Finite Group Databasebeta

← #7645731

Subgroups — #7645731

Order 512.

4252 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41766C214yesmaximal, complemented
2#41757C214yesmaximal, complemented
3#41682C214yesmaximal, complemented
4#41676C214yesmaximal, complemented
5#39689C212yesmaximal, complemented
6#39682C212yesmaximal, complemented
7#39299C212yesmaximal, complemented
8#39271C212yesmaximal, complemented
9#38275C212yesmaximal, complemented
10#38239C212yesmaximal, complemented
11#37986C212yesmaximal, complemented
12#37963C212yesmaximal, complemented
13#37549C211yesmaximal, characteristic
14#37540C211yesmaximal, characteristic, complemented
15#37503C212yesmaximal, complemented
16#36824C214yesmaximal, complemented
17#36764C212yesmaximal
18#36762C212yesmaximal, complemented
19#35458C214yesmaximal, complemented
20#35241C211yesmaximal, characteristic
21#35239C211yesmaximal, characteristic, complemented
22#35231C212yesmaximal, complemented
23#35104C212yesmaximal, complemented
24#35098C212yesmaximal
25#35017C212yesmaximal, complemented
26#34780C212yesmaximal, complemented
27#34213C211yesmaximal, characteristic, complemented
28C2×#2370C211yesmaximal, characteristic, complemented
29#34083C211yesmaximal, characteristic
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2863C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2212yes—
39#2852C2214yes—
40#2851C2212yes—
41#2851C2214yes—
42#2850C2212yes—
43#2839C2214yes—
44#2838C2214yes—
45#2822C2212yes—
46#2822C2212yes—
47#2822C2212yes—
48#2820C2212yes—
49#2807C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2796C2214yes—
54#2794C2214yes—
55#2793C2214yes—
56#2792C2214yes—
57#2791C2214yes—
58#2789C2214yes—
59#2783C2214yes—
60#2777C2214yes—
61#2777C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2773C2214yes—
65#2769C2214yes—
66#2767C2214yes—
67#2766C2214yes—
68#2765C2214yes—
69#2765C2214yes—
70#2762C2214yes—
71#2758C2214yes—
72#2755C2214yes—
73#2729C2214yes—
74#2726C2214yes—
75#2721C2214yes—
76#2720C2214yes—
77#2719C2214yes—
78#2713C2214yes—
79#2700C2214yes—
80#2689C2214yes—
81#2667C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2664C2214yes—
86#2664C2214yes—
87#2660C2212yes—
88#2655C2214yes—
89#2654C2214yes—
90#2654C2214yes—
91#2647C2212yes—
92#2645C2212yes—
93#2642C2212yes—
94#2634C2214yes—
95#2629C2212yes—
96#2629C2212yes—
97#2628C2212yes—
98#2627C2212yes—
99#2627C2214yes—
100#2627C2212yes—
101#2627C2212yes—
102#2625C2212yes—
103#2623C2214yes—
104#2618C2212yes—
105#2606C2214yes—
106#2606C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2596C2214yes—
110#2594C2214yes—
111#2590C2214yes—
112#2588C2214yes—
113#2585C2214yes—
114#2584C2212yes—
115#2577C2214yes—
116#2575C2214yes—
117#2574C2214yes—
118#2573C2214yes—
119#2571C2211yescharacteristic
120#2570C2214yes—
121#2570C2214yes—
122#2570C2212yes—
123#2568C2211yescharacteristic
124#2565C2212yes—
125#2565C2212yes—
126#2565C2212yes—
127#2562C2212yes—
128#2556C2214yes—
129#2552C2211yescharacteristic
130#2552C2211yescharacteristic
131#2551C2211yescharacteristic
132#2550C2214yes—
133#2550C2214yes—
134#2550C2212yes—
135#2547C2211yescharacteristic
136#2546C2211yescharacteristic
137#2545C2212yes—
138#2542C2211yescharacteristic
139#2533C2214yes—
140#2532C2214yes—
141#2529C2214yes—
142#2528C2214yes—
143#2525C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2524C2214yes—
149#2522C2214yes—
150#2521C2214yes—
151#2520C2214yes—
152#2519C2214yes—
153#2519C2214yes—
154#2516C2214yes—
155#2515C2214yes—
156#2515C2214yes—
157#2514C2212yes—
158#2514C2212yes—
159#2514C2214yes—
160#2510C2214yes—
161#2508C2212yes—
162#2508C2212yes—
163#2508C2214yes—
164#2507C2212yes—
165#2506C2212yes—
166#2505C2214yes—
167#2503C2212yes—
168#2502C2212yes—
169#2498C2214yes—
170#2497C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2495C2212yes—
174#2493C2214yes—
175#2493C2214yes—
176#2489C2212yes—
177#2489C2212yes—
178#2488C2214yes—
179#2487C2212yes—
180#2486C2212yes—
181#2484C2214yes—
182#2473C2214yes—
183#2451C2212yes—
184#2451C2212yes—
185#2449C2214yes—
186#2442C2212yes—
187#2440C2212yes—
188#2438C2214yes—
189#2423C2212yes—
190#2423C2212yes—
191#2419C2214yes—
192#2417C2212yes—
193#2417C2212yes—
194#2413C2214yes—
195#2402C2214yes—
196#2401C2214yes—
197#2370C2212yes—
198#2370C2212yes—
199#2370C2214yes—
200#2370C2212yes—
201#2370C2212yes—
202#2370C2214yes—
203#2370C2214yes—
204#2369C2212yes—
205#2365C2212yes—
206#2355C2214yes—
207#2355C2212yes—
208Q8×C4⋊C4C2212yes—
209#2337C2212yes—
210#2336C2212yes—
211#2334C2212yes—
212#2334C2212yes—
213#2331C2212yes—
214#2330C2212yes—
215#2330C2212yes—
216#2329C2212yes—
217#2329C2211yescharacteristic
218#2329C2214yes—
219#2329C2211yescharacteristic
220#2329C2212yes—
221#2325C2211yescharacteristic
222#2325C2211yescharacteristic
223#2323C2212yes—
224#2323C2212yes—
225#2323C2212yes—
226#2322C2212yes—
227#2322C2212yes—
228#2320C2212yes—
229#2318C2214yes—
230#2317C2212yes—
231#2314C2212yes—
232C4×#125C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2212yes—
236C4×#123C2214yes—
237#2298C2212yes—
238#2296C2212yes—
239#2295C2212yes—
240#2295C2212yes—
241C2×#389C2211yescharacteristic
242C2×#389C2211yescharacteristic
243C2×#389C2212yes—
244#2290C2212yes—
245#2290C2212yes—
246C2×#387C2212yes—
247C2×#387C2212yes—
248#2285C2211yescharacteristic
249#2283C2214yes—
250#2283C2211yescharacteristic
251#2283C2212yes—
252#2274C2212yes—
253C42×D4C2212yes—
254C2×C4×C4⋊C4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259#533—28no—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265#529—28no—
266C2×#126C2312yes—
267C2×#126C2314yes—
268C2×#125—28no—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×#121C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C42C2312yes—
315C22×C42C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
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#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#393C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#390C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2312yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
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#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2312yes—
583#386C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2312yes—
602#384C2312yes—
603#384C2312yes—
604#384C2312yes—
605#384C2311yescharacteristic
606#384C2314yes—
607#384C2312yes—
608#384C2311yescharacteristic
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2312yes—
614#383C2314yes—
615#383C2314yes—
616#383C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2311yescharacteristic
622#382C2311yescharacteristic
623#382C2312yes—
624#382C2314yes—
625#382C2314yes—
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#381C2314yes—
633#381C2312yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644#380C2312yes—
645#380C2311yescharacteristic
646#380C2311yescharacteristic
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2314yes—
707C2×#95C2312yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×D4C2412yes—
720C22×D4C2411yescharacteristic
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C4⋊Q8—24no—
736C4⋊Q8—24no—
737C4⋊Q8—44no—
738C4⋊Q8—82no—
739C4⋊Q8—82no—
740#126—28no—
741#126—84no—
742#125—28no—
743#125—28no—
744#125—28no—
745#125—28no—
746#125—28no—
747#125—24no—
748#125—28no—
749#125—84no—
750#125—82no—
751#125—84no—
752#124—24no—
753#124—82no—
754#123—28no—
755#123—48no—
756C22⋊Q8—24no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—48no—
761C22⋊Q8—44no—
762C22⋊Q8—84no—
763#121—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—24no—
772C4×D4—44no—
773#117—28no—
774#117—28no—
775#117—44no—
776#117—44no—
777C2×C4⋊C4—28no—
778C2×C4⋊C4—24no—
779C2×C4⋊C4—24no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—24no—
782C2×C4⋊C4—24no—
783C2×C4⋊C4—42no—
784C2×C4⋊C4—42no—
785C2×C4⋊C4—44no—
786C2×C4⋊C4—82no—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C42—28no—
886C2×C42—42no—
887C2×C42—44no—
888C2×C42—42no—
889C2×C42—82no—
890C2×C42—82no—
891C2×C42#4118yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2512yes—
1004C24C2511yescharacteristic
1005C2×Q8—24no—
1006C2×Q8—22no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—24no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8—41no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—22no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—22no—
1032C22×C4—24no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—41no—
1046C22×C4—42no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—41no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—41no—
1061C22×C4C2×#4114yes—
1062C22×C4C2×#4114yes—
1063C22×C4C2×#4114yes—
1064C22×C42−1+414yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—22no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—24no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C42−1+414yes—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C42—24no—
1191C42—28no—
1192C42—28no—
1193C42—28no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—42no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42—42no—
1209C42—44no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—42no—
1217C42C2×#4114yes—
1218C42C2×#4114yes—
1219C42C2×#4114yes—
1220C42C2×#4114yes—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23C22×#4112yes—
1233C23C2×2−1+412yes—
1234C23#58512yes—
1235C23C2611yescharacteristic
1236Q8—48no—
1237Q8—82no—
1238Q8—84no—
1239Q8—164no—
1240D4—48no—
1241D4—82no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—28no—
1257C2×C4—28no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—44no—
1316C2×C4—44no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—44no—
1320C2×C4—48no—
1321C2×C4—48no—
1322C2×C4—84no—
1323C2×C4—82no—
1324C2×C4—84no—
1325C2×C4—82no—
1326C2×C4—84no—
1327C2×C4C22×#4112yes—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4112yes—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4112yes—
1333C2×C4C2×2−1+414yes—
1334C2×C4C2×2−1+414yes—
1335C2×C4C2×2−1+412yes—
1336C2×C4#58512yes—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22#346114yes—
1351C22C23×#4111yescharacteristic
1352C22C22×2−1+411yescharacteristic
1353C22C22×2−1+411yescharacteristic
1354C22C2×#58511yescharacteristic
1355C22C2×#58511yescharacteristic
1356C22H(7,𝔽2)11yescharacteristic
1357C222−1+611yescharacteristic
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—24no—
1362C4—22no—
1363C4—22no—
1364C4—24no—
1365C4—42no—
1366C4—44no—
1367C4—44no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4#350714yes—
1385C2—24no—
1386C2—82no—
1387C2C2×#346111yescharacteristic
1388C2C2×#350711yescharacteristic
1389C2#6285611yescharacteristic
1390C2#6290411yescharacteristic
1391C2#6290811yescharacteristic
1392C2#6294511yescharacteristic
1393C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41766C2semidirect
2. #41757C2semidirect
3. #41682C2semidirect
4. #41676C2semidirect
5. #39689C2semidirect
6. #39682C2semidirect
7. #39299C2semidirect
8. #39271C2semidirect
9. #38275C2semidirect
10. #38239C2semidirect
11. #37986C2semidirect
12. #37963C2semidirect
14. #37540C2semidirect
15. #37503C2semidirect
16. #36824C2semidirect
18. #36762C2semidirect
19. #35458C2semidirect
21. #35239C2semidirect
22. #35231C2semidirect
23. #35104C2semidirect
25. #35017C2semidirect
26. #34780C2semidirect
27. #34213C2semidirect
28. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#417662
#417572
#416822
#416762
#396892
#396822
#392992
#392712
#382752
#382392
#379862
#379632
#375492
#375402
#375032
#368242
#367642
#367622
#354582
#352412
#352392
#352312
#351042
#350982
#350172
#347802
#342132
C2×#23702
#340832