Finite Group Databasebeta

← #8464337

Subgroups — #8464337

Order 512.

3933 conjugacy classes of subgroups.

The subgroup lattice has 1535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59668C211yesmaximal, characteristic, complemented
2#59259C211yesmaximal, characteristic, complemented
3#59245C211yesmaximal, characteristic, complemented
4#58830C214yesmaximal, complemented
5#56829C214yesmaximal
6#53854C214yesmaximal, complemented
7#53086C212yesmaximal, complemented
8#53048C212yesmaximal
9#50381C214yesmaximal, complemented
10#46181C212yesmaximal, complemented
11#46158C212yesmaximal
12#45317C212yesmaximal, complemented
13#45219C212yesmaximal, complemented
14#42849C212yesmaximal
15#42780C212yesmaximal, complemented
16#42780C212yesmaximal, complemented
17#42773C212yesmaximal, complemented
18#40083C212yesmaximal
19#39682C212yesmaximal, complemented
20#39607C211yesmaximal, characteristic, complemented
21#39182C212yesmaximal, complemented
22#39180C211yesmaximal, characteristic, complemented
23#39157C211yesmaximal, characteristic, complemented
24#38931C211yesmaximal, characteristic, complemented
25#38277C212yesmaximal, complemented
26#37624C211yesmaximal, characteristic, complemented
27#37344C212yesmaximal, complemented
28#37328C212yesmaximal, complemented
29#36447C211yesmaximal, characteristic, complemented
30#36287C211yesmaximal, characteristic, complemented
31#36209C211yesmaximal, characteristic
32#35208C211yesmaximal, characteristic, complemented
33#35202C211yesmaximal, characteristic, complemented
34#34945C211yesmaximal, characteristic
35#34793C211yesmaximal, characteristic
36#2864C2212yes—
37#2863C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2841C2214yes—
46#2839C2214yes—
47#2838C2214yes—
48#2836C2214yes—
49#2836C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2820C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2805C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2793C2214yes—
59#2788C2214yes—
60#2783C2214yes—
61#2777C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2773C2214yes—
65#2773C2214yes—
66#2773C2214yes—
67#2772C2214yes—
68#2772C2214yes—
69#2769C2214yes—
70#2768C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2766C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2762C2214yes—
77#2758C2214yes—
78#2755C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2754C2214yes—
84#2754C2214yes—
85#2731C2214yes—
86#2727C2214yes—
87#2726C2214yes—
88#2726C2214yes—
89#2725C2214yes—
90#2725C2214yes—
91#2725C2214yes—
92#2721C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2713C2214yes—
99#2704C2214yes—
100#2698C2214yes—
101#2689C2214yes—
102#2667C2214yes—
103#2666C2214yes—
104#2666C2214yes—
105#2664C2214yes—
106#2664C2214yes—
107#2660C2212yes—
108#2651C2214yes—
109#2647C2212yes—
110#2647C2212yes—
111#2647C2214yes—
112#2647C2212yes—
113#2645C2214yes—
114#2645C2212yes—
115#2629C2212yes—
116#2629C2212yes—
117#2628C2212yes—
118#2612C2214yes—
119#2606C2214yes—
120#2596C2214yes—
121#2590C2214yes—
122#2588C2214yes—
123#2585C2214yes—
124#2584C2212yes—
125#2584C2212yes—
126#2582C2212yes—
127#2582C2211yescharacteristic
128#2573C2212yes—
129#2573C2212yes—
130#2571C2212yes—
131#2571C2214yes—
132#2571C2211yescharacteristic
133#2571C2212yes—
134#2571C2211yescharacteristic
135#2570C2212yes—
136#2570C2212yes—
137#2568C2211yescharacteristic
138#2568C2212yes—
139#2567C2211yescharacteristic
140#2567C2211yescharacteristic
141#2565C2212yes—
142#2556C2214yes—
143#2552C2212yes—
144#2552C2211yescharacteristic
145#2552C2211yescharacteristic
146#2552C2211yescharacteristic
147#2552C2212yes—
148#2552C2212yes—
149#2552C2211yescharacteristic
150#2552C2211yescharacteristic
151#2551C2212yes—
152#2551C2211yescharacteristic
153#2550C2214yes—
154#2550C2212yes—
155#2550C2212yes—
156#2550C2212yes—
157#2547C2211yescharacteristic
158#2546C2212yes—
159#2538C2211yescharacteristic
160#2536C2212yes—
161#2533C2214yes—
162#2533C2214yes—
163#2532C2214yes—
164#2530C2212yes—
165#2528C2214yes—
166#2528C2214yes—
167#2528C2212yes—
168#2525C2214yes—
169#2520C2214yes—
170#2517C2212yes—
171#2514C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2211yescharacteristic
175#2509C2212yes—
176#2509C2212yes—
177#2508C2214yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2212yes—
182#2508C2212yes—
183#2508C2214yes—
184#2507C2212yes—
185#2507C2212yes—
186#2507C2212yes—
187#2507C2212yes—
188#2507C2212yes—
189#2506C2211yescharacteristic
190#2506C2212yes—
191#2506C2212yes—
192#2506C2212yes—
193#2506C2212yes—
194#2506C2212yes—
195#2506C2214yes—
196#2499C2211yescharacteristic
197#2497C2212yes—
198#2497C2212yes—
199#2497C2212yes—
200#2497C2212yes—
201#2497C2212yes—
202#2496C2212yes—
203#2496C2212yes—
204#2496C2212yes—
205#2496C2212yes—
206#2495C2212yes—
207#2495C2212yes—
208#2495C2212yes—
209#2494C2211yescharacteristic
210#2494C2211yescharacteristic
211#2494C2212yes—
212#2494C2211yescharacteristic
213#2492C2212yes—
214#2489C2212yes—
215#2489C2212yes—
216#2489C2212yes—
217#2489C2211yescharacteristic
218#2485C2212yes—
219#2485C2211yescharacteristic
220#2485C2212yes—
221#2462C2214yes—
222#2460C2212yes—
223#2453C2212yes—
224#2453C2212yes—
225#2453C2212yes—
226#2451C2214yes—
227#2447C2212yes—
228#2441C2212yes—
229#2441C2211yescharacteristic
230#2441C2212yes—
231#2441C2212yes—
232#2441C2212yes—
233#2441C2212yes—
234#2441C2212yes—
235#2441C2212yes—
236#2439C2212yes—
237#2439C2212yes—
238#2423C2212yes—
239#2423C2212yes—
240#2421C2211yescharacteristic
241#2421C2212yes—
242#2421C2211yescharacteristic
243#2415C2211yescharacteristic
244#2401C2212yes—
245#2401C2212yes—
246#2401C2212yes—
247#2395C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2369C2212yes—
252#2369C2211yescharacteristic
253#2369C2212yes—
254#2369C2211yescharacteristic
255#2362C2212yes—
256#2362C2212yes—
257#2356C2212yes—
258#2355C2212yes—
259#2355C2211yescharacteristic
260#2351C2212yes—
261Q8×C4⋊C4C2211yescharacteristic
262Q8×C4⋊C4C2212yes—
263Q8×C4⋊C4C2211yescharacteristic
264Q8×C4⋊C4C2211yescharacteristic
265#2346C2212yes—
266#2346C2212yes—
267#2346C2212yes—
268#2331C2214yes—
269#2330C2212yes—
270#2330C2212yes—
271#2330C2212yes—
272#2330C2212yes—
273#2330C2212yes—
274#2323C2212yes—
275#2320C2212yes—
276#2320C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×#125C2212yes—
280C4×#125C2212yes—
281C4×#125C2211yescharacteristic
282C4×#124C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287#2298C2212yes—
288#2295C2212yes—
289#2295C2211yescharacteristic
290#2295C2212yes—
291#2285C2211yescharacteristic
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic
294#2283C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2314yes—
303C2×C4⋊Q8C2312yes—
304C2×#126C2314yes—
305C2×#126C2314yes—
306C2×#125C2312yes—
307C2×#125C2311yescharacteristic
308C2×#125C2312yes—
309C2×#125C2314yes—
310C2×#125C2312yes—
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#124C2312yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2311yescharacteristic
343C22×C42C2311yescharacteristic
344C22×C42C2311yescharacteristic
345#401C2314yes—
346#401C2312yes—
347#401C2312yes—
348#401C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
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#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2312yes—
379#400C2312yes—
380#400C2312yes—
381#400C2312yes—
382#400C2312yes—
383#400C2312yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2312yes—
390#399C2314yes—
391#399C2314yes—
392#399C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2312yes—
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#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2312yes—
432#397C2312yes—
433#397C2312yes—
434#397C2312yes—
435#397C2314yes—
436#397C2312yes—
437#397C2314yes—
438#397C2312yes—
439#397C2312yes—
440#397C2314yes—
441#397C2312yes—
442#397C2312yes—
443#397C2312yes—
444#397C2312yes—
445#397C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2312yes—
451#396C2312yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2312yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#394C2312yes—
467#394C2314yes—
468#394C2312yes—
469#393C2314yes—
470#393C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2311yescharacteristic
478#391C2312yes—
479#391C2312yes—
480#391C2314yes—
481#391C2311yescharacteristic
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2311yescharacteristic
487#391C2311yescharacteristic
488#391C2314yes—
489#391C2312yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#390C2312yes—
499#389C2311yescharacteristic
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2311yescharacteristic
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2312yes—
578#389C2312yes—
579#389C2314yes—
580#389C2312yes—
581#389C2311yescharacteristic
582#389C2314yes—
583#389C2314yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2312yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
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#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2314yes—
669#387C2312yes—
670#387C2312yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2312yes—
675#384C2311yescharacteristic
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2312yes—
679#384C2312yes—
680#384C2312yes—
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2312yes—
684#384C2314yes—
685#384C2312yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2312yes—
689#384C2312yes—
690#384C2311yescharacteristic
691#384C2311yescharacteristic
692#383C2312yes—
693#383C2312yes—
694#383C2314yes—
695#383C2314yes—
696#383C2314yes—
697#382C2312yes—
698#382C2312yes—
699#382C2311yescharacteristic
700#382C2314yes—
701#382C2312yes—
702#382C2311yescharacteristic
703#382C2312yes—
704#382C2311yescharacteristic
705#382C2312yes—
706#382C2312yes—
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2314yes—
710#382C2314yes—
711#382C2314yes—
712#382C2314yes—
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#382C2314yes—
717#382C2312yes—
718#382C2314yes—
719#382C2312yes—
720#381C2312yes—
721#381C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2311yescharacteristic
729#380C2312yes—
730#380C2311yescharacteristic
731#380C2311yescharacteristic
732#380C2312yes—
733#380C2311yescharacteristic
734#380C2311yescharacteristic
735#380C2311yescharacteristic
736#380C2311yescharacteristic
737#380C2312yes—
738#380C2311yescharacteristic
739#380C2311yescharacteristic
740#380C2311yescharacteristic
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2311yescharacteristic
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2311yescharacteristic
801#376C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805#376C2314yes—
806#376C2312yes—
807C43C2311yescharacteristic
808C43C2312yes—
809C43C2312yes—
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2412yes—
813C22×Q8C2412yes—
814C22×Q8C2414yes—
815C22×D4C2411yescharacteristic
816C23×C4C2411yescharacteristic
817C23×C4C2411yescharacteristic
818C23×C4C2411yescharacteristic
819C23×C4C2411yescharacteristic
820C23×C4C2411yescharacteristic
821C23×C4C2411yescharacteristic
822C4⋊Q8—24no—
823C4⋊Q8—44no—
824C4⋊Q8—42no—
825C4⋊Q8—44no—
826C4⋊Q8—48no—
827#126—84no—
828#126—84no—
829#125—28no—
830#125—24no—
831#125—44no—
832#125—44no—
833#125—44no—
834#125—44no—
835#125—48no—
836#125—44no—
837#125—82no—
838#125—84no—
839#125—84no—
840#125—84no—
841#125—84no—
842#124—44no—
843C22⋊Q8—24no—
844C22⋊Q8—24no—
845C22⋊Q8—24no—
846C22⋊Q8—42no—
847C22⋊Q8—82no—
848C22⋊Q8—82no—
849C4×Q8—24no—
850C4×Q8—28no—
851C4×Q8—24no—
852C4×Q8—24no—
853C4×Q8—44no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×Q8—42no—
857C4×Q8—44no—
858C4×D4—42no—
859C4×D4—42no—
860C4×D4—42no—
861#117—24no—
862#117—44no—
863#117—44no—
864#117—44no—
865#117—42no—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2411yescharacteristic
967C2×C22⋊C4C2411yescharacteristic
968C2×C22⋊C4C2411yescharacteristic
969C2×C22⋊C4C2411yescharacteristic
970C2×C22⋊C4C2411yescharacteristic
971C2×C22⋊C4C2411yescharacteristic
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C42—24no—
984C2×C42—24no—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2411yescharacteristic
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2412yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2412yes—
1012C2×C42C2414yes—
1013C2×C42C2414yes—
1014C2×C42C2414yes—
1015C2×C42C2411yescharacteristic
1016C2×C42C2412yes—
1017C2×C42C2412yes—
1018C2×C42C2414yes—
1019C2×C42C2414yes—
1020C2×C42C2412yes—
1021C2×C42C2414yes—
1022C2×C42C2411yescharacteristic
1023#95C2411yescharacteristic
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2411yescharacteristic
1048#95C2411yescharacteristic
1049#95C2411yescharacteristic
1050#95C2411yescharacteristic
1051#95C2411yescharacteristic
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#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2412yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2412yes—
1087#95C2414yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2412yes—
1102#95C2414yes—
1103#95C2412yes—
1104#95C2412yes—
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—24no—
1128C2×Q8—42no—
1129C2×Q8—42no—
1130C2×Q8—42no—
1131C2×Q8—42no—
1132C2×Q8—44no—
1133C2×Q8—44no—
1134C2×Q8—44no—
1135C2×Q82−1+414yes—
1136C2×D4—22no—
1137C2×D4—41no—
1138C2×D4—41no—
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—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—22no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C22×C4C2512yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2514yes—
1181C22×C4C2512yes—
1182C22×C4C2514yes—
1183C22×C4C2512yes—
1184C22×C4C2512yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2512yes—
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—28no—
1194C4⋊C4—22no—
1195C4⋊C4—22no—
1196C4⋊C4—22no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—24no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—28no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—24no—
1209C4⋊C4—22no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—28no—
1221C4⋊C4—22no—
1222C4⋊C4—24no—
1223C4⋊C4—22no—
1224C4⋊C4—24no—
1225C4⋊C4—22no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—41no—
1229C4⋊C4—41no—
1230C4⋊C4—42no—
1231C4⋊C4—42no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—42no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—42no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—42no—
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—44no—
1255C4⋊C4—42no—
1256C4⋊C4—42no—
1257C4⋊C4—42no—
1258C4⋊C4—44no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—42no—
1266C4⋊C4—42no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—44no—
1270C4⋊C4—44no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—44no—
1276C4⋊C4—42no—
1277C4⋊C4—44no—
1278C4⋊C4—44no—
1279C4⋊C4—44no—
1280C4⋊C42−1+414yes—
1281C22⋊C4—24no—
1282C22⋊C4—24no—
1283C22⋊C4—24no—
1284C22⋊C4—24no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—42no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—42no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—42no—
1300C22⋊C4—42no—
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—24no—
1321C42—22no—
1322C42—24no—
1323C42—24no—
1324C42—22no—
1325C42—22no—
1326C42—22no—
1327C42—24no—
1328C42—24no—
1329C42—24no—
1330C42—44no—
1331C42—44no—
1332C42—42no—
1333C42—42no—
1334C42—44no—
1335C42—44no—
1336C42—44no—
1337C42—42no—
1338C42—41no—
1339C42—42no—
1340C42—42no—
1341C42—44no—
1342C42—44no—
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—
1363Q8—84no—
1364Q8—164no—
1365D4—44no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—21no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—21no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—24no—
1403C2×C4—21no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—22no—
1424C2×C4—24no—
1425C2×C4—22no—
1426C2×C4—22no—
1427C2×C4—24no—
1428C2×C4—24no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—21no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—21no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—21no—
1446C2×C4—22no—
1447C2×C4—24no—
1448C2×C4—22no—
1449C2×C4—24no—
1450C2×C4—22no—
1451C2×C4—22no—
1452C2×C4—21no—
1453C2×C4—24no—
1454C2×C4—21no—
1455C2×C4—44no—
1456C2×C4—44no—
1457C2×C4—44no—
1458C2×C4—44no—
1459C2×C4—82no—
1460C2×C4—82no—
1461C2×C4C2×2−1+414yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+414yes—
1464C2×C4C2×2−1+412yes—
1465C2×C4C2×2−1+412yes—
1466C2×C4C2×2−1+412yes—
1467C2×C4C2×2−1+412yes—
1468C2×C4#58512yes—
1469C2×C4#58512yes—
1470C2×C4#58512yes—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22—41no—
1485C22C22×2−1+411yescharacteristic
1486C22C22×2−1+411yescharacteristic
1487C22C22×2−1+411yescharacteristic
1488C22C2×#58511yescharacteristic
1489C22C2×#58511yescharacteristic
1490C22C2×#58511yescharacteristic
1491C22H(7,𝔽2)11yescharacteristic
1492C4—24no—
1493C4—24no—
1494C4—22no—
1495C4—22no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—41no—
1500C4—42no—
1501C4—41no—
1502C4—42no—
1503C4—42no—
1504C4—42no—
1505C4—42no—
1506C4—44no—
1507C4—42no—
1508C4—42no—
1509C4—42no—
1510C4—41no—
1511C4—41no—
1512C4—44no—
1513C4—41no—
1514C4—42no—
1515C4—41no—
1516C4—44no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—44no—
1523C4#355514yes—
1524C4#356314yes—
1525C2—81no—
1526C2—81no—
1527C2C2×#356311yescharacteristic
1528C2C2×#355511yescharacteristic
1529C2#6282711yescharacteristic
1530C2#6292911yescharacteristic
1531C2#6295211yescharacteristic
1532C2#6295211yescharacteristic
1533C2#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. #59668C2semidirect
2. #59259C2semidirect
3. #59245C2semidirect
4. #58830C2semidirect
6. #53854C2semidirect
7. #53086C2semidirect
9. #50381C2semidirect
10. #46181C2semidirect
12. #45317C2semidirect
13. #45219C2semidirect
15. #42780C2semidirect
16. #42780C2semidirect
17. #42773C2semidirect
19. #39682C2semidirect
20. #39607C2semidirect
21. #39182C2semidirect
22. #39180C2semidirect
23. #39157C2semidirect
24. #38931C2semidirect
25. #38277C2semidirect
26. #37624C2semidirect
27. #37344C2semidirect
28. #37328C2semidirect
29. #36447C2semidirect
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
#596682
#592592
#592452
#588302
#568292
#538542
#530862
#530482
#503812
#461812
#461582
#453172
#452192
#428492
#427802
#427732
#400832
#396822
#396072
#391822
#391802
#391572
#389312
#382772
#376242
#373442
#373282
#364472
#362872
#362092
#352082
#352022
#349452
#347932