Finite Group Databasebeta

← #8115440

Subgroups — #8115440

Order 512.

3850 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58954C214yesmaximal, complemented
2#58931C214yesmaximal, complemented
3#58111C214yesmaximal
4#57709C214yesmaximal, complemented
5#56753C214yesmaximal, complemented
6#55773C214yesmaximal, complemented
7#54475C214yesmaximal, complemented
8#54128C214yesmaximal, complemented
9#53119C212yesmaximal, complemented
10#52996C212yesmaximal, complemented
11#45127C212yesmaximal, complemented
12#44917C212yesmaximal, complemented
13#42981C211yesmaximal, characteristic, complemented
14#42933C211yesmaximal, characteristic, complemented
15#42738C212yesmaximal, complemented
16#42686C211yesmaximal, characteristic
17#42573C212yesmaximal, complemented
18#42502C211yesmaximal, characteristic
19#39680C212yesmaximal, complemented
20#39545C212yesmaximal, complemented
21#37887C212yesmaximal, complemented
22#37875C212yesmaximal, complemented
23#37434C212yesmaximal, complemented
24#37312C212yesmaximal, complemented
25#35339C211yesmaximal, characteristic, complemented
26#35283C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28#2868C2211yescharacteristic
29#2864C2212yes—
30#2864C2212yes—
31#2862C2211yescharacteristic
32#2857C2212yes—
33#2844C2212yes—
34#2843C2212yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2836C2214yes—
42#2835C2212yes—
43#2831C2214yes—
44#2827C2214yes—
45#2824C2212yes—
46#2821C2214yes—
47#2810C2214yes—
48#2809C2214yes—
49#2807C2212yes—
50#2807C2212yes—
51#2802C2214yes—
52#2799C2214yes—
53#2798C2214yes—
54#2798C2214yes—
55#2798C2214yes—
56#2798C2214yes—
57#2795C2212yes—
58#2794C2212yes—
59#2792C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2788C2214yes—
63#2782C2212yes—
64#2779C2214yes—
65#2777C2214yes—
66#2776C2214yes—
67#2775C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2771C2214yes—
73#2770C2214yes—
74#2770C2214yes—
75#2769C2212yes—
76#2769C2214yes—
77#2768C2214yes—
78#2763C2214yes—
79#2762C2214yes—
80#2758C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2755C2214yes—
87#2755C2214yes—
88#2751C2214yes—
89#2747C2214yes—
90#2744C2214yes—
91#2742C2212yes—
92#2741C2214yes—
93#2741C2214yes—
94#2734C2214yes—
95#2729C2214yes—
96#2729C2214yes—
97#2729C2214yes—
98#2726C2214yes—
99#2725C2214yes—
100#2720C2214yes—
101#2720C2214yes—
102#2719C2214yes—
103#2719C2214yes—
104#2716C2214yes—
105#2713C2214yes—
106#2713C2214yes—
107#2702C2214yes—
108#2702C2214yes—
109#2698C2214yes—
110#2690C2214yes—
111#2690C2214yes—
112#2689C2214yes—
113#2677C2214yes—
114#2677C2212yes—
115#2666C2214yes—
116#2666C2214yes—
117#2660C2212yes—
118#2655C2212yes—
119#2654C2212yes—
120#2653C2212yes—
121#2652C2212yes—
122#2651C2212yes—
123#2650C2214yes—
124#2650C2212yes—
125#2649C2212yes—
126#2649C2214yes—
127#2648C2212yes—
128#2647C2212yes—
129#2647C2212yes—
130#2647C2212yes—
131#2647C2212yes—
132#2647C2214yes—
133#2642C2214yes—
134#2633C2214yes—
135#2628C2211yescharacteristic
136#2628C2212yes—
137#2628C2212yes—
138#2628C2211yescharacteristic
139#2625C2214yes—
140#2612C2212yes—
141#2611C2214yes—
142#2606C2214yes—
143#2604C2214yes—
144#2599C2214yes—
145#2596C2214yes—
146#2590C2214yes—
147#2588C2214yes—
148#2584C2212yes—
149#2571C2212yes—
150#2570C2212yes—
151#2570C2212yes—
152#2570C2214yes—
153#2570C2214yes—
154#2569C2214yes—
155#2569C2214yes—
156#2564C2214yes—
157#2552C2212yes—
158#2551C2212yes—
159#2551C2212yes—
160#2550C2212yes—
161#2549C2214yes—
162#2546C2212yes—
163#2533C2214yes—
164#2533C2214yes—
165#2533C2214yes—
166#2533C2214yes—
167#2532C2214yes—
168#2530C2214yes—
169#2523C2212yes—
170#2520C2214yes—
171#2519C2214yes—
172#2511C2214yes—
173#2509C2212yes—
174#2509C2212yes—
175#2509C2212yes—
176#2509C2212yes—
177#2509C2212yes—
178#2509C2212yes—
179#2509C2212yes—
180#2507C2212yes—
181#2507C2212yes—
182#2507C2212yes—
183#2506C2212yes—
184#2506C2212yes—
185#2505C2214yes—
186#2497C2212yes—
187#2496C2212yes—
188#2496C2212yes—
189#2495C2212yes—
190#2495C2212yes—
191#2495C2212yes—
192#2495C2212yes—
193#2495C2212yes—
194#2495C2214yes—
195#2492C2214yes—
196#2487C2212yes—
197#2485C2212yes—
198#2485C2212yes—
199#2485C2212yes—
200#2479C2214yes—
201#2478C2214yes—
202#2468C2214yes—
203#2463C2212yes—
204#2453C2214yes—
205#2451C2214yes—
206#2451C2214yes—
207#2450C2214yes—
208#2442C2212yes—
209#2442C2212yes—
210#2441C2212yes—
211#2440C2212yes—
212#2440C2212yes—
213#2440C2212yes—
214#2439C2212yes—
215#2439C2212yes—
216#2423C2214yes—
217#2415C2214yes—
218#2402C2211yescharacteristic
219#2401C2212yes—
220#2398C2211yescharacteristic
221#2396C2211yescharacteristic
222#2395C2212yes—
223#2392C2211yescharacteristic
224#2370C2212yes—
225#2369C2212yes—
226#2352C2212yes—
227D4×C4⋊C4C2212yes—
228#2347C2212yes—
229#2346C2212yes—
230#2346C2212yes—
231#2344C2212yes—
232#2331C2212yes—
233#2331C2212yes—
234#2331C2211yescharacteristic
235#2331C2211yescharacteristic
236#2317C2211yescharacteristic
237#2317C2211yescharacteristic
238#2317C2212yes—
239#2316C2211yescharacteristic
240#2316C2211yescharacteristic
241#2314C2212yes—
242#2314C2212yes—
243C4×C4⋊Q8C2212yes—
244#2298C2212yes—
245#2295C2211yescharacteristic
246#2293C2211yescharacteristic
247#2290C2212yes—
248#2285C2211yescharacteristic
249C2×#382C2211yescharacteristic
250C4×#117C2211yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2314yes—
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2314yes—
273C2×#117C2311yescharacteristic
274C2×#117C2312yes—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2312yes—
279C2×#117C2314yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2312yes—
283C22×C42C2311yescharacteristic
284#401C2312yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2312yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2311yescharacteristic
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2312yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2312yes—
340#399C2312yes—
341#399C2312yes—
342#399C2314yes—
343#399C2311yescharacteristic
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2312yes—
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#398C2312yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2311yescharacteristic
378#398C2314yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2311yescharacteristic
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2314yes—
412#395C2314yes—
413#395C2311yescharacteristic
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2312yes—
423#394C2314yes—
424#394C2311yescharacteristic
425#394C2312yes—
426#394C2312yes—
427#393C2314yes—
428#393C2312yes—
429#393C2312yes—
430#393C2314yes—
431#393C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2311yescharacteristic
435#392C2311yescharacteristic
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#390C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2312yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#387C2314yes—
535#387C2314yes—
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#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2312yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2312yes—
598#385C2312yes—
599#385C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2312yes—
608#385C2314yes—
609#385C2314yes—
610#384C2312yes—
611#384C2312yes—
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2312yes—
616#384C2314yes—
617#384C2312yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2314yes—
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2314yes—
637#382C2314yes—
638#381C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2311yescharacteristic
683#376C2312yes—
684#376C2314yes—
685#376C2314yes—
686#376C2311yescharacteristic
687C2×#95C2314yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C22×Q8C2414yes—
691C22×Q8C2411yescharacteristic
692C22×Q8C2412yes—
693C22×Q8C2414yes—
694C22×Q8C2412yes—
695C22×D4C2412yes—
696C22×D4C2411yescharacteristic
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2414yes—
701C23×C4C2412yes—
702C23×C4C2412yes—
703C4⋊Q8—28no—
704C4⋊Q8—42no—
705C4⋊Q8—42no—
706C4⋊Q8—44no—
707C4⋊Q8—84no—
708C4⋊Q8—84no—
709C4⋊Q8—84no—
710#126—84no—
711#126—84no—
712#125—44no—
713#125—84no—
714#125—84no—
715#125—84no—
716C22⋊Q8—84no—
717C22⋊Q8—84no—
718C22⋊Q8—84no—
719C22⋊Q8—84no—
720C4×Q8—42no—
721C4×Q8—84no—
722C4×D4—28no—
723C4×D4—42no—
724C4×D4—84no—
725#117—24no—
726#117—24no—
727#117—24no—
728#117—28no—
729#117—42no—
730#117—44no—
731#117—84no—
732C2×C4⋊C4—42no—
733C2×C4⋊C4—44no—
734C2×C4⋊C4—42no—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C42—24no—
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2411yescharacteristic
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2411yescharacteristic
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2411yescharacteristic
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946C24C2512yes—
947C24C2511yescharacteristic
948C2×Q8—28no—
949C2×Q8—41no—
950C2×Q8—44no—
951C2×Q8—42no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×D4—24no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—41no—
964C2×D4—42no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C42−1+414yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—41no—
1042C4⋊C4—44no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—44no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C42—24no—
1106C42—22no—
1107C42—24no—
1108C42—24no—
1109C42—22no—
1110C42—22no—
1111C42—24no—
1112C42—24no—
1113C42—22no—
1114C42—22no—
1115C42—24no—
1116C42—42no—
1117C42—42no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—42no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—42no—
1129C422−1+414yes—
1130C23—21no—
1131C23—21no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23C2×2−1+412yes—
1142C23C2611yescharacteristic
1143Q8—88no—
1144Q8—82no—
1145Q8—164no—
1146Q8—162no—
1147Q8—162no—
1148D4—48no—
1149D4—82no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—28no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—48no—
1218C2×C4—84no—
1219C2×C4—88no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4C2×2−1+412yes—
1223C2×C4C2×2−1+414yes—
1224C2×C4C2×2−1+412yes—
1225C2×C4C2×2−1+412yes—
1226C2×C4#58512yes—
1227C22—22no—
1228C22—24no—
1229C22—42no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22C22×2−1+411yescharacteristic
1240C22C22×2−1+411yescharacteristic
1241C22C2×#58511yescharacteristic
1242C22H(7,𝔽2)12yes—
1243C222−1+612yes—
1244C4—22no—
1245C4—24no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—44no—
1250C4—44no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—44no—
1257C4—44no—
1258C4—44no—
1259C4—44no—
1260C4—41no—
1261C4—42no—
1262C4—44no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—44no—
1267C4—41no—
1268C4#356314yes—
1269C2—42no—
1270C2—82no—
1271C2C2×#356311yescharacteristic
1272C2#6287712yes—
1273C2#6287912yes—
1274C2#6288511yescharacteristic
1275C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58954C2semidirect
2. #58931C2semidirect
4. #57709C2semidirect
5. #56753C2semidirect
6. #55773C2semidirect
7. #54475C2semidirect
8. #54128C2semidirect
9. #53119C2semidirect
10. #52996C2semidirect
11. #45127C2semidirect
12. #44917C2semidirect
13. #42981C2semidirect
14. #42933C2semidirect
15. #42738C2semidirect
17. #42573C2semidirect
19. #39680C2semidirect
20. #39545C2semidirect
21. #37887C2semidirect
22. #37875C2semidirect
23. #37434C2semidirect
24. #37312C2semidirect
25. #35339C2semidirect
26. #35283C2semidirect

Maximal subgroups

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

subgroupindex
#589542
#589312
#581112
#577092
#567532
#557732
#544752
#541282
#531192
#529962
#451272
#449172
#429812
#429332
#427382
#426862
#425732
#425022
#396802
#395452
#378872
#378752
#374342
#373122
#353392
#352832
#346402