊D79C2412yes—
634C2×C22⋊D79C2412yes—
635C2×C22⋊D79C2412yes—
636C2×C22⋊D79C2414yes—
637C2×C22⋊D79C2414yes—
638C2×C22⋊D79C2412yes—
639C2×C22⋊D79C2412yes—
640C2×C22⋊D79C2418yes—
641C2×C22⋊D79C2418yes—
642C2×C22⋊D79C2418yes—
643C2×C22⋊D79C2414yes—
644C2×C22⋊D79C2418yes—
645D4×D79—28no—
646D4×D79—416no—
647D4×D79—48no—
648D4×D79—416no—
649D4×D79—416no—
650D4×D79—416no—
651D4×D79—44no—
652D4×D79—48no—
653D4×D79—48no—
654D4×D79—48no—
655D4×D79—44no—
656D4×D79—48no—
657C22×Dic79C2411yescharacteristic
658C22×Dic79C2411yescharacteristic
659C22×Dic79C2414yes—
660C22×Dic79C2411yescharacteristic
661C2×C4×D79—24no—
662C2×C4×D79—24no—
663C2×C4×D79—48no—
664C2×C4×D79—42no—
665C2×C4×D79—48no—
666C2×C4×D79C2411yescharacteristic
667C2×C4×D79C2411yescharacteristic
668C2×C4×D79C2411yescharacteristic
669C2×C4×D79C2414yes—
670C2×C4×D79C2411yescharacteristic
671C2×C4×D79C2412yes—
672C2×C4×D79C2412yes—
673C2×C4×D79C2418yes—
674C2×C4×D79C2412yes—
675C2×C4×D79C2411yescharacteristic
676C2×C4×D79C2411yescharacteristic
677C2×C4×D79C2411yescharacteristic
678C2×C4×D79C2411yescharacteristic
679C2×C4×D79C2411yescharacteristic
680C2×C4×D79C2414yes—
681C2×C4×D79C2414yes—
682C2×C4×D79C2418yes—
683C2×C4×D79C2418yes—
684C2×C4×D79C2418yes—
685C2×C4×D79C2418yes—
686C2×C4×D79C2411yescharacteristic
687C2×C4×D79C2411yescharacteristic
688C2×C4×D79C2411yescharacteristic
689C4⋊Dic79C2411yescharacteristic
690C4⋊Dic79C2412yes—
691C4⋊Dic79C2412yes—
692C4⋊Dic79C2418yes—
693C4⋊Dic79C2411yescharacteristic
694C4⋊Dic79C2412yes—
695C4⋊Dic79C2412yes—
696C4⋊Dic79C2412yes—
697C4⋊Dic79C2412yes—
698Dic79⋊C4C2412yes—
699Dic79⋊C4C2414yes—
700Dic79⋊C4C2414yes—
701Dic79⋊C4C2418yes—
702Dic79⋊C4C2412yes—
703Dic79⋊C4C2412yes—
704Dic79⋊C4C2412yes—
705Dic79⋊C4C2412yes—
706Dic79⋊C4C2412yes—
707Dic79⋊C4C2412yes—
708Dic79⋊C4C2412yes—
709Dic79⋊C4C2412yes—
710Dic79⋊C4C2412yes—
711C22⋊Dic79C2412yes—
712C22⋊Dic79C2412yes—
713C22⋊Dic79C2414yes—
714C22⋊Dic79C2414yes—
715C22⋊Dic79C2412yes—
716C22⋊Dic79C2412yes—
717C22⋊Dic79C2412yes—
718(C2×D79)⋊C4C2412yes—
719(C2×D79)⋊C4C2414yes—
720(C2×D79)⋊C4C2418yes—
721(C2×D79)⋊C4C2418yes—
722(C2×D79)⋊C4C2414yes—
723(C2×D79)⋊C4C2414yes—
724(C2×D79)⋊C4C2414yes—
725(C2×D79)⋊C4C2418yes—
726(C2×D79)⋊C4C2418yes—
727(C2×D79)⋊C4C2412yes—
728(C2×D79)⋊C4C2418yes—
729(C2×D79)⋊C4C2418yes—
730(C2×D79)⋊C4C2418yes—
731(C2×D79)⋊C4C2418yes—
732(C2×D79)⋊C4C2412yes—
733(C2×D79)⋊C4C2412yes—
734(C2×D79)⋊C4C2412yes—
735(C2×D79)⋊C4C2412yes—
736(C2×D79)⋊C4C2412yes—
737(C2×D79)⋊C4C2412yes—
738(C2×D79)⋊C4C2412yes—
739(C2×D79)⋊C4C2412yes—
740(C2×D79)⋊C4C2418yes—
741(C2×D79)⋊C4C2418yes—
742(C2×D79)⋊C4C2418yes—
743C4×Dic79C2411yescharacteristic
744C4×Dic79C2411yescharacteristic
745C4×Dic79C2411yescharacteristic
746C4×Dic79C2411yescharacteristic
747C4×Dic79C2411yescharacteristic
748C4×Dic79C2411yescharacteristic
749C4×Dic79C2411yescharacteristic
750C4×Dic79C2411yescharacteristic
751C4×Dic79C2411yescharacteristic
752C4×Dic79C2411yescharacteristic
753C4×Dic79C2411yescharacteristic
754C4×Dic79C2411yescharacteristic
755C4×Dic79C2412yes—
756C4×Dic79C2412yes—
757C4×Dic79C2412yes—
758C4×Dic79C2418yes—
759#41×C79—28no—
760#41×C79—24no—
761#41×C79—48no—
762C2×Q8×C79—44no—
763C2×Q8×C79C2412yes—
764C2×Q8×C79C2411yescharacteristic
765C2×Q8×C79C2414yes—
766C2×Q8×C79C2414yes—
767C2×D4×C79C2414yes—
768C2×D4×C79C2412yes—
769C2×D4×C79C2412yes—
770C2×D4×C79C2412yes—
771C2×D4×C79C2411yescharacteristic
772C2×D4×C79C2412yes—
773C2×D4×C79C2418yes—
774C22×C4×C79C2412yes—
775C22×C4×C79C2414yes—
776C22×C4×C79C2412yes—
777C22×C4×C79C2412yes—
778C22×C4×C79C2411yescharacteristic
779C22×C4×C79C2411yescharacteristic
780C22×C4×C79C2418yes—
781C22×C4×C79C2414yes—
782C22×C4×C79C2411yescharacteristic
783C4⋊C4×C79C2411yescharacteristic
784C4⋊C4×C79C2414yes—
785C4⋊C4×C79C2414yes—
786C4⋊C4×C79C2414yes—
787C4⋊C4×C79C2418yes—
788C4⋊C4×C79C2414yes—
789C4⋊C4×C79C2411yescharacteristic
790C4⋊C4×C79C2412yes—
791C4⋊C4×C79C2412yes—
792C4⋊C4×C79C2412yes—
793C4⋊C4×C79C2412yes—
794C4⋊C4×C79C2418yes—
795C22⋊C4×C79C2412yes—
796C22⋊C4×C79C2418yes—
797C22⋊C4×C79C2412yes—
798C22⋊C4×C79C2412yes—
799C22⋊C4×C79C2418yes—
800C22⋊C4×C79C2418yes—
801C22⋊C4×C79C2414yes—
802C22⋊C4×C79C2414yes—
803C42×C79C2411yescharacteristic
804C42×C79C2412yes—
805C42×C79C2411yescharacteristic
806C42×C79C2412yes—
807C42×C79C2411yescharacteristic
808C42×C79C2411yescharacteristic
809C42×C79C2412yes—
810C42×C79C2418yes—
811C23×C79C2512yes—
812C23×C79C2514yes—
813C23×C79C2511yescharacteristic
814C22×D79—22no—
815C22×D79—28no—
816C22×D79—22no—
817C22×D79—28no—
818C22×D79—41no—
819C22×D79—44no—
820C22×D79—44no—
821C22×D79—44no—
822C22×D79—44no—
823C22×D79—48no—
824C22×D79—48no—
825C22×D79—48no—
826C22×D79—48no—
827C22×D79—48no—
828C22×D79—48no—
829C22×D79C2512yes—
830C22×D79C2514yes—
831C22×D79C2518yes—
832C22×D79C2511yescharacteristic
833C22×D79C2511yescharacteristic
834Q8×C79—24no—
835Q8×C79—28no—
836Q8×C79—22no—
837Q8×C79—44no—
838D4×C79—24no—
839D4×C79—28no—
840D4×C79—24no—
841D4×C79—22no—
842D4×C79—24no—
843D4×C79—24no—
844D4×C79—48no—
845C2×C4×C79—22no—
846C2×C4×C79—28no—
847C2×C4×C79—24no—
848C2×C4×C79—24no—
849C2×C4×C79—22no—
850C2×C4×C79—24no—
851C2×C4×C79—44no—
852C2×C4×C79—48no—
853C2×C4×C79H(5,𝔽2)14yescomplemented
854C2×C4×C79C2511yescharacteristic
855C2×C4×C79C2511yescharacteristic
856C2×C4×C79C2518yes—
857C2×C4×C79C2512yes—
858C2×C4×C79C2512yes—
859C2×C4×C79C2514yes—
860C2×C4×C79C2512yes—
861C2×C4×C79C2511yescharacteristic
862C2×C4×C79C2511yescharacteristic
863C2×C4×C79C2511yescharacteristic
864C2×C4×C79C2511yescharacteristic
865C22⋊D79—24no—
866C22⋊D79—28no—
867C22⋊D79—24no—
868C22⋊D79—28no—
869C22⋊D79—24no—
870C22⋊D79—48no—
871C22⋊D79—48no—
872C22⋊D79—48no—
873C22⋊D79—48no—
874C22⋊D79—44no—
875C22⋊D79—44no—
876C22⋊D79—44no—
877C22⋊D79—42no—
878C22⋊D79—42no—
879C2×Dic79—22no—
880C2×Dic79—22no—
881C2×Dic79—41no—
882C2×Dic79—44no—
883C2×Dic79C2512yes—
884C2×Dic79C2511yescharacteristic
885C2×Dic79C2511yescharacteristic
886C2×Dic79C2511yescharacteristic
887C2×Dic79C2511yescharacteristic
888C2×Dic79C2511yescharacteristic
889C2×Dic79C2514yes—
890C2×Dic79C2512yes—
891C2×Dic79C2512yes—
892C2×Dic79C2511yescharacteristic
893D316—216no—
894D316—24no—
895D316—24no—
896D316—28no—
897D316—28no—
898D316—24no—
899D316—28no—
900D316—22no—
901D316—24no—
902D316—28no—
903D316—48no—
904D316—48no—
905D316—48no—
906D316—44no—
907D316—48no—
908D316—48no—
909D316—44no—
910D316—44no—
911D316—48no—
912D316—42no—
913C4×D79—22no—
914C4×D79—22no—
915C4×D79—22no—
916C4×D79—22no—
917C4×D79—22no—
918C4×D79—22no—
919C4×D79—28no—
920C4×D79—24no—
921C4×D79—24no—
922C4×D79—22no—
923C4×D79—22no—
924C4×D79—24no—
925C4×D79—22no—
926C4×D79—216no—
927C4×D79—41no—
928C4×D79—41no—
929C4×D79—44no—
930C4×D79—44no—
931C4×D79—48no—
932C4×D79—48no—
933C4×D79—48no—
934C4×D79—48no—
935C4×D79H(5,𝔽2)14yescomplemented
936Dic158—24no—
937Dic158—22no—
938Dic158—24no—
939Dic158—44no—
940Dic158—42no—
941C22×C79—21no—
942C22×C79—21no—
943C22×C79—22no—
944C22×C79—24no—
945C22×C79—22no—
946C22×C79—24no—
947C22×C79—24no—
948C22×C79—22no—
949C22×C79C2×H(5,𝔽2)12yes—
950C22×C79C2611yescharacteristic
951C2×D79—21no—
952C2×D79—21no—
953C2×D79—24no—
954C2×D79—24no—
955C2×D79—22no—
956C2×D79—22no—
957C2×D79—21no—
958C2×D79—28no—
959C2×D79—28no—
960C2×D79—21no—
961C2×D79—21no—
962C2×D79—22no—
963C2×D79—24no—
964C2×D79—28no—
965C2×D79—44no—
966C2×D79—88no—
967C2×D79—88no—
968C2×D79—168no—
969C2×D79—168no—
970C2×D79C2×H(5,𝔽2)12yes—
971C4×C79—22no—
972C4×C79—24no—
973C4×C79—22no—
974C4×C79—21no—
975C4×C79—28no—
976C4×C79—22no—
977C4×C79—21no—
978C4×C79C2×H(5,𝔽2)12yes—
979C4×C79C2×H(5,𝔽2)12yes—
980C4×C79C2×H(5,𝔽2)12yes—
981C4×C79#58512yes—
982Dic79—22no—
983Dic79—22no—
984Dic79—24no—
985Dic79—21no—
986Dic79—21no—
987Dic79—21no—
988Dic79—22no—
989Dic79—21no—
990Dic79—21no—
991Dic79C2×H(5,𝔽2)12yes—
992#62834—791nomaximal, Sylow
993C2×C79—22no—
994C2×C79—44no—
995C2×C79—42no—
996C2×C79C22×H(5,𝔽2)11yescharacteristic
997C2×C79C22×H(5,𝔽2)11yescharacteristic
998C2×C79C2×#58511yescharacteristic
999D79—22no—
1000D79—41no—
1001D79—44no—
1002D79—48no—
1003D79—42no—
1004#3558—794no—
1005#3558—794no—
1006#3549—792no—
1007#3548—792no—
1008#3546—792no—
1009#3546—792no—
1010#3546—794no—
1011#3537—794no—
1012#3519—792no—
1013#3519—792no—
1014#3519—794no—
1015#3511—792no—
1016#3511—791no—
1017#3511D7911yescharacteristic, complemented
1018#3508—792no—
1019#3508—792no—
1020#3506—792no—
1021#3506—792no—
1022#3498—792no—
1023#3498—791no—
1024#3498—791no—
1025#3496—792no—
1026#3496—792no—
1027#3488—794no—
1028#3488—792no—
1029#3488—792no—
1030#3444—791no—
1031C2×#532—791no—
1032C2×#532—791no—
1033C79#6283411yescharacteristic, complemented, Sylow
1034C2×H(5,𝔽2)—792no—
1035C2×H(5,𝔽2)—792no—
1036C2×H(5,𝔽2)—794no—
1037C22×#41—792no—
1038C22×#41—792no—
1039#562—798no—
1040H(3,𝔽4)—798no—
1041#560—798no—
1042#560—798no—
1043#559—794no—
1044#559—794no—
1045#559—794no—
1046#559—794no—
1047#556—792no—
1048#556—794no—
1049#556C2×D7912yescomplemented
1050#555—792no—
1051#555—794no—
1052#555—794no—
1053#555C2×D7912yescomplemented
1054#554—792no—
1055#554—794no—
1056#554C2×D7912yescomplemented
1057#553—798no—
1058#553—794no—
1059#553—794no—
1060#553—794no—
1061#553—794no—
1062#553—794no—
1063#553C2×D7914yescomplemented
1064#550—794no—
1065#550—794no—
1066#550—794no—
1067#550—794no—
1068#550—792no—
1069#550—792no—
1070#550—794no—
1071#550—792no—
1072#550—794no—
1073#550—792no—
1074#548—794no—
1075#548—794no—
1076#548—794no—
1077#548C2×D7914yescomplemented
1078#547—792no—
1079#547—794no—
1080#547—794no—
1081#547—794no—
1082#547C2×D7912yescomplemented
1083#546—794no—
1084#546—794no—
1085#546—798no—
1086#546—798no—
1087#546—794no—
1088#546—794no—
1089#546—798no—
1090#546—794no—
1091#546—794no—
1092#546—794no—
1093#546—798no—
1094#546—794no—
1095#546—794no—
1096#546—794no—
1097#546—798no—
1098D42—798no—
1099D42—794no—
1100D42—794no—
1101D42—794no—
1102D42—794no—
1103D42—794no—
1104D42—794no—
1105D42—794no—
1106D42—798no—
1107D42—794no—
1108D42—794no—
1109D42—792no—
1110D42—792no—
1111D42—794no—
1112D42—794no—
1113D42—792no—
1114D42—792no—
1115#542—794no—
1116#542—794no—
1117#542—794no—
1118#542C2×D7914yescomplemented
1119#540—794no—
1120#540—794no—
1121#540—794no—
1122#540—794no—
1123#538—798no—
1124#538—798no—
1125#538—798no—
1126#538—798no—
1127#538—798no—
1128#538—798no—
1129#537—794no—
1130#537—794no—
1131#537—798no—
1132#537—792no—
1133#537—794no—
1134#537C2×D7912yescomplemented
1135#535—792no—
1136#535—794no—
1137#535—794no—
1138#535—798no—
1139#535—794no—
1140#535—794no—
1141#535—794no—
1142#535—794no—
1143#535—792no—
1144#535—794no—
1145#535—794no—
1146#535—794no—
1147#534—798no—
1148#534—798no—
1149#533—792no—
1150#533—791no—
1151#533—791no—
1152#533—791no—
1153#533C2×D7912yescomplemented
1154#532—792no—
1155#532—791no—
1156#532—792no—
1157#532—792no—
1158#532—791no—
1159#532—792no—
1160#532—792no—
1161#532—792no—
1162#532—792no—
1163#532—792no—
1164#532—792no—
1165#532—792no—
1166#532—792no—
1167#532—791no—
1168#532—792no—
1169#532—792no—
1170#532—792no—
1171#532—792no—
1172#532—792no—
1173#532—791no—
1174#532—791no—
1175#532—791no—
1176#532—792no—
1177#532C2×D7911yescharacteristic, complemented
1178#532C2×D7912yescomplemented
1179C2×C4⋊Q8—791no—
1180C2×C4⋊Q8C2×D7911yescharacteristic, complemented
1181C2×#127—791no—
1182C2×#127—792no—
1183C2×#127—791no—
1184C2×#127—792no—
1185#529—791no—
1186#529—791no—
1187#529—792no—
1188#529—791no—
1189#529—792no—
1190#529—791no—
1191#529—792no—
1192#529—792no—
1193C2×#124—792no—
1194C2×#124—792no—
1195#525—791no—
1196#525—794no—
1197#525—792no—
1198#525—792no—
1199#525—798no—
1200#525—791no—
1201#525—794no—
1202C2×#121—792no—
1203C2×#121—792no—
1204C2×#121—794no—
1205C2×#121—798no—
1206C2×#121—792no—
1207C2×#121—792no—
1208C2×#121—794no—
1209#520—794no—
1210#520—792no—
1211#520C2×D7912yescomplemented
1212#518—794no—
1213#518—794no—
1214C4×#41—791no—
1215C4×#41—792no—
1216C4×#41—792no—
1217C4×#41C2×D7911yescharacteristic, complemented
1218C2×C4×D4—792no—
1219C2×C4×D4—792no—
1220C2×C4×D4—792no—
1221C2×C4×D4—792no—
1222C22×C42—791no—
1223H(5,𝔽2)—3168no—
1224H(5,𝔽2)—3168no—
1225H(5,𝔽2)—31616no—
1226C2×#41—3168no—
1227C2×#41—3168no—
1228C2×#41—794no—
1229C2×#41—794no—
1230C2×#41—794no—
1231C2×#41—794no—
1232C2×#41—792no—
1233C2×#41—794no—
1234C2×#41—794no—
1235C2×#41—794no—
1236C2×#41—794no—
1237C2×#41—792no—
1238C2×#41—792no—
1239C2×#41—794no—
1240C2×#41—798no—
1241C2×#41—794no—
1242C2×#41—794no—
1243C2×#41—792no—
1244C2×#41—791no—
1245C2×#41—792no—
1246C2×#41C22×D7911yescharacteristic
1247C2×#41C22×D7912yes—
1248C2×#41C22×D7914yes—
1249C22×Q8—792no—
1250C22×Q8C22×D7912yes—
1251C22×D4—792no—
1252C22×D4—794no—
1253C22×D4—794no—
1254C22×D4—798no—
1255C22×D4—798no—
1256C22×D4—798no—
1257C22×D4—794no—
1258C22×D4—798no—
1259C22×D4—792no—
1260C22×D4—794no—
1261C22×D4—794no—
1262C22×D4—792no—
1263C22×D4—792no—
1264C22×D4—794no—
1265C22×D4—794no—
1266C22×D4—798no—
1267C22×D4—794no—
1268C22×D4—792no—
1269C22×D4—794no—
1270C22×D4—794no—
1271C22×D4—792no—
1272C23×C4—794no—
1273C23×C4—794no—
1274C23×C4—791no—
1275C23×C4—791no—
1276C23×C4—791no—
1277C4⋊Q8—792no—
1278C4⋊Q8—791no—
1279C4⋊Q8—792no—
1280C4⋊Q8—792no—
1281C4⋊Q8—791no—
1282C4⋊Q8—791no—
1283C4⋊Q8—791no—
1284C4⋊Q8C22×D7911yescharacteristic
1285C4⋊Q8C22×D7912yes—
1286C4⋊Q8C22×D7912yes—
1287C4⋊Q8C22×D7912yes—
1288C4⋊Q8C22×D7912yes—
1289#127—792no—
1290#127—792no—
1291#127—792no—
1292#127—794no—
1293#127—794no—
1294#127—794no—
1295#127—791no—
1296#127—798no—
1297#127—791no—
1298#127—792no—
1299#127—792no—
1300#127—792no—
1301#127—792no—
1302#127—794no—
1303#127—794no—
1304#127—794no—
1305#127—798no—
1306#127C22×D7911yescharacteristic
1307#126—792no—
1308#126—792no—
1309#126—798no—
1310#126—798no—
1311#126—792no—
1312#126—792no—
1313#126—798no—
1314#126C22×D7918yes—
1315#125—792no—
1316#125—791no—
1317#125—791no—
1318#125—792no—
1319#125—794no—
1320#125C22×D7914yes—
1321#124—794no—
1322#124—794no—
1323#124—794no—
1324#124—792no—
1325#124—794no—
1326#124—791no—
1327#124—794no—
1328#124—794no—
1329#124—798no—
1330#124—792no—
1331#124—791no—
1332#124—794no—
1333#124—794no—
1334#124—792no—
1335#124—792no—
1336#124—798no—
1337#124—798no—
1338#124—792no—
1339#124—794no—
1340#124—798no—
1341#124—798no—
1342#124C22×D7912yes—
1343#124C22×D7914yes—
1344#124C22×D7918yes—
1345#123—792no—
1346#123—798no—
1347#123—792no—
1348#123—792no—
1349#123—798no—
1350#123—798no—
1351#123—798no—
1352#123—798no—
1353#123—798no—
1354#123—798no—
1355#123—792no—
1356#123—792no—
1357#123—792no—
1358#123—798no—
1359#123—798no—
1360#123—798no—
1361#123—798no—
1362#123C22×D7918yes—
1363C22⋊Q8—791no—
1364C22⋊Q8—791no—
1365C22⋊Q8—794no—
1366C22⋊Q8—798no—
1367C22⋊Q8—791no—
1368C22⋊Q8—792no—
1369C22⋊Q8—791no—
1370C22⋊Q8—792no—
1371C22⋊Q8—798no—
1372C22⋊Q8—794no—
1373C22⋊Q8—794no—
1374C22⋊Q8—798no—
1375C22⋊Q8—798no—
1376C22⋊Q8—792no—
1377C22⋊Q8—792no—
1378C22⋊Q8C22×D7914yes—
1379C22⋊Q8C22×D7914yes—
1380C22⋊Q8C22×D7914yes—
1381C22⋊Q8C22×D7918yes—
1382#121—791no—
1383#121—792no—
1384#121—794no—
1385#121—794no—
1386#121—792no—
1387#121—792no—
1388#121—798no—
1389#121—798no—
1390#121—792no—
1391#121—791no—
1392#121—792no—
1393#121—792no—
1394#121—798no—
1395#121—794no—
1396#121—794no—
1397#121—794no—
1398#121—794no—
1399#121—798no—
1400#121—798no—
1401#121—798no—
1402#121—791no—
1403#121—794no—
1404#121—794no—
1405#121—794no—
1406#121—792no—
1407#121—794no—
1408#121—794no—
1409#121—794no—
1410#121—792no—
1411#121—794no—
1412#121—794no—
1413#121—798no—
1414#121—794no—
1415#121—794no—
1416#121—798no—
1417#121—798no—
1418#121—791no—
1419#121—794no—
1420#121—794no—
1421#121—794no—
1422#121—794no—
1423#121—794no—
1424#121—798no—
1425#121—798no—
1426#121—798no—
1427#121—798no—
1428#121—794no—
1429#121—794no—
1430#121—798no—
1431#121—798no—
1432#121—798no—
1433#121—792no—
1434#121—792no—
1435#121—798no—
1436#121—798no—
1437#121—798no—
1438#121—798no—
1439#121—798no—
1440#121—798no—
1441#121C22×D7912yes—
1442#121C22×D7912yes—
1443#121C22×D7918yes—
1444#121C22×D7914yes—
1445#121C22×D7914yes—
1446#121C22×D7914yes—
1447#120—792no—
1448#120—798no—
1449#120—798no—
1450#120—798no—
1451#120—798no—
1452#120—792no—
1453#120—798no—
1454#120—798no—
1455#120—798no—
1456#120—798no—
1457#120—798no—
1458#120—798no—
1459#120—798no—
1460#120—798no—
1461#120—798no—
1462#120—798no—
1463#120—798no—
1464#120—798no—
1465C4×Q8—794no—
1466C4×Q8—794no—
1467C4×Q8—792no—
1468C4×Q8—791no—
1469C4×Q8—792no—
1470C4×Q8—791no—
1471C4×Q8—792no—
1472C4×Q8—792no—
1473C4×Q8C22×D7911yescharacteristic
1474C4×Q8C22×D7911yescharacteristic
1475C4×Q8C22×D7914yes—
1476C4×Q8C22×D7914yes—
1477C4×D4—792no—
1478C4×D4—792no—
1479C4×D4—794no—
1480C4×D4—794no—
1481C4×D4—792no—
1482C4×D4—792no—
1483C4×D4—792no—
1484C4×D4—792no—
1485C4×D4—792no—
1486C4×D4—792no—
1487C4×D4—792no—
1488C4×D4—792no—
1489C4×D4—792no—
1490C4×D4—792no—
1491C4×D4—798no—
1492C4×D4—798no—
1493C4×D4—792no—
1494C4×D4—794no—
1495C4×D4—794no—
1496C4×D4—794no—
1497C4×D4—794no—
1498C4×D4—794no—
1499C4×D4—794no—
1500C4×D4—794no—
1501C4×D4—792no—
1502C4×D4—794no—
1503C4×D4—794no—
1504C4×D4—794no—
1505C4×D4—798no—
1506C4×D4—794no—
1507C4×D4—794no—
1508C4×D4—794no—
1509C4×D4—794no—
1510C4×D4—798no—
1511C4×D4—792no—
1512C4×D4—792no—
1513C4×D4—792no—
1514C4×D4—792no—
1515C4×D4—792no—
1516C4×D4—792no—
1517C4×D4—791no—
1518C4×D4—791no—
1519C4×D4—798no—
1520C4×D4—798no—
1521C4×D4—794no—
1522C4×D4—798no—
1523C4×D4—794no—
1524C4×D4C22×D7912yes—
1525C4×D4C22×D7912yes—
1526C4×D4C22×D7912yes—
1527C4×D4C22×D7912yes—
1528C4×D4C22×D7911yescharacteristic
1529C4×D4C22×D7911yescharacteristic
1530C4×D4C22×D7914yes—
1531C4×D4C22×D7918yes—
1532C4×D4C22×D7914yes—
1533#117—792no—
1534#117—791no—
1535#117—792no—
1536#117—794no—
1537#117—794no—
1538#117—792no—
1539#117—792no—
1540#117—792no—
1541#117—792no—
1542#117—792no—
1543#117—798no—
1544#117C22×D7911yescharacteristic
1545#117C22×D7912yes—
1546#117C22×D7914yes—
1547#117C22×D7914yes—
1548C2×C4⋊C4—792no—
1549C2×C4⋊C4—792no—
1550C2×C4⋊C4—798no—
1551C2×C4⋊C4—794no—
1552C2×C4⋊C4C22×D7912yes—
1553C2×C4⋊C4C22×D7912yes—
1554C2×C4⋊C4C22×D7914yes—
1555C2×C22⋊C4—794no—
1556C2×C22⋊C4—794no—
1557C2×C22⋊C4—798no—
1558C2×C22⋊C4—794no—
1559C2×C22⋊C4—794no—
1560C2×C22⋊C4—798no—
1561C2×C22⋊C4—798no—
1562C2×C22⋊C4—798no—
1563C2×C42—791no—
1564C2×C42—791no—
1565C2×C42—791no—
1566C2×C42—791no—
1567C2×C42—791no—
1568C2×C42—792no—
1569C2×C42—791no—
1570C2×C42—791no—
1571C2×C42—791no—
1572C2×C42—791no—
1573C2×C42—791no—
1574C2×C42—791no—
1575C2×C42C22×D7912yes—
1576C2×C42C22×D7911yescharacteristic
1577C24—798no—
1578C24—798no—
1579C24—794no—
1580C24—794no—
1581C24—791no—
1582#41—28no—
1583#41—24no—
1584#41—48no—
1585#41—3168no—
1586#41—3168no—
1587#41—3168no—
1588#41—3164no—
1589#41—31616no—
1590#41—3164no—
1591#41—3168no—
1592#41—3168no—
1593#41—3164no—
1594#41—3168no—
1595#41—3168no—
1596#41—3168no—
1597#41—3168no—
1598#41—3168no—
1599#41—1588no—
1600#41—15816no—
1601#41—1588no—
1602#41—1584no—
1603C2×Q8—44no—
1604C2×Q8—3164no—
1605C2×Q8—792no—
1606C2×Q8—794no—
1607C2×Q8—792no—
1608C2×Q8—791no—
1609C2×Q8—792no—
1610C2×Q8C23×D7914yes—
1611C2×Q8C23×D7911yescharacteristic
1612C2×Q8C23×D7912yes—
1613C2×Q8C23×D7914yes—
1614C2×D4—3164no—
1615C2×D4—3168no—
1616C2×D4—3164no—
1617C2×D4—3168no—
1618C2×D4—3168no—
1619C2×D4—3168no—
1620C2×D4—3168no—
1621C2×D4—31616no—
1622C2×D4—3168no—
1623C2×D4—31616no—
1624C2×D4—31616no—
1625C2×D4—31616no—
1626C2×D4—3164no—
1627C2×D4—3168no—
1628C2×D4—3164no—
1629C2×D4—3168no—
1630C2×D4—3168no—
1631C2×D4—3168no—
1632C2×D4—31616no—
1633C2×D4—792no—
1634C2×D4—792no—
1635C2×D4—794no—
1636C2×D4—798no—
1637C2×D4—794no—
1638C2×D4—798no—
1639C2×D4—794no—
1640C2×D4—798no—
1641C2×D4—798no—
1642C2×D4—794no—
1643C2×D4—792no—
1644C2×D4—792no—
1645C2×D4—792no—
1646C2×D4—794no—
1647C2×D4—792no—
1648C2×D4—794no—
1649C2×D4—798no—
1650C2×D4—794no—
1651C2×D4—798no—
1652C2×D4—798no—
1653C2×D4—798no—
1654C2×D4—794no—
1655C2×D4—798no—
1656C2×D4—798no—
1657C2×D4—794no—
1658C2×D4—792no—
1659C2×D4—798no—
1660C2×D4—792no—
1661C2×D4—791no—
1662C2×D4—794no—
1663C2×D4—794no—
1664C2×D4—792no—
1665C2×D4—792no—
1666C2×D4—794no—
1667C2×D4—1588no—
1668C2×D4—1588no—
1669C2×D4C23×D7912yes—
1670C2×D4C23×D7912yes—
1671C2×D4C23×D7914yes—
1672C2×D4C23×D7912yes—
1673C2×D4C23×D7911yescharacteristic
1674C2×D4C23×D7912yes—
1675C2×D4C23×D7918yes—
1676C22×C4—3162no—
1677C22×C4—3168no—
1678C22×C4—3168no—
1679C22×C4—791no—
1680C22×C4—794no—
1681C22×C4—791no—
1682C22×C4—791no—
1683C22×C4—794no—
1684C22×C4—798no—
1685C22×C4—794no—
1686C22×C4—798no—
1687C22×C4—798no—
1688C22×C4—798no—
1689C22×C4—791no—
1690C22×C4—791no—
1691C22×C4—791no—
1692C22×C4—791no—
1693C22×C4—791no—
1694C22×C4—791no—
1695C22×C4—791no—
1696C22×C4—791no—
1697C22×C4—791no—
1698C22×C4—791no—
1699C22×C4—791no—
1700C22×C4—791no—
1701C22×C4—792no—
1702C22×C4—792no—
1703C22×C4—792no—
1704C22×C4—798no—
1705C22×C4—794no—
1706C22×C4—1584no—
1707C22×C4—1584no—
1708C22×C4C23×D7911yescharacteristic
1709C22×C4C23×D7911yescharacteristic
1710C22×C4C23×D7912yes—
1711C22×C4C23×D7912yes—
1712C22×C4C23×D7912yes—
1713C22×C4C23×D7914yes—
1714C22×C4C23×D7914yes—
1715C22×C4C23×D7918yes—
1716C22×C4C23×D7911yescharacteristic
1717C4⋊C4—792no—
1718C4⋊C4—794no—
1719C4⋊C4—794no—
1720C4⋊C4—798no—
1721C4⋊C4—792no—
1722C4⋊C4—792no—
1723C4⋊C4—792no—
1724C4⋊C4—792no—
1725C4⋊C4—792no—
1726C4⋊C4—792no—
1727C4⋊C4—792no—
1728C4⋊C4—792no—
1729C4⋊C4—792no—
1730C4⋊C4—791no—
1731C4⋊C4—792no—
1732C4⋊C4—792no—
1733C4⋊C4—798no—
1734C4⋊C4—791no—
1735C4⋊C4—792no—
1736C4⋊C4—792no—
1737C4⋊C4—792no—
1738C4⋊C4—792no—
1739C4⋊C4C23×D7914yes—
1740C4⋊C4C23×D7912yes—
1741C4⋊C4C23×D7912yes—
1742C4⋊C4C23×D7918yes—
1743C4⋊C4C23×D7911yescharacteristic
1744C4⋊C4C23×D7914yes—
1745C4⋊C4C23×D7914yes—
1746C4⋊C4C23×D7914yes—
1747C4⋊C4C23×D7918yes—
1748C4⋊C4C23×D7911yescharacteristic
1749C4⋊C4C23×D7912yes—
1750C4⋊C4C23×D7912yes—
1751C22⋊C4—792no—
1752C22⋊C4—792no—
1753C22⋊C4—794no—
1754C22⋊C4—794no—
1755C22⋊C4—792no—
1756C22⋊C4—792no—
1757C22⋊C4—792no—
1758C22⋊C4—792no—
1759C22⋊C4—792no—
1760C22⋊C4—798no—
1761C22⋊C4—794no—
1762C22⋊C4—798no—
1763C22⋊C4—798no—
1764C22⋊C4—798no—
1765C22⋊C4—798no—
1766C22⋊C4—798no—
1767C22⋊C4—794no—
1768C22⋊C4—798no—
1769C22⋊C4—794no—
1770C22⋊C4—798no—
1771C22⋊C4—794no—
1772C22⋊C4—792no—
1773C22⋊C4—792no—
1774C22⋊C4—792no—
1775C22⋊C4—792no—
1776C22⋊C4—792no—
1777C22⋊C4—792no—
1778C22⋊C4—798no—
1779C22⋊C4—798no—
1780C22⋊C4—798no—
1781C22⋊C4—792no—
1782C22⋊C4—792no—
1783C22⋊C4C23×D7918yes—
1784C22⋊C4C23×D7918yes—
1785C22⋊C4C23×D7914yes—
1786C22⋊C4C23×D7914yes—
1787C22⋊C4C23×D7912yes—
1788C22⋊C4C23×D7912yes—
1789C22⋊C4C23×D7912yes—
1790C22⋊C4C23×D7918yes—
1791C42—791no—
1792C42—791no—
1793C42—791no—
1794C42—791no—
1795C42—791no—
1796C42—791no—
1797C42—791no—
1798C42—791no—
1799C42—791no—
1800C42—791no—
1801C42—791no—
1802C42—791no—
1803C42—792no—
1804C42—792no—
1805C42—792no—
1806C42—798no—
1807C42C23×D7911yescharacteristic
1808C42C23×D7911yescharacteristic
1809C42C23×D7911yescharacteristic
1810C42C23×D7911yescharacteristic
1811C42C23×D7912yes—
1812C42C23×D7912yes—
1813C42C23×D7912yes—
1814C42C23×D7918yes—
1815C23—3161no—
1816C23—3164no—
1817C23—3164no—
1818C23—3164no—
1819C23—3164no—
1820C23—3168no—
1821C23—3168no—
1822C23—3168no—
1823C23—3168no—
1824C23—3168no—
1825C23—3168no—
1826C23—791no—
1827C23—792no—
1828C23—794no—
1829C23—798no—
1830C23—791no—
1831C23—1582no—
1832C23—1588no—
1833C23—1582no—
1834C23—1588no—
1835C23C24×D7912yes—
1836C23C24×D7914yes—
1837C23C24×D7911yescharacteristic
1838Q8—28no—
1839Q8—24no—
1840Q8—22no—
1841Q8—44no—
1842Q8—3164no—
1843Q8—3162no—
1844Q8—1584no—
1845Q8—1584no—
1846Q8—1582no—
1847D4—24no—
1848D4—28no—
1849D4—24no—
1850D4—22no—
1851D4—24no—
1852D4—24no—
1853D4—48no—
1854D4—3168no—
1855D4—3168no—
1856D4—3168no—
1857D4—3168no—
1858D4—3164no—
1859D4—3168no—
1860D4—3164no—
1861D4—3164no—
1862D4—3168no—
1863D4—3162no—
1864D4—3168no—
1865D4—3168no—
1866D4—3168no—
1867D4—3164no—
1868D4—3168no—
1869D4—3164no—
1870D4—3164no—
1871D4—3162no—
1872D4—3162no—
1873D4—1584no—
1874D4—15816no—
1875D4—1584no—
1876D4—1588no—
1877D4—1584no—
1878D4—1584no—
1879D4—1588no—
1880D4—1588no—
1881D4—1584no—
1882D4—1582no—
1883D4—1584no—
1884D4—1588no—
1885D4—1588no—
1886D4—1588no—
1887D4—1584no—
1888C2×C4—22no—
1889C2×C4—24no—
1890C2×C4—28no—
1891C2×C4—24no—
1892C2×C4—22no—
1893C2×C4—24no—
1894C2×C4—44no—
1895C2×C4—48no—
1896C2×C4—3164no—
1897C2×C4—3168no—
1898C2×C4—3164no—
1899C2×C4—3161no—
1900C2×C4—3161no—
1901C2×C4—3168no—
1902C2×C4—3168no—
1903C2×C4—3168no—
1904C2×C4—3164no—
1905C2×C4—3161no—
1906C2×C4—791no—
1907C2×C4—794no—
1908C2×C4—792no—
1909C2×C4—791no—
1910C2×C4—791no—
1911C2×C4—791no—
1912C2×C4—791no—
1913C2×C4—791no—
1914C2×C4—794no—
1915C2×C4—792no—
1916C2×C4—792no—
1917C2×C4—15816no—
1918C2×C4—1582no—
1919C2×C4—1582no—
1920C2×C4—1582no—
1921C2×C4—1582no—
1922C2×C4—1582no—
1923C2×C4—1584no—
1924C2×C4—1582no—
1925C2×C4—1588no—
1926C2×C4—1582no—
1927C2×C4—1582no—
1928C2×C4—1582no—
1929C2×C4—1584no—
1930C2×C4—1582no—
1931C2×C4—1582no—
1932C2×C4—1584no—
1933C2×C4#1457920714yescomplemented
1934C2×C4C24×D7911yescharacteristic
1935C2×C4C24×D7911yescharacteristic
1936C2×C4C24×D7918yes—
1937C2×C4C24×D7912yes—
1938C2×C4C24×D7914yes—
1939C2×C4C24×D7912yes—
1940C2×C4C24×D7912yes—
1941C2×C4C24×D7911yescharacteristic
1942C2×C4C24×D7911yescharacteristic
1943C2×C4C24×D7911yescharacteristic
1944C2×C4C24×D7911yescharacteristic
1945C22—21no—
1946C22—21no—
1947C22—22no—
1948C22—24no—
1949C22—24no—
1950C22—22no—
1951C22—22no—
1952C22—24no—
1953C22—3164no—
1954C22—792no—
1955C22—6328no—
1956C22—6328no—
1957C22—1584no—
1958C22—1588no—
1959C22—1581no—
1960C22—1582no—
1961C22—1588no—
1962C22—1584no—
1963C22—1581no—
1964C22—1582no—
1965C22—1581no—
1966C22—1582no—
1967C22—1588no—
1968C22—1584no—
1969C22—1581no—
1970C22—1581no—
1971C22—12648no—
1972C22—12648no—
1973C22C2×#1457920712yes—
1974C22C25×D7911yescharacteristic
1975C4—22no—
1976C4—21no—
1977C4—28no—
1978C4—22no—
1979C4—24no—
1980C4—21no—
1981C4—22no—
1982C4—792no—
1983C4—1581no—
1984C4—1582no—
1985C4—1581no—
1986C4—1582no—
1987C4—1584no—
1988C4—1581no—
1989C4—1581no—
1990C4—1581no—
1991C4—1582no—
1992C4H(5,𝔽2)×D7912yes—
1993C4C2×#1457920712yes—
1994C4C2×#1457920712yes—
1995C4#1909940012yes—
1996C2—22no—
1997C2—44no—
1998C2—42no—
1999C2—3161no—
2000C2—3168no—
2001C2—3164no—
2002C2—3162no—
2003C2—1582no—
2004C2C2×H(5,𝔽2)×D7911yescharacteristic
2005C2C22×#1457920711yescharacteristic
2006C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3511C2
hypercenter#3511D79
hypocenterC79#62834
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3511

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777917C2semidirect
2. #23777915C2semidirect
3. #23777801C2semidirect
4. #23777799C2semidirect
5. #23777775C2semidirect
6. #23777773C2semidirect
7. #23777769C2semidirect
8. #23777636C2semidirect
9. #23777435C2semidirect
10. #23777433C2semidirect
11. #23777428C2semidirect
12. #23777313C2semidirect
13. #23777312C2semidirect
14. #23777277C2semidirect
15. #23777269C2semidirect
16. #23777253C2semidirect
17. #23777245C2semidirect
18. #23777178C2semidirect
19. #23777173C2semidirect
20. #23777173C2semidirect
21. #23777163C2semidirect
22. #23777158C2semidirect
23. #23777070C2semidirect
24. #23777066C2semidirect
25. #23777064C2semidirect
26. #23776693C2semidirect
27. C2×#19099114C2semidirect
28. #532×D79C2semidirect
29. C79×#3511C2semidirect
30. C2×#14579207C22semidirect
31. C2×#14579207C22semidirect
32. C2×#14579207C22semidirect
33. C22×#11929625C22semidirect
34. C2×#41×D79C22semidirect
35. #19099309C22semidirect
36. #19099305C22semidirect
37. #19099304C22semidirect
38. #19099303C22semidirect
39. #19099298C22semidirect
40. #19099298C22semidirect
41. #19099296C22semidirect
42. #19099295C22semidirect
43. #19099287C22semidirect
44. #19099285C22semidirect
45. #19099279C22semidirect
46. #19099276C22semidirect
47. #19099276C22semidirect
48. #19099274C22semidirect
49. #19099269C22semidirect
50. #19099266C22semidirect
51. #19099264C22semidirect
52. #19099261C22semidirect
53. #19099261C22semidirect
54. #19099257C22semidirect
55. #19099257C22semidirect
56. #19099235C22semidirect
57. #19099235C22semidirect
58. #19099235C22semidirect
59. #19099235C22semidirect
60. #19099234C22semidirect
61. #19099234C22semidirect
62. #19099234C22semidirect
63. #19099234C22semidirect
64. #19099232C22semidirect
65. #19099231C22semidirect
66. #19099225C22semidirect
67. #19099224C22semidirect
68. #19099223C22semidirect
69. #19099216C22semidirect
70. #19099215C22semidirect
71. #19099215C22semidirect
72. #19099214C22semidirect
73. #19099210C22semidirect
74. #19099210C22semidirect
75. #19099208C22semidirect
76. #19099208C22semidirect
77. #19099206C22semidirect
78. #19099206C22semidirect
79. #19099205C22semidirect
80. #19099204C22semidirect
81. #19099204C22semidirect
82. #19099204C22semidirect
83. #19099204C22semidirect
84. #19099204C22semidirect
85. #19099204C22semidirect
86. #19099202C22semidirect
87. #19099201C22semidirect
88. D4×D316C22semidirect
89. D4×D316C22semidirect
90. D4×D316C22semidirect
91. D4×D316C22semidirect
92. D4×D316C22semidirect
93. D4×D316C22semidirect
94. D4×D316C22semidirect
95. D4×D316C22semidirect
96. D4×D316C22semidirect
97. #19099197C22semidirect
98. #19099197C22semidirect
99. #19099197C22semidirect
100. #19099197C22semidirect
101. #19099197C22semidirect
102. #19099197C22semidirect
103. #19099197C22semidirect
104. #19099197C22semidirect
105. #19099187C22semidirect
106. #19099186C22semidirect
107. #19099185C22semidirect
108. #19099169C22semidirect
109. #19099169C22semidirect
110. #19099166C22semidirect
111. #19099164C22semidirect
112. #19099153C22semidirect
113. #19099152C22semidirect
114. #19099152C22semidirect
115. #19099149C22semidirect
116. #19099147C22semidirect
117. #19099146C22semidirect
118. #19099144C22semidirect
119. #19099144C22semidirect
120. #19099143C22semidirect
121. #19099143C22semidirect
122. #19099143C22semidirect
123. #19099132C22semidirect
124. #19099132C22semidirect
125. #19099132C22semidirect
126. #19099132C22semidirect
127. #19099131C22semidirect
128. #19099131C22semidirect
129. #19099131C22semidirect
130. #19099131C22semidirect
131. #19099129C22semidirect
132. #19099129C22semidirect
133. #19099127C22semidirect
134. #19099127C22semidirect
135. #19099124C22semidirect
136. #19099121C22semidirect
137. #19099118C22semidirect
138. #19099117C22semidirect
139. #19099117C22semidirect
140. #19099116C22semidirect
141. #19099114C22semidirect
142. #19099114C22semidirect
143. #19099114C22semidirect
144. #19099114C22semidirect
145. #19099114C22semidirect
146. #19099114C22semidirect
147. #19099114C22semidirect
148. #19099114C22semidirect
149. #19099114C22semidirect
150. #19099114C22semidirect
151. #19099114C22semidirect
152. #19099113C22semidirect
153. #19099113C22semidirect
154. #19099112C22semidirect
155. #19099111C22semidirect
156. #19099110C22semidirect
157. #19099110C22semidirect
158. #19099110C22semidirect
159. #19099110C22semidirect
160. #19099109C22semidirect
161. #19099109C22semidirect
162. #19099108C22semidirect
163. #19099108C22semidirect
164. C4⋊Q8×D79C22semidirect
165. C2×#14579158C22semidirect
166. C2×#14579158C22semidirect
167. #127×D79C22semidirect
168. #127×D79C22semidirect
169. #19099100C22semidirect
170. #19099100C22semidirect
171. #19099095C22semidirect
172. #19099095C22semidirect
173. #19099093C22semidirect
174. #19099093C22semidirect
175. #19099091C22semidirect
176. #19099091C22semidirect
177. C2×#14579150C22semidirect
178. #124×D79C22semidirect
179. #19099076C22semidirect
180. #19099075C22semidirect
181. #19099075C22semidirect
182. #19099072C22semidirect
183. #19099072C22semidirect
184. #19099072C22semidirect
185. #19099070C22semidirect
186. C2×#14579136C22semidirect
187. C2×#14579136C22semidirect
188. C2×#14579136C22semidirect
189. #121×D79C22semidirect
190. #121×D79C22semidirect
191. #121×D79C22semidirect
192. #121×D79C22semidirect
193. #19099045C22semidirect
194. #19099044C22semidirect
195. #19099037C22semidirect
196. #19099035C22semidirect
197. C4×#11929624C22semidirect
198. C4×#11929624C22semidirect
199. C4×#11929624C22semidirect
200. C2×#14579123C22semidirect
201. C2×#14579123C22semidirect
202. C4×D4×D79C22semidirect
203. C4×D4×D79C22semidirect
204. C2×C42×D79C22semidirect
205. #556×C79C22semidirect
206. #555×C79C22semidirect
207. #554×C79C22semidirect
208. #553×C79C22semidirect
209. #548×C79C22semidirect
210. #547×C79C22semidirect
211. #542×C79C22semidirect
212. #537×C79C22semidirect
213. #533×C79C22semidirect
214. #532×C79C22semidirect
215. #532×C79C22semidirect
216. C2×C4⋊Q8×C79C22semidirect
217. #520×C79C22semidirect
218. C4×#41×C79C22semidirect
853. C2×C4×C79H(5,𝔽2)semidirect
935. C4×D79H(5,𝔽2)semidirect
1017. #3511D79semidirect
1033. C79#62834semidirect
1049. #556C2×D79semidirect
1053. #555C2×D79semidirect
1056. #554C2×D79semidirect
1063. #553C2×D79semidirect
1077. #548C2×D79semidirect
1082. #547C2×D79semidirect
1118. #542C2×D79semidirect
1134. #537C2×D79semidirect
1153. #533C2×D79semidirect
1177. #532C2×D79semidirect
1178. #532C2×D79semidirect
1180. C2×C4⋊Q8C2×D79semidirect
1211. #520C2×D79semidirect
1217. C4×#41C2×D79semidirect
1933. C2×C4#14579207semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237779172
#237779152
#237778012
#237777992
#237777752
#237777732
#237777692
#237776362
#237774352
#237774332
#237774282
#237773132
#237773122
#237772772
#237772692
#237772532
#237772452
#237771782
#237771732
#237771632
#237771582
#237770702
#237770662
#237770642
#237766932
C2×#190991142
#532×D792
C79×#35112
#6283479