Finite Group Databasebeta

← #35197168

Subgroups — #35197168

Order 20224.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777912C214yesmaximal, complemented
2#23777909C214yesmaximal, complemented
3#23777802C212yesmaximal, complemented
4#23777797C212yesmaximal, complemented
5#23777773C212yesmaximal, complemented
6#23777768C212yesmaximal, complemented
7#23777764C214yesmaximal, complemented
8#23777637C214yesmaximal, complemented
9#23777429C214yesmaximal, complemented
10#23777426C214yesmaximal, complemented
11#23777310C212yesmaximal, complemented
12#23777309C212yesmaximal, complemented
13#23777268C214yesmaximal, complemented
14#23777252C211yesmaximal, characteristic, complemented
15#23777250C212yesmaximal, complemented
16#23777249C211yesmaximal, characteristic, complemented
17#23777174C212yesmaximal, complemented
18#23777172C212yesmaximal, complemented
19#23777162C211yesmaximal, characteristic, complemented
20#23777156C212yesmaximal, complemented
21#23777065C214yesmaximal, complemented
22#23777064C212yesmaximal, complemented
23#23777062C212yesmaximal, complemented
24#23776695C211yesmaximal, characteristic, complemented
25C2×#19099110C211yesmaximal, characteristic, complemented
26#532×D79C211yesmaximal, characteristic, complemented
27C79×#3496C211yesmaximal, characteristic, complemented
28C2×#14579207C2212yescomplemented
29C2×#14579206C2214yescomplemented
30C22×#11929624C2212yescomplemented
31C2×#41×D79C2212yescomplemented
32#19099310C2218yescomplemented
33#19099306C2218yescomplemented
34#19099303C2218yescomplemented
35#19099302C2218yescomplemented
36#19099297C2218yescomplemented
37#19099296C2214yescomplemented
38#19099295C2214yescomplemented
39#19099287C2212yescomplemented
40#19099284C2214yescomplemented
41#19099283C2212yescomplemented
42#19099278C2212yescomplemented
43#19099278C2212yescomplemented
44#19099277C2214yescomplemented
45#19099277C2214yescomplemented
46#19099271C2214yescomplemented
47#19099268C2214yescomplemented
48#19099263C2214yescomplemented
49#19099261C2214yescomplemented
50#19099260C2214yescomplemented
51#19099259C2214yescomplemented
52#19099258C2218yescomplemented
53#19099256C2218yescomplemented
54#19099234C2212yescomplemented
55#19099233C2212yescomplemented
56#19099232C2214yescomplemented
57#19099232C2214yescomplemented
58#19099232C2214yescomplemented
59#19099231C2214yescomplemented
60#19099231C2214yescomplemented
61#19099231C2218yescomplemented
62#19099223C2214yescomplemented
63#19099220C2214yescomplemented
64#19099219C2218yescomplemented
65#19099218C2212yescomplemented
66#19099218C2212yescomplemented
67#19099217C2212yescomplemented
68#19099216C2212yescomplemented
69#19099213C2214yescomplemented
70#19099210C2218yescomplemented
71#19099210C2214yescomplemented
72#19099209C2214yescomplemented
73#19099207C2218yescomplemented
74#19099207C2214yescomplemented
75#19099207C2214yescomplemented
76#19099206C2214yescomplemented
77#19099204C2214yescomplemented
78#19099203C2218yescomplemented
79#19099203C2218yescomplemented
80#19099202C2218yescomplemented
81#19099200C2218yescomplemented
82D4×D316C2212yescomplemented
83#19099198C2212yescomplemented
84#19099197C2218yescomplemented
85#19099197C2214yescomplemented
86D4×C22⋊D79C2214yescomplemented
87D4×C22⋊D79C2214yescomplemented
88D4×C22⋊D79C2218yescomplemented
89D4×C22⋊D79C2214yescomplemented
90D4×C22⋊D79C2218yescomplemented
91D4×C22⋊D79C2218yescomplemented
92D4×C22⋊D79C2214yescomplemented
93#19099195C2218yescomplemented
94#19099186C2214yescomplemented
95#19099181C2218yescomplemented
96#19099180C2214yescomplemented
97#19099165C2218yescomplemented
98#19099163C2218yescomplemented
99#19099151C2214yescomplemented
100#19099151C2218yescomplemented
101#19099150C2214yescomplemented
102#19099149C2218yescomplemented
103#19099149C2218yescomplemented
104#19099148C2218yescomplemented
105#19099145C2218yescomplemented
106#19099144C2214yescomplemented
107#19099143C2214yescomplemented
108#19099142C2214yescomplemented
109#19099142C2214yescomplemented
110#19099141C2214yescomplemented
111#19099141C2212yescomplemented
112#19099130C2214yescomplemented
113#19099130C2214yescomplemented
114#19099130C2212yescomplemented
115#19099130C2214yescomplemented
116#19099129C2214yescomplemented
117#19099129C2214yescomplemented
118#19099129C2214yescomplemented
119#19099128C2218yescomplemented
120#19099128C2218yescomplemented
121#19099127C2212yescomplemented
122#19099127C2214yescomplemented
123#19099123C2218yescomplemented
124#19099121C2214yescomplemented
125#19099120C2211yescharacteristic, complemented
126#19099118C2211yescharacteristic, complemented
127#19099118C2211yescharacteristic, complemented
128#19099115C2214yescomplemented
129#19099114C2211yescharacteristic, complemented
130#19099113C2211yescharacteristic, complemented
131#19099112C2212yescomplemented
132#19099111C2211yescharacteristic, complemented
133#19099111C2211yescharacteristic, complemented
134#19099111C2211yescharacteristic, complemented
135#19099110C2212yescomplemented
136#19099110C2212yescomplemented
137#19099110C2212yescomplemented
138#19099110C2212yescomplemented
139#19099110C2212yescomplemented
140#19099110C2212yescomplemented
141#19099110C2212yescomplemented
142#19099110C2212yescomplemented
143#19099110C2212yescomplemented
144#19099110C2212yescomplemented
145#19099109C2212yescomplemented
146#19099109C2214yescomplemented
147#19099108C2214yescomplemented
148#19099108C2212yescomplemented
149#19099108C2212yescomplemented
150C2×#14579160C2211yescharacteristic, complemented
151C4⋊Q8×D79C2211yescharacteristic, complemented
152C2×#14579157C2214yescomplemented
153C2×#14579157C2211yescharacteristic, complemented
154#127×D79C2211yescharacteristic, complemented
155#19099095C2212yescomplemented
156#19099095C2212yescomplemented
157#19099094C2212yescomplemented
158#19099094C2212yescomplemented
159#19099092C2212yescomplemented
160#19099092C2212yescomplemented
161C2×#14579147C2212yescomplemented
162#124×D79C2212yescomplemented
163#19099076C2214yescomplemented
164#19099074C2214yescomplemented
165#19099073C2212yescomplemented
166#19099073C2214yescomplemented
167#19099073C2212yescomplemented
168#19099070C2212yescomplemented
169#19099070C2214yescomplemented
170C2×#14579136C2211yescharacteristic, complemented
171C2×#14579134C2212yescomplemented
172C2×#14579132C2211yescharacteristic, complemented
173C2×#14579132C2214yescomplemented
174#121×D79C2214yescomplemented
175#121×D79C2212yescomplemented
176#121×D79C2214yescomplemented
177#121×D79C2212yescomplemented
178#19099046C2212yescomplemented
179#19099044C2212yescomplemented
180#19099044C2214yescomplemented
181#19099036C2218yescomplemented
182#41×Dic79C2212yescomplemented
183C4×#11929623C2212yescomplemented
184C4×#11929623C2212yescomplemented
185C2×C4×D316C2211yescharacteristic, complemented
186C2×C4×C22⋊D79C2212yescomplemented
187C4×D4×D79C2212yescomplemented
188C4×D4×D79C2212yescomplemented
189C2×C42×D79C2211yescharacteristic, complemented
190C2×H(5,𝔽2)×C79C2212yescomplemented
191#547×C79C2212yescomplemented
192#547×C79C2212yescomplemented
193#546×C79C2214yescomplemented
194#546×C79C2214yescomplemented
195D42×C79C2212yescomplemented
196D42×C79C2212yescomplemented
197#537×C79C2212yescomplemented
198#534×C79C2214yescomplemented
199#532×C79C2211yescharacteristic, complemented
200#532×C79C2211yescharacteristic, complemented
201C2×#121×C79C2214yescomplemented
202C2×C4×D4×C79C2211yescharacteristic, complemented
203#14579207—48no—
204#14579206—416no—
205C2×#11929625C2314yes—
206C2×#11929625C2312yes—
207C2×#11929624—48no—
208C2×#11929624C2314yes—
209C2×#11929624C2312yes—
210C2×#11929624C2314yes—
211C2×#11929624C2314yes—
212C2×#11929624C2314yes—
213C2×#11929624C2314yes—
214C2×#11929624C2314yes—
215C2×#11929624C2314yes—
216C2×#11929623C2312yes—
217C2×#11929623C2314yes—
218C2×#11929623C2318yes—
219C2×#11929623C2314yes—
220C2×#11929623C2312yes—
221C2×#11929623C2312yes—
222#41×D79—48no—
223C22×Dic158C2312yes—
224C2×Q8×D79C2312yes—
225C22×D316C2311yescharacteristic
226C22×D316C2314yes—
227C22×D316C2312yes—
228C22×C22⋊D79C2318yes—
229C22×C22⋊D79C2318yes—
230C22×C22⋊D79C2318yes—
231C22×C22⋊D79C2312yes—
232C22×C22⋊D79C2312yes—
233C22×C22⋊D79C2312yes—
234C2×D4×D79C2312yes—
235C2×D4×D79C2318yes—
236C2×D4×D79C2314yes—
237C2×D4×D79C2318yes—
238C2×D4×D79C2314yes—
239C2×D4×D79C2312yes—
240C2×D4×D79C2314yes—
241C2×D4×D79C2312yes—
242C22×C4×D79C2311yescharacteristic
243C22×C4×D79C2311yescharacteristic
244C22×C4×D79C2311yescharacteristic
245C22×C4×D79C2314yes—
246C22×C4×D79C2312yes—
247#14579161C2311yescharacteristic
248#14579161C2311yescharacteristic
249#14579161C2311yescharacteristic
250#14579160C2312yes—
251#14579160C2312yes—
252#14579160C2312yes—
253#14579160C2312yes—
254#14579160C2312yes—
255#14579160C2312yes—
256#14579159C2312yes—
257#14579158C2311yescharacteristic
258#14579157C2318yes—
259#14579157C2312yes—
260#14579157C2312yes—
261#14579157C2312yes—
262#14579157C2318yes—
263#14579157C2318yes—
264#14579157C2314yes—
265#14579157C2318yes—
266#14579157C2314yes—
267#14579157C2312yes—
268#14579157C2312yes—
269#14579157C2312yes—
270#14579157C2312yes—
271#14579156C2318yes—
272#14579156C2318yes—
273#14579154C2314yes—
274#14579154C2314yes—
275#14579154C2318yes—
276#14579154C2318yes—
277#14579153C2312yes—
278#14579152C2312yes—
279#14579152C2312yes—
280#14579151C2318yes—
281#14579150C2312yes—
282#14579150C2314yes—
283#14579149C2312yes—
284#14579148C2318yes—
285#14579148C2318yes—
286#14579148C2312yes—
287#14579148C2312yes—
288#14579148C2314yes—
289#14579148C2312yes—
290#14579147C2314yes—
291#14579147C2314yes—
292#14579147C2318yes—
293#14579147C2318yes—
294#14579147C2318yes—
295#14579147C2318yes—
296#14579147C2314yes—
297#14579147C2314yes—
298#14579147C2318yes—
299#14579147C2314yes—
300#14579147C2314yes—
301#14579146C2318yes—
302#14579146C2318yes—
303#14579145C2318yes—
304#14579144C2318yes—
305#14579143C2318yes—
306#14579143C2318yes—
307#14579143C2318yes—
308#14579143C2318yes—
309#14579143C2314yes—
310#14579143C2314yes—
311#14579142C2318yes—
312#14579142C2318yes—
313#14579142C2314yes—
314#14579141C2312yes—
315#14579141C2314yes—
316#14579141C2318yes—
317#14579141C2312yes—
318#14579140C2318yes—
319#14579140C2314yes—
320#14579140C2314yes—
321#14579140C2312yes—
322#14579140C2312yes—
323#14579139C2318yes—
324#14579138C2318yes—
325#14579138C2318yes—
326#14579137C2312yes—
327#14579137C2314yes—
328#14579137C2312yes—
329#14579136C2312yes—
330#14579136C2318yes—
331#14579136C2312yes—
332#14579136C2314yes—
333#14579136C2312yes—
334#14579136C2312yes—
335#14579136C2312yes—
336#14579136C2312yes—
337#14579135C2318yes—
338#14579135C2314yes—
339#14579135C2314yes—
340#14579135C2318yes—
341#14579135C2318yes—
342#14579135C2312yes—
343#14579135C2314yes—
344#14579135C2314yes—
345#14579135C2312yes—
346#14579134C2318yes—
347#14579134C2318yes—
348#14579134C2318yes—
349#14579134C2314yes—
350#14579134C2318yes—
351#14579134C2318yes—
352#14579134C2314yes—
353#14579134C2314yes—
354#14579134C2314yes—
355#14579134C2314yes—
356#14579134C2314yes—
357#14579133C2318yes—
358#14579133C2318yes—
359#14579133C2318yes—
360#14579133C2318yes—
361#14579133C2318yes—
362#14579133C2318yes—
363#14579133C2318yes—
364#14579133C2318yes—
365#14579133C2314yes—
366#14579133C2314yes—
367#14579132C2312yes—
368#14579132C2314yes—
369#14579132C2314yes—
370#14579132C2312yes—
371#14579132C2318yes—
372#14579132C2318yes—
373#14579132C2314yes—
374#14579132C2318yes—
375#14579132C2318yes—
376#14579132C2312yes—
377#14579132C2314yes—
378#14579132C2314yes—
379#14579132C2312yes—
380#14579132C2312yes—
381#14579132C2312yes—
382#14579132C2312yes—
383#14579132C2312yes—
384#14579132C2312yes—
385#14579132C2312yes—
386#14579131C2318yes—
387#14579131C2318yes—
388#14579131C2318yes—
389#14579130C2318yes—
390#14579130C2318yes—
391#14579130C2318yes—
392#14579130C2318yes—
393#14579130C2318yes—
394#14579129C2318yes—
395#14579129C2318yes—
396#14579129C2318yes—
397#14579129C2318yes—
398#14579129C2318yes—
399#14579129C2314yes—
400#14579129C2318yes—
401Q8×Dic79C2314yes—
402Q8×Dic79C2312yes—
403Q8×Dic79C2312yes—
404C4×Dic158C2312yes—
405C4×Dic158C2312yes—
406#14579126C2314yes—
407#14579126C2318yes—
408#14579126C2312yes—
409#14579126C2312yes—
410C4×D316C2312yes—
411C4×D316C2312yes—
412C4×D316C2312yes—
413C4×D316C2312yes—
414C4×D316C2312yes—
415C4×D316C2312yes—
416D4×Dic79C2312yes—
417D4×Dic79C2318yes—
418D4×Dic79C2314yes—
419D4×Dic79C2312yes—
420D4×Dic79C2314yes—
421D4×Dic79C2314yes—
422D4×Dic79C2312yes—
423D4×Dic79C2312yes—
424D4×Dic79C2312yes—
425D4×Dic79C2312yes—
426#14579123C2312yes—
427#14579123C2318yes—
428#14579123C2314yes—
429#14579123C2312yes—
430C4×C22⋊D79C2314yes—
431C4×C22⋊D79C2318yes—
432C4×C22⋊D79C2318yes—
433C4×C22⋊D79C2318yes—
434C4×C22⋊D79C2318yes—
435C4×C22⋊D79C2314yes—
436C4×C22⋊D79C2318yes—
437C4×C22⋊D79C2318yes—
438C4×C22⋊D79C2314yes—
439C4×C22⋊D79C2314yes—
440C4×C22⋊D79C2314yes—
441C4×C22⋊D79C2314yes—
442C4×C22⋊D79C2314yes—
443C4×C22⋊D79C2314yes—
444(C22⋊D79)⋊C4C2318yes—
445(C22⋊D79)⋊C4C2318yes—
446(C22⋊D79)⋊C4C2314yes—
447(C22⋊D79)⋊C4C2318yes—
448(C22⋊D79)⋊C4C2314yes—
449(C22⋊D79)⋊C4C2314yes—
450(C22⋊D79)⋊C4C2314yes—
451#14579120C2314yes—
452#14579120C2314yes—
453#14579120C2314yes—
454#14579120C2312yes—
455#14579119C2312yes—
456#14579119C2314yes—
457#14579119C2314yes—
458#14579119C2312yes—
459#14579117C2314yes—
460#14579117C2314yes—
461#14579117C2318yes—
462C2×C4⋊Dic79C2311yescharacteristic
463C2×C4⋊Dic79C2314yes—
464C2×Dic79⋊C4C2312yes—
465C4⋊C4×D79C2312yes—
466C4⋊C4×D79C2314yes—
467C4⋊C4×D79C2314yes—
468C4⋊C4×D79C2312yes—
469C2×C22⋊Dic79C2318yes—
470C2×C22⋊Dic79C2312yes—
471C2×(C2×D79)⋊C4C2312yes—
472C2×(C2×D79)⋊C4C2312yes—
473C22⋊C4×D79C2318yes—
474C22⋊C4×D79C2314yes—
475C22⋊C4×D79C2318yes—
476C22⋊C4×D79C2314yes—
477C2×C4×Dic79C2311yescharacteristic
478C2×C4×Dic79C2311yescharacteristic
479C2×C4×Dic79C2311yescharacteristic
480C2×C4×Dic79C2314yes—
481C42×D79C2311yescharacteristic
482C42×D79C2311yescharacteristic
483C42×D79C2311yescharacteristic
484C42×D79C2311yescharacteristic
485C42×D79C2311yescharacteristic
486C42×D79C2311yescharacteristic
487C42×D79C2311yescharacteristic
488C42×D79C2311yescharacteristic
489H(5,𝔽2)×C79—48no—
490C2×#41×C79C2312yes—
491C2×#41×C79C2312yes—
492C2×#41×C79C2314yes—
493C2×#41×C79C2314yes—
494C22×D4×C79C2311yescharacteristic
495C22×D4×C79C2314yes—
496C22×D4×C79C2318yes—
497C22×D4×C79C2314yes—
498C22×D4×C79C2314yes—
499C23×C4×C79C2312yes—
500C4⋊Q8×C79C2311yescharacteristic
501C4⋊Q8×C79C2311yescharacteristic
502#127×C79C2311yescharacteristic
503#127×C79C2311yescharacteristic
504#124×C79C2312yes—
505#124×C79C2312yes—
506#123×C79C2318yes—
507#123×C79C2318yes—
508C22⋊Q8×C79C2314yes—
509C22⋊Q8×C79C2314yes—
510#121×C79C2314yes—
511#121×C79C2314yes—
512#121×C79C2318yes—
513#121×C79C2312yes—
514#121×C79C2314yes—
515#121×C79C2318yes—
516#121×C79C2314yes—
517#121×C79C2312yes—
518#121×C79C2312yes—
519#121×C79C2312yes—
520#120×C79C2318yes—
521#120×C79C2318yes—
522C4×D4×C79C2312yes—
523C4×D4×C79C2312yes—
524C4×D4×C79C2312yes—
525C4×D4×C79C2312yes—
526C4×D4×C79C2312yes—
527C4×D4×C79C2312yes—
528C4×D4×C79C2312yes—
529C4×D4×C79C2312yes—
530C2×C4⋊C4×C79C2314yes—
531C2×C4⋊C4×C79C2311yescharacteristic
532C2×C22⋊C4×C79C2312yes—
533C2×C22⋊C4×C79C2318yes—
534C2×C42×C79C2311yescharacteristic
535C23×D79C2411yescharacteristic
536C23×D79C2414yes—
537C23×D79C2412yes—
538C23×D79C2418yes—
539#11929625—44no—
540#11929625—48no—
541#11929624—216no—
542#11929624—28no—
543#11929624—48no—
544#11929624—48no—
545#11929624—48no—
546#11929624—48no—
547#11929624—48no—
548#11929624—48no—
549#11929623—28no—
550#11929623—48no—
551#11929623—416no—
552#11929623—44no—
553#11929623—48no—
554#11929623—44no—
555C2×Dic158—44no—
556C2×Dic158C2412yes—
557C2×Dic158C2414yes—
558C2×Dic158C2412yes—
559C2×Dic158C2414yes—
560C2×Dic158C2414yes—
561C2×Dic158C2412yes—
562Q8×D79—44no—
563C2×D316—24no—
564C2×D316—48no—
565C2×D316—44no—
566C2×D316C2414yes—
567C2×D316C2412yes—
568C2×D316C2412yes—
569C2×D316C2412yes—
570C2×D316C2412yes—
571C2×D316C2414yes—
572C2×D316C2414yes—
573C2×D316C2418yes—
574C2×D316C2412yes—
575C2×C22⋊D79—44no—
576C2×C22⋊D79—416no—
577C2×C22⋊D79—44no—
578C2×C22⋊D79—416no—
579C2×C22⋊D79—416no—
580C2×C22⋊D79—44no—
581C2×C22⋊D79C2414yes—
582C2×C22⋊D79C2414yes—
583C2×C22⋊D79C2414yes—
584C2×C22⋊D79C2414yes—
585C2×C22⋊D79C2414yes—
586C2×C22⋊D79C2414yes—
587C2×C22⋊D79C2414yes—
588C2×C22⋊D79C2414yes—
589C2×C22⋊D79C2414yes—
590C2×C22⋊D79C2414yes—
591C2×C22⋊D79C2418yes—
592C2×C22⋊D79C2418yes—
593C2×C22⋊D79C2414yes—
594C2×C22⋊D79C2414yes—
595C2×C22⋊D79C2418yes—
596C2×C22⋊D79C2418yes—
597C2×C22⋊D79C2418yes—
598C2×C22⋊D79C2414yes—
599C2×C22⋊D79C2418yes—
600D4×D79—28no—
601D4×D79—44no—
602D4×D79—48no—
603D4×D79—416no—
604D4×D79—416no—
605D4×D79—44no—
606D4×D79—48no—
607D4×D79—48no—
608C22×Dic79C2411yescharacteristic
609C22×Dic79C2411yescharacteristic
610C22×Dic79C2414yes—
611C22×Dic79C2414yes—
612C22×Dic79C2411yescharacteristic
613C22×Dic79C2412yes—
614C22×Dic79C2414yes—
615C22×Dic79C2418yes—
616C2×C4×D79—24no—
617C2×C4×D79—24no—
618C2×C4×D79—48no—
619C2×C4×D79—44no—
620C2×C4×D79—42no—
621C2×C4×D79C2411yescharacteristic
622C2×C4×D79C2411yescharacteristic
623C2×C4×D79C2411yescharacteristic
624C2×C4×D79C2414yes—
625C2×C4×D79C2411yescharacteristic
626C2×C4×D79C2411yescharacteristic
627C2×C4×D79C2411yescharacteristic
628C2×C4×D79C2411yescharacteristic
629C2×C4×D79C2414yes—
630C2×C4×D79C2411yescharacteristic
631C2×C4×D79C2411yescharacteristic
632C2×C4×D79C2414yes—
633C2×C4×D79C2418yes—
634C2×C4×D79C2414yes—
635C2×C4×D79C2414yes—
636C2×C4×D79C2418yes—
637C2×C4×D79C2411yescharacteristic
638C2×C4×D79C2411yescharacteristic
639C2×C4×D79C2411yescharacteristic
640C4⋊Dic79C2412yes—
641C4⋊Dic79C2412yes—
642C4⋊Dic79C2412yes—
643C4⋊Dic79C2412yes—
644C4⋊Dic79C2412yes—
645C4⋊Dic79C2418yes—
646C4⋊Dic79C2412yes—
647C4⋊Dic79C2412yes—
648C4⋊Dic79C2412yes—
649C4⋊Dic79C2414yes—
650C4⋊Dic79C2414yes—
651Dic79⋊C4C2414yes—
652Dic79⋊C4C2414yes—
653Dic79⋊C4C2418yes—
654Dic79⋊C4C2418yes—
655Dic79⋊C4C2414yes—
656Dic79⋊C4C2414yes—
657Dic79⋊C4C2414yes—
658Dic79⋊C4C2414yes—
659Dic79⋊C4C2414yes—
660Dic79⋊C4C2414yes—
661C22⋊Dic79C2414yes—
662C22⋊Dic79C2418yes—
663C22⋊Dic79C2414yes—
664C22⋊Dic79C2414yes—
665C22⋊Dic79C2414yes—
666C22⋊Dic79C2418yes—
667C22⋊Dic79C2414yes—
668C22⋊Dic79C2414yes—
669C22⋊Dic79C2414yes—
670C22⋊Dic79C2418yes—
671C22⋊Dic79C2414yes—
672C22⋊Dic79C2414yes—
673C22⋊Dic79C2418yes—
674(C2×D79)⋊C4C2414yes—
675(C2×D79)⋊C4C2414yes—
676(C2×D79)⋊C4C2418yes—
677(C2×D79)⋊C4C2418yes—
678(C2×D79)⋊C4C2414yes—
679(C2×D79)⋊C4C2414yes—
680(C2×D79)⋊C4C2414yes—
681(C2×D79)⋊C4C2414yes—
682(C2×D79)⋊C4C2414yes—
683(C2×D79)⋊C4C2414yes—
684(C2×D79)⋊C4C2414yes—
685(C2×D79)⋊C4C2414yes—
686(C2×D79)⋊C4C2418yes—
687(C2×D79)⋊C4C2418yes—
688C4×Dic79C2411yescharacteristic
689C4×Dic79C2411yescharacteristic
690C4×Dic79C2411yescharacteristic
691C4×Dic79C2411yescharacteristic
692C4×Dic79C2411yescharacteristic
693C4×Dic79C2411yescharacteristic
694C4×Dic79C2411yescharacteristic
695C4×Dic79C2411yescharacteristic
696C4×Dic79C2411yescharacteristic
697C4×Dic79C2411yescharacteristic
698C4×Dic79C2411yescharacteristic
699C4×Dic79C2411yescharacteristic
700C4×Dic79C2414yes—
701C4×Dic79C2414yes—
702C4×Dic79C2414yes—
703C4×Dic79C2418yes—
704C4×Dic79C2418yes—
705C24×C79C2412yes—
706C24×C79C2418yes—
707#41×C79—28no—
708#41×C79—28no—
709#41×C79—48no—
710#41×C79—48no—
711C2×Q8×C79C2412yes—
712C2×Q8×C79C2412yes—
713C2×D4×C79—24no—
714C2×D4×C79—48no—
715C2×D4×C79—48no—
716C2×D4×C79—48no—
717C2×D4×C79—416no—
718C2×D4×C79C2412yes—
719C2×D4×C79C2412yes—
720C2×D4×C79C2414yes—
721C2×D4×C79C2412yes—
722C2×D4×C79C2412yes—
723C2×D4×C79C2412yes—
724C2×D4×C79C2414yes—
725C2×D4×C79C2412yes—
726C2×D4×C79C2412yes—
727C2×D4×C79C2418yes—
728C2×D4×C79C2412yes—
729C2×D4×C79C2418yes—
730C2×D4×C79C2418yes—
731C22×C4×C79—44no—
732C22×C4×C79C2414yes—
733C22×C4×C79C2414yes—
734C22×C4×C79C2414yes—
735C22×C4×C79C2411yescharacteristic
736C22×C4×C79C2412yes—
737C22×C4×C79C2414yes—
738C22×C4×C79C2411yescharacteristic
739C22×C4×C79C2418yes—
740C22×C4×C79C2411yescharacteristic
741C4⋊C4×C79C2412yes—
742C4⋊C4×C79C2412yes—
743C4⋊C4×C79C2412yes—
744C4⋊C4×C79C2412yes—
745C4⋊C4×C79C2418yes—
746C4⋊C4×C79C2412yes—
747C4⋊C4×C79C2412yes—
748C22⋊C4×C79C2414yes—
749C22⋊C4×C79C2414yes—
750C22⋊C4×C79C2414yes—
751C22⋊C4×C79C2414yes—
752C22⋊C4×C79C2418yes—
753C22⋊C4×C79C2418yes—
754C22⋊C4×C79C2414yes—
755C22⋊C4×C79C2414yes—
756C42×C79C2411yescharacteristic
757C42×C79C2411yescharacteristic
758C42×C79C2411yescharacteristic
759C42×C79C2411yescharacteristic
760C23×C79—24no—
761C23×C79—42no—
762C23×C79—42no—
763C23×C79—48no—
764C23×C79—48no—
765C23×C79—48no—
766C23×C79C2514yes—
767C23×C79C2514yes—
768C23×C79C2514yes—
769C23×C79C2511yescharacteristic
770C22×D79—22no—
771C22×D79—24no—
772C22×D79—22no—
773C22×D79—28no—
774C22×D79—41no—
775C22×D79—44no—
776C22×D79—42no—
777C22×D79—44no—
778C22×D79—42no—
779C22×D79—48no—
780C22×D79—48no—
781C22×D79—48no—
782C22×D79C2514yes—
783C22×D79C2514yes—
784C22×D79C2511yescharacteristic
785C22×D79C2511yescharacteristic
786Q8×C79—24no—
787Q8×C79—24no—
788D4×C79—28no—
789D4×C79—28no—
790D4×C79—24no—
791D4×C79—24no—
792D4×C79—24no—
793D4×C79—24no—
794D4×C79—24no—
795D4×C79—24no—
796D4×C79—48no—
797D4×C79—42no—
798D4×C79—42no—
799D4×C79—48no—
800D4×C79—48no—
801C2×C4×C79—22no—
802C2×C4×C79—28no—
803C2×C4×C79—28no—
804C2×C4×C79—28no—
805C2×C4×C79—41no—
806C2×C4×C79—42no—
807C2×C4×C79—44no—
808C2×C4×C79—48no—
809C2×C4×C79H(5,𝔽2)14yescomplemented
810C2×C4×C79C2511yescharacteristic
811C2×C4×C79C2514yes—
812C2×C4×C79C2511yescharacteristic
813C2×C4×C79C2514yes—
814C2×C4×C79C2511yescharacteristic
815C2×C4×C79C2514yes—
816C2×C4×C79C2511yescharacteristic
817C2×C4×C79C2511yescharacteristic
818C2×C4×C79C2511yescharacteristic
819C22⋊D79—28no—
820C22⋊D79—28no—
821C22⋊D79—28no—
822C22⋊D79—28no—
823C22⋊D79—28no—
824C22⋊D79—28no—
825C22⋊D79—28no—
826C22⋊D79—48no—
827C22⋊D79—48no—
828C22⋊D79—48no—
829C22⋊D79—44no—
830C22⋊D79—44no—
831C22⋊D79—48no—
832C22⋊D79—48no—
833C22⋊D79—48no—
834C22⋊D79—44no—
835C22⋊D79—44no—
836C22⋊D79—44no—
837C22⋊D79—44no—
838C2×Dic79—22no—
839C2×Dic79—22no—
840C2×Dic79—28no—
841C2×Dic79—22no—
842C2×Dic79—28no—
843C2×Dic79—42no—
844C2×Dic79—44no—
845C2×Dic79—48no—
846C2×Dic79C2514yes—
847C2×Dic79C2511yescharacteristic
848C2×Dic79C2511yescharacteristic
849C2×Dic79C2511yescharacteristic
850C2×Dic79C2511yescharacteristic
851C2×Dic79C2514yes—
852C2×Dic79C2514yes—
853C2×Dic79C2514yes—
854C2×Dic79C2511yescharacteristic
855C2×Dic79C2511yescharacteristic
856D316—28no—
857D316—24no—
858D316—24no—
859D316—24no—
860D316—24no—
861D316—48no—
862D316—42no—
863D316—44no—
864D316—44no—
865C4×D79—22no—
866C4×D79—22no—
867C4×D79—22no—
868C4×D79—22no—
869C4×D79—22no—
870C4×D79—22no—
871C4×D79—28no—
872C4×D79—28no—
873C4×D79—22no—
874C4×D79—22no—
875C4×D79—22no—
876C4×D79—41no—
877C4×D79—41no—
878C4×D79—44no—
879C4×D79—44no—
880C4×D79—44no—
881C4×D79—48no—
882C4×D79—48no—
883C4×D79H(5,𝔽2)14yescomplemented
884Dic158—24no—
885Dic158—24no—
886Dic158—28no—
887Dic158—44no—
888Dic158—44no—
889Dic158—42no—
890C22×C79—21no—
891C22×C79—21no—
892C22×C79—24no—
893C22×C79—24no—
894C22×C79—24no—
895C22×C79—24no—
896C22×C79—24no—
897C22×C79—24no—
898C22×C79—24no—
899C22×C79—24no—
900C22×C79—24no—
901C22×C79—84no—
902C22×C79—168no—
903C22×C79C2×H(5,𝔽2)12yes—
904C22×C79C2611yescharacteristic
905C2×D79—21no—
906C2×D79—21no—
907C2×D79—24no—
908C2×D79—24no—
909C2×D79—24no—
910C2×D79—21no—
911C2×D79—21no—
912C2×D79—24no—
913C2×D79—24no—
914C2×D79—24no—
915C2×D79—21no—
916C2×D79—44no—
917C2×D79—88no—
918C2×D79—84no—
919C2×D79—168no—
920C2×D79C2×H(5,𝔽2)12yes—
921C4×C79—21no—
922C4×C79—24no—
923C4×C79—24no—
924C4×C79—24no—
925C4×C79—21no—
926C4×C79—21no—
927C4×C79C2×H(5,𝔽2)12yes—
928C4×C79C2×H(5,𝔽2)12yes—
929C4×C79C2×H(5,𝔽2)12yes—
930Dic79—24no—
931Dic79—24no—
932Dic79—24no—
933Dic79—21no—
934Dic79—21no—
935Dic79—21no—
936Dic79—24no—
937Dic79—21no—
938Dic79C2×H(5,𝔽2)12yes—
939Dic79#58512yes—
940#62834—791nomaximal, Sylow
941C2×C79—22no—
942C2×C79—44no—
943C2×C79—44no—
944C2×C79—44no—
945C2×C79C22×H(5,𝔽2)11yescharacteristic
946C2×C79C22×H(5,𝔽2)11yescharacteristic
947C2×C79C2×#58511yescharacteristic
948D79—22no—
949D79—41no—
950D79—44no—
951D79—44no—
952#3558—794no—
953#3558—794no—
954#3549—792no—
955#3548—792no—
956#3546—792no—
957#3546—794no—
958#3546—792no—
959#3537—794no—
960#3519—794no—
961#3519—794no—
962#3511—792no—
963#3511—792no—
964#3508—794no—
965#3506—792no—
966#3506—791no—
967#3506—791no—
968#3498—792no—
969#3498—792no—
970#3496—792no—
971#3496—791no—
972#3496D7911yescharacteristic, complemented
973#3488—792no—
974#3488—792no—
975#3488—794no—
976#3444—791no—
977C2×#532—791no—
978C2×#532—791no—
979C79#6283411yescharacteristic, complemented, Sylow
980C2×H(5,𝔽2)—792no—
981C2×H(5,𝔽2)—794no—
982C2×H(5,𝔽2)C2×D7912yescomplemented
983C22×#41—792no—
984C22×#41—792no—
985#562—798no—
986H(3,𝔽4)—798no—
987#560—798no—
988#560—798no—
989#559—794no—
990#559—798no—
991#559—794no—
992#556—792no—
993#556—794no—
994#556—792no—
995#555—794no—
996#555—794no—
997#555—792no—
998#555—792no—
999#554—794no—
1000#554—794no—
1001#553—798no—
1002#553—798no—
1003#553—794no—
1004#553—794no—
1005#553—794no—
1006#553—794no—
1007#550—794no—
1008#550—794no—
1009#550—794no—
1010#550—792no—
1011#550—794no—
1012#550—798no—
1013#550—794no—
1014#550—792no—
1015#548—794no—
1016#548—794no—
1017#548—798no—
1018#547—792no—
1019#547—794no—
1020#547—792no—
1021#547—792no—
1022#547—792no—
1023#547C2×D7912yescomplemented
1024#547C2×D7912yescomplemented
1025#546—794no—
1026#546—798no—
1027#546—794no—
1028#546—794no—
1029#546—794no—
1030#546—798no—
1031#546—798no—
1032#546—794no—
1033#546—798no—
1034#546—794no—
1035#546—798no—
1036#546—798no—
1037#546C2×D7914yescomplemented
1038#546C2×D7914yescomplemented
1039D42—798no—
1040D42—798no—
1041D42—794no—
1042D42—794no—
1043D42—798no—
1044D42—794no—
1045D42—794no—
1046D42—792no—
1047D42—798no—
1048D42—794no—
1049D42—798no—
1050D42—792no—
1051D42C2×D7912yescomplemented
1052D42C2×D7912yescomplemented
1053#542—798no—
1054#542—794no—
1055#542—794no—
1056#540—798no—
1057#540—798no—
1058#538—798no—
1059#538—798no—
1060#538—798no—
1061#538—794no—
1062#538—798no—
1063#538—794no—
1064#538—798no—
1065#537—792no—
1066#537—794no—
1067#537—794no—
1068#537—794no—
1069#537—794no—
1070#537—794no—
1071#537C2×D7912yescomplemented
1072#535—792no—
1073#535—794no—
1074#535—792no—
1075#535—794no—
1076#535—794no—
1077#535—794no—
1078#535—794no—
1079#535—794no—
1080#535—794no—
1081#535—798no—
1082#535—798no—
1083#534—794no—
1084#534—798no—
1085#534C2×D7914yescomplemented
1086#533—791no—
1087#533—791no—
1088#533—794no—
1089#533—791no—
1090#532—792no—
1091#532—794no—
1092#532—791no—
1093#532—791no—
1094#532—791no—
1095#532—791no—
1096#532—792no—
1097#532—792no—
1098#532—792no—
1099#532—794no—
1100#532—792no—
1101#532—792no—
1102#532—792no—
1103#532—792no—
1104#532—792no—
1105#532—792no—
1106#532—792no—
1107#532—792no—
1108#532—792no—
1109#532—792no—
1110#532—791no—
1111#532C2×D7911yescharacteristic, complemented
1112#532C2×D7911yescharacteristic, complemented
1113C2×C4⋊Q8—791no—
1114C2×C4⋊Q8—791no—
1115C2×#127—791no—
1116C2×#127—794no—
1117C2×#127—791no—
1118#529—792no—
1119#529—792no—
1120#529—792no—
1121#529—792no—
1122#529—792no—
1123#529—792no—
1124C2×#124—792no—
1125C2×#124—792no—
1126#525—792no—
1127#525—794no—
1128#525—794no—
1129#525—794no—
1130#525—792no—
1131#525—792no—
1132#525—794no—
1133C2×#121—791no—
1134C2×#121—794no—
1135C2×#121—792no—
1136C2×#121—792no—
1137C2×#121—794no—
1138C2×#121—794no—
1139C2×#121—791no—
1140C2×#121—792no—
1141C2×#121C2×D7914yescomplemented
1142#520—792no—
1143#520—794no—
1144#520—792no—
1145#518—798no—
1146C4×#41—792no—
1147C4×#41—792no—
1148C4×#41—792no—
1149C2×C4×D4—792no—
1150C2×C4×D4—792no—
1151C2×C4×D4—792no—
1152C2×C4×D4—791no—
1153C2×C4×D4C2×D7911yescharacteristic, complemented
1154C22×C42—791no—
1155H(5,𝔽2)—48no—
1156H(5,𝔽2)—31616no—
1157H(5,𝔽2)—3168no—
1158C2×#41—3168no—
1159C2×#41—3168no—
1160C2×#41—794no—
1161C2×#41—792no—
1162C2×#41—792no—
1163C2×#41—794no—
1164C2×#41—794no—
1165C2×#41—792no—
1166C2×#41—798no—
1167C2×#41—792no—
1168C2×#41—794no—
1169C2×#41—794no—
1170C2×#41—794no—
1171C2×#41—794no—
1172C2×#41—794no—
1173C2×#41—794no—
1174C2×#41—794no—
1175C2×#41—792no—
1176C2×#41C22×D7912yes—
1177C2×#41C22×D7912yes—
1178C2×#41C22×D7914yes—
1179C2×#41C22×D7914yes—
1180C22×Q8—792no—
1181C22×Q8—792no—
1182C22×D4—792no—
1183C22×D4—798no—
1184C22×D4—792no—
1185C22×D4—798no—
1186C22×D4—792no—
1187C22×D4—798no—
1188C22×D4—792no—
1189C22×D4—794no—
1190C22×D4—798no—
1191C22×D4—798no—
1192C22×D4—794no—
1193C22×D4—794no—
1194C22×D4—792no—
1195C22×D4—792no—
1196C22×D4—792no—
1197C22×D4—794no—
1198C22×D4—791no—
1199C22×D4C22×D7911yescharacteristic
1200C22×D4C22×D7914yes—
1201C22×D4C22×D7918yes—
1202C22×D4C22×D7914yes—
1203C22×D4C22×D7914yes—
1204C23×C4—792no—
1205C23×C4—794no—
1206C23×C4—791no—
1207C23×C4—791no—
1208C23×C4—791no—
1209C23×C4C22×D7912yes—
1210C4⋊Q8—792no—
1211C4⋊Q8—792no—
1212C4⋊Q8—792no—
1213C4⋊Q8—792no—
1214C4⋊Q8—792no—
1215C4⋊Q8—792no—
1216C4⋊Q8—792no—
1217C4⋊Q8—791no—
1218C4⋊Q8—791no—
1219C4⋊Q8—791no—
1220C4⋊Q8C22×D7911yescharacteristic
1221C4⋊Q8C22×D7911yescharacteristic
1222#127—792no—
1223#127—792no—
1224#127—792no—
1225#127—792no—
1226#127—792no—
1227#127—792no—
1228#127—792no—
1229#127—794no—
1230#127—794no—
1231#127—798no—
1232#127—798no—
1233#127—798no—
1234#127—798no—
1235#127—791no—
1236#127C22×D7911yescharacteristic
1237#127C22×D7911yescharacteristic
1238#126—798no—
1239#126—798no—
1240#126—794no—
1241#126—794no—
1242#126—798no—
1243#126—798no—
1244#125—792no—
1245#125—792no—
1246#125—798no—
1247#125—792no—
1248#124—792no—
1249#124—794no—
1250#124—792no—
1251#124—792no—
1252#124—792no—
1253#124—794no—
1254#124—798no—
1255#124—798no—
1256#124—794no—
1257#124—794no—
1258#124—794no—
1259#124—794no—
1260#124—794no—
1261#124—794no—
1262#124—798no—
1263#124—798no—
1264#124—798no—
1265#124—798no—
1266#124—798no—
1267#124—792no—
1268#124C22×D7912yes—
1269#124C22×D7912yes—
1270#123—794no—
1271#123—798no—
1272#123—798no—
1273#123—798no—
1274#123—798no—
1275#123—798no—
1276#123—794no—
1277#123—794no—
1278#123—798no—
1279#123—798no—
1280#123—798no—
1281#123—798no—
1282#123—798no—
1283#123C22×D7918yes—
1284#123C22×D7918yes—
1285C22⋊Q8—792no—
1286C22⋊Q8—792no—
1287C22⋊Q8—794no—
1288C22⋊Q8—792no—
1289C22⋊Q8—792no—
1290C22⋊Q8—794no—
1291C22⋊Q8—794no—
1292C22⋊Q8—798no—
1293C22⋊Q8—792no—
1294C22⋊Q8—792no—
1295C22⋊Q8—794no—
1296C22⋊Q8—798no—
1297C22⋊Q8—798no—
1298C22⋊Q8—798no—
1299C22⋊Q8—798no—
1300C22⋊Q8C22×D7914yes—
1301C22⋊Q8C22×D7914yes—
1302#121—792no—
1303#121—792no—
1304#121—792no—
1305#121—792no—
1306#121—792no—
1307#121—794no—
1308#121—794no—
1309#121—792no—
1310#121—792no—
1311#121—798no—
1312#121—798no—
1313#121—794no—
1314#121—794no—
1315#121—794no—
1316#121—798no—
1317#121—798no—
1318#121—792no—
1319#121—792no—
1320#121—792no—
1321#121—794no—
1322#121—794no—
1323#121—798no—
1324#121—798no—
1325#121—798no—
1326#121—798no—
1327#121—798no—
1328#121—798no—
1329#121—798no—
1330#121—798no—
1331#121—792no—
1332#121—792no—
1333#121—794no—
1334#121—794no—
1335#121—794no—
1336#121—794no—
1337#121—798no—
1338#121—798no—
1339#121—798no—
1340#121—792no—
1341#121—792no—
1342#121—792no—
1343#121—792no—
1344#121—792no—
1345#121—792no—
1346#121—794no—
1347#121—798no—
1348#121—794no—
1349#121—794no—
1350#121—794no—
1351#121—794no—
1352#121—794no—
1353#121—794no—
1354#121—798no—
1355#121—798no—
1356#121—798no—
1357#121—798no—
1358#121—798no—
1359#121C22×D7912yes—
1360#121C22×D7912yes—
1361#121C22×D7912yes—
1362#121C22×D7914yes—
1363#121C22×D7918yes—
1364#121C22×D7914yes—
1365#121C22×D7914yes—
1366#121C22×D7918yes—
1367#121C22×D7912yes—
1368#121C22×D7914yes—
1369#120—798no—
1370#120—798no—
1371#120—798no—
1372#120—798no—
1373#120—798no—
1374#120—794no—
1375#120—798no—
1376#120—798no—
1377#120—798no—
1378#120—798no—
1379#120—798no—
1380#120—798no—
1381#120—798no—
1382#120—798no—
1383#120—798no—
1384#120C22×D7918yes—
1385#120C22×D7918yes—
1386C4×Q8—792no—
1387C4×Q8—792no—
1388C4×Q8—794no—
1389C4×Q8—792no—
1390C4×Q8—792no—
1391C4×Q8—798no—
1392C4×Q8—794no—
1393C4×Q8—792no—
1394C4×Q8—792no—
1395C4×D4—792no—
1396C4×D4—792no—
1397C4×D4—794no—
1398C4×D4—794no—
1399C4×D4—792no—
1400C4×D4—792no—
1401C4×D4—792no—
1402C4×D4—792no—
1403C4×D4—798no—
1404C4×D4—794no—
1405C4×D4—794no—
1406C4×D4—794no—
1407C4×D4—794no—
1408C4×D4—794no—
1409C4×D4—794no—
1410C4×D4—794no—
1411C4×D4—794no—
1412C4×D4—794no—
1413C4×D4—798no—
1414C4×D4—798no—
1415C4×D4—798no—
1416C4×D4—798no—
1417C4×D4—798no—
1418C4×D4—798no—
1419C4×D4—792no—
1420C4×D4—792no—
1421C4×D4—798no—
1422C4×D4—794no—
1423C4×D4—794no—
1424C4×D4—794no—
1425C4×D4—794no—
1426C4×D4—794no—
1427C4×D4—798no—
1428C4×D4—798no—
1429C4×D4—798no—
1430C4×D4—792no—
1431C4×D4—792no—
1432C4×D4—792no—
1433C4×D4—792no—
1434C4×D4—792no—
1435C4×D4—792no—
1436C4×D4C22×D7912yes—
1437C4×D4C22×D7912yes—
1438C4×D4C22×D7912yes—
1439C4×D4C22×D7912yes—
1440C4×D4C22×D7912yes—
1441C4×D4C22×D7912yes—
1442C4×D4C22×D7912yes—
1443C4×D4C22×D7912yes—
1444#117—792no—
1445#117—794no—
1446#117—794no—
1447#117—794no—
1448#117—792no—
1449#117—792no—
1450#117—794no—
1451#117—794no—
1452#117—794no—
1453#117—794no—
1454#117—798no—
1455C2×C4⋊C4—791no—
1456C2×C4⋊C4—792no—
1457C2×C4⋊C4—794no—
1458C2×C4⋊C4—792no—
1459C2×C4⋊C4—792no—
1460C2×C4⋊C4—794no—
1461C2×C4⋊C4—794no—
1462C2×C4⋊C4C22×D7911yescharacteristic
1463C2×C4⋊C4C22×D7914yes—
1464C2×C22⋊C4—792no—
1465C2×C22⋊C4—798no—
1466C2×C22⋊C4—792no—
1467C2×C22⋊C4—792no—
1468C2×C22⋊C4—794no—
1469C2×C22⋊C4—794no—
1470C2×C22⋊C4—798no—
1471C2×C22⋊C4—798no—
1472C2×C22⋊C4C22×D7912yes—
1473C2×C22⋊C4C22×D7918yes—
1474C2×C42—791no—
1475C2×C42—794no—
1476C2×C42—791no—
1477C2×C42—791no—
1478C2×C42—791no—
1479C2×C42—791no—
1480C2×C42—791no—
1481C2×C42—791no—
1482C2×C42—791no—
1483C2×C42—791no—
1484C2×C42—791no—
1485C2×C42—791no—
1486C2×C42C22×D7911yescharacteristic
1487C24—798no—
1488C24—794no—
1489C24—792no—
1490C24—791no—
1491C24C23×D7912yes—
1492C24C23×D7918yes—
1493#41—28no—
1494#41—28no—
1495#41—48no—
1496#41—48no—
1497#41—3168no—
1498#41—3168no—
1499#41—3168no—
1500#41—3168no—
1501#41—3168no—
1502#41—3168no—
1503#41—3164no—
1504#41—3168no—
1505#41—3168no—
1506#41—31616no—
1507#41—3164no—
1508#41—3168no—
1509#41—3164no—
1510#41—15816no—
1511#41—1588no—
1512#41—1588no—
1513C2×Q8—3164no—
1514C2×Q8—3164no—
1515C2×Q8—792no—
1516C2×Q8—794no—
1517C2×Q8—794no—
1518C2×Q8—792no—
1519C2×Q8—794no—
1520C2×Q8—792no—
1521C2×Q8C23×D7912yes—
1522C2×Q8C23×D7912yes—
1523C2×D4—24no—
1524C2×D4—48no—
1525C2×D4—48no—
1526C2×D4—48no—
1527C2×D4—416no—
1528C2×D4—3168no—
1529C2×D4—3164no—
1530C2×D4—3168no—
1531C2×D4—31616no—
1532C2×D4—31616no—
1533C2×D4—3164no—
1534C2×D4—31616no—
1535C2×D4—3164no—
1536C2×D4—3168no—
1537C2×D4—3168no—
1538C2×D4—3164no—
1539C2×D4—3164no—
1540C2×D4—31616no—
1541C2×D4—3164no—
1542C2×D4—31616no—
1543C2×D4—794no—
1544C2×D4—794no—
1545C2×D4—798no—
1546C2×D4—798no—
1547C2×D4—794no—
1548C2×D4—794no—
1549C2×D4—798no—
1550C2×D4—798no—
1551C2×D4—794no—
1552C2×D4—794no—
1553C2×D4—798no—
1554C2×D4—798no—
1555C2×D4—794no—
1556C2×D4—794no—
1557C2×D4—794no—
1558C2×D4—794no—
1559C2×D4—794no—
1560C2×D4—794no—
1561C2×D4—794no—
1562C2×D4—792no—
1563C2×D4—794no—
1564C2×D4—794no—
1565C2×D4—798no—
1566C2×D4—794no—
1567C2×D4—792no—
1568C2×D4—792no—
1569C2×D4—792no—
1570C2×D4—792no—
1571C2×D4—1588no—
1572C2×D4—1584no—
1573C2×D4C23×D7914yes—
1574C2×D4C23×D7914yes—
1575C2×D4C23×D7912yes—
1576C2×D4C23×D7912yes—
1577C2×D4C23×D7912yes—
1578C2×D4C23×D7912yes—
1579C2×D4C23×D7912yes—
1580C2×D4C23×D7912yes—
1581C2×D4C23×D7912yes—
1582C2×D4C23×D7912yes—
1583C2×D4C23×D7918yes—
1584C2×D4C23×D7918yes—
1585C2×D4C23×D7918yes—
1586C22×C4—44no—
1587C22×C4—3164no—
1588C22×C4—3168no—
1589C22×C4—3162no—
1590C22×C4—792no—
1591C22×C4—794no—
1592C22×C4—798no—
1593C22×C4—791no—
1594C22×C4—791no—
1595C22×C4—794no—
1596C22×C4—794no—
1597C22×C4—794no—
1598C22×C4—798no—
1599C22×C4—798no—
1600C22×C4—791no—
1601C22×C4—791no—
1602C22×C4—791no—
1603C22×C4—791no—
1604C22×C4—794no—
1605C22×C4—794no—
1606C22×C4—791no—
1607C22×C4—791no—
1608C22×C4—791no—
1609C22×C4—791no—
1610C22×C4—791no—
1611C22×C4—791no—
1612C22×C4—791no—
1613C22×C4—791no—
1614C22×C4—791no—
1615C22×C4—794no—
1616C22×C4—794no—
1617C22×C4—1584no—
1618C22×C4—1584no—
1619C22×C4C23×D7911yescharacteristic
1620C22×C4C23×D7914yes—
1621C22×C4C23×D7914yes—
1622C22×C4C23×D7914yes—
1623C22×C4C23×D7911yescharacteristic
1624C22×C4C23×D7912yes—
1625C22×C4C23×D7914yes—
1626C22×C4C23×D7918yes—
1627C22×C4C23×D7911yescharacteristic
1628C4⋊C4—794no—
1629C4⋊C4—794no—
1630C4⋊C4—794no—
1631C4⋊C4—794no—
1632C4⋊C4—798no—
1633C4⋊C4—798no—
1634C4⋊C4—794no—
1635C4⋊C4—794no—
1636C4⋊C4—794no—
1637C4⋊C4—794no—
1638C4⋊C4—792no—
1639C4⋊C4—792no—
1640C4⋊C4—792no—
1641C4⋊C4—792no—
1642C4⋊C4—792no—
1643C4⋊C4—798no—
1644C4⋊C4—792no—
1645C4⋊C4—792no—
1646C4⋊C4—794no—
1647C4⋊C4—794no—
1648C4⋊C4—792no—
1649C4⋊C4C23×D7912yes—
1650C4⋊C4C23×D7912yes—
1651C4⋊C4C23×D7912yes—
1652C4⋊C4C23×D7912yes—
1653C4⋊C4C23×D7912yes—
1654C4⋊C4C23×D7918yes—
1655C4⋊C4C23×D7912yes—
1656C22⋊C4—794no—
1657C22⋊C4—794no—
1658C22⋊C4—798no—
1659C22⋊C4—798no—
1660C22⋊C4—794no—
1661C22⋊C4—794no—
1662C22⋊C4—794no—
1663C22⋊C4—794no—
1664C22⋊C4—794no—
1665C22⋊C4—794no—
1666C22⋊C4—794no—
1667C22⋊C4—798no—
1668C22⋊C4—798no—
1669C22⋊C4—794no—
1670C22⋊C4—794no—
1671C22⋊C4—798no—
1672C22⋊C4—798no—
1673C22⋊C4—794no—
1674C22⋊C4—794no—
1675C22⋊C4—794no—
1676C22⋊C4—794no—
1677C22⋊C4—794no—
1678C22⋊C4—794no—
1679C22⋊C4—794no—
1680C22⋊C4—798no—
1681C22⋊C4—798no—
1682C22⋊C4—794no—
1683C22⋊C4C23×D7914yes—
1684C22⋊C4C23×D7914yes—
1685C22⋊C4C23×D7918yes—
1686C22⋊C4C23×D7914yes—
1687C22⋊C4C23×D7918yes—
1688C22⋊C4C23×D7914yes—
1689C22⋊C4C23×D7914yes—
1690C22⋊C4C23×D7914yes—
1691C42—791no—
1692C42—791no—
1693C42—791no—
1694C42—791no—
1695C42—791no—
1696C42—791no—
1697C42—791no—
1698C42—791no—
1699C42—791no—
1700C42—791no—
1701C42—791no—
1702C42—791no—
1703C42—794no—
1704C42—794no—
1705C42—794no—
1706C42—798no—
1707C42—798no—
1708C42C23×D7911yescharacteristic
1709C42C23×D7911yescharacteristic
1710C42C23×D7911yescharacteristic
1711C42C23×D7911yescharacteristic
1712C23—24no—
1713C23—42no—
1714C23—42no—
1715C23—48no—
1716C23—48no—
1717C23—48no—
1718C23—3161no—
1719C23—3162no—
1720C23—3164no—
1721C23—3162no—
1722C23—3164no—
1723C23—3168no—
1724C23—3168no—
1725C23—3168no—
1726C23—791no—
1727C23—794no—
1728C23—794no—
1729C23—791no—
1730C23—1582no—
1731C23—1588no—
1732C23—1582no—
1733C23—1584no—
1734C23C24×D7914yes—
1735C23C24×D7914yes—
1736C23C24×D7914yes—
1737C23C24×D7911yescharacteristic
1738Q8—24no—
1739Q8—24no—
1740Q8—3164no—
1741Q8—3164no—
1742Q8—3162no—
1743Q8—1588no—
1744Q8—1584no—
1745Q8—1584no—
1746D4—28no—
1747D4—28no—
1748D4—24no—
1749D4—24no—
1750D4—24no—
1751D4—24no—
1752D4—24no—
1753D4—24no—
1754D4—48no—
1755D4—48no—
1756D4—48no—
1757D4—42no—
1758D4—42no—
1759D4—3168no—
1760D4—3164no—
1761D4—3164no—
1762D4—3162no—
1763D4—3168no—
1764D4—3168no—
1765D4—3168no—
1766D4—3168no—
1767D4—3164no—
1768D4—3168no—
1769D4—3168no—
1770D4—3164no—
1771D4—3164no—
1772D4—3164no—
1773D4—3164no—
1774D4—3164no—
1775D4—1588no—
1776D4—1588no—
1777D4—1588no—
1778D4—1588no—
1779D4—1588no—
1780D4—1588no—
1781D4—1588no—
1782D4—1588no—
1783D4—1584no—
1784D4—1584no—
1785D4—1584no—
1786D4—1584no—
1787C2×C4—22no—
1788C2×C4—28no—
1789C2×C4—28no—
1790C2×C4—28no—
1791C2×C4—42no—
1792C2×C4—44no—
1793C2×C4—41no—
1794C2×C4—48no—
1795C2×C4—3164no—
1796C2×C4—3164no—
1797C2×C4—3164no—
1798C2×C4—3161no—
1799C2×C4—3161no—
1800C2×C4—3168no—
1801C2×C4—3168no—
1802C2×C4—3162no—
1803C2×C4—3164no—
1804C2×C4—3168no—
1805C2×C4—791no—
1806C2×C4—791no—
1807C2×C4—794no—
1808C2×C4—794no—
1809C2×C4—791no—
1810C2×C4—791no—
1811C2×C4—791no—
1812C2×C4—791no—
1813C2×C4—794no—
1814C2×C4—794no—
1815C2×C4—794no—
1816C2×C4—1582no—
1817C2×C4—1582no—
1818C2×C4—1582no—
1819C2×C4—1582no—
1820C2×C4—1582no—
1821C2×C4—1582no—
1822C2×C4—1588no—
1823C2×C4—1588no—
1824C2×C4—1582no—
1825C2×C4—1588no—
1826C2×C4—1582no—
1827C2×C4—1582no—
1828C2×C4—1588no—
1829C2×C4—1582no—
1830C2×C4—1582no—
1831C2×C4—1582no—
1832C2×C4#1457920614yescomplemented
1833C2×C4C24×D7911yescharacteristic
1834C2×C4C24×D7911yescharacteristic
1835C2×C4C24×D7911yescharacteristic
1836C2×C4C24×D7914yes—
1837C2×C4C24×D7914yes—
1838C2×C4C24×D7914yes—
1839C2×C4C24×D7911yescharacteristic
1840C2×C4C24×D7911yescharacteristic
1841C2×C4C24×D7911yescharacteristic
1842C22—21no—
1843C22—21no—
1844C22—24no—
1845C22—24no—
1846C22—24no—
1847C22—24no—
1848C22—24no—
1849C22—24no—
1850C22—24no—
1851C22—24no—
1852C22—24no—
1853C22—84no—
1854C22—168no—
1855C22—3164no—
1856C22—792no—
1857C22—6324no—
1858C22—6328no—
1859C22—1584no—
1860C22—1584no—
1861C22—1581no—
1862C22—1584no—
1863C22—1584no—
1864C22—1581no—
1865C22—1581no—
1866C22—1584no—
1867C22—1584no—
1868C22—1581no—
1869C22—1581no—
1870C22—12648no—
1871C22C2×#1457920612yes—
1872C22C25×D7911yescharacteristic
1873C4—21no—
1874C4—24no—
1875C4—24no—
1876C4—24no—
1877C4—21no—
1878C4—21no—
1879C4—792no—
1880C4—792no—
1881C4—1584no—
1882C4—1584no—
1883C4—1581no—
1884C4—1581no—
1885C4—1584no—
1886C4—1581no—
1887C4—1581no—
1888C4—1584no—
1889C4H(5,𝔽2)×D7912yes—
1890C4C2×#1457920612yes—
1891C4C2×#1457920612yes—
1892C2—22no—
1893C2—44no—
1894C2—44no—
1895C2—44no—
1896C2—3161no—
1897C2—3164no—
1898C2—3164no—
1899C2—1582no—
1900C2C2×H(5,𝔽2)×D7911yescharacteristic
1901C2C22×#1457920611yescharacteristic
1902C2#585×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3496C2
hypercenter#3496D79
hypocenterC79#62834
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #23777912C2semidirect
2. #23777909C2semidirect
3. #23777802C2semidirect
4. #23777797C2semidirect
5. #23777773C2semidirect
6. #23777768C2semidirect
7. #23777764C2semidirect
8. #23777637C2semidirect
9. #23777429C2semidirect
10. #23777426C2semidirect
11. #23777310C2semidirect
12. #23777309C2semidirect
13. #23777268C2semidirect
14. #23777252C2semidirect
15. #23777250C2semidirect
16. #23777249C2semidirect
17. #23777174C2semidirect
18. #23777172C2semidirect
19. #23777162C2semidirect
20. #23777156C2semidirect
21. #23777065C2semidirect
22. #23777064C2semidirect
23. #23777062C2semidirect
24. #23776695C2semidirect
25. C2×#19099110C2semidirect
26. #532×D79C2semidirect
27. C79×#3496C2semidirect
28. C2×#14579207C22semidirect
29. C2×#14579206C22semidirect
30. C22×#11929624C22semidirect
31. C2×#41×D79C22semidirect
32. #19099310C22semidirect
33. #19099306C22semidirect
34. #19099303C22semidirect
35. #19099302C22semidirect
36. #19099297C22semidirect
37. #19099296C22semidirect
38. #19099295C22semidirect
39. #19099287C22semidirect
40. #19099284C22semidirect
41. #19099283C22semidirect
42. #19099278C22semidirect
43. #19099278C22semidirect
44. #19099277C22semidirect
45. #19099277C22semidirect
46. #19099271C22semidirect
47. #19099268C22semidirect
48. #19099263C22semidirect
49. #19099261C22semidirect
50. #19099260C22semidirect
51. #19099259C22semidirect
52. #19099258C22semidirect
53. #19099256C22semidirect
54. #19099234C22semidirect
55. #19099233C22semidirect
56. #19099232C22semidirect
57. #19099232C22semidirect
58. #19099232C22semidirect
59. #19099231C22semidirect
60. #19099231C22semidirect
61. #19099231C22semidirect
62. #19099223C22semidirect
63. #19099220C22semidirect
64. #19099219C22semidirect
65. #19099218C22semidirect
66. #19099218C22semidirect
67. #19099217C22semidirect
68. #19099216C22semidirect
69. #19099213C22semidirect
70. #19099210C22semidirect
71. #19099210C22semidirect
72. #19099209C22semidirect
73. #19099207C22semidirect
74. #19099207C22semidirect
75. #19099207C22semidirect
76. #19099206C22semidirect
77. #19099204C22semidirect
78. #19099203C22semidirect
79. #19099203C22semidirect
80. #19099202C22semidirect
81. #19099200C22semidirect
82. D4×D316C22semidirect
83. #19099198C22semidirect
84. #19099197C22semidirect
85. #19099197C22semidirect
86. D4×C22⋊D79C22semidirect
87. D4×C22⋊D79C22semidirect
88. D4×C22⋊D79C22semidirect
89. D4×C22⋊D79C22semidirect
90. D4×C22⋊D79C22semidirect
91. D4×C22⋊D79C22semidirect
92. D4×C22⋊D79C22semidirect
93. #19099195C22semidirect
94. #19099186C22semidirect
95. #19099181C22semidirect
96. #19099180C22semidirect
97. #19099165C22semidirect
98. #19099163C22semidirect
99. #19099151C22semidirect
100. #19099151C22semidirect
101. #19099150C22semidirect
102. #19099149C22semidirect
103. #19099149C22semidirect
104. #19099148C22semidirect
105. #19099145C22semidirect
106. #19099144C22semidirect
107. #19099143C22semidirect
108. #19099142C22semidirect
109. #19099142C22semidirect
110. #19099141C22semidirect
111. #19099141C22semidirect
112. #19099130C22semidirect
113. #19099130C22semidirect
114. #19099130C22semidirect
115. #19099130C22semidirect
116. #19099129C22semidirect
117. #19099129C22semidirect
118. #19099129C22semidirect
119. #19099128C22semidirect
120. #19099128C22semidirect
121. #19099127C22semidirect
122. #19099127C22semidirect
123. #19099123C22semidirect
124. #19099121C22semidirect
125. #19099120C22semidirect
126. #19099118C22semidirect
127. #19099118C22semidirect
128. #19099115C22semidirect
129. #19099114C22semidirect
130. #19099113C22semidirect
131. #19099112C22semidirect
132. #19099111C22semidirect
133. #19099111C22semidirect
134. #19099111C22semidirect
135. #19099110C22semidirect
136. #19099110C22semidirect
137. #19099110C22semidirect
138. #19099110C22semidirect
139. #19099110C22semidirect
140. #19099110C22semidirect
141. #19099110C22semidirect
142. #19099110C22semidirect
143. #19099110C22semidirect
144. #19099110C22semidirect
145. #19099109C22semidirect
146. #19099109C22semidirect
147. #19099108C22semidirect
148. #19099108C22semidirect
149. #19099108C22semidirect
150. C2×#14579160C22semidirect
151. C4⋊Q8×D79C22semidirect
152. C2×#14579157C22semidirect
153. C2×#14579157C22semidirect
154. #127×D79C22semidirect
155. #19099095C22semidirect
156. #19099095C22semidirect
157. #19099094C22semidirect
158. #19099094C22semidirect
159. #19099092C22semidirect
160. #19099092C22semidirect
161. C2×#14579147C22semidirect
162. #124×D79C22semidirect
163. #19099076C22semidirect
164. #19099074C22semidirect
165. #19099073C22semidirect
166. #19099073C22semidirect
167. #19099073C22semidirect
168. #19099070C22semidirect
169. #19099070C22semidirect
170. C2×#14579136C22semidirect
171. C2×#14579134C22semidirect
172. C2×#14579132C22semidirect
173. C2×#14579132C22semidirect
174. #121×D79C22semidirect
175. #121×D79C22semidirect
176. #121×D79C22semidirect
177. #121×D79C22semidirect
178. #19099046C22semidirect
179. #19099044C22semidirect
180. #19099044C22semidirect
181. #19099036C22semidirect
182. #41×Dic79C22semidirect
183. C4×#11929623C22semidirect
184. C4×#11929623C22semidirect
185. C2×C4×D316C22semidirect
186. C2×C4×C22⋊D79C22semidirect
187. C4×D4×D79C22semidirect
188. C4×D4×D79C22semidirect
189. C2×C42×D79C22semidirect
190. C2×H(5,𝔽2)×C79C22semidirect
191. #547×C79C22semidirect
192. #547×C79C22semidirect
193. #546×C79C22semidirect
194. #546×C79C22semidirect
195. D42×C79C22semidirect
196. D42×C79C22semidirect
197. #537×C79C22semidirect
198. #534×C79C22semidirect
199. #532×C79C22semidirect
200. #532×C79C22semidirect
201. C2×#121×C79C22semidirect
202. C2×C4×D4×C79C22semidirect
809. C2×C4×C79H(5,𝔽2)semidirect
883. C4×D79H(5,𝔽2)semidirect
972. #3496D79semidirect
979. C79#62834semidirect
982. C2×H(5,𝔽2)C2×D79semidirect
1023. #547C2×D79semidirect
1024. #547C2×D79semidirect
1037. #546C2×D79semidirect
1038. #546C2×D79semidirect
1051. D42C2×D79semidirect
1052. D42C2×D79semidirect
1071. #537C2×D79semidirect
1085. #534C2×D79semidirect
1111. #532C2×D79semidirect
1112. #532C2×D79semidirect
1141. C2×#121C2×D79semidirect
1153. C2×C4×D4C2×D79semidirect
1832. C2×C4#14579206semidirect

Maximal subgroups

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

subgroupindex
#237779122
#237779092
#237778022
#237777972
#237777732
#237777682
#237777642
#237776372
#237774292
#237774262
#237773102
#237773092
#237772682
#237772522
#237772502
#237772492
#237771742
#237771722
#237771622
#237771562
#237770652
#237770642
#237770622
#237766952
C2×#190991102
#532×D792
C79×#34962
#6283479