Finite Group Databasebeta

← #8115365

Subgroups — #8115365

Order 512.

4093 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57898C214yesmaximal, complemented
2#57532C214yesmaximal, complemented
3#57447C214yesmaximal, complemented
4#57361C214yesmaximal, complemented
5#57042C214yesmaximal, complemented
6#56235C214yesmaximal, complemented
7#55639C214yesmaximal, complemented
8#54778C214yesmaximal, complemented
9#53086C212yesmaximal, complemented
10#53041C212yesmaximal, complemented
11#45349C211yesmaximal, characteristic, complemented
12#45336C211yesmaximal, characteristic, complemented
13#45306C211yesmaximal, characteristic, complemented
14#45142C211yesmaximal, characteristic, complemented
15#42878C211yesmaximal, characteristic, complemented
16#42866C212yesmaximal, complemented
17#42791C211yesmaximal, characteristic, complemented
18#42788C211yesmaximal, characteristic
19#42784C212yesmaximal, complemented
20#42647C211yesmaximal, characteristic, complemented
21#39188C211yesmaximal, characteristic, complemented
22#39173C211yesmaximal, characteristic, complemented
23#38970C211yesmaximal, characteristic, complemented
24#38954C211yesmaximal, characteristic, complemented
25#38287C212yesmaximal, complemented
26#38255C212yesmaximal, complemented
27#37417C212yesmaximal, complemented
28#37398C212yesmaximal, complemented
29#35324C211yesmaximal, characteristic, complemented
30#35318C211yesmaximal, characteristic, complemented
31#34640C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#556C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2864C2211yescharacteristic
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2861C2211yescharacteristic
42#2857C2211yescharacteristic
43#2855C2212yes—
44#2850C2211yescharacteristic
45#2841C2214yes—
46#2839C2214yes—
47#2838C2214yes—
48#2838C2214yes—
49#2838C2214yes—
50#2836C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2829C2214yes—
54#2827C2214yes—
55#2822C2212yes—
56#2821C2212yes—
57#2820C2212yes—
58#2817C2212yes—
59#2809C2214yes—
60#2805C2214yes—
61#2805C2214yes—
62#2803C2214yes—
63#2800C2214yes—
64#2800C2214yes—
65#2798C2214yes—
66#2798C2214yes—
67#2796C2214yes—
68#2788C2214yes—
69#2786C2214yes—
70#2783C2214yes—
71#2780C2214yes—
72#2780C2214yes—
73#2777C2214yes—
74#2777C2214yes—
75#2776C2214yes—
76#2776C2214yes—
77#2775C2214yes—
78#2775C2214yes—
79#2774C2214yes—
80#2774C2214yes—
81#2774C2214yes—
82#2773C2214yes—
83#2773C2214yes—
84#2772C2214yes—
85#2771C2214yes—
86#2769C2214yes—
87#2768C2214yes—
88#2767C2214yes—
89#2765C2214yes—
90#2762C2214yes—
91#2761C2214yes—
92#2761C2214yes—
93#2758C2214yes—
94#2756C2214yes—
95#2753C2214yes—
96#2750C2214yes—
97#2749C2214yes—
98#2746C2214yes—
99#2746C2214yes—
100#2745C2214yes—
101#2743C2214yes—
102#2743C2214yes—
103#2742C2214yes—
104#2740C2214yes—
105#2739C2214yes—
106#2738C2214yes—
107#2730C2214yes—
108#2727C2214yes—
109#2726C2214yes—
110#2725C2214yes—
111#2725C2214yes—
112#2723C2214yes—
113#2713C2214yes—
114#2700C2214yes—
115#2698C2214yes—
116#2698C2214yes—
117#2698C2214yes—
118#2696C2214yes—
119#2692C2214yes—
120#2690C2214yes—
121#2690C2214yes—
122#2690C2214yes—
123#2667C2214yes—
124#2666C2214yes—
125#2664C2212yes—
126#2663C2212yes—
127#2662C2212yes—
128#2660C2211yescharacteristic
129#2658C2211yescharacteristic
130#2655C2212yes—
131#2654C2212yes—
132#2653C2212yes—
133#2652C2214yes—
134#2652C2212yes—
135#2651C2212yes—
136#2650C2212yes—
137#2649C2212yes—
138#2648C2212yes—
139#2645C2212yes—
140#2645C2212yes—
141#2644C2214yes—
142#2642C2212yes—
143#2640C2212yes—
144#2637C2212yes—
145#2637C2212yes—
146#2631C2212yes—
147#2628C2211yescharacteristic
148#2624C2212yes—
149#2623C2212yes—
150#2621C2211yescharacteristic
151#2621C2212yes—
152#2621C2211yescharacteristic
153#2620C2211yescharacteristic
154#2612C2214yes—
155#2612C2214yes—
156#2603C2212yes—
157#2596C2214yes—
158#2595C2214yes—
159#2589C2214yes—
160#2588C2214yes—
161#2584C2212yes—
162#2584C2212yes—
163#2581C2211yescharacteristic
164#2581C2211yescharacteristic
165#2575C2214yes—
166#2571C2212yes—
167#2568C2211yescharacteristic
168#2567C2211yescharacteristic
169#2565C2212yes—
170#2556C2214yes—
171#2553C2214yes—
172#2550C2212yes—
173#2547C2212yes—
174#2547C2211yescharacteristic
175#2546C2211yescharacteristic
176#2546C2212yes—
177#2545C2212yes—
178#2540C2212yes—
179#2538C2212yes—
180#2536C2211yescharacteristic
181#2535C2211yescharacteristic
182#2533C2214yes—
183#2532C2214yes—
184#2531C2214yes—
185#2529C2214yes—
186#2528C2214yes—
187#2528C2214yes—
188#2527C2214yes—
189#2527C2214yes—
190#2526C2214yes—
191#2524C2214yes—
192#2522C2214yes—
193#2521C2214yes—
194#2519C2214yes—
195#2518C2214yes—
196#2516C2214yes—
197#2516C2214yes—
198#2511C2212yes—
199#2511C2212yes—
200#2508C2214yes—
201#2507C2212yes—
202#2503C2212yes—
203#2499C2212yes—
204#2495C2212yes—
205#2492C2212yes—
206#2489C2212yes—
207#2489C2212yes—
208#2481C2214yes—
209#2465C2214yes—
210#2460C2214yes—
211#2453C2212yes—
212#2451C2214yes—
213#2448C2212yes—
214#2447C2214yes—
215#2447C2212yes—
216#2446C2212yes—
217#2446C2212yes—
218#2442C2214yes—
219#2441C2212yes—
220#2441C2212yes—
221#2436C2212yes—
222#2434C2212yes—
223#2434C2212yes—
224#2429C2212yes—
225#2429C2212yes—
226#2429C2212yes—
227#2429C2212yes—
228#2427C2212yes—
229#2426C2212yes—
230#2421C2214yes—
231#2421C2212yes—
232#2421C2214yes—
233#2420C2212yes—
234#2415C2212yes—
235#2409C2212yes—
236#2402C2211yescharacteristic
237#2401C2212yes—
238#2398C2211yescharacteristic
239#2396C2211yescharacteristic
240#2395C2212yes—
241#2392C2211yescharacteristic
242#2365C2212yes—
243#2363C2212yes—
244#2357C2211yescharacteristic
245#2356C2212yes—
246#2356C2211yescharacteristic
247#2351C2211yescharacteristic
248#2351C2211yescharacteristic
249Q8×C22⋊C4C2212yes—
250#2331C2211yescharacteristic
251#2327C2211yescharacteristic
252#2327C2211yescharacteristic
253#2326C2212yes—
254#2326C2211yescharacteristic
255#2323C2212yes—
256#2323C2212yes—
257#2320C2212yes—
258#2310C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×#124C2211yescharacteristic
261#2298C2212yes—
262#2295C2211yescharacteristic
263#2295C2212yes—
264#2293C2211yescharacteristic
265#2290C2212yes—
266C4×#117C2211yescharacteristic
267C23×Q8C2312yes—
268#557—44no—
269#556—44no—
270#554—44no—
271D4×Q8—44no—
272#542—44no—
273#541—44no—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2312yes—
283C2×#126C2312yes—
284C2×#126C2312yes—
285C2×#126C2312yes—
286C2×#126C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2311yescharacteristic
292C2×#125C2314yes—
293C2×#124C2312yes—
294C2×#124C2311yescharacteristic
295C2×#124C2312yes—
296C2×#124C2311yescharacteristic
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#123C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2311yescharacteristic
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2311yescharacteristic
312C2×#121C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C42C2311yescharacteristic
334#401C2314yes—
335#401C2312yes—
336#401C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2311yescharacteristic
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2312yes—
373#400C2312yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#399C2311yescharacteristic
383#399C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2311yescharacteristic
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#398C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2312yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#397C2312yes—
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2311yescharacteristic
439#397C2312yes—
440#397C2314yes—
441#397C2312yes—
442#397C2312yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2312yes—
457#396C2312yes—
458#395C2311yescharacteristic
459#395C2312yes—
460#395C2314yes—
461#395C2312yes—
462#395C2312yes—
463#395C2314yes—
464#395C2312yes—
465#395C2314yes—
466#395C2314yes—
467#395C2312yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#394C2311yescharacteristic
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2312yes—
482#394C2312yes—
483#394C2312yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2312yes—
489#393C2311yescharacteristic
490#393C2312yes—
491#392C2314yes—
492#392C2312yes—
493#392C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#391C2314yes—
520#391C2312yes—
521#391C2312yes—
522#390C2314yes—
523#390C2311yescharacteristic
524#390C2311yescharacteristic
525#390C2314yes—
526#390C2314yes—
527#390C2312yes—
528#390C2314yes—
529#390C2314yes—
530#390C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#387C2314yes—
602#387C2314yes—
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#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2312yes—
655#386C2312yes—
656#386C2314yes—
657#386C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#384C2311yescharacteristic
671#384C2312yes—
672#384C2311yescharacteristic
673#383C2312yes—
674#383C2314yes—
675#383C2314yes—
676#383C2314yes—
677#382C2312yes—
678#382C2311yescharacteristic
679#382C2312yes—
680#382C2312yes—
681#382C2311yescharacteristic
682#382C2314yes—
683#382C2314yes—
684#382C2314yes—
685#382C2311yescharacteristic
686#382C2311yescharacteristic
687#382C2314yes—
688#382C2314yes—
689#382C2314yes—
690#381C2312yes—
691#381C2314yes—
692#381C2314yes—
693#381C2314yes—
694#381C2314yes—
695#381C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2314yes—
699#380C2314yes—
700#380C2312yes—
701#380C2314yes—
702#380C2314yes—
703#380C2314yes—
704#380C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2314yes—
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735#376C2314yes—
736#376C2314yes—
737#376C2311yescharacteristic
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8—44no—
741C22×Q8—44no—
742C22×Q8—44no—
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2412yes—
750C22×Q8C2414yes—
751C22×D4C2411yescharacteristic
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2412yes—
755C22×D4C2414yes—
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C4⋊Q8—24no—
763C4⋊Q8—24no—
764C4⋊Q8—42no—
765C4⋊Q8—44no—
766C4⋊Q8—42no—
767C4⋊Q8—44no—
768C4⋊Q8—42no—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771#126—44no—
772#126—44no—
773#126—44no—
774#126—48no—
775#125—42no—
776#125—44no—
777#125—44no—
778#125—44no—
779#125—44no—
780#125—48no—
781#124—44no—
782#124—42no—
783#124—42no—
784#124—44no—
785#124—42no—
786#124—44no—
787#123—44no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—44no—
791C22⋊Q8—44no—
792C22⋊Q8—44no—
793C22⋊Q8—42no—
794C22⋊Q8—42no—
795C22⋊Q8—42no—
796C22⋊Q8—44no—
797C22⋊Q8—44no—
798C22⋊Q8—44no—
799#121—44no—
800#121—42no—
801C4×Q8—24no—
802C4×Q8—24no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×D4—24no—
812C4×D4—24no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—44no—
816#117—24no—
817#117—44no—
818#117—42no—
819#117—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C42—42no—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2411yescharacteristic
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2411yescharacteristic
995#95C2411yescharacteristic
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038C24C2511yescharacteristic
1039C24C2512yes—
1040C24C2512yes—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—24no—
1046C2×Q8—24no—
1047C2×Q8—22no—
1048C2×Q8—22no—
1049C2×Q8—24no—
1050C2×Q8—22no—
1051C2×Q8—24no—
1052C2×Q8—22no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—42no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—44no—
1060C2×Q8—42no—
1061C2×Q8—44no—
1062C2×Q8—816no—
1063C2×D4—22no—
1064C2×D4—22no—
1065C2×D4—22no—
1066C2×D4—22no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C22×C4—22no—
1077C22×C4—24no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—42no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C22⋊C4—22no—
1190C22⋊C4—22no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C42—22no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—24no—
1237C42—22no—
1238C42—22no—
1239C42—22no—
1240C42—24no—
1241C42—22no—
1242C42—24no—
1243C42—42no—
1244C42—42no—
1245C42—42no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42H(5,𝔽2)14yes—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—21no—
1262C23—21no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—24no—
1271C23—24no—
1272C23—22no—
1273C23—22no—
1274C23C2611yescharacteristic
1275Q8—44no—
1276Q8—44no—
1277Q8—44no—
1278Q8—48no—
1279Q8—44no—
1280Q8—84no—
1281Q8—88no—
1282Q8—162no—
1283D4—44no—
1284D4—44no—
1285D4—84no—
1286D4—162no—
1287D4—164no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—44no—
1360C2×C4—48no—
1361C2×C4—84no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4—164no—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4#58512yes—
1369C2×C4#58512yes—
1370C22—42no—
1371C22—41no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—41no—
1377C22—41no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—44no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—42no—
1387C22C22×H(5,𝔽2)11yescharacteristic
1388C22C2×#58511yescharacteristic
1389C22C2×#58511yescharacteristic
1390C222−1+612yes—
1391C222−1+612yes—
1392C4—22no—
1393C4—22no—
1394C4—41no—
1395C4—42no—
1396C4—42no—
1397C4—44no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—41no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—41no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4#355114yes—
1420C2—82no—
1421C2—81no—
1422C2—82no—
1423C2C2×#355111yescharacteristic
1424C2#6288711yescharacteristic
1425C2#6288711yescharacteristic
1426C2#6289012yes—
1427C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42788C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57898C2semidirect
2. #57532C2semidirect
3. #57447C2semidirect
4. #57361C2semidirect
5. #57042C2semidirect
6. #56235C2semidirect
7. #55639C2semidirect
8. #54778C2semidirect
9. #53086C2semidirect
10. #53041C2semidirect
11. #45349C2semidirect
12. #45336C2semidirect
13. #45306C2semidirect
14. #45142C2semidirect
15. #42878C2semidirect
16. #42866C2semidirect
17. #42791C2semidirect
19. #42784C2semidirect
20. #42647C2semidirect
21. #39188C2semidirect
22. #39173C2semidirect
23. #38970C2semidirect
24. #38954C2semidirect
25. #38287C2semidirect
26. #38255C2semidirect
27. #37417C2semidirect
28. #37398C2semidirect
29. #35324C2semidirect
30. #35318C2semidirect
31. #34640C2semidirect

Maximal subgroups

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

subgroupindex
#578982
#575322
#574472
#573612
#570422
#562352
#556392
#547782
#530862
#530412
#453492
#453362
#453062
#451422
#428782
#428662
#427912
#427882
#427842
#426472
#391882
#391732
#389702
#389542
#382872
#382552
#374172
#373982
#353242
#353182
#346402