Finite Group Databasebeta

← #7785359

Subgroups — #7785359

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59866C212yesmaximal, complemented
2#59151C212yesmaximal, complemented
3#51598C214yesmaximal, complemented
4#51595C214yesmaximal, complemented
5#48850C214yesmaximal, complemented
6#47975C214yesmaximal, complemented
7#45272C214yesmaximal, complemented
8#44894C214yesmaximal, complemented
9#43568C214yesmaximal, complemented
10#43556C214yesmaximal, complemented
11#43146C214yesmaximal, complemented
12#39677C212yesmaximal, complemented
13#39676C212yesmaximal, complemented
14#39623C212yesmaximal, complemented
15#37685C212yesmaximal
16#37685C212yesmaximal
17#36749C212yesmaximal
18#36545C212yesmaximal, complemented
19#35779C214yesmaximal
20#35012C211yesmaximal, characteristic
21C2×#2429C211yesmaximal, characteristic
22#34433C212yesmaximal
23#34270C211yesmaximal, characteristic
24C2×Q82C2212yescomplemented
25C2×#557C2212yescomplemented
26C2×#544C2212yes—
27C2×#544C2212yes—
28C2×#543C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2857C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2848C2212yes—
37#2809C2214yescomplemented
38#2809C2212yescomplemented
39#2806C2214yescomplemented
40#2806C2212yescomplemented
41#2806C2214yescomplemented
42#2806C2214yescomplemented
43#2805C2212yescomplemented
44#2802C2214yescomplemented
45#2802C2214yescomplemented
46#2799C2214yescomplemented
47#2792C2214yescomplemented
48#2792C2214yescomplemented
49#2791C2214yescomplemented
50#2791C2214yescomplemented
51#2790C2214yes—
52#2790C2214yes—
53#2788C2214yes—
54#2774C2214yescomplemented
55#2774C2214yescomplemented
56#2768C2214yes—
57#2755C2214yescomplemented
58#2742C2214yes—
59#2734C2214yescomplemented
60#2734C2214yescomplemented
61#2734C2214yescomplemented
62#2729C2214yes—
63#2729C2214yes—
64#2729C2214yes—
65#2726C2214yescomplemented
66#2726C2212yescomplemented
67#2720C2214yes—
68#2720C2214yes—
69#2720C2214yes—
70#2713C2214yescomplemented
71#2713C2214yescomplemented
72#2713C2214yescomplemented
73#2713C2214yescomplemented
74#2704C2214yes—
75#2704C2214yes—
76#2677C2214yes—
77#2677C2214yes—
78#2677C2214yes—
79#2667C2214yes—
80#2665C2214yes—
81#2659C2212yes—
82#2659C2212yes—
83#2659C2212yes—
84#2659C2211yescharacteristic
85#2659C2211yescharacteristic
86#2646C2212yes—
87#2627C2212yes—
88#2627C2212yes—
89#2626C2212yes—
90#2608C2214yes—
91#2608C2214yes—
92#2590C2214yescomplemented
93#2590C2214yescomplemented
94#2590C2214yescomplemented
95#2588C2214yescomplemented
96#2587C2214yes—
97#2587C2214yes—
98#2585C2214yescomplemented
99#2585C2214yescomplemented
100#2585C2214yescomplemented
101#2585C2214yescomplemented
102#2584C2214yescomplemented
103#2584C2212yescomplemented
104#2584C2212yescomplemented
105#2583C2214yes—
106#2582C2212yescomplemented
107#2581C2212yescomplemented
108#2581C2212yescomplemented
109#2574C2214yes—
110#2574C2214yes—
111#2569C2214yes—
112#2567C2212yescomplemented
113#2567C2212yescomplemented
114#2567C2214yescomplemented
115#2565C2214yescomplemented
116#2556C2214yes—
117#2556C2214yes—
118#2552C2214yescomplemented
119#2551C2214yescomplemented
120#2551C2214yescomplemented
121#2551C2214yescomplemented
122#2550C2214yescomplemented
123#2546C2214yescomplemented
124#2546C2212yescomplemented
125#2522C2214yes—
126#2522C2214yes—
127#2520C2214yescomplemented
128#2507C2214yescomplemented
129#2507C2214yescomplemented
130#2505C2214yes—
131#2497C2214yes—
132#2473C2214yes—
133#2473C2214yes—
134#2473C2214yes—
135#2473C2214yes—
136#2473C2214yes—
137#2465C2214yes—
138#2465C2214yes—
139#2462C2214yescomplemented
140#2462C2214yescomplemented
141#2462C2214yescomplemented
142#2462C2214yescomplemented
143#2462C2214yescomplemented
144#2453C2214yescomplemented
145#2453C2214yescomplemented
146#2451C2214yescomplemented
147#2451C2214yescomplemented
148#2451C2214yescomplemented
149#2451C2214yescomplemented
150#2446C2214yescomplemented
151#2441C2214yes—
152#2440C2214yes—
153#2440C2214yes—
154#2440C2214yes—
155#2440C2214yes—
156#2440C2214yes—
157#2440C2214yes—
158#2439C2214yes—
159#2438C2214yes—
160#2438C2214yes—
161#2437C2214yes—
162#2437C2214yes—
163#2434C2214yes—
164#2434C2214yes—
165#2429C2214yes—
166#2429C2214yes—
167#2429C2214yes—
168#2429C2214yes—
169#2429C2214yes—
170#2396C2214yes—
171#2396C2214yes—
172C2×#398C2212yes—
173C2×#396C2212yes—
174#2378C2214yes—
175#2378C2214yes—
176#2370C2214yescomplemented
177#2369C2212yescomplemented
178#2368C2214yes—
179#2368C2214yes—
180#2368C2214yes—
181#2368C2214yes—
182#2365C2214yescomplemented
183#2362C2214yes—
184#2362C2214yes—
185#2360C2214yes—
186#2360C2214yes—
187#2360C2214yes—
188#2360C2214yes—
189#2360C2214yes—
190#2355C2212yescomplemented
191#2345C2214yes—
192#2342C2214yes—
193#2342C2214yes—
194#2332C2214yes—
195#2332C2214yes—
196#2329C2212yes—
197#2329C2212yes—
198#2329C2212yes—
199#2329C2212yes—
200#2329C2212yes—
201#2329C2212yes—
202#2329C2212yes—
203#2323C2214yes—
204#2323C2214yes—
205#2315C2211yescharacteristic
206#2312C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×C22⋊Q8C2212yes—
210C4×C22⋊Q8C2212yes—
211C4×C22⋊Q8C2212yes—
212C2×#391C2211yescharacteristic
213C2×#389C2212yes—
214C2×#389C2211yescharacteristic
215C2×#388C2212yes—
216C2×#385C2212yes—
217#2273C2212yes—
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222Q82—48no—
223#557—48no—
224#544—48no—
225#544—48no—
226#543Q8116yescomplemented
227C2×C4⋊Q8—44no—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×C22⋊Q8—44no—
248C2×C22⋊Q8—44no—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C4×Q8—44no—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298C22×C42C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2311yescharacteristic
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
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#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
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#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#384C2314yes—
558#384C2314yes—
559#384C2314yes—
560#384C2314yes—
561#384C2312yes—
562#382C2314yes—
563#382C2312yes—
564#382C2312yes—
565#381C2314yes—
566#381C2314yes—
567#380C2312yes—
568#380C2312yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572#380C2312yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2314yes—
581#379C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C2×#95C2312yes—
617C2×#95C2311yescharacteristic
618C2×#95C2312yes—
619C2×#95C2311yescharacteristic
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C22×Q8—24no—
625C22×Q8—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2414yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2414yes—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2411yescharacteristic
641C23×C4—42no—
642C23×C4—42no—
643C23×C4—42no—
644C23×C4C2411yescharacteristic
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2411yescharacteristic
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C4⋊Q8—28no—
661C4⋊Q8—216no—
662C4⋊Q8—48no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665C4⋊Q8—48no—
666C4⋊Q8—48no—
667C4⋊Q8—48no—
668C4⋊Q8—48no—
669C4⋊Q8—48no—
670C4⋊Q8—48no—
671C4⋊Q8—48no—
672#125—216no—
673#125—48no—
674#125—44no—
675#125—44no—
676#125—48no—
677#125—48no—
678#125—48no—
679C22⋊Q8—28no—
680C22⋊Q8—28no—
681C22⋊Q8—28no—
682C22⋊Q8—48no—
683C22⋊Q8—48no—
684C22⋊Q8—44no—
685C22⋊Q8—48no—
686C22⋊Q8—48no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—44no—
690C22⋊Q8—44no—
691C22⋊Q8—44no—
692C22⋊Q8—44no—
693C22⋊Q8C2×Q8116yes—
694C22⋊Q8C2×Q8116yes—
695C22⋊Q8C2×Q8132yescomplemented
696C22⋊Q8C2×Q8132yescomplemented
697C4×Q8—28no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×Q8—44no—
702C4×Q8—44no—
703C4×Q8—48no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—48no—
707C4×Q8—48no—
708C4×Q8—44no—
709#117—48no—
710#117—48no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—24no—
713C2×C4⋊C4—44no—
714C2×C4⋊C4—42no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4—44no—
718C2×C4⋊C4—44no—
719C2×C4⋊C4—44no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C22⋊C4—24no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4C2×Q8116yes—
799C2×C22⋊C4C2×Q818yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C42—42no—
817C2×C42—44no—
818C2×C42—42no—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
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#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897C24—22no—
898C24—22no—
899C24—41no—
900C24—41no—
901C24—41no—
902C24—41no—
903C24C22×Q814yes—
904C24C2512yes—
905C24C2511yescharacteristic
906C2×Q8—24no—
907C2×Q8—24no—
908C2×Q8—22no—
909C2×Q8—24no—
910C2×Q8—28no—
911C2×Q8—24no—
912C2×Q8—24no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—41no—
919C2×Q8—42no—
920C2×Q8—41no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—44no—
925C2×Q8—42no—
926C2×Q8—44no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—44no—
932C2×Q8—42no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—416no—
937C2×Q8—88no—
938C2×Q8C22×Q818yes—
939C2×Q8C22×Q818yes—
940C2×Q8H(5,𝔽2)14yes—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—22no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—41no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—88no—
985C22×C4C22×Q814yes—
986C22×C4C22×Q814yes—
987C22×C4C22×Q818yes—
988C22×C4C22×Q818yes—
989C22×C42−1+414yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4C22×Q8116yes—
1080C4⋊C4C22×Q818yes—
1081C4⋊C4C22×Q818yes—
1082C4⋊C4C22×Q8116yes—
1083C4⋊C4H(5,𝔽2)14yes—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4C22×Q8116yes—
1098C22⋊C4C22×Q8116yes—
1099C22⋊C4C22×Q8116yes—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—28no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—28no—
1133C23—44no—
1134C23—44no—
1135C23—82no—
1136C23—82no—
1137C23—82no—
1138C23—82no—
1139C23C23×Q814yes—
1140C23C23×Q812yes—
1141C23C2×2−1+412yes—
1142C23#58512yes—
1143C23C2611yescharacteristic
1144Q8—44no—
1145Q8—48no—
1146Q8—48no—
1147Q8—48no—
1148Q8—48no—
1149Q8—44no—
1150Q8—88no—
1151Q8—84no—
1152Q8—84no—
1153Q8—162no—
1154Q8—164no—
1155C2×C4—28no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—48no—
1213C2×C4—48no—
1214C2×C4—44no—
1215C2×C4—48no—
1216C2×C4—48no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—82no—
1221C2×C4—82no—
1222C2×C4—84no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4C23×Q818yes—
1226C2×C4C23×Q818yes—
1227C2×C4C23×Q814yes—
1228C2×C4C23×Q814yes—
1229C2×C4C2×H(5,𝔽2)14yes—
1230C2×C4C2×H(5,𝔽2)14yes—
1231C2×C4C2×H(5,𝔽2)12yes—
1232C2×C4C2×H(5,𝔽2)12yes—
1233C2×C4C2×2−1+414yes—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—88no—
1248C22#350214yes—
1249C22C24×Q811yescharacteristic
1250C22C22×H(5,𝔽2)11yescharacteristic
1251C22C22×H(5,𝔽2)11yescharacteristic
1252C22C22×2−1+411yescharacteristic
1253C22C2×#58511yescharacteristic
1254C222−1+611yescharacteristic
1255C222−1+611yescharacteristic
1256C4—24no—
1257C4—24no—
1258C4—28no—
1259C4—28no—
1260C4—22no—
1261C4—22no—
1262C4—24no—
1263C4—24no—
1264C4—24no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—44no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C2—24no—
1278C2—44no—
1279C2C2×#350211yescharacteristic
1280C2#6281811yescharacteristic
1281C2#6287311yescharacteristic
1282C2#6289311yescharacteristic
1283C2#6291511yescharacteristic
1284C2Q8×H(5,𝔽2)11yescharacteristic
1285C2Q8×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59866C2semidirect
2. #59151C2semidirect
3. #51598C2semidirect
4. #51595C2semidirect
5. #48850C2semidirect
6. #47975C2semidirect
7. #45272C2semidirect
8. #44894C2semidirect
9. #43568C2semidirect
10. #43556C2semidirect
11. #43146C2semidirect
12. #39677C2semidirect
13. #39676C2semidirect
14. #39623C2semidirect
18. #36545C2semidirect
24. C2×Q82C22semidirect
25. C2×#557C22semidirect
37. #2809C22semidirect
38. #2809C22semidirect
39. #2806C22semidirect
40. #2806C22semidirect
41. #2806C22semidirect
42. #2806C22semidirect
43. #2805C22semidirect
44. #2802C22semidirect
45. #2802C22semidirect
46. #2799C22semidirect
47. #2792C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
54. #2774C22semidirect
55. #2774C22semidirect
57. #2755C22semidirect
59. #2734C22semidirect
60. #2734C22semidirect
61. #2734C22semidirect
65. #2726C22semidirect
66. #2726C22semidirect
70. #2713C22semidirect
71. #2713C22semidirect
72. #2713C22semidirect
73. #2713C22semidirect
92. #2590C22semidirect
93. #2590C22semidirect
94. #2590C22semidirect
95. #2588C22semidirect
98. #2585C22semidirect
99. #2585C22semidirect
100. #2585C22semidirect
101. #2585C22semidirect
102. #2584C22semidirect
103. #2584C22semidirect
104. #2584C22semidirect
106. #2582C22semidirect
107. #2581C22semidirect
108. #2581C22semidirect
112. #2567C22semidirect
113. #2567C22semidirect
114. #2567C22semidirect
115. #2565C22semidirect
118. #2552C22semidirect
119. #2551C22semidirect
120. #2551C22semidirect
121. #2551C22semidirect
122. #2550C22semidirect
123. #2546C22semidirect
124. #2546C22semidirect
127. #2520C22semidirect
128. #2507C22semidirect
129. #2507C22semidirect
139. #2462C22semidirect
140. #2462C22semidirect
141. #2462C22semidirect
142. #2462C22semidirect
143. #2462C22semidirect
144. #2453C22semidirect
145. #2453C22semidirect
146. #2451C22semidirect
147. #2451C22semidirect
148. #2451C22semidirect
149. #2451C22semidirect
150. #2446C22semidirect
176. #2370C22semidirect
177. #2369C22semidirect
182. #2365C22semidirect
190. #2355C22semidirect
226. #543Q8semidirect
695. C22⋊Q8C2×Q8semidirect
696. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598662
#591512
#515982
#515952
#488502
#479752
#452722
#448942
#435682
#435562
#431462
#396772
#396762
#396232
#376852
#367492
#365452
#357792
#350122
C2×#24292
#344332
#342702