Finite Group Databasebeta

← #35197456

Subgroups — #35197456

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#23777512C214yesmaximal, complemented
2#23777433C2112yesmaximal, complemented
3#23777407C214yesmaximal, complemented
4#23777343C2112yesmaximal, complemented
5#23777324C213yesmaximal, complemented
6#23777277C213yesmaximal, complemented
7#23777178C211yesmaximal, characteristic, complemented
8#23777138C216yesmaximal, complemented
9#23777070C212yesmaximal, complemented
10#23776823C216yesmaximal, complemented
11#23776792C213yesmaximal, complemented
12C2×#19099169C213yesmaximal, complemented
13#23776606C212yesmaximal, complemented
14#23776599C211yesmaximal, characteristic, complemented
15C79×#3504C211yesmaximal, characteristic, complemented
16C2×#14579207C2212yes—
17C2×#41×D79C2211yescharacteristic
18#19099298C22112yescomplemented
19#19099279C22112yescomplemented
20#19099266C22112yescomplemented
21#19099266C22112yescomplemented
22#19099266C22112yescomplemented
23#19099261C22124yescomplemented
24#19099251C22112yescomplemented
25#19099240C22124yescomplemented
26#19099235C2214yescomplemented
27#19099235C22112yescomplemented
28#19099235C2214yescomplemented
29#19099225C2214yescomplemented
30#19099216C22112yescomplemented
31#19099208C22112yescomplemented
32#19099204C22124yescomplemented
33#19099204C22124yescomplemented
34D4×D316C22112yescomplemented
35D4×D316C22112yescomplemented
36#19099187C2216yescomplemented
37#19099187C2216yescomplemented
38#19099187C22112yescomplemented
39#19099176C2211yescharacteristic, complemented
40#19099176C2213yescomplemented
41#19099169C2213yescomplemented
42#19099169C2213yescomplemented
43#19099169C2216yescomplemented
44#19099169C2216yescomplemented
45#19099169C22112yescomplemented
46#19099169C22112yescomplemented
47#19099169C2216yescomplemented
48#19099169C22112yescomplemented
49#19099162C22112yescomplemented
50#19099153C22112yescomplemented
51#19099153C22124yescomplemented
52#19099144C2216yescomplemented
53#19099132C2216yescomplemented
54#19099132C2216yescomplemented
55#19099114C22112yescomplemented
56#19099114C22112yescomplemented
57#19099113C2213yescomplemented
58C2×#14579158C2213yescomplemented
59#19099100C22112yescomplemented
60#19099100C22112yescomplemented
61#19099098C22112yescomplemented
62#19099098C22112yescomplemented
63#19099076C22124yescomplemented
64#19099075C2216yescomplemented
65C2×#14579146C22112yescomplemented
66C2×#14579136C2216yescomplemented
67C2×#14579136C22112yescomplemented
68#19099045C2212yescomplemented
69#19099045C2214yescomplemented
70#19099044C2216yescomplemented
71#19099042C2216yescomplemented
72#19099039C2212yescomplemented
73#19099037C2216yescomplemented
74#19099035C22112yescomplemented
75#19099035C2216yescomplemented
76#41×Dic79C2211yescharacteristic
77C4×#11929625C2214yescomplemented
78C4×#11929624C2213yescomplemented
79#19099031C2216yescomplemented
80#19099031C2213yescomplemented
81C2×#14579123C2216yescomplemented
82C4×D4×D79C22112yescomplemented
83C2×#14579118C2213yescomplemented
84#117×D79C2213yescomplemented
85#557×C79C2214yescomplemented
86#554×C79C22112yescomplemented
87#544×C79C2216yescomplemented
88#533×C79C2213yescomplemented
89C2×#125×C79C2213yescomplemented
90#520×C79C2212yes—
91C4×#41×C79C2211yescharacteristic
92#14579207—216no—
93C2×#11929625C2314yes—
94C2×#11929625C2311yescharacteristic
95C2×#11929625C23124yes—
96C2×#11929624C2316yes—
97C2×#11929624C2313yes—
98C2×#11929623C2313yes—
99#41×D79—28no—
100C2×Q8×D79C2311yescharacteristic
101C22×D316C2316yes—
102C22×D316C23112yes—
103C22×D316C23112yes—
104C2×D4×D79C23112yes—
105C2×D4×D79C2313yes—
106C22×C4×D79C2313yes—
107C22×C4×D79C23112yes—
108#14579161C2311yescharacteristic
109#14579158C2313yes—
110#14579158C23112yes—
111#14579158C2316yes—
112#14579158C23112yes—
113#14579156C2314yes—
114#14579156C23112yes—
115#14579156C23112yes—
116#14579156C23124yes—
117#14579156C23112yes—
118#14579152C2314yes—
119#14579152C23112yes—
120#14579150C23112yes—
121#14579150C23112yes—
122#14579150C23124yes—
123#14579149C2316yes—
124#14579149C23112yes—
125#14579146C23124yes—
126#14579146C23112yes—
127#14579146C23124yes—
128#14579146C23112yes—
129#14579146C23112yes—
130#14579146C23112yes—
131#14579146C23124yes—
132#14579146C23124yes—
133#14579145C23112yes—
134#14579141C2316yes—
135#14579141C23112yes—
136#14579141C2312yes—
137#14579137C23112yes—
138#14579137C23112yes—
139#14579136C23112yes—
140#14579136C23112yes—
141#14579136C23112yes—
142#14579136C23124yes—
143#14579136C23112yes—
144#14579136C23124yes—
145#14579136C2316yes—
146#14579136C23112yes—
147#14579136C23124yes—
148#14579136C23124yes—
149#14579136C23112yes—
150#14579136C2316yes—
151#14579136C23112yes—
152#14579136C23112yes—
153#14579135C23124yes—
154#14579135C23112yes—
155#14579131C23112yes—
156#14579131C23124yes—
157#14579131C23124yes—
158Q8×Dic79C2312yes—
159C4×Dic158C2316yes—
160#14579126C2312yes—
161#14579126C2316yes—
162#14579126C2316yes—
163C4×D316C23112yes—
164C4×D316C23112yes—
165C4×D316C23112yes—
166C4×D316C23112yes—
167C4×D316C2316yes—
168C4×D316C23112yes—
169D4×Dic79C2316yes—
170#14579123C23112yes—
171#14579123C2316yes—
172#14579123C23112yes—
173#14579123C23112yes—
174#14579123C2316yes—
175#14579123C2316yes—
176#14579123C23124yes—
177#14579123C23124yes—
178C4×C22⋊D79C23112yes—
179C4×C22⋊D79C23124yes—
180(C22⋊D79)⋊C4C23112yes—
181(C22⋊D79)⋊C4C23112yes—
182(C22⋊D79)⋊C4C23112yes—
183#14579120C2313yes—
184#14579119C23124yes—
185#14579119C23112yes—
186#14579119C2316yes—
187#14579118C2311yescharacteristic
188#14579118C2313yes—
189#14579118C2313yes—
190#14579118C2313yes—
191#14579118C2316yes—
192#14579118C2316yes—
193#14579118C23112yes—
194#14579117C2316yes—
195C2×Dic79⋊C4C2316yes—
196C4⋊C4×D79C2316yes—
197C4⋊C4×D79C23112yes—
198C2×(C2×D79)⋊C4C2316yes—
199C2×(C2×D79)⋊C4C23112yes—
200C2×(C2×D79)⋊C4C23112yes—
201C22⋊C4×D79C2316yes—
202C22⋊C4×D79C23124yes—
203C2×C4×Dic79C2313yes—
204C42×D79C2316yes—
205C42×D79C23112yes—
206C2×#41×C79C2311yescharacteristic
207C4⋊Q8×C79C2316yes—
208C4⋊Q8×C79C23112yes—
209#125×C79C2313yes—
210#125×C79C2311yescharacteristic
211#125×C79C23112yes—
212#125×C79C2316yes—
213#125×C79C23112yes—
214C22⋊Q8×C79C23112yes—
215C22⋊Q8×C79C23124yes—
216C4×Q8×C79C2314yes—
217C4×Q8×C79C2312yes—
218C4×Q8×C79C23112yes—
219C4×D4×C79C2316yes—
220C4×D4×C79C23112yes—
221#117×C79C2313yes—
222#117×C79C2316yes—
223C2×C4⋊C4×C79C2316yes—
224C2×C4⋊C4×C79C23112yes—
225C2×C42×C79C2313yes—
226C23×D79C2413yes—
227C23×D79C24112yes—
228#11929625—24no—
229#11929625—216no—
230#11929625—824no—
231#11929624—212no—
232#11929624—224no—
233#11929623—212no—
234C2×Dic158C2413yes—
235C2×Dic158C2412yes—
236Q8×D79—24no—
237C2×D316—224no—
238C2×D316—812no—
239C2×D316—812no—
240C2×D316C2413yes—
241C2×D316C2416yes—
242C2×D316C24112yes—
243C2×D316C24112yes—
244C2×D316C24124yes—
245C2×D316C24124yes—
246C2×D316C24112yes—
247C2×D316C24112yes—
248C2×C22⋊D79C2416yes—
249C2×C22⋊D79C24112yes—
250D4×D79—212no—
251D4×D79—248no—
252C22×Dic79C2413yes—
253C22×Dic79C2416yes—
254C2×C4×D79—212no—
255C2×C4×D79—812no—
256C2×C4×D79C2413yes—
257C2×C4×D79C2413yes—
258C2×C4×D79C2413yes—
259C2×C4×D79C24112yes—
260C2×C4×D79C2411yescharacteristic
261C2×C4×D79C24112yes—
262C2×C4×D79C24112yes—
263C2×C4×D79C24124yes—
264C2×C4×D79C24112yes—
265C4⋊Dic79C2416yes—
266C4⋊Dic79C24112yes—
267C4⋊Dic79C2414yes—
268C4⋊Dic79C2414yes—
269Dic79⋊C4C2416yes—
270Dic79⋊C4C24112yes—
271Dic79⋊C4C2412yes—
272Dic79⋊C4C2416yes—
273Dic79⋊C4C2416yes—
274Dic79⋊C4C2414yes—
275C22⋊Dic79C2416yes—
276(C2×D79)⋊C4C2416yes—
277(C2×D79)⋊C4C24112yes—
278(C2×D79)⋊C4C24124yes—
279(C2×D79)⋊C4C2412yes—
280(C2×D79)⋊C4C24112yes—
281(C2×D79)⋊C4C24112yes—
282(C2×D79)⋊C4C2416yes—
283(C2×D79)⋊C4C2416yes—
284(C2×D79)⋊C4C24124yes—
285(C2×D79)⋊C4C24112yes—
286(C2×D79)⋊C4C24112yes—
287(C2×D79)⋊C4C24112yes—
288(C2×D79)⋊C4C24112yes—
289(C2×D79)⋊C4C2414yes—
290C4×Dic79C2414yes—
291C4×Dic79C2416yes—
292C4×Dic79C2413yes—
293C4×Dic79C24112yes—
294C4×Dic79C24112yes—
295C4×Dic79C2411yescharacteristic
296#41×C79#4118yescomplemented
297C2×Q8×C79C24112yes—
298C2×Q8×C79C2411yescharacteristic
299C2×D4×C79C2413yes—
300C22×C4×C79C2416yes—
301C22×C4×C79C24112yes—
302C22×C4×C79C2413yes—
303C4⋊C4×C79C2416yes—
304C4⋊C4×C79C24112yes—
305C4⋊C4×C79C24112yes—
306C4⋊C4×C79C24124yes—
307C4⋊C4×C79C2412yes—
308C4⋊C4×C79C2416yes—
309C4⋊C4×C79C2414yes—
310C4⋊C4×C79C24112yes—
311C22⋊C4×C79C24112yes—
312C22⋊C4×C79C2416yes—
313C42×C79C2411yescharacteristic
314C42×C79C2413yes—
315C42×C79C2416yes—
316C42×C79C24112yes—
317C23×C79C2513yes—
318C22×D79—26no—
319C22×D79—224no—
320C22×D79—412no—
321C22×D79—46no—
322C22×D79—412no—
323C22×D79C2511yescharacteristic
324C22×D79C25112yes—
325C22×D79C2513yes—
326Q8×C79—412no—
327Q8×C79C2×#4114yes—
328D4×C79C2×#41112yes—
329C2×C4×C79—412no—
330C2×C4×C79—46no—
331C2×C4×C79C2×#41112yes—
332C2×C4×C79C2516yes—
333C2×C4×C79C2514yes—
334C2×C4×C79C25112yes—
335C2×C4×C79C2512yes—
336C2×C4×C79C2511yescharacteristic
337C2×C4×C79C2513yes—
338C22⋊D79—224no—
339C22⋊D79—212no—
340C2×Dic79—26no—
341C2×Dic79—46no—
342C2×Dic79C2512yes—
343C2×Dic79C2516yes—
344C2×Dic79C2513yes—
345C2×Dic79C2514yes—
346C2×Dic79C2511yescharacteristic
347D316—224no—
348D316—26no—
349D316—212no—
350D316—412no—
351D316—412no—
352D316—424no—
353D316—424no—
354D316—412no—
355C4×D79—22no—
356C4×D79—26no—
357C4×D79—26no—
358C4×D79—26no—
359C4×D79—224no—
360C4×D79—412no—
361C4×D79—424no—
362C4×D79—412no—
363C4×D79—412no—
364Dic158—26no—
365Dic158—24no—
366C22×C79—26no—
367C22×C79C22×#4116yes—
368C22×C79C2611yescharacteristic
369C2×D79—23no—
370C2×D79—212no—
371C2×D79—21no—
372C2×D79—22no—
373C2×D79—212no—
374C2×D79—212no—
375C2×D79—26no—
376C2×D79—86no—
377C2×D79—824no—
378C4×C79—22no—
379C4×C79—212no—
380C4×C79—26no—
381C4×C79—24no—
382C4×C79C22×#4112yes—
383C4×C79C22×#4116yes—
384Dic79—24no—
385Dic79—23no—
386Dic79—21no—
387Dic79—26no—
388Dic79—22no—
389#62858—791nomaximal, Sylow
390C2×C79—26no—
391C2×C79C23×#4111yescharacteristic
392C2×C79H(7,𝔽2)12yes—
393D79—43no—
394D79—412no—
395D79—41no—
396#3524—794no—
397#3519—7912no—
398#3517—794no—
399#3513—7912no—
400#3512—793no—
401#3508—793no—
402#3504D7911yescharacteristic, complemented
403#3498—791no—
404#3494—796no—
405#3488—792no—
406#3460—796no—
407#3455—793no—
408C2×#540—793no—
409C4×H(5,𝔽2)—792no—
410#3428—791no—
411C79#6285811yescharacteristic, complemented, Sylow
412C2×H(5,𝔽2)—792no—
413C22×#41—791no—
414#559—7912no—
415#557C2×D7914yescomplemented
416#555—7912no—
417#554C2×D79112yescomplemented
418#553—7912no—
419#553—7912no—
420#553—7912no—
421#553—7924no—
422#552—7912no—
423#551—7924no—
424#550—794no—
425#550—794no—
426#550—7912no—
427#548—794no—
428#547—7912no—
429#546—7924no—
430#546—7924no—
431#546—7912no—
432D42—7912no—
433D42—7912no—
434#544C2×D7916yescomplemented
435#542—796no—
436#542—796no—
437#542—7912no—
438#541—791no—
439#541—793no—
440#540—793no—
441#540—796no—
442#540—796no—
443#540—796no—
444#540—7912no—
445#540—7912no—
446#540—793no—
447#540—7912no—
448#539—7912no—
449#538—7912no—
450#538—7924no—
451#537—796no—
452#535—796no—
453#535—796no—
454#533C2×D7913yescomplemented
455#532—7912no—
456#532—7912no—
457#532—793no—
458C2×#127—793no—
459#529—7912no—
460#529—7912no—
461#529—7912no—
462#529—7912no—
463C2×#125C2×D7913yescomplemented
464#525—7924no—
465#525—796no—
466C2×#123—7912no—
467C2×#121—796no—
468C2×#121—7912no—
469#520—792no—
470#520—794no—
471#520—796no—
472#520—796no—
473#520C2×D7912yes—
474#519—792no—
475#518—796no—
476#518—7912no—
477#518—796no—
478C4×#41—791no—
479C4×#41—794no—
480C4×#41—793no—
481C4×#41—796no—
482C4×#41—793no—
483C4×#41C2×D7911yescharacteristic
484C2×C4×D4—7912no—
485C2×C4×D4—796no—
486C2×#117—793no—
487C2×#117—793no—
488H(5,𝔽2)—15816no—
489C2×#41—7924no—
490C2×#41—794no—
491C2×#41—791no—
492C2×#41—793no—
493C2×#41—793no—
494C2×#41—796no—
495C2×#41—1588no—
496C2×#41C22×D7911yescharacteristic
497C22×Q8—791no—
498C22×D4—7912no—
499C22×D4—793no—
500C22×D4—7912no—
501C22×D4—7912no—
502C22×D4—796no—
503C23×C4—7912no—
504C23×C4—793no—
505C4⋊Q8—791no—
506C4⋊Q8C22×D7916yes—
507C4⋊Q8C22×D79112yes—
508#127—793no—
509#127—796no—
510#127—7912no—
511#127—7912no—
512#126—794no—
513#126—7912no—
514#126—7912no—
515#126—7924no—
516#126—7912no—
517#125—794no—
518#125—7912no—
519#125C22×D7913yes—
520#125C22×D7916yes—
521#125C22×D79112yes—
522#125C22×D79112yes—
523#125C22×D7911yescharacteristic
524#124—7912no—
525#124—7912no—
526#124—7924no—
527#124—796no—
528#124—7912no—
529#123—7912no—
530#123—7924no—
531#123—7924no—
532#123—7924no—
533#123—7912no—
534#123—7924no—
535#123—7912no—
536#123—7912no—
537#123—7912no—
538C22⋊Q8—7912no—
539C22⋊Q8—7912no—
540C22⋊Q8—792no—
541C22⋊Q8—796no—
542C22⋊Q8—7912no—
543C22⋊Q8C22×D79124yes—
544C22⋊Q8C22×D79112yes—
545#121—7924no—
546#121—7912no—
547#121—796no—
548#121—7912no—
549#121—7924no—
550#121—7912no—
551#121—7912no—
552#121—7924no—
553#121—7912no—
554#121—7924no—
555#121—796no—
556#121—7912no—
557#121—7912no—
558#121—7912no—
559#121—7912no—
560#121—7924no—
561#120—7924no—
562#120—7924no—
563#120—7912no—
564C4×Q8—792no—
565C4×Q8—792no—
566C4×Q8—796no—
567C4×Q8—796no—
568C4×Q8—796no—
569C4×Q8C22×D7914yes—
570C4×Q8C22×D7912yes—
571C4×Q8C22×D79112yes—
572C4×D4—796no—
573C4×D4—7924no—
574C4×D4—7912no—
575C4×D4—7912no—
576C4×D4—796no—
577C4×D4—7912no—
578C4×D4—7912no—
579C4×D4—796no—
580C4×D4—796no—
581C4×D4—7924no—
582C4×D4—7924no—
583C4×D4—7912no—
584C4×D4—7912no—
585C4×D4—7912no—
586C4×D4—7912no—
587C4×D4—7912no—
588C4×D4—796no—
589C4×D4—7912no—
590C4×D4—7912no—
591C4×D4—7912no—
592C4×D4C22×D79112yes—
593C4×D4C22×D7916yes—
594#117—793no—
595#117—796no—
596#117—7912no—
597#117—7924no—
598#117—796no—
599#117—791no—
600#117—793no—
601#117—793no—
602#117—793no—
603#117—796no—
604#117—796no—
605#117—7912no—
606#117C22×D7913yes—
607#117C22×D7916yes—
608C2×C4⋊C4—796no—
609C2×C4⋊C4—796no—
610C2×C4⋊C4—7912no—
611C2×C4⋊C4C22×D7916yes—
612C2×C4⋊C4C22×D79112yes—
613C2×C22⋊C4—796no—
614C2×C22⋊C4—7912no—
615C2×C22⋊C4—7912no—
616C2×C22⋊C4—796no—
617C2×C22⋊C4—7924no—
618C2×C42—793no—
619C2×C42—796no—
620C2×C42—7912no—
621C2×C42C22×D7913yes—
622C24—7912no—
623C24—793no—
624#41—63224no—
625#41—1584no—
626#41—15816no—
627#41—15812no—
628#41—15812no—
629#41—15824no—
630#41#1192962518yescomplemented
631C2×Q8—793no—
632C2×Q8—792no—
633C2×Q8—1584no—
634C2×Q8C23×D79112yes—
635C2×Q8C23×D7911yescharacteristic
636C2×D4—796no—
637C2×D4—7912no—
638C2×D4—7912no—
639C2×D4—7924no—
640C2×D4—7912no—
641C2×D4—7924no—
642C2×D4—7912no—
643C2×D4—796no—
644C2×D4—7912no—
645C2×D4—793no—
646C2×D4—63212no—
647C2×D4—63212no—
648C2×D4—15812no—
649C2×D4—15848no—
650C2×D4—15824no—
651C2×D4C23×D7913yes—
652C22×C4—796no—
653C22×C4—7912no—
654C22×C4—7912no—
655C22×C4—7912no—
656C22×C4—7924no—
657C22×C4—793no—
658C22×C4—793no—
659C22×C4—7912no—
660C22×C4—793no—
661C22×C4—793no—
662C22×C4—791no—
663C22×C4—63212no—
664C22×C4—15812no—
665C22×C4C23×D7916yes—
666C22×C4C23×D79112yes—
667C22×C4C23×D7913yes—
668C4⋊C4—796no—
669C4⋊C4—792no—
670C4⋊C4—7912no—
671C4⋊C4—796no—
672C4⋊C4—796no—
673C4⋊C4—794no—
674C4⋊C4—796no—
675C4⋊C4—7912no—
676C4⋊C4—794no—
677C4⋊C4—794no—
678C4⋊C4C23×D79112yes—
679C4⋊C4C23×D7916yes—
680C4⋊C4C23×D7916yes—
681C4⋊C4C23×D79112yes—
682C4⋊C4C23×D79124yes—
683C4⋊C4C23×D7912yes—
684C4⋊C4C23×D79112yes—
685C4⋊C4C23×D7914yes—
686C22⋊C4—796no—
687C22⋊C4—792no—
688C22⋊C4—796no—
689C22⋊C4—7924no—
690C22⋊C4—7912no—
691C22⋊C4—7912no—
692C22⋊C4—7912no—
693C22⋊C4—796no—
694C22⋊C4—796no—
695C22⋊C4—7924no—
696C22⋊C4—7912no—
697C22⋊C4—794no—
698C22⋊C4—7912no—
699C22⋊C4—7912no—
700C22⋊C4—7912no—
701C22⋊C4C23×D79112yes—
702C22⋊C4C23×D7916yes—
703C42—793no—
704C42—791no—
705C42—796no—
706C42—794no—
707C42—7912no—
708C42—7912no—
709C42C23×D7913yes—
710C42C23×D79112yes—
711C42C23×D7911yescharacteristic
712C42C23×D7916yes—
713C23—31612no—
714C23—3166no—
715C23—31612no—
716C23—791no—
717C23—7912no—
718C23—793no—
719C23—1586no—
720C23—15824no—
721C23C24×D7913yes—
722Q8—412no—
723Q8—1586no—
724Q8—1584no—
725Q8C2×#1192962514yes—
726D4—31612no—
727D4—31612no—
728D4—31624no—
729D4—31624no—
730D4—31612no—
731D4—15824no—
732D4—15812no—
733D4—15824no—
734D4—15812no—
735D4—1586no—
736D4C2×#11929625112yes—
737C2×C4—412no—
738C2×C4—46no—
739C2×C4—31612no—
740C2×C4—31624no—
741C2×C4—31612no—
742C2×C4—31612no—
743C2×C4—3166no—
744C2×C4—792no—
745C2×C4—796no—
746C2×C4—793no—
747C2×C4—794no—
748C2×C4—791no—
749C2×C4—1586no—
750C2×C4—1582no—
751C2×C4—1586no—
752C2×C4—1586no—
753C2×C4—1586no—
754C2×C4—15824no—
755C2×C4C2×#11929625112yes—
756C2×C4C24×D7916yes—
757C2×C4C24×D7914yes—
758C2×C4C24×D79112yes—
759C2×C4C24×D7912yes—
760C2×C4C24×D7911yescharacteristic
761C2×C4C24×D7913yes—
762C22—26no—
763C22—6326no—
764C22—63224no—
765C22—1581no—
766C22—1583no—
767C22—15812no—
768C22—15812no—
769C22—1586no—
770C22—15812no—
771C22—1582no—
772C22C22×#1192962516yes—
773C22C25×D7911yescharacteristic
774C4—22no—
775C4—212no—
776C4—26no—
777C4—24no—
778C4—1581no—
779C4—1584no—
780C4—1583no—
781C4—1582no—
782C4—1586no—
783C4C22×#1192962516yes—
784C4C22×#1192962512yes—
785C2—26no—
786C2—3161no—
787C2—31612no—
788C2—3163no—
789C2C23×#1192962511yescharacteristic
790C2#2377821112yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3504C2
hypercenter#3504D79
hypocenterC79#62858
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #23777512C2semidirect
2. #23777433C2semidirect
3. #23777407C2semidirect
4. #23777343C2semidirect
5. #23777324C2semidirect
6. #23777277C2semidirect
7. #23777178C2semidirect
8. #23777138C2semidirect
9. #23777070C2semidirect
10. #23776823C2semidirect
11. #23776792C2semidirect
12. C2×#19099169C2semidirect
13. #23776606C2semidirect
14. #23776599C2semidirect
15. C79×#3504C2semidirect
18. #19099298C22semidirect
19. #19099279C22semidirect
20. #19099266C22semidirect
21. #19099266C22semidirect
22. #19099266C22semidirect
23. #19099261C22semidirect
24. #19099251C22semidirect
25. #19099240C22semidirect
26. #19099235C22semidirect
27. #19099235C22semidirect
28. #19099235C22semidirect
29. #19099225C22semidirect
30. #19099216C22semidirect
31. #19099208C22semidirect
32. #19099204C22semidirect
33. #19099204C22semidirect
34. D4×D316C22semidirect
35. D4×D316C22semidirect
36. #19099187C22semidirect
37. #19099187C22semidirect
38. #19099187C22semidirect
39. #19099176C22semidirect
40. #19099176C22semidirect
41. #19099169C22semidirect
42. #19099169C22semidirect
43. #19099169C22semidirect
44. #19099169C22semidirect
45. #19099169C22semidirect
46. #19099169C22semidirect
47. #19099169C22semidirect
48. #19099169C22semidirect
49. #19099162C22semidirect
50. #19099153C22semidirect
51. #19099153C22semidirect
52. #19099144C22semidirect
53. #19099132C22semidirect
54. #19099132C22semidirect
55. #19099114C22semidirect
56. #19099114C22semidirect
57. #19099113C22semidirect
58. C2×#14579158C22semidirect
59. #19099100C22semidirect
60. #19099100C22semidirect
61. #19099098C22semidirect
62. #19099098C22semidirect
63. #19099076C22semidirect
64. #19099075C22semidirect
65. C2×#14579146C22semidirect
66. C2×#14579136C22semidirect
67. C2×#14579136C22semidirect
68. #19099045C22semidirect
69. #19099045C22semidirect
70. #19099044C22semidirect
71. #19099042C22semidirect
72. #19099039C22semidirect
73. #19099037C22semidirect
74. #19099035C22semidirect
75. #19099035C22semidirect
77. C4×#11929625C22semidirect
78. C4×#11929624C22semidirect
79. #19099031C22semidirect
80. #19099031C22semidirect
81. C2×#14579123C22semidirect
82. C4×D4×D79C22semidirect
83. C2×#14579118C22semidirect
84. #117×D79C22semidirect
85. #557×C79C22semidirect
86. #554×C79C22semidirect
87. #544×C79C22semidirect
88. #533×C79C22semidirect
89. C2×#125×C79C22semidirect
296. #41×C79#41semidirect
402. #3504D79semidirect
411. C79#62858semidirect
415. #557C2×D79semidirect
417. #554C2×D79semidirect
434. #544C2×D79semidirect
454. #533C2×D79semidirect
463. C2×#125C2×D79semidirect
630. #41#11929625semidirect

Maximal subgroups

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

subgroupindex
#237775122
#237774332
#237774072
#237773432
#237773242
#237772772
#237771782
#237771382
#237770702
#237768232
#237767922
C2×#190991692
#237766062
#237765992
C79×#35042
#6285879