Finite Group Databasebeta

← #7658422

Subgroups — #7658422

Order 512.

4330 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42826C213yesmaximal, complemented
2#42825C213yesmaximal, complemented
3#42824C213yesmaximal, complemented
4#42823C213yesmaximal, complemented
5#42822C213yesmaximal, complemented
6#42821C213yesmaximal, complemented
7#42820C213yesmaximal, complemented
8#42819C213yesmaximal, complemented
9#42492C213yesmaximal
10#42491C213yesmaximal
11#42489C213yesmaximal
12#42488C213yesmaximal
13#37624C213yesmaximal
14#37624C213yesmaximal
15#37567C213yesmaximal
16#36691C213yesmaximal
17#35971C211yesmaximal, characteristic, complemented
18#35971C211yesmaximal, characteristic, complemented
19#35957C211yesmaximal, characteristic, complemented
20#35957C211yesmaximal, characteristic, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35937C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35868C211yesmaximal, characteristic, complemented
25#35845C211yesmaximal, characteristic
26#35786C211yesmaximal, characteristic
27#35786C211yesmaximal, characteristic
28#35711C211yesmaximal, characteristic
29#34196C211yesmaximal, characteristic
30#34192C211yesmaximal, characteristic
31#34182C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2845C2213yes—
40#2845C2213yes—
41#2844C2213yes—
42#2844C2213yes—
43#2843C2213yes—
44#2843C2213yes—
45#2843C2213yes—
46#2843C2213yes—
47#2841C2211yescharacteristic
48#2841C2213yes—
49#2841C2213yes—
50#2841C2213yes—
51#2841C2213yes—
52#2841C2213yes—
53#2841C2213yes—
54#2841C2213yes—
55#2841C2216yes—
56#2806C2216yes—
57#2805C2216yes—
58#2802C2216yes—
59#2802C2216yes—
60#2792C2216yes—
61#2792C2216yes—
62#2791C2216yes—
63#2791C2216yes—
64#2774C2216yes—
65#2774C2216yes—
66#2755C2216yes—
67#2755C2216yes—
68#2734C2216yes—
69#2726C2216yes—
70#2713C2216yes—
71#2713C2216yes—
72#2667C2216yes—
73#2666C2216yes—
74#2666C2216yes—
75#2666C2216yes—
76#2666C2216yes—
77#2666C2216yes—
78#2666C2216yes—
79#2665C2216yes—
80#2660C2216yes—
81#2660C2213yes—
82#2660C2213yes—
83#2660C2213yes—
84#2660C2213yes—
85#2647C2213yes—
86#2647C2213yes—
87#2647C2216yes—
88#2647C2213yes—
89#2647C2213yes—
90#2629C2213yes—
91#2629C2213yes—
92#2629C2216yes—
93#2628C2213yes—
94#2628C2213yes—
95#2628C2216yes—
96#2606C2216yes—
97#2605C2216yes—
98#2584C2213yes—
99#2584C2213yes—
100#2584C2213yes—
101#2584C2213yes—
102#2582C2213yes—
103#2582C2213yes—
104#2581C2213yes—
105#2581C2213yes—
106#2571C2213yes—
107#2571C2213yes—
108#2570C2213yes—
109#2570C2213yes—
110#2570C2213yes—
111#2570C2216yes—
112#2570C2213yes—
113#2568C2213yes—
114#2567C2213yes—
115#2567C2213yes—
116#2567C2213yes—
117#2565C2213yes—
118#2565C2213yes—
119#2552C2213yes—
120#2552C2213yes—
121#2552C2213yes—
122#2552C2213yes—
123#2552C2213yes—
124#2552C2213yes—
125#2551C2213yes—
126#2551C2213yes—
127#2551C2213yes—
128#2551C2213yes—
129#2550C2213yes—
130#2550C2216yes—
131#2550C2213yes—
132#2550C2213yes—
133#2550C2213yes—
134#2550C2213yes—
135#2550C2213yes—
136#2550C2213yes—
137#2550C2213yes—
138#2546C2213yes—
139#2546C2213yes—
140#2509C2213yes—
141#2509C2213yes—
142#2509C2213yes—
143#2509C2213yes—
144#2508C2213yes—
145#2508C2213yes—
146#2508C2213yes—
147#2508C2213yes—
148#2507C2213yes—
149#2507C2213yes—
150#2507C2213yes—
151#2507C2213yes—
152#2506C2213yes—
153#2506C2213yes—
154#2506C2213yes—
155#2506C2213yes—
156#2453C2213yes—
157#2453C2213yes—
158#2453C2213yes—
159#2453C2213yes—
160#2451C2213yes—
161#2451C2213yes—
162#2451C2213yes—
163#2451C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2441C2213yes—
167#2441C2213yes—
168#2441C2216yes—
169#2439C2213yes—
170#2439C2213yes—
171#2439C2213yes—
172#2439C2213yes—
173#2439C2216yes—
174#2402C2213yes—
175#2402C2213yes—
176#2402C2213yes—
177#2402C2213yes—
178#2399C2213yes—
179#2399C2213yes—
180#2399C2213yes—
181#2399C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2396C2213yes—
185#2396C2213yes—
186#2356C2213yes—
187#2356C2213yes—
188#2355C2213yes—
189#2355C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2213yes—
196#2351C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2213yes—
210Q8×C4⋊C4C2213yes—
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214#2345C2213yes—
215#2345C2213yes—
216#2344C2213yes—
217#2344C2213yes—
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222#2320C2213yes—
223#2320C2213yes—
224#2320C2213yes—
225#2320C2213yes—
226#2316C2213yes—
227#2316C2213yes—
228#2285C2213yes—
229#2285C2213yes—
230#2285C2213yes—
231#2283C2213yes—
232#2283C2213yes—
233#2283C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237#2276C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239Q82—44no—
240#557—44no—
241#557—44no—
242#557—44no—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×C4⋊Q8C2316yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2316yes—
258C2×#125C2316yes—
259#519—44no—
260#519—44no—
261C2×C4×Q8Q8116yescomplemented
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2316yes—
291C22×C4⋊C4C2313yes—
292C22×C42C2313yes—
293#400C2313yes—
294#400C2316yes—
295#400C2316yes—
296#400C2313yes—
297#400C2313yes—
298#400C2313yes—
299#400C2316yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2311yescharacteristic
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2311yescharacteristic
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#399C2311yescharacteristic
322#399C2313yes—
323#399C2313yes—
324#399C2313yes—
325#399C2316yes—
326#398C2313yes—
327#398C2313yes—
328#398C2316yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2316yes—
341#398C2316yes—
342#398C2311yescharacteristic
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2311yescharacteristic
357#398C2311yescharacteristic
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2313yes—
369#398C2316yes—
370#398C2313yes—
371#398C2313yes—
372#398C2313yes—
373#398C2313yes—
374#398C2316yes—
375#398C2316yes—
376#398C2316yes—
377#398C2316yes—
378#398C2316yes—
379#398C2316yes—
380#398C2316yes—
381#398C2316yes—
382#396C2311yescharacteristic
383#396C2311yescharacteristic
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2316yes—
391#396C2316yes—
392#395C2313yes—
393#395C2313yes—
394#395C2313yes—
395#395C2316yes—
396#395C2316yes—
397#395C2316yes—
398#395C2313yes—
399#395C2313yes—
400#395C2313yes—
401#395C2311yescharacteristic
402#395C2313yes—
403#395C2313yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#395C2311yescharacteristic
408#395C2313yes—
409#395C2313yes—
410#395C2313yes—
411#395C2313yes—
412#395C2313yes—
413#395C2316yes—
414#395C2316yes—
415#395C2313yes—
416#395C2313yes—
417#395C2316yes—
418#395C2316yes—
419#395C2316yes—
420#393C2311yescharacteristic
421#393C2313yes—
422#393C2313yes—
423#393C2313yes—
424#393C2316yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2316yes—
430#391C2316yes—
431#391C2316yes—
432#391C2316yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2316yes—
438#391C2316yes—
439#391C2316yes—
440#391C2316yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2316yes—
470#389C2316yes—
471#389C2316yes—
472#389C2313yes—
473#389C2313yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2316yes—
487#389C2313yes—
488#389C2316yes—
489#389C2316yes—
490#389C2316yes—
491#389C2313yes—
492#389C2316yes—
493#389C2316yes—
494#389C2316yes—
495#389C2316yes—
496#389C2316yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2316yes—
529#384C2313yes—
530#384C2316yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#383C2313yes—
540#383C2313yes—
541#383C2316yes—
542#383C2313yes—
543#383C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2316yes—
553#382C2313yes—
554#382C2313yes—
555#382C2316yes—
556#382C2313yes—
557#382C2316yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#381C2311yescharacteristic
564#381C2313yes—
565#381C2313yes—
566#381C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2316yes—
570#380C2311yescharacteristic
571#380C2313yes—
572#380C2311yescharacteristic
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2316yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620#376C2313yes—
621#376C2313yes—
622#376C2313yes—
623#376C2313yes—
624#376C2316yes—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8C2×Q818yes—
628C22×Q8C2413yes—
629C22×Q8C2411yescharacteristic
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2416yes—
634C22×Q8C2411yescharacteristic
635C23×C4C2413yes—
636C23×C4C2413yes—
637C23×C4C2411yescharacteristic
638C4⋊Q8—46no—
639C4⋊Q8—46no—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—86no—
645C4⋊Q8—86no—
646#125—46no—
647#125—46no—
648#125—46no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—86no—
653#125—86no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—46no—
667C4×Q8—46no—
668C4×Q8—46no—
669C4×Q8—46no—
670C4×Q8—46no—
671C4×Q8—46no—
672C4×Q8—46no—
673C4×Q8—46no—
674C4×Q8C2×Q8124yes—
675C4×Q8C2×Q8124yes—
676C4×Q8C2×Q818yes—
677C4×Q8C2×Q818yes—
678#117—46no—
679#117—46no—
680#117—46no—
681#117—46no—
682#117—86no—
683C2×C4⋊C4C2×Q8124yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2416yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2416yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C42C2×Q8124yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2416yes—
794C2×C42C2416yes—
795C2×C42C2416yes—
796C2×C42C2416yes—
797C2×C42C2416yes—
798C2×C42C2416yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803#95C2411yescharacteristic
804#95C2411yescharacteristic
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2416yes—
822#95C2416yes—
823#95C2416yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2416yes—
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2413yes—
835#95C2413yes—
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2416yes—
846#95C2416yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2416yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881C24C2511yescharacteristic
882C2×Q8—232no—
883C2×Q8—26no—
884C2×Q8—26no—
885C2×Q8—41no—
886C2×Q8—41no—
887C2×Q8—41no—
888C2×Q8—43no—
889C2×Q8—43no—
890C2×Q8—43no—
891C2×Q8—43no—
892C2×Q8—43no—
893C2×Q8—43no—
894C2×Q8—43no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8—46no—
898C2×Q8—46no—
899C2×Q8—46no—
900C2×Q8C22×Q8112yes—
901C2×Q8C22×Q814yes—
902C2×Q8H(5,𝔽2)14yes—
903C2×Q82−1+414yes—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—43no—
907C22×C4—43no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4C22×Q8112yes—
911C22×C4C22×Q814yes—
912C22×C4C22×Q8112yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920C22×C4C2513yes—
921C22×C4C2513yes—
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C22×C4C2513yes—
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2511yescharacteristic
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—41no—
960C4⋊C4—43no—
961C4⋊C4—41no—
962C4⋊C4—43no—
963C4⋊C4—46no—
964C4⋊C4—41no—
965C4⋊C4—43no—
966C4⋊C4—41no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—41no—
976C4⋊C4—43no—
977C4⋊C4—46no—
978C4⋊C4—43no—
979C4⋊C4—41no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—46no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—41no—
987C4⋊C4—43no—
988C4⋊C4—41no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—46no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4C22×Q8124yes—
1025C4⋊C4C22×Q8112yes—
1026C4⋊C4C22×Q8112yes—
1027C22⋊C4—41no—
1028C22⋊C4—43no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—43no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—43no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C42—26no—
1040C42—26no—
1041C42—26no—
1042C42—26no—
1043C42—26no—
1044C42—26no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—46no—
1052C42—46no—
1053C42—46no—
1054C42—46no—
1055C42—46no—
1056C42—46no—
1057C42C22×Q8112yes—
1058C42C22×Q8112yes—
1059C42C22×Q8112yes—
1060C42C22×Q8112yes—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23C23×Q812yes—
1068C23C2611yescharacteristic
1069Q8—224no—
1070Q8—44no—
1071Q8—86no—
1072Q8—86no—
1073Q8—86no—
1074Q8—166no—
1075Q8#544116yes—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—23no—
1086C2×C4—224no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—44no—
1160C2×C4—412no—
1161C2×C4C23×Q812yes—
1162C2×C4C23×Q812yes—
1163C2×C4C23×Q816yes—
1164C2×C4C23×Q816yes—
1165C2×C4C23×Q816yes—
1166C2×C4C23×Q816yes—
1167C2×C4C2×H(5,𝔽2)16yes—
1168C2×C4C2×2−1+416yes—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22C24×Q811yescharacteristic
1177C22C22×H(5,𝔽2)11yescharacteristic
1178C22C22×2−1+411yescharacteristic
1179C22H(7,𝔽2)11yescharacteristic
1180C222−1+611yescharacteristic
1181C222−1+611yescharacteristic
1182C222−1+611yescharacteristic
1183C4—22no—
1184C4—22no—
1185C4—26no—
1186C4—26no—
1187C4—26no—
1188C4—41no—
1189C4—43no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—43no—
1194C4—43no—
1195C4—41no—
1196C4—41no—
1197C4—43no—
1198C4—43no—
1199C4—41no—
1200C4—41no—
1201C4—43no—
1202C4—43no—
1203C4—43no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—43no—
1208C4—41no—
1209C4—43no—
1210C4—43no—
1211C4—43no—
1212C4C2×#544112yes—
1213C2—42no—
1214C2C22×#54411yescharacteristic
1215C2#6284911yescharacteristic
1216C2#6285411yescharacteristic
1217C2#6304411yescharacteristic
1218C2#6305211yescharacteristic
1219C2#6305711yescharacteristic
1220C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42826C2semidirect
2. #42825C2semidirect
3. #42824C2semidirect
4. #42823C2semidirect
5. #42822C2semidirect
6. #42821C2semidirect
7. #42820C2semidirect
8. #42819C2semidirect
17. #35971C2semidirect
18. #35971C2semidirect
19. #35957C2semidirect
20. #35957C2semidirect
21. #35937C2semidirect
22. #35937C2semidirect
23. #35868C2semidirect
24. #35868C2semidirect
261. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#428262
#428252
#428242
#428232
#428222
#428212
#428202
#428192
#424922
#424912
#424892
#424882
#376242
#375672
#366912
#359712
#359572
#359372
#358682
#358452
#357862
#357112
#341962
#341922
#341822