Finite Group Databasebeta

← #7671753

Subgroups — #7671753

Order 512.

4548 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59666C212yesmaximal, complemented
2#59447C214yesmaximal, complemented
3#59443C212yesmaximal, complemented
4#59330C214yesmaximal
5#59256C212yesmaximal
6#59242C212yesmaximal
7#40028C214yesmaximal
8#40024C214yesmaximal, complemented
9#39819C214yesmaximal
10#39734C212yesmaximal
11#39724C212yesmaximal
12#36645C211yesmaximal, characteristic
13#36608C212yesmaximal, complemented
14#36598C211yesmaximal, characteristic, complemented
15#36598C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36598C211yesmaximal, characteristic, complemented
18#36593C211yesmaximal, characteristic, complemented
19#36535C212yesmaximal, complemented
20#36450C212yesmaximal
21#36314C212yesmaximal
22#36285C212yesmaximal, complemented
23#35656C214yesmaximal, complemented
24#35322C212yesmaximal
25#35187C212yesmaximal, complemented
26#34328C212yesmaximal, complemented
27#34225C212yesmaximal
28C4×#533C211yesmaximal, characteristic
29C4×#533C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#533C2212yes—
32C2×#533C2211yescharacteristic
33C2×#533C2211yescharacteristic
34#2868C2211yescharacteristic
35#2868C2211yescharacteristic
36#2868C2212yes—
37#2864C2214yes—
38#2863C2214yes—
39#2862C2212yes—
40#2862C2212yes—
41#2862C2212yes—
42#2862C2212yes—
43#2859C2212yes—
44#2859C2212yes—
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2802C2218yes—
50#2787C2218yes—
51#2776C2218yes—
52#2770C2218yes—
53#2766C2218yes—
54#2747C2218yes—
55#2719C2218yes—
56#2690C2218yes—
57#2655C2218yes—
58#2621C2214yes—
59#2621C2214yes—
60#2606C2218yes—
61#2590C2218yes—
62#2590C2218yes—
63#2588C2218yes—
64#2582C2214yes—
65#2582C2212yes—
66#2582C2212yes—
67#2582C2212yes—
68#2581C2214yes—
69#2581C2214yes—
70#2581C2214yes—
71#2577C2218yes—
72#2571C2212yes—
73#2571C2212yes—
74#2571C2214yes—
75#2571C2212yes—
76#2570C2214yes—
77#2570C2214yes—
78#2570C2214yes—
79#2570C2214yes—
80#2570C2214yes—
81#2570C2214yes—
82#2568C2214yes—
83#2568C2212yes—
84#2568C2212yes—
85#2568C2212yes—
86#2565C2214yes—
87#2565C2214yes—
88#2565C2214yes—
89#2565C2214yes—
90#2552C2212yes—
91#2552C2214yes—
92#2552C2214yes—
93#2552C2212yes—
94#2550C2214yes—
95#2546C2212yes—
96#2546C2214yes—
97#2533C2218yes—
98#2533C2218yes—
99#2530C2218yes—
100#2528C2218yes—
101#2528C2218yes—
102#2524C2218yes—
103#2524C2218yes—
104#2520C2218yes—
105#2514C2214yes—
106#2514C2214yes—
107#2514C2214yes—
108#2514C2214yes—
109#2514C2214yes—
110#2514C2214yes—
111#2514C2214yes—
112#2511C2214yes—
113#2511C2214yes—
114#2511C2214yes—
115#2511C2214yes—
116#2511C2214yes—
117#2508C2214yes—
118#2507C2214yes—
119#2499C2214yes—
120#2499C2214yes—
121#2499C2214yes—
122#2499C2214yes—
123#2495C2214yes—
124#2494C2214yes—
125#2489C2214yes—
126#2446C2214yes—
127#2446C2214yes—
128#2446C2214yes—
129#2446C2214yes—
130#2446C2214yes—
131#2446C2214yes—
132#2421C2214yes—
133#2371C2218yes—
134#2370C2214yes—
135#2370C2214yes—
136#2370C2214yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2214yes—
141#2362C2214yes—
142#2362C2214yes—
143#2356C2214yes—
144#2356C2214yes—
145#2356C2214yes—
146#2356C2214yes—
147#2356C2214yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2212yes—
151#2355C2214yes—
152#2355C2212yes—
153#2355C2212yes—
154#2355C2212yes—
155#2355C2214yes—
156#2351C2214yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159#2347C2214yes—
160#2346C2214yes—
161#2336C2218yes—
162#2327C2214yes—
163#2327C2214yes—
164#2323C2214yes—
165#2323C2214yes—
166#2320C2214yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2212yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#125C2212yes—
184C4×#125C2214yes—
185C4×#125C2212yes—
186C4×#125C2212yes—
187C4×#125C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2211yescharacteristic
191C4×C22⋊Q8C2211yescharacteristic
192C4×C22⋊Q8C2212yes—
193C4×C22⋊Q8C2211yescharacteristic
194C4×C22⋊Q8C2212yes—
195C4×C22⋊Q8C2212yes—
196C4×C22⋊Q8C2212yes—
197C4×C22⋊Q8C2211yescharacteristic
198#2296C2212yes—
199#2296C2212yes—
200#2295C2211yescharacteristic
201#2295C2214yes—
202#2295C2212yes—
203#2295C2212yes—
204#2295C2212yes—
205#2295C2211yescharacteristic
206#2285C2212yes—
207#2285C2212yes—
208#2285C2211yescharacteristic
209#2285C2211yescharacteristic
210#2276C2214yes—
211C42×Q8C2212yes—
212C42×Q8C2212yes—
213C42×Q8C2212yes—
214C42×Q8C2211yescharacteristic
215C42×Q8C2211yescharacteristic
216C4×#117C2212yes—
217C4×#117C2212yes—
218C2×C43C2211yescharacteristic
219#557—216no—
220#533—28no—
221#533—216no—
222#533—28no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281#401C2318yes—
282#401C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#395C2318yes—
313#391C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2312yes—
326#391C2312yes—
327#391C2311yescharacteristic
328#391C2312yes—
329#391C2312yes—
330#391C2311yescharacteristic
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2318yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#389C2311yescharacteristic
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2312yes—
381#389C2314yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2314yes—
390#389C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2312yes—
398#387C2312yes—
399#387C2312yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2312yes—
404#387C2312yes—
405#387C2314yes—
406#387C2312yes—
407#387C2312yes—
408#387C2312yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#385C2312yes—
441#385C2314yes—
442#385C2312yes—
443#385C2314yes—
444#385C2312yes—
445#385C2312yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2314yes—
455#384C2314yes—
456#384C2314yes—
457#384C2314yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#383C2318yes—
463#383C2318yes—
464#383C2318yes—
465#383C2318yes—
466#382C2312yes—
467#382C2312yes—
468#382C2314yes—
469#382C2314yes—
470#382C2314yes—
471#382C2314yes—
472#382C2314yes—
473#382C2314yes—
474#382C2314yes—
475#382C2318yes—
476#382C2314yes—
477#382C2314yes—
478#382C2314yes—
479#382C2314yes—
480#382C2318yes—
481#380C2314yes—
482#380C2312yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488#380C2311yescharacteristic
489#380C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2311yescharacteristic
526C4×C4⋊C4C2311yescharacteristic
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2312yes—
529C4×C4⋊C4C2314yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2311yescharacteristic
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2311yescharacteristic
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2311yescharacteristic
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2318yes—
543C4×C4⋊C4C2311yescharacteristic
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2312yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2312yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2312yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2314yes—
556#376C2312yes—
557#376C2312yes—
558#376C2318yes—
559#376C2318yes—
560#376C2314yes—
561C43C2311yescharacteristic
562C43C2311yescharacteristic
563C43C2311yescharacteristic
564C43C2314yes—
565C43C2311yescharacteristic
566C43C2311yescharacteristic
567C43C2312yes—
568C43C2312yes—
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C22×Q8C2414yes—
573C22×Q8C2412yes—
574C22×Q8C2414yes—
575C22×Q8C2411yescharacteristic
576C22×Q8C2412yes—
577C22×Q8C2412yes—
578C22×Q8C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C4⋊Q8—24no—
587C4⋊Q8—24no—
588C4⋊Q8—24no—
589C4⋊Q8—28no—
590C4⋊Q8—24no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593C4⋊Q8—216no—
594C4⋊Q8—28no—
595C4⋊Q8—44no—
596C4⋊Q8—44no—
597C4⋊Q8—48no—
598#125—28no—
599#125—232no—
600#125—216no—
601#125—28no—
602#125—216no—
603C22⋊Q8—24no—
604C22⋊Q8—28no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—28no—
608C22⋊Q8—24no—
609C22⋊Q8—28no—
610C4×Q8—216no—
611C4×Q8—28no—
612C4×Q8—24no—
613C4×Q8—216no—
614C4×Q8—28no—
615C4×Q8—216no—
616C4×Q8—28no—
617C4×Q8—28no—
618C4×Q8—216no—
619C4×Q8—24no—
620C4×Q8—28no—
621C4×Q8—28no—
622C4×Q8—24no—
623C4×Q8—28no—
624C4×Q8—24no—
625C4×Q8—24no—
626C4×Q8—44no—
627C4×Q8—44no—
628C4×Q8—48no—
629C4×Q8—48no—
630C4×Q8—48no—
631C4×Q8#4118yes—
632#117—216no—
633#117—28no—
634#117—28no—
635#117—44no—
636#117—44no—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C42—24no—
708C2×C42—24no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42—42no—
712C2×C42—42no—
713C2×C42#4118yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2418yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2418yes—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2418yes—
750C2×C42C2418yes—
751C2×C42C2418yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765#95C2412yes—
766#95C2412yes—
767#95C2414yes—
768#95C2412yes—
769#95C2412yes—
770#95C2412yes—
771#95C2412yes—
772#95C2414yes—
773#95C2412yes—
774#95C2414yes—
775#95C2412yes—
776#95C2412yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2412yes—
785#95C2412yes—
786#95C2414yes—
787#95C2412yes—
788#95C2412yes—
789#95C2412yes—
790#95C2412yes—
791#95C2414yes—
792#95C2412yes—
793#95C2412yes—
794#95C2414yes—
795#95C2412yes—
796#95C2412yes—
797#95C2414yes—
798#95C2414yes—
799#95C2412yes—
800#95C2418yes—
801#95C2418yes—
802#95C2418yes—
803#95C2418yes—
804#95C2418yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810#95C2418yes—
811#95C2418yes—
812#95C2418yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819C24C2511yescharacteristic
820C2×Q8—24no—
821C2×Q8—28no—
822C2×Q8—24no—
823C2×Q8—28no—
824C2×Q8—22no—
825C2×Q8—24no—
826C2×Q8—24no—
827C2×Q8—28no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—24no—
831C2×Q8—24no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—22no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—24no—
838C2×Q8—28no—
839C2×Q8—42no—
840C2×Q8C2×#4114yes—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4C2×#4114yes—
860C22×C4C2×#4114yes—
861C22×C4C2×#4114yes—
862C22×C4C2511yescharacteristic
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2518yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2518yes—
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2512yes—
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—216no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—216no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—22no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—216no—
912C4⋊C4—216no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—216no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—24no—
928C4⋊C4—28no—
929C4⋊C4—24no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—48no—
950C4⋊C4—48no—
951C4⋊C4C2×#4118yes—
952C4⋊C4C2×#4114yes—
953C22⋊C4—28no—
954C22⋊C4—216no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—44no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—216no—
964C42—28no—
965C42—24no—
966C42—216no—
967C42—28no—
968C42—22no—
969C42—22no—
970C42—22no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—28no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—28no—
985C42—22no—
986C42—22no—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—44no—
998C42—44no—
999C42—48no—
1000C42—48no—
1001C42—48no—
1002C42C2×#4114yes—
1003C42C2×#4114yes—
1004C42C2×#4114yes—
1005C42C2×#4114yes—
1006C42C2×#4114yes—
1007C42C2×#4118yes—
1008C422−1+414yes—
1009C422−1+414yes—
1010C422−1+414yes—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23C22×#4112yes—
1018C23C2611yescharacteristic
1019Q8—28no—
1020Q8—48no—
1021Q8—416no—
1022Q8—48no—
1023Q8—416no—
1024Q8—48no—
1025Q8—44no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—28no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—28no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—28no—
1056C2×C4—24no—
1057C2×C4—28no—
1058C2×C4—24no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—24no—
1090C2×C4—28no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4114yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4114yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C22×#4112yes—
1104C2×C4C22×#4112yes—
1105C2×C4C22×#4112yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4C2×2−1+412yes—
1109C2×C4C2×2−1+412yes—
1110C2×C4C2×2−1+412yes—
1111C2×C4C2×2−1+412yes—
1112C2×C4C2×2−1+412yes—
1113C2×C4C2×2−1+412yes—
1114C2×C4C2×2−1+412yes—
1115C2×C4#58512yes—
1116C2×C4#58512yes—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22C23×#4111yescharacteristic
1125C22C23×#4111yescharacteristic
1126C22C22×2−1+411yescharacteristic
1127C22C22×2−1+411yescharacteristic
1128C22C22×2−1+411yescharacteristic
1129C22C2×#58511yescharacteristic
1130C22C2×#58511yescharacteristic
1131C4—22no—
1132C4—22no—
1133C4—24no—
1134C4—22no—
1135C4—22no—
1136C4—24no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—48no—
1142C4—41no—
1143C4—42no—
1144C4—44no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—44no—
1152C4—41no—
1153C4—48no—
1154C4—44no—
1155C4#348014yes—
1156C4#350714yes—
1157C4#350914yes—
1158C4#350914yes—
1159C2—42no—
1160C2C2×#348011yescharacteristic
1161C2C2×#350711yescharacteristic
1162C2C2×#350911yescharacteristic
1163C2C2×#350911yescharacteristic
1164C2#6280511yescharacteristic
1165C2#6283711yescharacteristic
1166C2#6283811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59666C2semidirect
2. #59447C2semidirect
3. #59443C2semidirect
8. #40024C2semidirect
13. #36608C2semidirect
14. #36598C2semidirect
15. #36598C2semidirect
16. #36598C2semidirect
17. #36598C2semidirect
18. #36593C2semidirect
19. #36535C2semidirect
22. #36285C2semidirect
23. #35656C2semidirect
25. #35187C2semidirect
26. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#596662
#594472
#594432
#593302
#592562
#592422
#400282
#400242
#398192
#397342
#397242
#366452
#366082
#365982
#365932
#365352
#364502
#363142
#362852
#356562
#353222
#351872
#343282
#342252
C4×#5332