Finite Group Databasebeta

← #8467095

Subgroups — #8467095

Order 512.

3927 conjugacy classes of subgroups.

The subgroup lattice has 1533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59672C211yesmaximal, characteristic, complemented
2#59259C211yesmaximal, characteristic, complemented
3#59249C211yesmaximal, characteristic, complemented
4#57909C214yesmaximal, complemented
5#55927C214yesmaximal, complemented
6#55370C214yesmaximal
7#53067C212yesmaximal
8#53067C212yesmaximal
9#49901C214yesmaximal, complemented
10#46181C212yesmaximal, complemented
11#46079C212yesmaximal, complemented
12#45339C212yesmaximal, complemented
13#45223C212yesmaximal, complemented
14#42870C212yesmaximal
15#42777C212yesmaximal
16#42716C212yesmaximal, complemented
17#42710C212yesmaximal, complemented
18#40075C212yesmaximal, complemented
19#39607C211yesmaximal, characteristic, complemented
20#39607C211yesmaximal, characteristic, complemented
21#39299C212yesmaximal, complemented
22#39183C211yesmaximal, characteristic, complemented
23#39183C212yesmaximal, complemented
24#39157C211yesmaximal, characteristic, complemented
25#38279C212yesmaximal, complemented
26#37643C211yesmaximal, characteristic, complemented
27#37328C212yesmaximal, complemented
28#37328C212yesmaximal, complemented
29Q8×#125C211yesmaximal, characteristic, complemented
30#36287C211yesmaximal, characteristic, complemented
31#36210C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic, complemented
33#35202C211yesmaximal, characteristic, complemented
34#34898C211yesmaximal, characteristic
35#34793C211yesmaximal, characteristic
36#2864C2212yes—
37#2863C2212yes—
38#2859C2211yescharacteristic
39#2859C2212yes—
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2845C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2837C2214yes—
49#2837C2214yes—
50#2836C2214yes—
51#2836C2214yes—
52#2823C2214yes—
53#2809C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2795C2214yes—
59#2794C2214yes—
60#2793C2214yes—
61#2793C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2783C2214yes—
68#2783C2214yes—
69#2777C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2773C2214yes—
74#2773C2214yes—
75#2772C2214yes—
76#2772C2214yes—
77#2768C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2767C2214yes—
81#2766C2214yes—
82#2766C2214yes—
83#2766C2214yes—
84#2762C2214yes—
85#2755C2214yes—
86#2755C2214yes—
87#2726C2214yes—
88#2725C2214yes—
89#2725C2214yes—
90#2725C2214yes—
91#2725C2214yes—
92#2721C2214yes—
93#2721C2214yes—
94#2721C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2719C2214yes—
99#2704C2214yes—
100#2704C2214yes—
101#2689C2214yes—
102#2667C2214yes—
103#2666C2214yes—
104#2655C2214yes—
105#2655C2214yes—
106#2654C2214yes—
107#2654C2214yes—
108#2647C2214yes—
109#2647C2212yes—
110#2645C2212yes—
111#2629C2212yes—
112#2629C2214yes—
113#2629C2212yes—
114#2629C2212yes—
115#2629C2212yes—
116#2629C2212yes—
117#2629C2212yes—
118#2612C2214yes—
119#2606C2214yes—
120#2594C2214yes—
121#2590C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2582C2211yescharacteristic
125#2577C2212yes—
126#2575C2212yes—
127#2571C2212yes—
128#2570C2212yes—
129#2570C2214yes—
130#2570C2211yescharacteristic
131#2567C2211yescharacteristic
132#2567C2211yescharacteristic
133#2565C2211yescharacteristic
134#2565C2212yes—
135#2565C2212yes—
136#2565C2214yes—
137#2562C2212yes—
138#2562C2211yescharacteristic
139#2556C2214yes—
140#2552C2211yescharacteristic
141#2552C2212yes—
142#2552C2211yescharacteristic
143#2552C2212yes—
144#2552C2211yescharacteristic
145#2552C2212yes—
146#2552C2212yes—
147#2552C2211yescharacteristic
148#2552C2212yes—
149#2552C2212yes—
150#2552C2214yes—
151#2552C2212yes—
152#2552C2211yescharacteristic
153#2552C2212yes—
154#2552C2211yescharacteristic
155#2552C2212yes—
156#2552C2212yes—
157#2552C2212yes—
158#2552C2211yescharacteristic
159#2552C2212yes—
160#2536C2211yescharacteristic
161#2530C2212yes—
162#2529C2214yes—
163#2528C2212yes—
164#2528C2214yes—
165#2525C2214yes—
166#2524C2214yes—
167#2524C2212yes—
168#2519C2214yes—
169#2517C2212yes—
170#2514C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2511C2211yescharacteristic
174#2509C2212yes—
175#2509C2212yes—
176#2509C2212yes—
177#2509C2212yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2507C2212yes—
182#2507C2214yes—
183#2507C2212yes—
184#2507C2212yes—
185#2507C2214yes—
186#2507C2212yes—
187#2507C2212yes—
188#2507C2212yes—
189#2506C2212yes—
190#2506C2212yes—
191#2506C2214yes—
192#2506C2212yes—
193#2506C2212yes—
194#2506C2212yes—
195#2506C2211yescharacteristic
196#2506C2214yes—
197#2506C2212yes—
198#2499C2211yescharacteristic
199#2497C2212yes—
200#2497C2212yes—
201#2497C2212yes—
202#2497C2212yes—
203#2497C2212yes—
204#2497C2212yes—
205#2496C2212yes—
206#2496C2212yes—
207#2496C2212yes—
208#2496C2212yes—
209#2496C2211yescharacteristic
210#2495C2211yescharacteristic
211#2495C2212yes—
212#2494C2212yes—
213#2494C2212yes—
214#2494C2212yes—
215#2494C2211yescharacteristic
216#2489C2212yes—
217#2489C2212yes—
218#2489C2211yescharacteristic
219#2485C2211yescharacteristic
220#2485C2212yes—
221#2478C2214yes—
222#2468C2212yes—
223#2462C2214yes—
224#2460C2212yes—
225#2453C2212yes—
226#2453C2212yes—
227#2453C2212yes—
228#2453C2212yes—
229#2441C2212yes—
230#2441C2212yes—
231#2441C2212yes—
232#2441C2212yes—
233#2441C2212yes—
234#2441C2212yes—
235#2441C2211yescharacteristic
236#2423C2212yes—
237#2423C2211yescharacteristic
238#2423C2212yes—
239#2421C2211yescharacteristic
240#2421C2212yes—
241#2421C2212yes—
242#2415C2211yescharacteristic
243#2415C2212yes—
244#2402C2212yes—
245#2401C2212yes—
246#2395C2212yes—
247#2395C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2370C2212yes—
253#2370C2212yes—
254#2369C2211yescharacteristic
255#2369C2211yescharacteristic
256#2362C2212yes—
257#2362C2212yes—
258#2355C2212yes—
259#2355C2211yescharacteristic
260#2355C2212yes—
261Q8×C4⋊C4C2212yes—
262Q8×C4⋊C4C2211yescharacteristic
263Q8×C4⋊C4C2212yes—
264Q8×C4⋊C4C2211yescharacteristic
265Q8×C4⋊C4C2211yescharacteristic
266#2347C2212yes—
267#2346C2212yes—
268#2330C2212yes—
269#2330C2214yes—
270#2330C2212yes—
271#2330C2212yes—
272#2330C2212yes—
273#2330C2212yes—
274#2323C2212yes—
275#2323C2212yes—
276#2320C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×#125C2211yescharacteristic
279C4×#125C2212yes—
280C4×#125C2211yescharacteristic
281C4×#125C2212yes—
282C4×#126C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287#2298C2212yes—
288#2298C2212yes—
289#2295C2212yes—
290#2295C2211yescharacteristic
291#2285C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×#126C2312yes—
301C2×#126C2314yes—
302C2×#126C2314yes—
303C2×#125C2311yescharacteristic
304C2×#125C2312yes—
305C2×#125C2311yescharacteristic
306C2×#125C2312yes—
307C2×#125C2312yes—
308C2×#125C2312yes—
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#125C2314yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2311yescharacteristic
325C2×C22⋊Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345#401C2314yes—
346#401C2312yes—
347#401C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2314yes—
379#400C2312yes—
380#400C2314yes—
381#399C2312yes—
382#399C2314yes—
383#399C2314yes—
384#399C2314yes—
385#399C2314yes—
386#399C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#398C2314yes—
431#398C2312yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2312yes—
439#397C2312yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2312yes—
447#397C2312yes—
448#397C2312yes—
449#397C2312yes—
450#397C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2312yes—
464#395C2314yes—
465#395C2314yes—
466#394C2312yes—
467#394C2314yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#391C2311yescharacteristic
487#389C2312yes—
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2311yescharacteristic
491#389C2311yescharacteristic
492#389C2312yes—
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2311yescharacteristic
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2311yescharacteristic
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2312yes—
570#389C2314yes—
571#389C2311yescharacteristic
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2314yes—
623#387C2314yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2314yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2312yes—
675#384C2311yescharacteristic
676#384C2314yes—
677#384C2312yes—
678#384C2312yes—
679#384C2311yescharacteristic
680#384C2312yes—
681#384C2312yes—
682#384C2314yes—
683#384C2312yes—
684#384C2311yescharacteristic
685#384C2312yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2312yes—
690#384C2312yes—
691#384C2312yes—
692#384C2312yes—
693#384C2314yes—
694#384C2314yes—
695#384C2312yes—
696#384C2314yes—
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#383C2312yes—
700#383C2314yes—
701#383C2312yes—
702#383C2314yes—
703#382C2312yes—
704#382C2311yescharacteristic
705#382C2312yes—
706#382C2311yescharacteristic
707#382C2311yescharacteristic
708#382C2312yes—
709#382C2314yes—
710#382C2311yescharacteristic
711#382C2312yes—
712#382C2314yes—
713#382C2314yes—
714#382C2312yes—
715#382C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2314yes—
719#382C2314yes—
720#381C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2311yescharacteristic
726#380C2312yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2312yes—
735#380C2311yescharacteristic
736#380C2311yescharacteristic
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2311yescharacteristic
740#380C2311yescharacteristic
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803#376C2312yes—
804#376C2312yes—
805#376C2314yes—
806#376C2312yes—
807C43C2312yes—
808C43C2311yescharacteristic
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2412yes—
813C22×D4C2411yescharacteristic
814C23×C4C2411yescharacteristic
815C23×C4C2411yescharacteristic
816C23×C4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C4⋊Q8—24no—
821#126—44no—
822#126—84no—
823#126—84no—
824#125—24no—
825#125—28no—
826#125—44no—
827#125—44no—
828#125—44no—
829#125—44no—
830#125—44no—
831#125—44no—
832#125—42no—
833#125—44no—
834#125—44no—
835#125—48no—
836#125—48no—
837#125—84no—
838#125—84no—
839#125—84no—
840#125—84no—
841C22⋊Q8—24no—
842C22⋊Q8—24no—
843C22⋊Q8—24no—
844C22⋊Q8—44no—
845C22⋊Q8—42no—
846C22⋊Q8—82no—
847C4×Q8—24no—
848C4×Q8—28no—
849C4×Q8—24no—
850C4×Q8—24no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×Q8—42no—
854C4×Q8—82no—
855C4×D4—42no—
856C4×D4—42no—
857C4×D4—42no—
858#117—24no—
859#117—44no—
860#117—44no—
861#117—44no—
862#117—42no—
863#117—82no—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2411yescharacteristic
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2411yescharacteristic
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2411yescharacteristic
974C2×C22⋊C4C2411yescharacteristic
975C2×C22⋊C4C2411yescharacteristic
976C2×C22⋊C4C2411yescharacteristic
977C2×C22⋊C4C2411yescharacteristic
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C42—24no—
988C2×C42—24no—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2411yescharacteristic
997C2×C42C2412yes—
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2414yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2412yes—
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2411yescharacteristic
1009C2×C42C2411yescharacteristic
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2414yes—
1013C2×C42C2411yescharacteristic
1014C2×C42C2411yescharacteristic
1015C2×C42C2414yes—
1016C2×C42C2412yes—
1017C2×C42C2414yes—
1018C2×C42C2414yes—
1019C2×C42C2412yes—
1020C2×C42C2412yes—
1021C2×C42C2412yes—
1022C2×C42C2414yes—
1023C2×C42C2414yes—
1024C2×C42C2414yes—
1025C2×C42C2412yes—
1026C2×C42C2411yescharacteristic
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2411yescharacteristic
1044#95C2411yescharacteristic
1045#95C2411yescharacteristic
1046#95C2411yescharacteristic
1047#95C2411yescharacteristic
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2414yes—
1087#95C2412yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2412yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2414yes—
1099#95C2412yes—
1100#95C2414yes—
1101#95C2412yes—
1102#95C2414yes—
1103#95C2412yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2511yescharacteristic
1120C24C2511yescharacteristic
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—22no—
1126C2×Q8—22no—
1127C2×Q8—42no—
1128C2×Q8—42no—
1129C2×Q82−1+414yes—
1130C2×D4—41no—
1131C2×D4—41no—
1132C2×D4—41no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—22no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2514yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2512yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C22×C4C2512yes—
1181C22×C4C2511yescharacteristic
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C4⋊C4—22no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—22no—
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—22no—
1194C4⋊C4—22no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—22no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—22no—
1211C4⋊C4—24no—
1212C4⋊C4—22no—
1213C4⋊C4—28no—
1214C4⋊C4—22no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—42no—
1264C4⋊C4—42no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—42no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—44no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—42no—
1280C4⋊C42−1+414yes—
1281C22⋊C4—24no—
1282C22⋊C4—24no—
1283C22⋊C4—24no—
1284C22⋊C4—24no—
1285C22⋊C4—22no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—42no—
1290C22⋊C4—44no—
1291C22⋊C4—42no—
1292C22⋊C4—44no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—44no—
1299C22⋊C4—42no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—42no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—42no—
1306C22⋊C4—42no—
1307C42—22no—
1308C42—22no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—22no—
1313C42—24no—
1314C42—28no—
1315C42—24no—
1316C42—24no—
1317C42—24no—
1318C42—22no—
1319C42—24no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—24no—
1324C42—24no—
1325C42—24no—
1326C42—22no—
1327C42—22no—
1328C42—44no—
1329C42—42no—
1330C42—44no—
1331C42—41no—
1332C42—42no—
1333C42—44no—
1334C42—44no—
1335C42—41no—
1336C42—44no—
1337C42—44no—
1338C42—42no—
1339C42—44no—
1340C42—42no—
1341C42—42no—
1342C42—42no—
1343C42—44no—
1344C422−1+414yes—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23C2611yescharacteristic
1360Q8—28no—
1361Q8—44no—
1362Q8—84no—
1363D4—44no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—21no—
1381C2×C4—22no—
1382C2×C4—21no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—24no—
1400C2×C4—21no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—21no—
1418C2×C4—24no—
1419C2×C4—21no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—21no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—24no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—22no—
1453C2×C4—44no—
1454C2×C4—44no—
1455C2×C4—44no—
1456C2×C4—44no—
1457C2×C4—44no—
1458C2×C4—82no—
1459C2×C4C2×2−1+414yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+414yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4C2×2−1+412yes—
1466C2×C4#58512yes—
1467C2×C4#58512yes—
1468C2×C4#58512yes—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22C22×2−1+411yescharacteristic
1484C22C22×2−1+411yescharacteristic
1485C22C22×2−1+411yescharacteristic
1486C22C2×#58511yescharacteristic
1487C22C2×#58511yescharacteristic
1488C22C2×#58511yescharacteristic
1489C22H(7,𝔽2)11yescharacteristic
1490C4—24no—
1491C4—24no—
1492C4—22no—
1493C4—22no—
1494C4—41no—
1495C4—41no—
1496C4—41no—
1497C4—41no—
1498C4—42no—
1499C4—41no—
1500C4—42no—
1501C4—42no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—44no—
1506C4—41no—
1507C4—42no—
1508C4—41no—
1509C4—41no—
1510C4—42no—
1511C4—42no—
1512C4—44no—
1513C4—42no—
1514C4—42no—
1515C4—42no—
1516C4—44no—
1517C4—42no—
1518C4—42no—
1519C4—41no—
1520C4—44no—
1521C4#355514yes—
1522C4#356314yes—
1523C2—81no—
1524C2—81no—
1525C2C2×#356311yescharacteristic
1526C2C2×#355511yescharacteristic
1527C2#6284011yescharacteristic
1528C2#6295211yescharacteristic
1529C2#6295211yescharacteristic
1530C2#6295811yescharacteristic
1531C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59672C2semidirect
2. #59259C2semidirect
3. #59249C2semidirect
4. #57909C2semidirect
5. #55927C2semidirect
9. #49901C2semidirect
10. #46181C2semidirect
11. #46079C2semidirect
12. #45339C2semidirect
13. #45223C2semidirect
16. #42716C2semidirect
17. #42710C2semidirect
18. #40075C2semidirect
19. #39607C2semidirect
20. #39607C2semidirect
21. #39299C2semidirect
22. #39183C2semidirect
23. #39183C2semidirect
24. #39157C2semidirect
25. #38279C2semidirect
26. #37643C2semidirect
27. #37328C2semidirect
28. #37328C2semidirect
29. Q8×#125C2semidirect
30. #36287C2semidirect
32. #35208C2semidirect
33. #35202C2semidirect

Maximal subgroups

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

subgroupindex
#596722
#592592
#592492
#579092
#559272
#553702
#530672
#499012
#461812
#460792
#453392
#452232
#428702
#427772
#427162
#427102
#400752
#396072
#392992
#391832
#391572
#382792
#376432
#373282
Q8×#1252
#362872
#362102
#352082
#352022
#348982
#347932