Finite Group Databasebeta

← #7697451

Subgroups — #7697451

Order 512.

4829 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60043C212yesmaximal, complemented
2#59879C212yesmaximal, complemented
3#59836C211yesmaximal, characteristic
4#59132C214yesmaximal, complemented
5#52306C211yesmaximal, characteristic, complemented
6#52162C212yesmaximal, complemented
7#44706C212yesmaximal, complemented
8#44384C214yesmaximal, complemented
9#43831C214yesmaximal, complemented
10#43588C214yesmaximal, complemented
11#43157C214yesmaximal, complemented
12#39840C214yesmaximal, complemented
13#39829C212yesmaximal, complemented
14#38808C212yesmaximal, complemented
15#38798C214yesmaximal, complemented
16#38432C212yesmaximal
17#38422C214yesmaximal, complemented
18#36403C211yesmaximal, characteristic, complemented
19#36151C212yesmaximal, complemented
20#35954C212yesmaximal, complemented
21#35935C214yesmaximal, complemented
22#34317C212yesmaximal, complemented
23#34315C214yesmaximal, complemented
24C2×#554C2212yes—
25C2×#551C2214yes—
26C2×#551C2212yes—
27C2×#533C2214yescomplemented
28#2864C2211yescharacteristic, complemented
29#2862C2212yescomplemented
30#2860C2212yes—
31#2857C2214yescomplemented
32#2810C2212yescomplemented
33#2809C2211yescharacteristic, complemented
34#2794C2212yescomplemented
35#2790C2214yescomplemented
36#2775C2214yescomplemented
37#2769C2212yescomplemented
38#2764C2214yescomplemented
39#2764C2212yescomplemented
40#2758C2214yescomplemented
41#2747C2214yescomplemented
42#2744C2214yescomplemented
43#2743C2214yes—
44#2741C2214yes—
45#2738C2214yescomplemented
46#2735C2212yescomplemented
47#2734C2211yescharacteristic, complemented
48#2732C2212yes—
49#2731C2212yes—
50#2729C2214yescomplemented
51#2727C2212yes—
52#2726C2212yescomplemented
53#2724C2212yes—
54#2724C2211yescharacteristic
55#2721C2214yescomplemented
56#2720C2214yescomplemented
57#2716C2214yescomplemented
58#2716C2214yescomplemented
59#2713C2214yescomplemented
60#2704C2214yescomplemented
61#2702C2214yes—
62#2700C2214yes—
63#2697C2214yes—
64#2692C2214yes—
65#2690C2214yescomplemented
66#2687C2214yes—
67#2683C2212yes—
68#2680C2212yes—
69#2679C2211yescharacteristic
70#2677C2214yescomplemented
71#2674C2214yes—
72#2666C2214yescomplemented
73#2665C2212yescomplemented
74#2664C2214yescomplemented
75#2663C2214yes—
76#2663C2214yes—
77#2611C2214yescomplemented
78#2609C2214yes—
79#2609C2212yes—
80#2607C2212yescomplemented
81#2606C2214yescomplemented
82#2605C2214yescomplemented
83#2604C2214yescomplemented
84#2601C2214yes—
85#2599C2214yescomplemented
86#2596C2214yescomplemented
87#2589C2214yescomplemented
88#2588C2214yescomplemented
89#2586C2212yescomplemented
90#2585C2214yescomplemented
91#2585C2214yescomplemented
92#2585C2214yescomplemented
93#2583C2214yescomplemented
94#2581C2211yescharacteristic, complemented
95#2580C2211yescharacteristic
96#2577C2214yescomplemented
97#2575C2214yescomplemented
98#2575C2214yescomplemented
99#2574C2214yescomplemented
100#2573C2214yescomplemented
101#2573C2214yescomplemented
102#2573C2214yescomplemented
103#2573C2214yescomplemented
104#2572C2214yes—
105#2572C2212yes—
106#2564C2214yes—
107#2561C2214yescomplemented
108#2561C2214yescomplemented
109#2558C2214yes—
110#2553C2214yes—
111#2536C2212yes—
112#2536C2212yes—
113#2534C2212yes—
114#2532C2214yescomplemented
115#2530C2214yescomplemented
116#2525C2214yescomplemented
117#2524C2214yescomplemented
118#2524C2214yescomplemented
119#2519C2214yescomplemented
120#2516C2214yes—
121#2515C2214yescomplemented
122#2515C2214yescomplemented
123#2509C2212yescomplemented
124#2489C2214yescomplemented
125#2489C2214yescomplemented
126#2488C2214yes—
127#2482C2212yescomplemented
128#2475C2214yescomplemented
129#2474C2214yes—
130#2472C2214yes—
131#2470C2214yes—
132#2469C2214yescomplemented
133#2469C2214yescomplemented
134#2468C2214yes—
135#2460C2214yes—
136#2458C2214yes—
137#2458C2214yes—
138#2453C2214yescomplemented
139#2453C2214yescomplemented
140#2448C2212yes—
141#2438C2214yescomplemented
142#2438C2214yescomplemented
143#2438C2214yescomplemented
144#2437C2212yescomplemented
145#2437C2214yescomplemented
146#2421C2214yescomplemented
147#2421C2214yescomplemented
148#2419C2214yes—
149#2419C2214yes—
150#2418C2214yes—
151#2418C2214yes—
152#2415C2214yes—
153#2415C2214yes—
154#2413C2214yes—
155#2411C2214yes—
156#2399C2214yescomplemented
157#2396C2214yescomplemented
158#2396C2214yescomplemented
159#2396C2214yescomplemented
160#2395C2212yes—
161#2374C2214yes—
162#2374C2214yes—
163#2373C2214yescomplemented
164#2373C2214yescomplemented
165#2370C2212yescomplemented
166#2370C2212yescomplemented
167#2369C2212yescomplemented
168#2368C2214yescomplemented
169#2368C2214yescomplemented
170#2367C2214yes—
171#2362C2214yescomplemented
172#2362C2214yescomplemented
173#2362C2214yescomplemented
174#2362C2214yescomplemented
175#2359C2214yes—
176#2358C2214yes—
177#2357C2212yes—
178#2357C2212yes—
179#2357C2211yescharacteristic
180#2355C2212yescomplemented
181#2354C2212yes—
182#2353C2214yes—
183#2351C2211yescharacteristic, complemented
184#2351C2212yescomplemented
185#2347C2214yescomplemented
186#2347C2212yescomplemented
187#2344C2214yescomplemented
188#2343C2214yescomplemented
189#2342C2214yescomplemented
190#2342C2214yescomplemented
191#2337C2214yes—
192#2335C2214yes—
193#2334C2214yescomplemented
194#2332C2214yescomplemented
195#2332C2214yescomplemented
196#2332C2214yescomplemented
197#2323C2214yescomplemented
198#2322C2214yes—
199#2321C2214yes—
200C4×C4⋊Q8C2212yescomplemented
201C4×C4⋊Q8C2212yescomplemented
202C4×#125C2212yescomplemented
203C4×#125C2212yescomplemented
204C4×#126C2214yescomplemented
205C4×#124C2211yescharacteristic
206C4×C22⋊Q8C2214yescomplemented
207C4×#123C2214yes—
208#2298C2214yescomplemented
209#2295C2212yescomplemented
210#2293C2212yes—
211#2293C2212yes—
212#2293C2212yes—
213#2290C2214yes—
214C2×#388C2214yescomplemented
215#2274C2214yescomplemented
216#2273C2212yescomplemented
217C42×Q8C2211yescharacteristic, complemented
218C42×D4C2212yes—
219#554—216no—
220#551—232no—
221#551—48no—
222#533—416no—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#124C2314yes—
234C2×#124C2311yescharacteristic
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×#120C2314yes—
250C2×#120C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C22⋊C4C2314yes—
275C22×C22⋊C4C2314yes—
276C22×C22⋊C4C2314yes—
277C22×C22⋊C4C2312yes—
278C22×C42C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2312yes—
282#400C2312yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#399C2314yes—
297#399C2314yes—
298#399C2312yes—
299#399C2314yes—
300#399C2312yes—
301#399C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2312yes—
313#398C2314yes—
314#398C2312yes—
315#398C2314yes—
316#398C2312yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2312yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2312yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#394C2314yes—
349#394C2312yes—
350#394C2314yes—
351#394C2314yes—
352#394C2312yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#393C2314yes—
357#393C2314yes—
358#393C2314yes—
359#393C2314yes—
360#393C2314yes—
361#393C2314yes—
362#393C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2311yescharacteristic
378#390C2312yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#390C2311yescharacteristic
383#390C2312yes—
384#390C2312yes—
385#390C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2314yes—
402#389C2312yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#384C2312yes—
526#384C2312yes—
527#383C2314yes—
528#383C2314yes—
529#383C2314yes—
530#383C2314yes—
531#383C2314yes—
532#382C2312yes—
533#382C2312yes—
534#382C2314yes—
535#382C2312yes—
536#382C2314yes—
537#382C2311yescharacteristic
538#382C2311yescharacteristic
539#382C2312yes—
540#382C2311yescharacteristic
541#381C2314yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#381C2312yes—
546#381C2312yes—
547#381C2314yes—
548#381C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2312yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#379C2314yes—
558#379C2312yes—
559#379C2314yes—
560C4×C4⋊C4C2312yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2312yes—
566C4×C4⋊C4C2312yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2311yescharacteristic
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611#376C2314yes—
612#376C2314yes—
613C2×#95C2314yes—
614C2×#95C2314yes—
615C43C2312yes—
616C43C2311yescharacteristic
617C43C2312yes—
618C25C2412yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2414yes—
623C22×Q8C2411yescharacteristic
624C22×D4C2412yes—
625C22×D4C2414yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C23×C4C2414yes—
629C23×C4C2414yes—
630C23×C4C2412yes—
631C23×C4C2414yes—
632C23×C4C2414yes—
633C23×C4C2414yes—
634C23×C4C2412yes—
635C23×C4C2414yes—
636C4⋊Q8—28no—
637C4⋊Q8—28no—
638C4⋊Q8—48no—
639#126—216no—
640#126—216no—
641#126—48no—
642#125—28no—
643#125—28no—
644#125—48no—
645#125—48no—
646#124—24no—
647#124—216no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—48no—
652#123—44no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—48no—
660C22⋊Q8—48no—
661C22⋊Q8—48no—
662#120—216no—
663#120—44no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—44no—
667C4×Q8—42no—
668C4×Q8—42no—
669C4×Q8—48no—
670C4×Q8—48no—
671C4×Q8—48no—
672C4×D4—28no—
673C4×D4—28no—
674C4×D4—216no—
675C4×D4—44no—
676C4×D4—42no—
677C4×D4—48no—
678C4×D4#41116yes—
679#117—216no—
680#117—216no—
681#117—44no—
682#117—48no—
683#117—48no—
684#117—48no—
685#117—48no—
686C2×C4⋊C4—216no—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C22⋊C4—216no—
741C2×C22⋊C4—216no—
742C2×C22⋊C4—44no—
743C2×C22⋊C4—48no—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C42—48no—
780C2×C42C2411yescharacteristic
781C2×C42C2412yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2412yes—
787C2×C42C2411yescharacteristic
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2411yescharacteristic
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2412yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2411yescharacteristic
823#95C2414yes—
824#95C2412yes—
825#95C2412yes—
826#95C2414yes—
827#95C2412yes—
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2411yescharacteristic
845#95C2412yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2414yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869C24—28no—
870C24—42no—
871C24—42no—
872C24—44no—
873C24—42no—
874C24C2512yes—
875C24C2514yes—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—41no—
881C2×Q8—42no—
882C2×Q8—41no—
883C2×Q8—41no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8H(5,𝔽2)14yes—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—22no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—44no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—44no—
900C2×D4C2×#4118yes—
901C22×C4—28no—
902C22×C4—28no—
903C22×C4—28no—
904C22×C4—28no—
905C22×C4—28no—
906C22×C4—28no—
907C22×C4—24no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4C2×#41116yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2511yescharacteristic
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2514yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C4⋊C4—24no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—28no—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—28no—
963C4⋊C4—28no—
964C4⋊C4—28no—
965C4⋊C4—28no—
966C4⋊C4—24no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—41no—
987C4⋊C4—42no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—44no—
992C4⋊C4—41no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4C2×#4118yes—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4C2×#41116yes—
1033C42—28no—
1034C42—28no—
1035C42—24no—
1036C42—24no—
1037C42—24no—
1038C42—28no—
1039C42—22no—
1040C42—24no—
1041C42—28no—
1042C42—22no—
1043C42—24no—
1044C42—44no—
1045C42—44no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—44no—
1050C42—44no—
1051C42—41no—
1052C42—42no—
1053C42—44no—
1054C42—44no—
1055C42—44no—
1056C42—44no—
1057C42—44no—
1058C42—44no—
1059C42—42no—
1060C42C2×#4118yes—
1061C23—24no—
1062C23—24no—
1063C23—24no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—22no—
1069C23—22no—
1070C23—24no—
1071C23—22no—
1072C23—48no—
1073C23—88no—
1074C23—88no—
1075C23—162no—
1076C23—162no—
1077C23C22×#4118yes—
1078C23C2611yescharacteristic
1079Q8—44no—
1080Q8—44no—
1081Q8—48no—
1082Q8—88no—
1083Q8—88no—
1084D4—48no—
1085D4—48no—
1086D4—82no—
1087D4—88no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—88no—
1143C2×C4—84no—
1144C2×C4—88no—
1145C2×C4—88no—
1146C2×C4—88no—
1147C2×C4—162no—
1148C2×C4C22×#4114yes—
1149C2×C4C22×#4114yes—
1150C2×C4C22×#4118yes—
1151C2×C4C22×#4114yes—
1152C2×C4C2×H(5,𝔽2)12yes—
1153C2×C4C2×H(5,𝔽2)14yes—
1154C2×C4#58512yes—
1155C22—28no—
1156C22—28no—
1157C22—28no—
1158C22—44no—
1159C22—44no—
1160C22—44no—
1161C22—44no—
1162C22—44no—
1163C22—42no—
1164C22—44no—
1165C22—42no—
1166C22—42no—
1167C22—168no—
1168C22C23×#4112yes—
1169C22C22×H(5,𝔽2)11yescharacteristic
1170C22C2×#58511yescharacteristic
1171C222−1+612yes—
1172C222−1+611yescharacteristic
1173C4—24no—
1174C4—28no—
1175C4—22no—
1176C4—24no—
1177C4—24no—
1178C4—22no—
1179C4—24no—
1180C4—42no—
1181C4—44no—
1182C4—44no—
1183C4—44no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—44no—
1188C4—44no—
1189C4—44no—
1190C4—44no—
1191C4—44no—
1192C4—42no—
1193C4—41no—
1194C2—48no—
1195C2—82no—
1196C2#41211yescharacteristic
1197C2#6286012yes—
1198C2#6290111yescharacteristic
1199C2#6298412yes—
1200C2#6306411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2679C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60043C2semidirect
2. #59879C2semidirect
4. #59132C2semidirect
5. #52306C2semidirect
6. #52162C2semidirect
7. #44706C2semidirect
8. #44384C2semidirect
9. #43831C2semidirect
10. #43588C2semidirect
11. #43157C2semidirect
12. #39840C2semidirect
13. #39829C2semidirect
14. #38808C2semidirect
15. #38798C2semidirect
17. #38422C2semidirect
18. #36403C2semidirect
19. #36151C2semidirect
20. #35954C2semidirect
21. #35935C2semidirect
22. #34317C2semidirect
23. #34315C2semidirect
27. C2×#533C22semidirect
28. #2864C22semidirect
29. #2862C22semidirect
31. #2857C22semidirect
32. #2810C22semidirect
33. #2809C22semidirect
34. #2794C22semidirect
35. #2790C22semidirect
36. #2775C22semidirect
37. #2769C22semidirect
38. #2764C22semidirect
39. #2764C22semidirect
40. #2758C22semidirect
41. #2747C22semidirect
42. #2744C22semidirect
45. #2738C22semidirect
46. #2735C22semidirect
47. #2734C22semidirect
50. #2729C22semidirect
52. #2726C22semidirect
55. #2721C22semidirect
56. #2720C22semidirect
57. #2716C22semidirect
58. #2716C22semidirect
59. #2713C22semidirect
60. #2704C22semidirect
65. #2690C22semidirect
70. #2677C22semidirect
72. #2666C22semidirect
73. #2665C22semidirect
74. #2664C22semidirect
77. #2611C22semidirect
80. #2607C22semidirect
81. #2606C22semidirect
82. #2605C22semidirect
83. #2604C22semidirect
85. #2599C22semidirect
86. #2596C22semidirect
87. #2589C22semidirect
88. #2588C22semidirect
89. #2586C22semidirect
90. #2585C22semidirect
91. #2585C22semidirect
92. #2585C22semidirect
93. #2583C22semidirect
94. #2581C22semidirect
96. #2577C22semidirect
97. #2575C22semidirect
98. #2575C22semidirect
99. #2574C22semidirect
100. #2573C22semidirect
101. #2573C22semidirect
102. #2573C22semidirect
103. #2573C22semidirect
107. #2561C22semidirect
108. #2561C22semidirect
114. #2532C22semidirect
115. #2530C22semidirect
116. #2525C22semidirect
117. #2524C22semidirect
118. #2524C22semidirect
119. #2519C22semidirect
121. #2515C22semidirect
122. #2515C22semidirect
123. #2509C22semidirect
124. #2489C22semidirect
125. #2489C22semidirect
127. #2482C22semidirect
128. #2475C22semidirect
132. #2469C22semidirect
133. #2469C22semidirect
138. #2453C22semidirect
139. #2453C22semidirect
141. #2438C22semidirect
142. #2438C22semidirect
143. #2438C22semidirect
144. #2437C22semidirect
145. #2437C22semidirect
146. #2421C22semidirect
147. #2421C22semidirect
156. #2399C22semidirect
157. #2396C22semidirect
158. #2396C22semidirect
159. #2396C22semidirect
163. #2373C22semidirect
164. #2373C22semidirect
165. #2370C22semidirect
166. #2370C22semidirect
167. #2369C22semidirect
168. #2368C22semidirect
169. #2368C22semidirect
171. #2362C22semidirect
172. #2362C22semidirect
173. #2362C22semidirect
174. #2362C22semidirect
180. #2355C22semidirect
183. #2351C22semidirect
184. #2351C22semidirect
185. #2347C22semidirect
186. #2347C22semidirect
187. #2344C22semidirect
188. #2343C22semidirect
189. #2342C22semidirect
190. #2342C22semidirect
193. #2334C22semidirect
194. #2332C22semidirect
195. #2332C22semidirect
196. #2332C22semidirect
197. #2323C22semidirect
200. C4×C4⋊Q8C22semidirect
201. C4×C4⋊Q8C22semidirect
202. C4×#125C22semidirect
203. C4×#125C22semidirect
204. C4×#126C22semidirect
206. C4×C22⋊Q8C22semidirect
208. #2298C22semidirect
209. #2295C22semidirect
214. C2×#388C22semidirect
215. #2274C22semidirect
216. #2273C22semidirect
217. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#600432
#598792
#598362
#591322
#523062
#521622
#447062
#443842
#438312
#435882
#431572
#398402
#398292
#388082
#387982
#384322
#384222
#364032
#361512
#359542
#359352
#343172
#343152