Finite Group Databasebeta

← #35197446

Subgroups — #35197446

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#23777498C214yesmaximal, complemented
2#23777419C2112yesmaximal, complemented
3#23777397C214yesmaximal, complemented
4#23777325C2112yesmaximal, complemented
5#23777320C213yesmaximal, complemented
6#23777274C213yesmaximal, complemented
7#23777226C211yesmaximal, characteristic, complemented
8#23777132C216yesmaximal, complemented
9#23777062C212yesmaximal, complemented
10#23776813C216yesmaximal, complemented
11#23776789C213yesmaximal, complemented
12C2×#19099167C213yesmaximal, complemented
13H(5,𝔽2)×Dic79C212yesmaximal, complemented
14#23776599C211yesmaximal, characteristic, complemented
15C79×#3498C211yesmaximal, characteristic, complemented
16C2×#41×D79C2211yescharacteristic
17#19099299C22112yescomplemented
18#19099289C2214yescomplemented
19#19099277C22112yescomplemented
20#19099272C22112yescomplemented
21#19099265C22112yescomplemented
22#19099260C22112yescomplemented
23#19099259C22112yescomplemented
24#19099256C22124yescomplemented
25#19099253C22112yescomplemented
26#19099244C22124yescomplemented
27#19099233C22112yescomplemented
28#19099232C2214yescomplemented
29#19099220C2214yescomplemented
30#19099213C22112yescomplemented
31#19099207C22112yescomplemented
32#19099207C22124yescomplemented
33#19099200C22124yescomplemented
34D4×C22⋊D79C22112yescomplemented
35#19099191C2216yescomplemented
36#19099182C2216yescomplemented
37#19099182C2216yescomplemented
38#19099180C22112yescomplemented
39#19099174C2211yescharacteristic, complemented
40#19099174C2213yescomplemented
41#19099167C2213yescomplemented
42#19099167C2213yescomplemented
43#19099167C2216yescomplemented
44#19099167C2216yescomplemented
45#19099167C22112yescomplemented
46#19099167C2216yescomplemented
47#19099167C22112yescomplemented
48#19099166C22112yescomplemented
49#19099158C22112yescomplemented
50#19099150C22112yescomplemented
51#19099148C22124yescomplemented
52#19099141C2216yescomplemented
53#19099130C2216yescomplemented
54#19099120C2213yescomplemented
55#19099111C22112yescomplemented
56#19099108C22112yescomplemented
57#19099094C22112yescomplemented
58#19099093C22112yescomplemented
59#19099093C22112yescomplemented
60#19099092C22112yescomplemented
61C2×#14579153C2213yescomplemented
62#19099070C2216yescomplemented
63#19099069C22124yescomplemented
64C2×#14579142C22112yescomplemented
65C2×#14579133C22112yescomplemented
66C2×#14579132C2216yescomplemented
67#19099046C2212yes—
68#19099046C2216yescomplemented
69#19099046C2214yescomplemented
70#19099045C2212yescomplemented
71#19099042C2216yescomplemented
72#19099039C2212yescomplemented
73#19099038C22112yescomplemented
74#19099038C2216yescomplemented
75#19099035C2216yescomplemented
76#41×Dic79C2211yescharacteristic
77#41×Dic79C2216yescomplemented
78#41×Dic79C2214yescomplemented
79C4×#11929624C2213yescomplemented
80#19099031C2213yescomplemented
81C2×D4×Dic79C2216yescomplemented
82C2×D4×Dic79C22112yescomplemented
83C2×#14579118C2213yescomplemented
84#117×D79C2213yescomplemented
85C2×H(5,𝔽2)×C79C2212yes—
86#550×C79C2214yescomplemented
87D42×C79C22112yescomplemented
88#535×C79C2216yescomplemented
89#532×C79C2213yescomplemented
90C2×#127×C79C2213yescomplemented
91C4×#41×C79C2211yescharacteristic
92C2×#11929625C2311yescharacteristic
93C2×#11929624C2313yes—
94C2×#11929623C2313yes—
95C2×#11929623C23124yes—
96#41×D79—28no—
97C2×Q8×D79C2311yescharacteristic
98C22×C22⋊D79C23112yes—
99C2×D4×D79C2313yes—
100C23×Dic79C23112yes—
101C22×C4×D79C2313yes—
102#14579161C2316yes—
103#14579160C23112yes—
104#14579157C23112yes—
105#14579156C2314yes—
106#14579156C23112yes—
107#14579154C23112yes—
108#14579154C23124yes—
109#14579154C23112yes—
110#14579153C2313yes—
111#14579153C2311yescharacteristic
112#14579153C2316yes—
113#14579153C23112yes—
114#14579152C23112yes—
115#14579151C2314yes—
116#14579151C23112yes—
117#14579148C23124yes—
118#14579148C23112yes—
119#14579147C23112yes—
120#14579147C23112yes—
121#14579145C23112yes—
122#14579145C23112yes—
123#14579143C23124yes—
124#14579142C23124yes—
125#14579142C23112yes—
126#14579142C23112yes—
127#14579142C23112yes—
128#14579142C23124yes—
129#14579142C23124yes—
130#14579140C23112yes—
131#14579140C23112yes—
132#14579138C23124yes—
133#14579138C23112yes—
134#14579138C23112yes—
135#14579137C2316yes—
136#14579137C2312yes—
137#14579135C23112yes—
138#14579133C23124yes—
139#14579133C23124yes—
140#14579133C23112yes—
141#14579133C23112yes—
142#14579133C23124yes—
143#14579133C23124yes—
144#14579132C23112yes—
145#14579132C23124yes—
146#14579132C2316yes—
147#14579132C23112yes—
148#14579132C23112yes—
149#14579132C2316yes—
150#14579130C23124yes—
151#14579129C23112yes—
152Q8×Dic79C2312yes—
153Q8×Dic79C2316yes—
154Q8×Dic79C2314yes—
155Q8×Dic79C2312yes—
156C4×Dic158C23112yes—
157C4×Dic158C2316yes—
158#14579126C2316yes—
159C4×D316C2316yes—
160D4×Dic79C23112yes—
161D4×Dic79C23112yes—
162D4×Dic79C23112yes—
163D4×Dic79C2316yes—
164D4×Dic79C23112yes—
165D4×Dic79C23112yes—
166D4×Dic79C2316yes—
167D4×Dic79C23112yes—
168D4×Dic79C23124yes—
169D4×Dic79C23124yes—
170D4×Dic79C23112yes—
171D4×Dic79C23112yes—
172D4×Dic79C2316yes—
173#14579123C2316yes—
174C4×C22⋊D79C23112yes—
175C4×C22⋊D79C23112yes—
176C4×C22⋊D79C23112yes—
177(C22⋊D79)⋊C4C23112yes—
178(C22⋊D79)⋊C4C23124yes—
179#14579120C23112yes—
180#14579120C2316yes—
181#14579120C23112yes—
182#14579120C2313yes—
183#14579119C2316yes—
184#14579118C2311yescharacteristic
185#14579118C2313yes—
186#14579118C2313yes—
187#14579118C2313yes—
188#14579118C2316yes—
189#14579118C2316yes—
190#14579117C2316yes—
191#14579117C23124yes—
192C2×C4⋊Dic79C2316yes—
193C2×C4⋊Dic79C23112yes—
194C2×Dic79⋊C4C2316yes—
195C2×Dic79⋊C4C23112yes—
196C4⋊C4×D79C2316yes—
197C2×C22⋊Dic79C23112yes—
198C2×C22⋊Dic79C23124yes—
199C2×C22⋊Dic79C23112yes—
200C2×(C2×D79)⋊C4C2316yes—
201C22⋊C4×D79C2316yes—
202C2×C4×Dic79C2313yes—
203C2×C4×Dic79C23112yes—
204C42×D79C2316yes—
205H(5,𝔽2)×C79—216no—
206C2×#41×C79C2316yes—
207C2×#41×C79C2314yes—
208C2×#41×C79C2311yescharacteristic
209C22×D4×C79C23112yes—
210C22×D4×C79C2316yes—
211C22×D4×C79C23112yes—
212C4⋊Q8×C79C2311yescharacteristic
213#127×C79C2313yes—
214#127×C79C23112yes—
215#127×C79C2316yes—
216#124×C79C2316yes—
217#121×C79C23112yes—
218#121×C79C23112yes—
219#121×C79C23112yes—
220#120×C79C23124yes—
221C4×Q8×C79C2312yes—
222C4×D4×C79C2316yes—
223C4×D4×C79C23112yes—
224#117×C79C2313yes—
225C2×C42×C79C2313yes—
226C23×D79C2413yes—
227#11929625—24no—
228#11929624—212no—
229#11929623—212no—
230#11929623—824no—
231C2×Dic158C2413yes—
232C2×Dic158C24112yes—
233Q8×D79—24no—
234C2×D316C2413yes—
235C2×C22⋊D79—812no—
236C2×C22⋊D79C2416yes—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C24124yes—
239C2×C22⋊D79C24112yes—
240D4×D79—212no—
241C22×Dic79—812no—
242C22×Dic79C2413yes—
243C22×Dic79C24112yes—
244C22×Dic79C24124yes—
245C22×Dic79C2416yes—
246C22×Dic79C24112yes—
247C22×Dic79C24112yes—
248C2×C4×D79—212no—
249C2×C4×D79C2413yes—
250C2×C4×D79C2413yes—
251C2×C4×D79C2413yes—
252C2×C4×D79C2411yescharacteristic
253C2×C4×D79C24112yes—
254C4⋊Dic79C2416yes—
255C4⋊Dic79C2416yes—
256C4⋊Dic79C24112yes—
257C4⋊Dic79C24112yes—
258C4⋊Dic79C2412yes—
259C4⋊Dic79C2414yes—
260C4⋊Dic79C24112yes—
261Dic79⋊C4C2416yes—
262Dic79⋊C4C2412yes—
263Dic79⋊C4C24112yes—
264Dic79⋊C4C24124yes—
265Dic79⋊C4C2416yes—
266Dic79⋊C4C2416yes—
267Dic79⋊C4C24112yes—
268Dic79⋊C4C2414yes—
269Dic79⋊C4C2414yes—
270C22⋊Dic79C2416yes—
271C22⋊Dic79C24112yes—
272C22⋊Dic79C24112yes—
273C22⋊Dic79C24124yes—
274C22⋊Dic79C24112yes—
275C22⋊Dic79C24112yes—
276C22⋊Dic79C24124yes—
277C22⋊Dic79C24112yes—
278(C2×D79)⋊C4C2416yes—
279(C2×D79)⋊C4C2412yes—
280(C2×D79)⋊C4C2416yes—
281(C2×D79)⋊C4C2416yes—
282(C2×D79)⋊C4C24112yes—
283(C2×D79)⋊C4C2414yes—
284C4×Dic79C2413yes—
285C4×Dic79C24112yes—
286C4×Dic79C2411yescharacteristic
287C4×Dic79C2416yes—
288C4×Dic79C2414yes—
289C4×Dic79C24112yes—
290C4×Dic79C24112yes—
291C24×C79C24112yes—
292#41×C79—216no—
293#41×C79—224no—
294#41×C79#4118yescomplemented
295C2×Q8×C79C2412yes—
296C2×Q8×C79C2411yescharacteristic
297C2×D4×C79—248no—
298C2×D4×C79—224no—
299C2×D4×C79—812no—
300C2×D4×C79C24112yes—
301C2×D4×C79C24112yes—
302C2×D4×C79C2416yes—
303C2×D4×C79C24124yes—
304C2×D4×C79C24112yes—
305C2×D4×C79C2413yes—
306C22×C4×C79C24112yes—
307C22×C4×C79C2416yes—
308C22×C4×C79C2413yes—
309C4⋊C4×C79C2416yes—
310C4⋊C4×C79C2414yes—
311C22⋊C4×C79C2416yes—
312C22⋊C4×C79C24112yes—
313C22⋊C4×C79C24112yes—
314C42×C79C2411yescharacteristic
315C42×C79C2413yes—
316C42×C79C2416yes—
317C23×C79—224no—
318C23×C79—412no—
319C23×C79—412no—
320C23×C79C25112yes—
321C23×C79C2513yes—
322C22×D79—26no—
323C22×D79—46no—
324C22×D79C2511yescharacteristic
325C22×D79C2513yes—
326Q8×C79—24no—
327Q8×C79C2×#4114yes—
328D4×C79—224no—
329D4×C79—224no—
330D4×C79—212no—
331D4×C79—424no—
332D4×C79—412no—
333D4×C79C2×#41112yes—
334C2×C4×C79—224no—
335C2×C4×C79—46no—
336C2×C4×C79C2×#41112yes—
337C2×C4×C79C2514yes—
338C2×C4×C79C2516yes—
339C2×C4×C79C2512yes—
340C2×C4×C79C2513yes—
341C2×C4×C79C2511yescharacteristic
342C22⋊D79—212no—
343C22⋊D79—412no—
344C22⋊D79—424no—
345C22⋊D79—412no—
346C2×Dic79—26no—
347C2×Dic79—412no—
348C2×Dic79—46no—
349C2×Dic79—412no—
350C2×Dic79—424no—
351C2×Dic79—412no—
352C2×Dic79C2512yes—
353C2×Dic79C2516yes—
354C2×Dic79C2514yes—
355C2×Dic79C2513yes—
356C2×Dic79C25112yes—
357C2×Dic79C2511yescharacteristic
358D316—26no—
359C4×D79—22no—
360C4×D79—26no—
361C4×D79—26no—
362C4×D79—26no—
363C4×D79—412no—
364Dic158—26no—
365Dic158—412no—
366C22×C79—26no—
367C22×C79—212no—
368C22×C79—212no—
369C22×C79—212no—
370C22×C79—824no—
371C22×C79C22×#4116yes—
372C22×C79C2611yescharacteristic
373C2×D79—23no—
374C2×D79—21no—
375C2×D79—22no—
376C2×D79—26no—
377C2×D79—86no—
378C4×C79—24no—
379C4×C79—22no—
380C4×C79—26no—
381C4×C79C22×#4116yes—
382C4×C79C22×#4112yes—
383Dic79—23no—
384Dic79—21no—
385Dic79—24no—
386Dic79—212no—
387Dic79—26no—
388Dic79—22no—
389#62858—791nomaximal, Sylow
390C2×C79—26no—
391C2×C79—412no—
392C2×C79C23×#4111yescharacteristic
393C2×C79H(7,𝔽2)12yes—
394D79—43no—
395D79—41no—
396#3524—794no—
397#3519—7912no—
398#3517—794no—
399#3513—7912no—
400#3512—793no—
401#3508—793no—
402#3504—791no—
403#3498D7911yescharacteristic, complemented
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)C2×D7912yes—
413C22×#41—791no—
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—7912no—
426#550C2×D7914yescomplemented
427#548—794no—
428#547—7912no—
429#546—7912no—
430#546—7924no—
431#546—7924no—
432D42—7912no—
433D42C2×D79112yescomplemented
434#544—796no—
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#535C2×D7916yescomplemented
454#533—793no—
455#532—7912no—
456#532—7912no—
457#532C2×D7913yescomplemented
458C2×#127C2×D7913yescomplemented
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—796no—
471#520—794no—
472#520—792no—
473#520—796no—
474#519—792no—
475#518—796no—
476#518—7912no—
477#518—796no—
478C4×#41—791no—
479C4×#41—796no—
480C4×#41—794no—
481C4×#41—793no—
482C4×#41—793no—
483C4×#41C2×D7911yescharacteristic
484C2×C4×D4—796no—
485C2×C4×D4—7912no—
486C2×#117—793no—
487C2×#117—793no—
488H(5,𝔽2)—216no—
489C2×#41—791no—
490C2×#41—7924no—
491C2×#41—793no—
492C2×#41—793no—
493C2×#41—1588no—
494C2×#41C22×D7916yes—
495C2×#41C22×D7914yes—
496C2×#41C22×D7911yescharacteristic
497C22×Q8—791no—
498C22×D4—7912no—
499C22×D4—793no—
500C22×D4C22×D7916yes—
501C22×D4C22×D79112yes—
502C22×D4C22×D79112yes—
503C23×C4—7912no—
504C23×C4—793no—
505C4⋊Q8—7912no—
506C4⋊Q8—796no—
507C4⋊Q8C22×D7911yescharacteristic
508#127—7912no—
509#127C22×D7913yes—
510#127C22×D7916yes—
511#127C22×D79112yes—
512#126—794no—
513#126—7912no—
514#126—7912no—
515#126—7924no—
516#126—7912no—
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—7924no—
526#124—7912no—
527#124—7912no—
528#124C22×D7916yes—
529#123—7912no—
530#123—7924no—
531#123—7924no—
532#123—7924no—
533#123—7912no—
534#123—7912no—
535#123—7912no—
536#123—7924no—
537#123—7912no—
538C22⋊Q8—792no—
539C22⋊Q8—796no—
540C22⋊Q8—7912no—
541C22⋊Q8—7912no—
542C22⋊Q8—7912no—
543C22⋊Q8—7924no—
544C22⋊Q8—7912no—
545#121—796no—
546#121—7912no—
547#121—7924no—
548#121—7912no—
549#121—7912no—
550#121—7924no—
551#121—7912no—
552#121—7924no—
553#121—796no—
554#121—7924no—
555#121—7912no—
556#121—7924no—
557#121—7912no—
558#121C22×D79112yes—
559#121C22×D79112yes—
560#121C22×D79112yes—
561#120—7924no—
562#120—7912no—
563#120C22×D79124yes—
564C4×Q8—792no—
565C4×Q8—792no—
566C4×Q8—796no—
567C4×Q8—794no—
568C4×Q8—796no—
569C4×Q8—796no—
570C4×Q8—7912no—
571C4×Q8C22×D7912yes—
572C4×D4—796no—
573C4×D4—7912no—
574C4×D4—796no—
575C4×D4—7912no—
576C4×D4—7912no—
577C4×D4—7912no—
578C4×D4—7912no—
579C4×D4—7924no—
580C4×D4—7912no—
581C4×D4—7912no—
582C4×D4—796no—
583C4×D4—7912no—
584C4×D4—7924no—
585C4×D4—7912no—
586C4×D4—7912no—
587C4×D4—7912no—
588C4×D4—796no—
589C4×D4—7912no—
590C4×D4—7924no—
591C4×D4—796no—
592C4×D4C22×D7916yes—
593C4×D4C22×D79112yes—
594#117—793no—
595#117—796no—
596#117—7912no—
597#117—7912no—
598#117—796no—
599#117—796no—
600#117—7924no—
601#117—791no—
602#117—793no—
603#117—793no—
604#117—793no—
605#117—796no—
606#117—796no—
607#117C22×D7913yes—
608C2×C4⋊C4—796no—
609C2×C4⋊C4—796no—
610C2×C4⋊C4—7912no—
611C2×C4⋊C4—7912no—
612C2×C4⋊C4—796no—
613C2×C22⋊C4—7912no—
614C2×C22⋊C4—7924no—
615C2×C22⋊C4—7912no—
616C2×C22⋊C4—796no—
617C2×C22⋊C4—796no—
618C2×C42—793no—
619C2×C42—7912no—
620C2×C42—796no—
621C2×C42C22×D7913yes—
622C24—793no—
623C24C23×D79112yes—
624#41—216no—
625#41—224no—
626#41—63224no—
627#41—1584no—
628#41—15812no—
629#41—15812no—
630#41#1192962318yescomplemented
631C2×Q8—7912no—
632C2×Q8—793no—
633C2×Q8—1584no—
634C2×Q8C23×D7912yes—
635C2×Q8C23×D7911yescharacteristic
636C2×D4—248no—
637C2×D4—224no—
638C2×D4—812no—
639C2×D4—7912no—
640C2×D4—7912no—
641C2×D4—7924no—
642C2×D4—796no—
643C2×D4—793no—
644C2×D4—63212no—
645C2×D4—15812no—
646C2×D4C23×D79112yes—
647C2×D4C23×D7916yes—
648C2×D4C23×D79112yes—
649C2×D4C23×D79124yes—
650C2×D4C23×D79112yes—
651C2×D4C23×D7913yes—
652C22×C4—796no—
653C22×C4—7912no—
654C22×C4—7912no—
655C22×C4—7912no—
656C22×C4—7924no—
657C22×C4—7912no—
658C22×C4—793no—
659C22×C4—793no—
660C22×C4—793no—
661C22×C4—793no—
662C22×C4—791no—
663C22×C4—63212no—
664C22×C4—15812no—
665C22×C4C23×D79112yes—
666C22×C4C23×D7916yes—
667C22×C4C23×D7913yes—
668C4⋊C4—796no—
669C4⋊C4—792no—
670C4⋊C4—7912no—
671C4⋊C4—796no—
672C4⋊C4—796no—
673C4⋊C4—7924no—
674C4⋊C4—7912no—
675C4⋊C4—794no—
676C4⋊C4—794no—
677C4⋊C4—796no—
678C4⋊C4—7912no—
679C4⋊C4—796no—
680C4⋊C4—7912no—
681C4⋊C4—792no—
682C4⋊C4—794no—
683C4⋊C4—7912no—
684C4⋊C4C23×D7916yes—
685C4⋊C4C23×D7914yes—
686C22⋊C4—796no—
687C22⋊C4—7912no—
688C22⋊C4—7924no—
689C22⋊C4—7912no—
690C22⋊C4—7912no—
691C22⋊C4—7912no—
692C22⋊C4—7924no—
693C22⋊C4—7912no—
694C22⋊C4—792no—
695C22⋊C4—796no—
696C22⋊C4—796no—
697C22⋊C4—796no—
698C22⋊C4—794no—
699C22⋊C4—7912no—
700C22⋊C4C23×D7916yes—
701C22⋊C4C23×D79112yes—
702C22⋊C4C23×D79112yes—
703C42—796no—
704C42—793no—
705C42—791no—
706C42—794no—
707C42—7912no—
708C42—7912no—
709C42—7912no—
710C42C23×D7913yes—
711C42C23×D7911yescharacteristic
712C42C23×D7916yes—
713C23—224no—
714C23—412no—
715C23—412no—
716C23—3166no—
717C23—791no—
718C23—793no—
719C23—1586no—
720C23C24×D79112yes—
721C23C24×D7913yes—
722Q8—24no—
723Q8—31612no—
724Q8—1586no—
725Q8C2×#1192962314yes—
726D4—224no—
727D4—224no—
728D4—212no—
729D4—412no—
730D4—424no—
731D4—31612no—
732D4—31624no—
733D4—31612no—
734D4—15812no—
735D4—1586no—
736D4C2×#11929623112yes—
737C2×C4—224no—
738C2×C4—46no—
739C2×C4—31612no—
740C2×C4—3166no—
741C2×C4—31612no—
742C2×C4—31612no—
743C2×C4—31624no—
744C2×C4—31612no—
745C2×C4—792no—
746C2×C4—796no—
747C2×C4—793no—
748C2×C4—794no—
749C2×C4—7912no—
750C2×C4—791no—
751C2×C4—1586no—
752C2×C4—1582no—
753C2×C4—1586no—
754C2×C4—1586no—
755C2×C4—1586no—
756C2×C4C2×#11929623112yes—
757C2×C4C24×D7914yes—
758C2×C4C24×D7916yes—
759C2×C4C24×D7912yes—
760C2×C4C24×D7913yes—
761C2×C4C24×D7911yescharacteristic
762C22—26no—
763C22—212no—
764C22—212no—
765C22—212no—
766C22—824no—
767C22—6326no—
768C22—1581no—
769C22—1583no—
770C22—1586no—
771C22—1582no—
772C22C22×#1192962316yes—
773C22C25×D7911yescharacteristic
774C4—24no—
775C4—22no—
776C4—26no—
777C4—1581no—
778C4—1583no—
779C4—1586no—
780C4—1582no—
781C4—15812no—
782C4—1584no—
783C4C22×#1192962316yes—
784C4C22×#1192962312yes—
785C2—26no—
786C2—412no—
787C2—3161no—
788C2—3163no—
789C2C23×#1192962311yescharacteristic
790C2#2377821012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3498C2
hypercenter#3498D79
hypocenterC79#62858
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #23777498C2semidirect
2. #23777419C2semidirect
3. #23777397C2semidirect
4. #23777325C2semidirect
5. #23777320C2semidirect
6. #23777274C2semidirect
7. #23777226C2semidirect
8. #23777132C2semidirect
9. #23777062C2semidirect
10. #23776813C2semidirect
11. #23776789C2semidirect
12. C2×#19099167C2semidirect
13. H(5,𝔽2)×Dic79C2semidirect
14. #23776599C2semidirect
15. C79×#3498C2semidirect
17. #19099299C22semidirect
18. #19099289C22semidirect
19. #19099277C22semidirect
20. #19099272C22semidirect
21. #19099265C22semidirect
22. #19099260C22semidirect
23. #19099259C22semidirect
24. #19099256C22semidirect
25. #19099253C22semidirect
26. #19099244C22semidirect
27. #19099233C22semidirect
28. #19099232C22semidirect
29. #19099220C22semidirect
30. #19099213C22semidirect
31. #19099207C22semidirect
32. #19099207C22semidirect
33. #19099200C22semidirect
34. D4×C22⋊D79C22semidirect
35. #19099191C22semidirect
36. #19099182C22semidirect
37. #19099182C22semidirect
38. #19099180C22semidirect
39. #19099174C22semidirect
40. #19099174C22semidirect
41. #19099167C22semidirect
42. #19099167C22semidirect
43. #19099167C22semidirect
44. #19099167C22semidirect
45. #19099167C22semidirect
46. #19099167C22semidirect
47. #19099167C22semidirect
48. #19099166C22semidirect
49. #19099158C22semidirect
50. #19099150C22semidirect
51. #19099148C22semidirect
52. #19099141C22semidirect
53. #19099130C22semidirect
54. #19099120C22semidirect
55. #19099111C22semidirect
56. #19099108C22semidirect
57. #19099094C22semidirect
58. #19099093C22semidirect
59. #19099093C22semidirect
60. #19099092C22semidirect
61. C2×#14579153C22semidirect
62. #19099070C22semidirect
63. #19099069C22semidirect
64. C2×#14579142C22semidirect
65. C2×#14579133C22semidirect
66. C2×#14579132C22semidirect
68. #19099046C22semidirect
69. #19099046C22semidirect
70. #19099045C22semidirect
71. #19099042C22semidirect
72. #19099039C22semidirect
73. #19099038C22semidirect
74. #19099038C22semidirect
75. #19099035C22semidirect
77. #41×Dic79C22semidirect
78. #41×Dic79C22semidirect
79. C4×#11929624C22semidirect
80. #19099031C22semidirect
81. C2×D4×Dic79C22semidirect
82. C2×D4×Dic79C22semidirect
83. C2×#14579118C22semidirect
84. #117×D79C22semidirect
86. #550×C79C22semidirect
87. D42×C79C22semidirect
88. #535×C79C22semidirect
89. #532×C79C22semidirect
90. C2×#127×C79C22semidirect
294. #41×C79#41semidirect
403. #3498D79semidirect
411. C79#62858semidirect
426. #550C2×D79semidirect
433. D42C2×D79semidirect
453. #535C2×D79semidirect
457. #532C2×D79semidirect
458. C2×#127C2×D79semidirect
630. #41#11929623semidirect

Maximal subgroups

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

subgroupindex
#237774982
#237774192
#237773972
#237773252
#237773202
#237772742
#237772262
#237771322
#237770622
#237768132
#237767892
C2×#190991672
H(5,𝔽2)×Dic792
#237765992
C79×#34982
#6285879