Finite Group Databasebeta

← #7644272

Subgroups — #7644272

Order 512.

4018 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42826C212yesmaximal, complemented
2#42823C212yesmaximal, complemented
3#42822C212yesmaximal, complemented
4#42819C212yesmaximal, complemented
5#42818C212yesmaximal
6#42816C212yesmaximal
7#42489C212yesmaximal
8#42488C212yesmaximal
9#42185C214yesmaximal, complemented
10#42002C214yesmaximal, complemented
11#40629C214yesmaximal
12#40628C214yesmaximal
13#37567C212yesmaximal
14#37566C212yesmaximal
15#37565C212yesmaximal
16#37564C212yesmaximal
17#37197C214yesmaximal, complemented
18#37196C214yesmaximal, complemented
19#35642C212yesmaximal, complemented
20#35642C212yesmaximal, complemented
21#35583C212yesmaximal, complemented
22#35582C212yesmaximal, complemented
23#35213C211yesmaximal, characteristic
24#35202C211yesmaximal, characteristic
25#34644C211yesmaximal, characteristic
26#34625C211yesmaximal, characteristic
27#34196C211yesmaximal, characteristic
28#34192C211yesmaximal, characteristic
29#34059C211yesmaximal, characteristic
30C22×C4×Q8C2211yescharacteristic
31#2864C2212yes—
32#2863C2214yes—
33#2859C2212yes—
34#2845C2214yes—
35#2845C2214yes—
36#2843C2214yes—
37#2843C2214yes—
38#2841C2214yes—
39#2841C2214yes—
40#2841C2214yes—
41#2841C2214yes—
42#2809C2214yes—
43#2809C2214yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2805C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2792C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2792C2214yes—
60#2791C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2734C2214yes—
69#2726C2214yes—
70#2726C2214yes—
71#2726C2214yes—
72#2713C2214yes—
73#2713C2214yes—
74#2667C2214yes—
75#2667C2212yes—
76#2667C2214yes—
77#2667C2214yes—
78#2667C2212yes—
79#2667C2211yescharacteristic
80#2667C2211yescharacteristic
81#2667C2212yes—
82#2667C2212yes—
83#2667C2212yes—
84#2667C2214yes—
85#2667C2214yes—
86#2666C2212yes—
87#2666C2214yes—
88#2666C2214yes—
89#2666C2214yes—
90#2666C2214yes—
91#2666C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2666C2212yes—
95#2666C2212yes—
96#2666C2212yes—
97#2665C2214yes—
98#2665C2212yes—
99#2665C2212yes—
100#2665C2211yescharacteristic
101#2665C2211yescharacteristic
102#2665C2212yes—
103#2660C2214yes—
104#2660C2212yes—
105#2647C2212yes—
106#2647C2214yes—
107#2629C2212yes—
108#2629C2214yes—
109#2628C2212yes—
110#2628C2214yes—
111#2612C2214yes—
112#2612C2214yes—
113#2612C2214yes—
114#2612C2214yes—
115#2612C2214yes—
116#2608C2214yes—
117#2608C2212yes—
118#2607C2214yes—
119#2607C2212yes—
120#2606C2214yes—
121#2606C2214yes—
122#2606C2214yes—
123#2606C2214yes—
124#2606C2214yes—
125#2606C2214yes—
126#2606C2214yes—
127#2606C2214yes—
128#2606C2214yes—
129#2605C2214yes—
130#2605C2214yes—
131#2590C2214yes—
132#2590C2214yes—
133#2590C2214yes—
134#2588C2214yes—
135#2586C2214yes—
136#2585C2214yes—
137#2585C2214yes—
138#2585C2214yes—
139#2584C2212yes—
140#2584C2212yes—
141#2584C2212yes—
142#2582C2212yes—
143#2582C2212yes—
144#2582C2212yes—
145#2581C2212yes—
146#2570C2214yes—
147#2570C2214yes—
148#2570C2212yes—
149#2570C2214yes—
150#2567C2212yes—
151#2565C2212yes—
152#2565C2212yes—
153#2565C2212yes—
154#2552C2212yes—
155#2552C2212yes—
156#2552C2212yes—
157#2552C2212yes—
158#2551C2212yes—
159#2550C2214yes—
160#2550C2212yes—
161#2550C2212yes—
162#2550C2214yes—
163#2550C2214yes—
164#2546C2212yes—
165#2520C2214yes—
166#2520C2214yes—
167#2509C2212yes—
168#2508C2212yes—
169#2508C2212yes—
170#2507C2214yes—
171#2507C2212yes—
172#2507C2212yes—
173#2507C2214yes—
174#2507C2212yes—
175#2506C2212yes—
176#2506C2212yes—
177#2462C2214yes—
178#2462C2214yes—
179#2453C2212yes—
180#2453C2212yes—
181#2453C2212yes—
182#2453C2212yes—
183#2453C2212yes—
184#2451C2214yes—
185#2451C2212yes—
186#2451C2212yes—
187#2451C2212yes—
188#2446C2214yes—
189#2441C2212yes—
190#2441C2212yes—
191#2441C2212yes—
192#2441C2214yes—
193#2441C2214yes—
194#2439C2212yes—
195#2439C2214yes—
196#2402C2212yes—
197#2402C2212yes—
198#2399C2212yes—
199#2399C2212yes—
200#2396C2212yes—
201#2396C2214yes—
202#2396C2212yes—
203#2356C2214yes—
204#2356C2212yes—
205#2355C2214yes—
206#2355C2212yes—
207#2351C2212yes—
208Q8×C4⋊C4C2212yes—
209#2345C2214yes—
210#2345C2212yes—
211#2344C2212yes—
212#2344C2212yes—
213#2344C2211yescharacteristic
214#2344C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2212yes—
217Q8×C22⋊C4C2211yescharacteristic
218#2331C2212yes—
219#2330C2212yes—
220#2330C2212yes—
221#2330C2212yes—
222#2320C2212yes—
223#2320C2211yescharacteristic
224#2320C2211yescharacteristic
225#2320C2211yescharacteristic
226#2320C2211yescharacteristic
227#2320C2212yes—
228#2320C2211yescharacteristic
229#2320C2212yes—
230#2320C2212yes—
231#2320C2214yes—
232#2320C2212yes—
233#2320C2211yescharacteristic
234#2316C2212yes—
235#2313C2214yes—
236#2310C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×#125C2212yes—
239#2295C2212yes—
240#2295C2212yes—
241#2295C2214yes—
242#2295C2212yes—
243#2295C2212yes—
244#2285C2211yescharacteristic
245#2285C2212yes—
246#2283C2212yes—
247#2283C2212yes—
248#2283C2211yescharacteristic
249#2283C2211yescharacteristic
250#2283C2211yescharacteristic
251#2283C2212yes—
252#2283C2212yes—
253#2283C2212yes—
254#2276C2211yescharacteristic
255#2276C2212yes—
256#2276C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2314yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×C4×Q8Q8116yescomplemented
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2312yes—
313#400C2312yes—
314#400C2312yes—
315#400C2312yes—
316#399C2312yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2312yes—
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#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#396C2312yes—
387#396C2314yes—
388#396C2312yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2312yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
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#387C2314yes—
537#387C2312yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#384C2312yes—
589#384C2312yes—
590#384C2312yes—
591#384C2312yes—
592#384C2314yes—
593#384C2314yes—
594#384C2314yes—
595#384C2314yes—
596#384C2312yes—
597#383C2312yes—
598#383C2312yes—
599#383C2312yes—
600#383C2314yes—
601#383C2312yes—
602#383C2312yes—
603#383C2312yes—
604#383C2312yes—
605#383C2312yes—
606#383C2314yes—
607#383C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#382C2312yes—
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2311yescharacteristic
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2312yes—
626#381C2314yes—
627#381C2314yes—
628#381C2312yes—
629#381C2312yes—
630#381C2311yescharacteristic
631#381C2311yescharacteristic
632#381C2311yescharacteristic
633#381C2312yes—
634#381C2311yescharacteristic
635#380C2314yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2311yescharacteristic
642#380C2311yescharacteristic
643#380C2312yes—
644#380C2312yes—
645#380C2311yescharacteristic
646#380C2311yescharacteristic
647#380C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2311yescharacteristic
697C4×C22⋊C4C2312yes—
698#376C2312yes—
699#376C2311yescharacteristic
700#376C2311yescharacteristic
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2312yes—
711C43C2312yes—
712C43C2312yes—
713C22×Q8—44no—
714C22×Q8C2×Q818yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C23×C4C2411yescharacteristic
723C23×C4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2411yescharacteristic
727C4⋊Q8—44no—
728C4⋊Q8—44no—
729C4⋊Q8—84no—
730C4⋊Q8—84no—
731#125—44no—
732#125—44no—
733#125—44no—
734#125—44no—
735#125—84no—
736#125—84no—
737#125—84no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×Q8—44no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—84no—
745C4×Q8C2×Q818yes—
746C4×Q8C2×Q818yes—
747C4×Q8C2×Q818yes—
748C4×Q8C2×Q818yes—
749C4×Q8C2×Q8116yes—
750C4×Q8C2×Q8116yes—
751#117—44no—
752#117—44no—
753#117—82no—
754#117—82no—
755#117—82no—
756C2×C4⋊C4C2×Q818yes—
757C2×C4⋊C4C2×Q8116yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2411yescharacteristic
851C2×C42C2×Q818yes—
852C2×C42C2×Q8116yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2412yes—
886#95C2412yes—
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2414yes—
890#95C2412yes—
891#95C2411yescharacteristic
892#95C2412yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2412yes—
896#95C2411yescharacteristic
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2411yescharacteristic
907#95C2412yes—
908#95C2411yescharacteristic
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
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#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977C24C2511yescharacteristic
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—44no—
981C2×Q8—42no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×Q8—44no—
992C2×Q8—44no—
993C2×Q8—416no—
994C2×Q8C22×Q814yes—
995C2×Q8C22×Q814yes—
996C2×Q8C22×Q818yes—
997C22×C4—24no—
998C22×C4—41no—
999C22×C4—42no—
1000C22×C4—41no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4C22×Q814yes—
1005C22×C4C22×Q814yes—
1006C22×C4C22×Q814yes—
1007C22×C4C22×Q818yes—
1008C22×C4C22×Q818yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
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—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
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—42no—
1111C4⋊C4C22×Q818yes—
1112C4⋊C4C22×Q818yes—
1113C4⋊C4C22×Q818yes—
1114C4⋊C4C22×Q818yes—
1115C4⋊C4C22×Q818yes—
1116C4⋊C4C22×Q814yes—
1117C4⋊C4C22×Q814yes—
1118C22⋊C4—42no—
1119C22⋊C4—41no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—41no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—44no—
1126C22⋊C4—42no—
1127C22⋊C4—41no—
1128C22⋊C4—42no—
1129C22⋊C4—41no—
1130C42—24no—
1131C42—24no—
1132C42—24no—
1133C42—24no—
1134C42—24no—
1135C42—24no—
1136C42—42no—
1137C42—42no—
1138C42—44no—
1139C42—42no—
1140C42—42no—
1141C42—44no—
1142C42—42no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—44no—
1155C42C22×Q814yes—
1156C42C22×Q818yes—
1157C42C22×Q818yes—
1158C42C22×Q814yes—
1159C42C22×Q818yes—
1160C42C22×Q818yes—
1161C42C22×Q814yes—
1162C42C22×Q814yes—
1163C23—22no—
1164C23—21no—
1165C23—22no—
1166C23—21no—
1167C23C23×Q812yes—
1168C23C2611yescharacteristic
1169Q8—28no—
1170Q8—28no—
1171Q8—48no—
1172Q8—84no—
1173Q8—88no—
1174Q8—84no—
1175Q8—164no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—28no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—48no—
1247C2×C4—48no—
1248C2×C4C23×Q812yes—
1249C2×C4C23×Q812yes—
1250C2×C4C23×Q812yes—
1251C2×C4C23×Q814yes—
1252C2×C4C23×Q812yes—
1253C2×C4C23×Q814yes—
1254C2×C4C23×Q812yes—
1255C2×C4C23×Q814yes—
1256C2×C4C23×Q814yes—
1257C2×C4C23×Q812yes—
1258C2×C4#58514yes—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—42no—
1263C22—42no—
1264C22C24×Q811yescharacteristic
1265C22C2×#58512yes—
1266C22H(7,𝔽2)11yescharacteristic
1267C222−1+612yes—
1268C222−1+611yescharacteristic
1269C4—22no—
1270C4—22no—
1271C4—22no—
1272C4—24no—
1273C4—22no—
1274C4—24no—
1275C4—22no—
1276C4—24no—
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—44no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—44no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4#345814yes—
1297C2—42no—
1298C2C2×#345811yescharacteristic
1299C2#6284911yescharacteristic
1300C2#6285411yescharacteristic
1301C2#6288412yes—
1302C2#6289012yes—
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. #42823C2semidirect
3. #42822C2semidirect
4. #42819C2semidirect
9. #42185C2semidirect
10. #42002C2semidirect
17. #37197C2semidirect
18. #37196C2semidirect
19. #35642C2semidirect
20. #35642C2semidirect
21. #35583C2semidirect
22. #35582C2semidirect
271. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#428262
#428232
#428222
#428192
#428182
#428162
#424892
#424882
#421852
#420022
#406292
#406282
#375672
#375662
#375652
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