Finite Group Databasebeta

← #7645597

Subgroups — #7645597

Order 512.

4280 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42319C214yesmaximal, complemented
2#42209C214yesmaximal, complemented
3#42032C214yesmaximal, complemented
4#41965C214yesmaximal, complemented
5#39638C212yesmaximal, complemented
6#39637C212yesmaximal, complemented
7#38981C212yesmaximal, complemented
8#38980C212yesmaximal, complemented
9#38069C212yesmaximal, complemented
10#38068C212yesmaximal
11#38067C212yesmaximal
12#38066C212yesmaximal, complemented
13#37580C212yesmaximal, complemented
14#37571C212yesmaximal, complemented
15#37028C212yesmaximal, complemented
16#37023C212yesmaximal, complemented
17#36834C212yesmaximal, complemented
18#36829C212yesmaximal, complemented
19#35380C214yesmaximal, complemented
20#35221C212yesmaximal, complemented
21#35175C212yesmaximal, complemented
22#35139C211yesmaximal, characteristic
23#35111C211yesmaximal, characteristic
24#35026C214yesmaximal, complemented
25#34966C211yesmaximal, characteristic, complemented
26C2×#2584C211yesmaximal, characteristic, complemented
27#34239C211yesmaximal, characteristic, complemented
28#34153C211yesmaximal, characteristic
29#34059C211yesmaximal, characteristic, complemented
30C2×#529C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2864C2214yes—
34#2863C2214yes—
35#2861C2212yes—
36#2859C2212yes—
37#2855C2212yes—
38#2855C2214yes—
39#2854C2212yes—
40#2851C2214yes—
41#2839C2214yes—
42#2836C2214yes—
43#2833C2214yes—
44#2831C2214yes—
45#2809C2214yes—
46#2806C2214yes—
47#2805C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2788C2214yes—
51#2787C2214yes—
52#2783C2214yes—
53#2777C2214yes—
54#2777C2214yes—
55#2776C2214yes—
56#2775C2214yes—
57#2775C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2772C2214yes—
63#2770C2214yes—
64#2769C2214yes—
65#2768C2214yes—
66#2767C2214yes—
67#2766C2214yes—
68#2766C2214yes—
69#2759C2214yes—
70#2758C2214yes—
71#2745C2214yes—
72#2738C2214yes—
73#2726C2214yes—
74#2719C2214yes—
75#2698C2214yes—
76#2689C2214yes—
77#2667C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2665C2214yes—
82#2664C2212yes—
83#2664C2214yes—
84#2664C2212yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2652C2214yes—
89#2652C2214yes—
90#2650C2214yes—
91#2647C2212yes—
92#2647C2212yes—
93#2647C2212yes—
94#2647C2212yes—
95#2645C2212yes—
96#2645C2212yes—
97#2644C2212yes—
98#2644C2212yes—
99#2623C2212yes—
100#2614C2212yes—
101#2611C2212yes—
102#2611C2212yes—
103#2606C2212yes—
104#2605C2212yes—
105#2604C2214yes—
106#2599C2212yes—
107#2599C2212yes—
108#2596C2214yes—
109#2594C2214yes—
110#2592C2211yescharacteristic
111#2592C2211yescharacteristic
112#2590C2214yes—
113#2589C2214yes—
114#2588C2214yes—
115#2587C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2585C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2584C2211yescharacteristic
123#2584C2211yescharacteristic
124#2584C2214yes—
125#2584C2212yes—
126#2584C2212yes—
127#2584C2212yes—
128#2584C2212yes—
129#2584C2212yes—
130#2584C2212yes—
131#2581C2212yes—
132#2580C2212yes—
133#2574C2214yes—
134#2573C2214yes—
135#2573C2214yes—
136#2570C2212yes—
137#2566C2212yes—
138#2565C2212yes—
139#2556C2214yes—
140#2550C2212yes—
141#2533C2214yes—
142#2528C2214yes—
143#2525C2214yes—
144#2514C2212yes—
145#2513C2212yes—
146#2512C2212yes—
147#2511C2212yes—
148#2509C2214yes—
149#2509C2212yes—
150#2509C2212yes—
151#2509C2214yes—
152#2508C2212yes—
153#2508C2212yes—
154#2507C2212yes—
155#2507C2212yes—
156#2506C2212yes—
157#2506C2212yes—
158#2504C2211yescharacteristic
159#2503C2211yescharacteristic
160#2503C2214yes—
161#2502C2211yescharacteristic
162#2501C2211yescharacteristic
163#2498C2214yes—
164#2494C2214yes—
165#2493C2214yes—
166#2493C2214yes—
167#2493C2214yes—
168#2488C2214yes—
169#2486C2214yes—
170#2484C2214yes—
171#2481C2214yes—
172#2478C2214yes—
173#2475C2214yes—
174#2473C2214yes—
175#2469C2214yes—
176#2454C2212yes—
177#2453C2214yes—
178#2453C2214yes—
179#2453C2212yes—
180#2452C2212yes—
181#2451C2212yes—
182#2442C2212yes—
183#2442C2214yes—
184#2440C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2421C2214yes—
188#2419C2214yes—
189#2419C2214yes—
190#2417C2214yes—
191#2413C2214yes—
192#2413C2214yes—
193#2402C2212yes—
194#2399C2212yes—
195C2×#398C2212yes—
196C2×#395C2212yes—
197#2373C2214yes—
198#2371C2214yes—
199#2370C2212yes—
200#2370C2212yes—
201#2370C2212yes—
202#2367C2212yes—
203#2361C2212yes—
204#2360C2212yes—
205#2359C2214yes—
206#2345C2212yes—
207#2344C2214yes—
208#2344C2212yes—
209#2336C2212yes—
210#2336C2212yes—
211#2331C2212yes—
212#2331C2212yes—
213#2330C2212yes—
214#2330C2212yes—
215#2322C2214yes—
216#2322C2214yes—
217#2320C2212yes—
218#2320C2211yescharacteristic
219#2320C2211yescharacteristic
220#2320C2211yescharacteristic
221#2320C2212yes—
222#2320C2211yescharacteristic
223#2320C2212yes—
224#2320C2212yes—
225#2319C2212yes—
226#2319C2212yes—
227#2316C2212yes—
228#2313C2212yes—
229#2313C2212yes—
230#2313C2212yes—
231#2310C2212yes—
232C4×C4⋊Q8C2212yes—
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2212yes—
236C4×C22⋊Q8C2214yes—
237#2298C2212yes—
238#2296C2212yes—
239#2295C2212yes—
240#2295C2212yes—
241#2295C2212yes—
242#2295C2212yes—
243#2295C2211yescharacteristic
244#2293C2211yescharacteristic
245C2×#389C2214yes—
246C2×#389C2212yes—
247C2×#389C2212yes—
248#2290C2212yes—
249#2283C2212yes—
250#2283C2212yes—
251#2283C2211yescharacteristic
252#2274C2212yes—
253C42×Q8C2211yescharacteristic
254C42×D4C2211yescharacteristic
255C42×D4C2212yes—
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261#529—28no—
262C2×#126C2312yes—
263C2×#126C2314yes—
264C2×#125—28no—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2311yescharacteristic
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#124C2311yescharacteristic
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2311yescharacteristic
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×#121C2311yescharacteristic
281C2×C4×Q8—28no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2314yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2314yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2314yes—
309C22×C42C2312yes—
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
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#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2312yes—
350#399C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2312yes—
416#393C2312yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
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#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2312yes—
533#387C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#383C2314yes—
611#383C2314yes—
612#383C2312yes—
613#383C2312yes—
614#383C2312yes—
615#383C2312yes—
616#383C2312yes—
617#383C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2314yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#381C2312yes—
631#381C2312yes—
632#381C2312yes—
633#381C2312yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2312yes—
649#380C2314yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699#376C2312yes—
700#376C2312yes—
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708C2×#95C2312yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C43C2311yescharacteristic
712C43C2311yescharacteristic
713C43C2312yes—
714C43C2312yes—
715C22×Q8—24no—
716C22×Q8—44no—
717C22×Q8C2411yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2411yescharacteristic
734C4⋊Q8—28no—
735#126—28no—
736#126—84no—
737#125—28no—
738#125—28no—
739#125—28no—
740#125—28no—
741#125—28no—
742#125—24no—
743#125—84no—
744#125—84no—
745#124—24no—
746#123—28no—
747#123—48no—
748#123—48no—
749C22⋊Q8—24no—
750C22⋊Q8—48no—
751C22⋊Q8—84no—
752#121—24no—
753C4×Q8—28no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—28no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—84no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—24no—
765C4×D4—48no—
766#117—28no—
767#117—44no—
768#117—48no—
769#117—44no—
770#117—82no—
771C2×C4⋊C4—28no—
772C2×C4⋊C4—24no—
773C2×C4⋊C4—24no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—28no—
776C2×C4⋊C4—24no—
777C2×C4⋊C4—28no—
778C2×C4⋊C4—48no—
779C2×C4⋊C4—84no—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C42—28no—
872C2×C42—82no—
873C2×C42—82no—
874C2×C42#4118yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2411yescharacteristic
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2512yes—
997C24C2511yescharacteristic
998C2×Q8—22no—
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—28no—
1004C2×Q8—42no—
1005C2×Q8—42no—
1006C2×Q8—42no—
1007C2×Q8—42no—
1008C2×Q8—44no—
1009C2×Q8—44no—
1010C2×Q8—416no—
1011C2×D4—24no—
1012C2×D4—28no—
1013C2×D4—22no—
1014C2×D4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—41no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—41no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4C2×#4114yes—
1040C22×C4C2×#4114yes—
1041C22×C4C2×#4114yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2514yes—
1068C22×C4C2511yescharacteristic
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C42−1+418yes—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—28no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C42—24no—
1161C42—24no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—28no—
1168C42—24no—
1169C42—24no—
1170C42—42no—
1171C42—41no—
1172C42—42no—
1173C42—44no—
1174C42—44no—
1175C42—42no—
1176C42—42no—
1177C42—41no—
1178C42—41no—
1179C42—44no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—41no—
1187C42—44no—
1188C42—42no—
1189C42—42no—
1190C42—44no—
1191C42C2×#4114yes—
1192C42C2×#4114yes—
1193C42C2×#4114yes—
1194C42C2×#4114yes—
1195C23—22no—
1196C23—21no—
1197C23—21no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23C22×#4112yes—
1204C23#58514yes—
1205C23C2611yescharacteristic
1206Q8—44no—
1207Q8—44no—
1208Q8—48no—
1209Q8—44no—
1210Q8—88no—
1211D4—48no—
1212D4—44no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—24no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—28no—
1223C2×C4—28no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—44no—
1283C2×C4—416no—
1284C2×C4—48no—
1285C2×C4—48no—
1286C2×C4—48no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4112yes—
1296C2×C4C2×2−1+418yes—
1297C2×C4C2×2−1+414yes—
1298C22—22no—
1299C22—22no—
1300C22—24no—
1301C22—24no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—44no—
1306C22—44no—
1307C22#345514yes—
1308C22C23×#4111yescharacteristic
1309C22C22×2−1+412yes—
1310C22C2×#58512yes—
1311C22H(7,𝔽2)11yescharacteristic
1312C222−1+611yescharacteristic
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—28no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—44no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4#350914yes—
1340C2—24no—
1341C2—82no—
1342C2C2×#345511yescharacteristic
1343C2C2×#350911yescharacteristic
1344C2#6285611yescharacteristic
1345C2#6294812yes—
1346C2#6294912yes—
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. #42319C2semidirect
2. #42209C2semidirect
3. #42032C2semidirect
4. #41965C2semidirect
5. #39638C2semidirect
6. #39637C2semidirect
7. #38981C2semidirect
8. #38980C2semidirect
9. #38069C2semidirect
12. #38066C2semidirect
13. #37580C2semidirect
14. #37571C2semidirect
15. #37028C2semidirect
16. #37023C2semidirect
17. #36834C2semidirect
18. #36829C2semidirect
19. #35380C2semidirect
20. #35221C2semidirect
21. #35175C2semidirect
24. #35026C2semidirect
25. #34966C2semidirect
26. C2×#2584C2semidirect
27. #34239C2semidirect
29. #34059C2semidirect

Maximal subgroups

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

subgroupindex
#423192
#422092
#420322
#419652
#396382
#396372
#389812
#389802
#380692
#380682
#380672
#380662
#375802
#375712
#370282
#370232
#368342
#368292
#353802
#352212
#351752
#351392
#351112
#350262
#349662
C2×#25842
#342392
#341532
#340592