Finite Group Databasebeta

← #35197455

Subgroups — #35197455

Order 20224.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777511C214yesmaximal, complemented
2#23777422C2112yesmaximal, complemented
3#23777400C214yesmaximal, complemented
4#23777342C2112yesmaximal, complemented
5#23777322C213yesmaximal, complemented
6#23777276C213yesmaximal, complemented
7#23777226C211yesmaximal, characteristic, complemented
8#23777178C211yesmaximal, characteristic, complemented
9#23777135C216yesmaximal, complemented
10#23777069C212yesmaximal, complemented
11#23776816C216yesmaximal, complemented
12#23776790C213yesmaximal, complemented
13C2×#19099168C213yesmaximal, complemented
14C4×#14579207C212yesmaximal, complemented
15C79×#3428C211yesmaximal, characteristic, complemented
16C2×#14579207C2212yes—
17#19099298C22112yescomplemented
18#19099289C2214yescomplemented
19#19099276C22112yescomplemented
20#19099272C22112yescomplemented
21#19099263C22112yescomplemented
22#19099262C22124yescomplemented
23#19099261C22112yescomplemented
24#19099257C22112yescomplemented
25#19099254C22112yescomplemented
26#19099237C22124yescomplemented
27#19099235C2214yescomplemented
28#19099234C22112yescomplemented
29#19099232C2214yescomplemented
30#19099224C2214yescomplemented
31#19099214C22112yescomplemented
32#19099209C22124yescomplemented
33#19099203C22124yescomplemented
34#19099201C22112yescomplemented
35D4×D316C22112yescomplemented
36D4×C22⋊D79C22112yescomplemented
37#19099191C2216yescomplemented
38#19099185C22112yescomplemented
39#19099184C2216yescomplemented
40#19099184C2216yescomplemented
41#19099175C2211yescharacteristic, complemented
42#19099175C2213yescomplemented
43#19099168C2213yescomplemented
44#19099168C2213yescomplemented
45#19099168C2216yescomplemented
46#19099168C2216yescomplemented
47#19099168C22112yescomplemented
48#19099168C2216yescomplemented
49#19099168C22112yescomplemented
50#19099164C22112yescomplemented
51#19099160C22112yescomplemented
52#19099151C22112yescomplemented
53#19099146C22124yescomplemented
54#19099141C2216yescomplemented
55#19099132C2216yescomplemented
56#19099127C2216yescomplemented
57#19099120C2213yescomplemented
58#19099113C2213yescomplemented
59#19099113C22112yescomplemented
60#19099110C22112yescomplemented
61C2×#14579158C2213yescomplemented
62#19099100C22112yescomplemented
63#19099097C22112yescomplemented
64#19099091C22112yescomplemented
65#19099091C22112yescomplemented
66C2×#14579153C2213yescomplemented
67#19099074C2216yescomplemented
68#19099072C22124yescomplemented
69C2×#14579146C22112yescomplemented
70C2×#14579135C2216yescomplemented
71C2×#14579134C22112yescomplemented
72#19099046C2212yes—
73#19099045C2214yescomplemented
74#19099043C2216yescomplemented
75#19099037C2216yescomplemented
76#19099035C22112yescomplemented
77C4×#11929625C2214yescomplemented
78C4×#11929624C2216yescomplemented
79C2×C4×D316C2216yescomplemented
80C4×D4×D79C22112yescomplemented
81C22×#41×C79C2211yescharacteristic
82#520×C79C2216yescomplemented
83#520×C79C2212yescomplemented
84#519×C79C2212yescomplemented
85#518×C79C2216yescomplemented
86C4×#41×C79C2211yescharacteristic
87C4×#41×C79C2211yescharacteristic
88C4×#41×C79C2213yescomplemented
89C4×#41×C79C2213yescomplemented
90C2×#117×C79C2213yescomplemented
91C2×#117×C79C2213yescomplemented
92#14579207—216no—
93C2×#11929625C2314yes—
94C2×#11929624C2316yes—
95C2×#11929624C23124yes—
96C22×D316C2316yes—
97C22×D316C23112yes—
98C22×C22⋊D79C23112yes—
99C2×D4×D79C23112yes—
100C22×C4×D79C23112yes—
101#14579161C2311yescharacteristic
102#14579161C2316yes—
103#14579160C23112yes—
104#14579158C2313yes—
105#14579158C23112yes—
106#14579158C2316yes—
107#14579157C23112yes—
108#14579156C23112yes—
109#14579156C23112yes—
110#14579155C23124yes—
111#14579154C2314yes—
112#14579154C23112yes—
113#14579153C2313yes—
114#14579153C2311yescharacteristic
115#14579153C2316yes—
116#14579153C23112yes—
117#14579152C23112yes—
118#14579151C2314yes—
119#14579151C23112yes—
120#14579150C23112yes—
121#14579149C23124yes—
122#14579149C2316yes—
123#14579147C23112yes—
124#14579147C23112yes—
125#14579146C23124yes—
126#14579146C23112yes—
127#14579146C23112yes—
128#14579146C23124yes—
129#14579146C23124yes—
130#14579144C23124yes—
131#14579144C23112yes—
132#14579143C23112yes—
133#14579143C23112yes—
134#14579140C2316yes—
135#14579140C23112yes—
136#14579140C2312yes—
137#14579139C23112yes—
138#14579139C23112yes—
139#14579138C23124yes—
140#14579137C23112yes—
141#14579136C23112yes—
142#14579136C23112yes—
143#14579135C23112yes—
144#14579135C23124yes—
145#14579135C23112yes—
146#14579135C2316yes—
147#14579135C23112yes—
148#14579135C23112yes—
149#14579135C2316yes—
150#14579134C23124yes—
151#14579134C23112yes—
152#14579134C23112yes—
153#14579134C23124yes—
154#14579134C23124yes—
155#14579133C23124yes—
156#14579132C23112yes—
157#14579131C23124yes—
158#14579130C23112yes—
159#14579129C23124yes—
160Q8×Dic79C2314yes—
161C4×Dic158C2312yes—
162C4×Dic158C2316yes—
163C4×Dic158C23112yes—
164C4×D316C23112yes—
165C4×D316C2316yes—
166C4×D316C23112yes—
167C4×D316C23112yes—
168C4×D316C2316yes—
169C4×D316C23112yes—
170C4×D316C23124yes—
171D4×Dic79C23112yes—
172#14579123C23112yes—
173#14579123C23112yes—
174C4×C22⋊D79C23112yes—
175C4×C22⋊D79C23112yes—
176C4×C22⋊D79C23112yes—
177C4×C22⋊D79C23112yes—
178C4×C22⋊D79C23124yes—
179(C22⋊D79)⋊C4C23124yes—
180#14579120C2316yes—
181#14579119C23112yes—
182#14579118C23112yes—
183#14579118C23124yes—
184C2×C4⋊Dic79C2316yes—
185C2×Dic79⋊C4C23112yes—
186C4⋊C4×D79C23112yes—
187C2×(C2×D79)⋊C4C23112yes—
188C2×(C2×D79)⋊C4C23112yes—
189C22⋊C4×D79C23124yes—
190C42×D79C23112yes—
191C2×#41×C79—28no—
192C2×#41×C79C2313yes—
193C2×#41×C79C2313yes—
194C2×#41×C79C2311yescharacteristic
195C2×#41×C79C2311yescharacteristic
196C22×Q8×C79C2311yescharacteristic
197C22×D4×C79C2313yes—
198C23×C4×C79C2313yes—
199C4×Q8×C79C2316yes—
200C4×Q8×C79C2312yes—
201C4×Q8×C79C2312yes—
202C4×Q8×C79C2316yes—
203C4×D4×C79C23112yes—
204C4×D4×C79C2316yes—
205C4×D4×C79C2316yes—
206C4×D4×C79C23112yes—
207C4×D4×C79C2316yes—
208C4×D4×C79C2316yes—
209#117×C79C2311yescharacteristic
210#117×C79C2313yes—
211#117×C79C2313yes—
212#117×C79C2313yes—
213#117×C79C2316yes—
214#117×C79C2316yes—
215#117×C79C2313yes—
216#117×C79C2313yes—
217#117×C79C2316yes—
218#117×C79C2316yes—
219C2×C4⋊C4×C79C2316yes—
220C2×C4⋊C4×C79C2316yes—
221C2×C22⋊C4×C79C2316yes—
222C2×C22⋊C4×C79C2316yes—
223C2×C42×C79C2313yes—
224C2×C42×C79C2313yes—
225C2×C42×C79C2316yes—
226C23×D79C24112yes—
227#11929625—216no—
228#11929624—224no—
229#11929624—824no—
230C2×Dic158C2412yes—
231C2×Dic158C24112yes—
232C2×D316—224no—
233C2×D316—812no—
234C2×D316C2416yes—
235C2×D316C24112yes—
236C2×D316C24124yes—
237C2×D316C24112yes—
238C2×C22⋊D79—812no—
239C2×C22⋊D79C24112yes—
240C2×C22⋊D79C24112yes—
241C2×C22⋊D79C24124yes—
242C2×C22⋊D79C24112yes—
243D4×D79—248no—
244C22×Dic79C24112yes—
245C2×C4×D79—812no—
246C2×C4×D79C24112yes—
247C2×C4×D79C24112yes—
248C2×C4×D79C24124yes—
249C2×C4×D79C24112yes—
250C4⋊Dic79C24112yes—
251C4⋊Dic79C2416yes—
252C4⋊Dic79C2412yes—
253C4⋊Dic79C2414yes—
254C4⋊Dic79C24112yes—
255Dic79⋊C4C24112yes—
256Dic79⋊C4C24112yes—
257Dic79⋊C4C24124yes—
258Dic79⋊C4C2414yes—
259Dic79⋊C4C24112yes—
260Dic79⋊C4C2414yes—
261Dic79⋊C4C2414yes—
262C22⋊Dic79C24112yes—
263C22⋊Dic79C2414yes—
264C22⋊Dic79C24112yes—
265(C2×D79)⋊C4C24112yes—
266(C2×D79)⋊C4C24124yes—
267(C2×D79)⋊C4C24112yes—
268(C2×D79)⋊C4C24112yes—
269(C2×D79)⋊C4C24124yes—
270(C2×D79)⋊C4C24112yes—
271(C2×D79)⋊C4C24112yes—
272(C2×D79)⋊C4C24112yes—
273C4×Dic79C2414yes—
274C4×Dic79C24112yes—
275C4×Dic79C24112yes—
276C24×C79C2413yes—
277#41×C79—24no—
278#41×C79—212no—
279#41×C79—212no—
280#41×C79#4118yescomplemented
281C2×Q8×C79—24no—
282C2×Q8×C79C2413yes—
283C2×Q8×C79C2411yescharacteristic
284C2×D4×C79—212no—
285C2×D4×C79C2416yes—
286C2×D4×C79C2413yes—
287C2×D4×C79C2413yes—
288C22×C4×C79—212no—
289C22×C4×C79C2413yes—
290C22×C4×C79C2413yes—
291C22×C4×C79C2413yes—
292C22×C4×C79C2411yescharacteristic
293C22×C4×C79C2413yes—
294C22×C4×C79C24112yes—
295C22×C4×C79C2416yes—
296C22×C4×C79C2416yes—
297C22×C4×C79C2413yes—
298C4⋊C4×C79C2416yes—
299C4⋊C4×C79C2412yes—
300C4⋊C4×C79C2416yes—
301C4⋊C4×C79C2416yes—
302C4⋊C4×C79C2416yes—
303C4⋊C4×C79C2416yes—
304C22⋊C4×C79C2412yes—
305C22⋊C4×C79C2416yes—
306C22⋊C4×C79C2416yes—
307C22⋊C4×C79C2416yes—
308C22⋊C4×C79C2416yes—
309C22⋊C4×C79C2416yes—
310C42×C79C2411yescharacteristic
311C42×C79C2413yes—
312C42×C79C2413yes—
313C42×C79C2411yescharacteristic
314C42×C79C2416yes—
315C42×C79C24112yes—
316C42×C79C2416yes—
317C23×C79—26no—
318C23×C79—46no—
319C23×C79C2511yescharacteristic
320C23×C79C2513yes—
321C23×C79C2513yes—
322C22×D79—224no—
323C22×D79—412no—
324C22×D79—412no—
325C22×D79C25112yes—
326Q8×C79—26no—
327Q8×C79C2×#4114yes—
328D4×C79—212no—
329D4×C79—26no—
330D4×C79C2×#41112yes—
331C2×C4×C79—26no—
332C2×C4×C79—22no—
333C2×C4×C79—26no—
334C2×C4×C79—26no—
335C2×C4×C79—26no—
336C2×C4×C79—46no—
337C2×C4×C79—46no—
338C2×C4×C79—412no—
339C2×C4×C79C2×#41112yes—
340C2×C4×C79C2512yes—
341C2×C4×C79C2516yes—
342C2×C4×C79C2513yes—
343C2×C4×C79C2511yescharacteristic
344C2×C4×C79C2516yes—
345C2×C4×C79C2512yes—
346C2×C4×C79C2513yes—
347C2×C4×C79C2511yescharacteristic
348C22⋊D79—224no—
349C22⋊D79—412no—
350C22⋊D79—424no—
351C22⋊D79—412no—
352C2×Dic79—412no—
353C2×Dic79C2514yes—
354C2×Dic79C2514yes—
355C2×Dic79C25112yes—
356D316—224no—
357D316—212no—
358D316—412no—
359D316—424no—
360C4×D79—224no—
361C4×D79—412no—
362C4×D79—424no—
363C4×D79—412no—
364Dic158—24no—
365Dic158—412no—
366C22×C79—26no—
367C22×C79—21no—
368C22×C79—23no—
369C22×C79—26no—
370C22×C79—22no—
371C22×C79—86no—
372C22×C79C22×#4116yes—
373C22×C79C2611yescharacteristic
374C2×D79—212no—
375C2×D79—212no—
376C2×D79—212no—
377C2×D79—824no—
378C4×C79—21no—
379C4×C79—23no—
380C4×C79—26no—
381C4×C79—22no—
382C4×C79—26no—
383C4×C79—22no—
384C4×C79C22×#4112yes—
385C4×C79C22×#4116yes—
386Dic79—24no—
387Dic79—24no—
388Dic79—212no—
389#62858—791nomaximal, Sylow
390C2×C79—26no—
391C2×C79—43no—
392C2×C79—41no—
393C2×C79C23×#4111yescharacteristic
394C2×C79H(7,𝔽2)12yes—
395D79—412no—
396#3524—794no—
397#3519—7912no—
398#3517—794no—
399#3513—7912no—
400#3512—793no—
401#3508—793no—
402#3504—791no—
403#3498—791no—
404#3494—796no—
405#3488—792no—
406#3460—796no—
407#3455—793no—
408C2×#540—793no—
409C4×H(5,𝔽2)—792no—
410#3428D7911yescharacteristic, complemented
411C79#6285811yescharacteristic, complemented, Sylow
412C2×H(5,𝔽2)—792no—
413C22×#41C2×D7911yescharacteristic
414#559—7912no—
415#557—794no—
416#555—7912no—
417#554—7912no—
418#553—7924no—
419#553—7912no—
420#553—7912no—
421#553—7912no—
422#552—7912no—
423#551—7924no—
424#550—794no—
425#550—794no—
426#550—7912no—
427#548—794no—
428#547—7912no—
429#546—7912no—
430#546—7924no—
431#546—7924no—
432D42—7912no—
433D42—7912no—
434#544—796no—
435#542—7912no—
436#542—796no—
437#542—796no—
438#541—791no—
439#541—793no—
440#540—7912no—
441#540—793no—
442#540—796no—
443#540—796no—
444#540—796no—
445#540—7912no—
446#540—7912no—
447#540—793no—
448#539—7912no—
449#538—7924no—
450#538—7912no—
451#537—796no—
452#535—796no—
453#535—796no—
454#533—793no—
455#532—7912no—
456#532—793no—
457#532—7912no—
458C2×#127—793no—
459#529—7912no—
460#529—7912no—
461#529—7912no—
462#529—7912no—
463C2×#125—793no—
464#525—796no—
465#525—7924no—
466C2×#123—7912no—
467C2×#121—796no—
468C2×#121—7912no—
469#520—792no—
470#520—794no—
471#520—796no—
472#520C2×D7916yescomplemented
473#520C2×D7912yescomplemented
474#519C2×D7912yescomplemented
475#518—7912no—
476#518—796no—
477#518C2×D7916yescomplemented
478C4×#41—794no—
479C4×#41—796no—
480C4×#41C2×D7911yescharacteristic
481C4×#41C2×D7911yescharacteristic
482C4×#41C2×D7913yescomplemented
483C4×#41C2×D7913yescomplemented
484C2×C4×D4—7912no—
485C2×C4×D4—796no—
486C2×#117C2×D7913yescomplemented
487C2×#117C2×D7913yescomplemented
488H(5,𝔽2)—15816no—
489C2×#41—28no—
490C2×#41—794no—
491C2×#41—7924no—
492C2×#41—796no—
493C2×#41C22×D7913yes—
494C2×#41C22×D7913yes—
495C2×#41C22×D7911yescharacteristic
496C2×#41C22×D7911yescharacteristic
497C22×Q8C22×D7911yescharacteristic
498C22×D4—7912no—
499C22×D4—7912no—
500C22×D4—7912no—
501C22×D4—796no—
502C22×D4C22×D7913yes—
503C23×C4—7912no—
504C23×C4C22×D7913yes—
505C4⋊Q8—7912no—
506C4⋊Q8—791no—
507C4⋊Q8—796no—
508#127—7912no—
509#127—793no—
510#127—796no—
511#127—7912no—
512#126—7912no—
513#126—7912no—
514#126—794no—
515#126—7912no—
516#126—7924no—
517#125—794no—
518#125—7912no—
519#125—7912no—
520#125—793no—
521#125—796no—
522#125—7912no—
523#125—791no—
524#124—7912no—
525#124—7912no—
526#124—7912no—
527#124—796no—
528#124—7924no—
529#123—7912no—
530#123—7924no—
531#123—7912no—
532#123—7924no—
533#123—7924no—
534#123—7924no—
535#123—7912no—
536#123—7912no—
537#123—7912no—
538C22⋊Q8—7912no—
539C22⋊Q8—792no—
540C22⋊Q8—796no—
541C22⋊Q8—7912no—
542C22⋊Q8—7912no—
543C22⋊Q8—7912no—
544C22⋊Q8—7924no—
545#121—7924no—
546#121—7912no—
547#121—796no—
548#121—7912no—
549#121—7912no—
550#121—7912no—
551#121—796no—
552#121—7912no—
553#121—7924no—
554#121—7912no—
555#121—7912no—
556#121—7912no—
557#121—7924no—
558#121—7924no—
559#121—7924no—
560#121—7912no—
561#120—7912no—
562#120—7924no—
563#120—7924no—
564C4×Q8—794no—
565C4×Q8—792no—
566C4×Q8—796no—
567C4×Q8—7912no—
568C4×Q8C22×D7912yes—
569C4×Q8C22×D7912yes—
570C4×Q8C22×D7916yes—
571C4×Q8C22×D7916yes—
572C4×D4—7912no—
573C4×D4—7912no—
574C4×D4—7912no—
575C4×D4—7912no—
576C4×D4—7912no—
577C4×D4—7924no—
578C4×D4—7912no—
579C4×D4—7912no—
580C4×D4—7924no—
581C4×D4—7912no—
582C4×D4—796no—
583C4×D4—7912no—
584C4×D4—7912no—
585C4×D4—796no—
586C4×D4—7924no—
587C4×D4—7912no—
588C4×D4C22×D7916yes—
589C4×D4C22×D7916yes—
590C4×D4C22×D79112yes—
591C4×D4C22×D7916yes—
592C4×D4C22×D79112yes—
593C4×D4C22×D7916yes—
594#117—796no—
595#117—7912no—
596#117—7912no—
597#117—7924no—
598#117C22×D7911yescharacteristic
599#117C22×D7913yes—
600#117C22×D7913yes—
601#117C22×D7913yes—
602#117C22×D7913yes—
603#117C22×D7913yes—
604#117C22×D7916yes—
605#117C22×D7916yes—
606#117C22×D7916yes—
607#117C22×D7916yes—
608C2×C4⋊C4—796no—
609C2×C4⋊C4—7912no—
610C2×C4⋊C4—7912no—
611C2×C4⋊C4C22×D7916yes—
612C2×C4⋊C4C22×D7916yes—
613C2×C22⋊C4—7912no—
614C2×C22⋊C4—7912no—
615C2×C22⋊C4—7924no—
616C2×C22⋊C4C22×D7916yes—
617C2×C22⋊C4C22×D7916yes—
618C2×C42—7912no—
619C2×C42C22×D7913yes—
620C2×C42C22×D7913yes—
621C2×C42C22×D7916yes—
622C24—7912no—
623C24C23×D7913yes—
624#41—24no—
625#41—212no—
626#41—212no—
627#41—63224no—
628#41—15816no—
629#41—15824no—
630#41#1192962418yescomplemented
631C2×Q8—24no—
632C2×Q8—7912no—
633C2×Q8—792no—
634C2×Q8C23×D7913yes—
635C2×Q8C23×D7911yescharacteristic
636C2×D4—212no—
637C2×D4—7912no—
638C2×D4—7912no—
639C2×D4—7924no—
640C2×D4—7912no—
641C2×D4—7924no—
642C2×D4—7912no—
643C2×D4—7912no—
644C2×D4—796no—
645C2×D4—63212no—
646C2×D4—63212no—
647C2×D4—15848no—
648C2×D4—15824no—
649C2×D4C23×D7916yes—
650C2×D4C23×D7913yes—
651C2×D4C23×D7913yes—
652C22×C4—212no—
653C22×C4—7912no—
654C22×C4—7912no—
655C22×C4—7912no—
656C22×C4—7924no—
657C22×C4—7912no—
658C22×C4—63212no—
659C22×C4C23×D7913yes—
660C22×C4C23×D7913yes—
661C22×C4C23×D7913yes—
662C22×C4C23×D7913yes—
663C22×C4C23×D7911yescharacteristic
664C22×C4C23×D7916yes—
665C22×C4C23×D7916yes—
666C22×C4C23×D79112yes—
667C22×C4C23×D7913yes—
668C4⋊C4—7912no—
669C4⋊C4—7912no—
670C4⋊C4—7924no—
671C4⋊C4—794no—
672C4⋊C4—7912no—
673C4⋊C4—794no—
674C4⋊C4—794no—
675C4⋊C4—7912no—
676C4⋊C4—796no—
677C4⋊C4—792no—
678C4⋊C4—794no—
679C4⋊C4—7912no—
680C4⋊C4C23×D7916yes—
681C4⋊C4C23×D7916yes—
682C4⋊C4C23×D7912yes—
683C4⋊C4C23×D7916yes—
684C4⋊C4C23×D7916yes—
685C4⋊C4C23×D7916yes—
686C22⋊C4—7912no—
687C22⋊C4—794no—
688C22⋊C4—7912no—
689C22⋊C4—7924no—
690C22⋊C4—7912no—
691C22⋊C4—7912no—
692C22⋊C4—7912no—
693C22⋊C4—7924no—
694C22⋊C4—7912no—
695C22⋊C4—7912no—
696C22⋊C4—7912no—
697C22⋊C4C23×D7916yes—
698C22⋊C4C23×D7912yes—
699C22⋊C4C23×D7916yes—
700C22⋊C4C23×D7916yes—
701C22⋊C4C23×D7916yes—
702C22⋊C4C23×D7916yes—
703C42—794no—
704C42—7912no—
705C42—7912no—
706C42C23×D7916yes—
707C42C23×D7911yescharacteristic
708C42C23×D7913yes—
709C42C23×D7913yes—
710C42C23×D7911yescharacteristic
711C42C23×D79112yes—
712C42C23×D7916yes—
713C23—26no—
714C23—46no—
715C23—31612no—
716C23—31612no—
717C23—7912no—
718C23—15824no—
719C23C24×D7911yescharacteristic
720C23C24×D7913yes—
721C23C24×D7913yes—
722Q8—26no—
723Q8—31612no—
724Q8—1584no—
725Q8C2×#1192962414yes—
726D4—212no—
727D4—26no—
728D4—31612no—
729D4—31624no—
730D4—31612no—
731D4—31624no—
732D4—31612no—
733D4—15824no—
734D4—15812no—
735D4—15824no—
736D4C2×#11929624112yes—
737C2×C4—26no—
738C2×C4—22no—
739C2×C4—26no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—46no—
743C2×C4—46no—
744C2×C4—412no—
745C2×C4—31612no—
746C2×C4—31624no—
747C2×C4—31612no—
748C2×C4—31612no—
749C2×C4—794no—
750C2×C4—794no—
751C2×C4—7912no—
752C2×C4—15824no—
753C2×C4C2×#11929624112yes—
754C2×C4C24×D7912yes—
755C2×C4C24×D7916yes—
756C2×C4C24×D7913yes—
757C2×C4C24×D7916yes—
758C2×C4C24×D7912yes—
759C2×C4C24×D7911yescharacteristic
760C2×C4C24×D7913yes—
761C2×C4C24×D7911yescharacteristic
762C22—26no—
763C22—21no—
764C22—23no—
765C22—26no—
766C22—22no—
767C22—86no—
768C22—63224no—
769C22—15812no—
770C22—15812no—
771C22—15812no—
772C22C22×#1192962416yes—
773C22C25×D7911yescharacteristic
774C4—21no—
775C4—23no—
776C4—22no—
777C4—26no—
778C4—22no—
779C4—26no—
780C4—1584no—
781C4—15812no—
782C4—1584no—
783C4C22×#1192962412yes—
784C4C22×#1192962416yes—
785C2—26no—
786C2—41no—
787C2—43no—
788C2—31612no—
789C2C23×#1192962411yescharacteristic
790C2#2377821112yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3428C2
hypercenter#3428D79
hypocenterC79#62858
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #23777511C2semidirect
2. #23777422C2semidirect
3. #23777400C2semidirect
4. #23777342C2semidirect
5. #23777322C2semidirect
6. #23777276C2semidirect
7. #23777226C2semidirect
8. #23777178C2semidirect
9. #23777135C2semidirect
10. #23777069C2semidirect
11. #23776816C2semidirect
12. #23776790C2semidirect
13. C2×#19099168C2semidirect
14. C4×#14579207C2semidirect
15. C79×#3428C2semidirect
17. #19099298C22semidirect
18. #19099289C22semidirect
19. #19099276C22semidirect
20. #19099272C22semidirect
21. #19099263C22semidirect
22. #19099262C22semidirect
23. #19099261C22semidirect
24. #19099257C22semidirect
25. #19099254C22semidirect
26. #19099237C22semidirect
27. #19099235C22semidirect
28. #19099234C22semidirect
29. #19099232C22semidirect
30. #19099224C22semidirect
31. #19099214C22semidirect
32. #19099209C22semidirect
33. #19099203C22semidirect
34. #19099201C22semidirect
35. D4×D316C22semidirect
36. D4×C22⋊D79C22semidirect
37. #19099191C22semidirect
38. #19099185C22semidirect
39. #19099184C22semidirect
40. #19099184C22semidirect
41. #19099175C22semidirect
42. #19099175C22semidirect
43. #19099168C22semidirect
44. #19099168C22semidirect
45. #19099168C22semidirect
46. #19099168C22semidirect
47. #19099168C22semidirect
48. #19099168C22semidirect
49. #19099168C22semidirect
50. #19099164C22semidirect
51. #19099160C22semidirect
52. #19099151C22semidirect
53. #19099146C22semidirect
54. #19099141C22semidirect
55. #19099132C22semidirect
56. #19099127C22semidirect
57. #19099120C22semidirect
58. #19099113C22semidirect
59. #19099113C22semidirect
60. #19099110C22semidirect
61. C2×#14579158C22semidirect
62. #19099100C22semidirect
63. #19099097C22semidirect
64. #19099091C22semidirect
65. #19099091C22semidirect
66. C2×#14579153C22semidirect
67. #19099074C22semidirect
68. #19099072C22semidirect
69. C2×#14579146C22semidirect
70. C2×#14579135C22semidirect
71. C2×#14579134C22semidirect
73. #19099045C22semidirect
74. #19099043C22semidirect
75. #19099037C22semidirect
76. #19099035C22semidirect
77. C4×#11929625C22semidirect
78. C4×#11929624C22semidirect
79. C2×C4×D316C22semidirect
80. C4×D4×D79C22semidirect
82. #520×C79C22semidirect
83. #520×C79C22semidirect
84. #519×C79C22semidirect
85. #518×C79C22semidirect
88. C4×#41×C79C22semidirect
89. C4×#41×C79C22semidirect
90. C2×#117×C79C22semidirect
91. C2×#117×C79C22semidirect
280. #41×C79#41semidirect
410. #3428D79semidirect
411. C79#62858semidirect
472. #520C2×D79semidirect
473. #520C2×D79semidirect
474. #519C2×D79semidirect
477. #518C2×D79semidirect
482. C4×#41C2×D79semidirect
483. C4×#41C2×D79semidirect
486. C2×#117C2×D79semidirect
487. C2×#117C2×D79semidirect
630. #41#11929624semidirect

Maximal subgroups

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

subgroupindex
#237775112
#237774222
#237774002
#237773422
#237773222
#237772762
#237772262
#237771782
#237771352
#237770692
#237768162
#237767902
C2×#190991682
C4×#145792072
C79×#34282
#6285879