Finite Group Databasebeta

← #7643152

Subgroups — #7643152

Order 512.

4712 conjugacy classes of subgroups.

The subgroup lattice has 1483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40215C212yesmaximal, complemented
2#40190C212yesmaximal, complemented
3#39831C212yesmaximal, complemented
4#39797C212yesmaximal
5#39791C212yesmaximal, complemented
6#39760C211yesmaximal, characteristic
7#39752C211yesmaximal, characteristic, complemented
8#39703C212yesmaximal, complemented
9#39677C212yesmaximal, complemented
10#39663C212yesmaximal, complemented
11#39640C211yesmaximal, characteristic, complemented
12#39615C211yesmaximal, characteristic
13#39593C212yesmaximal, complemented
14#39476C212yesmaximal, complemented
15#38887C214yesmaximal, complemented
16#37978C214yesmaximal, complemented
17#37266C212yesmaximal, complemented
18#37265C212yesmaximal, complemented
19#37264C214yesmaximal, complemented
20#36638C211yesmaximal, characteristic
21#36635C211yesmaximal, characteristic, complemented
22#35671C212yesmaximal, complemented
23#35670C212yesmaximal, complemented
24#35656C212yesmaximal, complemented
25#35594C212yesmaximal, complemented
26#35244C212yesmaximal, complemented
27#35061C214yesmaximal, complemented
28#35042C212yesmaximal
29#35013C212yesmaximal, complemented
30#34291C212yesmaximal, complemented
31C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2212yes—
33C2×#541C2212yes—
34C22×C4⋊Q8C2211yescharacteristic
35C2×#519C2212yes—
36C22×C4×Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2866C2212yes—
39#2865C2212yes—
40#2864C2212yes—
41#2864C2211yescharacteristic
42#2863C2211yescharacteristic
43#2863C2212yes—
44#2863C2212yes—
45#2862C2211yescharacteristic
46#2861C2211yescharacteristic
47#2860C2211yescharacteristic
48#2859C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2855C2211yescharacteristic
54#2854C2211yescharacteristic
55#2853C2212yes—
56#2852C2212yes—
57#2852C2214yes—
58#2851C2212yes—
59#2851C2211yescharacteristic
60#2851C2214yes—
61#2850C2211yescharacteristic
62#2809C2212yes—
63#2808C2212yes—
64#2806C2212yes—
65#2806C2212yes—
66#2806C2214yes—
67#2805C2212yes—
68#2805C2212yes—
69#2802C2214yes—
70#2799C2214yes—
71#2794C2214yes—
72#2793C2214yes—
73#2791C2214yes—
74#2788C2214yes—
75#2783C2214yes—
76#2776C2214yes—
77#2775C2214yes—
78#2774C2214yes—
79#2774C2214yes—
80#2774C2214yes—
81#2773C2214yes—
82#2770C2214yes—
83#2769C2214yes—
84#2768C2214yes—
85#2767C2214yes—
86#2767C2214yes—
87#2759C2214yes—
88#2734C2214yes—
89#2734C2212yes—
90#2734C2214yes—
91#2732C2212yes—
92#2729C2214yes—
93#2729C2214yes—
94#2729C2214yes—
95#2726C2214yes—
96#2721C2214yes—
97#2715C2214yes—
98#2666C2214yes—
99#2664C2214yes—
100#2659C2212yes—
101#2659C2212yes—
102#2655C2214yes—
103#2650C2214yes—
104#2646C2212yes—
105#2639C2212yes—
106#2637C2214yes—
107#2634C2214yes—
108#2627C2214yes—
109#2623C2214yes—
110#2611C2214yes—
111#2604C2214yes—
112#2601C2214yes—
113#2597C2214yes—
114#2596C2214yes—
115#2596C2214yes—
116#2590C2214yes—
117#2590C2214yes—
118#2589C2214yes—
119#2588C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2214yes—
126#2583C2214yes—
127#2581C2212yes—
128#2579C2214yes—
129#2570C2212yes—
130#2569C2214yes—
131#2568C2212yes—
132#2565C2212yes—
133#2565C2212yes—
134#2564C2214yes—
135#2546C2212yes—
136#2546C2212yes—
137#2546C2212yes—
138#2533C2214yes—
139#2533C2214yes—
140#2533C2214yes—
141#2532C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2524C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2519C2214yes—
148#2514C2212yes—
149#2511C2212yes—
150#2511C2212yes—
151#2510C2214yes—
152#2506C2212yes—
153#2505C2214yes—
154#2499C2212yes—
155#2499C2212yes—
156#2496C2212yes—
157#2492C2212yes—
158#2481C2214yes—
159#2481C2214yes—
160#2479C2214yes—
161#2478C2214yes—
162#2478C2214yes—
163#2478C2214yes—
164#2478C2214yes—
165#2475C2214yes—
166#2473C2214yes—
167#2473C2214yes—
168#2469C2214yes—
169#2469C2214yes—
170#2469C2214yes—
171#2462C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2462C2214yes—
177#2453C2214yes—
178#2453C2212yes—
179#2453C2212yes—
180#2451C2212yes—
181#2446C2212yes—
182#2446C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2442C2212yes—
187#2441C2212yes—
188#2434C2212yes—
189#2434C2212yes—
190#2434C2212yes—
191#2434C2212yes—
192#2429C2212yes—
193#2429C2212yes—
194#2429C2212yes—
195#2423C2212yes—
196#2423C2212yes—
197#2421C2212yes—
198#2417C2212yes—
199#2415C2212yes—
200#2409C2212yes—
201#2409C2212yes—
202#2365C2214yes—
203#2365C2212yes—
204#2362C2212yes—
205#2362C2214yes—
206#2360C2212yes—
207#2360C2214yes—
208#2352C2212yes—
209#2352C2214yes—
210#2351C2212yes—
211Q8×C22⋊C4C2212yes—
212Q8×C22⋊C4C2212yes—
213#2336C2214yes—
214#2336C2214yes—
215#2334C2214yes—
216#2334C2214yes—
217#2329C2212yes—
218#2329C2212yes—
219#2329C2212yes—
220#2327C2212yes—
221#2327C2212yes—
222#2327C2214yes—
223#2325C2212yes—
224#2323C2212yes—
225#2323C2212yes—
226#2323C2214yes—
227#2322C2214yes—
228#2320C2212yes—
229#2313C2214yes—
230C4×C4⋊Q8C2211yescharacteristic
231C4×C4⋊Q8C2212yes—
232C4×C4⋊Q8C2212yes—
233C4×C4⋊Q8C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×C4⋊Q8C2212yes—
240C4×#125C2212yes—
241C4×#125C2211yescharacteristic
242C4×#126C2212yes—
243C4×#124C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2214yes—
248C4×#123C2212yes—
249C4×#121C2211yescharacteristic
250#2298C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2211yescharacteristic
255C2×#391C2211yescharacteristic
256#2293C2211yescharacteristic
257C2×#389C2212yes—
258C2×#389C2212yes—
259#2290C2212yes—
260#2290C2214yes—
261C2×#384C2211yescharacteristic
262#2283C2212yes—
263#2276C2212yes—
264C2×C4×C4⋊C4C2212yes—
265C2×C4×C4⋊C4C2212yes—
266C2×C43C2211yescharacteristic
267C23×Q8C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2311yescharacteristic
270D4×Q8—216no—
271#541—48no—
272C2×C4⋊Q8—28no—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×#126C2312yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2311yescharacteristic
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#124C2311yescharacteristic
294C2×#123C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×#121C2311yescharacteristic
305#519—48no—
306C2×C4×Q8—44no—
307C2×C4×Q8—44no—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2314yes—
324C2×C4×Q8C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2312yes—
347C22×C42C2311yescharacteristic
348C22×C42C2312yes—
349#401C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#394C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2314yes—
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2311yescharacteristic
460#391C2312yes—
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2312yes—
464#390C2311yescharacteristic
465#390C2311yescharacteristic
466#390C2311yescharacteristic
467#390C2311yescharacteristic
468#389C2311yescharacteristic
469#389C2311yescharacteristic
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2311yescharacteristic
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2312yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#388C2312yes—
549#388C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2312yes—
555#387C2312yes—
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#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2314yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#386C2312yes—
628#386C2314yes—
629#386C2314yes—
630#386C2312yes—
631#386C2314yes—
632#386C2312yes—
633#386C2312yes—
634#386C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#385C2314yes—
649#385C2312yes—
650#385C2314yes—
651#385C2312yes—
652#385C2314yes—
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2312yes—
657#384C2311yescharacteristic
658#384C2311yescharacteristic
659#383C2312yes—
660#383C2314yes—
661#383C2314yes—
662#383C2314yes—
663#382C2312yes—
664#382C2311yescharacteristic
665#382C2312yes—
666#382C2312yes—
667#382C2314yes—
668#382C2314yes—
669#382C2314yes—
670#382C2311yescharacteristic
671#382C2312yes—
672#382C2312yes—
673#381C2312yes—
674#381C2314yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2311yescharacteristic
685#380C2311yescharacteristic
686#380C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725#376C2312yes—
726#376C2314yes—
727#376C2314yes—
728C2×#95C2312yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2312yes—
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8—28no—
741C22×Q8—24no—
742C22×Q8—42no—
743C22×Q8—42no—
744C22×Q8—44no—
745C22×Q8—42no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8#4118yes—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2412yes—
752C22×Q8C2414yes—
753C22×Q8C2412yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2412yes—
756C22×Q8C2412yes—
757C22×D4C2412yes—
758C22×D4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2412yes—
771C23×C4C2411yescharacteristic
772C4⋊Q8—28no—
773C4⋊Q8—28no—
774C4⋊Q8—28no—
775C4⋊Q8—28no—
776C4⋊Q8—28no—
777C4⋊Q8—216no—
778C4⋊Q8—42no—
779C4⋊Q8—42no—
780C4⋊Q8—44no—
781C4⋊Q8—44no—
782#126—28no—
783#126—48no—
784#126—48no—
785#126—48no—
786#125—28no—
787#125—42no—
788#125—48no—
789#125—44no—
790#125—48no—
791#125—48no—
792#124—42no—
793#123—28no—
794C22⋊Q8—28no—
795C22⋊Q8—216no—
796C22⋊Q8—28no—
797C22⋊Q8—216no—
798C22⋊Q8—24no—
799C22⋊Q8—28no—
800C22⋊Q8—44no—
801C22⋊Q8—44no—
802C22⋊Q8—44no—
803#121—24no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—28no—
807C4×Q8—28no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—42no—
811C4×Q8—44no—
812C4×Q8—44no—
813C4×Q8—44no—
814C4×Q8—48no—
815C4×Q8—48no—
816C4×Q8—44no—
817C4×Q8—44no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—44no—
821C4×D4—28no—
822C4×D4—216no—
823C4×D4—42no—
824#117—28no—
825#117—48no—
826#117—48no—
827#117—44no—
828C2×C4⋊C4—28no—
829C2×C4⋊C4—28no—
830C2×C4⋊C4—28no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—42no—
833C2×C4⋊C4—44no—
834C2×C4⋊C4—42no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42—24no—
931C2×C42—24no—
932C2×C42—24no—
933C2×C42—24no—
934C2×C42—24no—
935C2×C42—44no—
936C2×C42—44no—
937C2×C42—42no—
938C2×C42—42no—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057C24C2512yes—
1058C24C2511yescharacteristic
1059C2×Q8—28no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—24no—
1067C2×Q8—22no—
1068C2×Q8—24no—
1069C2×Q8—24no—
1070C2×Q8—24no—
1071C2×Q8—42no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—42no—
1075C2×Q8—42no—
1076C2×Q8—44no—
1077C2×Q8—41no—
1078C2×Q8—42no—
1079C2×Q8—41no—
1080C2×Q8—42no—
1081C2×Q8—416no—
1082C2×Q8—416no—
1083C2×Q8—432no—
1084C2×Q8C2×#4118yes—
1085C2×Q8C2×#4118yes—
1086C2×D4—24no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—22no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—24no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—28no—
1108C22×C4—24no—
1109C22×C4—22no—
1110C22×C4—24no—
1111C22×C4—22no—
1112C22×C4—24no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—41no—
1118C22×C4—41no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4C2×#4114yes—
1128C22×C4C2×#4118yes—
1129C22×C42−1+414yes—
1130C22×C42−1+414yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2514yes—
1142C22×C4C2514yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2514yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—28no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—24no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—24no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C42—22no—
1255C42—22no—
1256C42—22no—
1257C42—22no—
1258C42—28no—
1259C42—24no—
1260C42—22no—
1261C42—22no—
1262C42—22no—
1263C42—28no—
1264C42—28no—
1265C42—24no—
1266C42—28no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—22no—
1275C42—22no—
1276C42—22no—
1277C42—22no—
1278C42—22no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—24no—
1283C42—41no—
1284C42—41no—
1285C42—41no—
1286C42—41no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—44no—
1292C42—44no—
1293C42—44no—
1294C42—44no—
1295C42—44no—
1296C42H(5,𝔽2)14yes—
1297C422−1+414yes—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23C22×#4112yes—
1310C23C2×2−1+412yes—
1311C23C2×2−1+412yes—
1312C23C2611yescharacteristic
1313Q8—216no—
1314Q8—48no—
1315Q8—48no—
1316Q8—416no—
1317Q8—48no—
1318Q8—48no—
1319Q8—82no—
1320Q8—84no—
1321D4—48no—
1322D4—82no—
1323C2×C4—28no—
1324C2×C4—28no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—24no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—24no—
1349C2×C4—28no—
1350C2×C4—28no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—21no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—48no—
1400C2×C4—44no—
1401C2×C4—44no—
1402C2×C4—44no—
1403C2×C4—416no—
1404C2×C4—48no—
1405C2×C4—48no—
1406C2×C4—84no—
1407C2×C4—84no—
1408C2×C4C22×#4112yes—
1409C2×C4C22×#4118yes—
1410C2×C4C22×#4112yes—
1411C2×C4C2×H(5,𝔽2)12yes—
1412C2×C4C2×H(5,𝔽2)12yes—
1413C2×C4C2×H(5,𝔽2)12yes—
1414C2×C4C2×2−1+412yes—
1415C2×C4C2×2−1+412yes—
1416C2×C4C2×2−1+412yes—
1417C2×C4C2×2−1+412yes—
1418C2×C4C2×2−1+412yes—
1419C2×C4C2×2−1+412yes—
1420C2×C4C2×2−1+412yes—
1421C2×C4#58512yes—
1422C2×C4#58512yes—
1423C22—22no—
1424C22—22no—
1425C22—22no—
1426C22—22no—
1427C22—22no—
1428C22—22no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22#352314yes—
1437C22C23×#4111yescharacteristic
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C22×2−1+411yescharacteristic
1440C22C22×2−1+411yescharacteristic
1441C22C22×2−1+411yescharacteristic
1442C22C2×#58511yescharacteristic
1443C22C2×#58511yescharacteristic
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—28no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—42no—
1460C4—44no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4—41no—
1465C4—44no—
1466C4—44no—
1467C4—42no—
1468C4—41no—
1469C4—44no—
1470C4—42no—
1471C4—44no—
1472C4#345914yes—
1473C2—24no—
1474C2—82no—
1475C2C2×#345911yescharacteristic
1476C2C2×#352311yescharacteristic
1477C2#6278811yescharacteristic
1478C2#6282311yescharacteristic
1479C2#6283311yescharacteristic
1480C2#6283511yescharacteristic
1481C2#6283711yescharacteristic
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
1. #40215C2semidirect
2. #40190C2semidirect
3. #39831C2semidirect
5. #39791C2semidirect
7. #39752C2semidirect
8. #39703C2semidirect
9. #39677C2semidirect
10. #39663C2semidirect
11. #39640C2semidirect
13. #39593C2semidirect
14. #39476C2semidirect
15. #38887C2semidirect
16. #37978C2semidirect
17. #37266C2semidirect
18. #37265C2semidirect
19. #37264C2semidirect
21. #36635C2semidirect
22. #35671C2semidirect
23. #35670C2semidirect
24. #35656C2semidirect
25. #35594C2semidirect
26. #35244C2semidirect
27. #35061C2semidirect
29. #35013C2semidirect
30. #34291C2semidirect
31. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#402152
#401902
#398312
#397972
#397912
#397602
#397522
#397032
#396772
#396632
#396402
#396152
#395932
#394762
#388872
#379782
#372662
#372652
#372642
#366382
#366352
#356712
#356702
#356562
#355942
#352442
#350612
#350422
#350132
#342912
C2×C4×C4⋊Q82