Finite Group Databasebeta

← #35197194

Subgroups — #35197194

Order 20224.

7148 conjugacy classes of subgroups.

The subgroup lattice has 1796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777969C214yesmaximal, complemented
2#23777936C214yesmaximal, complemented
3#23777874C212yesmaximal, complemented
4#23777859C212yesmaximal, complemented
5#23777813C212yesmaximal, complemented
6#23777799C212yesmaximal, complemented
7#23777788C214yesmaximal, complemented
8#23777624C214yesmaximal, complemented
9#23777483C214yesmaximal, complemented
10#23777446C214yesmaximal, complemented
11#23777304C214yesmaximal, complemented
12#23777303C212yesmaximal, complemented
13#23777273C212yesmaximal, complemented
14#23777267C211yesmaximal, characteristic, complemented
15#23777253C212yesmaximal, complemented
16#23777217C212yesmaximal, complemented
17#23777197C212yesmaximal, complemented
18#23777182C212yesmaximal, complemented
19#23777171C211yesmaximal, characteristic, complemented
20#23777166C211yesmaximal, characteristic, complemented
21#23777123C214yesmaximal, complemented
22#23777081C212yesmaximal, complemented
23#23777078C212yesmaximal, complemented
24#23776697C211yesmaximal, characteristic, complemented
25C2×#19099117C211yesmaximal, characteristic, complemented
26#532×D79C211yesmaximal, characteristic, complemented
27C79×#3507C211yesmaximal, characteristic, complemented
28C2×#14579209C2212yescomplemented
29C2×#14579208C2212yescomplemented
30C2×#41×D79C2212yes—
31#19099315C2218yescomplemented
32#19099311C2218yescomplemented
33#19099310C2218yescomplemented
34#19099309C2218yescomplemented
35#19099298C2214yescomplemented
36#19099298C2212yescomplemented
37#19099295C2214yescomplemented
38#19099295C2214yescomplemented
39Q8×Dic158C2214yescomplemented
40#19099292C2212yescomplemented
41#19099287C2212yescomplemented
42#19099286C2214yescomplemented
43#19099281C2214yescomplemented
44#19099276C2214yescomplemented
45#19099276C2218yescomplemented
46#19099274C2212yescomplemented
47#19099271C2218yescomplemented
48#19099270C2214yescomplemented
49#19099269C2218yes—
50#19099269C2214yescomplemented
51#19099269C2214yescomplemented
52#19099268C2214yescomplemented
53#19099264C2218yescomplemented
54#19099264C2218yescomplemented
55#19099262C2218yescomplemented
56#19099251C2214yescomplemented
57#19099238C2218yes—
58#19099237C2218yes—
59#19099235C2212yescomplemented
60#19099235C2212yescomplemented
61#19099234C2212yescomplemented
62#19099234C2214yescomplemented
63#19099233C2212yescomplemented
64Q8×D316C2214yes—
65Q8×D316C2212yescomplemented
66Q8×D316C2212yescomplemented
67D4×Dic158C2212yescomplemented
68#19099228C2214yes—
69#19099228C2212yescomplemented
70#19099226C2214yescomplemented
71#19099226C2214yescomplemented
72#19099225C2214yescomplemented
73#19099225C2214yescomplemented
74#19099225C2214yescomplemented
75#19099222C2218yescomplemented
76#19099222C2214yescomplemented
77#19099221C2214yescomplemented
78#19099221C2214yescomplemented
79#19099217C2214yescomplemented
80#19099217C2218yescomplemented
81#19099216C2214yescomplemented
82#19099215C2214yescomplemented
83#19099215C2214yescomplemented
84#19099214C2214yescomplemented
85#19099211C2218yescomplemented
86#19099211C2218yescomplemented
87#19099211C2218yescomplemented
88#19099208C2218yes—
89#19099208C2214yes—
90#19099206C2214yes—
91#19099205C2218yes—
92#19099205C2218yes—
93#19099193C2214yes—
94#19099193C2218yescomplemented
95#19099188C2218yes—
96#19099185C2214yescomplemented
97#19099185C2214yescomplemented
98#19099184C2218yescomplemented
99#19099182C2214yescomplemented
100#19099179C2218yescomplemented
101#19099179C2218yescomplemented
102#19099179C2218yescomplemented
103#19099178C2214yescomplemented
104#19099169C2214yescomplemented
105#19099165C2218yescomplemented
106#19099164C2214yescomplemented
107#19099162C2214yescomplemented
108#19099161C2218yescomplemented
109#19099157C2218yescomplemented
110#19099152C2218yes—
111#19099144C2214yescomplemented
112#19099144C2212yescomplemented
113#19099144C2214yescomplemented
114#19099143C2218yescomplemented
115#19099143C2214yescomplemented
116#19099141C2212yescomplemented
117#19099140C2214yescomplemented
118#19099139C2214yescomplemented
119#19099139C2212yescomplemented
120#19099138C2214yescomplemented
121#19099136C2214yescomplemented
122#19099133C2214yescomplemented
123#19099131C2214yes—
124#19099118C2211yescharacteristic
125#19099118C2211yescharacteristic, complemented
126#19099117C2212yes—
127#19099117C2212yes—
128#19099117C2212yes—
129#19099117C2212yes—
130#19099117C2212yescomplemented
131#19099117C2214yescomplemented
132#19099117C2212yescomplemented
133#19099117C2212yescomplemented
134#19099117C2212yescomplemented
135#19099114C2211yescharacteristic
136#19099114C2211yescharacteristic
137#19099114C2211yescharacteristic, complemented
138#19099113C2211yescharacteristic
139#19099113C2214yescomplemented
140#19099113C2211yescharacteristic, complemented
141#19099112C2212yes—
142#19099112C2214yescomplemented
143#19099111C2211yescharacteristic
144#19099110C2212yes—
145#19099110C2212yes—
146#19099110C2214yescomplemented
147#19099109C2212yes—
148#19099108C2212yes—
149#19099108C2212yes—
150#19099108C2214yescomplemented
151C2×#14579160C2211yescharacteristic, complemented
152C2×#14579159C2211yescharacteristic, complemented
153C4⋊Q8×D79C2211yescharacteristic
154C4⋊Q8×D79C2214yescomplemented
155#127×D79C2211yescharacteristic
156#19099100C2212yes—
157#19099100C2212yescomplemented
158#19099099C2214yescomplemented
159#19099099C2212yescomplemented
160#19099099C2212yescomplemented
161#19099098C2212yes—
162#19099098C2212yescomplemented
163C2×#14579151C2212yescomplemented
164#124×D79C2212yes—
165#19099076C2214yes—
166#19099076C2212yes—
167#19099076C2212yes—
168#19099075C2212yes—
169#19099075C2214yes—
170C2×#14579141C2211yescharacteristic
171C2×#14579141C2214yes—
172C2×#14579139C2212yes—
173C2×#14579137C2211yescharacteristic
174C22⋊Q8×D79C2214yes—
175#121×D79C2212yes—
176#121×D79C2212yes—
177#19099045C2214yes—
178#19099043C2212yescomplemented
179#19099043C2218yescomplemented
180#19099035C2214yes—
181C4×#11929625C2212yes—
182C4×#11929625C2212yescomplemented
183#19099031C2212yescomplemented
184C2×C4×Dic158C2211yescharacteristic, complemented
185C2×C4×Dic158C2212yescomplemented
186C4×D4×D79C2212yes—
187C4×D4×D79C2212yes—
188C2×#14579118C2212yes—
189C2×C42×D79C2211yescharacteristic
190#559×C79C2212yescomplemented
191#557×C79C2212yescomplemented
192#556×C79C2212yescomplemented
193#556×C79C2214yescomplemented
194#554×C79C2212yescomplemented
195#552×C79C2214yescomplemented
196#539×C79C2214yescomplemented
197#536×C79C2212yescomplemented
198#533×C79C2211yescharacteristic, complemented
199#532×C79C2211yescharacteristic
200#529×C79C2214yescomplemented
201#520×C79C2212yescomplemented
202C2×C4×Q8×C79C2211yescharacteristic, complemented
203#14579209—48no—
204#14579208—48no—
205C2×#11929625C2312yes—
206C2×#11929625C2314yes—
207C2×#11929625C2314yes—
208C2×#11929625C2312yes—
209C2×#11929625C2312yes—
210C2×#11929624C2312yes—
211C2×#11929624C2312yes—
212C2×#11929624C2314yes—
213C2×#11929624C2314yes—
214C2×#11929624C2318yes—
215C2×#11929624C2318yes—
216C2×#11929623C2318yes—
217C2×#11929623C2314yes—
218C2×#11929623C2314yes—
219C2×#11929623C2312yes—
220#41×D79—48no—
221C22×Dic158C2311yescharacteristic
222C22×Dic158C2314yes—
223C22×Dic158C2312yes—
224C2×Q8×D79C2314yes—
225C2×Q8×D79C2314yes—
226C2×Q8×D79C2314yes—
227C2×Q8×D79C2312yes—
228C2×D4×D79C2312yes—
229C2×D4×D79C2312yes—
230C2×D4×D79C2314yes—
231C2×D4×D79C2312yes—
232C22×C4×D79C2311yescharacteristic
233C22×C4×D79C2311yescharacteristic
234C22×C4×D79C2311yescharacteristic
235C22×C4×D79C2314yes—
236#14579161C2318yes—
237#14579161C2314yes—
238#14579161C2314yes—
239#14579161C2311yescharacteristic
240#14579161C2311yescharacteristic
241#14579160C2318yes—
242#14579160C2312yes—
243#14579160C2318yes—
244#14579160C2314yes—
245#14579160C2318yes—
246#14579160C2312yes—
247#14579160C2312yes—
248#14579160C2312yes—
249#14579160C2312yes—
250#14579160C2312yes—
251#14579159C2312yes—
252#14579159C2312yes—
253#14579159C2312yes—
254#14579159C2312yes—
255#14579159C2312yes—
256#14579158C2314yes—
257#14579158C2311yescharacteristic
258#14579158C2311yescharacteristic
259#14579157C2314yes—
260#14579157C2312yes—
261#14579157C2312yes—
262#14579157C2312yes—
263#14579156C2318yes—
264#14579156C2314yes—
265#14579156C2314yes—
266#14579156C2318yes—
267#14579155C2318yes—
268#14579154C2318yes—
269#14579152C2318yes—
270#14579152C2314yes—
271#14579152C2312yes—
272#14579152C2312yes—
273#14579151C2314yes—
274#14579151C2314yes—
275#14579151C2318yes—
276#14579151C2314yes—
277#14579151C2314yes—
278#14579150C2312yes—
279#14579150C2314yes—
280#14579150C2312yes—
281#14579150C2312yes—
282#14579149C2314yes—
283#14579149C2318yes—
284#14579149C2318yes—
285#14579149C2318yes—
286#14579149C2312yes—
287#14579149C2312yes—
288#14579148C2312yes—
289#14579147C2318yes—
290#14579147C2318yes—
291#14579147C2314yes—
292#14579147C2318yes—
293#14579147C2318yes—
294#14579147C2314yes—
295#14579146C2318yes—
296#14579146C2318yes—
297#14579146C2318yes—
298#14579146C2318yes—
299#14579146C2318yes—
300#14579146C2318yes—
301#14579146C2314yes—
302#14579146C2314yes—
303#14579145C2318yes—
304#14579145C2318yes—
305#14579145C2318yes—
306#14579145C2318yes—
307#14579145C2314yes—
308#14579144C2318yes—
309#14579143C2318yes—
310#14579143C2318yes—
311#14579143C2318yes—
312#14579141C2312yes—
313#14579141C2312yes—
314#14579141C2314yes—
315#14579141C2314yes—
316#14579141C2314yes—
317#14579141C2318yes—
318#14579141C2314yes—
319#14579141C2318yes—
320#14579141C2318yes—
321#14579141C2318yes—
322#14579141C2318yes—
323#14579141C2312yes—
324#14579141C2312yes—
325#14579141C2312yes—
326#14579141C2312yes—
327#14579140C2314yes—
328#14579140C2318yes—
329#14579139C2318yes—
330#14579139C2318yes—
331#14579139C2318yes—
332#14579139C2314yes—
333#14579139C2318yes—
334#14579139C2318yes—
335#14579139C2314yes—
336#14579139C2318yes—
337#14579139C2318yes—
338#14579139C2314yes—
339#14579139C2314yes—
340#14579138C2318yes—
341#14579138C2318yes—
342#14579138C2318yes—
343#14579138C2318yes—
344#14579137C2312yes—
345#14579137C2314yes—
346#14579137C2318yes—
347#14579137C2312yes—
348#14579137C2312yes—
349#14579137C2312yes—
350#14579137C2312yes—
351#14579137C2312yes—
352#14579136C2312yes—
353#14579136C2318yes—
354#14579136C2318yes—
355#14579136C2318yes—
356#14579136C2314yes—
357#14579136C2318yes—
358#14579136C2314yes—
359#14579136C2312yes—
360#14579136C2312yes—
361#14579136C2312yes—
362#14579136C2312yes—
363#14579136C2312yes—
364#14579135C2312yes—
365#14579135C2314yes—
366#14579135C2318yes—
367#14579135C2312yes—
368#14579135C2318yes—
369#14579135C2318yes—
370#14579135C2312yes—
371#14579135C2312yes—
372#14579134C2318yes—
373#14579134C2318yes—
374#14579134C2314yes—
375#14579134C2318yes—
376#14579134C2318yes—
377#14579134C2318yes—
378#14579134C2318yes—
379#14579134C2314yes—
380#14579133C2318yes—
381#14579133C2318yes—
382#14579133C2314yes—
383#14579133C2314yes—
384#14579132C2314yes—
385#14579132C2312yes—
386#14579132C2312yes—
387#14579131C2318yes—
388#14579131C2318yes—
389#14579131C2314yes—
390Q8×Dic79C2314yes—
391Q8×Dic79C2312yes—
392Q8×Dic79C2312yes—
393C4×Dic158C2314yes—
394C4×Dic158C2314yes—
395C4×Dic158C2314yes—
396C4×Dic158C2318yes—
397C4×Dic158C2312yes—
398C4×Dic158C2312yes—
399C4×Dic158C2312yes—
400C4×Dic158C2312yes—
401C4×Dic158C2314yes—
402C4×Dic158C2314yes—
403#14579126C2312yes—
404#14579126C2312yes—
405C4×D316C2318yes—
406C4×D316C2318yes—
407C4×D316C2314yes—
408C4×D316C2318yes—
409C4×D316C2314yes—
410C4×D316C2314yes—
411C4×D316C2314yes—
412C4×D316C2314yes—
413C4×D316C2312yes—
414C4×D316C2312yes—
415C4×D316C2312yes—
416C4×D316C2312yes—
417D4×Dic79C2312yes—
418D4×Dic79C2314yes—
419D4×Dic79C2312yes—
420#14579123C2318yes—
421#14579123C2312yes—
422#14579123C2314yes—
423#14579123C2314yes—
424#14579123C2314yes—
425#14579123C2312yes—
426#14579123C2312yes—
427#14579123C2312yes—
428#14579123C2312yes—
429#14579123C2314yes—
430#14579123C2312yes—
431C4×C22⋊D79C2318yes—
432C4×C22⋊D79C2314yes—
433C4×C22⋊D79C2314yes—
434(C22⋊D79)⋊C4C2318yes—
435(C22⋊D79)⋊C4C2318yes—
436(C22⋊D79)⋊C4C2318yes—
437(C22⋊D79)⋊C4C2314yes—
438(C22⋊D79)⋊C4C2318yes—
439(C22⋊D79)⋊C4C2318yes—
440(C22⋊D79)⋊C4C2314yes—
441(C22⋊D79)⋊C4C2314yes—
442(C22⋊D79)⋊C4C2314yes—
443#14579119C2314yes—
444#14579119C2314yes—
445#14579119C2312yes—
446#14579119C2314yes—
447#14579119C2318yes—
448#14579119C2312yes—
449#14579118C2314yes—
450#14579118C2314yes—
451#14579118C2314yes—
452#14579118C2318yes—
453#14579118C2314yes—
454#14579118C2314yes—
455C2×C4⋊Dic79C2311yescharacteristic
456C2×C4⋊Dic79C2318yes—
457C2×C4⋊Dic79C2312yes—
458C2×Dic79⋊C4C2312yes—
459C2×Dic79⋊C4C2312yes—
460C2×Dic79⋊C4C2312yes—
461C2×Dic79⋊C4C2312yes—
462C2×Dic79⋊C4C2312yes—
463C4⋊C4×D79C2318yes—
464C4⋊C4×D79C2314yes—
465C4⋊C4×D79C2318yes—
466C4⋊C4×D79C2312yes—
467C4⋊C4×D79C2318yes—
468C4⋊C4×D79C2312yes—
469C2×(C2×D79)⋊C4C2318yes—
470C2×(C2×D79)⋊C4C2312yes—
471C2×(C2×D79)⋊C4C2312yes—
472C22⋊C4×D79C2314yes—
473C22⋊C4×D79C2318yes—
474C22⋊C4×D79C2314yes—
475C2×C4×Dic79C2311yescharacteristic
476C2×C4×Dic79C2311yescharacteristic
477C2×C4×Dic79C2311yescharacteristic
478C2×C4×Dic79C2312yes—
479C42×D79C2311yescharacteristic
480C42×D79C2311yescharacteristic
481C42×D79C2311yescharacteristic
482C42×D79C2311yescharacteristic
483C42×D79C2311yescharacteristic
484C42×D79C2311yescharacteristic
485C42×D79C2311yescharacteristic
486C42×D79C2311yescharacteristic
487C42×D79C2314yes—
488C2×#41×C79C2312yes—
489C22×Q8×C79C2311yescharacteristic
490C4⋊Q8×C79C2314yes—
491C4⋊Q8×C79C2311yescharacteristic
492C4⋊Q8×C79C2311yescharacteristic
493C4⋊Q8×C79C2311yescharacteristic
494#127×C79C2311yescharacteristic
495#126×C79C2318yes—
496#126×C79C2318yes—
497#125×C79C2318yes—
498#125×C79C2314yes—
499#125×C79C2312yes—
500#124×C79C2314yes—
501#124×C79C2314yes—
502#124×C79C2312yes—
503#123×C79C2318yes—
504#123×C79C2318yes—
505C22⋊Q8×C79C2314yes—
506C22⋊Q8×C79C2318yes—
507C22⋊Q8×C79C2314yes—
508C22⋊Q8×C79C2312yes—
509C22⋊Q8×C79C2312yes—
510#121×C79C2312yes—
511#121×C79C2312yes—
512C4×Q8×C79C2314yes—
513C4×Q8×C79C2314yes—
514C4×Q8×C79C2312yes—
515C4×Q8×C79C2312yes—
516C4×Q8×C79C2312yes—
517C4×Q8×C79C2312yes—
518C4×Q8×C79C2312yes—
519C4×Q8×C79C2312yes—
520C4×D4×C79C2314yes—
521C4×D4×C79C2314yes—
522C4×D4×C79C2318yes—
523C4×D4×C79C2312yes—
524C4×D4×C79C2312yes—
525#117×C79C2312yes—
526#117×C79C2314yes—
527#117×C79C2318yes—
528C2×C4⋊C4×C79C2311yescharacteristic
529C2×C4⋊C4×C79C2312yes—
530C2×C4⋊C4×C79C2314yes—
531C2×C42×C79C2312yes—
532C2×C42×C79C2311yescharacteristic
533C23×D79C2411yescharacteristic
534C23×D79C2414yes—
535#11929625—28no—
536#11929625—44no—
537#11929625—48no—
538#11929625—48no—
539#11929625—44no—
540#11929624—28no—
541#11929624—28no—
542#11929624—416no—
543#11929624—416no—
544#11929624—48no—
545#11929624—48no—
546#11929623—48no—
547#11929623—416no—
548#11929623—44no—
549#11929623—48no—
550C2×Dic158—24no—
551C2×Dic158—48no—
552C2×Dic158—44no—
553C2×Dic158C2412yes—
554C2×Dic158C2412yes—
555C2×Dic158C2412yes—
556C2×Dic158C2412yes—
557C2×Dic158C2414yes—
558C2×Dic158C2418yes—
559C2×Dic158C2418yes—
560C2×Dic158C2414yes—
561C2×Dic158C2414yes—
562Q8×D79—44no—
563Q8×D79—48no—
564Q8×D79—48no—
565Q8×D79—48no—
566C2×D316C2412yes—
567C2×D316C2412yes—
568C2×D316C2414yes—
569C2×D316C2412yes—
570C2×D316C2412yes—
571C2×D316C2418yes—
572C2×D316C2414yes—
573C2×D316C2418yes—
574C2×D316C2414yes—
575C2×D316C2412yes—
576C2×D316C2412yes—
577C2×C22⋊D79C2414yes—
578C2×C22⋊D79C2414yes—
579C2×C22⋊D79C2414yes—
580C2×C22⋊D79C2414yes—
581C2×C22⋊D79C2418yes—
582C2×C22⋊D79C2414yes—
583C2×C22⋊D79C2414yes—
584C2×C22⋊D79C2418yes—
585D4×D79—28no—
586D4×D79—44no—
587D4×D79—48no—
588D4×D79—44no—
589C22×Dic79C2411yescharacteristic
590C22×Dic79C2412yes—
591C22×Dic79C2411yescharacteristic
592C22×Dic79C2411yescharacteristic
593C22×Dic79C2418yes—
594C22×Dic79C2412yes—
595C22×Dic79C2414yes—
596C2×C4×D79—24no—
597C2×C4×D79—24no—
598C2×C4×D79—48no—
599C2×C4×D79—42no—
600C2×C4×D79C2414yes—
601C2×C4×D79C2411yescharacteristic
602C2×C4×D79C2414yes—
603C2×C4×D79C2411yescharacteristic
604C2×C4×D79C2411yescharacteristic
605C2×C4×D79C2414yes—
606C2×C4×D79C2411yescharacteristic
607C2×C4×D79C2414yes—
608C2×C4×D79C2411yescharacteristic
609C2×C4×D79C2411yescharacteristic
610C2×C4×D79C2411yescharacteristic
611C2×C4×D79C2411yescharacteristic
612C2×C4×D79C2411yescharacteristic
613C2×C4×D79C2418yes—
614C2×C4×D79C2418yes—
615C2×C4×D79C2418yes—
616C2×C4×D79C2414yes—
617C2×C4×D79C2414yes—
618C2×C4×D79C2418yes—
619C2×C4×D79C2411yescharacteristic
620C2×C4×D79C2411yescharacteristic
621C2×C4×D79C2411yescharacteristic
622C4⋊Dic79C2414yes—
623C4⋊Dic79C2412yes—
624C4⋊Dic79C2418yes—
625C4⋊Dic79C2412yes—
626C4⋊Dic79C2412yes—
627C4⋊Dic79C2418yes—
628C4⋊Dic79C2414yes—
629C4⋊Dic79C2412yes—
630C4⋊Dic79C2418yes—
631C4⋊Dic79C2414yes—
632C4⋊Dic79C2412yes—
633C4⋊Dic79C2412yes—
634C4⋊Dic79C2414yes—
635Dic79⋊C4C2414yes—
636Dic79⋊C4C2414yes—
637Dic79⋊C4C2414yes—
638Dic79⋊C4C2414yes—
639Dic79⋊C4C2414yes—
640Dic79⋊C4C2418yes—
641Dic79⋊C4C2418yes—
642Dic79⋊C4C2414yes—
643Dic79⋊C4C2414yes—
644Dic79⋊C4C2414yes—
645Dic79⋊C4C2414yes—
646Dic79⋊C4C2414yes—
647Dic79⋊C4C2414yes—
648Dic79⋊C4C2414yes—
649Dic79⋊C4C2414yes—
650Dic79⋊C4C2414yes—
651C22⋊Dic79C2418yes—
652C22⋊Dic79C2414yes—
653C22⋊Dic79C2414yes—
654(C2×D79)⋊C4C2414yes—
655(C2×D79)⋊C4C2414yes—
656(C2×D79)⋊C4C2414yes—
657(C2×D79)⋊C4C2414yes—
658(C2×D79)⋊C4C2414yes—
659(C2×D79)⋊C4C2414yes—
660(C2×D79)⋊C4C2414yes—
661(C2×D79)⋊C4C2414yes—
662(C2×D79)⋊C4C2414yes—
663(C2×D79)⋊C4C2418yes—
664(C2×D79)⋊C4C2418yes—
665(C2×D79)⋊C4C2414yes—
666(C2×D79)⋊C4C2414yes—
667(C2×D79)⋊C4C2418yes—
668(C2×D79)⋊C4C2418yes—
669(C2×D79)⋊C4C2414yes—
670(C2×D79)⋊C4C2414yes—
671(C2×D79)⋊C4C2418yes—
672(C2×D79)⋊C4C2418yes—
673(C2×D79)⋊C4C2414yes—
674(C2×D79)⋊C4C2414yes—
675(C2×D79)⋊C4C2414yes—
676C4×Dic79C2411yescharacteristic
677C4×Dic79C2411yescharacteristic
678C4×Dic79C2411yescharacteristic
679C4×Dic79C2411yescharacteristic
680C4×Dic79C2411yescharacteristic
681C4×Dic79C2411yescharacteristic
682C4×Dic79C2411yescharacteristic
683C4×Dic79C2411yescharacteristic
684C4×Dic79C2411yescharacteristic
685C4×Dic79C2411yescharacteristic
686C4×Dic79C2411yescharacteristic
687C4×Dic79C2411yescharacteristic
688C4×Dic79C2414yes—
689C4×Dic79C2414yes—
690C4×Dic79C2414yes—
691C4×Dic79C2414yes—
692C4×Dic79C2418yes—
693#41×C79—28no—
694C2×Q8×C79—24no—
695C2×Q8×C79C2412yes—
696C2×Q8×C79C2412yes—
697C2×Q8×C79C2412yes—
698C2×Q8×C79C2412yes—
699C2×Q8×C79C2412yes—
700C2×D4×C79C2414yes—
701C2×D4×C79C2412yes—
702C2×D4×C79C2412yes—
703C2×D4×C79C2412yes—
704C22×C4×C79C2414yes—
705C22×C4×C79C2412yes—
706C22×C4×C79C2411yescharacteristic
707C22×C4×C79C2412yes—
708C22×C4×C79C2418yes—
709C22×C4×C79C2411yescharacteristic
710C22×C4×C79C2411yescharacteristic
711C4⋊C4×C79C2412yes—
712C4⋊C4×C79C2412yes—
713C4⋊C4×C79C2412yes—
714C4⋊C4×C79C2418yes—
715C4⋊C4×C79C2414yes—
716C4⋊C4×C79C2414yes—
717C4⋊C4×C79C2412yes—
718C4⋊C4×C79C2414yes—
719C4⋊C4×C79C2418yes—
720C4⋊C4×C79C2412yes—
721C4⋊C4×C79C2412yes—
722C4⋊C4×C79C2412yes—
723C4⋊C4×C79C2414yes—
724C4⋊C4×C79C2418yes—
725C4⋊C4×C79C2412yes—
726C22⋊C4×C79C2414yes—
727C22⋊C4×C79C2414yes—
728C22⋊C4×C79C2418yes—
729C22⋊C4×C79C2418yes—
730C22⋊C4×C79C2414yes—
731C22⋊C4×C79C2418yes—
732C42×C79C2414yes—
733C42×C79C2411yescharacteristic
734C42×C79C2411yescharacteristic
735C42×C79C2414yes—
736C42×C79C2411yescharacteristic
737C42×C79C2411yescharacteristic
738C42×C79C2418yes—
739C42×C79C2414yes—
740C23×C79C2514yes—
741C23×C79C2511yescharacteristic
742C22×D79—22no—
743C22×D79—22no—
744C22×D79—28no—
745C22×D79—41no—
746C22×D79—44no—
747C22×D79—44no—
748C22×D79C2514yes—
749C22×D79C2511yescharacteristic
750C22×D79C2514yes—
751C22×D79C2511yescharacteristic
752Q8×C79—24no—
753Q8×C79—24no—
754Q8×C79—24no—
755Q8×C79—24no—
756Q8×C79—42no—
757D4×C79—28no—
758D4×C79—24no—
759D4×C79—24no—
760D4×C79—42no—
761C2×C4×C79—24no—
762C2×C4×C79—28no—
763C2×C4×C79—22no—
764C2×C4×C79—41no—
765C2×C4×C79—42no—
766C2×C4×C79—48no—
767C2×C4×C79H(5,𝔽2)14yes—
768C2×C4×C79C2511yescharacteristic
769C2×C4×C79C2514yes—
770C2×C4×C79C2511yescharacteristic
771C2×C4×C79C2511yescharacteristic
772C2×C4×C79C2514yes—
773C2×C4×C79C2514yes—
774C2×C4×C79C2514yes—
775C2×C4×C79C2514yes—
776C2×C4×C79C2511yescharacteristic
777C2×C4×C79C2511yescharacteristic
778C2×C4×C79C2511yescharacteristic
779C22⋊D79—28no—
780C22⋊D79—28no—
781C22⋊D79—28no—
782C22⋊D79—28no—
783C22⋊D79—44no—
784C22⋊D79—44no—
785C22⋊D79—48no—
786C22⋊D79—48no—
787C2×Dic79—22no—
788C2×Dic79—24no—
789C2×Dic79—22no—
790C2×Dic79—22no—
791C2×Dic79—44no—
792C2×Dic79—42no—
793C2×Dic79—48no—
794C2×Dic79C2511yescharacteristic
795C2×Dic79C2511yescharacteristic
796C2×Dic79C2514yes—
797C2×Dic79C2511yescharacteristic
798C2×Dic79C2511yescharacteristic
799C2×Dic79C2514yes—
800C2×Dic79C2514yes—
801C2×Dic79C2514yes—
802C2×Dic79C2511yescharacteristic
803C2×Dic79C2511yescharacteristic
804D316—28no—
805D316—24no—
806D316—24no—
807D316—24no—
808D316—24no—
809D316—42no—
810D316—44no—
811D316—48no—
812D316—48no—
813D316—44no—
814D316—42no—
815C4×D79—22no—
816C4×D79—22no—
817C4×D79—22no—
818C4×D79—22no—
819C4×D79—22no—
820C4×D79—28no—
821C4×D79—28no—
822C4×D79—22no—
823C4×D79—22no—
824C4×D79—28no—
825C4×D79—22no—
826C4×D79—22no—
827C4×D79—28no—
828C4×D79—41no—
829C4×D79—41no—
830C4×D79—44no—
831C4×D79—44no—
832C4×D79—48no—
833C4×D79—48no—
834C4×D79—48no—
835C4×D79—48no—
836C4×D792−1+414yescomplemented
837Dic158—24no—
838Dic158—24no—
839Dic158—24no—
840Dic158—24no—
841Dic158—28no—
842Dic158—48no—
843Dic158—48no—
844Dic158—44no—
845Dic158—44no—
846C22×C79—21no—
847C22×C79—21no—
848C22×C79—24no—
849C22×C79—24no—
850C22×C79—24no—
851C22×C79C2×H(5,𝔽2)12yes—
852C22×C79C2611yescharacteristic
853C2×D79—21no—
854C2×D79—21no—
855C2×D79—24no—
856C2×D79—24no—
857C2×D79—21no—
858C2×D79—24no—
859C2×D79—21no—
860C2×D79—24no—
861C2×D79—24no—
862C2×D79—24no—
863C2×D79—21no—
864C2×D79—44no—
865C2×D79—88no—
866C2×D79C2×2−1+412yes—
867C4×C79—24no—
868C4×C79—24no—
869C4×C79—21no—
870C4×C79—24no—
871C4×C79—24no—
872C4×C79—24no—
873C4×C79—21no—
874C4×C79—21no—
875C4×C79C2×H(5,𝔽2)12yes—
876C4×C79C2×H(5,𝔽2)12yes—
877C4×C79C2×2−1+412yes—
878Dic79—24no—
879Dic79—24no—
880Dic79—21no—
881Dic79—24no—
882Dic79—21no—
883Dic79—21no—
884Dic79—24no—
885Dic79—21no—
886Dic79C2×2−1+412yes—
887Dic79#58512yes—
888#62835—791nomaximal, Sylow
889C2×C79—22no—
890C2×C79—44no—
891C2×C79C22×H(5,𝔽2)11yescharacteristic
892C2×C79C22×2−1+411yescharacteristic
893C2×C79C2×#58511yescharacteristic
894D79—22no—
895D79—44no—
896D79—41no—
897D79—44no—
898#3561—794no—
899#3559—794no—
900#3554—792no—
901#3554—792no—
902#3550—792no—
903#3548—792no—
904#3547—794no—
905#3536—794no—
906#3522—794no—
907#3520—794no—
908#3511—794no—
909#3511—792no—
910#3508—792no—
911#3507—791no—
912#3507D7911yescharacteristic, complemented
913#3506—792no—
914#3503—792no—
915#3501—792no—
916#3499—792no—
917#3497—791no—
918#3497—791no—
919#3494—794no—
920#3489—792no—
921#3489—792no—
922#3444—791no—
923C2×#533—791no—
924C2×#532—791no—
925C79#6283511yescharacteristic, complemented, Sylow
926C2×2−1+4—792no—
927C2×2−1+4—792no—
928C22×#41—792no—
929#563—798no—
930#562—798no—
931#562—798no—
932#562—798no—
933#559—794no—
934#559—794no—
935#559—794no—
936#559—792no—
937#559C2×D7912yescomplemented
938Q82—794no—
939#557—792no—
940#557C2×D7912yescomplemented
941#556—792no—
942#556—794no—
943#556—794no—
944#556C2×D7912yescomplemented
945#556C2×D7914yescomplemented
946#555—798no—
947#555—794no—
948#554—792no—
949#554—798no—
950#554—794no—
951#554—794no—
952#554—798no—
953#554—794no—
954#554—794no—
955#554C2×D7912yescomplemented
956#553—798no—
957#553—798no—
958#553—798no—
959#552—794no—
960#552C2×D7914yescomplemented
961#551—798no—
962#551—798no—
963#550—792no—
964#550—792no—
965#550—792no—
966#550—792no—
967#550—794no—
968D4×Q8—794no—
969D4×Q8—792no—
970D4×Q8—794no—
971D4×Q8—794no—
972D4×Q8—794no—
973D4×Q8—792no—
974D4×Q8—792no—
975D4×Q8—792no—
976#548—794no—
977#548—794no—
978#548—794no—
979#548—794no—
980#548—794no—
981#548—794no—
982#548—798no—
983#547—794no—
984#547—798no—
985#547—798no—
986#547—798no—
987#547—794no—
988#547—794no—
989#547—794no—
990#547—798no—
991#547—794no—
992#546—794no—
993#546—798no—
994#546—798no—
995#546—798no—
996#546—794no—
997#544—794no—
998#544—798no—
999#543—798no—
1000#542—798no—
1001#542—798no—
1002#542—798no—
1003#542—794no—
1004#542—794no—
1005#542—794no—
1006#542—794no—
1007#542—798no—
1008#540—794no—
1009#540—798no—
1010#540—794no—
1011#539—798no—
1012#539—798no—
1013#539—794no—
1014#539C2×D7914yescomplemented
1015#538—798no—
1016#537—792no—
1017#537—794no—
1018#537—798no—
1019#537—794no—
1020#537—792no—
1021#537—794no—
1022#537—794no—
1023#536—794no—
1024#536—794no—
1025#536—794no—
1026#536—792no—
1027#536—794no—
1028#536C2×D7912yescomplemented
1029#535—794no—
1030#533—791no—
1031#533—791no—
1032#533—792no—
1033#533—792no—
1034#533—792no—
1035#533—792no—
1036#533—792no—
1037#533—792no—
1038#533—792no—
1039#533—792no—
1040#533—794no—
1041#533C2×D7911yescharacteristic, complemented
1042#532—792no—
1043#532—791no—
1044#532—791no—
1045#532—791no—
1046#532—791no—
1047#532—792no—
1048#532—794no—
1049#532—792no—
1050#532—792no—
1051#532—794no—
1052#532—792no—
1053#532—792no—
1054#532—794no—
1055#532—791no—
1056#532—791no—
1057#532—794no—
1058#532C2×D7911yescharacteristic
1059C2×C4⋊Q8—791no—
1060C2×C4⋊Q8—791no—
1061C2×C4⋊Q8—794no—
1062C2×C4⋊Q8—791no—
1063C2×#127—791no—
1064#529—792no—
1065#529—792no—
1066#529—792no—
1067#529—792no—
1068#529—794no—
1069#529—792no—
1070#529—792no—
1071#529C2×D7914yescomplemented
1072C2×#125—792no—
1073C2×#124—792no—
1074#525—792no—
1075#525—792no—
1076#525—794no—
1077#525—792no—
1078#525—794no—
1079C2×C22⋊Q8—791no—
1080C2×C22⋊Q8—794no—
1081C2×C22⋊Q8—791no—
1082C2×C22⋊Q8—792no—
1083C2×C22⋊Q8—794no—
1084C2×#121—792no—
1085C2×#121—792no—
1086#520—794no—
1087#520—792no—
1088#520—798no—
1089#520C2×D7912yescomplemented
1090#518—794no—
1091C4×#41—792no—
1092C4×#41—792no—
1093C4×#41—792no—
1094C2×C4×Q8—791no—
1095C2×C4×Q8—792no—
1096C2×C4×Q8C2×D7911yescharacteristic, complemented
1097C2×C4×D4—792no—
1098C2×C4×D4—792no—
1099C2×#117—792no—
1100C22×C42—791no—
11012−1+4—3168no—
11022−1+4—3168no—
1103C2×#41—3168no—
1104C2×#41—792no—
1105C2×#41—794no—
1106C2×#41—792no—
1107C2×#41—794no—
1108C2×#41—792no—
1109C2×#41—794no—
1110C2×#41—792no—
1111C2×#41—794no—
1112C2×#41—798no—
1113C2×#41—798no—
1114C2×#41—794no—
1115C2×#41—794no—
1116C2×#41—798no—
1117C2×#41—792no—
1118C2×#41—792no—
1119C2×#41C22×D7912yes—
1120C22×Q8—794no—
1121C22×Q8—792no—
1122C22×Q8—794no—
1123C22×Q8—794no—
1124C22×Q8—792no—
1125C22×Q8—794no—
1126C22×Q8—791no—
1127C22×Q8C22×D7911yescharacteristic
1128C22×D4—792no—
1129C22×D4—794no—
1130C22×D4—792no—
1131C22×D4—792no—
1132C23×C4—794no—
1133C23×C4—791no—
1134C23×C4—791no—
1135C23×C4—791no—
1136C4⋊Q8—792no—
1137C4⋊Q8—792no—
1138C4⋊Q8—792no—
1139C4⋊Q8—792no—
1140C4⋊Q8—792no—
1141C4⋊Q8—792no—
1142C4⋊Q8—792no—
1143C4⋊Q8—792no—
1144C4⋊Q8—792no—
1145C4⋊Q8—792no—
1146C4⋊Q8—792no—
1147C4⋊Q8—798no—
1148C4⋊Q8—798no—
1149C4⋊Q8—794no—
1150C4⋊Q8—798no—
1151C4⋊Q8—791no—
1152C4⋊Q8—794no—
1153C4⋊Q8—791no—
1154C4⋊Q8—794no—
1155C4⋊Q8—798no—
1156C4⋊Q8C22×D7911yescharacteristic
1157C4⋊Q8C22×D7914yes—
1158C4⋊Q8C22×D7911yescharacteristic
1159C4⋊Q8C22×D7911yescharacteristic
1160#127—792no—
1161#127—792no—
1162#127—792no—
1163#127—794no—
1164#127—791no—
1165#127—791no—
1166#127—794no—
1167#127C22×D7911yescharacteristic
1168#126—794no—
1169#126—794no—
1170#126—798no—
1171#126—798no—
1172#126—798no—
1173#126—798no—
1174#126C22×D7918yes—
1175#126C22×D7918yes—
1176#125—794no—
1177#125—794no—
1178#125—794no—
1179#125—794no—
1180#125—792no—
1181#125—792no—
1182#125—794no—
1183#125—798no—
1184#125—798no—
1185#125C22×D7912yes—
1186#125C22×D7914yes—
1187#125C22×D7918yes—
1188#124—792no—
1189#124—792no—
1190#124—792no—
1191#124—794no—
1192#124—792no—
1193#124—794no—
1194#124—794no—
1195#124—798no—
1196#124—798no—
1197#124—798no—
1198#124—798no—
1199#124—792no—
1200#124—792no—
1201#124—794no—
1202#124—798no—
1203#124—798no—
1204#124—798no—
1205#124C22×D7912yes—
1206#124C22×D7914yes—
1207#124C22×D7914yes—
1208#123—798no—
1209#123—794no—
1210#123—794no—
1211#123—798no—
1212#123—798no—
1213#123—798no—
1214#123—798no—
1215#123—798no—
1216#123—798no—
1217#123—794no—
1218#123—798no—
1219#123—798no—
1220#123—798no—
1221#123—798no—
1222#123—798no—
1223#123—798no—
1224#123—798no—
1225#123C22×D7918yes—
1226#123C22×D7918yes—
1227C22⋊Q8—792no—
1228C22⋊Q8—792no—
1229C22⋊Q8—792no—
1230C22⋊Q8—792no—
1231C22⋊Q8—792no—
1232C22⋊Q8—792no—
1233C22⋊Q8—794no—
1234C22⋊Q8—798no—
1235C22⋊Q8—794no—
1236C22⋊Q8—798no—
1237C22⋊Q8—792no—
1238C22⋊Q8—792no—
1239C22⋊Q8—792no—
1240C22⋊Q8—794no—
1241C22⋊Q8—794no—
1242C22⋊Q8—792no—
1243C22⋊Q8—794no—
1244C22⋊Q8—792no—
1245C22⋊Q8—794no—
1246C22⋊Q8—794no—
1247C22⋊Q8—794no—
1248C22⋊Q8—798no—
1249C22⋊Q8—798no—
1250C22⋊Q8—798no—
1251C22⋊Q8—792no—
1252C22⋊Q8—794no—
1253C22⋊Q8—794no—
1254C22⋊Q8—798no—
1255C22⋊Q8—798no—
1256C22⋊Q8—798no—
1257C22⋊Q8—798no—
1258C22⋊Q8—798no—
1259C22⋊Q8—798no—
1260C22⋊Q8—798no—
1261C22⋊Q8—798no—
1262C22⋊Q8—798no—
1263C22⋊Q8—798no—
1264C22⋊Q8—798no—
1265C22⋊Q8—798no—
1266C22⋊Q8—798no—
1267C22⋊Q8C22×D7914yes—
1268C22⋊Q8C22×D7912yes—
1269C22⋊Q8C22×D7912yes—
1270C22⋊Q8C22×D7914yes—
1271C22⋊Q8C22×D7918yes—
1272#121—792no—
1273#121—794no—
1274#121—794no—
1275#121—792no—
1276#121—798no—
1277#121—794no—
1278#121—798no—
1279#121—792no—
1280#121—792no—
1281#121—792no—
1282#121—792no—
1283#121—794no—
1284#121—798no—
1285#121—798no—
1286#121—798no—
1287#121—792no—
1288#121—792no—
1289#121—792no—
1290#121—792no—
1291#121—792no—
1292#121—792no—
1293#121—794no—
1294#121—794no—
1295#121—798no—
1296#121—798no—
1297#121—798no—
1298#121—798no—
1299#121—794no—
1300#121—794no—
1301#121—798no—
1302#121—798no—
1303#121—798no—
1304#121—798no—
1305#121—798no—
1306#121—798no—
1307#121C22×D7912yes—
1308#121C22×D7912yes—
1309#120—794no—
1310#120—798no—
1311#120—798no—
1312C4×Q8—792no—
1313C4×Q8—792no—
1314C4×Q8—794no—
1315C4×Q8—792no—
1316C4×Q8—792no—
1317C4×Q8—794no—
1318C4×Q8—794no—
1319C4×Q8—792no—
1320C4×Q8—792no—
1321C4×Q8—792no—
1322C4×Q8—792no—
1323C4×Q8—794no—
1324C4×Q8—794no—
1325C4×Q8—794no—
1326C4×Q8—798no—
1327C4×Q8C22×D7912yes—
1328C4×Q8C22×D7912yes—
1329C4×Q8C22×D7912yes—
1330C4×Q8C22×D7912yes—
1331C4×Q8C22×D7912yes—
1332C4×Q8C22×D7912yes—
1333C4×Q8C22×D7914yes—
1334C4×Q8C22×D7914yes—
1335C4×D4—792no—
1336C4×D4—792no—
1337C4×D4—794no—
1338C4×D4—794no—
1339C4×D4—794no—
1340C4×D4—798no—
1341C4×D4—792no—
1342C4×D4—792no—
1343C4×D4—794no—
1344C4×D4—794no—
1345C4×D4—792no—
1346C4×D4—792no—
1347C4×D4—792no—
1348C4×D4—792no—
1349C4×D4—794no—
1350C4×D4—798no—
1351C4×D4—794no—
1352C4×D4—794no—
1353C4×D4—794no—
1354C4×D4—794no—
1355C4×D4—794no—
1356C4×D4—798no—
1357C4×D4—798no—
1358C4×D4—798no—
1359C4×D4—798no—
1360C4×D4—798no—
1361C4×D4—792no—
1362C4×D4—792no—
1363C4×D4—794no—
1364C4×D4—794no—
1365C4×D4—792no—
1366C4×D4—792no—
1367C4×D4—794no—
1368C4×D4—798no—
1369C4×D4—798no—
1370C4×D4—794no—
1371C4×D4—794no—
1372C4×D4—798no—
1373C4×D4C22×D7912yes—
1374C4×D4C22×D7912yes—
1375C4×D4C22×D7914yes—
1376C4×D4C22×D7918yes—
1377C4×D4C22×D7914yes—
1378#117—792no—
1379#117—794no—
1380#117—792no—
1381#117—794no—
1382#117—794no—
1383#117—798no—
1384#117—794no—
1385#117—794no—
1386#117—794no—
1387#117—794no—
1388#117—794no—
1389#117—798no—
1390#117C22×D7912yes—
1391#117C22×D7918yes—
1392#117C22×D7914yes—
1393C2×C4⋊C4—792no—
1394C2×C4⋊C4—792no—
1395C2×C4⋊C4—791no—
1396C2×C4⋊C4—792no—
1397C2×C4⋊C4—792no—
1398C2×C4⋊C4—792no—
1399C2×C4⋊C4—792no—
1400C2×C4⋊C4—798no—
1401C2×C4⋊C4—792no—
1402C2×C4⋊C4—792no—
1403C2×C4⋊C4—794no—
1404C2×C4⋊C4—798no—
1405C2×C4⋊C4—798no—
1406C2×C4⋊C4—798no—
1407C2×C4⋊C4C22×D7911yescharacteristic
1408C2×C4⋊C4C22×D7912yes—
1409C2×C4⋊C4C22×D7914yes—
1410C2×C22⋊C4—792no—
1411C2×C22⋊C4—792no—
1412C2×C22⋊C4—798no—
1413C2×C22⋊C4—794no—
1414C2×C22⋊C4—794no—
1415C2×C22⋊C4—798no—
1416C2×C42—792no—
1417C2×C42—791no—
1418C2×C42—791no—
1419C2×C42—791no—
1420C2×C42—791no—
1421C2×C42—791no—
1422C2×C42—794no—
1423C2×C42—791no—
1424C2×C42—791no—
1425C2×C42—791no—
1426C2×C42—791no—
1427C2×C42—791no—
1428C2×C42—791no—
1429C2×C42C22×D7912yes—
1430C2×C42C22×D7911yescharacteristic
1431C24—794no—
1432C24—791no—
1433#41—28no—
1434#41—3168no—
1435#41—31616no—
1436#41—3168no—
1437#41—31616no—
1438#41—3164no—
1439#41—3168no—
1440#41—3168no—
1441#41—31616no—
1442#41—3164no—
1443#41—3168no—
1444#41—3168no—
1445#41—3164no—
1446#41—1588no—
1447#41—1588no—
1448#41—1588no—
1449C2×Q8—24no—
1450C2×Q8—3168no—
1451C2×Q8—3164no—
1452C2×Q8—3164no—
1453C2×Q8—3168no—
1454C2×Q8—3168no—
1455C2×Q8—3168no—
1456C2×Q8—794no—
1457C2×Q8—798no—
1458C2×Q8—798no—
1459C2×Q8—794no—
1460C2×Q8—794no—
1461C2×Q8—792no—
1462C2×Q8—792no—
1463C2×Q8—792no—
1464C2×Q8—792no—
1465C2×Q8—1584no—
1466C2×Q8C23×D7912yes—
1467C2×Q8C23×D7912yes—
1468C2×Q8C23×D7912yes—
1469C2×Q8C23×D7912yes—
1470C2×Q8C23×D7912yes—
1471C2×D4—3168no—
1472C2×D4—3164no—
1473C2×D4—3164no—
1474C2×D4—798no—
1475C2×D4—798no—
1476C2×D4—794no—
1477C2×D4—794no—
1478C2×D4—794no—
1479C2×D4—794no—
1480C2×D4—794no—
1481C2×D4—794no—
1482C2×D4—794no—
1483C2×D4—798no—
1484C2×D4—792no—
1485C2×D4—792no—
1486C2×D4—798no—
1487C2×D4—794no—
1488C2×D4—794no—
1489C2×D4—792no—
1490C2×D4—792no—
1491C2×D4—792no—
1492C2×D4—792no—
1493C2×D4—1588no—
1494C2×D4C23×D7912yes—
1495C2×D4C23×D7914yes—
1496C2×D4C23×D7912yes—
1497C2×D4C23×D7912yes—
1498C22×C4—3168no—
1499C22×C4—3162no—
1500C22×C4—792no—
1501C22×C4—798no—
1502C22×C4—794no—
1503C22×C4—791no—
1504C22×C4—791no—
1505C22×C4—794no—
1506C22×C4—798no—
1507C22×C4—798no—
1508C22×C4—794no—
1509C22×C4—798no—
1510C22×C4—798no—
1511C22×C4—791no—
1512C22×C4—791no—
1513C22×C4—791no—
1514C22×C4—791no—
1515C22×C4—792no—
1516C22×C4—791no—
1517C22×C4—791no—
1518C22×C4—791no—
1519C22×C4—791no—
1520C22×C4—791no—
1521C22×C4—791no—
1522C22×C4—791no—
1523C22×C4—791no—
1524C22×C4—791no—
1525C22×C4—794no—
1526C22×C4—794no—
1527C22×C4—794no—
1528C22×C4—794no—
1529C22×C4—1584no—
1530C22×C4—1584no—
1531C22×C4C23×D7911yescharacteristic
1532C22×C4C23×D7912yes—
1533C22×C4C23×D7914yes—
1534C22×C4C23×D7911yescharacteristic
1535C22×C4C23×D7912yes—
1536C22×C4C23×D7918yes—
1537C22×C4C23×D7911yescharacteristic
1538C4⋊C4—794no—
1539C4⋊C4—794no—
1540C4⋊C4—794no—
1541C4⋊C4—794no—
1542C4⋊C4—794no—
1543C4⋊C4—794no—
1544C4⋊C4—794no—
1545C4⋊C4—794no—
1546C4⋊C4—798no—
1547C4⋊C4—798no—
1548C4⋊C4—794no—
1549C4⋊C4—794no—
1550C4⋊C4—794no—
1551C4⋊C4—794no—
1552C4⋊C4—794no—
1553C4⋊C4—794no—
1554C4⋊C4—794no—
1555C4⋊C4—792no—
1556C4⋊C4—794no—
1557C4⋊C4—798no—
1558C4⋊C4—792no—
1559C4⋊C4—792no—
1560C4⋊C4—792no—
1561C4⋊C4—798no—
1562C4⋊C4—798no—
1563C4⋊C4—794no—
1564C4⋊C4—792no—
1565C4⋊C4—792no—
1566C4⋊C4—794no—
1567C4⋊C4C23×D7912yes—
1568C4⋊C4C23×D7918yes—
1569C4⋊C4C23×D7912yes—
1570C4⋊C4C23×D7912yes—
1571C4⋊C4C23×D7918yes—
1572C4⋊C4C23×D7912yes—
1573C4⋊C4C23×D7912yes—
1574C4⋊C4C23×D7918yes—
1575C4⋊C4C23×D7914yes—
1576C4⋊C4C23×D7914yes—
1577C4⋊C4C23×D7914yes—
1578C4⋊C4C23×D7912yes—
1579C4⋊C4C23×D7912yes—
1580C4⋊C4C23×D7912yes—
1581C4⋊C4C23×D7914yes—
1582C22⋊C4—798no—
1583C22⋊C4—794no—
1584C22⋊C4—794no—
1585C22⋊C4—794no—
1586C22⋊C4—794no—
1587C22⋊C4—794no—
1588C22⋊C4—794no—
1589C22⋊C4—794no—
1590C22⋊C4—794no—
1591C22⋊C4—794no—
1592C22⋊C4—798no—
1593C22⋊C4—798no—
1594C22⋊C4—794no—
1595C22⋊C4—794no—
1596C22⋊C4—794no—
1597C22⋊C4—794no—
1598C22⋊C4—798no—
1599C22⋊C4—798no—
1600C22⋊C4—794no—
1601C22⋊C4—794no—
1602C22⋊C4—794no—
1603C22⋊C4—798no—
1604C22⋊C4—798no—
1605C22⋊C4—794no—
1606C22⋊C4—794no—
1607C22⋊C4C23×D7914yes—
1608C22⋊C4C23×D7914yes—
1609C22⋊C4C23×D7918yes—
1610C22⋊C4C23×D7914yes—
1611C22⋊C4C23×D7918yes—
1612C22⋊C4C23×D7918yes—
1613C42—791no—
1614C42—791no—
1615C42—791no—
1616C42—791no—
1617C42—791no—
1618C42—791no—
1619C42—791no—
1620C42—791no—
1621C42—791no—
1622C42—791no—
1623C42—791no—
1624C42—791no—
1625C42—794no—
1626C42—794no—
1627C42—794no—
1628C42—794no—
1629C42—798no—
1630C42C23×D7911yescharacteristic
1631C42C23×D7911yescharacteristic
1632C42C23×D7911yescharacteristic
1633C42C23×D7911yescharacteristic
1634C42C23×D7914yes—
1635C42C23×D7914yes—
1636C42C23×D7914yes—
1637C42C23×D7918yes—
1638C23—3161no—
1639C23—3164no—
1640C23—3164no—
1641C23—791no—
1642C23—794no—
1643C23—791no—
1644C23—794no—
1645C23—1582no—
1646C23—1588no—
1647C23—1582no—
1648C23C24×D7914yes—
1649C23C24×D7911yescharacteristic
1650Q8—24no—
1651Q8—24no—
1652Q8—24no—
1653Q8—24no—
1654Q8—42no—
1655Q8—3168no—
1656Q8—3168no—
1657Q8—3164no—
1658Q8—3164no—
1659Q8—1588no—
1660Q8—1584no—
1661Q8—1584no—
1662Q8—1584no—
1663Q8—1584no—
1664D4—28no—
1665D4—24no—
1666D4—24no—
1667D4—42no—
1668D4—3164no—
1669D4—3162no—
1670D4—3168no—
1671D4—3168no—
1672D4—3164no—
1673D4—3162no—
1674D4—3164no—
1675D4—3164no—
1676D4—3168no—
1677D4—3168no—
1678D4—1588no—
1679D4—1588no—
1680D4—1588no—
1681D4—1588no—
1682D4—1588no—
1683D4—1584no—
1684D4—1584no—
1685D4—1584no—
1686D4—1584no—
1687C2×C4—24no—
1688C2×C4—28no—
1689C2×C4—22no—
1690C2×C4—41no—
1691C2×C4—42no—
1692C2×C4—48no—
1693C2×C4—3164no—
1694C2×C4—3164no—
1695C2×C4—3161no—
1696C2×C4—3161no—
1697C2×C4—3168no—
1698C2×C4—3168no—
1699C2×C4—3168no—
1700C2×C4—3168no—
1701C2×C4—3164no—
1702C2×C4—3168no—
1703C2×C4—3162no—
1704C2×C4—791no—
1705C2×C4—791no—
1706C2×C4—794no—
1707C2×C4—791no—
1708C2×C4—791no—
1709C2×C4—794no—
1710C2×C4—791no—
1711C2×C4—791no—
1712C2×C4—794no—
1713C2×C4—794no—
1714C2×C4—794no—
1715C2×C4—1582no—
1716C2×C4—1582no—
1717C2×C4—1582no—
1718C2×C4—1588no—
1719C2×C4—1588no—
1720C2×C4—1582no—
1721C2×C4—1582no—
1722C2×C4—1582no—
1723C2×C4—1582no—
1724C2×C4—1584no—
1725C2×C4—1582no—
1726C2×C4—1588no—
1727C2×C4—1582no—
1728C2×C4—1582no—
1729C2×C4—1582no—
1730C2×C4—1588no—
1731C2×C4—1582no—
1732C2×C4#1457920714yes—
1733C2×C4C24×D7911yescharacteristic
1734C2×C4C24×D7914yes—
1735C2×C4C24×D7911yescharacteristic
1736C2×C4C24×D7911yescharacteristic
1737C2×C4C24×D7914yes—
1738C2×C4C24×D7914yes—
1739C2×C4C24×D7914yes—
1740C2×C4C24×D7914yes—
1741C2×C4C24×D7911yescharacteristic
1742C2×C4C24×D7911yescharacteristic
1743C2×C4C24×D7911yescharacteristic
1744C22—21no—
1745C22—21no—
1746C22—24no—
1747C22—24no—
1748C22—24no—
1749C22—3164no—
1750C22—792no—
1751C22—6328no—
1752C22—1584no—
1753C22—1584no—
1754C22—1581no—
1755C22—1581no—
1756C22—1584no—
1757C22—1584no—
1758C22—1584no—
1759C22—1581no—
1760C22—1584no—
1761C22—1581no—
1762C22—1581no—
1763C22C2×#1457920712yes—
1764C22C25×D7911yescharacteristic
1765C4—24no—
1766C4—24no—
1767C4—21no—
1768C4—24no—
1769C4—24no—
1770C4—24no—
1771C4—21no—
1772C4—21no—
1773C4—792no—
1774C4—792no—
1775C4—1581no—
1776C4—1584no—
1777C4—1584no—
1778C4—1584no—
1779C4—1581no—
1780C4—1581no—
1781C4—1584no—
1782C4—1581no—
1783C4C2×#1457920712yes—
1784C4C2×#1457920712yes—
1785C42−1+4×D7912yes—
1786C2—22no—
1787C2—44no—
1788C2—3161no—
1789C2—3164no—
1790C2—3164no—
1791C2—1582no—
1792C2C22×#1457920711yescharacteristic
1793C2C2×2−1+4×D7911yescharacteristic
1794C2#585×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3507C2
hypercenter#3507D79
hypocenterC79#62835
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #23777969C2semidirect
2. #23777936C2semidirect
3. #23777874C2semidirect
4. #23777859C2semidirect
5. #23777813C2semidirect
6. #23777799C2semidirect
7. #23777788C2semidirect
8. #23777624C2semidirect
9. #23777483C2semidirect
10. #23777446C2semidirect
11. #23777304C2semidirect
12. #23777303C2semidirect
13. #23777273C2semidirect
14. #23777267C2semidirect
15. #23777253C2semidirect
16. #23777217C2semidirect
17. #23777197C2semidirect
18. #23777182C2semidirect
19. #23777171C2semidirect
20. #23777166C2semidirect
21. #23777123C2semidirect
22. #23777081C2semidirect
23. #23777078C2semidirect
24. #23776697C2semidirect
25. C2×#19099117C2semidirect
26. #532×D79C2semidirect
27. C79×#3507C2semidirect
28. C2×#14579209C22semidirect
29. C2×#14579208C22semidirect
31. #19099315C22semidirect
32. #19099311C22semidirect
33. #19099310C22semidirect
34. #19099309C22semidirect
35. #19099298C22semidirect
36. #19099298C22semidirect
37. #19099295C22semidirect
38. #19099295C22semidirect
39. Q8×Dic158C22semidirect
40. #19099292C22semidirect
41. #19099287C22semidirect
42. #19099286C22semidirect
43. #19099281C22semidirect
44. #19099276C22semidirect
45. #19099276C22semidirect
46. #19099274C22semidirect
47. #19099271C22semidirect
48. #19099270C22semidirect
50. #19099269C22semidirect
51. #19099269C22semidirect
52. #19099268C22semidirect
53. #19099264C22semidirect
54. #19099264C22semidirect
55. #19099262C22semidirect
56. #19099251C22semidirect
59. #19099235C22semidirect
60. #19099235C22semidirect
61. #19099234C22semidirect
62. #19099234C22semidirect
63. #19099233C22semidirect
65. Q8×D316C22semidirect
66. Q8×D316C22semidirect
67. D4×Dic158C22semidirect
69. #19099228C22semidirect
70. #19099226C22semidirect
71. #19099226C22semidirect
72. #19099225C22semidirect
73. #19099225C22semidirect
74. #19099225C22semidirect
75. #19099222C22semidirect
76. #19099222C22semidirect
77. #19099221C22semidirect
78. #19099221C22semidirect
79. #19099217C22semidirect
80. #19099217C22semidirect
81. #19099216C22semidirect
82. #19099215C22semidirect
83. #19099215C22semidirect
84. #19099214C22semidirect
85. #19099211C22semidirect
86. #19099211C22semidirect
87. #19099211C22semidirect
94. #19099193C22semidirect
96. #19099185C22semidirect
97. #19099185C22semidirect
98. #19099184C22semidirect
99. #19099182C22semidirect
100. #19099179C22semidirect
101. #19099179C22semidirect
102. #19099179C22semidirect
103. #19099178C22semidirect
104. #19099169C22semidirect
105. #19099165C22semidirect
106. #19099164C22semidirect
107. #19099162C22semidirect
108. #19099161C22semidirect
109. #19099157C22semidirect
111. #19099144C22semidirect
112. #19099144C22semidirect
113. #19099144C22semidirect
114. #19099143C22semidirect
115. #19099143C22semidirect
116. #19099141C22semidirect
117. #19099140C22semidirect
118. #19099139C22semidirect
119. #19099139C22semidirect
120. #19099138C22semidirect
121. #19099136C22semidirect
122. #19099133C22semidirect
125. #19099118C22semidirect
130. #19099117C22semidirect
131. #19099117C22semidirect
132. #19099117C22semidirect
133. #19099117C22semidirect
134. #19099117C22semidirect
137. #19099114C22semidirect
139. #19099113C22semidirect
140. #19099113C22semidirect
142. #19099112C22semidirect
146. #19099110C22semidirect
150. #19099108C22semidirect
151. C2×#14579160C22semidirect
152. C2×#14579159C22semidirect
154. C4⋊Q8×D79C22semidirect
157. #19099100C22semidirect
158. #19099099C22semidirect
159. #19099099C22semidirect
160. #19099099C22semidirect
162. #19099098C22semidirect
163. C2×#14579151C22semidirect
178. #19099043C22semidirect
179. #19099043C22semidirect
182. C4×#11929625C22semidirect
183. #19099031C22semidirect
184. C2×C4×Dic158C22semidirect
185. C2×C4×Dic158C22semidirect
190. #559×C79C22semidirect
191. #557×C79C22semidirect
192. #556×C79C22semidirect
193. #556×C79C22semidirect
194. #554×C79C22semidirect
195. #552×C79C22semidirect
196. #539×C79C22semidirect
197. #536×C79C22semidirect
198. #533×C79C22semidirect
200. #529×C79C22semidirect
201. #520×C79C22semidirect
202. C2×C4×Q8×C79C22semidirect
836. C4×D792−1+4semidirect
912. #3507D79semidirect
925. C79#62835semidirect
937. #559C2×D79semidirect
940. #557C2×D79semidirect
944. #556C2×D79semidirect
945. #556C2×D79semidirect
955. #554C2×D79semidirect
960. #552C2×D79semidirect
1014. #539C2×D79semidirect
1028. #536C2×D79semidirect
1041. #533C2×D79semidirect
1071. #529C2×D79semidirect
1089. #520C2×D79semidirect
1096. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779692
#237779362
#237778742
#237778592
#237778132
#237777992
#237777882
#237776242
#237774832
#237774462
#237773042
#237773032
#237772732
#237772672
#237772532
#237772172
#237771972
#237771822
#237771712
#237771662
#237771232
#237770812
#237770782
#237766972
C2×#190991172
#532×D792
C79×#35072
#6283579