Finite Group Databasebeta

← #8094897

Subgroups — #8094897

Order 512.

4543 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53125C211yesmaximal, characteristic, complemented
2#53121C211yesmaximal, characteristic, complemented
3#53094C212yesmaximal, complemented
4#53076C211yesmaximal, characteristic, complemented
5#52987C211yesmaximal, characteristic, complemented
6#52974C212yesmaximal, complemented
7#52466C214yesmaximal, complemented
8#52456C214yesmaximal, complemented
9#52443C214yesmaximal, complemented
10#52438C214yesmaximal, complemented
11#46301C214yesmaximal, complemented
12#46227C214yesmaximal, complemented
13#46062C212yesmaximal, complemented
14#45993C212yesmaximal, complemented
15#45789C214yesmaximal, complemented
16#45762C214yesmaximal, complemented
17#45627C212yesmaximal, complemented
18#45486C212yesmaximal, complemented
19#35598C212yesmaximal, complemented
20#35597C212yesmaximal, complemented
21#35578C212yesmaximal, complemented
22#35295C211yesmaximal, characteristic, complemented
23#35283C211yesmaximal, characteristic, complemented
24#35207C212yesmaximal, complemented
25#35193C212yesmaximal, complemented
26#34929C212yesmaximal, complemented
27#34881C211yesmaximal, characteristic, complemented
28C2×#563C2214yes—
29C2×#562C2214yes—
30C2×#533C2214yes—
31#2868C2211yescharacteristic
32#2862C2211yescharacteristic
33#2860C2212yes—
34#2857C2212yes—
35#2856C2211yescharacteristic
36#2854C2214yes—
37#2853C2214yes—
38#2851C2211yescharacteristic
39#2851C2214yes—
40#2850C2214yes—
41#2839C2214yes—
42#2838C2214yes—
43#2838C2214yes—
44#2837C2214yes—
45#2834C2214yes—
46#2833C2214yes—
47#2832C2214yes—
48#2832C2214yes—
49#2832C2214yes—
50#2831C2214yes—
51#2829C2214yes—
52#2824C2214yes—
53#2822C2214yes—
54#2821C2214yes—
55#2820C2214yes—
56#2816C2214yes—
57#2816C2214yes—
58#2814C2214yes—
59#2814C2214yes—
60#2813C2214yes—
61#2789C2214yes—
62#2787C2214yes—
63#2779C2214yes—
64#2759C2214yes—
65#2745C2214yes—
66#2745C2214yes—
67#2744C2214yes—
68#2731C2214yes—
69#2731C2214yes—
70#2729C2214yes—
71#2728C2214yes—
72#2726C2214yes—
73#2723C2214yes—
74#2721C2214yes—
75#2720C2214yes—
76#2719C2214yes—
77#2718C2214yes—
78#2716C2214yes—
79#2716C2214yes—
80#2715C2214yes—
81#2711C2214yes—
82#2710C2214yes—
83#2707C2214yes—
84#2702C2214yes—
85#2702C2214yes—
86#2695C2214yes—
87#2694C2214yes—
88#2692C2214yes—
89#2692C2214yes—
90#2681C2214yes—
91#2681C2214yes—
92#2680C2214yes—
93#2677C2214yes—
94#2677C2214yes—
95#2677C2214yes—
96#2676C2214yes—
97#2674C2214yes—
98#2674C2214yes—
99#2672C2214yes—
100#2671C2214yes—
101#2653C2214yes—
102#2653C2214yes—
103#2653C2214yes—
104#2648C2214yes—
105#2647C2211yescharacteristic
106#2647C2211yescharacteristic
107#2647C2211yescharacteristic
108#2641C2211yescharacteristic
109#2628C2212yes—
110#2624C2212yes—
111#2597C2214yes—
112#2596C2214yes—
113#2595C2214yes—
114#2593C2214yes—
115#2593C2212yes—
116#2590C2214yes—
117#2589C2214yes—
118#2589C2214yes—
119#2587C2214yes—
120#2586C2214yes—
121#2585C2212yes—
122#2576C2214yes—
123#2573C2212yes—
124#2570C2212yes—
125#2563C2212yes—
126#2563C2212yes—
127#2559C2214yes—
128#2559C2214yes—
129#2557C2214yes—
130#2557C2214yes—
131#2556C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2554C2214yes—
135#2554C2212yes—
136#2552C2212yes—
137#2552C2212yes—
138#2551C2212yes—
139#2551C2212yes—
140#2550C2212yes—
141#2546C2212yes—
142#2542C2212yes—
143#2538C2212yes—
144#2537C2212yes—
145#2525C2212yes—
146#2516C2212yes—
147#2513C2212yes—
148#2513C2212yes—
149#2512C2212yes—
150#2511C2214yes—
151#2509C2212yes—
152#2508C2212yes—
153#2507C2212yes—
154#2506C2212yes—
155#2506C2212yes—
156#2501C2212yes—
157#2500C2212yes—
158#2497C2212yes—
159#2496C2212yes—
160#2494C2212yes—
161#2494C2212yes—
162#2494C2214yes—
163#2494C2212yes—
164#2492C2214yes—
165#2492C2214yes—
166#2491C2212yes—
167#2491C2212yes—
168#2491C2212yes—
169#2490C2214yes—
170#2487C2212yes—
171#2485C2212yes—
172#2479C2214yes—
173#2479C2214yes—
174#2477C2214yes—
175#2477C2214yes—
176#2476C2214yes—
177#2476C2214yes—
178#2474C2214yes—
179#2470C2214yes—
180#2469C2214yes—
181#2469C2212yes—
182#2465C2214yes—
183#2462C2214yes—
184#2458C2214yes—
185#2458C2212yes—
186#2458C2214yes—
187#2458C2214yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2451C2214yes—
192#2451C2214yes—
193#2448C2214yes—
194#2445C2212yes—
195#2441C2212yes—
196#2440C2212yes—
197#2440C2212yes—
198#2440C2212yes—
199#2439C2212yes—
200#2439C2212yes—
201#2429C2214yes—
202#2429C2214yes—
203#2428C2212yes—
204#2426C2214yes—
205#2423C2214yes—
206#2422C2212yes—
207#2422C2212yes—
208#2420C2212yes—
209#2416C2212yes—
210#2414C2212yes—
211#2402C2211yescharacteristic
212#2398C2211yescharacteristic
213#2396C2211yescharacteristic
214#2396C2214yes—
215#2396C2214yes—
216#2392C2211yescharacteristic
217#2382C2214yes—
218#2378C2214yes—
219#2331C2212yes—
220#2330C2211yescharacteristic
221#2328C2211yescharacteristic
222#2324C2212yes—
223#2324C2212yes—
224#2324C2212yes—
225#2314C2211yescharacteristic
226#2314C2212yes—
227#2314C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×#126C2212yes—
232C4×C22⋊Q8C2214yes—
233C4×#123C2212yes—
234#2298C2212yes—
235#2293C2212yes—
236#2293C2212yes—
237#2293C2211yescharacteristic
238#2293C2212yes—
239#2274C2212yes—
240C42×Q8C2211yescharacteristic
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243#563—416no—
244#562—416no—
245#533—416no—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2314yes—
254C2×#127C2311yescharacteristic
255C2×#126C2312yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2311yescharacteristic
263C2×#125C2314yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2311yescharacteristic
303C2×#117C2314yes—
304C2×#117C2314yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C42C2314yes—
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#401C2314yes—
311#401C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2311yescharacteristic
328#400C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2311yescharacteristic
337#399C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2311yescharacteristic
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2311yescharacteristic
367#397C2312yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#396C2312yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2311yescharacteristic
399#395C2314yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2311yescharacteristic
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2311yescharacteristic
437#393C2312yes—
438#392C2314yes—
439#392C2314yes—
440#392C2311yescharacteristic
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2312yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2312yes—
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#388C2312yes—
545#388C2312yes—
546#388C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2312yes—
591#385C2314yes—
592#385C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#384C2311yescharacteristic
609#384C2311yescharacteristic
610#384C2312yes—
611#384C2311yescharacteristic
612#384C2314yes—
613#383C2312yes—
614#382C2311yescharacteristic
615#382C2314yes—
616#382C2312yes—
617#382C2314yes—
618#382C2311yescharacteristic
619#382C2312yes—
620#382C2311yescharacteristic
621#381C2312yes—
622#381C2314yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2312yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2414yes—
679C22×Q8C2414yes—
680C22×Q8C2414yes—
681C22×Q8C2414yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C22×D4C2414yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C4⋊Q8—44no—
697C4⋊Q8—44no—
698C4⋊Q8—44no—
699C4⋊Q8—44no—
700C4⋊Q8—48no—
701C4⋊Q8—48no—
702C4⋊Q8—48no—
703C4⋊Q8—48no—
704#127—42no—
705#126—28no—
706#126—48no—
707#126—48no—
708#126—48no—
709#125—216no—
710#125—42no—
711#125—48no—
712#125—48no—
713#125—48no—
714#124—48no—
715#124—48no—
716#124—48no—
717#123—28no—
718#123—48no—
719#123—48no—
720#123—48no—
721#123—48no—
722#123—48no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728C22⋊Q8—48no—
729C22⋊Q8—48no—
730C22⋊Q8—48no—
731C22⋊Q8—48no—
732C22⋊Q8—48no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—44no—
737#121—44no—
738#121—44no—
739#121—48no—
740C4×Q8—28no—
741C4×Q8—42no—
742C4×Q8—48no—
743C4×Q8—48no—
744C4×Q8—48no—
745C4×D4—28no—
746C4×D4—44no—
747C4×D4—44no—
748C4×D4—42no—
749C4×D4—44no—
750#117—24no—
751#117—28no—
752#117—42no—
753#117—48no—
754#117—48no—
755#117—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C42—48no—
865C2×C42—42no—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2411yescharacteristic
921#95C2414yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2411yescharacteristic
934#95C2411yescharacteristic
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955C24C2512yes—
956C24C2514yes—
957C24C2511yescharacteristic
958C2×Q8—24no—
959C2×Q8—28no—
960C2×Q8—28no—
961C2×Q8—41no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—42no—
977C2×D4—41no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C22×C4—24no—
993C22×C4—22no—
994C22×C4—28no—
995C22×C4—22no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—22no—
999C22×C4—28no—
1000C22×C4—24no—
1001C22×C4—28no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4C2511yescharacteristic
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4H(5,𝔽2)18yes—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—24no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C42—24no—
1145C42—28no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—22no—
1150C42—24no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—24no—
1156C42—24no—
1157C42—42no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C422−1+414yes—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—21no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—21no—
1181C23—21no—
1182C23—24no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—24no—
1187C23—24no—
1188C23—22no—
1189C23C2611yescharacteristic
1190Q8—44no—
1191Q8—88no—
1192Q8—88no—
1193Q8—88no—
1194Q8—164no—
1195D4—48no—
1196D4—84no—
1197D4—82no—
1198D4—164no—
1199D4—164no—
1200D4—164no—
1201D4—164no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—416no—
1264C2×C4—44no—
1265C2×C4—48no—
1266C2×C4—88no—
1267C2×C4—88no—
1268C2×C4—84no—
1269C2×C4—164no—
1270C2×C4C2×H(5,𝔽2)14yes—
1271C2×C4C2×H(5,𝔽2)14yes—
1272C2×C4C2×H(5,𝔽2)14yes—
1273C2×C4C2×2−1+414yes—
1274C2×C4C2×2−1+412yes—
1275C2×C4#58512yes—
1276C2×C4#58512yes—
1277C22—44no—
1278C22—42no—
1279C22—41no—
1280C22—42no—
1281C22—44no—
1282C22—41no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—42no—
1291C22—44no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—44no—
1296C22C22×H(5,𝔽2)12yes—
1297C22C22×2−1+411yescharacteristic
1298C22C2×#58511yescharacteristic
1299C22C2×#58511yescharacteristic
1300C222−1+612yes—
1301C4—24no—
1302C4—24no—
1303C4—24no—
1304C4—24no—
1305C4—44no—
1306C4—44no—
1307C4—44no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—41no—
1324C4#353114yes—
1325C2—84no—
1326C2—82no—
1327C2—81no—
1328C2C2×#353111yescharacteristic
1329C2#6283411yescharacteristic
1330C2#6289011yescharacteristic
1331C2#6291312yes—
1332C2#6292112yes—
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. #53125C2semidirect
2. #53121C2semidirect
3. #53094C2semidirect
4. #53076C2semidirect
5. #52987C2semidirect
6. #52974C2semidirect
7. #52466C2semidirect
8. #52456C2semidirect
9. #52443C2semidirect
10. #52438C2semidirect
11. #46301C2semidirect
12. #46227C2semidirect
13. #46062C2semidirect
14. #45993C2semidirect
15. #45789C2semidirect
16. #45762C2semidirect
17. #45627C2semidirect
18. #45486C2semidirect
19. #35598C2semidirect
20. #35597C2semidirect
21. #35578C2semidirect
22. #35295C2semidirect
23. #35283C2semidirect
24. #35207C2semidirect
25. #35193C2semidirect
26. #34929C2semidirect
27. #34881C2semidirect

Maximal subgroups

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

subgroupindex
#531252
#531212
#530942
#530762
#529872
#529742
#524662
#524562
#524432
#524382
#463012
#462272
#460622
#459932
#457892
#457622
#456272
#454862
#355982
#355972
#355782
#352952
#352832
#352072
#351932
#349292
#348812