Finite Group Databasebeta

← #8552369

Subgroups — #8552369

Order 512.

4561 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59651C212yesmaximal, complemented
2#58084C214yesmaximal, complemented
3#57133C214yesmaximal, complemented
4#55231C214yesmaximal, complemented
5#55017C214yesmaximal, complemented
6#54045C214yesmaximal, complemented
7#53979C212yesmaximal, complemented
8#53100C211yesmaximal, characteristic, complemented
9#53017C212yesmaximal, complemented
10#52962C212yesmaximal, complemented
11#52228C211yesmaximal, characteristic, complemented
12#49581C214yesmaximal, complemented
13#47800C212yesmaximal, complemented
14#46147C211yesmaximal, characteristic, complemented
15#45384C211yesmaximal, characteristic, complemented
16#45071C212yesmaximal, complemented
17#42970C212yesmaximal, complemented
18#42829C212yesmaximal, complemented
19#42678C211yesmaximal, characteristic, complemented
20#42252C212yesmaximal, complemented
21#39410C212yesmaximal, complemented
22#39171C211yesmaximal, characteristic, complemented
23#39056C212yesmaximal, complemented
24#38261C212yesmaximal, complemented
25#38055C212yesmaximal, complemented
26#37494C212yesmaximal, complemented
27#37329C212yesmaximal, complemented
28#36051C211yesmaximal, characteristic, complemented
29#35548C212yesmaximal, complemented
30C2×#563C2212yes—
31C2×#559C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#552C2212yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#540C2214yes—
37#2859C2212yes—
38#2858C2211yescharacteristic
39#2854C2212yes—
40#2841C2214yes—
41#2839C2214yes—
42#2833C2212yes—
43#2832C2214yes—
44#2831C2214yes—
45#2831C2214yes—
46#2830C2214yes—
47#2827C2214yes—
48#2824C2214yes—
49#2822C2212yes—
50#2822C2212yes—
51#2820C2214yes—
52#2814C2212yes—
53#2809C2212yes—
54#2804C2214yes—
55#2803C2214yes—
56#2800C2214yes—
57#2799C2212yes—
58#2791C2214yes—
59#2789C2212yes—
60#2788C2214yes—
61#2785C2211yescharacteristic
62#2784C2211yescharacteristic
63#2784C2214yes—
64#2781C2212yes—
65#2780C2214yes—
66#2775C2212yes—
67#2772C2214yes—
68#2771C2214yes—
69#2769C2211yescharacteristic
70#2769C2212yes—
71#2767C2214yes—
72#2765C2214yes—
73#2764C2214yes—
74#2763C2214yes—
75#2761C2214yes—
76#2759C2214yes—
77#2756C2212yes—
78#2754C2214yes—
79#2753C2214yes—
80#2746C2214yes—
81#2744C2212yes—
82#2744C2214yes—
83#2737C2212yes—
84#2734C2212yes—
85#2724C2212yes—
86#2723C2214yes—
87#2718C2214yes—
88#2716C2214yes—
89#2715C2214yes—
90#2713C2214yes—
91#2711C2214yes—
92#2709C2214yes—
93#2708C2214yes—
94#2708C2214yes—
95#2707C2214yes—
96#2707C2214yes—
97#2702C2214yes—
98#2701C2214yes—
99#2699C2211yescharacteristic
100#2699C2214yes—
101#2698C2214yes—
102#2698C2214yes—
103#2696C2214yes—
104#2696C2214yes—
105#2695C2214yes—
106#2691C2214yes—
107#2691C2214yes—
108#2691C2214yes—
109#2690C2214yes—
110#2690C2214yes—
111#2688C2214yes—
112#2688C2214yes—
113#2687C2214yes—
114#2686C2212yes—
115#2681C2214yes—
116#2674C2214yes—
117#2672C2214yes—
118#2671C2214yes—
119#2665C2214yes—
120#2661C2212yes—
121#2653C2214yes—
122#2653C2214yes—
123#2653C2214yes—
124#2645C2212yes—
125#2645C2212yes—
126#2643C2214yes—
127#2640C2212yes—
128#2640C2211yescharacteristic
129#2640C2211yescharacteristic
130#2639C2214yes—
131#2638C2212yes—
132#2630C2214yes—
133#2629C2214yes—
134#2625C2212yes—
135#2623C2212yes—
136#2620C2212yes—
137#2620C2212yes—
138#2620C2214yes—
139#2611C2214yes—
140#2609C2214yes—
141#2609C2212yes—
142#2597C2214yes—
143#2592C2211yescharacteristic
144#2582C2212yes—
145#2578C2214yes—
146#2576C2214yes—
147#2572C2212yes—
148#2568C2211yescharacteristic
149#2564C2214yes—
150#2563C2212yes—
151#2560C2214yes—
152#2559C2214yes—
153#2559C2214yes—
154#2557C2214yes—
155#2553C2214yes—
156#2550C2214yes—
157#2546C2211yescharacteristic
158#2546C2211yescharacteristic
159#2544C2212yes—
160#2543C2212yes—
161#2541C2211yescharacteristic
162#2540C2211yescharacteristic
163#2537C2212yes—
164#2528C2214yes—
165#2517C2214yes—
166#2515C2214yes—
167#2511C2212yes—
168#2511C2212yes—
169#2510C2214yes—
170#2507C2212yes—
171#2506C2214yes—
172#2506C2212yes—
173#2505C2214yes—
174#2502C2212yes—
175#2498C2212yes—
176#2497C2214yes—
177#2496C2212yes—
178#2496C2212yes—
179#2495C2214yes—
180#2492C2212yes—
181#2491C2214yes—
182#2489C2212yes—
183#2488C2214yes—
184#2488C2214yes—
185#2486C2212yes—
186#2486C2212yes—
187#2477C2214yes—
188#2476C2214yes—
189#2475C2214yes—
190#2466C2214yes—
191#2457C2214yes—
192#2454C2212yes—
193#2453C2212yes—
194#2451C2212yes—
195#2450C2214yes—
196#2448C2212yes—
197#2447C2212yes—
198#2447C2212yes—
199#2446C2212yes—
200#2445C2212yes—
201#2444C2214yes—
202#2443C2214yes—
203#2442C2214yes—
204#2441C2212yes—
205#2440C2212yes—
206#2440C2212yes—
207#2439C2214yes—
208#2438C2214yes—
209#2436C2212yes—
210#2436C2212yes—
211#2429C2212yes—
212#2428C2212yes—
213#2427C2212yes—
214#2427C2212yes—
215#2427C2212yes—
216#2427C2212yes—
217#2426C2212yes—
218#2425C2214yes—
219#2422C2212yes—
220#2419C2214yes—
221#2419C2214yes—
222#2417C2212yes—
223#2416C2212yes—
224#2416C2212yes—
225#2416C2212yes—
226#2415C2212yes—
227#2415C2214yes—
228#2409C2212yes—
229#2409C2212yes—
230#2399C2211yescharacteristic
231#2398C2212yes—
232#2398C2211yescharacteristic
233#2395C2212yes—
234#2392C2212yes—
235#2363C2212yes—
236#2362C2212yes—
237#2361C2212yes—
238#2360C2212yes—
239#2359C2214yes—
240#2344C2212yes—
241Q8×C22⋊C4C2212yes—
242#2330C2212yes—
243#2328C2212yes—
244#2326C2212yes—
245#2326C2212yes—
246#2320C2212yes—
247#2319C2211yescharacteristic
248#2317C2212yes—
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×#121C2212yes—
252C4×#121C2212yes—
253#2298C2212yes—
254#2295C2211yescharacteristic
255C2×#391C2212yes—
256#2290C2212yes—
257#2283C2212yes—
258#2275C2211yescharacteristic
259C23×Q8C2312yes—
260#563—48no—
261#559—44no—
262#555—44no—
263#554—44no—
264#552—48no—
265D4×Q8—44no—
266#540—416no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C42C2312yes—
342#401C2314yes—
343#401C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2311yescharacteristic
367#400C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2312yes—
372#398C2314yes—
373#398C2312yes—
374#398C2311yescharacteristic
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2311yescharacteristic
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2312yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2312yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2312yes—
419#397C2312yes—
420#397C2314yes—
421#397C2314yes—
422#396C2312yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2311yescharacteristic
442#395C2312yes—
443#395C2311yescharacteristic
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2312yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2311yescharacteristic
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2311yescharacteristic
459#394C2314yes—
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2314yes—
467#394C2312yes—
468#394C2312yes—
469#394C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2312yes—
481#393C2312yes—
482#393C2312yes—
483#392C2312yes—
484#392C2314yes—
485#392C2312yes—
486#392C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2314yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2312yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2312yes—
627#386C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2312yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2312yes—
649#384C2314yes—
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#383C2314yes—
654#383C2312yes—
655#383C2312yes—
656#382C2311yescharacteristic
657#382C2312yes—
658#382C2314yes—
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#382C2312yes—
663#382C2312yes—
664#381C2314yes—
665#381C2312yes—
666#381C2314yes—
667#381C2314yes—
668#381C2312yes—
669#381C2312yes—
670#381C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711#376C2311yescharacteristic
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C2×#95C2312yes—
717C2×#95C2314yes—
718C43C2311yescharacteristic
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2411yescharacteristic
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—42no—
755C4⋊Q8—42no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758#127—28no—
759#127—42no—
760#126—48no—
761#126—48no—
762#126—48no—
763#125—28no—
764#125—48no—
765#125—48no—
766#125—48no—
767#124—24no—
768#124—48no—
769#124—44no—
770#124—44no—
771#124—44no—
772#124—42no—
773#124—42no—
774#123—216no—
775#123—48no—
776#123—48no—
777#123—44no—
778#123—44no—
779#123—48no—
780#123—48no—
781C22⋊Q8—28no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790#121—28no—
791#121—44no—
792#121—48no—
793#121—48no—
794#121—48no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—44no—
799#121—44no—
800#121—48no—
801C4×Q8—24no—
802C4×Q8—42no—
803C4×Q8—42no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×D4—24no—
807C4×D4—24no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—44no—
814C4×D4—42no—
815C4×D4—44no—
816C4×D4—48no—
817C4×D4—48no—
818#117—28no—
819#117—44no—
820#117—44no—
821#117—48no—
822#117—48no—
823C2×C4⋊C4—44no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C42—44no—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2411yescharacteristic
971#95C2412yes—
972#95C2412yes—
973#95C2411yescharacteristic
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2512yes—
1027C24C2512yes—
1028C24C2512yes—
1029C24C2512yes—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—816no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—22no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—41no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4H(5,𝔽2)14yes—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2514yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—41no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—41no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4H(5,𝔽2)14yes—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C42—28no—
1248C42—24no—
1249C42—22no—
1250C42—22no—
1251C42—24no—
1252C42—24no—
1253C42—22no—
1254C42—22no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—42no—
1259C42—42no—
1260C42—44no—
1261C42—41no—
1262C42—42no—
1263C42—44no—
1264C42—44no—
1265C42—44no—
1266C42—42no—
1267C42—42no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—24no—
1282C23—24no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—22no—
1291C23C2×H(5,𝔽2)14yes—
1292C23C2611yescharacteristic
1293Q8—48no—
1294Q8—44no—
1295Q8—82no—
1296Q8—82no—
1297Q8—88no—
1298Q8—162no—
1299Q8—162no—
1300D4—44no—
1301D4—44no—
1302D4—44no—
1303D4—84no—
1304D4—84no—
1305D4—84no—
1306D4—88no—
1307D4—88no—
1308D4—82no—
1309D4—162no—
1310D4—164no—
1311D4—164no—
1312C2×C4—21no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—21no—
1377C2×C4—48no—
1378C2×C4—48no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4—84no—
1384C2×C4—88no—
1385C2×C4—88no—
1386C2×C4—164no—
1387C2×C4—164no—
1388C2×C4C2×H(5,𝔽2)14yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4C2×H(5,𝔽2)12yes—
1391C2×C4#58514yes—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—44no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—44no—
1414C22—42no—
1415C22—44no—
1416C22C22×H(5,𝔽2)11yescharacteristic
1417C22C22×H(5,𝔽2)11yescharacteristic
1418C22C2×#58512yes—
1419C222−1+612yes—
1420C222−1+611yescharacteristic
1421C4—24no—
1422C4—22no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—44no—
1427C4—41no—
1428C4—41no—
1429C4—41no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—44no—
1436C4—42no—
1437C4—41no—
1438C4—41no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—44no—
1444C4—44no—
1445C4#355114yes—
1446C2—44no—
1447C2—82no—
1448C2—82no—
1449C2—82no—
1450C2C2×#355111yescharacteristic
1451C2#6289012yes—
1452C2#6289511yescharacteristic
1453C2#6292112yes—
1454C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59651C2semidirect
2. #58084C2semidirect
3. #57133C2semidirect
4. #55231C2semidirect
5. #55017C2semidirect
6. #54045C2semidirect
7. #53979C2semidirect
8. #53100C2semidirect
9. #53017C2semidirect
10. #52962C2semidirect
11. #52228C2semidirect
12. #49581C2semidirect
13. #47800C2semidirect
14. #46147C2semidirect
15. #45384C2semidirect
16. #45071C2semidirect
17. #42970C2semidirect
18. #42829C2semidirect
19. #42678C2semidirect
20. #42252C2semidirect
21. #39410C2semidirect
22. #39171C2semidirect
23. #39056C2semidirect
24. #38261C2semidirect
25. #38055C2semidirect
26. #37494C2semidirect
27. #37329C2semidirect
28. #36051C2semidirect
29. #35548C2semidirect

Maximal subgroups

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

subgroupindex
#596512
#580842
#571332
#552312
#550172
#540452
#539792
#531002
#530172
#529622
#522282
#495812
#478002
#461472
#453842
#450712
#429702
#428292
#426782
#422522
#394102
#391712
#390562
#382612
#380552
#374942
#373292
#360512
#355482