Finite Group Databasebeta

← #7732256

Subgroups — #7732256

Order 512.

4474 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48877C214yesmaximal, complemented
2#48006C214yesmaximal, complemented
3#47224C212yesmaximal, complemented
4#47032C212yesmaximal, complemented
5#46855C212yesmaximal, complemented
6#46453C212yesmaximal, complemented
7#43052C214yesmaximal, complemented
8#43052C214yesmaximal, complemented
9#40333C214yesmaximal, complemented
10#39799C212yesmaximal, complemented
11#39797C212yesmaximal, complemented
12#39751C212yesmaximal, complemented
13#39748C212yesmaximal, complemented
14#38733C214yesmaximal, complemented
15#38482C214yesmaximal, complemented
16#37447C211yesmaximal, characteristic
17#37011C212yesmaximal, complemented
18#36819C212yesmaximal, complemented
19#36387C214yesmaximal, complemented
20#35496C212yesmaximal, complemented
21#35440C212yesmaximal, complemented
22#35085C211yesmaximal, characteristic
23#35011C211yesmaximal, characteristic, complemented
24C2×#2608C211yesmaximal, characteristic, complemented
25#34359C211yesmaximal, characteristic, complemented
26#34245C211yesmaximal, characteristic, complemented
27#34082C211yesmaximal, characteristic
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31#2864C2214yescomplemented
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2851C2214yescomplemented
37#2850C2211yescharacteristic
38#2850C2211yescharacteristic
39#2817C2212yes—
40#2816C2212yes—
41#2805C2214yescomplemented
42#2802C2214yescomplemented
43#2798C2214yescomplemented
44#2794C2214yescomplemented
45#2791C2214yescomplemented
46#2789C2214yescomplemented
47#2789C2214yescomplemented
48#2788C2214yescomplemented
49#2787C2214yescomplemented
50#2786C2214yescomplemented
51#2783C2214yescomplemented
52#2775C2214yescomplemented
53#2774C2214yescomplemented
54#2767C2214yescomplemented
55#2765C2214yes—
56#2765C2214yes—
57#2765C2214yes—
58#2765C2214yes—
59#2761C2214yes—
60#2761C2214yes—
61#2758C2214yescomplemented
62#2755C2214yescomplemented
63#2755C2214yescomplemented
64#2754C2214yescomplemented
65#2750C2214yes—
66#2750C2214yes—
67#2744C2214yes—
68#2744C2214yes—
69#2739C2214yes—
70#2739C2214yes—
71#2726C2214yescomplemented
72#2721C2214yescomplemented
73#2716C2214yescomplemented
74#2715C2214yescomplemented
75#2713C2214yescomplemented
76#2713C2214yescomplemented
77#2707C2214yes—
78#2707C2214yes—
79#2695C2214yes—
80#2695C2214yes—
81#2663C2214yes—
82#2659C2212yes—
83#2659C2212yes—
84#2659C2212yes—
85#2655C2214yescomplemented
86#2652C2214yescomplemented
87#2639C2212yes—
88#2638C2214yes—
89#2623C2212yes—
90#2614C2212yes—
91#2609C2214yes—
92#2609C2214yes—
93#2608C2212yes—
94#2608C2214yes—
95#2608C2212yes—
96#2608C2212yes—
97#2608C2214yes—
98#2608C2212yes—
99#2601C2214yes—
100#2601C2214yes—
101#2601C2214yescomplemented
102#2599C2214yescomplemented
103#2594C2214yescomplemented
104#2590C2214yescomplemented
105#2590C2214yescomplemented
106#2590C2214yescomplemented
107#2589C2214yescomplemented
108#2589C2214yescomplemented
109#2588C2214yescomplemented
110#2588C2214yescomplemented
111#2588C2214yescomplemented
112#2588C2214yescomplemented
113#2587C2214yescomplemented
114#2587C2214yescomplemented
115#2584C2214yescomplemented
116#2583C2214yes—
117#2583C2212yes—
118#2583C2212yes—
119#2579C2214yes—
120#2579C2214yes—
121#2573C2214yes—
122#2573C2214yes—
123#2570C2214yescomplemented
124#2569C2214yes—
125#2569C2214yes—
126#2564C2214yes—
127#2564C2214yes—
128#2558C2214yes—
129#2558C2214yes—
130#2550C2214yescomplemented
131#2550C2214yescomplemented
132#2533C2214yescomplemented
133#2528C2214yescomplemented
134#2524C2214yescomplemented
135#2520C2214yescomplemented
136#2515C2214yes—
137#2515C2214yes—
138#2510C2214yes—
139#2510C2214yes—
140#2508C2214yescomplemented
141#2506C2214yescomplemented
142#2503C2211yescharacteristic
143#2502C2212yes—
144#2502C2212yes—
145#2501C2211yescharacteristic
146#2499C2211yescharacteristic
147#2499C2211yescharacteristic
148#2484C2212yes—
149#2481C2214yes—
150#2481C2214yes—
151#2478C2214yescomplemented
152#2478C2214yescomplemented
153#2475C2214yes—
154#2475C2214yes—
155#2475C2214yes—
156#2475C2214yes—
157#2475C2214yescomplemented
158#2474C2214yescomplemented
159#2470C2214yes—
160#2470C2214yes—
161#2469C2214yescomplemented
162#2462C2214yescomplemented
163#2442C2214yes—
164#2442C2214yes—
165#2442C2214yes—
166#2442C2214yes—
167#2441C2214yescomplemented
168#2439C2214yescomplemented
169#2436C2211yescharacteristic
170#2434C2211yescharacteristic
171#2434C2212yes—
172#2434C2212yes—
173#2432C2211yescharacteristic
174#2432C2211yescharacteristic
175#2412C2214yes—
176#2412C2212yes—
177#2412C2212yes—
178#2406C2212yes—
179C2×#396C2212yes—
180C2×#396C2212yes—
181#2378C2214yes—
182#2368C2214yes—
183#2368C2214yes—
184#2362C2212yes—
185#2362C2212yes—
186#2352C2214yes—
187#2352C2214yes—
188#2345C2214yes—
189#2345C2214yes—
190#2344C2212yes—
191#2344C2212yes—
192#2344C2212yes—
193#2342C2212yes—
194#2342C2212yes—
195#2342C2214yes—
196Q8×C22⋊C4C2212yes—
197#2336C2214yescomplemented
198#2335C2214yes—
199#2334C2214yescomplemented
200#2333C2212yes—
201#2332C2212yes—
202#2332C2212yes—
203#2332C2212yes—
204#2332C2212yes—
205#2332C2212yes—
206#2329C2212yes—
207#2329C2212yes—
208#2329C2212yes—
209#2325C2212yes—
210#2322C2214yes—
211#2321C2214yes—
212#2315C2214yes—
213#2313C2212yes—
214#2313C2212yes—
215#2310C2212yes—
216C4×#125C2214yescomplemented
217C4×C22⋊Q8C2212yes—
218C4×C22⋊Q8C2212yes—
219#2298C2212yes—
220#2297C2212yes—
221#2296C2214yescomplemented
222#2293C2212yes—
223C2×#389C2212yes—
224C2×#389C2212yes—
225#2290C2212yes—
226#2290C2212yes—
227C2×#387C2212yes—
228C2×#387C2212yes—
229#2280C2211yescharacteristic
230C2×#381C2211yescharacteristic
231#2274C2212yes—
232C42×D4C2212yes—
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×Q8C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251#525—28no—
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×C22⋊Q8—28no—
257C2×C22⋊Q8—28no—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×#121C2311yescharacteristic
271C2×#121C2311yescharacteristic
272C2×#120C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×#117C2311yescharacteristic
279C2×#117C2314yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308#401C2314yes—
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2314yes—
332#399C2314yes—
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#398C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2312yes—
406#391C2312yes—
407#391C2311yescharacteristic
408#391C2312yes—
409#391C2312yes—
410#391C2311yescharacteristic
411#391C2312yes—
412#391C2312yes—
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#390C2314yes—
416#390C2314yes—
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
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#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#387C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2312yes—
546#386C2312yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2312yes—
571#385C2312yes—
572#384C2312yes—
573#384C2312yes—
574#384C2311yescharacteristic
575#384C2311yescharacteristic
576#383C2314yes—
577#383C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2314yes—
581#382C2314yes—
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#382C2314yes—
585#382C2314yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2312yes—
590#381C2314yes—
591#381C2312yes—
592#381C2314yes—
593#381C2312yes—
594#381C2312yes—
595#381C2312yes—
596#381C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2312yes—
609#380C2312yes—
610#380C2314yes—
611#380C2314yes—
612#379C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2311yescharacteristic
644C4×C22⋊C4C2311yescharacteristic
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2311yescharacteristic
652C4×C22⋊C4C2312yes—
653#376C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C25C2411yescharacteristic
662C2×#41—24no—
663C2×#41—81no—
664C2×#41—81no—
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8—81no—
668C22×Q8—81no—
669C22×Q8—81no—
670C22×Q8—81no—
671C22×Q8C2412yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2411yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2412yes—
680C22×D4C2411yescharacteristic
681C23×C4—81no—
682C23×C4—81no—
683C23×C4#4118yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C4⋊Q8—82no—
703C4⋊Q8—81no—
704C4⋊Q8—81no—
705C4⋊Q8—82no—
706#126—48no—
707#126—84no—
708#125—48no—
709#125—48no—
710#125—84no—
711#125—84no—
712#124—81no—
713#124—81no—
714#123—28no—
715#123—48no—
716#123—82no—
717#123—82no—
718C22⋊Q8—24no—
719C22⋊Q8—24no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C22⋊Q8—28no—
725C22⋊Q8—28no—
726C22⋊Q8—24no—
727C22⋊Q8—24no—
728C22⋊Q8—24no—
729C22⋊Q8—24no—
730#121—24no—
731#121—24no—
732#120—28no—
733C4×Q8—82no—
734C4×Q8—82no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—216no—
738#117—24no—
739#117—48no—
740#117—48no—
741#117—81no—
742#117—82no—
743#117—82no—
744#117—81no—
745#117—84no—
746#117—82no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4—28no—
749C2×C4⋊C4—28no—
750C2×C4⋊C4—24no—
751C2×C4⋊C4—28no—
752C2×C4⋊C4—28no—
753C2×C4⋊C4—44no—
754C2×C4⋊C4—44no—
755C2×C4⋊C4—82no—
756C2×C4⋊C4—82no—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C22⋊C4—28no—
814C2×C22⋊C4—28no—
815C2×C22⋊C4—28no—
816C2×C22⋊C4—44no—
817C2×C22⋊C4—81no—
818C2×C22⋊C4—81no—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C42—81no—
856C2×C42—82no—
857C2×C42—81no—
858C2×C42—81no—
859C2×C42—81no—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946C24—24no—
947C24—42no—
948C24—41no—
949C24—41no—
950C24C2×#4114yes—
951C24C2512yes—
952C24C2511yescharacteristic
953C24C2511yescharacteristic
954C24C2511yescharacteristic
955#41—88no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—22no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—41no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—41no—
973C2×Q8—41no—
974C2×Q8—88no—
975C2×Q8—88no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—22no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—41no—
985C2×D4—41no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—88no—
1032C22×C4C2×#4114yes—
1033C22×C4C2×#4114yes—
1034C22×C4C2×#4114yes—
1035C22×C4C2×#4114yes—
1036C22×C4C2×#4114yes—
1037C22×C4C2×#4114yes—
1038C22×C42−1+418yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C42—24no—
1155C42—28no—
1156C42—28no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—41no—
1163C42—41no—
1164C42—44no—
1165C42—41no—
1166C42—42no—
1167C42—41no—
1168C42—42no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C23—22no—
1179C23—21no—
1180C23—21no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—28no—
1190C23—22no—
1191C23—24no—
1192C23—24no—
1193C23—22no—
1194C23—22no—
1195C23—44no—
1196C23—44no—
1197C23—84no—
1198C23—84no—
1199C23C22×#4112yes—
1200C23C22×#4112yes—
1201C23C22×#4112yes—
1202C23C2×2−1+414yes—
1203C23C2611yescharacteristic
1204Q8—48no—
1205Q8—82no—
1206Q8—82no—
1207Q8—84no—
1208Q8—84no—
1209Q8—82no—
1210D4—48no—
1211D4—82no—
1212D4—84no—
1213D4—84no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—24no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—44no—
1274C2×C4—44no—
1275C2×C4—44no—
1276C2×C4—44no—
1277C2×C4—44no—
1278C2×C4—44no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—416no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—48no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4C2×2−1+418yes—
1296C2×C4#58514yes—
1297C22—22no—
1298C22—22no—
1299C22—24no—
1300C22—24no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—44no—
1316C22—88no—
1317C22#350914yes—
1318C22C23×#4111yescharacteristic
1319C22C22×2−1+412yes—
1320C22C2×#58512yes—
1321C22H(7,𝔽2)11yescharacteristic
1322C22H(7,𝔽2)11yescharacteristic
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—28no—
1328C4—24no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—44no—
1338C4—44no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C2—24no—
1347C2—42no—
1348C2—42no—
1349C2—82no—
1350C2C2×#350911yescharacteristic
1351C2#6281511yescharacteristic
1352C2#6284411yescharacteristic
1353C2#6290212yes—
1354C2#6295812yes—
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. #48877C2semidirect
2. #48006C2semidirect
3. #47224C2semidirect
4. #47032C2semidirect
5. #46855C2semidirect
6. #46453C2semidirect
7. #43052C2semidirect
8. #43052C2semidirect
9. #40333C2semidirect
10. #39799C2semidirect
11. #39797C2semidirect
12. #39751C2semidirect
13. #39748C2semidirect
14. #38733C2semidirect
15. #38482C2semidirect
17. #37011C2semidirect
18. #36819C2semidirect
19. #36387C2semidirect
20. #35496C2semidirect
21. #35440C2semidirect
23. #35011C2semidirect
24. C2×#2608C2semidirect
25. #34359C2semidirect
26. #34245C2semidirect
31. #2864C22semidirect
36. #2851C22semidirect
41. #2805C22semidirect
42. #2802C22semidirect
43. #2798C22semidirect
44. #2794C22semidirect
45. #2791C22semidirect
46. #2789C22semidirect
47. #2789C22semidirect
48. #2788C22semidirect
49. #2787C22semidirect
50. #2786C22semidirect
51. #2783C22semidirect
52. #2775C22semidirect
53. #2774C22semidirect
54. #2767C22semidirect
61. #2758C22semidirect
62. #2755C22semidirect
63. #2755C22semidirect
64. #2754C22semidirect
71. #2726C22semidirect
72. #2721C22semidirect
73. #2716C22semidirect
74. #2715C22semidirect
75. #2713C22semidirect
76. #2713C22semidirect
85. #2655C22semidirect
86. #2652C22semidirect
101. #2601C22semidirect
102. #2599C22semidirect
103. #2594C22semidirect
104. #2590C22semidirect
105. #2590C22semidirect
106. #2590C22semidirect
107. #2589C22semidirect
108. #2589C22semidirect
109. #2588C22semidirect
110. #2588C22semidirect
111. #2588C22semidirect
112. #2588C22semidirect
113. #2587C22semidirect
114. #2587C22semidirect
115. #2584C22semidirect
123. #2570C22semidirect
130. #2550C22semidirect
131. #2550C22semidirect
132. #2533C22semidirect
133. #2528C22semidirect
134. #2524C22semidirect
135. #2520C22semidirect
140. #2508C22semidirect
141. #2506C22semidirect
151. #2478C22semidirect
152. #2478C22semidirect
157. #2475C22semidirect
158. #2474C22semidirect
161. #2469C22semidirect
162. #2462C22semidirect
167. #2441C22semidirect
168. #2439C22semidirect
197. #2336C22semidirect
199. #2334C22semidirect
216. C4×#125C22semidirect
221. #2296C22semidirect

Maximal subgroups

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

subgroupindex
#488772
#480062
#472242
#470322
#468552
#464532
#430522
#403332
#397992
#397972
#397512
#397482
#387332
#384822
#374472
#370112
#368192
#363872
#354962
#354402
#350852
#350112
C2×#26082
#343592
#342452
#340822