Finite Group Databasebeta

← #7987153

Subgroups — #7987153

Order 512.

4945 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59450C212yesmaximal, complemented
3#59418C212yesmaximal, complemented
4#59321C212yesmaximal, complemented
5#50438C218yesmaximal, complemented
6#46108C214yesmaximal, complemented
7#45175C214yesmaximal, complemented
8#45147C214yesmaximal, complemented
9#42939C214yesmaximal, complemented
10#42776C214yesmaximal, complemented
11#40099C214yesmaximal, complemented
12#39736C212yesmaximal, complemented
13#39488C212yesmaximal, complemented
14#39385C212yesmaximal, complemented
15#38955C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36562C212yesmaximal, complemented
19#36460C212yesmaximal, complemented
20#36179C211yesmaximal, characteristic
21#35286C212yesmaximal, complemented
22#35209C212yesmaximal, complemented
23#34954C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic, complemented
25#34480C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#556C2211yescharacteristic
29C2×#554C2212yes—
30C2×#547C2212yes—
31C2×#547C2212yes—
32C2×#547C2212yes—
33C2×#541C2214yes—
34#2868C2212yes—
35#2868C2211yescharacteristic
36#2862C2212yes—
37#2860C2214yes—
38#2859C2214yes—
39#2859C2214yes—
40#2856C2212yes—
41#2836C2218yes—
42#2791C2218yes—
43#2777C2218yes—
44#2771C2218yes—
45#2761C2218yes—
46#2738C2218yes—
47#2732C2214yes—
48#2721C2218yes—
49#2721C2218yes—
50#2718C2218yes—
51#2718C2218yes—
52#2707C2218yes—
53#2707C2218yes—
54#2695C2218yes—
55#2694C2218yes—
56#2691C2218yes—
57#2687C2218yes—
58#2687C2218yes—
59#2667C2218yes—
60#2664C2218yes—
61#2647C2218yes—
62#2621C2214yes—
63#2620C2214yes—
64#2593C2214yes—
65#2582C2211yescharacteristic
66#2582C2212yes—
67#2575C2218yes—
68#2574C2214yes—
69#2571C2214yes—
70#2571C2212yes—
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2568C2212yes—
74#2567C2211yescharacteristic
75#2566C2214yes—
76#2565C2214yes—
77#2563C2211yescharacteristic
78#2559C2218yes—
79#2558C2218yes—
80#2556C2218yes—
81#2556C2218yes—
82#2553C2218yes—
83#2552C2214yes—
84#2552C2212yes—
85#2552C2212yes—
86#2552C2214yes—
87#2552C2214yes—
88#2552C2211yescharacteristic
89#2552C2212yes—
90#2552C2214yes—
91#2548C2211yescharacteristic
92#2548C2211yescharacteristic
93#2546C2214yes—
94#2546C2212yes—
95#2542C2212yes—
96#2542C2212yes—
97#2542C2212yes—
98#2542C2212yes—
99#2538C2211yescharacteristic
100#2538C2212yes—
101#2538C2214yes—
102#2526C2218yes—
103#2519C2218yes—
104#2513C2212yes—
105#2513C2212yes—
106#2512C2214yes—
107#2512C2214yes—
108#2512C2214yes—
109#2511C2214yes—
110#2511C2214yes—
111#2508C2212yes—
112#2506C2214yes—
113#2503C2214yes—
114#2502C2214yes—
115#2501C2214yes—
116#2501C2214yes—
117#2501C2214yes—
118#2500C2214yes—
119#2497C2212yes—
120#2490C2214yes—
121#2489C2214yes—
122#2473C2218yes—
123#2454C2214yes—
124#2454C2212yes—
125#2448C2212yes—
126#2448C2212yes—
127#2447C2214yes—
128#2446C2214yes—
129#2442C2218yes—
130#2442C2214yes—
131#2442C2214yes—
132#2442C2214yes—
133#2432C2214yes—
134#2432C2214yes—
135#2429C2214yes—
136#2429C2214yes—
137#2429C2214yes—
138#2429C2214yes—
139#2426C2214yes—
140#2423C2212yes—
141#2421C2214yes—
142#2420C2214yes—
143#2420C2214yes—
144#2417C2214yes—
145#2396C2214yes—
146#2395C2214yes—
147#2376C2218yes—
148#2373C2214yes—
149#2367C2212yes—
150#2366C2212yes—
151#2365C2211yescharacteristic
152#2365C2212yes—
153#2363C2214yes—
154#2362C2212yes—
155#2360C2214yes—
156#2360C2214yes—
157#2360C2214yes—
158#2357C2214yes—
159#2356C2212yes—
160#2355C2212yes—
161#2355C2211yescharacteristic
162#2355C2212yes—
163#2354C2211yescharacteristic
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167#2347C2212yes—
168#2345C2214yes—
169#2341C2214yes—
170#2335C2218yes—
171#2324C2214yes—
172#2323C2214yes—
173#2317C2214yes—
174#2316C2214yes—
175#2311C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#127C2211yescharacteristic
181C4×#125C2212yes—
182C4×#126C2214yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2214yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2293C2212yes—
190#2293C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193C2×#384C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2314yes—
200#557—48no—
201#556—28no—
202#554—48no—
203#547—216no—
204#547—48no—
205#547—48no—
206#541—416no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2311yescharacteristic
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#125C2318yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×#117C2312yes—
263C2×#117C2314yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C42C2312yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2314yes—
282#399C2314yes—
283#399C2318yes—
284#399C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#397C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#396C2314yes—
312#396C2318yes—
313#396C2318yes—
314#395C2314yes—
315#394C2314yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#393C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2318yes—
345#390C2318yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2312yes—
352#390C2312yes—
353#390C2314yes—
354#390C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2318yes—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2314yes—
453#383C2314yes—
454#382C2312yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#382C2312yes—
459#382C2318yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#381C2318yes—
464#381C2318yes—
465#380C2312yes—
466#380C2312yes—
467#380C2318yes—
468#380C2318yes—
469#380C2318yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2318yes—
474#380C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522C43C2314yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C2×#41—216no—
527C2×#41—48no—
528C2×#41—48no—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2414yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2412yes—
538C22×D4C2418yes—
539C23×C4C2412yes—
540C23×C4C2414yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2418yes—
544C23×C4C2418yes—
545C4⋊Q8—28no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—48no—
550C4⋊Q8—44no—
551C4⋊Q8—48no—
552#127—24no—
553#126—216no—
554#126—416no—
555#126—416no—
556#125—28no—
557#125—416no—
558#125—48no—
559#125—48no—
560#125—416no—
561#125—416no—
562#124—28no—
563#124—28no—
564#124—44no—
565#123—232no—
566#123—416no—
567#123—416no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—216no—
571C22⋊Q8—216no—
572C22⋊Q8—416no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—216no—
577#121—48no—
578#121—48no—
579C4×Q8—24no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—44no—
588C4×Q8—42no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×D4—24no—
593C4×D4—28no—
594C4×D4—24no—
595C4×D4—28no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—44no—
599C4×D4#4118yes—
600#117—28no—
601#117—48no—
602#117—48no—
603#117—44no—
604C2×C4⋊C4—216no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C42—28no—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2411yescharacteristic
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2414yes—
734#95C2412yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765C24C2514yes—
766C24C2512yes—
767#41—832no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q82−1+414yes—
783C2×D4—216no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—42no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—42no—
797C2×D4C2×#4114yes—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—216no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—42no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4C2×#4118yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2518yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—216no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—216no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—42no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—42no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4C2×#4114yes—
897C4⋊C4H(5,𝔽2)14yes—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—216no—
902C22⋊C4—28no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—28no—
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—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4C2×#4118yes—
926C42—28no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—22no—
931C42—28no—
932C42—24no—
933C42—28no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—28no—
944C42—22no—
945C42—41no—
946C42—42no—
947C42—42no—
948C42—44no—
949C42—44no—
950C42—42no—
951C42—48no—
952C42—48no—
953C42C2×#4114yes—
954C42H(5,𝔽2)14yes—
955C422−1+414yes—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23C22×#4114yes—
970C23C2611yescharacteristic
971Q8—28no—
972Q8—48no—
973Q8—416no—
974Q8—44no—
975Q8—84no—
976D4—28no—
977D4—48no—
978D4—48no—
979D4—84no—
980D4—816no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—216no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—48no—
1040C2×C4—416no—
1041C2×C4—48no—
1042C2×C4—816no—
1043C2×C4—168no—
1044C2×C4C22×#4114yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4112yes—
1048C2×C4C2×H(5,𝔽2)14yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4C2×2−1+414yes—
1055C2×C4C2×2−1+412yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4#58512yes—
1059C22—24no—
1060C22—24no—
1061C22—24no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22C23×#4111yescharacteristic
1074C22C22×H(5,𝔽2)11yescharacteristic
1075C22C22×H(5,𝔽2)11yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C22×2−1+411yescharacteristic
1078C22C2×#58511yescharacteristic
1079C222−1+611yescharacteristic
1080C4—24no—
1081C4—22no—
1082C4—24no—
1083C4—22no—
1084C4—24no—
1085C4—22no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—41no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—48no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—44no—
1101C4#350814yes—
1102C4#351514yes—
1103C4#355214yes—
1104C2—44no—
1105C2—84no—
1106C2C2×#355211yescharacteristic
1107C2C2×#351511yescharacteristic
1108C2C2×#350811yescharacteristic
1109C2#6291511yescharacteristic
1110C2#6293111yescharacteristic
1111C2#6300111yescharacteristic
1112C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36179C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59450C2semidirect
3. #59418C2semidirect
4. #59321C2semidirect
5. #50438C2semidirect
6. #46108C2semidirect
7. #45175C2semidirect
8. #45147C2semidirect
9. #42939C2semidirect
10. #42776C2semidirect
11. #40099C2semidirect
12. #39736C2semidirect
13. #39488C2semidirect
14. #39385C2semidirect
15. #38955C2semidirect
16. #36598C2semidirect
17. #36593C2semidirect
18. #36562C2semidirect
19. #36460C2semidirect
21. #35286C2semidirect
22. #35209C2semidirect
23. #34954C2semidirect
24. #34941C2semidirect
25. #34480C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#594502
#594182
#593212
#504382
#461082
#451752
#451472
#429392
#427762
#400992
#397362
#394882
#393852
#389552
#365982
#365932
#365622
#364602
#361792
#352862
#352092
#349542
#349412
#344802
C4×#5562