Finite Group Databasebeta

← #7679717

Subgroups — #7679717

Order 512.

5026 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C212yesmaximal, complemented
2#59864C212yesmaximal, complemented
3#59666C212yesmaximal, complemented
4#59457C212yesmaximal, complemented
5#59454C214yesmaximal, complemented
6#59326C214yesmaximal, complemented
7#45425C214yesmaximal, complemented
8#44966C214yesmaximal, complemented
9#43128C218yesmaximal, complemented
10#38967C212yesmaximal, complemented
11#38964C212yesmaximal, complemented
12#38106C214yesmaximal, complemented
13#38101C214yesmaximal, complemented
14#36416C212yesmaximal, complemented
15#36290C212yesmaximal, complemented
16#35620C212yesmaximal, complemented
17#35519C212yesmaximal, complemented
18#35334C212yesmaximal, complemented
19#35286C211yesmaximal, characteristic, complemented
20C2×#2571C211yesmaximal, characteristic, complemented
21#34938C211yesmaximal, characteristic, complemented
22#34250C212yesmaximal, complemented
23#34207C211yesmaximal, characteristic
24#34206C211yesmaximal, characteristic
25#34141C211yesmaximal, characteristic
26C4×#544C211yesmaximal, characteristic, complemented
27C2×#544C2211yescharacteristic
28C2×#533C2212yes—
29C2×#532C2211yescharacteristic
30C2×#520C2212yes—
31C2×#520C2212yes—
32C2×C4×#41C2212yes—
33#2859C2212yes—
34#2859C2212yes—
35#2851C2214yes—
36#2851C2214yes—
37#2805C2218yes—
38#2804C2218yes—
39#2802C2218yes—
40#2790C2218yes—
41#2788C2218yes—
42#2780C2218yes—
43#2768C2218yes—
44#2763C2218yes—
45#2763C2218yes—
46#2742C2218yes—
47#2742C2218yes—
48#2720C2218yes—
49#2647C2214yes—
50#2628C2214yes—
51#2628C2214yes—
52#2589C2218yes—
53#2589C2218yes—
54#2587C2218yes—
55#2583C2218yes—
56#2582C2214yes—
57#2581C2214yes—
58#2581C2214yes—
59#2581C2214yes—
60#2580C2214yes—
61#2580C2214yes—
62#2580C2214yes—
63#2580C2214yes—
64#2580C2214yes—
65#2574C2218yes—
66#2571C2212yes—
67#2571C2212yes—
68#2571C2212yes—
69#2571C2212yes—
70#2571C2212yes—
71#2571C2214yes—
72#2571C2214yes—
73#2571C2212yes—
74#2568C2214yes—
75#2567C2214yes—
76#2566C2214yes—
77#2566C2214yes—
78#2565C2214yes—
79#2564C2218yes—
80#2564C2218yes—
81#2563C2214yes—
82#2563C2214yes—
83#2552C2212yes—
84#2552C2211yescharacteristic
85#2552C2211yescharacteristic
86#2552C2212yes—
87#2551C2211yescharacteristic
88#2551C2211yescharacteristic
89#2550C2214yes—
90#2550C2212yes—
91#2550C2212yes—
92#2549C2214yes—
93#2538C2214yes—
94#2520C2218yes—
95#2511C2218yes—
96#2509C2214yes—
97#2509C2214yes—
98#2508C2214yes—
99#2507C2214yes—
100#2505C2218yes—
101#2505C2218yes—
102#2487C2218yes—
103#2473C2218yes—
104#2454C2214yes—
105#2452C2214yes—
106#2450C2218yes—
107#2450C2218yes—
108#2450C2218yes—
109#2450C2218yes—
110#2449C2218yes—
111#2442C2214yes—
112#2442C2214yes—
113#2442C2214yes—
114#2442C2214yes—
115#2442C2214yes—
116#2441C2214yes—
117#2440C2214yes—
118#2440C2212yes—
119#2440C2212yes—
120#2439C2214yes—
121#2439C2214yes—
122#2439C2214yes—
123#2399C2214yes—
124C2×#400C2214yes—
125#2370C2214yes—
126#2367C2212yes—
127#2367C2212yes—
128#2367C2214yes—
129#2366C2211yescharacteristic
130#2366C2212yes—
131#2366C2211yescharacteristic
132#2365C2211yescharacteristic
133#2365C2212yes—
134#2365C2211yescharacteristic
135#2364C2214yes—
136#2361C2212yes—
137#2361C2214yes—
138#2361C2212yes—
139#2361C2214yes—
140#2355C2214yes—
141#2354C2212yes—
142#2354C2212yes—
143#2354C2212yes—
144#2352C2214yes—
145#2351C2214yes—
146Q8×C4⋊C4C2214yes—
147#2349C2214yes—
148#2349C2214yes—
149#2349C2218yes—
150D4×C4⋊C4C2212yes—
151D4×C4⋊C4C2212yes—
152D4×C4⋊C4C2218yes—
153D4×C4⋊C4C2214yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2214yes—
156#2331C2212yes—
157#2331C2212yes—
158#2330C2212yes—
159#2330C2212yes—
160#2329C2214yes—
161#2326C2214yes—
162#2325C2214yes—
163#2317C2212yes—
164#2317C2211yescharacteristic
165#2317C2211yescharacteristic
166#2317C2214yes—
167#2316C2211yescharacteristic
168#2316C2212yes—
169#2316C2214yes—
170#2311C2212yes—
171#2311C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×#127C2212yes—
178C4×#125C2212yes—
179C4×#125C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×#121C2214yes—
182#2297C2212yes—
183#2296C2212yes—
184#2296C2214yes—
185#2293C2212yes—
186C2×#389C2212yes—
187C2×#389C2212yes—
188C2×#389C2214yes—
189#2290C2214yes—
190#2285C2211yescharacteristic
191C2×#384C2211yescharacteristic
192C2×#382C2212yes—
193C2×#382C2212yes—
194C42×D4C2212yes—
195C4×#117C2211yescharacteristic
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2312yes—
200#544—28no—
201#533—48no—
202#532Q8116yescomplemented
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#124C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2318yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224#520—216no—
225#520—48no—
226C4×#41—48no—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2318yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2318yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2318yes—
284#399C2318yes—
285#399C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2314yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2314yes—
304#395C2314yes—
305#395C2314yes—
306#395C2314yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2318yes—
320#391C2312yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2312yes—
332#390C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2318yes—
377#389C2318yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2314yes—
410#386C2314yes—
411#386C2314yes—
412#386C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2318yes—
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#382C2312yes—
448#382C2312yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2318yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#382C2318yes—
460#382C2312yes—
461#380C2318yes—
462#380C2318yes—
463#380C2318yes—
464#380C2314yes—
465#380C2318yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2318yes—
472#380C2312yes—
473#380C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2318yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515#376C2312yes—
516#376C2312yes—
517C2×#95C2314yes—
518C2×#95C2314yes—
519C2×#95C2312yes—
520C2×#95C2318yes—
521C2×#95C2314yes—
522C2×#95C2312yes—
523C43C2312yes—
524C43C2312yes—
525C2×#41—28no—
526C2×#41—28no—
527C2×#41C2×Q8116yes—
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×Q8C2414yes—
531C22×Q8C2414yes—
532C22×D4C2412yes—
533C22×D4C2414yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2418yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C4⋊Q8—28no—
550C4⋊Q8—28no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8C2×Q818yes—
556#127C2×Q818yes—
557#125—28no—
558#125—28no—
559#125—48no—
560#125—44no—
561#125—44no—
562#125—84no—
563#124C2×Q8116yes—
564C22⋊Q8—216no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—88no—
568#121C2×Q8116yes—
569#121C2×Q8116yes—
570C4×Q8—216no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×Q8—48no—
577C4×D4—232no—
578C4×D4—216no—
579C4×D4—48no—
580C4×D4—48no—
581C4×D4—44no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—48no—
586C4×D4—48no—
587C4×D4—48no—
588C4×D4—416no—
589C4×D4—84no—
590C4×D4C2×Q8116yes—
591C4×D4C2×Q8116yes—
592#117—24no—
593#117—24no—
594#117—28no—
595#117—24no—
596#117—216no—
597#117—48no—
598#117—48no—
599#117#4118yes—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—216no—
604C2×C4⋊C4—42no—
605C2×C4⋊C4—42no—
606C2×C4⋊C4—44no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—88no—
609C2×C4⋊C4—84no—
610C2×C4⋊C4—82no—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C42—28no—
692C2×C42—48no—
693C2×C42—44no—
694C2×C42C2×Q818yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2418yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766C24C2514yes—
767C24C2511yescharacteristic
768#41—264no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8C22×Q818yes—
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4C22×Q818yes—
790C2×D4C22×Q8116yes—
791C2×D4C22×Q818yes—
792C2×D4C22×Q818yes—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—216no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—42no—
814C22×C4—44no—
815C22×C4—42no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4C22×Q814yes—
827C22×C4C22×Q8116yes—
828C22×C4C22×Q814yes—
829C22×C4C22×Q814yes—
830C22×C4C2×#4114yes—
831C22×C4H(5,𝔽2)14yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2518yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2514yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C4⋊C4—28no—
857C4⋊C4—216no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—42no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4C22×Q818yes—
914C4⋊C4C22×Q818yes—
915C4⋊C4C2×#4114yes—
916C4⋊C4C2×#4114yes—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—216no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4C22×Q8116yes—
934C22⋊C4C22×Q8116yes—
935C22⋊C4C2×#4118yes—
936C42—216no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—28no—
944C42—24no—
945C42—28no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—42no—
954C42—42no—
955C42—48no—
956C42—42no—
957C42—42no—
958C42C22×Q814yes—
959C42C22×Q814yes—
960C42C22×Q814yes—
961C42C22×Q814yes—
962C42C2×#4118yes—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23C23×Q818yes—
974C23C23×Q812yes—
975C23C22×#4112yes—
976C23C2×H(5,𝔽2)12yes—
977C23C2611yescharacteristic
978Q8—216no—
979Q8—88no—
980Q8—88no—
981Q8—88no—
982D4—232no—
983D4—216no—
984D4—216no—
985D4—48no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—232no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—28no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—28no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—44no—
1046C2×C4—816no—
1047C2×C4—84no—
1048C2×C4—88no—
1049C2×C4—84no—
1050C2×C4—84no—
1051C2×C4—84no—
1052C2×C4—88no—
1053C2×C4—88no—
1054C2×C4—168no—
1055C2×C4#554116yes—
1056C2×C4C23×Q812yes—
1057C2×C4C23×Q812yes—
1058C2×C4C23×Q812yes—
1059C2×C4C23×Q818yes—
1060C2×C4C23×Q812yes—
1061C2×C4C23×Q812yes—
1062C2×C4C23×Q812yes—
1063C2×C4C22×#4114yes—
1064C2×C4C22×#4114yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4#58512yes—
1070C2×C4#58512yes—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—28no—
1078C22—28no—
1079C22—28no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22C2×#55414yes—
1085C22C24×Q811yescharacteristic
1086C22C23×#4111yescharacteristic
1087C22C22×H(5,𝔽2)11yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22C2×#58511yescharacteristic
1090C22H(7,𝔽2)11yescharacteristic
1091C222−1+611yescharacteristic
1092C4—24no—
1093C4—24no—
1094C4—22no—
1095C4—22no—
1096C4—22no—
1097C4—28no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—48no—
1102C4—42no—
1103C4—42no—
1104C4—44no—
1105C4—42no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—44no—
1112C4—42no—
1113C4C2×#55414yes—
1114C4C2×#55414yes—
1115C4#350414yes—
1116C2—24no—
1117C2—48no—
1118C2C22×#55411yescharacteristic
1119C2C2×#350411yescharacteristic
1120C2#6285411yescharacteristic
1121C2#6293011yescharacteristic
1122C2#6296011yescharacteristic
1123C2#6299511yescharacteristic
1124C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
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. #59864C2semidirect
3. #59666C2semidirect
4. #59457C2semidirect
5. #59454C2semidirect
6. #59326C2semidirect
7. #45425C2semidirect
8. #44966C2semidirect
9. #43128C2semidirect
10. #38967C2semidirect
11. #38964C2semidirect
12. #38106C2semidirect
13. #38101C2semidirect
14. #36416C2semidirect
15. #36290C2semidirect
16. #35620C2semidirect
17. #35519C2semidirect
18. #35334C2semidirect
19. #35286C2semidirect
20. C2×#2571C2semidirect
21. #34938C2semidirect
22. #34250C2semidirect
26. C4×#544C2semidirect
202. #532Q8semidirect

Maximal subgroups

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

subgroupindex
#598702
#598642
#596662
#594572
#594542
#593262
#454252
#449662
#431282
#389672
#389642
#381062
#381012
#364162
#362902
#356202
#355192
#353342
#352862
C2×#25712
#349382
#342502
#342072
#342062
#341412
C4×#5442