Finite Group Databasebeta

← #7670569

Subgroups — #7670569

Order 512.

5198 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60049C212yesmaximal, complemented
2#60047C211yesmaximal, characteristic, complemented
3#60046C211yesmaximal, characteristic, complemented
4#59913C214yesmaximal, complemented
5#59849C214yesmaximal, complemented
6#59285C212yesmaximal, complemented
7#59107C212yesmaximal
8#38663C214yesmaximal, complemented
9#38631C214yesmaximal, complemented
10#38485C212yesmaximal, complemented
11#38465C212yesmaximal, complemented
12#38447C212yesmaximal, complemented
13#38427C212yesmaximal, complemented
14#36626C211yesmaximal, characteristic
15#36425C214yesmaximal, complemented
16#36353C214yesmaximal, complemented
17#36341C214yesmaximal, complemented
18#36223C214yesmaximal, complemented
19#35444C212yesmaximal, complemented
20#35440C212yesmaximal, complemented
21#35059C214yesmaximal, complemented
22#34304C214yesmaximal, complemented
23C2×#2296C212yesmaximal, complemented
24C2×#552C2214yes—
25C2×#551C2212yes—
26C2×#525C2211yescharacteristic
27C22×#117C2212yes—
28C22×#117C2212yes—
29C23×C42C2211yescharacteristic
30#2855C2212yes—
31#2855C2212yes—
32#2855C2214yes—
33#2854C2212yes—
34#2854C2212yes—
35#2853C2214yes—
36#2853C2214yes—
37#2852C2214yes—
38#2851C2214yes—
39#2849C2214yes—
40#2810C2212yescomplemented
41#2809C2211yescharacteristic, complemented
42#2807C2214yescomplemented
43#2805C2212yescomplemented
44#2802C2214yescomplemented
45#2802C2214yescomplemented
46#2792C2214yescomplemented
47#2783C2214yescomplemented
48#2776C2214yescomplemented
49#2771C2212yes—
50#2765C2214yes—
51#2764C2212yes—
52#2734C2211yescharacteristic, complemented
53#2727C2212yescomplemented
54#2726C2212yescomplemented
55#2726C2212yescomplemented
56#2726C2212yescomplemented
57#2725C2214yescomplemented
58#2724C2212yes—
59#2724C2211yescharacteristic, complemented
60#2718C2214yes—
61#2717C2212yes—
62#2704C2214yescomplemented
63#2683C2211yescharacteristic, complemented
64#2666C2214yescomplemented
65#2664C2214yescomplemented
66#2655C2214yescomplemented
67#2654C2214yescomplemented
68#2611C2214yes—
69#2611C2212yes—
70#2609C2214yes—
71#2608C2212yescomplemented
72#2606C2214yescomplemented
73#2606C2212yescomplemented
74#2601C2214yes—
75#2601C2214yescomplemented
76#2599C2214yes—
77#2599C2212yes—
78#2596C2214yescomplemented
79#2594C2214yescomplemented
80#2594C2214yescomplemented
81#2593C2212yescomplemented
82#2590C2214yescomplemented
83#2590C2214yescomplemented
84#2590C2214yescomplemented
85#2590C2214yescomplemented
86#2588C2214yescomplemented
87#2588C2214yescomplemented
88#2587C2214yescomplemented
89#2587C2214yescomplemented
90#2586C2214yescomplemented
91#2586C2212yescomplemented
92#2585C2214yescomplemented
93#2585C2214yescomplemented
94#2585C2214yescomplemented
95#2585C2214yescomplemented
96#2584C2212yescomplemented
97#2584C2214yescomplemented
98#2583C2214yes—
99#2583C2212yescomplemented
100#2579C2214yes—
101#2573C2214yescomplemented
102#2558C2214yescomplemented
103#2556C2214yescomplemented
104#2550C2214yescomplemented
105#2525C2214yescomplemented
106#2522C2214yescomplemented
107#2509C2214yescomplemented
108#2507C2214yescomplemented
109#2498C2214yes—
110#2493C2214yes—
111#2493C2214yes—
112#2484C2214yes—
113#2484C2214yes—
114#2483C2212yes—
115#2481C2214yes—
116#2479C2214yes—
117#2478C2214yes—
118#2478C2214yes—
119#2478C2214yes—
120#2478C2214yes—
121#2478C2214yes—
122#2477C2214yes—
123#2475C2214yes—
124#2475C2214yes—
125#2475C2214yes—
126#2474C2214yes—
127#2474C2214yes—
128#2473C2214yes—
129#2473C2214yes—
130#2473C2214yes—
131#2473C2214yes—
132#2470C2214yes—
133#2470C2214yes—
134#2449C2214yes—
135#2449C2214yes—
136#2443C2214yes—
137#2442C2214yes—
138#2440C2214yes—
139#2438C2214yes—
140#2438C2214yes—
141#2438C2214yes—
142#2438C2214yes—
143#2438C2214yes—
144#2437C2212yes—
145#2432C2212yes—
146#2425C2214yes—
147#2419C2214yes—
148#2413C2214yes—
149#2413C2214yes—
150#2413C2214yes—
151#2413C2214yes—
152#2412C2214yes—
153#2406C2212yes—
154#2374C2212yescomplemented
155#2373C2214yescomplemented
156#2373C2214yescomplemented
157#2370C2214yescomplemented
158#2370C2214yescomplemented
159#2370C2214yescomplemented
160#2370C2214yescomplemented
161#2369C2212yescomplemented
162#2360C2214yes—
163#2360C2214yescomplemented
164#2359C2214yes—
165#2359C2214yes—
166#2359C2214yes—
167#2359C2214yes—
168#2358C2212yes—
169#2355C2214yescomplemented
170D4×C4⋊C4C2214yes—
171#2347C2214yescomplemented
172#2344C2214yes—
173#2344C2214yes—
174#2344C2214yes—
175#2343C2214yes—
176#2343C2214yes—
177#2342C2214yes—
178#2336C2214yescomplemented
179#2336C2214yescomplemented
180#2336C2212yescomplemented
181#2334C2214yescomplemented
182#2334C2214yescomplemented
183#2332C2212yescomplemented
184#2330C2214yescomplemented
185#2323C2214yescomplemented
186C4×C22⋊Q8C2214yes—
187C4×#123C2214yes—
188C4×#123C2214yes—
189C4×#123C2214yes—
190#2297C2211yescharacteristic
191#2297C2211yescharacteristic
192#2296C2212yes—
193#2296C2214yes—
194#2296C2214yes—
195#2296C2212yes—
196#2296C2214yes—
197#2296C2214yes—
198#2296C2211yescharacteristic
199#2296C2211yescharacteristic
200#2296C2212yes—
201#2296C2212yes—
202#2296C2214yes—
203#2296C2212yes—
204#2296C2212yes—
205#2296C2212yes—
206#2296C2212yes—
207C2×#389C2212yes—
208C2×#389C2212yes—
209C2×#389C2212yes—
210C2×#389C2212yes—
211#2290C2214yes—
212C2×#385C2214yes—
213C2×#385C2214yes—
214#2280C2211yescharacteristic
215#2276C2212yescomplemented
216#2274C2212yescomplemented
217C2×C4×C4⋊C4C2214yes—
218C2×C4×C4⋊C4C2214yes—
219C22×#41C2311yescharacteristic
220C24×C4C2312yes—
221C24×C4C2311yescharacteristic
222#552—232no—
223#551—48no—
224C2×C4⋊Q8C2312yes—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#125C2312yes—
232C2×#125C2314yes—
233C2×#124C2312yes—
234#525—44no—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2312yes—
239C2×#123C2314yes—
240C2×#123C2312yes—
241C2×#123C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×#121C2312yes—
248C2×#120C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×#117—216no—
255C2×#117—48no—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2311yescharacteristic
272C2×#117C2311yescharacteristic
273C2×#117C2312yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2314yes—
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2314yes—
285C22×C42—44no—
286C22×C42C2314yes—
287C22×C42C2312yes—
288C22×C42C2314yes—
289C22×C42C2312yes—
290C22×C42C2312yes—
291C22×C42C2312yes—
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#399C2314yes—
310#399C2312yes—
311#399C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2312yes—
342#397C2314yes—
343#397C2312yes—
344#397C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2312yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#393C2312yes—
363#391C2314yes—
364#391C2311yescharacteristic
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2312yes—
369#391C2312yes—
370#391C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2312yes—
373#390C2311yescharacteristic
374#390C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2314yes—
397#389C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2312yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2312yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2312yes—
513#386C2312yes—
514#386C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#384C2314yes—
550#383C2312yes—
551#383C2314yes—
552#383C2314yes—
553#382C2314yes—
554#382C2314yes—
555#381C2312yes—
556#381C2314yes—
557#381C2314yes—
558#381C2312yes—
559#381C2314yes—
560#381C2314yes—
561#381C2314yes—
562#381C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2314yes—
567#380C2312yes—
568#380C2312yes—
569#380C2314yes—
570#379C2312yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614#376C2314yes—
615#376C2312yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C2×#95C2314yes—
620C25C2411yescharacteristic
621C2×#41—42no—
622C2×#41—42no—
623C2×#41—42no—
624C22×Q8C2412yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×D4C2414yes—
628C22×D4C2412yes—
629C22×D4C2411yescharacteristic
630C23×C4—28no—
631C23×C4—28no—
632C23×C4—28no—
633C23×C4—24no—
634C23×C4—42no—
635C23×C4—42no—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2412yes—
642C23×C4C2414yes—
643C23×C4C2414yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C4⋊Q8—44no—
654#126—216no—
655#126—216no—
656#126—48no—
657#125—216no—
658#125—216no—
659#125—216no—
660#125—44no—
661#125—48no—
662#124—44no—
663#123—216no—
664#123—216no—
665#123—216no—
666#123—44no—
667#123—44no—
668#123—48no—
669#123—44no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—44no—
673C22⋊Q8—48no—
674C22⋊Q8—44no—
675#121—44no—
676#120—28no—
677C4×Q8—216no—
678C4×Q8—44no—
679C4×D4—216no—
680C4×D4—48no—
681C4×D4—48no—
682#117—28no—
683#117—28no—
684#117—28no—
685#117—216no—
686#117—216no—
687#117—216no—
688#117—216no—
689#117—42no—
690#117—44no—
691#117—48no—
692#117—44no—
693#117—44no—
694#117—48no—
695#117—44no—
696#117—42no—
697#117—48no—
698#117—42no—
699#117#41116yescomplemented
700C2×C4⋊C4—216no—
701C2×C4⋊C4—216no—
702C2×C4⋊C4—28no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—44no—
705C2×C4⋊C4—48no—
706C2×C4⋊C4—48no—
707C2×C4⋊C4—44no—
708C2×C4⋊C4—44no—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C22⋊C4—216no—
769C2×C22⋊C4—216no—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C42—216no—
798C2×C42—48no—
799C2×C42—44no—
800C2×C42—44no—
801C2×C42—44no—
802C2×C42—44no—
803C2×C42—42no—
804C2×C42—42no—
805C2×C42—44no—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2411yescharacteristic
825C2×C42C2412yes—
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2411yescharacteristic
834C2×C42C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2412yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891C24—24no—
892C24—24no—
893C24—41no—
894C24—41no—
895C24H(5,𝔽2)14yes—
896C24C2512yes—
897C24C2511yescharacteristic
898C24C2512yes—
899#41—88no—
900C2×Q8—28no—
901C2×Q8—22no—
902C2×Q8—42no—
903C2×Q8—41no—
904C2×Q8—41no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—24no—
912C2×D4—22no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—42no—
916C2×D4—42no—
917C22×C4—264no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—28no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—44no—
953C22×C4—42no—
954C22×C4—44no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—416no—
967C22×C4C2×#4118yes—
968C22×C42−1+418yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4C2×#4118yes—
1047C4⋊C4C2×#4118yes—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4C2×#41116yes—
1075C42—28no—
1076C42—28no—
1077C42—28no—
1078C42—28no—
1079C42—28no—
1080C42—28no—
1081C42—24no—
1082C42—41no—
1083C42—41no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—42no—
1088C42—42no—
1089C42—41no—
1090C42—41no—
1091C42—42no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—42no—
1103C42C2×#41116yes—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—21no—
1111C23—21no—
1112C23—216no—
1113C23—24no—
1114C23—22no—
1115C23—24no—
1116C23—22no—
1117C23—22no—
1118C23—44no—
1119C23—48no—
1120C23—44no—
1121C23—44no—
1122C23C22×#4114yes—
1123C23C2×H(5,𝔽2)12yes—
1124C23C2×H(5,𝔽2)14yes—
1125C23C2×2−1+414yes—
1126C23C2611yescharacteristic
1127Q8—48no—
1128Q8—82no—
1129Q8—162no—
1130D4—416no—
1131D4—82no—
1132D4—84no—
1133C2×C4—216no—
1134C2×C4—216no—
1135C2×C4—216no—
1136C2×C4—216no—
1137C2×C4—28no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—21no—
1152C2×C4—24no—
1153C2×C4—21no—
1154C2×C4—216no—
1155C2×C4—216no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—48no—
1191C2×C4—416no—
1192C2×C4—416no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—44no—
1196C2×C4—416no—
1197C2×C4—84no—
1198C2×C4—88no—
1199C2×C4—162no—
1200C2×C4C22×#4118yes—
1201C2×C4C22×#4114yes—
1202C2×C4C22×#4118yes—
1203C2×C4C22×#4114yes—
1204C2×C4C2×2−1+414yes—
1205C2×C4C2×2−1+414yes—
1206C2×C4#58512yes—
1207C2×C4#58512yes—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—22no—
1216C22—416no—
1217C22—42no—
1218C22—41no—
1219C22—41no—
1220C22—44no—
1221C22—44no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22#349218yes—
1226C22C23×#4112yes—
1227C22C22×H(5,𝔽2)11yescharacteristic
1228C22C22×2−1+412yes—
1229C22C2×#58511yescharacteristic
1230C22C2×#58511yescharacteristic
1231C4—24no—
1232C4—24no—
1233C4—24no—
1234C4—24no—
1235C4—28no—
1236C4—22no—
1237C4—22no—
1238C4—28no—
1239C4—44no—
1240C4—44no—
1241C4—44no—
1242C4—44no—
1243C4—44no—
1244C4—42no—
1245C4—44no—
1246C4—42no—
1247C4—44no—
1248C4—42no—
1249C4—44no—
1250C4—42no—
1251C2—28no—
1252C2—42no—
1253C2—82no—
1254C2#41211yescharacteristic
1255C2C2×#349212yes—
1256C2#6280512yes—
1257C2#6282011yescharacteristic
1258C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60049C2semidirect
2. #60047C2semidirect
3. #60046C2semidirect
4. #59913C2semidirect
5. #59849C2semidirect
6. #59285C2semidirect
8. #38663C2semidirect
9. #38631C2semidirect
10. #38485C2semidirect
11. #38465C2semidirect
12. #38447C2semidirect
13. #38427C2semidirect
15. #36425C2semidirect
16. #36353C2semidirect
17. #36341C2semidirect
18. #36223C2semidirect
19. #35444C2semidirect
20. #35440C2semidirect
21. #35059C2semidirect
22. #34304C2semidirect
23. C2×#2296C2semidirect
40. #2810C22semidirect
41. #2809C22semidirect
42. #2807C22semidirect
43. #2805C22semidirect
44. #2802C22semidirect
45. #2802C22semidirect
46. #2792C22semidirect
47. #2783C22semidirect
48. #2776C22semidirect
52. #2734C22semidirect
53. #2727C22semidirect
54. #2726C22semidirect
55. #2726C22semidirect
56. #2726C22semidirect
57. #2725C22semidirect
59. #2724C22semidirect
62. #2704C22semidirect
63. #2683C22semidirect
64. #2666C22semidirect
65. #2664C22semidirect
66. #2655C22semidirect
67. #2654C22semidirect
71. #2608C22semidirect
72. #2606C22semidirect
73. #2606C22semidirect
75. #2601C22semidirect
78. #2596C22semidirect
79. #2594C22semidirect
80. #2594C22semidirect
81. #2593C22semidirect
82. #2590C22semidirect
83. #2590C22semidirect
84. #2590C22semidirect
85. #2590C22semidirect
86. #2588C22semidirect
87. #2588C22semidirect
88. #2587C22semidirect
89. #2587C22semidirect
90. #2586C22semidirect
91. #2586C22semidirect
92. #2585C22semidirect
93. #2585C22semidirect
94. #2585C22semidirect
95. #2585C22semidirect
96. #2584C22semidirect
97. #2584C22semidirect
99. #2583C22semidirect
101. #2573C22semidirect
102. #2558C22semidirect
103. #2556C22semidirect
104. #2550C22semidirect
105. #2525C22semidirect
106. #2522C22semidirect
107. #2509C22semidirect
108. #2507C22semidirect
154. #2374C22semidirect
155. #2373C22semidirect
156. #2373C22semidirect
157. #2370C22semidirect
158. #2370C22semidirect
159. #2370C22semidirect
160. #2370C22semidirect
161. #2369C22semidirect
163. #2360C22semidirect
169. #2355C22semidirect
171. #2347C22semidirect
178. #2336C22semidirect
179. #2336C22semidirect
180. #2336C22semidirect
181. #2334C22semidirect
182. #2334C22semidirect
183. #2332C22semidirect
184. #2330C22semidirect
185. #2323C22semidirect
215. #2276C22semidirect
216. #2274C22semidirect
699. #117#41semidirect

Maximal subgroups

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

subgroupindex
#600492
#600472
#600462
#599132
#598492
#592852
#591072
#386632
#386312
#384852
#384652
#384472
#384272
#366262
#364252
#363532
#363412
#362232
#354442
#354402
#350592
#343042
C2×#22962