Finite Group Databasebeta

← #7711776

Subgroups — #7711776

Order 512.

4316 conjugacy classes of subgroups.

The subgroup lattice has 1434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59873C212yesmaximal
2#59868C212yesmaximal, complemented
3#59866C212yesmaximal, complemented
4#59855C212yesmaximal
5#46160C212yesmaximal, complemented
6#46159C212yesmaximal, complemented
7#46158C211yesmaximal, characteristic, complemented
8#46157C211yesmaximal, characteristic, complemented
9#46023C211yesmaximal, characteristic, complemented
10#46022C211yesmaximal, characteristic, complemented
11#39826C214yesmaximal, complemented
12#39791C212yesmaximal, complemented
13#39788C212yesmaximal, complemented
14#39476C212yesmaximal, complemented
15#39476C212yesmaximal, complemented
16#39473C214yesmaximal, complemented
17#38496C214yesmaximal, complemented
18#38461C214yesmaximal, complemented
19#37607C212yesmaximal
20#37203C212yesmaximal, complemented
21#37146C212yesmaximal, complemented
22#36635C211yesmaximal, characteristic, complemented
23C2×#2859C211yesmaximal, characteristic, complemented
24#36400C212yesmaximal, complemented
25#36387C212yesmaximal, complemented
26#36384C212yesmaximal, complemented
27#36278C212yesmaximal, complemented
28#35115C212yesmaximal, complemented
29#35045C212yesmaximal, complemented
30#34372C212yesmaximal, complemented
31C4×#529C211yesmaximal, characteristic
32C2×#529C2211yescharacteristic
33C22×#125C2212yes—
34#2864C2212yes—
35#2864C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2859C2212yes—
41#2859C2211yescharacteristic
42#2859C2212yes—
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2211yescharacteristic
46#2859C2212yes—
47#2859C2212yes—
48#2859C2212yes—
49#2859C2212yes—
50#2859C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2855C2212yes—
54#2855C2212yes—
55#2855C2212yes—
56#2851C2212yes—
57#2851C2212yes—
58#2822C2212yes—
59#2822C2212yes—
60#2820C2212yes—
61#2820C2212yes—
62#2810C2212yes—
63#2809C2212yes—
64#2808C2212yes—
65#2806C2212yes—
66#2805C2212yes—
67#2805C2212yes—
68#2802C2214yes—
69#2802C2214yes—
70#2800C2214yes—
71#2794C2214yes—
72#2794C2214yes—
73#2793C2214yes—
74#2793C2214yes—
75#2791C2214yes—
76#2791C2214yes—
77#2783C2214yes—
78#2776C2214yes—
79#2776C2214yes—
80#2774C2214yes—
81#2773C2214yes—
82#2773C2214yes—
83#2772C2214yes—
84#2767C2214yes—
85#2767C2214yes—
86#2766C2214yes—
87#2762C2214yes—
88#2762C2214yes—
89#2754C2214yes—
90#2754C2214yes—
91#2727C2212yes—
92#2726C2212yes—
93#2725C2214yes—
94#2725C2214yes—
95#2721C2214yes—
96#2721C2214yes—
97#2719C2214yes—
98#2664C2214yes—
99#2664C2214yes—
100#2655C2214yes—
101#2652C2214yes—
102#2634C2214yes—
103#2633C2214yes—
104#2623C2214yes—
105#2623C2214yes—
106#2611C2214yes—
107#2611C2214yes—
108#2608C2214yes—
109#2606C2214yes—
110#2596C2214yes—
111#2594C2214yes—
112#2591C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2590C2214yes—
116#2589C2214yes—
117#2588C2214yes—
118#2587C2214yes—
119#2587C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2585C2214yes—
123#2584C2212yes—
124#2583C2214yes—
125#2581C2212yes—
126#2579C2214yes—
127#2579C2214yes—
128#2575C2214yes—
129#2575C2214yes—
130#2573C2214yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2569C2214yes—
135#2565C2212yes—
136#2565C2212yes—
137#2564C2214yes—
138#2550C2212yes—
139#2533C2214yes—
140#2533C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2517C2214yes—
148#2517C2214yes—
149#2514C2212yes—
150#2511C2212yes—
151#2511C2212yes—
152#2510C2214yes—
153#2510C2214yes—
154#2509C2212yes—
155#2509C2212yes—
156#2509C2214yes—
157#2508C2212yes—
158#2507C2212yes—
159#2506C2212yes—
160#2506C2212yes—
161#2505C2214yes—
162#2505C2214yes—
163#2499C2212yes—
164#2499C2212yes—
165#2497C2212yes—
166#2496C2212yes—
167#2496C2212yes—
168#2494C2212yes—
169#2485C2212yes—
170#2481C2214yes—
171#2481C2214yes—
172#2478C2214yes—
173#2475C2214yes—
174#2473C2214yes—
175#2473C2214yes—
176#2469C2214yes—
177#2466C2214yes—
178#2462C2214yes—
179#2453C2212yes—
180#2453C2214yes—
181#2453C2212yes—
182#2446C2212yes—
183#2442C2212yes—
184#2442C2212yes—
185#2441C2212yes—
186#2441C2212yes—
187#2441C2212yes—
188#2439C2212yes—
189#2429C2212yes—
190#2423C2212yes—
191#2423C2212yes—
192#2421C2212yes—
193#2417C2212yes—
194#2417C2212yes—
195#2415C2212yes—
196#2382C2212yes—
197#2382C2212yes—
198#2382C2212yes—
199#2382C2212yes—
200#2373C2214yes—
201#2371C2214yes—
202#2371C2214yes—
203#2370C2212yes—
204#2370C2214yes—
205#2368C2214yes—
206#2362C2212yes—
207#2360C2212yes—
208#2360C2212yes—
209#2353C2214yes—
210#2352C2212yes—
211#2352C2212yes—
212#2351C2212yes—
213#2347C2212yes—
214#2345C2214yes—
215#2345C2214yes—
216#2345C2214yes—
217#2345C2214yes—
218#2336C2214yes—
219#2336C2214yes—
220#2336C2214yes—
221#2336C2214yes—
222#2336C2214yes—
223#2334C2214yes—
224#2313C2214yes—
225#2313C2214yes—
226C4×C4⋊Q8C2211yescharacteristic
227C4×C4⋊Q8C2211yescharacteristic
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#125C2211yescharacteristic
231C4×#125C2211yescharacteristic
232C4×#126C2212yes—
233C4×#126C2212yes—
234C4×#124C2211yescharacteristic
235C4×#124C2211yescharacteristic
236C4×C22⋊Q8C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2211yescharacteristic
240C4×C22⋊Q8C2211yescharacteristic
241C4×#123C2212yes—
242C4×#123C2212yes—
243C4×#121C2211yescharacteristic
244C4×#121C2211yescharacteristic
245#2298C2212yes—
246#2296C2212yes—
247#2295C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2295C2212yes—
251#2293C2211yescharacteristic
252C2×#389C2212yes—
253C2×#389C2212yes—
254C2×#389C2212yes—
255C2×#389C2212yes—
256#2290C2212yes—
257C2×#384C2211yescharacteristic
258C2×#384C2211yescharacteristic
259#2283C2212yes—
260#2283C2211yescharacteristic
261C2×#382C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2212yes—
264C42×D4C2211yescharacteristic
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269#529—28no—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125—216no—
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#123C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×#121C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327#401C2314yes—
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
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#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2311yescharacteristic
430#389C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2312yes—
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#387C2314yes—
538#387C2314yes—
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#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2312yes—
600#386C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2312yes—
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2312yes—
627#383C2312yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#382C2312yes—
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#381C2312yes—
650#381C2314yes—
651#381C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2311yescharacteristic
664#380C2311yescharacteristic
665#380C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2314yes—
722#376C2314yes—
723#376C2312yes—
724#376C2312yes—
725C2×#95C2314yes—
726C2×#95C2314yes—
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2312yes—
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8C2412yes—
737C22×Q8C2411yescharacteristic
738C22×Q8C2412yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2414yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755#126—28no—
756#126—48no—
757#126—48no—
758#125—28no—
759#125—28no—
760#125—216no—
761#125—28no—
762#125—28no—
763#125—216no—
764#125—24no—
765#125—44no—
766#125—44no—
767#125—44no—
768#125—48no—
769#125—48no—
770#124—24no—
771#123—28no—
772C22⋊Q8—24no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777#121—24no—
778C4×Q8—24no—
779C4×Q8—42no—
780C4×Q8—42no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—24no—
789C4×D4—42no—
790C4×D4—42no—
791#117—28no—
792#117—44no—
793#117—44no—
794#117—44no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—28no—
797C2×C4⋊C4—216no—
798C2×C4⋊C4—216no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C42—24no—
901C2×C42—24no—
902C2×C42—44no—
903C2×C42—42no—
904C2×C42—42no—
905C2×C42—42no—
906C2×C42—42no—
907C2×C42#4118yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2512yes—
1030C24C2511yescharacteristic
1031C2×Q8—22no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—22no—
1044C2×D4—41no—
1045C2×D4—41no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—28no—
1055C22×C4—28no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—42no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2×#4114yes—
1080C22×C42−1+414yes—
1081C22×C42−1+414yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—41no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C42—24no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—22no—
1224C42—22no—
1225C42—24no—
1226C42—22no—
1227C42—22no—
1228C42—24no—
1229C42—41no—
1230C42—41no—
1231C42—41no—
1232C42—41no—
1233C42—41no—
1234C42—42no—
1235C42—42no—
1236C42—41no—
1237C42—41no—
1238C42—41no—
1239C42—42no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—42no—
1245C42—44no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42C2×#4114yes—
1252C42C2×#4114yes—
1253C42C2×#4114yes—
1254C42C2×#4114yes—
1255C23—21no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23C22×#4112yes—
1267C23C2×2−1+412yes—
1268C23C2×2−1+412yes—
1269C23C2611yescharacteristic
1270Q8—44no—
1271Q8—48no—
1272Q8—84no—
1273D4—44no—
1274D4—48no—
1275C2×C4—28no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—28no—
1299C2×C4—28no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—44no—
1352C2×C4—44no—
1353C2×C4—44no—
1354C2×C4—48no—
1355C2×C4—44no—
1356C2×C4—48no—
1357C2×C4—84no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C22×#4112yes—
1365C2×C4C22×#4112yes—
1366C2×C4C2×2−1+412yes—
1367C2×C4C2×2−1+412yes—
1368C2×C4C2×2−1+412yes—
1369C2×C4C2×2−1+412yes—
1370C2×C4#58512yes—
1371C2×C4#58512yes—
1372C2×C4#58512yes—
1373C2×C4#58512yes—
1374C22—22no—
1375C22—22no—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22#350914yes—
1388C22C23×#4111yescharacteristic
1389C22C22×2−1+411yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C2×#58511yescharacteristic
1392C22C2×#58511yescharacteristic
1393C22C2×#58511yescharacteristic
1394C22C2×#58511yescharacteristic
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—22no—
1400C4—22no—
1401C4—22no—
1402C4—22no—
1403C4—22no—
1404C4—22no—
1405C4—22no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—44no—
1410C4—41no—
1411C4—41no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—44no—
1417C4—44no—
1418C4—42no—
1419C4—42no—
1420C4—44no—
1421C4—42no—
1422C4—44no—
1423C4#355314yes—
1424C2—24no—
1425C2—82no—
1426C2C2×#355311yescharacteristic
1427C2#6276111yescharacteristic
1428C2C2×#350911yescharacteristic
1429C2#6281511yescharacteristic
1430C2#6281511yescharacteristic
1431C2#6282311yescharacteristic
1432C2#6282511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59868C2semidirect
3. #59866C2semidirect
5. #46160C2semidirect
6. #46159C2semidirect
7. #46158C2semidirect
8. #46157C2semidirect
9. #46023C2semidirect
10. #46022C2semidirect
11. #39826C2semidirect
12. #39791C2semidirect
13. #39788C2semidirect
14. #39476C2semidirect
15. #39476C2semidirect
16. #39473C2semidirect
17. #38496C2semidirect
18. #38461C2semidirect
20. #37203C2semidirect
21. #37146C2semidirect
22. #36635C2semidirect
23. C2×#2859C2semidirect
24. #36400C2semidirect
25. #36387C2semidirect
26. #36384C2semidirect
27. #36278C2semidirect
28. #35115C2semidirect
29. #35045C2semidirect
30. #34372C2semidirect

Maximal subgroups

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

subgroupindex
#598732
#598682
#598662
#598552
#461602
#461592
#461582
#461572
#460232
#460222
#398262
#397912
#397882
#394762
#394732
#384962
#384612
#376072
#372032
#371462
#366352
C2×#28592
#364002
#363872
#363842
#362782
#351152
#350452
#343722
C4×#5292