Finite Group Databasebeta

← #35197364

Subgroups — #35197364

Order 20224.

7066 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777511C214yesmaximal, complemented
2#23777509C214yesmaximal, complemented
3#23777485C214yesmaximal, complemented
4#23777479C214yesmaximal, complemented
5#23777406C214yesmaximal, complemented
6#23777400C214yesmaximal, complemented
7#23777395C214yesmaximal, complemented
8#23777393C214yesmaximal, complemented
9#23777245C216yesmaximal, complemented
10#23777206C211yesmaximal, characteristic, complemented
11#23777167C211yesmaximal, characteristic, complemented
12#23777103C216yesmaximal, complemented
13#23777059C211yesmaximal, characteristic, complemented
14#23777055C211yesmaximal, characteristic, complemented
15#23776816C216yesmaximal, complemented
16#23776785C216yesmaximal, complemented
17C4×#14579209C211yesmaximal, characteristic, complemented
18C2×#19099045C211yesmaximal, characteristic, complemented
19C4×2−1+4×C79C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21C22×#11929625C2211yescharacteristic
22#19099298C22112yescomplemented
23#19099296C22112yescomplemented
24Q8×Dic158C2214yescomplemented
25#19099292C2214yescomplemented
26#19099289C2214yescomplemented
27#19099289C2214yescomplemented
28#19099285C22112yescomplemented
29#19099276C22112yescomplemented
30#19099273C22112yescomplemented
31#19099268C22112yescomplemented
32#19099263C22112yescomplemented
33#19099261C22112yescomplemented
34#19099257C22112yescomplemented
35#19099257C22112yescomplemented
36#19099254C22112yescomplemented
37#19099252C22112yescomplemented
38#19099235C2214yes—
39#19099235C2214yes—
40#19099234C22112yescomplemented
41#19099232C2214yes—
42#19099232C2214yes—
43#19099232C2214yescomplemented
44Q8×C22⋊D79C2214yescomplemented
45#19099225C2214yes—
46#19099225C2214yes—
47#19099224C2214yes—
48#19099224C2214yes—
49#19099224C2214yescomplemented
50#19099220C2214yescomplemented
51#19099218C22112yescomplemented
52#19099214C22112yescomplemented
53#19099214C22112yescomplemented
54#19099191C2216yes—
55#19099185C2216yescomplemented
56#19099185C2216yescomplemented
57#19099185C22112yescomplemented
58#19099184C22112yescomplemented
59#19099178C2216yescomplemented
60#19099178C2216yescomplemented
61#19099171C2216yescomplemented
62#19099171C2216yescomplemented
63#19099168C22112yescomplemented
64#19099164C2216yescomplemented
65#19099164C2216yescomplemented
66#19099164C22112yescomplemented
67#19099155C2214yes—
68#19099155C22112yes—
69#19099146C22112yes—
70#19099146C22112yes—
71#19099141C2216yes—
72#19099132C2216yes—
73#19099127C2216yes—
74#19099116C2216yes—
75#19099113C22112yescomplemented
76#19099110C22112yescomplemented
77#19099109C2216yes—
78#19099100C22112yescomplemented
79#19099097C22112yescomplemented
80#19099097C22112yescomplemented
81#19099097C22112yescomplemented
82#19099091C22112yescomplemented
83#19099091C22112yescomplemented
84#19099075C2216yes—
85#19099072C22124yes—
86#19099070C2216yes—
87#19099045C2214yes—
88#19099045C2214yes—
89#19099045C2214yes—
90#19099045C2214yes—
91#19099045C2214yescomplemented
92#19099044C2216yes—
93#19099041C2211yescharacteristic
94#19099039C2214yescomplemented
95C4×#11929625C2214yescomplemented
96C4×#11929624C2216yes—
97C2×Q8×Dic79C2211yescharacteristic
98C4×Q8×D79C2214yescomplemented
99C2×C4×D316C2213yes—
100C2×#14579123C2213yes—
101C2×#14579118C2213yes—
102C2×C4⋊C4×D79C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104#520×C79C2216yes—
105#520×C79C2214yescomplemented
106#519×C79C2211yescharacteristic
107#519×C79C2214yescomplemented
108C4×#41×C79C2216yes—
109C4×#41×C79C2214yescomplemented
110C2×C4×Q8×C79C2211yescharacteristic
111C2×C4×Q8×C79C2214yescomplemented
112#14579209—28no—
113C2×#11929625—28no—
114C2×#11929625C2314yes—
115C2×#11929625C2314yes—
116C2×#11929625C2314yes—
117C2×#11929624C2316yes—
118C2×#11929624C23124yes—
119C2×Q8×D79C2314yes—
120C22×D316C2313yes—
121C22×C4×D79C2313yes—
122C22×C4×D79C2316yes—
123#14579161C23112yes—
124#14579160C2316yes—
125#14579160C2316yes—
126#14579160C23112yes—
127#14579159C2316yes—
128#14579158C23112yes—
129#14579157C2316yes—
130#14579157C23112yes—
131#14579156C23112yes—
132#14579156C23112yes—
133#14579155C23112yes—
134#14579155C23112yes—
135#14579155C2314yes—
136#14579155C23112yes—
137#14579154C2314yes—
138#14579154C23112yes—
139#14579153C2314yes—
140#14579153C23112yes—
141#14579153C23112yes—
142#14579152C2316yes—
143#14579152C2316yes—
144#14579152C23112yes—
145#14579151C2314yes—
146#14579151C23112yes—
147#14579150C2316yes—
148#14579150C23112yes—
149#14579149C23112yes—
150#14579149C23112yes—
151#14579149C23112yes—
152#14579148C2316yes—
153#14579147C23112yes—
154#14579147C23112yes—
155#14579146C23112yes—
156#14579146C23112yes—
157#14579146C23124yes—
158#14579145C2314yes—
159#14579144C23112yes—
160#14579144C23112yes—
161#14579144C2314yes—
162#14579144C23112yes—
163#14579143C2314yes—
164#14579143C23112yes—
165#14579143C23124yes—
166#14579142C2314yes—
167#14579141C2316yes—
168#14579141C2316yes—
169#14579140C23112yes—
170#14579140C2314yes—
171#14579140C23112yes—
172#14579139C2314yes—
173#14579139C23112yes—
174#14579139C23124yes—
175#14579138C2314yes—
176#14579138C23112yes—
177#14579137C23112yes—
178#14579137C2316yes—
179#14579137C2316yes—
180#14579136C2316yes—
181#14579136C2316yes—
182#14579136C23112yes—
183#14579136C23112yes—
184#14579135C23112yes—
185#14579135C23112yes—
186#14579135C23112yes—
187#14579135C23112yes—
188#14579135C23112yes—
189#14579134C23112yes—
190#14579134C23112yes—
191#14579134C23124yes—
192#14579133C23112yes—
193#14579133C2314yes—
194#14579132C23112yes—
195#14579132C2316yes—
196#14579132C2316yes—
197#14579131C23112yes—
198#14579129C23112yes—
199Q8×Dic79C2314yes—
200Q8×Dic79C2314yes—
201Q8×Dic79C2314yes—
202Q8×Dic79C2314yes—
203C4×Dic158C2316yes—
204C4×Dic158C2316yes—
205C4×Dic158C23112yes—
206C4×Dic158C23112yes—
207#14579126C23112yes—
208C4×D316C2316yes—
209C4×D316C23112yes—
210C4×D316C2316yes—
211C4×D316C23112yes—
212C4×D316C23112yes—
213C4×D316C23112yes—
214C4×D316C23124yes—
215#14579123C23112yes—
216#14579123C23112yes—
217#14579123C23112yes—
218C4×C22⋊D79C2314yes—
219C4×C22⋊D79C23112yes—
220C4×C22⋊D79C23112yes—
221C4×C22⋊D79C23112yes—
222C4×C22⋊D79C23112yes—
223C4×C22⋊D79C23112yes—
224C4×C22⋊D79C23124yes—
225#14579120C2316yes—
226#14579119C23112yes—
227#14579118C2316yes—
228#14579118C2316yes—
229#14579118C23112yes—
230#14579118C2316yes—
231#14579118C2316yes—
232#14579118C23124yes—
233C2×C4⋊Dic79C2313yes—
234C2×Dic79⋊C4C2313yes—
235C2×Dic79⋊C4C2311yescharacteristic
236C4⋊C4×D79C23112yes—
237C4⋊C4×D79C23112yes—
238C4⋊C4×D79C23112yes—
239C2×(C2×D79)⋊C4C2313yes—
240C2×(C2×D79)⋊C4C2313yes—
241C2×C4×Dic79C2313yes—
242C42×D79C23112yes—
2432−1+4×C79—28no—
244C2×#41×C79C2316yes—
245C2×#41×C79C2314yes—
246C22×Q8×C79C2314yes—
247C22×Q8×C79C2311yescharacteristic
248C4×Q8×C79C2316yes—
249C4×Q8×C79C2316yes—
250C4×Q8×C79C2314yes—
251C4×Q8×C79C2314yes—
252C4×Q8×C79C2314yes—
253C4×Q8×C79C2314yes—
254C4×Q8×C79C23112yes—
255C4×D4×C79C2314yes—
256C4×D4×C79C23112yes—
257C4×D4×C79C2316yes—
258C4×D4×C79C2316yes—
259C4×D4×C79C23112yes—
260#117×C79C23112yes—
261#117×C79C2316yes—
262#117×C79C23112yes—
263C2×C4⋊C4×C79C23112yes—
264C2×C4⋊C4×C79C2313yes—
265C2×C42×C79C2313yes—
266C2×C42×C79C23112yes—
267C23×D79C2413yes—
268#11929625—216no—
269#11929625—216no—
270#11929625—216no—
271#11929624—224no—
272#11929624—824no—
273C2×Dic158C2416yes—
274C2×Dic158C24112yes—
275C2×Dic158C2414yes—
276Q8×D79—216no—
277C2×D316—212no—
278C2×D316C2416yes—
279C2×D316C24112yes—
280C2×D316C24112yes—
281C2×D316C24112yes—
282C2×C22⋊D79C2414yes—
283C2×C22⋊D79C24112yes—
284C2×C22⋊D79C24112yes—
285C2×C22⋊D79C24112yes—
286C2×C22⋊D79C2414yes—
287C22×Dic79C2411yescharacteristic
288C22×Dic79C2411yescharacteristic
289C22×Dic79C2413yes—
290C2×C4×D79—212no—
291C2×C4×D79—86no—
292C2×C4×D79C24112yes—
293C2×C4×D79C2416yes—
294C2×C4×D79C2416yes—
295C2×C4×D79C24112yes—
296C2×C4×D79C24124yes—
297C2×C4×D79C2414yes—
298C4⋊Dic79C24112yes—
299C4⋊Dic79C2416yes—
300C4⋊Dic79C2416yes—
301C4⋊Dic79C2414yes—
302C4⋊Dic79C2414yes—
303C4⋊Dic79C24112yes—
304C4⋊Dic79C2414yes—
305Dic79⋊C4C2416yes—
306Dic79⋊C4C2416yes—
307Dic79⋊C4C24112yes—
308Dic79⋊C4C2411yescharacteristic
309Dic79⋊C4C2411yescharacteristic
310Dic79⋊C4C2411yescharacteristic
311Dic79⋊C4C2411yescharacteristic
312Dic79⋊C4C2414yes—
313Dic79⋊C4C24112yes—
314Dic79⋊C4C24112yes—
315Dic79⋊C4C2414yes—
316Dic79⋊C4C2414yes—
317Dic79⋊C4C2414yes—
318Dic79⋊C4C24112yes—
319Dic79⋊C4C2414yes—
320Dic79⋊C4C2414yes—
321C22⋊Dic79C2414yes—
322C22⋊Dic79C2414yes—
323C22⋊Dic79C2414yes—
324C22⋊Dic79C24112yes—
325C22⋊Dic79C2414yes—
326(C2×D79)⋊C4C2416yes—
327(C2×D79)⋊C4C2416yes—
328(C2×D79)⋊C4C2416yes—
329(C2×D79)⋊C4C2416yes—
330(C2×D79)⋊C4C2414yes—
331(C2×D79)⋊C4C24112yes—
332(C2×D79)⋊C4C24112yes—
333(C2×D79)⋊C4C24112yes—
334(C2×D79)⋊C4C2414yes—
335(C2×D79)⋊C4C24112yes—
336(C2×D79)⋊C4C24112yes—
337(C2×D79)⋊C4C24112yes—
338(C2×D79)⋊C4C2414yes—
339(C2×D79)⋊C4C2414yes—
340C4×Dic79C2414yes—
341C4×Dic79C24112yes—
342C4×Dic79C24112yes—
343C4×Dic79C2416yes—
344C4×Dic79C2416yes—
345#41×C79—216no—
346#41×C79—224no—
347C2×Q8×C79—216no—
348C2×Q8×C79#4118yescomplemented
349C2×Q8×C79C2416yes—
350C2×Q8×C79C2414yes—
351C2×D4×C79C2414yes—
352C2×D4×C79C2416yes—
353C22×C4×C79C24112yes—
354C22×C4×C79C24112yes—
355C22×C4×C79C2411yescharacteristic
356C22×C4×C79C2414yes—
357C22×C4×C79C2413yes—
358C22×C4×C79C2413yes—
359C4⋊C4×C79C24112yes—
360C4⋊C4×C79C2416yes—
361C4⋊C4×C79C24112yes—
362C4⋊C4×C79C2416yes—
363C4⋊C4×C79C2414yes—
364C22⋊C4×C79C2414yes—
365C22⋊C4×C79C24112yes—
366C22⋊C4×C79C2414yes—
367C42×C79C2416yes—
368C42×C79C2414yes—
369C42×C79C2416yes—
370C42×C79C24112yes—
371C42×C79C24112yes—
372C23×C79C2514yes—
373C23×C79C2511yescharacteristic
374C22×D79—26no—
375C22×D79—43no—
376C22×D79—43no—
377C22×D79C2516yes—
378C22×D79C2514yes—
379Q8×C79—212no—
380Q8×C79C2×#41116yes—
381D4×C79—28no—
382D4×C79—212no—
383C2×C4×C79—224no—
384C2×C4×C79—43no—
385C2×C4×C79—412no—
386C2×C4×C79—44no—
387C2×C4×C79—41no—
388C2×C4×C79C2×#41112yes—
389C2×C4×C79C2511yescharacteristic
390C2×C4×C79C2516yes—
391C2×C4×C79C2511yescharacteristic
392C2×C4×C79C2514yes—
393C2×C4×C79C2514yes—
394C2×C4×C79C2514yes—
395C2×C4×C79C2516yes—
396C22⋊D79—28no—
397C22⋊D79—44no—
398C22⋊D79—412no—
399C22⋊D79—412no—
400C22⋊D79—412no—
401C2×Dic79—22no—
402C2×Dic79—43no—
403C2×Dic79—41no—
404C2×Dic79C2511yescharacteristic
405C2×Dic79C2514yes—
406C2×Dic79C2511yescharacteristic
407C2×Dic79C2514yes—
408C2×Dic79C2514yes—
409C2×Dic79C2516yes—
410C2×Dic79C2511yescharacteristic
411C2×Dic79C2511yescharacteristic
412D316—224no—
413D316—212no—
414D316—412no—
415D316—412no—
416C4×D79—212no—
417C4×D79—212no—
418C4×D79—224no—
419C4×D79—424no—
420C4×D79—44no—
421C4×D79—412no—
422Dic158—212no—
423Dic158—44no—
424Dic158—412no—
425C22×C79—21no—
426C22×C79—21no—
427C22×C79—24no—
428C22×C79—24no—
429C22×C79—24no—
430C22×C79C22×#4112yes—
431C22×C79C2611yescharacteristic
432C2×D79—24no—
433C2×D79—26no—
434C2×D79—24no—
435C2×D79—26no—
436C2×D79—26no—
437C2×D79—24no—
438C2×D79—412no—
439C4×C79—24no—
440C4×C79—24no—
441C4×C79—26no—
442C4×C79—21no—
443C4×C79—24no—
444C4×C79—21no—
445C4×C79C22×#41112yes—
446Dic79—24no—
447Dic79—21no—
448Dic79—21no—
449Dic79—24no—
450Dic79—26no—
451Dic79—21no—
452Dic79—24no—
453Dic79—21no—
454#62851—791nomaximal, Sylow
455C2×C79—22no—
456C2×C79—44no—
457C2×C79C23×#4111yescharacteristic
458C2×C79H(7,𝔽2)11yescharacteristic
459C2×C792−1+611yescharacteristic
460D79—44no—
461D79—46no—
462#3524—794no—
463#3524—794no—
464#3522—794no—
465#3522—794no—
466#3517—794no—
467#3517—794no—
468#3516—794no—
469#3516—794no—
470#3506—796no—
471#3502—791no—
472#3497—791no—
473#3492—796no—
474#3487—791no—
475#3487—791no—
476#3460—796no—
477#3455—796no—
478C4×2−1+4—791no—
479C4×2−1+4D7911yescharacteristic, complemented
480C2×#520—791no—
481C79#6285111yescharacteristic, complemented, Sylow
482C2×2−1+4—791no—
483C2×2−1+4C2×D7911yescharacteristic
484C22×#41—791no—
485#559—7912no—
486#559—7912no—
487Q82—794no—
488#557—794no—
489#557—794no—
490#557—794no—
491#556—7912no—
492#555—7912no—
493#554—7912no—
494#554—7912no—
495#553—7912no—
496#553—7912no—
497#553—7912no—
498#553—7912no—
499#552—7912no—
500#552—7912no—
501#550—794no—
502#550—794no—
503#550—794no—
504#550—794no—
505#550—794no—
506#550—7912no—
507D4×Q8—794no—
508#548—794no—
509#548—794no—
510#548—794no—
511#548—794no—
512#548—794no—
513#548—794no—
514#547—7912no—
515#547—7912no—
516#547—7912no—
517#544—796no—
518#542—796no—
519#542—796no—
520#542—7912no—
521#542—796no—
522#542—796no—
523#542—7912no—
524#541—796no—
525#541—796no—
526#540—796no—
527#540—796no—
528#540—7912no—
529#540—7912no—
530#539—794no—
531#539—7912no—
532#538—7912no—
533#538—7912no—
534#537—796no—
535#535—796no—
536#535—796no—
537#533—796no—
538#532—796no—
539#532—7912no—
540#532—7912no—
541#529—7912no—
542#529—7912no—
543#529—7912no—
544#529—7912no—
545#529—7912no—
546#529—7912no—
547#525—796no—
548#525—7924no—
549#525—796no—
550#520—794no—
551#520—794no—
552#520—794no—
553#520—794no—
554#520—794no—
555#520—796no—
556#520C2×D7916yes—
557#520C2×D7914yescomplemented
558#519—791no—
559#519—794no—
560#519C2×D7911yescharacteristic
561#519C2×D7914yescomplemented
562C4×#41—794no—
563C4×#41—796no—
564C4×#41C2×D7916yes—
565C4×#41C2×D7914yescomplemented
566C2×C4×Q8—791no—
567C2×C4×Q8—794no—
568C2×C4×Q8C2×D7911yescharacteristic
569C2×C4×Q8C2×D7914yescomplemented
570C2×C4×D4—793no—
571C2×C4×D4—793no—
572C2×#117—793no—
573C22×C4⋊C4—793no—
5742−1+4—28no—
5752−1+4—1588no—
576C2×#41—794no—
577C2×#41—794no—
578C2×#41—794no—
579C2×#41—7924no—
580C2×#41—796no—
581C2×#41—1588no—
582C2×#41C22×D7916yes—
583C2×#41C22×D7914yes—
584C22×Q8—794no—
585C22×Q8C22×D7914yes—
586C22×Q8C22×D7911yescharacteristic
587C22×D4—793no—
588C23×C4—796no—
589C23×C4—793no—
590C4⋊Q8—796no—
591C4⋊Q8—7912no—
592C4⋊Q8—796no—
593C4⋊Q8—796no—
594C4⋊Q8—7912no—
595#127—7912no—
596#127—796no—
597#127—7912no—
598#126—7912no—
599#126—7912no—
600#126—794no—
601#126—7912no—
602#126—7912no—
603#126—794no—
604#126—7912no—
605#126—7912no—
606#125—794no—
607#125—7912no—
608#125—7912no—
609#125—796no—
610#125—796no—
611#125—794no—
612#125—7912no—
613#125—7912no—
614#124—7912no—
615#124—796no—
616#124—796no—
617#124—7912no—
618#124—7912no—
619#124—7912no—
620#124—7912no—
621#124—7912no—
622#123—794no—
623#123—7912no—
624#123—794no—
625#123—7912no—
626#123—7912no—
627#123—7924no—
628#123—7912no—
629#123—7912no—
630#123—794no—
631#123—7924no—
632#123—794no—
633#123—7912no—
634C22⋊Q8—796no—
635C22⋊Q8—796no—
636C22⋊Q8—7912no—
637C22⋊Q8—794no—
638C22⋊Q8—7912no—
639C22⋊Q8—7912no—
640C22⋊Q8—796no—
641C22⋊Q8—796no—
642C22⋊Q8—7924no—
643C22⋊Q8—794no—
644C22⋊Q8—7912no—
645C22⋊Q8—7912no—
646C22⋊Q8—794no—
647#121—7912no—
648#121—796no—
649#121—796no—
650#121—794no—
651#121—7912no—
652#121—7912no—
653#121—7912no—
654#121—7912no—
655#121—7912no—
656#121—7912no—
657#121—796no—
658#121—796no—
659#121—7912no—
660#121—7912no—
661#121—7924no—
662#121—7912no—
663#121—7912no—
664#120—7912no—
665#120—7912no—
666C4×Q8—794no—
667C4×Q8—794no—
668C4×Q8—794no—
669C4×Q8—794no—
670C4×Q8—7912no—
671C4×Q8—796no—
672C4×Q8—796no—
673C4×Q8—7912no—
674C4×Q8—7912no—
675C4×Q8C22×D7914yes—
676C4×Q8C22×D7914yes—
677C4×Q8C22×D7916yes—
678C4×Q8C22×D7914yes—
679C4×Q8C22×D79112yes—
680C4×Q8C22×D7916yes—
681C4×Q8C22×D7914yes—
682C4×D4—794no—
683C4×D4—7912no—
684C4×D4—7912no—
685C4×D4—7912no—
686C4×D4—7924no—
687C4×D4—7912no—
688C4×D4—7912no—
689C4×D4—7912no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—796no—
695C4×D4—796no—
696C4×D4—7912no—
697C4×D4—7912no—
698C4×D4—7924no—
699C4×D4C22×D7914yes—
700C4×D4C22×D7916yes—
701C4×D4C22×D79112yes—
702C4×D4C22×D7916yes—
703C4×D4C22×D79112yes—
704#117—796no—
705#117—7912no—
706#117—796no—
707#117—796no—
708#117—796no—
709#117—796no—
710#117—7912no—
711#117—7924no—
712#117C22×D7916yes—
713#117C22×D79112yes—
714#117C22×D79112yes—
715C2×C4⋊C4—793no—
716C2×C4⋊C4—793no—
717C2×C4⋊C4—791no—
718C2×C4⋊C4—7912no—
719C2×C4⋊C4—7912no—
720C2×C4⋊C4—7912no—
721C2×C4⋊C4C22×D7913yes—
722C2×C4⋊C4C22×D79112yes—
723C2×C22⋊C4—793no—
724C2×C22⋊C4—793no—
725C2×C42—793no—
726C2×C42—7912no—
727C2×C42C22×D7913yes—
728C2×C42C22×D79112yes—
729C24—793no—
730#41—216no—
731#41—224no—
732#41—63224no—
733#41—15816no—
734#41—15816no—
735#41—15816no—
736#41—15824no—
737C2×Q8—216no—
738C2×Q8—794no—
739C2×Q8—7912no—
740C2×Q8—796no—
741C2×Q8—15816no—
742C2×Q8#1192962418yescomplemented
743C2×Q8C23×D7916yes—
744C2×Q8C23×D7914yes—
745C2×D4—7912no—
746C2×D4—794no—
747C2×D4—7912no—
748C2×D4—7912no—
749C2×D4—794no—
750C2×D4—7912no—
751C2×D4—7912no—
752C2×D4—7912no—
753C2×D4—796no—
754C2×D4—15812no—
755C2×D4C23×D7914yes—
756C2×D4C23×D7916yes—
757C22×C4—791no—
758C22×C4—793no—
759C22×C4—794no—
760C22×C4—7912no—
761C22×C4—7924no—
762C22×C4—791no—
763C22×C4—7912no—
764C22×C4—796no—
765C22×C4—796no—
766C22×C4—6326no—
767C22×C4—15812no—
768C22×C4C23×D79112yes—
769C22×C4C23×D7911yescharacteristic
770C22×C4C23×D7914yes—
771C22×C4C23×D7913yes—
772C22×C4C23×D79112yes—
773C22×C4C23×D7913yes—
774C4⋊C4—796no—
775C4⋊C4—796no—
776C4⋊C4—7912no—
777C4⋊C4—791no—
778C4⋊C4—791no—
779C4⋊C4—791no—
780C4⋊C4—791no—
781C4⋊C4—794no—
782C4⋊C4—7912no—
783C4⋊C4—7912no—
784C4⋊C4—794no—
785C4⋊C4—794no—
786C4⋊C4—794no—
787C4⋊C4—7912no—
788C4⋊C4—794no—
789C4⋊C4—794no—
790C4⋊C4—7912no—
791C4⋊C4—796no—
792C4⋊C4—796no—
793C4⋊C4—794no—
794C4⋊C4—794no—
795C4⋊C4—7912no—
796C4⋊C4—794no—
797C4⋊C4C23×D79112yes—
798C4⋊C4C23×D7916yes—
799C4⋊C4C23×D79112yes—
800C4⋊C4C23×D7916yes—
801C4⋊C4C23×D7914yes—
802C22⋊C4—794no—
803C22⋊C4—794no—
804C22⋊C4—7912no—
805C22⋊C4—794no—
806C22⋊C4—794no—
807C22⋊C4—796no—
808C22⋊C4—796no—
809C22⋊C4—796no—
810C22⋊C4—796no—
811C22⋊C4—7912no—
812C22⋊C4—794no—
813C22⋊C4—7912no—
814C22⋊C4—7912no—
815C22⋊C4—7912no—
816C22⋊C4—7912no—
817C22⋊C4—794no—
818C22⋊C4—7912no—
819C22⋊C4—794no—
820C22⋊C4—794no—
821C22⋊C4C23×D7914yes—
822C22⋊C4C23×D79112yes—
823C22⋊C4C23×D7914yes—
824C42—794no—
825C42—7912no—
826C42—796no—
827C42—796no—
828C42—7912no—
829C42C23×D7916yes—
830C42C23×D7916yes—
831C42C23×D7914yes—
832C42C23×D79112yes—
833C42C23×D79112yes—
834C23—3163no—
835C23—3163no—
836C23—796no—
837C23—794no—
838C23—1586no—
839C23C24×D7914yes—
840C23C24×D7911yescharacteristic
841Q8—212no—
842Q8—31612no—
843Q8—3164no—
844Q8—15812no—
845Q8C2×#11929624116yes—
846D4—28no—
847D4—212no—
848D4—31612no—
849D4—31612no—
850D4—3164no—
851D4—31612no—
852D4—31612no—
853D4—31612no—
854D4—1588no—
855D4—15824no—
856D4—15812no—
857C2×C4—224no—
858C2×C4—43no—
859C2×C4—41no—
860C2×C4—44no—
861C2×C4—412no—
862C2×C4—31624no—
863C2×C4—31612no—
864C2×C4—3164no—
865C2×C4—3163no—
866C2×C4—3161no—
867C2×C4—791no—
868C2×C4—794no—
869C2×C4—791no—
870C2×C4—794no—
871C2×C4—794no—
872C2×C4—796no—
873C2×C4—791no—
874C2×C4—791no—
875C2×C4—1582no—
876C2×C4—15812no—
877C2×C4—15812no—
878C2×C4—15824no—
879C2×C4C2×#11929624112yes—
880C2×C4C24×D7911yescharacteristic
881C2×C4C24×D7916yes—
882C2×C4C24×D7911yescharacteristic
883C2×C4C24×D7914yes—
884C2×C4C24×D7914yes—
885C2×C4C24×D7914yes—
886C2×C4C24×D7916yes—
887C22—21no—
888C22—21no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—31612no—
893C22—1584no—
894C22—1586no—
895C22—1586no—
896C22—1584no—
897C22—1584no—
898C22—1586no—
899C22C22×#1192962412yes—
900C22C25×D7911yescharacteristic
901C4—24no—
902C4—26no—
903C4—24no—
904C4—21no—
905C4—21no—
906C4—24no—
907C4—1581no—
908C4—1581no—
909C4—1584no—
910C4—1586no—
911C4—1584no—
912C4—1581no—
913C4—1584no—
914C4—1581no—
915C4C22×#11929624112yes—
916C2—22no—
917C2—44no—
918C2—3166no—
919C2—3164no—
920C2C23×#1192962411yescharacteristic
921C2#2377821111yescharacteristic
922C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62851
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #23777511C2semidirect
2. #23777509C2semidirect
3. #23777485C2semidirect
4. #23777479C2semidirect
5. #23777406C2semidirect
6. #23777400C2semidirect
7. #23777395C2semidirect
8. #23777393C2semidirect
9. #23777245C2semidirect
10. #23777206C2semidirect
11. #23777167C2semidirect
12. #23777103C2semidirect
13. #23777059C2semidirect
14. #23777055C2semidirect
15. #23776816C2semidirect
16. #23776785C2semidirect
17. C4×#14579209C2semidirect
18. C2×#19099045C2semidirect
19. C4×2−1+4×C79C2semidirect
22. #19099298C22semidirect
23. #19099296C22semidirect
24. Q8×Dic158C22semidirect
25. #19099292C22semidirect
26. #19099289C22semidirect
27. #19099289C22semidirect
28. #19099285C22semidirect
29. #19099276C22semidirect
30. #19099273C22semidirect
31. #19099268C22semidirect
32. #19099263C22semidirect
33. #19099261C22semidirect
34. #19099257C22semidirect
35. #19099257C22semidirect
36. #19099254C22semidirect
37. #19099252C22semidirect
40. #19099234C22semidirect
43. #19099232C22semidirect
44. Q8×C22⋊D79C22semidirect
49. #19099224C22semidirect
50. #19099220C22semidirect
51. #19099218C22semidirect
52. #19099214C22semidirect
53. #19099214C22semidirect
55. #19099185C22semidirect
56. #19099185C22semidirect
57. #19099185C22semidirect
58. #19099184C22semidirect
59. #19099178C22semidirect
60. #19099178C22semidirect
61. #19099171C22semidirect
62. #19099171C22semidirect
63. #19099168C22semidirect
64. #19099164C22semidirect
65. #19099164C22semidirect
66. #19099164C22semidirect
75. #19099113C22semidirect
76. #19099110C22semidirect
78. #19099100C22semidirect
79. #19099097C22semidirect
80. #19099097C22semidirect
81. #19099097C22semidirect
82. #19099091C22semidirect
83. #19099091C22semidirect
91. #19099045C22semidirect
94. #19099039C22semidirect
95. C4×#11929625C22semidirect
98. C4×Q8×D79C22semidirect
105. #520×C79C22semidirect
107. #519×C79C22semidirect
109. C4×#41×C79C22semidirect
111. C2×C4×Q8×C79C22semidirect
348. C2×Q8×C79#41semidirect
479. C4×2−1+4D79semidirect
481. C79#62851semidirect
557. #520C2×D79semidirect
561. #519C2×D79semidirect
565. C4×#41C2×D79semidirect
569. C2×C4×Q8C2×D79semidirect
742. C2×Q8#11929624semidirect

Maximal subgroups

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

subgroupindex
#237775112
#237775092
#237774852
#237774792
#237774062
#237774002
#237773952
#237773932
#237772452
#237772062
#237771672
#237771032
#237770592
#237770552
#237768162
#237767852
C4×#145792092
C2×#190990452
C4×2−1+4×C792
#6285179