Finite Group Databasebeta

← #8096408

Subgroups — #8096408

Order 512.

4309 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53100C211yesmaximal, characteristic, complemented
2#53041C212yesmaximal, complemented
3#53037C212yesmaximal, complemented
4#53032C211yesmaximal, characteristic, complemented
5#52908C212yesmaximal, complemented
6#52838C214yesmaximal, complemented
7#52814C214yesmaximal, complemented
8#52702C212yesmaximal, complemented
9#52302C211yesmaximal, characteristic, complemented
10#52246C212yesmaximal, complemented
11#46346C211yesmaximal, characteristic, complemented
12#46235C212yesmaximal, complemented
13#46002C212yesmaximal, complemented
14#45798C214yesmaximal, complemented
15#45679C214yesmaximal, complemented
16#45669C212yesmaximal
17#45666C214yesmaximal, complemented
18#45662C212yesmaximal, complemented
19#45634C212yesmaximal, complemented
20#45555C214yesmaximal, complemented
21#36547C212yesmaximal, complemented
22#36545C212yesmaximal, complemented
23#36452C212yesmaximal, complemented
24#36233C212yesmaximal, complemented
25#36188C211yesmaximal, characteristic, complemented
26#35938C211yesmaximal, characteristic, complemented
27#35909C211yesmaximal, characteristic
28#35886C212yesmaximal, complemented
29#35870C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C22×C4×Q8C2212yes—
35#2868C2211yescharacteristic
36#2863C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2855C2212yes—
40#2855C2214yes—
41#2852C2214yes—
42#2851C2214yes—
43#2851C2214yes—
44#2850C2212yes—
45#2844C2212yes—
46#2844C2212yes—
47#2843C2214yes—
48#2841C2214yes—
49#2841C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2838C2214yes—
53#2838C2214yes—
54#2838C2214yes—
55#2836C2214yes—
56#2836C2214yes—
57#2835C2214yes—
58#2833C2212yes—
59#2833C2212yes—
60#2831C2214yes—
61#2827C2214yes—
62#2827C2214yes—
63#2822C2212yes—
64#2802C2214yes—
65#2799C2211yescharacteristic
66#2799C2212yes—
67#2798C2214yes—
68#2798C2214yes—
69#2796C2214yes—
70#2794C2212yes—
71#2794C2211yescharacteristic
72#2792C2214yes—
73#2792C2214yes—
74#2792C2214yes—
75#2790C2214yes—
76#2790C2214yes—
77#2790C2214yes—
78#2789C2212yes—
79#2788C2214yes—
80#2784C2214yes—
81#2783C2214yes—
82#2782C2212yes—
83#2782C2212yes—
84#2780C2214yes—
85#2778C2214yes—
86#2776C2212yes—
87#2770C2212yes—
88#2768C2214yes—
89#2766C2214yes—
90#2763C2214yes—
91#2758C2214yes—
92#2757C2214yes—
93#2755C2214yes—
94#2747C2214yes—
95#2747C2214yes—
96#2747C2214yes—
97#2746C2214yes—
98#2745C2212yes—
99#2744C2214yes—
100#2742C2214yes—
101#2742C2214yes—
102#2740C2214yes—
103#2739C2214yes—
104#2739C2214yes—
105#2737C2214yes—
106#2734C2212yes—
107#2729C2212yes—
108#2728C2211yescharacteristic
109#2713C2214yes—
110#2704C2214yes—
111#2695C2212yes—
112#2693C2214yes—
113#2689C2212yes—
114#2687C2214yes—
115#2680C2211yescharacteristic
116#2664C2212yes—
117#2664C2212yes—
118#2658C2211yescharacteristic
119#2655C2214yes—
120#2655C2214yes—
121#2645C2212yes—
122#2642C2212yes—
123#2640C2211yescharacteristic
124#2611C2212yes—
125#2611C2212yes—
126#2604C2214yes—
127#2604C2212yes—
128#2603C2212yes—
129#2599C2214yes—
130#2592C2211yescharacteristic
131#2590C2214yes—
132#2587C2214yes—
133#2585C2214yes—
134#2584C2214yes—
135#2583C2214yes—
136#2582C2212yes—
137#2581C2212yes—
138#2581C2214yes—
139#2579C2214yes—
140#2578C2214yes—
141#2577C2214yes—
142#2577C2214yes—
143#2573C2214yes—
144#2568C2211yescharacteristic
145#2568C2211yescharacteristic
146#2568C2211yescharacteristic
147#2565C2212yes—
148#2560C2214yes—
149#2556C2214yes—
150#2553C2214yes—
151#2547C2212yes—
152#2547C2212yes—
153#2546C2211yescharacteristic
154#2546C2212yes—
155#2546C2212yes—
156#2546C2212yes—
157#2545C2212yes—
158#2545C2212yes—
159#2540C2211yescharacteristic
160#2533C2214yes—
161#2533C2214yes—
162#2533C2214yes—
163#2530C2214yes—
164#2528C2214yes—
165#2528C2214yes—
166#2524C2214yes—
167#2519C2214yes—
168#2517C2214yes—
169#2514C2212yes—
170#2511C2212yes—
171#2509C2212yes—
172#2509C2214yes—
173#2506C2212yes—
174#2499C2212yes—
175#2499C2212yes—
176#2496C2214yes—
177#2496C2214yes—
178#2489C2212yes—
179#2489C2212yes—
180#2481C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2469C2214yes—
184#2465C2214yes—
185#2465C2214yes—
186#2465C2214yes—
187#2462C2214yes—
188#2462C2214yes—
189#2462C2214yes—
190#2462C2214yes—
191#2460C2214yes—
192#2454C2212yes—
193#2453C2212yes—
194#2452C2214yes—
195#2451C2212yes—
196#2451C2212yes—
197#2449C2214yes—
198#2448C2212yes—
199#2447C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2436C2212yes—
207#2434C2212yes—
208#2434C2212yes—
209#2434C2212yes—
210#2434C2212yes—
211#2429C2212yes—
212#2429C2212yes—
213#2429C2212yes—
214#2429C2212yes—
215#2427C2212yes—
216#2426C2212yes—
217#2422C2212yes—
218#2421C2212yes—
219#2409C2212yes—
220#2402C2214yes—
221#2402C2212yes—
222#2401C2214yes—
223#2401C2212yes—
224#2399C2211yescharacteristic
225#2398C2211yescharacteristic
226#2396C2212yes—
227#2392C2212yes—
228#2383C2214yes—
229#2382C2214yes—
230#2381C2212yes—
231#2376C2214yes—
232#2376C2214yes—
233#2370C2212yes—
234#2367C2212yes—
235#2365C2212yes—
236#2365C2212yes—
237#2365C2212yes—
238#2365C2212yes—
239#2361C2212yes—
240#2360C2212yes—
241#2360C2212yes—
242#2360C2212yes—
243#2356C2212yes—
244#2355C2212yes—
245#2345C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×#126C2212yes—
248C4×C22⋊Q8C2214yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2214yes—
252C4×#123C2214yes—
253C4×#123C2212yes—
254#2290C2214yes—
255#2285C2212yes—
256#2276C2211yescharacteristic
257#2276C2211yescharacteristic
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260#557—44no—
261#556—44no—
262#556—44no—
263#554—44no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#123C2314yes—
289C2×#123C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×#121C2312yes—
300C2×C4×Q8—48no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326C22×C42C2314yes—
327#401C2314yes—
328#401C2314yes—
329#401C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2314yes—
361#400C2311yescharacteristic
362#400C2311yescharacteristic
363#400C2314yes—
364#400C2312yes—
365#400C2312yes—
366#400C2314yes—
367#400C2312yes—
368#399C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2312yes—
372#399C2312yes—
373#399C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2311yescharacteristic
388#398C2314yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#397C2312yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2312yes—
424#397C2314yes—
425#397C2312yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2312yes—
435#396C2314yes—
436#396C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2311yescharacteristic
450#395C2311yescharacteristic
451#395C2312yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2311yescharacteristic
456#394C2311yescharacteristic
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2312yes—
462#393C2312yes—
463#392C2312yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2311yescharacteristic
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#390C2314yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2312yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2312yes—
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#385C2314yes—
644#384C2311yescharacteristic
645#384C2312yes—
646#384C2314yes—
647#384C2312yes—
648#384C2312yes—
649#383C2312yes—
650#383C2314yes—
651#383C2314yes—
652#383C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2314yes—
659#382C2314yes—
660#381C2314yes—
661#381C2314yes—
662#381C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2311yescharacteristic
715#376C2311yescharacteristic
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2414yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C4⋊Q8—42no—
740C4⋊Q8—42no—
741C4⋊Q8—44no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—42no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750#126—28no—
751#126—48no—
752#126—44no—
753#126—44no—
754#125—48no—
755#125—44no—
756#125—44no—
757#125—48no—
758#125—44no—
759#124—44no—
760#124—44no—
761#124—42no—
762#124—42no—
763#123—28no—
764#123—216no—
765C22⋊Q8—28no—
766C22⋊Q8—44no—
767C22⋊Q8—48no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774#121—44no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—42no—
780C4×Q8—42no—
781C4×Q8—44no—
782C4×Q8—42no—
783C4×Q8—48no—
784C4×Q8—48no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×D4—24no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—42no—
793C4×D4—48no—
794#117—44no—
795#117—44no—
796C2×C4⋊C4—28no—
797C2×C4⋊C4—48no—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C42—48no—
901C2×C42—44no—
902C2×C42—44no—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2411yescharacteristic
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011C24C2512yes—
1012C24C2512yes—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—22no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—432no—
1038C2×D4—24no—
1039C2×D4—28no—
1040C2×D4—22no—
1041C2×D4—24no—
1042C2×D4—41no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—28no—
1053C22×C4—28no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—41no—
1122C4⋊C4—41no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—41no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—41no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4H(5,𝔽2)14yes—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C42−1+418yes—
1195C42—28no—
1196C42—24no—
1197C42—28no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—22no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—44no—
1211C42—42no—
1212C42—44no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—41no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—42no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—24no—
1230C23—24no—
1231C23—22no—
1232C23—22no—
1233C23C2×2−1+414yes—
1234C23C2611yescharacteristic
1235Q8—44no—
1236Q8—416no—
1237Q8—44no—
1238Q8—44no—
1239Q8—48no—
1240Q8—48no—
1241Q8—82no—
1242Q8—82no—
1243Q8—162no—
1244D4—44no—
1245D4—44no—
1246D4—88no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—21no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—48no—
1317C2×C4—48no—
1318C2×C4—416no—
1319C2×C4—48no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4—84no—
1323C2×C4C2×H(5,𝔽2)14yes—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×2−1+414yes—
1326C2×C4C2×2−1+414yes—
1327C2×C4#58512yes—
1328C2×C4#58514yes—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22C22×H(5,𝔽2)11yescharacteristic
1342C22C22×2−1+412yes—
1343C22C2×#58511yescharacteristic
1344C22C2×#58512yes—
1345C222−1+611yescharacteristic
1346C4—24no—
1347C4—24no—
1348C4—22no—
1349C4—24no—
1350C4—41no—
1351C4—42no—
1352C4—41no—
1353C4—41no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—41no—
1362C4—41no—
1363C4—44no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—42no—
1372C4#352914yes—
1373C2—44no—
1374C2—82no—
1375C2C2×#352911yescharacteristic
1376C2#6289811yescharacteristic
1377C2#6295612yes—
1378C2#6301611yescharacteristic
1379C2#6302512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2540C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53100C2semidirect
2. #53041C2semidirect
3. #53037C2semidirect
4. #53032C2semidirect
5. #52908C2semidirect
6. #52838C2semidirect
7. #52814C2semidirect
8. #52702C2semidirect
9. #52302C2semidirect
10. #52246C2semidirect
11. #46346C2semidirect
12. #46235C2semidirect
13. #46002C2semidirect
14. #45798C2semidirect
15. #45679C2semidirect
17. #45666C2semidirect
18. #45662C2semidirect
19. #45634C2semidirect
20. #45555C2semidirect
21. #36547C2semidirect
22. #36545C2semidirect
23. #36452C2semidirect
24. #36233C2semidirect
25. #36188C2semidirect
26. #35938C2semidirect
28. #35886C2semidirect
29. #35870C2semidirect

Maximal subgroups

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

subgroupindex
#531002
#530412
#530372
#530322
#529082
#528382
#528142
#527022
#523022
#522462
#463462
#462352
#460022
#457982
#456792
#456692
#456662
#456622
#456342
#455552
#365472
#365452
#364522
#362332
#361882
#359382
#359092
#358862
#358702