Finite Group Databasebeta

← #7648513

Subgroups — #7648513

Order 512.

4280 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42333C212yesmaximal, complemented
2#42332C212yesmaximal, complemented
3#42331C212yesmaximal, complemented
4#42330C212yesmaximal, complemented
5#42209C214yesmaximal, complemented
6#42032C214yesmaximal, complemented
7#39636C214yesmaximal, complemented
8#38979C214yesmaximal
9#38071C214yesmaximal, complemented
10#38070C214yesmaximal, complemented
11#37504C212yesmaximal, complemented
12#37495C212yesmaximal, complemented
13#37401C212yesmaximal, complemented
14#37399C212yesmaximal, complemented
15#37359C212yesmaximal, complemented
16#37354C212yesmaximal, complemented
17#35650C212yesmaximal, complemented
18#35594C212yesmaximal, complemented
19#35321C212yesmaximal, complemented
20#35291C212yesmaximal, complemented
21#35245C211yesmaximal, characteristic
22#35241C211yesmaximal, characteristic
23#35017C212yesmaximal, complemented
24#35016C212yesmaximal, complemented
25#34966C211yesmaximal, characteristic, complemented
26#34953C211yesmaximal, characteristic, complemented
27#34221C211yesmaximal, characteristic, complemented
28#34149C211yesmaximal, characteristic
29C2×#2320C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2863C2212yes—
34#2863C2212yes—
35#2862C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2212yes—
41#2855C2212yes—
42#2853C2214yes—
43#2850C2212yes—
44#2839C2214yes—
45#2836C2214yes—
46#2833C2214yes—
47#2831C2214yes—
48#2799C2214yes—
49#2799C2214yes—
50#2791C2214yes—
51#2791C2214yes—
52#2789C2214yes—
53#2786C2214yes—
54#2777C2214yes—
55#2776C2214yes—
56#2775C2214yes—
57#2774C2214yes—
58#2773C2214yes—
59#2772C2214yes—
60#2770C2214yes—
61#2769C2214yes—
62#2768C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2762C2214yes—
68#2758C2214yes—
69#2758C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2740C2214yes—
73#2738C2214yes—
74#2719C2214yes—
75#2715C2214yes—
76#2713C2214yes—
77#2713C2214yes—
78#2700C2214yes—
79#2698C2214yes—
80#2667C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2665C2214yes—
85#2664C2214yes—
86#2664C2214yes—
87#2655C2214yes—
88#2650C2214yes—
89#2647C2212yes—
90#2646C2214yes—
91#2646C2214yes—
92#2645C2212yes—
93#2645C2212yes—
94#2643C2214yes—
95#2643C2214yes—
96#2642C2212yes—
97#2634C2212yes—
98#2632C2212yes—
99#2629C2212yes—
100#2625C2212yes—
101#2625C2212yes—
102#2621C2212yes—
103#2606C2212yes—
104#2605C2212yes—
105#2604C2214yes—
106#2596C2214yes—
107#2594C2214yes—
108#2591C2212yes—
109#2586C2214yes—
110#2585C2214yes—
111#2585C2214yes—
112#2585C2214yes—
113#2585C2214yes—
114#2585C2214yes—
115#2584C2212yes—
116#2584C2212yes—
117#2583C2214yes—
118#2583C2212yes—
119#2581C2212yes—
120#2574C2214yes—
121#2573C2214yes—
122#2573C2214yes—
123#2570C2212yes—
124#2568C2211yescharacteristic
125#2567C2212yes—
126#2565C2212yes—
127#2556C2214yes—
128#2550C2212yes—
129#2547C2211yescharacteristic
130#2546C2212yes—
131#2546C2211yescharacteristic
132#2545C2212yes—
133#2542C2211yescharacteristic
134#2536C2212yes—
135#2533C2214yes—
136#2532C2214yes—
137#2529C2214yes—
138#2528C2214yes—
139#2525C2214yes—
140#2525C2214yes—
141#2524C2214yes—
142#2524C2214yes—
143#2524C2214yes—
144#2520C2214yes—
145#2519C2214yes—
146#2515C2214yes—
147#2515C2214yes—
148#2514C2212yes—
149#2514C2214yes—
150#2511C2212yes—
151#2510C2214yes—
152#2509C2214yes—
153#2509C2214yes—
154#2508C2214yes—
155#2507C2212yes—
156#2506C2212yes—
157#2505C2214yes—
158#2505C2214yes—
159#2502C2211yescharacteristic
160#2502C2211yescharacteristic
161#2498C2214yes—
162#2497C2212yes—
163#2496C2212yes—
164#2495C2214yes—
165#2494C2214yes—
166#2492C2212yes—
167#2489C2212yes—
168#2489C2214yes—
169#2487C2212yes—
170#2481C2214yes—
171#2473C2214yes—
172#2473C2214yes—
173#2469C2214yes—
174#2453C2214yes—
175#2453C2212yes—
176#2453C2214yes—
177#2451C2212yes—
178#2450C2214yes—
179#2449C2214yes—
180#2446C2212yes—
181#2446C2212yes—
182#2442C2212yes—
183#2440C2212yes—
184#2438C2214yes—
185#2434C2211yescharacteristic
186#2434C2211yescharacteristic
187#2429C2212yes—
188#2429C2212yes—
189#2423C2212yes—
190#2421C2212yes—
191#2421C2214yes—
192#2417C2212yes—
193#2417C2212yes—
194#2409C2212yes—
195#2402C2212yes—
196#2399C2212yes—
197#2399C2212yes—
198#2399C2212yes—
199#2373C2212yes—
200#2373C2212yes—
201#2372C2211yescharacteristic
202#2372C2211yescharacteristic
203#2371C2214yes—
204#2371C2211yescharacteristic
205#2371C2211yescharacteristic
206#2368C2214yes—
207#2368C2212yes—
208#2364C2212yes—
209#2359C2212yes—
210#2359C2212yes—
211#2356C2212yes—
212#2356C2212yes—
213#2343C2212yes—
214#2343C2212yes—
215#2331C2212yes—
216#2329C2214yes—
217#2329C2214yes—
218#2327C2212yes—
219#2323C2212yes—
220#2323C2212yes—
221#2323C2212yes—
222#2323C2212yes—
223#2320C2212yes—
224#2320C2212yes—
225#2320C2212yes—
226#2320C2214yes—
227#2320C2212yes—
228#2320C2212yes—
229#2320C2212yes—
230#2320C2211yescharacteristic
231#2320C2211yescharacteristic
232#2318C2214yes—
233#2318C2214yes—
234C4×C4⋊Q8C2212yes—
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2212yes—
237C4×#125C2212yes—
238C4×C22⋊Q8C2214yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241#2298C2212yes—
242#2296C2214yes—
243#2295C2212yes—
244C2×#391C2212yes—
245C2×#389C2212yes—
246#2290C2212yes—
247#2290C2212yes—
248C2×#387C2214yes—
249#2283C2211yescharacteristic
250C2×#383C2212yes—
251C2×#382C2212yes—
252#2276C2211yescharacteristic
253#2276C2211yescharacteristic
254C42×D4C2212yes—
255C4×#117C2211yescharacteristic
256C4×#117C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260#533—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#124C2311yescharacteristic
276C2×#124C2312yes—
277C2×#123C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2311yescharacteristic
289C2×C4×Q8—28no—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2314yes—
313C22×C42C2312yes—
314C22×C42C2312yes—
315C22×C42C2312yes—
316C22×C42C2312yes—
317C22×C42C2311yescharacteristic
318#401C2314yes—
319#401C2314yes—
320#401C2314yes—
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#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
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#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#390C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2314yes—
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#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#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2312yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2312yes—
603#385C2314yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2314yes—
614#383C2312yes—
615#383C2312yes—
616#383C2312yes—
617#383C2314yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#382C2312yes—
629#382C2312yes—
630#382C2314yes—
631#381C2314yes—
632#381C2314yes—
633#381C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2312yes—
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2312yes—
699#376C2311yescharacteristic
700#376C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2311yescharacteristic
704#376C2311yescharacteristic
705#376C2312yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2314yes—
713C43C2312yes—
714C43C2312yes—
715C22×Q8—24no—
716C22×Q8—44no—
717C22×Q8C2411yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×D4C2412yes—
725C22×D4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C4⋊Q8—24no—
738C4⋊Q8—24no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—82no—
743#126—28no—
744#126—84no—
745#125—24no—
746#125—28no—
747#125—44no—
748#125—84no—
749#125—84no—
750#124—24no—
751#124—82no—
752#123—28no—
753C22⋊Q8—24no—
754C22⋊Q8—24no—
755C22⋊Q8—24no—
756C22⋊Q8—28no—
757C22⋊Q8—216no—
758C22⋊Q8—44no—
759C22⋊Q8—44no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762C22⋊Q8—84no—
763#121—24no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—28no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—28no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×Q8—84no—
775C4×D4—28no—
776C4×D4—28no—
777C4×D4—28no—
778C4×D4—24no—
779#117—28no—
780#117—28no—
781#117—28no—
782#117—44no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—44no—
786C2×C4⋊C4—84no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C42—28no—
877C2×C42—44no—
878C2×C42—44no—
879C2×C42—82no—
880C2×C42#4118yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
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—
1001C24C2512yes—
1002C24C2511yescharacteristic
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—22no—
1006C2×Q8—22no—
1007C2×Q8—22no—
1008C2×Q8—24no—
1009C2×Q8—28no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—416no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—28no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—41no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4C2×#4114yes—
1056C22×C4C2×#4114yes—
1057C22×C4C2×#4114yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—28no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C42−1+418yes—
1174C42—28no—
1175C42—28no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—42no—
1196C42—42no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—44no—
1204C42C2×#4114yes—
1205C42C2×#4114yes—
1206C42C2×#4114yes—
1207C42C2×#4114yes—
1208C23—22no—
1209C23—21no—
1210C23—21no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23C22×#4112yes—
1219C23C2×2−1+414yes—
1220C23C2611yescharacteristic
1221Q8—48no—
1222Q8—44no—
1223Q8—44no—
1224Q8—48no—
1225Q8—82no—
1226Q8—84no—
1227Q8—88no—
1228D4—48no—
1229D4—82no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—28no—
1242C2×C4—28no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—44no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—88no—
1307C2×C4C22×#4112yes—
1308C2×C4C22×#4112yes—
1309C2×C4C22×#4112yes—
1310C2×C4C22×#4112yes—
1311C2×C4C22×#4112yes—
1312C2×C4C22×#4112yes—
1313C2×C4C2×2−1+414yes—
1314C2×C4C2×2−1+414yes—
1315C2×C4#58514yes—
1316C22—22no—
1317C22—22no—
1318C22—24no—
1319C22—24no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22#350914yes—
1328C22C23×#4111yescharacteristic
1329C22C22×2−1+412yes—
1330C22C2×#58512yes—
1331C22H(7,𝔽2)11yescharacteristic
1332C222−1+611yescharacteristic
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—24no—
1339C4—24no—
1340C4—42no—
1341C4—44no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4#345514yes—
1360C2—24no—
1361C2—82no—
1362C2C2×#345511yescharacteristic
1363C2C2×#350911yescharacteristic
1364C2#6285611yescharacteristic
1365C2#6295012yes—
1366C2#6295112yes—
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. #42333C2semidirect
2. #42332C2semidirect
3. #42331C2semidirect
4. #42330C2semidirect
5. #42209C2semidirect
6. #42032C2semidirect
7. #39636C2semidirect
9. #38071C2semidirect
10. #38070C2semidirect
11. #37504C2semidirect
12. #37495C2semidirect
13. #37401C2semidirect
14. #37399C2semidirect
15. #37359C2semidirect
16. #37354C2semidirect
17. #35650C2semidirect
18. #35594C2semidirect
19. #35321C2semidirect
20. #35291C2semidirect
23. #35017C2semidirect
24. #35016C2semidirect
25. #34966C2semidirect
26. #34953C2semidirect
27. #34221C2semidirect
29. C2×#2320C2semidirect

Maximal subgroups

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

subgroupindex
#423332
#423322
#423312
#423302
#422092
#420322
#396362
#389792
#380712
#380702
#375042
#374952
#374012
#373992
#373592
#373542
#356502
#355942
#353212
#352912
#352452
#352412
#350172
#350162
#349662
#349532
#342212
#341492
C2×#23202