Finite Group Databasebeta

← #7711341

Subgroups — #7711341

Order 512.

5070 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59869C211yesmaximal, characteristic, complemented
3#59821C211yesmaximal, characteristic, complemented
4#59817C211yesmaximal, characteristic, complemented
5#59302C212yesmaximal, complemented
6#59127C212yesmaximal, complemented
7#46341C214yesmaximal, complemented
8#46091C214yesmaximal, complemented
9#40213C214yesmaximal, complemented
10#40190C214yesmaximal, complemented
11#39192C212yesmaximal, complemented
12#39181C212yesmaximal, complemented
13#38985C212yesmaximal, complemented
14#38954C212yesmaximal, complemented
15#38068C214yesmaximal, complemented
16#38027C214yesmaximal, complemented
17#37628C212yesmaximal, complemented
18#37252C214yesmaximal, complemented
19#36635C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36587C212yesmaximal
22#36579C212yesmaximal, complemented
23#36564C212yesmaximal, complemented
24Q8×#121C212yesmaximal, complemented
25#35083C214yesmaximal, complemented
26#34487C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2214yes—
32C22×C4⋊Q8C2211yescharacteristic
33C2×#529C2212yes—
34C22×C4×Q8C2212yes—
35#2864C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2861C2212yes—
40#2860C2212yes—
41#2860C2212yes—
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2858C2211yescharacteristic
45#2857C2214yes—
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2855C2212yes—
51#2855C2212yes—
52#2854C2212yes—
53#2854C2212yes—
54#2851C2212yes—
55#2850C2214yes—
56#2850C2212yes—
57#2836C2218yes—
58#2809C2214yes—
59#2805C2214yes—
60#2793C2218yes—
61#2775C2218yes—
62#2774C2218yes—
63#2772C2218yes—
64#2770C2218yes—
65#2727C2214yes—
66#2725C2218yes—
67#2716C2218yes—
68#2715C2218yes—
69#2713C2218yes—
70#2700C2218yes—
71#2698C2218yes—
72#2698C2218yes—
73#2698C2218yes—
74#2683C2214yes—
75#2677C2218yes—
76#2654C2218yes—
77#2650C2218yes—
78#2647C2214yes—
79#2644C2214yes—
80#2625C2214yes—
81#2621C2214yes—
82#2597C2218yes—
83#2592C2214yes—
84#2586C2218yes—
85#2581C2214yes—
86#2581C2214yes—
87#2571C2212yes—
88#2571C2212yes—
89#2570C2214yes—
90#2568C2212yes—
91#2568C2214yes—
92#2567C2212yes—
93#2551C2214yes—
94#2551C2212yes—
95#2549C2218yes—
96#2548C2212yes—
97#2546C2214yes—
98#2546C2212yes—
99#2546C2212yes—
100#2542C2212yes—
101#2538C2214yes—
102#2538C2212yes—
103#2538C2212yes—
104#2538C2212yes—
105#2513C2214yes—
106#2513C2214yes—
107#2512C2214yes—
108#2512C2214yes—
109#2512C2214yes—
110#2511C2214yes—
111#2509C2214yes—
112#2509C2214yes—
113#2508C2214yes—
114#2508C2214yes—
115#2507C2214yes—
116#2507C2214yes—
117#2504C2214yes—
118#2499C2214yes—
119#2496C2214yes—
120#2488C2218yes—
121#2481C2218yes—
122#2481C2218yes—
123#2469C2218yes—
124#2452C2214yes—
125#2452C2214yes—
126#2452C2214yes—
127#2451C2214yes—
128#2451C2214yes—
129#2449C2218yes—
130#2448C2214yes—
131#2447C2214yes—
132#2447C2214yes—
133#2444C2218yes—
134#2440C2214yes—
135#2434C2214yes—
136#2429C2218yes—
137#2429C2214yes—
138#2429C2214yes—
139#2421C2214yes—
140#2419C2218yes—
141#2417C2218yes—
142#2417C2214yes—
143#2415C2214yes—
144#2409C2214yes—
145#2409C2214yes—
146#2378C2218yes—
147#2369C2214yes—
148#2369C2212yes—
149#2366C2212yes—
150#2365C2212yes—
151#2362C2214yes—
152#2361C2214yes—
153#2357C2214yes—
154#2355C2212yes—
155#2355C2212yes—
156#2355C2212yes—
157#2354C2212yes—
158#2352C2214yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161#2345C2214yes—
162Q8×C22⋊C4C2214yes—
163#2334C2218yes—
164#2332C2218yes—
165#2331C2214yes—
166#2323C2214yes—
167#2319C2214yes—
168#2310C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×#127C2211yescharacteristic
183C4×#125C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2214yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2214yes—
189C4×#121C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193C2×#391C2212yes—
194#2293C2212yes—
195#2293C2212yes—
196C2×#389C2212yes—
197C2×#389C2212yes—
198C2×#384C2211yescharacteristic
199#2283C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2314yes—
205#556—48no—
206D4×Q8—216no—
207D4×Q8—48no—
208D4×Q8—416no—
209C2×C4⋊Q8—28no—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2314yes—
219C2×C4⋊Q8C2314yes—
220C2×C4⋊Q8C2318yes—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223#529—48no—
224C2×#126C2318yes—
225C2×#126C2314yes—
226C2×#126C2318yes—
227C2×#125C2312yes—
228C2×#125C2312yes—
229C2×#124C2314yes—
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#123C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×C4×Q8—48no—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2318yes—
265C2×C4×D4C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#394C2318yes—
320#393C2318yes—
321#393C2318yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2318yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2314yes—
340#391C2312yes—
341#391C2312yes—
342#391C2318yes—
343#391C2318yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#389C2318yes—
392#389C2312yes—
393#389C2314yes—
394#389C2318yes—
395#389C2318yes—
396#389C2312yes—
397#389C2318yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2318yes—
409#389C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2314yes—
422#388C2318yes—
423#388C2318yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2314yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2314yes—
442#387C2318yes—
443#387C2318yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2318yes—
448#386C2314yes—
449#386C2314yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2314yes—
457#385C2314yes—
458#385C2318yes—
459#385C2318yes—
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2312yes—
465#384C2312yes—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2314yes—
470#384C2314yes—
471#383C2314yes—
472#382C2312yes—
473#382C2314yes—
474#382C2318yes—
475#382C2314yes—
476#382C2314yes—
477#382C2314yes—
478#382C2312yes—
479#382C2312yes—
480#382C2312yes—
481#381C2318yes—
482#381C2318yes—
483#381C2314yes—
484#380C2318yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492#380C2318yes—
493#380C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2314yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2318yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2318yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2314yes—
526#376C2314yes—
527C2×#95C2314yes—
528C2×#95C2314yes—
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C43C2311yescharacteristic
537C22×Q8—28no—
538C22×Q8—216no—
539C22×Q8—28no—
540C22×Q8—44no—
541C22×Q8—48no—
542C22×Q8—48no—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2412yes—
546C22×Q8C2414yes—
547C22×Q8C2412yes—
548C22×Q8C2412yes—
549C22×Q8C2418yes—
550C22×D4C2414yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2414yes—
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2414yes—
564C23×C4C2418yes—
565C4⋊Q8—28no—
566C4⋊Q8—28no—
567C4⋊Q8—28no—
568C4⋊Q8—216no—
569C4⋊Q8—24no—
570C4⋊Q8—24no—
571C4⋊Q8—24no—
572C4⋊Q8—24no—
573C4⋊Q8—48no—
574C4⋊Q8—48no—
575C4⋊Q8—416no—
576C4⋊Q8#4118yes—
577#127—24no—
578#126—48no—
579#126—416no—
580#126—416no—
581#125—44no—
582#125—44no—
583#124—44no—
584#124—44no—
585#124—48no—
586#123—48no—
587C22⋊Q8—216no—
588C22⋊Q8—28no—
589C22⋊Q8—28no—
590C22⋊Q8—232no—
591C22⋊Q8—44no—
592C22⋊Q8—416no—
593C22⋊Q8—416no—
594C22⋊Q8—416no—
595C22⋊Q8—48no—
596C22⋊Q8—48no—
597C22⋊Q8—48no—
598#121—28no—
599#121—28no—
600#121—44no—
601C4×Q8—28no—
602C4×Q8—28no—
603C4×Q8—28no—
604C4×Q8—28no—
605C4×Q8—48no—
606C4×Q8—44no—
607C4×Q8—48no—
608C4×Q8—44no—
609C4×Q8—44no—
610C4×Q8—48no—
611C4×Q8—48no—
612C4×D4—216no—
613C4×D4—216no—
614C4×D4—28no—
615C4×D4—28no—
616C4×D4—48no—
617C4×D4—44no—
618C4×D4—416no—
619#117—48no—
620#117—48no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—48no—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C42—24no—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42—48no—
709C2×C42—42no—
710C2×C42C2411yescharacteristic
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2418yes—
739C2×C42C2418yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2418yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2414yes—
780#95C2418yes—
781#95C2414yes—
782#95C2414yes—
783#95C2418yes—
784#95C2414yes—
785#95C2414yes—
786#95C2418yes—
787#95C2418yes—
788C24C2514yes—
789C24C2511yescharacteristic
790C2×Q8—24no—
791C2×Q8—28no—
792C2×Q8—24no—
793C2×Q8—216no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—24no—
800C2×Q8—28no—
801C2×Q8—24no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—44no—
806C2×Q8—42no—
807C2×Q8—48no—
808C2×Q8—48no—
809C2×Q8—42no—
810C2×Q8—432no—
811C2×Q8—832no—
812C2×Q8C2×#4118yes—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—42no—
824C2×D4—42no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—28no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—28no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—216no—
848C22×C4—44no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4H(5,𝔽2)14yes—
856C22×C42−1+414yes—
857C22×C42−1+414yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2511yescharacteristic
873C22×C4C2514yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—216no—
891C4⋊C4—24no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—28no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—42no—
924C4⋊C4—48no—
925C4⋊C4—42no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—44no—
935C4⋊C4—48no—
936C4⋊C4C2×#4118yes—
937C4⋊C4C2×#4118yes—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—216no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—28no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—22no—
967C42—22no—
968C42—22no—
969C42—28no—
970C42—28no—
971C42—28no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42—22no—
983C42—28no—
984C42—22no—
985C42—22no—
986C42—41no—
987C42—41no—
988C42—44no—
989C42—44no—
990C42—48no—
991C42—48no—
992C42—48no—
993C42C2×#4114yes—
994C42H(5,𝔽2)14yes—
995C422−1+414yes—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23C2×H(5,𝔽2)12yes—
1008C23C2×2−1+412yes—
1009C23C2×2−1+412yes—
1010C23C2611yescharacteristic
1011Q8—216no—
1012Q8—416no—
1013Q8—48no—
1014Q8—48no—
1015Q8—48no—
1016Q8—84no—
1017Q8—816no—
1018D4—416no—
1019D4—48no—
1020D4—48no—
1021D4—84no—
1022C2×C4—28no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—416no—
1087C2×C4—44no—
1088C2×C4—416no—
1089C2×C4—816no—
1090C2×C4—88no—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4118yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4C2×2−1+412yes—
1103C2×C4C2×2−1+412yes—
1104C2×C4C2×2−1+412yes—
1105C2×C4C2×2−1+412yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4#58512yes—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—44no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22—44no—
1119C22—44no—
1120C22—44no—
1121C22#355014yes—
1122C22C23×#4111yescharacteristic
1123C22C22×H(5,𝔽2)11yescharacteristic
1124C22C22×H(5,𝔽2)11yescharacteristic
1125C22C22×2−1+411yescharacteristic
1126C22C22×2−1+411yescharacteristic
1127C22C22×2−1+411yescharacteristic
1128C22C2×#58511yescharacteristic
1129C4—22no—
1130C4—22no—
1131C4—28no—
1132C4—22no—
1133C4—22no—
1134C4—22no—
1135C4—22no—
1136C4—22no—
1137C4—44no—
1138C4—41no—
1139C4—41no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4—41no—
1147C4—41no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4#351914yes—
1152C4#352314yes—
1153C4#355214yes—
1154C2—24no—
1155C2—84no—
1156C2C2×#355211yescharacteristic
1157C2C2×#355011yescharacteristic
1158C2C2×#351911yescharacteristic
1159C2C2×#352311yescharacteristic
1160C2#6278811yescharacteristic
1161C2#6283511yescharacteristic
1162C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59869C2semidirect
3. #59821C2semidirect
4. #59817C2semidirect
5. #59302C2semidirect
6. #59127C2semidirect
7. #46341C2semidirect
8. #46091C2semidirect
9. #40213C2semidirect
10. #40190C2semidirect
11. #39192C2semidirect
12. #39181C2semidirect
13. #38985C2semidirect
14. #38954C2semidirect
15. #38068C2semidirect
16. #38027C2semidirect
17. #37628C2semidirect
18. #37252C2semidirect
19. #36635C2semidirect
22. #36579C2semidirect
23. #36564C2semidirect
24. Q8×#121C2semidirect
25. #35083C2semidirect
26. #34487C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#598692
#598212
#598172
#593022
#591272
#463412
#460912
#402132
#401902
#391922
#391812
#389852
#389542
#380682
#380272
#376282
#372522
#366352
#366312
#365872
#365792
#365642
Q8×#1212
#350832
#344872
C2×C4×C4⋊Q82