Finite Group Databasebeta

← #7675037

Subgroups — #7675037

Order 512.

5108 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59716C212yesmaximal, complemented
2#59670C212yesmaximal, complemented
3#59632C212yesmaximal, complemented
4#59580C212yesmaximal, complemented
5#59545C212yesmaximal, complemented
6#59454C212yesmaximal, complemented
7#59254C212yesmaximal, complemented
8#59247C212yesmaximal, complemented
9#44674C214yesmaximal, complemented
10#44616C214yesmaximal, complemented
11#43811C214yesmaximal, complemented
12#43780C214yesmaximal, complemented
13#39767C211yesmaximal, characteristic, complemented
14#39631C211yesmaximal, characteristic, complemented
15#39063C214yesmaximal, complemented
16#38907C212yesmaximal, complemented
17#37896C212yesmaximal, complemented
18#37698C212yesmaximal, complemented
19#36488C212yesmaximal, complemented
20#36193C211yesmaximal, characteristic, complemented
21#36126C211yesmaximal, characteristic
22#35363C214yesmaximal, complemented
23#35042C212yesmaximal, complemented
24#35006C211yesmaximal, characteristic, complemented
25#34788C212yesmaximal, complemented
26#34308C212yesmaximal, complemented
27#34206C212yesmaximal, complemented
28C2×#2370C211yesmaximal, characteristic, complemented
29C4×#539C211yesmaximal, characteristic, complemented
30C2×#547C2212yes—
31C2×#539C2211yescharacteristic
32C2×#539C2212yes—
33C2×#532C2212yes—
34C22×#125C2211yescharacteristic
35C2×#520C2214yes—
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2855C2212yes—
39#2854C2212yes—
40#2854C2212yes—
41#2852C2214yes—
42#2808C2212yes—
43#2807C2214yes—
44#2805C2212yes—
45#2796C2214yes—
46#2793C2214yes—
47#2790C2214yes—
48#2766C2214yes—
49#2761C2214yes—
50#2759C2214yes—
51#2755C2214yes—
52#2752C2214yes—
53#2742C2214yes—
54#2741C2214yes—
55#2740C2214yes—
56#2740C2214yes—
57#2738C2214yes—
58#2732C2212yes—
59#2724C2212yes—
60#2715C2214yes—
61#2713C2214yes—
62#2709C2214yes—
63#2700C2214yes—
64#2694C2214yes—
65#2694C2214yes—
66#2690C2214yes—
67#2690C2214yes—
68#2646C2212yes—
69#2639C2212yes—
70#2639C2212yes—
71#2623C2214yes—
72#2618C2212yes—
73#2611C2214yes—
74#2604C2214yes—
75#2602C2214yes—
76#2602C2214yes—
77#2601C2214yes—
78#2597C2214yes—
79#2597C2214yes—
80#2596C2214yes—
81#2595C2214yes—
82#2594C2214yes—
83#2590C2214yes—
84#2589C2214yes—
85#2588C2214yes—
86#2587C2214yes—
87#2585C2214yes—
88#2584C2214yes—
89#2583C2214yes—
90#2580C2212yes—
91#2577C2214yes—
92#2573C2214yes—
93#2570C2212yes—
94#2567C2211yescharacteristic
95#2564C2214yes—
96#2560C2214yes—
97#2560C2214yes—
98#2558C2214yes—
99#2553C2214yes—
100#2552C2211yescharacteristic
101#2551C2211yescharacteristic
102#2550C2212yes—
103#2550C2212yes—
104#2541C2211yescharacteristic
105#2533C2214yes—
106#2532C2214yes—
107#2525C2214yes—
108#2525C2214yes—
109#2523C2214yes—
110#2520C2214yes—
111#2516C2214yes—
112#2513C2212yes—
113#2513C2212yes—
114#2512C2212yes—
115#2512C2212yes—
116#2511C2212yes—
117#2510C2214yes—
118#2509C2212yes—
119#2508C2212yes—
120#2507C2212yes—
121#2507C2212yes—
122#2507C2212yes—
123#2506C2212yes—
124#2504C2212yes—
125#2497C2212yes—
126#2495C2212yes—
127#2494C2212yes—
128#2493C2214yes—
129#2491C2212yes—
130#2490C2212yes—
131#2490C2212yes—
132#2490C2212yes—
133#2490C2212yes—
134#2487C2212yes—
135#2487C2212yes—
136#2479C2214yes—
137#2478C2214yes—
138#2478C2214yes—
139#2473C2214yes—
140#2470C2214yes—
141#2468C2214yes—
142#2466C2214yes—
143#2466C2214yes—
144#2465C2214yes—
145#2462C2214yes—
146#2461C2214yes—
147#2460C2214yes—
148#2455C2214yes—
149#2454C2212yes—
150#2454C2212yes—
151#2452C2212yes—
152#2452C2212yes—
153#2450C2214yes—
154#2449C2214yes—
155#2449C2214yes—
156#2445C2212yes—
157#2445C2212yes—
158#2445C2212yes—
159#2444C2214yes—
160#2443C2214yes—
161#2442C2212yes—
162#2442C2212yes—
163#2442C2212yes—
164#2440C2212yes—
165#2438C2214yes—
166#2430C2214yes—
167#2425C2214yes—
168#2419C2214yes—
169#2419C2214yes—
170#2416C2212yes—
171#2415C2214yes—
172#2413C2214yes—
173#2413C2214yes—
174#2406C2214yes—
175#2401C2214yes—
176#2395C2214yes—
177#2370C2214yes—
178#2370C2212yes—
179#2370C2212yes—
180#2370C2212yes—
181#2370C2214yes—
182#2370C2212yes—
183#2370C2212yes—
184#2370C2212yes—
185#2369C2211yescharacteristic
186#2367C2214yes—
187#2367C2214yes—
188#2366C2214yes—
189#2366C2211yescharacteristic
190#2365C2212yes—
191#2365C2214yes—
192#2361C2212yes—
193#2361C2212yes—
194#2361C2212yes—
195#2361C2212yes—
196#2360C2214yes—
197#2359C2214yes—
198#2359C2214yes—
199#2357C2212yes—
200#2355C2211yescharacteristic
201#2354C2214yes—
202#2352C2214yes—
203#2352C2214yes—
204D4×C4⋊C4C2212yes—
205D4×C4⋊C4C2212yes—
206D4×C4⋊C4C2211yescharacteristic
207D4×C4⋊C4C2214yes—
208#2345C2212yes—
209#2344C2212yes—
210#2344C2212yes—
211#2339C2214yes—
212#2336C2212yes—
213#2335C2212yes—
214#2334C2212yes—
215#2332C2212yes—
216#2329C2211yescharacteristic
217#2325C2212yes—
218#2325C2211yescharacteristic
219#2325C2212yes—
220#2325C2212yes—
221#2323C2214yes—
222#2322C2214yes—
223#2322C2214yes—
224#2322C2212yes—
225#2318C2212yes—
226#2313C2211yescharacteristic
227#2311C2214yes—
228C4×C4⋊Q8C2212yes—
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#126C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2211yescharacteristic
234C4×#123C2212yes—
235C4×#123C2212yes—
236C4×#121C2212yes—
237C4×#121C2212yes—
238C4×#121C2211yescharacteristic
239C4×#121C2214yes—
240C4×#121C2212yes—
241C4×#121C2214yes—
242#2293C2212yes—
243#2293C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2212yes—
246C2×#389C2212yes—
247C2×#389C2211yescharacteristic
248#2290C2214yes—
249C2×#387C2212yes—
250C2×#387C2212yes—
251#2285C2212yes—
252#2283C2212yes—
253C42×D4C2212yes—
254C2×C4×C4⋊C4C2211yescharacteristic
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2314yes—
260#547—216no—
261#539—28no—
262#539—48no—
263#532—216no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2312yes—
268C2×#127C2311yescharacteristic
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125—28no—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300#520—416no—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×#117C2314yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2314yes—
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2312yes—
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2312yes—
344C22×C42C2312yes—
345C22×C42C2312yes—
346#401C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#392C2314yes—
418#391C2312yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2311yescharacteristic
427#391C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2312yes—
432#390C2312yes—
433#390C2311yescharacteristic
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2311yescharacteristic
472#389C2311yescharacteristic
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2312yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2312yes—
581#386C2314yes—
582#386C2312yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#384C2312yes—
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2312yes—
621#383C2312yes—
622#383C2314yes—
623#383C2314yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2312yes—
629#381C2312yes—
630#381C2314yes—
631#381C2312yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2311yescharacteristic
641#380C2311yescharacteristic
642#380C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#380C2312yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708#376C2314yes—
709C2×#95C2314yes—
710C2×#95C2311yescharacteristic
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C43C2312yes—
718C2×#41—216no—
719C2×#41—216no—
720C2×#41—48no—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×D4C2412yes—
725C22×D4C2414yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C4⋊Q8—28no—
752C4⋊Q8—28no—
753C4⋊Q8—42no—
754#127—28no—
755#127—42no—
756#126—28no—
757#126—48no—
758#126—84no—
759#125—28no—
760#125—28no—
761#125—216no—
762#125—28no—
763#125—28no—
764#125—48no—
765#124—216no—
766#123—28no—
767#123—28no—
768#123—216no—
769#123—216no—
770#123—48no—
771#123—48no—
772#123—84no—
773C22⋊Q8—24no—
774C22⋊Q8—216no—
775C22⋊Q8—28no—
776C22⋊Q8—44no—
777C22⋊Q8—48no—
778C22⋊Q8—84no—
779#121—216no—
780#121—28no—
781#121—28no—
782#121—28no—
783#121—28no—
784#121—44no—
785#121#4118yes—
786C4×Q8—42no—
787C4×Q8—48no—
788C4×Q8—48no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—216no—
794C4×D4—28no—
795C4×D4—28no—
796C4×D4—216no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—42no—
800C4×D4—48no—
801C4×D4—48no—
802C4×D4—48no—
803C4×D4—48no—
804C4×D4—84no—
805C4×D4—84no—
806#117—48no—
807#117—48no—
808#117—48no—
809#117—84no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—24no—
814C2×C4⋊C4—28no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—28no—
817C2×C4⋊C4—24no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—48no—
821C2×C4⋊C4—48no—
822C2×C4⋊C4—82no—
823C2×C4⋊C4#4118yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C42—24no—
930C2×C42—28no—
931C2×C42—42no—
932C2×C42—44no—
933C2×C42—42no—
934C2×C42—82no—
935C2×C42—82no—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030C24C2514yes—
1031C24C2512yes—
1032C24C2511yescharacteristic
1033#41—464no—
1034C2×Q8—28no—
1035C2×Q8—28no—
1036C2×Q8—22no—
1037C2×Q8—44no—
1038C2×Q8—41no—
1039C2×Q8—41no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—28no—
1046C2×D4—28no—
1047C2×D4—28no—
1048C2×D4—28no—
1049C2×D4—28no—
1050C2×D4—24no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—44no—
1057C2×D4—41no—
1058C2×D4—44no—
1059C2×D4—41no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4C2×#4118yes—
1066C2×D4C2×#4114yes—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—22no—
1076C22×C4—28no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—28no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—42no—
1095C22×C4—41no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—41no—
1100C22×C4—42no—
1101C22×C4—41no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—42no—
1105C22×C4—41no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—41no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—41no—
1113C22×C4—42no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4C2×#4114yes—
1121C22×C4C2×#4118yes—
1122C22×C4C2×#4114yes—
1123C22×C4H(5,𝔽2)14yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2511yescharacteristic
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—22no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—22no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—41no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—41no—
1198C4⋊C4—44no—
1199C4⋊C4—41no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4C2×#4114yes—
1211C4⋊C4C2×#4114yes—
1212C4⋊C4C2×#4118yes—
1213C4⋊C4C2×#4114yes—
1214C4⋊C42−1+414yes—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—42no—
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—42no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4C2×#4118yes—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—24no—
1264C42—28no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—22no—
1269C42—22no—
1270C42—42no—
1271C42—42no—
1272C42—41no—
1273C42—41no—
1274C42—42no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—42no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23—24no—
1301C23—24no—
1302C23C22×#4114yes—
1303C23C22×#4112yes—
1304C23C22×#4112yes—
1305C23C2×H(5,𝔽2)12yes—
1306C23C2611yescharacteristic
1307Q8—416no—
1308Q8—82no—
1309Q8—162no—
1310D4—216no—
1311D4—44no—
1312D4—416no—
1313D4—416no—
1314D4—416no—
1315D4—48no—
1316D4—84no—
1317D4—162no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—216no—
1335C2×C4—28no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—416no—
1390C2×C4—48no—
1391C2×C4—416no—
1392C2×C4—44no—
1393C2×C4—48no—
1394C2×C4—44no—
1395C2×C4—48no—
1396C2×C4—84no—
1397C2×C4—88no—
1398C2×C4—82no—
1399C2×C4—84no—
1400C2×C4—84no—
1401C2×C4—82no—
1402C2×C4—164no—
1403C2×C4—164no—
1404C2×C4C22×#4112yes—
1405C2×C4C22×#4112yes—
1406C2×C4C22×#4112yes—
1407C2×C4C22×#4114yes—
1408C2×C4C22×#4114yes—
1409C2×C4C22×#4114yes—
1410C2×C4C22×#4112yes—
1411C2×C4C2×H(5,𝔽2)14yes—
1412C2×C4C2×2−1+414yes—
1413C2×C4C2×2−1+412yes—
1414C2×C4#58512yes—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—24no—
1422C22—24no—
1423C22—24no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—44no—
1429C22—44no—
1430C22—44no—
1431C22—44no—
1432C22—44no—
1433C22—44no—
1434C22—44no—
1435C22#348114yes—
1436C22C23×#4111yescharacteristic
1437C22C23×#4111yescharacteristic
1438C22C22×H(5,𝔽2)11yescharacteristic
1439C22C22×2−1+411yescharacteristic
1440C22C2×#58511yescharacteristic
1441C22H(7,𝔽2)11yescharacteristic
1442C222−1+611yescharacteristic
1443C4—22no—
1444C4—22no—
1445C4—24no—
1446C4—22no—
1447C4—24no—
1448C4—24no—
1449C4—24no—
1450C4—24no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—42no—
1460C4—44no—
1461C4—44no—
1462C4—41no—
1463C4—41no—
1464C4—42no—
1465C4—44no—
1466C4—42no—
1467C4—44no—
1468C4#350714yes—
1469C2—24no—
1470C2—44no—
1471C2—84no—
1472C2C2×#348111yescharacteristic
1473C2C2×#350711yescharacteristic
1474C2#6285111yescharacteristic
1475C2#6290511yescharacteristic
1476C2#6294611yescharacteristic
1477C2#6299111yescharacteristic
1478C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36126C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59716C2semidirect
2. #59670C2semidirect
3. #59632C2semidirect
4. #59580C2semidirect
5. #59545C2semidirect
6. #59454C2semidirect
7. #59254C2semidirect
8. #59247C2semidirect
9. #44674C2semidirect
10. #44616C2semidirect
11. #43811C2semidirect
12. #43780C2semidirect
13. #39767C2semidirect
14. #39631C2semidirect
15. #39063C2semidirect
16. #38907C2semidirect
17. #37896C2semidirect
18. #37698C2semidirect
19. #36488C2semidirect
20. #36193C2semidirect
22. #35363C2semidirect
23. #35042C2semidirect
24. #35006C2semidirect
25. #34788C2semidirect
26. #34308C2semidirect
27. #34206C2semidirect
28. C2×#2370C2semidirect
29. C4×#539C2semidirect

Maximal subgroups

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

subgroupindex
#597162
#596702
#596322
#595802
#595452
#594542
#592542
#592472
#446742
#446162
#438112
#437802
#397672
#396312
#390632
#389072
#378962
#376982
#364882
#361932
#361262
#353632
#350422
#350062
#347882
#343082
#342062
C2×#23702
C4×#5392