Finite Group Databasebeta

← #8096270

Subgroups — #8096270

Order 512.

4349 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53138C212yesmaximal, complemented
2#53047C212yesmaximal, complemented
3#53013C212yesmaximal, complemented
4#52866C214yesmaximal, complemented
5#52364C214yesmaximal, complemented
6#52354C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic, complemented
8#52270C212yesmaximal, complemented
9#46345C211yesmaximal, characteristic, complemented
10#46331C211yesmaximal, characteristic, complemented
11#46323C212yesmaximal, complemented
12#46269C212yesmaximal, complemented
13#46240C212yesmaximal, complemented
14#46084C211yesmaximal, characteristic
15#46063C212yesmaximal, complemented
16#46057C212yesmaximal, complemented
17#46020C212yesmaximal, complemented
18#45861C214yesmaximal, complemented
19#45855C214yesmaximal, complemented
20#45849C214yesmaximal, complemented
21#36562C211yesmaximal, characteristic, complemented
22#36560C211yesmaximal, characteristic, complemented
23#36538C211yesmaximal, characteristic, complemented
24#36421C212yesmaximal, complemented
25#36408C212yesmaximal, complemented
26#36298C212yesmaximal, complemented
27#35778C212yesmaximal, complemented
28#35724C212yesmaximal, complemented
29#35712C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#520C2212yes—
35#2868C2211yescharacteristic
36#2866C2214yes—
37#2865C2214yes—
38#2864C2214yes—
39#2863C2212yes—
40#2862C2211yescharacteristic
41#2861C2212yes—
42#2861C2212yes—
43#2860C2212yes—
44#2859C2212yes—
45#2859C2212yes—
46#2858C2211yescharacteristic
47#2845C2214yes—
48#2843C2212yes—
49#2839C2214yes—
50#2837C2214yes—
51#2837C2214yes—
52#2837C2214yes—
53#2836C2214yes—
54#2836C2214yes—
55#2836C2214yes—
56#2832C2212yes—
57#2831C2214yes—
58#2831C2214yes—
59#2829C2214yes—
60#2829C2214yes—
61#2828C2212yes—
62#2827C2214yes—
63#2827C2214yes—
64#2823C2214yes—
65#2809C2212yes—
66#2809C2211yescharacteristic
67#2808C2214yes—
68#2803C2214yes—
69#2803C2214yes—
70#2802C2214yes—
71#2799C2212yes—
72#2796C2214yes—
73#2795C2214yes—
74#2795C2214yes—
75#2795C2214yes—
76#2791C2214yes—
77#2790C2214yes—
78#2790C2214yes—
79#2790C2214yes—
80#2790C2214yes—
81#2790C2214yes—
82#2783C2214yes—
83#2783C2214yes—
84#2782C2212yes—
85#2775C2212yes—
86#2775C2212yes—
87#2774C2214yes—
88#2772C2214yes—
89#2769C2212yes—
90#2768C2214yes—
91#2768C2214yes—
92#2761C2214yes—
93#2757C2214yes—
94#2757C2214yes—
95#2756C2214yes—
96#2755C2214yes—
97#2754C2214yes—
98#2754C2214yes—
99#2753C2214yes—
100#2753C2214yes—
101#2748C2214yes—
102#2744C2214yes—
103#2739C2214yes—
104#2734C2211yescharacteristic
105#2733C2212yes—
106#2731C2212yes—
107#2731C2211yescharacteristic
108#2731C2211yescharacteristic
109#2727C2212yes—
110#2723C2214yes—
111#2721C2212yes—
112#2721C2212yes—
113#2718C2214yes—
114#2705C2214yes—
115#2704C2214yes—
116#2680C2212yes—
117#2638C2214yes—
118#2633C2214yes—
119#2630C2214yes—
120#2625C2212yes—
121#2621C2212yes—
122#2620C2212yes—
123#2611C2214yes—
124#2600C2214yes—
125#2599C2214yes—
126#2596C2214yes—
127#2585C2214yes—
128#2582C2212yes—
129#2580C2212yes—
130#2579C2214yes—
131#2577C2214yes—
132#2573C2214yes—
133#2568C2211yescharacteristic
134#2568C2211yescharacteristic
135#2568C2211yescharacteristic
136#2567C2211yescharacteristic
137#2566C2212yes—
138#2566C2212yes—
139#2565C2212yes—
140#2565C2212yes—
141#2565C2212yes—
142#2565C2212yes—
143#2558C2214yes—
144#2558C2214yes—
145#2556C2214yes—
146#2556C2214yes—
147#2548C2211yescharacteristic
148#2547C2212yes—
149#2546C2212yes—
150#2546C2212yes—
151#2545C2212yes—
152#2545C2212yes—
153#2545C2212yes—
154#2545C2212yes—
155#2545C2212yes—
156#2542C2211yescharacteristic
157#2533C2214yes—
158#2529C2214yes—
159#2525C2214yes—
160#2525C2214yes—
161#2524C2214yes—
162#2522C2214yes—
163#2522C2214yes—
164#2516C2214yes—
165#2515C2214yes—
166#2513C2212yes—
167#2511C2212yes—
168#2508C2212yes—
169#2507C2212yes—
170#2506C2214yes—
171#2506C2214yes—
172#2490C2212yes—
173#2489C2212yes—
174#2479C2214yes—
175#2478C2214yes—
176#2478C2214yes—
177#2477C2214yes—
178#2475C2214yes—
179#2475C2214yes—
180#2474C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2473C2214yes—
184#2470C2214yes—
185#2468C2214yes—
186#2460C2214yes—
187#2460C2214yes—
188#2459C2214yes—
189#2455C2214yes—
190#2453C2212yes—
191#2453C2212yes—
192#2452C2212yes—
193#2451C2212yes—
194#2449C2214yes—
195#2448C2212yes—
196#2448C2212yes—
197#2447C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2445C2212yes—
203#2432C2212yes—
204#2432C2212yes—
205#2432C2212yes—
206#2432C2212yes—
207#2431C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2429C2212yes—
212#2427C2212yes—
213#2426C2212yes—
214#2423C2212yes—
215#2421C2212yes—
216#2415C2214yes—
217#2413C2214yes—
218#2407C2212yes—
219#2398C2214yes—
220#2396C2212yes—
221#2396C2212yes—
222#2395C2212yes—
223#2392C2214yes—
224#2392C2214yes—
225#2383C2214yes—
226#2381C2212yes—
227#2379C2212yes—
228#2379C2212yes—
229#2378C2214yes—
230#2376C2214yes—
231#2370C2212yes—
232#2367C2212yes—
233#2367C2212yes—
234#2367C2212yes—
235#2365C2212yes—
236#2365C2212yes—
237#2361C2212yes—
238#2360C2212yes—
239#2360C2212yes—
240#2360C2212yes—
241#2356C2212yes—
242#2354C2212yes—
243#2344C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×#125C2212yes—
248C4×#126C2212yes—
249C4×#126C2212yes—
250C4×#124C2211yescharacteristic
251C4×#124C2212yes—
252C4×#124C2212yes—
253#2298C2214yes—
254#2298C2214yes—
255#2293C2214yes—
256C42×Q8C2211yescharacteristic
257C42×Q8C2211yescharacteristic
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260#559—44no—
261#557—44no—
262#557—44no—
263#554—44no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×#121C2312yes—
302#520—48no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2311yescharacteristic
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C2×#117C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#399C2312yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2312yes—
355#399C2312yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2312yes—
422#396C2314yes—
423#396C2312yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#395C2314yes—
431#395C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2312yes—
439#394C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2312yes—
447#394C2314yes—
448#394C2312yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2312yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#391C2311yescharacteristic
460#391C2311yescharacteristic
461#391C2312yes—
462#391C2312yes—
463#391C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2311yescharacteristic
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#390C2311yescharacteristic
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2314yes—
496#390C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#388C2312yes—
534#388C2312yes—
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#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
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#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#384C2311yescharacteristic
648#384C2311yescharacteristic
649#384C2312yes—
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#383C2312yes—
656#383C2312yes—
657#383C2314yes—
658#383C2314yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2314yes—
666#382C2314yes—
667#382C2311yescharacteristic
668#382C2312yes—
669#381C2314yes—
670#381C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710#376C2314yes—
711C43C2311yescharacteristic
712C43C2311yescharacteristic
713C43C2311yescharacteristic
714C43C2312yes—
715C43C2312yes—
716C43C2312yes—
717C2×#41—44no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C4⋊Q8—24no—
740C4⋊Q8—24no—
741C4⋊Q8—42no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—42no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749#127—42no—
750#126—48no—
751#126—44no—
752#126—44no—
753#125—44no—
754#125—44no—
755#125—48no—
756#125—44no—
757#125—44no—
758#125—44no—
759#125—44no—
760#125—44no—
761#124—24no—
762#124—28no—
763#124—44no—
764#124—44no—
765#124—44no—
766#124—44no—
767#124—44no—
768#123—48no—
769#123—48no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776#121—44no—
777C4×Q8—28no—
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—44no—
782C4×Q8—42no—
783C4×Q8—44no—
784C4×Q8—42no—
785C4×Q8—42no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×D4—28no—
791C4×D4—48no—
792C4×D4—44no—
793C4×D4—48no—
794C4×D4—44no—
795C4×D4—42no—
796C4×D4—44no—
797C4×D4—48no—
798#117—44no—
799#117—48no—
800#117—48no—
801#117—48no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—48no—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
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—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2514yes—
1015C24C2512yes—
1016#41—432no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—22no—
1020C2×Q8—22no—
1021C2×Q8—22no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—41no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q82−1+414yes—
1037C2×D4—24no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—41no—
1043C2×D4—44no—
1044C2×D4—41no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—42no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—28no—
1058C22×C4—28no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
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—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4H(5,𝔽2)14yes—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C42—24no—
1209C42—28no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—22no—
1216C42—22no—
1217C42—24no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—41no—
1227C42—42no—
1228C42—41no—
1229C42—42no—
1230C42—41no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—42no—
1238C42—42no—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—24no—
1245C23—22no—
1246C23—24no—
1247C23—22no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23C2611yescharacteristic
1254Q8—44no—
1255Q8—44no—
1256Q8—44no—
1257Q8—44no—
1258Q8—44no—
1259Q8—48no—
1260Q8—82no—
1261Q8—162no—
1262D4—44no—
1263D4—416no—
1264D4—48no—
1265D4—84no—
1266D4—88no—
1267D4—162no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—416no—
1335C2×C4—48no—
1336C2×C4—88no—
1337C2×C4—88no—
1338C2×C4—164no—
1339C2×C4C2×H(5,𝔽2)14yes—
1340C2×C4C2×H(5,𝔽2)12yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4C2×2−1+412yes—
1344C2×C4#58514yes—
1345C2×C4#58514yes—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—42no—
1353C22—44no—
1354C22—44no—
1355C22—42no—
1356C22—42no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22C22×H(5,𝔽2)11yescharacteristic
1361C22C22×2−1+411yescharacteristic
1362C22C2×#58512yes—
1363C22C2×#58512yes—
1364C222−1+611yescharacteristic
1365C4—24no—
1366C4—24no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—41no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—44no—
1391C4#352914yes—
1392C2—82no—
1393C2—84no—
1394C2C2×#352911yescharacteristic
1395C2#6289311yescharacteristic
1396C2#6296712yes—
1397C2#6302411yescharacteristic
1398C2#6303312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#46084C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53138C2semidirect
2. #53047C2semidirect
3. #53013C2semidirect
4. #52866C2semidirect
5. #52364C2semidirect
6. #52354C2semidirect
7. #52306C2semidirect
8. #52270C2semidirect
9. #46345C2semidirect
10. #46331C2semidirect
11. #46323C2semidirect
12. #46269C2semidirect
13. #46240C2semidirect
15. #46063C2semidirect
16. #46057C2semidirect
17. #46020C2semidirect
18. #45861C2semidirect
19. #45855C2semidirect
20. #45849C2semidirect
21. #36562C2semidirect
22. #36560C2semidirect
23. #36538C2semidirect
24. #36421C2semidirect
25. #36408C2semidirect
26. #36298C2semidirect
27. #35778C2semidirect
28. #35724C2semidirect
29. #35712C2semidirect

Maximal subgroups

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

subgroupindex
#531382
#530472
#530132
#528662
#523642
#523542
#523062
#522702
#463452
#463312
#463232
#462692
#462402
#460842
#460632
#460572
#460202
#458612
#458552
#458492
#365622
#365602
#365382
#364212
#364082
#362982
#357782
#357242
#357122