Finite Group Databasebeta

← #8726580

Subgroups — #8726580

Order 512.

5040 conjugacy classes of subgroups.

The subgroup lattice has 1475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59717C212yesmaximal, complemented
2#59716C212yesmaximal, complemented
3#59668C212yesmaximal, complemented
4#59632C211yesmaximal, characteristic, complemented
5#59127C212yesmaximal, complemented
6#58006C214yesmaximal, complemented
7#57190C214yesmaximal, complemented
8#56775C214yesmaximal, complemented
9#53669C212yesmaximal, complemented
10#52997C212yesmaximal, complemented
11#52987C211yesmaximal, characteristic, complemented
12#52300C211yesmaximal, characteristic, complemented
13#46578C212yesmaximal, complemented
14#46420C214yesmaximal, complemented
15#45321C212yesmaximal, complemented
16#45047C211yesmaximal, characteristic, complemented
17#44883C214yesmaximal, complemented
18#44879C212yesmaximal, complemented
19#42914C211yesmaximal, characteristic, complemented
20#42751C212yesmaximal, complemented
21#41241C214yesmaximal, complemented
22#41174C212yesmaximal, complemented
23#40050C212yesmaximal, complemented
24#39720C211yesmaximal, characteristic, complemented
25#39406C212yesmaximal, complemented
26#39363C212yesmaximal, complemented
27#39221C212yesmaximal, complemented
28#35941C211yesmaximal, characteristic
29#35871C212yesmaximal, complemented
30C2×#553C2211yescharacteristic
31C2×#550C2211yescharacteristic
32C2×D4×Q8C2214yes—
33C2×D4×Q8C2212yes—
34C2×#544C2211yescharacteristic
35C2×#542C2214yes—
36C2×#536C2214yes—
37C22×C4⋊Q8C2211yescharacteristic
38#2858C2212yes—
39#2854C2211yescharacteristic
40#2837C2214yes—
41#2837C2214yes—
42#2834C2212yes—
43#2834C2212yes—
44#2833C2214yes—
45#2829C2214yes—
46#2827C2214yes—
47#2821C2212yes—
48#2814C2214yes—
49#2806C2214yes—
50#2806C2214yes—
51#2804C2212yes—
52#2801C2214yes—
53#2800C2214yes—
54#2791C2212yes—
55#2777C2212yes—
56#2771C2211yescharacteristic
57#2764C2211yescharacteristic
58#2759C2214yes—
59#2759C2214yes—
60#2758C2212yes—
61#2757C2214yes—
62#2752C2212yes—
63#2746C2214yes—
64#2732C2214yes—
65#2730C2214yes—
66#2730C2214yes—
67#2729C2214yes—
68#2728C2214yes—
69#2728C2214yes—
70#2722C2211yescharacteristic
71#2718C2214yes—
72#2718C2212yes—
73#2717C2214yes—
74#2716C2214yes—
75#2716C2212yes—
76#2715C2214yes—
77#2712C2212yes—
78#2710C2214yes—
79#2710C2214yes—
80#2710C2214yes—
81#2709C2212yes—
82#2704C2214yes—
83#2702C2214yes—
84#2702C2212yes—
85#2701C2214yes—
86#2701C2214yes—
87#2700C2214yes—
88#2692C2214yes—
89#2691C2214yes—
90#2683C2214yes—
91#2681C2214yes—
92#2681C2214yes—
93#2681C2214yes—
94#2681C2214yes—
95#2681C2214yes—
96#2680C2214yes—
97#2680C2214yes—
98#2677C2211yescharacteristic
99#2677C2212yes—
100#2677C2214yes—
101#2677C2212yes—
102#2677C2214yes—
103#2674C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2672C2214yes—
107#2665C2214yes—
108#2664C2212yes—
109#2661C2212yes—
110#2653C2214yes—
111#2653C2214yes—
112#2651C2214yes—
113#2651C2214yes—
114#2647C2212yes—
115#2641C2211yescharacteristic
116#2633C2212yes—
117#2632C2214yes—
118#2624C2211yescharacteristic
119#2620C2214yes—
120#2618C2212yes—
121#2602C2214yes—
122#2597C2214yes—
123#2594C2214yes—
124#2594C2214yes—
125#2593C2212yes—
126#2592C2214yes—
127#2589C2214yes—
128#2587C2214yes—
129#2584C2211yescharacteristic
130#2584C2212yes—
131#2566C2212yes—
132#2560C2214yes—
133#2560C2214yes—
134#2559C2214yes—
135#2556C2214yes—
136#2552C2212yes—
137#2551C2214yes—
138#2551C2212yes—
139#2551C2212yes—
140#2550C2212yes—
141#2550C2212yes—
142#2550C2212yes—
143#2549C2214yes—
144#2548C2212yes—
145#2546C2212yes—
146#2546C2212yes—
147#2544C2214yes—
148#2543C2212yes—
149#2542C2212yes—
150#2542C2212yes—
151#2541C2211yescharacteristic
152#2523C2214yes—
153#2513C2212yes—
154#2513C2212yes—
155#2513C2212yes—
156#2512C2212yes—
157#2507C2214yes—
158#2507C2214yes—
159#2504C2211yescharacteristic
160#2501C2211yescharacteristic
161#2494C2212yes—
162#2494C2212yes—
163#2492C2214yes—
164#2491C2212yes—
165#2491C2212yes—
166#2491C2212yes—
167#2491C2214yes—
168#2490C2212yes—
169#2490C2212yes—
170#2490C2212yes—
171#2487C2211yescharacteristic
172#2487C2211yescharacteristic
173#2479C2214yes—
174#2478C2214yes—
175#2474C2214yes—
176#2474C2214yes—
177#2465C2214yes—
178#2461C2214yes—
179#2461C2214yes—
180#2461C2214yes—
181#2455C2212yes—
182#2455C2212yes—
183#2454C2212yes—
184#2454C2212yes—
185#2452C2212yes—
186#2452C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2452C2214yes—
192#2451C2214yes—
193#2451C2214yes—
194#2449C2214yes—
195#2449C2214yes—
196#2445C2212yes—
197#2445C2212yes—
198#2445C2212yes—
199#2445C2212yes—
200#2440C2212yes—
201#2440C2212yes—
202#2440C2212yes—
203#2439C2212yes—
204#2438C2214yes—
205#2436C2212yes—
206#2436C2214yes—
207#2434C2214yes—
208#2434C2214yes—
209#2432C2214yes—
210#2430C2212yes—
211#2429C2214yes—
212#2429C2214yes—
213#2428C2212yes—
214#2428C2214yes—
215#2428C2212yes—
216#2427C2214yes—
217#2415C2214yes—
218#2409C2212yes—
219#2409C2214yes—
220#2409C2214yes—
221#2402C2212yes—
222#2398C2211yescharacteristic
223#2396C2214yes—
224#2396C2212yes—
225#2395C2211yescharacteristic
226#2388C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2369C2214yes—
230#2369C2212yes—
231#2369C2212yes—
232#2369C2212yes—
233#2367C2214yes—
234#2366C2212yes—
235#2365C2212yes—
236#2363C2212yes—
237#2362C2214yes—
238#2361C2212yes—
239#2361C2212yes—
240#2361C2212yes—
241#2357C2212yes—
242#2354C2212yes—
243#2347C2211yescharacteristic
244#2345C2211yescharacteristic
245#2335C2214yes—
246#2324C2212yes—
247#2324C2214yes—
248#2322C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×#125C2212yes—
252C4×#126C2212yes—
253C4×#126C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2211yescharacteristic
256C4×#121C2212yes—
257#2293C2212yes—
258#2275C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261C23×Q8C2314yes—
262#553—44no—
263#550—44no—
264D4×Q8—48no—
265D4×Q8—416no—
266#544—44no—
267#542—416no—
268#536—416no—
269C2×C4⋊Q8—44no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2314yes—
282C2×#127C2312yes—
283C2×#127C2312yes—
284C2×#127C2311yescharacteristic
285C2×#126C2312yes—
286C2×#126C2312yes—
287C2×#126C2314yes—
288C2×#126C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2311yescharacteristic
292C2×#125C2312yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#123C2314yes—
300C2×#123C2312yes—
301C2×#123C2314yes—
302C2×#123C2311yescharacteristic
303C2×#123C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×#121C2311yescharacteristic
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2311yescharacteristic
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2314yes—
335C2×C4×Q8C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2311yescharacteristic
347C2×#117C2311yescharacteristic
348C2×#117C2311yescharacteristic
349C2×#117C2314yes—
350C2×#117C2314yes—
351C22×C4⋊C4C2311yescharacteristic
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2311yescharacteristic
355C22×C42C2311yescharacteristic
356#401C2314yes—
357#401C2314yes—
358#400C2311yescharacteristic
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2312yes—
366#400C2312yes—
367#400C2312yes—
368#400C2312yes—
369#399C2312yes—
370#399C2312yes—
371#399C2314yes—
372#399C2312yes—
373#399C2312yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2311yescharacteristic
379#399C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2311yescharacteristic
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2311yescharacteristic
411#397C2311yescharacteristic
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2312yes—
418#397C2311yescharacteristic
419#397C2312yes—
420#397C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2311yescharacteristic
479#393C2312yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2311yescharacteristic
485#392C2314yes—
486#392C2312yes—
487#392C2314yes—
488#392C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#390C2314yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2314yes—
515#390C2314yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#388C2312yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2312yes—
615#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2312yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2312yes—
631#386C2311yescharacteristic
632#386C2312yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2311yescharacteristic
655#385C2314yes—
656#385C2312yes—
657#385C2312yes—
658#384C2312yes—
659#384C2312yes—
660#384C2312yes—
661#384C2314yes—
662#383C2312yes—
663#383C2312yes—
664#383C2312yes—
665#382C2312yes—
666#382C2312yes—
667#381C2311yescharacteristic
668#381C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2311yescharacteristic
673#380C2312yes—
674#380C2311yescharacteristic
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717#376C2311yescharacteristic
718C2×#95C2312yes—
719C43C2312yes—
720C2×#41—44no—
721C2×#41—48no—
722C22×Q8—44no—
723C22×Q8—48no—
724C22×Q8—48no—
725C22×Q8—48no—
726C22×Q8—48no—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×Q8C2414yes—
733C22×Q8C2414yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2414yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2412yes—
744C22×D4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2414yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C4⋊Q8—28no—
758C4⋊Q8—28no—
759C4⋊Q8—216no—
760C4⋊Q8—28no—
761C4⋊Q8—28no—
762C4⋊Q8—44no—
763C4⋊Q8—44no—
764C4⋊Q8—44no—
765C4⋊Q8—48no—
766C4⋊Q8—48no—
767C4⋊Q8—48no—
768C4⋊Q8—48no—
769#127—42no—
770#127—44no—
771#127—44no—
772#126—28no—
773#126—44no—
774#126—44no—
775#126—48no—
776#125—28no—
777#125—44no—
778#125—44no—
779#125—42no—
780#124—48no—
781#124—48no—
782#124—48no—
783#124—48no—
784#124—48no—
785#124—48no—
786#123—216no—
787#123—48no—
788#123—48no—
789#123—48no—
790#123—44no—
791#123—44no—
792#123—42no—
793#123—48no—
794C22⋊Q8—216no—
795C22⋊Q8—28no—
796C22⋊Q8—48no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—48no—
801C22⋊Q8—48no—
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—48no—
805C22⋊Q8—48no—
806C22⋊Q8—48no—
807C22⋊Q8—48no—
808C22⋊Q8—48no—
809C22⋊Q8—48no—
810#121—28no—
811#121—28no—
812#121—48no—
813#121—44no—
814#121—44no—
815#121—48no—
816#121—48no—
817#121—42no—
818#121—42no—
819C4×Q8—44no—
820C4×Q8—42no—
821C4×Q8—48no—
822C4×Q8—48no—
823C4×D4—28no—
824C4×D4—24no—
825C4×D4—28no—
826C4×D4—48no—
827C4×D4—44no—
828C4×D4—44no—
829C4×D4—44no—
830C4×D4—42no—
831C4×D4—48no—
832C4×D4—48no—
833C4×D4—48no—
834#117—24no—
835#117—42no—
836#117—48no—
837#117—48no—
838C2×C4⋊C4—24no—
839C2×C4⋊C4—42no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4—42no—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2411yescharacteristic
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2411yescharacteristic
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2411yescharacteristic
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C42—42no—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2414yes—
981#95C2411yescharacteristic
982#95C2414yes—
983#95C2412yes—
984#95C2411yescharacteristic
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2411yescharacteristic
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2411yescharacteristic
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2414yes—
1042C24C2511yescharacteristic
1043C24C2512yes—
1044C24C2514yes—
1045C24C2511yescharacteristic
1046#41—816no—
1047C2×Q8—28no—
1048C2×Q8—24no—
1049C2×Q8—28no—
1050C2×Q8—24no—
1051C2×Q8—24no—
1052C2×Q8—28no—
1053C2×Q8—28no—
1054C2×Q8—28no—
1055C2×Q8—28no—
1056C2×Q8—42no—
1057C2×Q8—44no—
1058C2×Q8—41no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—44no—
1067C2×Q8—816no—
1068C2×Q8—832no—
1069C2×D4—28no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—24no—
1073C2×D4—22no—
1074C2×D4—28no—
1075C2×D4—24no—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—28no—
1080C2×D4—44no—
1081C2×D4—41no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—41no—
1091C2×D4—42no—
1092C2×D4—44no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—28no—
1103C22×C4—24no—
1104C22×C4—28no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—24no—
1109C22×C4—28no—
1110C22×C4—28no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4—44no—
1114C22×C4—41no—
1115C22×C4—42no—
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—44no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—44no—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2514yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2512yes—
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2512yes—
1151C22×C4C2514yes—
1152C22×C4C2511yescharacteristic
1153C4⋊C4—22no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—28no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—28no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—28no—
1177C4⋊C4—24no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—42no—
1190C4⋊C4—41no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—41no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4H(5,𝔽2)14yes—
1215C4⋊C4H(5,𝔽2)18yes—
1216C4⋊C42−1+418yes—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—22no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—24no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—28no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—41no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—41no—
1248C22⋊C4—42no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—41no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—42no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C42—24no—
1270C42—24no—
1271C42—24no—
1272C42—28no—
1273C42—24no—
1274C42—22no—
1275C42—24no—
1276C42—24no—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—42no—
1281C42—44no—
1282C42—42no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—42no—
1290C42—42no—
1291C23—22no—
1292C23—21no—
1293C23—22no—
1294C23—21no—
1295C23—22no—
1296C23—24no—
1297C23—24no—
1298C23—21no—
1299C23—24no—
1300C23—24no—
1301C23—22no—
1302C23—24no—
1303C23—24no—
1304C23—24no—
1305C23—22no—
1306C23—24no—
1307C23—22no—
1308C23—21no—
1309C23—21no—
1310C23—24no—
1311C23—22no—
1312C23#58512yes—
1313C23C2611yescharacteristic
1314Q8—416no—
1315Q8—48no—
1316Q8—44no—
1317Q8—88no—
1318Q8—88no—
1319Q8—88no—
1320Q8—88no—
1321D4—416no—
1322D4—48no—
1323D4—44no—
1324D4—88no—
1325D4—88no—
1326D4—84no—
1327D4—82no—
1328D4—84no—
1329D4—162no—
1330D4—162no—
1331D4—164no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—21no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—21no—
1394C2×C4—44no—
1395C2×C4—416no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—44no—
1399C2×C4—88no—
1400C2×C4—84no—
1401C2×C4—88no—
1402C2×C4—84no—
1403C2×C4—84no—
1404C2×C4—88no—
1405C2×C4—162no—
1406C2×C4C2×H(5,𝔽2)14yes—
1407C2×C4C2×H(5,𝔽2)14yes—
1408C2×C4C2×H(5,𝔽2)14yes—
1409C2×C4C2×H(5,𝔽2)14yes—
1410C2×C4C2×H(5,𝔽2)12yes—
1411C2×C4C2×2−1+418yes—
1412C2×C4C2×2−1+414yes—
1413C22—24no—
1414C22—22no—
1415C22—41no—
1416C22—41no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22—41no—
1421C22—41no—
1422C22—44no—
1423C22—42no—
1424C22—44no—
1425C22—44no—
1426C22—42no—
1427C22—44no—
1428C22—42no—
1429C22—41no—
1430C22—44no—
1431C22—42no—
1432C22—44no—
1433C22—44no—
1434C22—44no—
1435C22C22×H(5,𝔽2)11yescharacteristic
1436C22C22×H(5,𝔽2)12yes—
1437C22C22×2−1+412yes—
1438C22C2×#58511yescharacteristic
1439C222−1+611yescharacteristic
1440C4—24no—
1441C4—24no—
1442C4—24no—
1443C4—28no—
1444C4—24no—
1445C4—41no—
1446C4—44no—
1447C4—42no—
1448C4—44no—
1449C4—42no—
1450C4—41no—
1451C4—41no—
1452C4—42no—
1453C4—42no—
1454C4—44no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—41no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4#355014yes—
1465C2—42no—
1466C2—84no—
1467C2—82no—
1468C2—81no—
1469C2C2×#355011yescharacteristic
1470C2#6291911yescharacteristic
1471C2#6294612yes—
1472C2#6301111yescharacteristic
1473C2#6301512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35941C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59717C2semidirect
2. #59716C2semidirect
3. #59668C2semidirect
4. #59632C2semidirect
5. #59127C2semidirect
6. #58006C2semidirect
7. #57190C2semidirect
8. #56775C2semidirect
9. #53669C2semidirect
10. #52997C2semidirect
11. #52987C2semidirect
12. #52300C2semidirect
13. #46578C2semidirect
14. #46420C2semidirect
15. #45321C2semidirect
16. #45047C2semidirect
17. #44883C2semidirect
18. #44879C2semidirect
19. #42914C2semidirect
20. #42751C2semidirect
21. #41241C2semidirect
22. #41174C2semidirect
23. #40050C2semidirect
24. #39720C2semidirect
25. #39406C2semidirect
26. #39363C2semidirect
27. #39221C2semidirect
29. #35871C2semidirect

Maximal subgroups

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

subgroupindex
#597172
#597162
#596682
#596322
#591272
#580062
#571902
#567752
#536692
#529972
#529872
#523002
#465782
#464202
#453212
#450472
#448832
#448792
#429142
#427512
#412412
#411742
#400502
#397202
#394062
#393632
#392212
#359412
#358712