Finite Group Databasebeta

← #7642203

Subgroups — #7642203

Order 512.

4168 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37429C212yesmaximal, complemented
2#37428C211yesmaximal, characteristic, complemented
3#37426C211yesmaximal, characteristic
4#37314C212yesmaximal, complemented
5#37314C212yesmaximal, complemented
6#37312C212yesmaximal, complemented
7#37311C212yesmaximal, complemented
8#37310C212yesmaximal
9#37308C211yesmaximal, characteristic, complemented
10#37306C211yesmaximal, characteristic
11#37197C214yesmaximal, complemented
12#37195C214yesmaximal, complemented
13#37138C214yesmaximal, complemented
14#37136C214yesmaximal, complemented
15#36755C214yesmaximal, complemented
16#36755C214yesmaximal, complemented
17#36754C214yesmaximal, complemented
18#36753C214yesmaximal, complemented
19#35344C211yesmaximal, characteristic, complemented
20#35304C212yesmaximal, complemented
21#35294C211yesmaximal, characteristic, complemented
22#35239C212yesmaximal, complemented
23#35235C212yesmaximal, complemented
24#35213C212yesmaximal, complemented
25#35192C212yesmaximal, complemented
26#34060C212yesmaximal
27#34056C211yesmaximal, characteristic
28C2×C4×#41C2211yescharacteristic
29#2868C2211yescharacteristic
30#2864C2212yes—
31#2864C2214yes—
32#2863C2214yes—
33#2863C2214yes—
34#2862C2211yescharacteristic
35#2862C2211yescharacteristic
36#2862C2214yes—
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2857C2214yes—
40#2857C2212yes—
41#2857C2212yes—
42#2855C2214yes—
43#2855C2214yes—
44#2851C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2811C2212yes—
48#2809C2212yes—
49#2807C2212yes—
50#2807C2212yes—
51#2806C2214yes—
52#2806C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2805C2214yes—
56#2804C2214yes—
57#2804C2212yes—
58#2802C2214yes—
59#2802C2214yes—
60#2799C2212yes—
61#2799C2212yes—
62#2799C2214yes—
63#2792C2214yes—
64#2792C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2790C2214yes—
68#2790C2214yes—
69#2788C2214yes—
70#2788C2214yes—
71#2788C2214yes—
72#2788C2214yes—
73#2784C2214yes—
74#2784C2212yes—
75#2784C2212yes—
76#2780C2214yes—
77#2780C2214yes—
78#2774C2214yes—
79#2774C2214yes—
80#2774C2214yes—
81#2774C2214yes—
82#2768C2214yes—
83#2768C2214yes—
84#2763C2212yes—
85#2763C2214yes—
86#2763C2212yes—
87#2763C2214yes—
88#2755C2214yes—
89#2755C2214yes—
90#2755C2214yes—
91#2755C2214yes—
92#2748C2214yes—
93#2742C2212yes—
94#2742C2214yes—
95#2742C2212yes—
96#2734C2214yes—
97#2734C2214yes—
98#2732C2214yes—
99#2729C2214yes—
100#2729C2214yes—
101#2729C2214yes—
102#2729C2214yes—
103#2720C2214yes—
104#2720C2214yes—
105#2713C2214yes—
106#2713C2214yes—
107#2713C2214yes—
108#2713C2214yes—
109#2704C2214yes—
110#2704C2214yes—
111#2692C2214yes—
112#2692C2214yes—
113#2692C2214yes—
114#2692C2214yes—
115#2683C2212yes—
116#2677C2212yes—
117#2677C2214yes—
118#2677C2212yes—
119#2667C2214yes—
120#2666C2214yes—
121#2666C2214yes—
122#2666C2214yes—
123#2666C2214yes—
124#2665C2214yes—
125#2665C2214yes—
126#2665C2214yes—
127#2660C2212yes—
128#2660C2212yes—
129#2647C2212yes—
130#2647C2212yes—
131#2629C2212yes—
132#2628C2211yescharacteristic
133#2628C2211yescharacteristic
134#2628C2212yes—
135#2628C2211yescharacteristic
136#2628C2211yescharacteristic
137#2612C2214yes—
138#2612C2214yes—
139#2612C2214yes—
140#2612C2214yes—
141#2608C2214yes—
142#2607C2214yes—
143#2607C2214yes—
144#2607C2214yes—
145#2606C2214yes—
146#2606C2214yes—
147#2605C2214yes—
148#2605C2214yes—
149#2605C2214yes—
150#2605C2214yes—
151#2605C2214yes—
152#2605C2214yes—
153#2571C2212yes—
154#2571C2212yes—
155#2571C2212yes—
156#2570C2212yes—
157#2570C2214yes—
158#2570C2214yes—
159#2570C2212yes—
160#2570C2212yes—
161#2570C2212yes—
162#2569C2214yes—
163#2569C2214yes—
164#2552C2212yes—
165#2552C2212yes—
166#2551C2212yes—
167#2551C2212yes—
168#2551C2212yes—
169#2550C2212yes—
170#2550C2212yes—
171#2550C2212yes—
172#2550C2214yes—
173#2550C2214yes—
174#2550C2212yes—
175#2549C2214yes—
176#2549C2214yes—
177#2442C2212yes—
178#2442C2212yes—
179#2442C2212yes—
180#2442C2212yes—
181#2441C2214yes—
182#2441C2212yes—
183#2441C2212yes—
184#2440C2212yes—
185#2440C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2439C2214yes—
189#2439C2214yes—
190#2439C2214yes—
191#2439C2212yes—
192#2439C2212yes—
193#2439C2212yes—
194#2439C2212yes—
195#2439C2212yes—
196#2439C2212yes—
197#2438C2214yes—
198#2438C2214yes—
199#2438C2214yes—
200#2438C2214yes—
201#2331C2212yes—
202#2331C2211yescharacteristic
203#2331C2211yescharacteristic
204#2331C2211yescharacteristic
205#2331C2212yes—
206#2331C2212yes—
207#2331C2211yescharacteristic
208#2330C2212yes—
209#2330C2212yes—
210#2330C2212yes—
211#2320C2212yes—
212#2320C2212yes—
213#2320C2214yes—
214#2319C2212yes—
215#2319C2212yes—
216#2319C2214yes—
217#2318C2212yes—
218#2318C2212yes—
219#2318C2212yes—
220#2318C2212yes—
221#2318C2214yes—
222#2318C2214yes—
223#2317C2212yes—
224#2317C2212yes—
225#2314C2212yes—
226#2314C2212yes—
227#2314C2212yes—
228#2314C2212yes—
229#2311C2212yes—
230#2311C2212yes—
231#2298C2212yes—
232#2298C2212yes—
233#2297C2211yescharacteristic
234#2297C2211yescharacteristic
235#2296C2211yescharacteristic
236#2296C2211yescharacteristic
237#2295C2214yes—
238#2293C2214yes—
239#2290C2214yes—
240#2290C2214yes—
241#2285C2212yes—
242#2285C2212yes—
243#2283C2212yes—
244#2283C2212yes—
245#2283C2212yes—
246#2283C2212yes—
247C4×#117C2211yescharacteristic
248C4×#117C2212yes—
249C2×C4×C4⋊C4C2212yes—
250C2×#376C2211yescharacteristic
251C22×#41C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2314yes—
260C2×C4⋊Q8C2314yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2314yes—
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C4×#41Q8116yescomplemented
275C2×C4×Q8C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2311yescharacteristic
286C2×#117C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2314yes—
292C22×C42C2311yescharacteristic
293C22×C42C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2312yes—
299#400C2312yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2312yes—
320#399C2314yes—
321#399C2314yes—
322#399C2312yes—
323#399C2312yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
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#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2312yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#393C2312yes—
388#393C2314yes—
389#393C2312yes—
390#393C2314yes—
391#393C2314yes—
392#393C2312yes—
393#393C2312yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2311yescharacteristic
432#390C2312yes—
433#390C2311yescharacteristic
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2312yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2311yescharacteristic
573#385C2311yescharacteristic
574#385C2312yes—
575#385C2312yes—
576#385C2311yescharacteristic
577#385C2311yescharacteristic
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#384C2312yes—
587#384C2312yes—
588#384C2312yes—
589#384C2312yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2314yes—
594#384C2314yes—
595#383C2312yes—
596#383C2314yes—
597#383C2312yes—
598#383C2312yes—
599#383C2312yes—
600#383C2314yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2311yescharacteristic
607#382C2311yescharacteristic
608#382C2312yes—
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#382C2314yes—
613#382C2312yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2314yes—
617#382C2314yes—
618#382C2312yes—
619#382C2314yes—
620#382C2312yes—
621#382C2312yes—
622#381C2312yes—
623#381C2312yes—
624#381C2314yes—
625#381C2312yes—
626#381C2314yes—
627#381C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646#380C2314yes—
647#380C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676#376C2312yes—
677#376C2314yes—
678#376C2312yes—
679#376C2312yes—
680#376C2311yescharacteristic
681#376C2311yescharacteristic
682#376C2314yes—
683#376C2314yes—
684#376C2312yes—
685C2×#95C2312yes—
686C2×#95C2314yes—
687C2×#95C2312yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C43C2314yes—
691C2×#41—42no—
692C2×#41—42no—
693C2×#41C2×Q818yes—
694C22×Q8C2412yes—
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×Q8C2414yes—
698C22×Q8C2414yes—
699C22×Q8C2412yes—
700C22×Q8C2412yes—
701C22×Q8C2411yescharacteristic
702C22×D4C2412yes—
703C22×D4C2411yescharacteristic
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C4⋊Q8—44no—
715C4⋊Q8—44no—
716C4⋊Q8—42no—
717C4⋊Q8—44no—
718C4⋊Q8—42no—
719C4⋊Q8—42no—
720C4⋊Q8—42no—
721C4⋊Q8—84no—
722C4⋊Q8—84no—
723C4⋊Q8—84no—
724C4⋊Q8—84no—
725#125—44no—
726#125—44no—
727#125—44no—
728#125—84no—
729#125—84no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732C22⋊Q8—84no—
733C22⋊Q8—84no—
734C22⋊Q8—84no—
735C22⋊Q8—84no—
736C4×Q8C2×Q8116yes—
737C4×D4C2×Q8116yes—
738C4×D4C2×Q8116yes—
739C4×D4C2×Q8116yes—
740#117—42no—
741#117—42no—
742#117—44no—
743#117—44no—
744#117—84no—
745#117—84no—
746#117C2×Q818yes—
747#117C2×Q8116yes—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C42—42no—
843C2×C42—42no—
844C2×C42—84no—
845C2×C42C2×Q818yes—
846C2×C42C2×Q8116yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2411yescharacteristic
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2411yescharacteristic
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958C24C2511yescharacteristic
959C24C2512yes—
960#41—416no—
961C2×Q8—41no—
962C2×Q8—41no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—42no—
971C2×Q8—44no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8C22×Q814yes—
981C2×D4—41no—
982C2×D4—42no—
983C2×D4—41no—
984C2×D4—42no—
985C2×D4C22×Q818yes—
986C2×D4C22×Q814yes—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—41no—
998C22×C4—42no—
999C22×C4—41no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4C22×Q818yes—
1011C22×C4C22×Q814yes—
1012C22×C4C22×Q818yes—
1013C22×C4C22×Q818yes—
1014C22×C4C22×Q818yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
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—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4C22×Q818yes—
1105C4⋊C4C22×Q818yes—
1106C4⋊C4C22×Q818yes—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4C22×Q814yes—
1129C22⋊C4C22×Q814yes—
1130C22⋊C4C22×Q818yes—
1131C22⋊C4C22×Q818yes—
1132C42—24no—
1133C42—24no—
1134C42—22no—
1135C42—22no—
1136C42—22no—
1137C42—22no—
1138C42—41no—
1139C42—42no—
1140C42—41no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—42no—
1147C42—42no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—44no—
1154C42—42no—
1155C42C22×Q814yes—
1156C42C22×Q814yes—
1157C42C22×Q818yes—
1158C42C22×Q818yes—
1159C42C22×Q818yes—
1160C42C22×Q818yes—
1161C23—22no—
1162C23—21no—
1163C23—22no—
1164C23—21no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23C23×Q812yes—
1172C23C23×Q814yes—
1173C23C2611yescharacteristic
1174Q8—44no—
1175Q8—164no—
1176Q8—164no—
1177Q8—162no—
1178Q8—164no—
1179Q8—162no—
1180Q8—162no—
1181Q8—162no—
1182D4—44no—
1183D4—48no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—28no—
1197C2×C4—216no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—48no—
1249C2×C4—48no—
1250C2×C4—48no—
1251C2×C4—88no—
1252C2×C4—84no—
1253C2×C4—88no—
1254C2×C4—82no—
1255C2×C4—82no—
1256C2×C4C23×Q814yes—
1257C2×C4C23×Q814yes—
1258C2×C4C23×Q814yes—
1259C2×C4C23×Q814yes—
1260C2×C4C23×Q814yes—
1261C2×C4C23×Q812yes—
1262C2×C4C23×Q812yes—
1263C2×C4#58512yes—
1264C2×C4#58512yes—
1265C22—24no—
1266C22—24no—
1267C22—24no—
1268C22—24no—
1269C22—22no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22C24×Q811yescharacteristic
1278C22C2×#58511yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22H(7,𝔽2)12yes—
1281C222−1+612yes—
1282C4—24no—
1283C4—24no—
1284C4—24no—
1285C4—24no—
1286C4—22no—
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—42no—
1298C4—44no—
1299C4—41no—
1300C4—44no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—44no—
1305C4—41no—
1306C4#345814yes—
1307C2—44no—
1308C2—42no—
1309C2C2×#345811yescharacteristic
1310C2#6285412yes—
1311C2#6288212yes—
1312C2#6288511yescharacteristic
1313C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37429C2semidirect
2. #37428C2semidirect
4. #37314C2semidirect
5. #37314C2semidirect
6. #37312C2semidirect
7. #37311C2semidirect
9. #37308C2semidirect
11. #37197C2semidirect
12. #37195C2semidirect
13. #37138C2semidirect
14. #37136C2semidirect
15. #36755C2semidirect
16. #36755C2semidirect
17. #36754C2semidirect
18. #36753C2semidirect
19. #35344C2semidirect
20. #35304C2semidirect
21. #35294C2semidirect
22. #35239C2semidirect
23. #35235C2semidirect
24. #35213C2semidirect
25. #35192C2semidirect
274. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#374292
#374282
#374262
#373142
#373122
#373112
#373102
#373082
#373062
#371972
#371952
#371382
#371362
#367552
#367542
#367532
#353442
#353042
#352942
#352392
#352352
#352132
#351922
#340602
#340562