Finite Group Databasebeta

← #35197353

Subgroups — #35197353

Order 20224.

6846 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#23777509C214yesmaximal, complemented
2#23777501C214yesmaximal, complemented
3#23777496C214yesmaximal, complemented
4#23777490C214yesmaximal, complemented
5#23777417C214yesmaximal, complemented
6#23777411C214yesmaximal, complemented
7#23777393C214yesmaximal, complemented
8#23777385C214yesmaximal, complemented
9#23777258C216yesmaximal, complemented
10#23777206C211yesmaximal, characteristic, complemented
11#23777167C211yesmaximal, characteristic, complemented
12#23777113C216yesmaximal, complemented
13#23777052C211yesmaximal, characteristic, complemented
14#23777048C211yesmaximal, characteristic, complemented
15#23776827C216yesmaximal, complemented
16#23776785C216yesmaximal, complemented
17C4×#14579209C211yesmaximal, characteristic, complemented
18C2×#19099039C211yesmaximal, characteristic, complemented
19C4×2−1+4×C79C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21C22×Q8×D79C2211yescharacteristic
22#19099296C22112yescomplemented
23Q8×Dic158C2214yescomplemented
24#19099292C2214yescomplemented
25#19099291C22112yescomplemented
26#19099289C2214yescomplemented
27#19099289C2214yescomplemented
28#19099286C22112yes—
29#19099285C22112yescomplemented
30#19099283C22112yescomplemented
31#19099281C22112yes—
32#19099281C22112yescomplemented
33#19099278C22112yes—
34#19099276C22112yes—
35#19099268C22112yescomplemented
36#19099263C22112yes—
37#19099261C22112yes—
38#19099254C22112yes—
39#19099252C22112yescomplemented
40#19099248C22112yes—
41#19099248C22112yescomplemented
42#19099232C2214yescomplemented
43Q8×D316C2214yes—
44Q8×D316C2214yes—
45Q8×C22⋊D79C2214yes—
46Q8×C22⋊D79C2214yes—
47Q8×C22⋊D79C2214yescomplemented
48#19099225C2214yes—
49#19099225C2214yes—
50#19099224C2214yescomplemented
51#19099220C2214yes—
52#19099220C2214yes—
53#19099220C2214yescomplemented
54#19099191C2216yes—
55#19099185C2216yes—
56#19099185C2216yes—
57#19099184C22112yescomplemented
58#19099178C2216yes—
59#19099178C2216yes—
60#19099178C22112yescomplemented
61#19099175C22112yescomplemented
62#19099171C2216yes—
63#19099171C2216yes—
64#19099171C22112yescomplemented
65#19099164C2216yes—
66#19099164C2216yes—
67#19099155C22112yes—
68#19099155C22112yes—
69#19099146C2214yes—
70#19099146C22112yes—
71#19099141C2216yes—
72#19099139C2216yes—
73#19099134C2216yes—
74#19099120C22112yescomplemented
75#19099117C22112yescomplemented
76#19099116C2216yes—
77#19099109C2216yes—
78#19099097C22112yes—
79#19099097C22112yes—
80#19099097C22112yescomplemented
81#19099095C22112yescomplemented
82#19099093C22124yes—
83#19099091C22112yes—
84#19099091C22112yes—
85#19099075C2216yes—
86#19099070C2216yes—
87#19099045C2214yescomplemented
88#19099044C2216yes—
89#19099041C2211yescharacteristic
90#19099039C2214yes—
91#19099039C2214yes—
92#19099039C2214yes—
93#19099039C2214yes—
94#19099039C2214yescomplemented
95C4×#11929625C2214yescomplemented
96C4×#11929624C2216yes—
97C2×Q8×Dic79C2211yescharacteristic
98C2×C4×Dic158C2213yes—
99C2×#14579126C2213yes—
100C4×Q8×D79C2214yescomplemented
101C2×#14579119C2213yes—
102C2×#14579118C2213yes—
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×#11929625C2314yes—
114C2×#11929624C2316yes—
115C22×Dic158C2313yes—
116C2×Q8×D79—28no—
117C2×Q8×D79C2314yes—
118C2×Q8×D79C2314yes—
119C2×Q8×D79C2314yes—
120C22×C4×D79C2313yes—
121#14579161C23112yes—
122#14579161C23112yes—
123#14579160C2316yes—
124#14579160C2316yes—
125#14579160C23112yes—
126#14579159C2316yes—
127#14579159C23112yes—
128#14579157C2316yes—
129#14579156C2314yes—
130#14579156C23112yes—
131#14579156C23124yes—
132#14579155C2314yes—
133#14579155C23112yes—
134#14579155C23112yes—
135#14579155C23112yes—
136#14579154C23112yes—
137#14579154C23112yes—
138#14579154C23124yes—
139#14579153C23112yes—
140#14579153C23112yes—
141#14579153C23112yes—
142#14579152C2316yes—
143#14579152C2316yes—
144#14579152C23112yes—
145#14579151C23112yes—
146#14579151C23112yes—
147#14579151C23124yes—
148#14579150C2316yes—
149#14579149C23112yes—
150#14579149C2314yes—
151#14579149C23112yes—
152#14579148C2316yes—
153#14579148C23112yes—
154#14579147C2314yes—
155#14579147C23112yes—
156#14579147C23124yes—
157#14579146C2314yes—
158#14579146C23112yes—
159#14579145C23112yes—
160#14579144C2314yes—
161#14579144C23112yes—
162#14579144C23112yes—
163#14579144C23112yes—
164#14579143C23112yes—
165#14579143C23112yes—
166#14579142C23112yes—
167#14579141C23112yes—
168#14579141C23112yes—
169#14579141C2316yes—
170#14579141C2316yes—
171#14579140C23112yes—
172#14579140C23112yes—
173#14579140C23112yes—
174#14579140C23112yes—
175#14579140C23112yes—
176#14579139C23112yes—
177#14579139C23112yes—
178#14579138C2314yes—
179#14579138C23112yes—
180#14579137C23112yes—
181#14579137C2316yes—
182#14579137C2316yes—
183#14579136C2316yes—
184#14579136C2316yes—
185#14579135C23112yes—
186#14579135C2314yes—
187#14579135C23112yes—
188#14579134C2314yes—
189#14579134C23112yes—
190#14579133C23112yes—
191#14579133C2314yes—
192#14579132C23112yes—
193#14579132C2316yes—
194#14579132C2316yes—
195#14579131C2314yes—
196#14579129C2314yes—
197Q8×Dic79C2314yes—
198Q8×Dic79C2314yes—
199Q8×Dic79C2314yes—
200Q8×Dic79C2314yes—
201C4×Dic158C2316yes—
202C4×Dic158C2316yes—
203C4×Dic158C23112yes—
204C4×Dic158C23112yes—
205C4×Dic158C23124yes—
206C4×Dic158C23112yes—
207C4×Dic158C23112yes—
208#14579126C23112yes—
209#14579126C23112yes—
210#14579126C23112yes—
211C4×D316C2316yes—
212C4×D316C2316yes—
213C4×D316C23112yes—
214C4×D316C23112yes—
215#14579123C23112yes—
216C4×C22⋊D79C2314yes—
217C4×C22⋊D79C23112yes—
218C4×C22⋊D79C23112yes—
219C4×C22⋊D79C23112yes—
220C4×C22⋊D79C23112yes—
221C4×C22⋊D79C23112yes—
222C4×C22⋊D79C23124yes—
223#14579120C2316yes—
224#14579120C23124yes—
225#14579119C23112yes—
226#14579119C23112yes—
227#14579119C23112yes—
228#14579118C2316yes—
229#14579118C2316yes—
230#14579118C23112yes—
231#14579118C2316yes—
232#14579118C2316yes—
233#14579118C23124yes—
234C2×C4⋊Dic79C2313yes—
235C2×Dic79⋊C4C2313yes—
236C2×Dic79⋊C4C2313yes—
237C4⋊C4×D79C23112yes—
238C2×(C2×D79)⋊C4C2311yescharacteristic
239C2×(C2×D79)⋊C4C2313yes—
240C2×C4×Dic79C2313yes—
241C2×C4×Dic79C2316yes—
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×C79C2316yes—
261#117×C79C23112yes—
262#117×C79C23112yes—
263C2×C4⋊C4×C79C2313yes—
264C2×C4⋊C4×C79C23112yes—
265C2×C42×C79C2313yes—
266C2×C42×C79C23112yes—
267C23×D79C2411yescharacteristic
268#11929625—216no—
269#11929624—224no—
270C2×Dic158—212no—
271C2×Dic158C24112yes—
272C2×Dic158C2416yes—
273C2×Dic158C2414yes—
274C2×Dic158C24112yes—
275Q8×D79—216no—
276Q8×D79—216no—
277Q8×D79—216no—
278C2×D316C2416yes—
279C2×D316C2414yes—
280C2×D316C2414yes—
281C2×C22⋊D79C2414yes—
282C2×C22⋊D79C2414yes—
283C2×C22⋊D79C2414yes—
284C2×C22⋊D79C24112yes—
285C2×C22⋊D79C2414yes—
286C22×Dic79C2413yes—
287C22×Dic79C2411yescharacteristic
288C22×Dic79C2413yes—
289C2×C4×D79—212no—
290C2×C4×D79C2416yes—
291C2×C4×D79C2416yes—
292C2×C4×D79C24112yes—
293C2×C4×D79C2414yes—
294C2×C4×D79C24112yes—
295C4⋊Dic79C2416yes—
296C4⋊Dic79C24112yes—
297C4⋊Dic79C2416yes—
298C4⋊Dic79C24112yes—
299C4⋊Dic79C24112yes—
300C4⋊Dic79C24112yes—
301C4⋊Dic79C2414yes—
302Dic79⋊C4C24112yes—
303Dic79⋊C4C2416yes—
304Dic79⋊C4C2416yes—
305Dic79⋊C4C2416yes—
306Dic79⋊C4C2416yes—
307Dic79⋊C4C2414yes—
308Dic79⋊C4C24112yes—
309Dic79⋊C4C24112yes—
310Dic79⋊C4C2414yes—
311Dic79⋊C4C24112yes—
312Dic79⋊C4C24112yes—
313Dic79⋊C4C24112yes—
314Dic79⋊C4C2414yes—
315Dic79⋊C4C2414yes—
316C22⋊Dic79C2414yes—
317C22⋊Dic79C24112yes—
318C22⋊Dic79C24112yes—
319C22⋊Dic79C24112yes—
320C22⋊Dic79C2414yes—
321(C2×D79)⋊C4C2411yescharacteristic
322(C2×D79)⋊C4C2411yescharacteristic
323(C2×D79)⋊C4C2411yescharacteristic
324(C2×D79)⋊C4C2411yescharacteristic
325(C2×D79)⋊C4C2416yes—
326(C2×D79)⋊C4C2416yes—
327(C2×D79)⋊C4C2414yes—
328(C2×D79)⋊C4C24112yes—
329(C2×D79)⋊C4C24112yes—
330(C2×D79)⋊C4C24112yes—
331(C2×D79)⋊C4C2414yes—
332(C2×D79)⋊C4C2414yes—
333(C2×D79)⋊C4C2414yes—
334(C2×D79)⋊C4C24112yes—
335(C2×D79)⋊C4C2414yes—
336(C2×D79)⋊C4C2414yes—
337C4×Dic79C2414yes—
338C4×Dic79C24112yes—
339C4×Dic79C24112yes—
340C4×Dic79C2416yes—
341C4×Dic79C2416yes—
342C4×Dic79C24124yes—
343#41×C79—216no—
344#41×C79—224no—
345C2×Q8×C79—216no—
346C2×Q8×C79#4118yes—
347C2×Q8×C79C2416yes—
348C2×Q8×C79C2414yes—
349C2×D4×C79C2414yes—
350C2×D4×C79C2416yes—
351C22×C4×C79C24112yes—
352C22×C4×C79C2411yescharacteristic
353C22×C4×C79C2414yes—
354C22×C4×C79C2413yes—
355C22×C4×C79C24112yes—
356C22×C4×C79C2413yes—
357C4⋊C4×C79C24112yes—
358C4⋊C4×C79C2416yes—
359C4⋊C4×C79C24112yes—
360C4⋊C4×C79C2416yes—
361C4⋊C4×C79C2414yes—
362C22⋊C4×C79C2414yes—
363C22⋊C4×C79C2414yes—
364C22⋊C4×C79C24112yes—
365C42×C79C2416yes—
366C42×C79C2414yes—
367C42×C79C2416yes—
368C42×C79C24112yes—
369C42×C79C24112yes—
370C23×C79C2514yes—
371C23×C79C2511yescharacteristic
372C22×D79—22no—
373C22×D79—41no—
374C22×D79—41no—
375C22×D79C2511yescharacteristic
376C22×D79C2511yescharacteristic
377C22×D79C2514yes—
378Q8×C79—212no—
379Q8×C79C2×#41116yes—
380D4×C79—28no—
381D4×C79—212no—
382C2×C4×C79—224no—
383C2×C4×C79—44no—
384C2×C4×C79—41no—
385C2×C4×C79—412no—
386C2×C4×C79—43no—
387C2×C4×C79C2×#41112yes—
388C2×C4×C79C2516yes—
389C2×C4×C79C2511yescharacteristic
390C2×C4×C79C2511yescharacteristic
391C2×C4×C79C2514yes—
392C2×C4×C79C2514yes—
393C2×C4×C79C2514yes—
394C2×C4×C79C2516yes—
395C22⋊D79—28no—
396C22⋊D79—44no—
397C22⋊D79—412no—
398C22⋊D79—44no—
399C22⋊D79—44no—
400C2×Dic79—26no—
401C2×Dic79—41no—
402C2×Dic79—43no—
403C2×Dic79C2511yescharacteristic
404C2×Dic79C2514yes—
405C2×Dic79C2516yes—
406C2×Dic79C2511yescharacteristic
407C2×Dic79C2516yes—
408C2×Dic79C2514yes—
409C2×Dic79C2514yes—
410D316—212no—
411D316—44no—
412D316—44no—
413C4×D79—212no—
414C4×D79—212no—
415C4×D79—224no—
416C4×D79—44no—
417C4×D79—412no—
418Dic158—224no—
419Dic158—212no—
420Dic158—412no—
421Dic158—44no—
422C22×C79—21no—
423C22×C79—21no—
424C22×C79—24no—
425C22×C79—24no—
426C22×C79—24no—
427C22×C79C22×#4112yes—
428C22×C79C2611yescharacteristic
429C2×D79—24no—
430C2×D79—21no—
431C2×D79—21no—
432C2×D79—21no—
433C2×D79—21no—
434C2×D79—24no—
435C2×D79—24no—
436C2×D79—21no—
437C2×D79—21no—
438C2×D79—44no—
439C4×C79—24no—
440C4×C79—21no—
441C4×C79—24no—
442C4×C79—26no—
443C4×C79—24no—
444C4×C79—21no—
445C4×C79C22×#41112yes—
446Dic79—24no—
447Dic79—26no—
448Dic79—21no—
449Dic79—26no—
450Dic79—24no—
451Dic79—24no—
452Dic79—21no—
453#62850—791nomaximal, Sylow
454C2×C79—22no—
455C2×C79—44no—
456C2×C79C23×#4111yescharacteristic
457C2×C792−1+611yescharacteristic
458C2×C792−1+611yescharacteristic
459D79—44no—
460D79—41no—
461D79—41no—
462#3524—794no—
463#3524—794no—
464#3523—794no—
465#3523—794no—
466#3518—794no—
467#3518—794no—
468#3516—794no—
469#3516—794no—
470#3507—796no—
471#3502—791no—
472#3497—791no—
473#3493—796no—
474#3486—791no—
475#3486—791no—
476#3461—796no—
477#3455—796no—
478C4×2−1+4—791no—
479C4×2−1+4D7911yescharacteristic, complemented
480C2×#519—791no—
481C79#6285011yescharacteristic, complemented, Sylow
482C2×2−1+4—791no—
483C2×2−1+4C2×D7911yescharacteristic
484C23×Q8—791no—
485#559—7912no—
486Q82—794no—
487#557—794no—
488#557—794no—
489#557—7912no—
490#557—794no—
491#556—7912no—
492#556—7912no—
493#556—7912no—
494#556—7912no—
495#556—7912no—
496#555—7912no—
497#555—7912no—
498#554—7912no—
499#553—7912no—
500#553—7912no—
501#552—7912no—
502#552—7912no—
503#552—7912no—
504#552—7912no—
505#550—794no—
506D4×Q8—794no—
507D4×Q8—794no—
508D4×Q8—794no—
509D4×Q8—794no—
510D4×Q8—794no—
511#548—794no—
512#548—794no—
513#548—794no—
514#548—794no—
515#548—794no—
516#548—794no—
517#544—796no—
518#542—796no—
519#542—796no—
520#542—796no—
521#542—796no—
522#542—7912no—
523#542—7912no—
524#541—796no—
525#541—796no—
526#541—7912no—
527#541—7912no—
528#540—796no—
529#540—796no—
530#539—7912no—
531#539—7912no—
532#538—794no—
533#538—7912no—
534#537—796no—
535#536—796no—
536#536—796no—
537#533—7912no—
538#533—796no—
539#533—7912no—
540#532—796no—
541#529—7924no—
542#529—7912no—
543#529—7912no—
544#529—7912no—
545#529—7912no—
546#529—7912no—
547#529—7912no—
548#525—796no—
549#525—796no—
550#520—794no—
551#520—796no—
552#520C2×D7916yes—
553#520C2×D7914yescomplemented
554#519—791no—
555#519—794no—
556#519—794no—
557#519—794no—
558#519—794no—
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×Q8—793no—
569C2×C4×Q8—793no—
570C2×C4×Q8C2×D7911yescharacteristic
571C2×C4×Q8C2×D7914yescomplemented
572C2×#117—793no—
573C2×#117—793no—
5742−1+4—28no—
5752−1+4—1588no—
576C2×#41—794no—
577C2×#41—796no—
578C2×#41C22×D7916yes—
579C2×#41C22×D7914yes—
580C22×Q8—794no—
581C22×Q8—794no—
582C22×Q8—794no—
583C22×Q8—793no—
584C22×Q8—1588no—
585C22×Q8C22×D7914yes—
586C22×Q8C22×D7911yescharacteristic
587C23×C4—793no—
588C4⋊Q8—796no—
589C4⋊Q8—7912no—
590C4⋊Q8—796no—
591C4⋊Q8—796no—
592C4⋊Q8—7912no—
593C4⋊Q8—7912no—
594C4⋊Q8—7912no—
595#127—796no—
596#126—794no—
597#126—7912no—
598#126—7924no—
599#126—7912no—
600#126—7912no—
601#126—7924no—
602#126—794no—
603#126—7912no—
604#126—7912no—
605#126—7912no—
606#125—7912no—
607#125—7912no—
608#125—7924no—
609#125—7912no—
610#125—796no—
611#125—796no—
612#125—7912no—
613#125—7912no—
614#125—7912no—
615#124—796no—
616#124—7912no—
617#124—796no—
618#124—794no—
619#124—7912no—
620#124—7924no—
621#124—794no—
622#124—7912no—
623#124—7912no—
624#123—7912no—
625#123—794no—
626#123—7912no—
627#123—7912no—
628#123—7912no—
629#123—794no—
630#123—7912no—
631#123—7912no—
632#123—7912no—
633#123—7912no—
634C22⋊Q8—796no—
635C22⋊Q8—796no—
636C22⋊Q8—7912no—
637C22⋊Q8—7912no—
638C22⋊Q8—7912no—
639C22⋊Q8—7912no—
640C22⋊Q8—7912no—
641C22⋊Q8—7912no—
642C22⋊Q8—796no—
643C22⋊Q8—796no—
644C22⋊Q8—7912no—
645C22⋊Q8—7912no—
646C22⋊Q8—7912no—
647C22⋊Q8—7912no—
648C22⋊Q8—7912no—
649C22⋊Q8—794no—
650#121—796no—
651#121—796no—
652#121—7912no—
653#121—7912no—
654#121—794no—
655#121—794no—
656#121—7912no—
657#121—7912no—
658#121—796no—
659#121—796no—
660#121—794no—
661#121—7912no—
662#120—794no—
663#120—794no—
664C4×Q8—794no—
665C4×Q8—794no—
666C4×Q8—794no—
667C4×Q8—794no—
668C4×Q8—7912no—
669C4×Q8—7912no—
670C4×Q8—7912no—
671C4×Q8—796no—
672C4×Q8—7912no—
673C4×Q8—7912no—
674C4×Q8—796no—
675C4×Q8—7912no—
676C4×Q8—7912no—
677C4×Q8—7924no—
678C4×Q8C22×D7914yes—
679C4×Q8C22×D7914yes—
680C4×Q8C22×D7916yes—
681C4×Q8C22×D7914yes—
682C4×Q8C22×D79112yes—
683C4×Q8C22×D7916yes—
684C4×Q8C22×D7914yes—
685C4×D4—794no—
686C4×D4—7912no—
687C4×D4—7912no—
688C4×D4—7912no—
689C4×D4—7924no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—796no—
694C4×D4—796no—
695C4×D4—7912no—
696C4×D4—7912no—
697C4×D4C22×D7914yes—
698C4×D4C22×D7916yes—
699C4×D4C22×D79112yes—
700C4×D4C22×D7916yes—
701C4×D4C22×D79112yes—
702#117—796no—
703#117—7924no—
704#117—7912no—
705#117—7912no—
706#117—7912no—
707#117—796no—
708#117—796no—
709#117—796no—
710#117—796no—
711#117—7912no—
712#117—7924no—
713#117C22×D7916yes—
714#117C22×D79112yes—
715#117C22×D79112yes—
716C2×C4⋊C4—793no—
717C2×C4⋊C4—793no—
718C2×C4⋊C4—793no—
719C2×C4⋊C4—7912no—
720C2×C4⋊C4C22×D7913yes—
721C2×C4⋊C4C22×D79112yes—
722C2×C22⋊C4—791no—
723C2×C22⋊C4—793no—
724C2×C42—796no—
725C2×C42—793no—
726C2×C42—7912no—
727C2×C42C22×D7913yes—
728C2×C42C22×D79112yes—
729C24—791no—
730#41—216no—
731#41—224no—
732#41—15816no—
733#41—15824no—
734C2×Q8—216no—
735C2×Q8—794no—
736C2×Q8—7912no—
737C2×Q8—7912no—
738C2×Q8—796no—
739C2×Q8—15816no—
740C2×Q8—15816no—
741C2×Q8—15816no—
742C2×Q8—15812no—
743C2×Q8#1192962418yes—
744C2×Q8C23×D7916yes—
745C2×Q8C23×D7914yes—
746C2×D4—794no—
747C2×D4—794no—
748C2×D4—7912no—
749C2×D4—794no—
750C2×D4—794no—
751C2×D4—794no—
752C2×D4—794no—
753C2×D4—796no—
754C2×D4C23×D7914yes—
755C2×D4C23×D7916yes—
756C22×C4—791no—
757C22×C4—793no—
758C22×C4—794no—
759C22×C4—7912no—
760C22×C4—793no—
761C22×C4—7912no—
762C22×C4—796no—
763C22×C4—796no—
764C22×C4—15812no—
765C22×C4C23×D79112yes—
766C22×C4C23×D7913yes—
767C22×C4C23×D7911yescharacteristic
768C22×C4C23×D7914yes—
769C22×C4C23×D79112yes—
770C22×C4C23×D7913yes—
771C4⋊C4—7912no—
772C4⋊C4—796no—
773C4⋊C4—796no—
774C4⋊C4—796no—
775C4⋊C4—796no—
776C4⋊C4—794no—
777C4⋊C4—7912no—
778C4⋊C4—7912no—
779C4⋊C4—794no—
780C4⋊C4—7912no—
781C4⋊C4—7912no—
782C4⋊C4—7912no—
783C4⋊C4—794no—
784C4⋊C4—794no—
785C4⋊C4—796no—
786C4⋊C4—7912no—
787C4⋊C4—796no—
788C4⋊C4—7912no—
789C4⋊C4—7912no—
790C4⋊C4—7912no—
791C4⋊C4—794no—
792C4⋊C4C23×D79112yes—
793C4⋊C4C23×D7916yes—
794C4⋊C4C23×D79112yes—
795C4⋊C4C23×D7916yes—
796C4⋊C4C23×D7914yes—
797C22⋊C4—794no—
798C22⋊C4—7912no—
799C22⋊C4—7912no—
800C22⋊C4—7912no—
801C22⋊C4—794no—
802C22⋊C4—791no—
803C22⋊C4—791no—
804C22⋊C4—796no—
805C22⋊C4—796no—
806C22⋊C4—791no—
807C22⋊C4—791no—
808C22⋊C4—794no—
809C22⋊C4—7912no—
810C22⋊C4—7912no—
811C22⋊C4—7912no—
812C22⋊C4—794no—
813C22⋊C4—794no—
814C22⋊C4—794no—
815C22⋊C4—794no—
816C22⋊C4—7912no—
817C22⋊C4—794no—
818C22⋊C4C23×D7914yes—
819C22⋊C4C23×D7914yes—
820C22⋊C4C23×D79112yes—
821C42—794no—
822C42—7912no—
823C42—7924no—
824C42—7912no—
825C42—796no—
826C42—796no—
827C42C23×D7916yes—
828C42C23×D7916yes—
829C42C23×D7914yes—
830C42C23×D79112yes—
831C42C23×D79112yes—
832C23—3161no—
833C23—3161no—
834C23—791no—
835C23—791no—
836C23—794no—
837C23—1582no—
838C23C24×D7914yes—
839C23C24×D7911yescharacteristic
840Q8—212no—
841Q8—31612no—
842Q8—3164no—
843Q8—15824no—
844Q8—15812no—
845Q8C2×#11929624116yes—
846D4—28no—
847D4—212no—
848D4—3164no—
849D4—3164no—
850D4—31612no—
851D4—3164no—
852D4—3164no—
853D4—3164no—
854D4—1588no—
855D4—15812no—
856C2×C4—224no—
857C2×C4—41no—
858C2×C4—44no—
859C2×C4—43no—
860C2×C4—412no—
861C2×C4—3164no—
862C2×C4—31612no—
863C2×C4—3163no—
864C2×C4—3161no—
865C2×C4—791no—
866C2×C4—794no—
867C2×C4—796no—
868C2×C4—791no—
869C2×C4—796no—
870C2×C4—794no—
871C2×C4—794no—
872C2×C4—1586no—
873C2×C4—15812no—
874C2×C4—15812no—
875C2×C4—15824no—
876C2×C4C2×#11929624112yes—
877C2×C4C24×D7916yes—
878C2×C4C24×D7911yescharacteristic
879C2×C4C24×D7911yescharacteristic
880C2×C4C24×D7914yes—
881C2×C4C24×D7914yes—
882C2×C4C24×D7914yes—
883C2×C4C24×D7916yes—
884C22—21no—
885C22—21no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—3164no—
890C22—1581no—
891C22—1581no—
892C22—1584no—
893C22—1584no—
894C22—1581no—
895C22—1581no—
896C22—1584no—
897C22—1581no—
898C22—1581no—
899C22C22×#1192962412yes—
900C22C25×D7911yescharacteristic
901C4—24no—
902C4—21no—
903C4—21no—
904C4—24no—
905C4—26no—
906C4—24no—
907C4—1584no—
908C4—1586no—
909C4—1586no—
910C4—1584no—
911C4—1584no—
912C4—1581no—
913C4—1581no—
914C4C22×#11929624112yes—
915C2—22no—
916C2—44no—
917C2—3161no—
918C2—3161no—
919C2—3164no—
920C2C23×#1192962411yescharacteristic
921C2#2377821211yescharacteristic
922C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62850
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. #23777509C2semidirect
2. #23777501C2semidirect
3. #23777496C2semidirect
4. #23777490C2semidirect
5. #23777417C2semidirect
6. #23777411C2semidirect
7. #23777393C2semidirect
8. #23777385C2semidirect
9. #23777258C2semidirect
10. #23777206C2semidirect
11. #23777167C2semidirect
12. #23777113C2semidirect
13. #23777052C2semidirect
14. #23777048C2semidirect
15. #23776827C2semidirect
16. #23776785C2semidirect
17. C4×#14579209C2semidirect
18. C2×#19099039C2semidirect
19. C4×2−1+4×C79C2semidirect
22. #19099296C22semidirect
23. Q8×Dic158C22semidirect
24. #19099292C22semidirect
25. #19099291C22semidirect
26. #19099289C22semidirect
27. #19099289C22semidirect
29. #19099285C22semidirect
30. #19099283C22semidirect
32. #19099281C22semidirect
35. #19099268C22semidirect
39. #19099252C22semidirect
41. #19099248C22semidirect
42. #19099232C22semidirect
47. Q8×C22⋊D79C22semidirect
50. #19099224C22semidirect
53. #19099220C22semidirect
57. #19099184C22semidirect
60. #19099178C22semidirect
61. #19099175C22semidirect
64. #19099171C22semidirect
74. #19099120C22semidirect
75. #19099117C22semidirect
80. #19099097C22semidirect
81. #19099095C22semidirect
87. #19099045C22semidirect
94. #19099039C22semidirect
95. C4×#11929625C22semidirect
100. C4×Q8×D79C22semidirect
105. #520×C79C22semidirect
107. #519×C79C22semidirect
109. C4×#41×C79C22semidirect
111. C2×C4×Q8×C79C22semidirect
479. C4×2−1+4D79semidirect
481. C79#62850semidirect
553. #520C2×D79semidirect
561. #519C2×D79semidirect
565. C4×#41C2×D79semidirect
571. C2×C4×Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237775092
#237775012
#237774962
#237774902
#237774172
#237774112
#237773932
#237773852
#237772582
#237772062
#237771672
#237771132
#237770522
#237770482
#237768272
#237767852
C4×#145792092
C2×#190990392
C4×2−1+4×C792
#6285079