Finite Group Databasebeta

← #7695645

Subgroups — #7695645

Order 512.

4925 conjugacy classes of subgroups.

The subgroup lattice has 1459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59878C212yesmaximal, complemented
2#59863C211yesmaximal, characteristic, complemented
3#59597C214yesmaximal, complemented
4#59427C212yesmaximal, complemented
5#52303C212yesmaximal, complemented
6#52287C211yesmaximal, characteristic, complemented
7#45369C212yesmaximal, complemented
8#45151C212yesmaximal, complemented
9#44963C212yesmaximal, complemented
10#44643C214yesmaximal, complemented
11#43857C214yesmaximal, complemented
12#43454C214yesmaximal, complemented
13#39746C212yesmaximal, complemented
14#39741C212yesmaximal, complemented
15#39740C211yesmaximal, characteristic, complemented
16#39739C211yesmaximal, characteristic
17#38830C212yesmaximal, complemented
18#38829C212yesmaximal, complemented
19#38827C214yesmaximal, complemented
20#38817C214yesmaximal, complemented
21#36538C211yesmaximal, characteristic, complemented
22#36469C212yesmaximal, complemented
23#35959C212yesmaximal, complemented
24#35956C212yesmaximal, complemented
25#35938C212yesmaximal, complemented
26#34331C211yesmaximal, characteristic, complemented
27#34329C212yesmaximal, complemented
28#34328C211yesmaximal, characteristic, complemented
29#34324C212yesmaximal, complemented
30C2×#559C2212yes—
31C2×#559C2211yescharacteristic
32C2×#559C2212yes—
33C2×#559C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#556C2212yes—
37C2×#556C2212yes—
38#2861C2212yes—
39#2858C2211yescharacteristic
40#2858C2212yes—
41#2854C2214yes—
42#2811C2211yescharacteristic
43#2808C2212yes—
44#2808C2212yes—
45#2806C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2806C2211yescharacteristic
49#2792C2212yes—
50#2792C2212yes—
51#2792C2212yes—
52#2785C2214yes—
53#2784C2214yes—
54#2783C2214yes—
55#2783C2214yes—
56#2781C2214yes—
57#2781C2214yes—
58#2775C2214yes—
59#2775C2214yes—
60#2756C2214yes—
61#2756C2214yes—
62#2744C2214yes—
63#2744C2214yes—
64#2734C2212yes—
65#2734C2211yescharacteristic
66#2733C2212yes—
67#2733C2212yes—
68#2732C2212yes—
69#2732C2212yes—
70#2730C2214yes—
71#2730C2214yes—
72#2727C2212yes—
73#2727C2212yes—
74#2705C2214yes—
75#2705C2214yes—
76#2694C2214yes—
77#2694C2214yes—
78#2694C2214yes—
79#2694C2214yes—
80#2686C2214yes—
81#2686C2214yes—
82#2682C2212yes—
83#2682C2212yes—
84#2664C2214yes—
85#2663C2214yes—
86#2662C2214yes—
87#2658C2212yes—
88#2658C2212yes—
89#2657C2212yes—
90#2611C2214yes—
91#2610C2214yes—
92#2610C2214yes—
93#2610C2214yes—
94#2609C2214yes—
95#2604C2214yes—
96#2603C2214yes—
97#2602C2214yes—
98#2602C2214yes—
99#2593C2214yes—
100#2592C2212yes—
101#2592C2212yes—
102#2592C2212yes—
103#2592C2212yes—
104#2592C2212yes—
105#2574C2214yes—
106#2574C2214yes—
107#2568C2211yescharacteristic
108#2568C2212yes—
109#2568C2212yes—
110#2566C2212yes—
111#2564C2214yes—
112#2563C2212yes—
113#2558C2214yes—
114#2558C2214yes—
115#2557C2214yes—
116#2557C2214yes—
117#2556C2214yes—
118#2556C2214yes—
119#2554C2214yes—
120#2554C2214yes—
121#2553C2214yes—
122#2553C2214yes—
123#2548C2212yes—
124#2548C2212yes—
125#2548C2212yes—
126#2548C2211yescharacteristic
127#2547C2212yes—
128#2547C2212yes—
129#2547C2212yes—
130#2546C2212yes—
131#2546C2212yes—
132#2545C2212yes—
133#2545C2212yes—
134#2545C2212yes—
135#2545C2212yes—
136#2545C2212yes—
137#2545C2212yes—
138#2545C2212yes—
139#2544C2212yes—
140#2544C2212yes—
141#2544C2212yes—
142#2544C2212yes—
143#2541C2212yes—
144#2532C2214yes—
145#2532C2214yes—
146#2529C2214yes—
147#2529C2214yes—
148#2521C2214yes—
149#2521C2214yes—
150#2519C2214yes—
151#2519C2214yes—
152#2513C2214yes—
153#2498C2214yes—
154#2497C2214yes—
155#2495C2214yes—
156#2491C2214yes—
157#2485C2214yes—
158#2479C2214yes—
159#2479C2214yes—
160#2476C2214yes—
161#2476C2214yes—
162#2474C2214yes—
163#2474C2214yes—
164#2471C2214yes—
165#2471C2214yes—
166#2467C2214yes—
167#2467C2214yes—
168#2461C2214yes—
169#2461C2214yes—
170#2456C2214yes—
171#2456C2214yes—
172#2454C2214yes—
173#2454C2214yes—
174#2448C2214yes—
175#2448C2214yes—
176#2439C2214yes—
177#2422C2214yes—
178#2399C2212yes—
179#2399C2212yes—
180#2399C2212yes—
181#2396C2214yes—
182#2395C2214yes—
183#2392C2214yes—
184#2374C2214yes—
185#2373C2214yes—
186#2373C2214yes—
187#2372C2214yes—
188#2371C2214yes—
189#2370C2212yes—
190#2367C2212yes—
191#2367C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2367C2212yes—
195#2367C2212yes—
196#2366C2212yes—
197#2366C2211yescharacteristic
198#2365C2212yes—
199#2365C2212yes—
200#2365C2211yescharacteristic
201#2362C2214yes—
202#2359C2214yes—
203#2359C2214yes—
204#2357C2212yes—
205#2356C2212yes—
206#2356C2212yes—
207#2356C2212yes—
208#2355C2212yes—
209#2355C2212yes—
210#2355C2211yescharacteristic
211#2355C2211yescharacteristic
212#2355C2211yescharacteristic
213#2354C2212yes—
214#2354C2212yes—
215#2354C2212yes—
216#2354C2212yes—
217#2353C2214yes—
218Q8×C4⋊C4C2211yescharacteristic
219#2349C2212yes—
220#2346C2214yes—
221#2346C2214yes—
222#2337C2214yes—
223#2336C2214yes—
224#2335C2214yes—
225#2335C2214yes—
226#2334C2214yes—
227#2334C2214yes—
228#2328C2212yes—
229#2327C2212yes—
230#2326C2212yes—
231#2326C2212yes—
232#2326C2212yes—
233#2326C2212yes—
234C4×C4⋊Q8C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2212yes—
237C4×C4⋊Q8C2211yescharacteristic
238C4×#127C2211yescharacteristic
239C4×#125C2212yes—
240C4×#124C2212yes—
241C4×#124C2212yes—
242C4×#124C2212yes—
243C4×C22⋊Q8C2214yes—
244C4×#123C2214yes—
245C4×#121C2214yes—
246#2296C2214yes—
247#2295C2212yes—
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252#2293C2212yes—
253#2290C2214yes—
254#2276C2212yes—
255#2276C2212yes—
256#2275C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259#559—28no—
260#559—216no—
261#559—48no—
262#559—44no—
263#557—28no—
264#557—44no—
265#556—216no—
266#556—48no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×#127C2311yescharacteristic
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×#117C2314yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2314yes—
349C2×#117C2314yes—
350C22×C42C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2312yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2311yescharacteristic
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2314yes—
490#390C2314yes—
491#390C2314yes—
492#390C2312yes—
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2311yescharacteristic
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2311yescharacteristic
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2311yescharacteristic
634#384C2312yes—
635#383C2314yes—
636#383C2314yes—
637#382C2312yes—
638#382C2314yes—
639#382C2312yes—
640#382C2314yes—
641#382C2314yes—
642#382C2312yes—
643#382C2314yes—
644#382C2312yes—
645#381C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709#376C2312yes—
710#376C2312yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714#376C2314yes—
715#376C2314yes—
716C2×#95C2314yes—
717C43C2312yes—
718C43C2311yescharacteristic
719C43C2312yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C4⋊Q8—28no—
746C4⋊Q8—24no—
747C4⋊Q8—28no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753#127—28no—
754#127—24no—
755#127—44no—
756#127—42no—
757#126—216no—
758#126—216no—
759#126—48no—
760#126—48no—
761#125—216no—
762#125—28no—
763#125—48no—
764#125—44no—
765#124—28no—
766#124—216no—
767#124—28no—
768#124—28no—
769#124—28no—
770#124—28no—
771#124—28no—
772#124—48no—
773#124—44no—
774#124—44no—
775#124—44no—
776#124—44no—
777#124—44no—
778#124—44no—
779#124—44no—
780#124—84no—
781#123—216no—
782#123—216no—
783#123—216no—
784#123—48no—
785#123—48no—
786#123—48no—
787C22⋊Q8—216no—
788C22⋊Q8—48no—
789#121—48no—
790#121—84no—
791C4×Q8—28no—
792C4×Q8—28no—
793C4×Q8—28no—
794C4×Q8—24no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8—24no—
798C4×Q8—28no—
799C4×Q8—28no—
800C4×Q8—24no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—42no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—82no—
807C4×Q8#4118yes—
808C4×Q8#4118yes—
809C4×D4—216no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—44no—
818C4×D4—48no—
819C4×D4—44no—
820C4×D4—84no—
821C4×D4—82no—
822C4×D4—82no—
823#117—216no—
824#117—48no—
825#117—48no—
826#117—84no—
827#117—84no—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2411yescharacteristic
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C42—84no—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2411yescharacteristic
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2411yescharacteristic
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2412yes—
1033C24C2514yes—
1034C24C2514yes—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—22no—
1043C2×Q8—24no—
1044C2×Q8—22no—
1045C2×Q8—22no—
1046C2×Q8—41no—
1047C2×Q8—41no—
1048C2×Q8—41no—
1049C2×Q8—41no—
1050C2×Q8—41no—
1051C2×Q8—41no—
1052C2×Q8—42no—
1053C2×Q8—41no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—41no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8C2×#4114yes—
1061C2×Q8C2×#4114yes—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—24no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—28no—
1068C2×D4—24no—
1069C2×D4—28no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—42no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—42no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—44no—
1092C22×C4—28no—
1093C22×C4—28no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C4⋊C4—28no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—41no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4C2×#4118yes—
1199C4⋊C4C2×#4118yes—
1200C4⋊C4C2×#4114yes—
1201C4⋊C4C2×#4114yes—
1202C4⋊C4H(5,𝔽2)14yes—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C42—28no—
1246C42—28no—
1247C42—28no—
1248C42—24no—
1249C42—28no—
1250C42—24no—
1251C42—28no—
1252C42—28no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—22no—
1259C42—24no—
1260C42—22no—
1261C42—42no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42—41no—
1266C42—42no—
1267C42—41no—
1268C42—42no—
1269C42—42no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—41no—
1274C42—42no—
1275C42—42no—
1276C42C2×#4114yes—
1277C42C2×#4118yes—
1278C42C2×#4118yes—
1279C42C2×#4114yes—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—24no—
1284C23—24no—
1285C23—24no—
1286C23—24no—
1287C23—24no—
1288C23—24no—
1289C23—24no—
1290C23—24no—
1291C23—24no—
1292C23—24no—
1293C23—24no—
1294C23C2611yescharacteristic
1295Q8—44no—
1296Q8—44no—
1297Q8—44no—
1298Q8—48no—
1299Q8—44no—
1300Q8—48no—
1301Q8—82no—
1302Q8—84no—
1303Q8—84no—
1304D4—48no—
1305D4—48no—
1306D4—48no—
1307D4—84no—
1308D4—88no—
1309D4—88no—
1310D4—84no—
1311D4—88no—
1312D4—162no—
1313D4—164no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—416no—
1383C2×C4—88no—
1384C2×C4—88no—
1385C2×C4—88no—
1386C2×C4—88no—
1387C2×C4—88no—
1388C2×C4C22×#4112yes—
1389C2×C4C22×#4114yes—
1390C2×C4C22×#4112yes—
1391C2×C4C22×#4114yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4114yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4114yes—
1396C2×C4C22×#4112yes—
1397C2×C4C22×#4112yes—
1398C2×C4C2×H(5,𝔽2)14yes—
1399C2×C4C2×H(5,𝔽2)12yes—
1400C2×C4#58512yes—
1401C22—44no—
1402C22—44no—
1403C22—44no—
1404C22—44no—
1405C22—44no—
1406C22—44no—
1407C22—44no—
1408C22—44no—
1409C22—44no—
1410C22—44no—
1411C22—44no—
1412C22—44no—
1413C22—44no—
1414C22—44no—
1415C22C23×#4111yescharacteristic
1416C22C23×#4111yescharacteristic
1417C22C22×H(5,𝔽2)11yescharacteristic
1418C22C2×#58511yescharacteristic
1419C22H(7,𝔽2)11yescharacteristic
1420C222−1+611yescharacteristic
1421C222−1+611yescharacteristic
1422C4—24no—
1423C4—22no—
1424C4—22no—
1425C4—24no—
1426C4—24no—
1427C4—24no—
1428C4—22no—
1429C4—24no—
1430C4—22no—
1431C4—22no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—44no—
1446C4—42no—
1447C4—44no—
1448C4#348314yes—
1449C2—84no—
1450C2—84no—
1451C2C2×#348311yescharacteristic
1452C2#6284511yescharacteristic
1453C2#6286011yescharacteristic
1454C2#6289711yescharacteristic
1455C2#6299511yescharacteristic
1456C2#6301011yescharacteristic
1457C2#6304911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39739C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59878C2semidirect
2. #59863C2semidirect
3. #59597C2semidirect
4. #59427C2semidirect
5. #52303C2semidirect
6. #52287C2semidirect
7. #45369C2semidirect
8. #45151C2semidirect
9. #44963C2semidirect
10. #44643C2semidirect
11. #43857C2semidirect
12. #43454C2semidirect
13. #39746C2semidirect
14. #39741C2semidirect
15. #39740C2semidirect
17. #38830C2semidirect
18. #38829C2semidirect
19. #38827C2semidirect
20. #38817C2semidirect
21. #36538C2semidirect
22. #36469C2semidirect
23. #35959C2semidirect
24. #35956C2semidirect
25. #35938C2semidirect
26. #34331C2semidirect
27. #34329C2semidirect
28. #34328C2semidirect
29. #34324C2semidirect

Maximal subgroups

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

subgroupindex
#598782
#598632
#595972
#594272
#523032
#522872
#453692
#451512
#449632
#446432
#438572
#434542
#397462
#397412
#397402
#397392
#388302
#388292
#388272
#388172
#365382
#364692
#359592
#359562
#359382
#343312
#343292
#343282
#343242