Finite Group Databasebeta

← #7687958

Subgroups — #7687958

Order 512.

5131 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59919C214yesmaximal, complemented
2#59864C212yesmaximal, complemented
3#59864C212yesmaximal, complemented
4#59856C214yesmaximal, complemented
5#59823C211yesmaximal, characteristic, complemented
6#59230C212yesmaximal, complemented
7#45362C214yesmaximal, complemented
8#43143C218yesmaximal, complemented
9#39984C214yesmaximal, complemented
10#39754C212yesmaximal, complemented
11#39666C214yesmaximal, complemented
12#39618C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36544C212yesmaximal, complemented
16#36476C212yesmaximal, complemented
17#36416C212yesmaximal, complemented
18#36275C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#35952C214yesmaximal, complemented
21#34952C212yesmaximal, complemented
22#34950C211yesmaximal, characteristic, complemented
23#34332C212yesmaximal, complemented
24#34330C212yesmaximal
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×#554C2212yes—
29C2×#550C2211yescharacteristic
30C2×D4×Q8C2211yescharacteristic
31C2×C4×#41C2212yes—
32C22×C4×Q8C2212yes—
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2855C2214yes—
38#2851C2214yes—
39#2804C2218yes—
40#2804C2218yes—
41#2802C2218yes—
42#2784C2218yes—
43#2784C2218yes—
44#2780C2218yes—
45#2780C2218yes—
46#2774C2218yes—
47#2732C2214yes—
48#2692C2218yes—
49#2692C2218yes—
50#2665C2218yes—
51#2660C2214yes—
52#2607C2218yes—
53#2589C2218yes—
54#2589C2218yes—
55#2587C2218yes—
56#2586C2214yes—
57#2584C2214yes—
58#2582C2211yescharacteristic
59#2582C2212yes—
60#2581C2214yes—
61#2580C2218yes—
62#2580C2214yes—
63#2580C2214yes—
64#2580C2214yes—
65#2580C2214yes—
66#2580C2214yes—
67#2579C2218yes—
68#2579C2218yes—
69#2574C2218yes—
70#2574C2218yes—
71#2571C2212yes—
72#2571C2212yes—
73#2571C2214yes—
74#2570C2214yes—
75#2570C2214yes—
76#2569C2218yes—
77#2568C2212yes—
78#2567C2211yescharacteristic
79#2567C2211yescharacteristic
80#2566C2214yes—
81#2566C2214yes—
82#2563C2214yes—
83#2563C2214yes—
84#2563C2212yes—
85#2563C2214yes—
86#2563C2212yes—
87#2552C2212yes—
88#2551C2211yescharacteristic
89#2542C2212yes—
90#2538C2212yes—
91#2538C2214yes—
92#2538C2212yes—
93#2538C2212yes—
94#2538C2212yes—
95#2522C2218yes—
96#2511C2214yes—
97#2508C2214yes—
98#2507C2212yes—
99#2507C2212yes—
100#2497C2214yes—
101#2492C2214yes—
102#2492C2214yes—
103#2487C2218yes—
104#2487C2214yes—
105#2487C2214yes—
106#2465C2218yes—
107#2454C2214yes—
108#2453C2214yes—
109#2452C2214yes—
110#2452C2214yes—
111#2451C2212yes—
112#2451C2212yes—
113#2449C2218yes—
114#2449C2218yes—
115#2446C2214yes—
116#2441C2214yes—
117#2439C2214yes—
118#2439C2214yes—
119#2438C2218yes—
120#2423C2214yes—
121#2417C2214yes—
122#2417C2214yes—
123#2417C2214yes—
124#2409C2214yes—
125#2409C2214yes—
126#2399C2214yes—
127#2396C2218yes—
128#2370C2214yes—
129#2369C2212yes—
130#2366C2214yes—
131#2366C2212yes—
132#2366C2212yes—
133#2366C2211yescharacteristic
134#2365C2212yes—
135#2365C2212yes—
136#2365C2211yescharacteristic
137#2364C2218yes—
138#2363C2212yes—
139#2363C2214yes—
140#2363C2214yes—
141#2360C2218yes—
142#2360C2214yes—
143#2360C2214yes—
144#2360C2212yes—
145#2357C2214yes—
146#2355C2212yes—
147#2355C2214yes—
148#2355C2212yes—
149#2355C2212yes—
150#2354C2212yes—
151#2354C2211yescharacteristic
152#2354C2212yes—
153Q8×C4⋊C4C2211yescharacteristic
154Q8×C4⋊C4C2211yescharacteristic
155D4×C4⋊C4C2214yes—
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2212yes—
163#2345C2214yes—
164#2341C2212yes—
165Q8×C22⋊C4C2212yes—
166#2339C2214yes—
167#2333C2218yes—
168#2330C2214yes—
169#2329C2218yes—
170#2328C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×#127C2212yes—
178C4×#127C2211yescharacteristic
179C4×#127C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186C4×#121C2214yes—
187#2297C2214yes—
188#2296C2214yes—
189#2295C2212yes—
190#2295C2212yes—
191C2×#389C2214yes—
192#2285C2212yes—
193#2275C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C42×D4C2211yescharacteristic
199C22×#41C2312yes—
200C23×Q8C2312yes—
201#554—216no—
202#554—48no—
203#550Q8116yescomplemented
204D4×Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2312yes—
214C2×#127C2311yescharacteristic
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×#121C2314yes—
226C2×#121C2312yes—
227C4×#41—48no—
228C2×C4×Q8—48no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×#117C2314yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2318yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274C22×C42C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2318yes—
291#398C2314yes—
292#398C2314yes—
293#398C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2314yes—
302#395C2314yes—
303#395C2314yes—
304#395C2318yes—
305#395C2318yes—
306#395C2314yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2318yes—
330#391C2314yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2318yes—
348#390C2314yes—
349#390C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2318yes—
376#389C2314yes—
377#389C2318yes—
378#389C2314yes—
379#389C2318yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#386C2314yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2318yes—
432#385C2314yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2311yescharacteristic
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2318yes—
455#382C2314yes—
456#382C2314yes—
457#381C2318yes—
458#380C2318yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2318yes—
467#380C2314yes—
468#380C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2314yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—44no—
526C2×#41—44no—
527C2×#41C2×Q8116yescomplemented
528C22×Q8—28no—
529C22×Q8—44no—
530C22×Q8—44no—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C23×C4C2418yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—82no—
562#127C2×Q8116yes—
563#127C2×Q818yescomplemented
564#125—216no—
565#125—48no—
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—216no—
569C22⋊Q8—232no—
570C22⋊Q8—416no—
571C22⋊Q8—48no—
572C22⋊Q8—48no—
573C22⋊Q8—84no—
574#121C2×Q8132yescomplemented
575#121C2×Q8116yescomplemented
576C4×Q8—24no—
577C4×Q8—28no—
578C4×Q8—24no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—44no—
582C4×Q8—48no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—42no—
586C4×Q8—42no—
587C4×Q8—44no—
588C4×Q8—84no—
589C4×Q8C2×Q818yescomplemented
590C4×Q8#4118yescomplemented
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—48no—
597C4×D4—44no—
598C4×D4—44no—
599C4×D4—42no—
600C4×D4—48no—
601C4×D4—44no—
602C4×D4—48no—
603C4×D4—44no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—84no—
608C4×D4—88no—
609C4×D4C2×Q818yes—
610C4×D4C2×Q8116yescomplemented
611#117—48no—
612#117—48no—
613#117—44no—
614C2×C4⋊C4—216no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—88no—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2414yes—
698C2×C42—28no—
699C2×C42—48no—
700C2×C42—48no—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2414yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2412yes—
746#95C2418yes—
747#95C2412yes—
748#95C2412yes—
749#95C2414yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2514yes—
772C24C2512yes—
773#41—432no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—28no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—42no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—42no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—432no—
794C2×Q8C22×Q814yes—
795C2×Q8C2×#4114yes—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4C22×Q814yes—
809C2×D4C22×Q818yes—
810C2×D4C22×Q818yes—
811C2×D4C22×Q8116yes—
812C2×D4C22×Q818yes—
813C2×D4C22×Q8116yes—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—216no—
824C22×C4—24no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—42no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4C22×Q818yes—
843C22×C4C22×Q8116yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2518yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2511yescharacteristic
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2511yescharacteristic
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—216no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—216no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—22no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—42no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4C22×Q814yes—
921C4⋊C4C22×Q818yes—
922C4⋊C4C22×Q814yes—
923C4⋊C4C2×#4114yes—
924C4⋊C4C2×#4118yes—
925C22⋊C4—28no—
926C22⋊C4—216no—
927C22⋊C4—24no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—42no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4C22×Q818yes—
946C22⋊C4C22×Q8116yes—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—28no—
953C42—22no—
954C42—24no—
955C42—24no—
956C42—22no—
957C42—28no—
958C42—24no—
959C42—24no—
960C42—22no—
961C42—44no—
962C42—44no—
963C42—44no—
964C42—44no—
965C42—48no—
966C42—42no—
967C42—48no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—41no—
972C42C22×Q814yes—
973C42C22×Q818yes—
974C42C2×#4118yes—
975C42C2×#4114yes—
976C42H(5,𝔽2)14yes—
977C23—24no—
978C23—22no—
979C23—24no—
980C23—22no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23C23×Q814yes—
990C23C23×Q818yes—
991C23C2611yescharacteristic
992Q8—28no—
993Q8—28no—
994Q8—416no—
995Q8—48no—
996Q8—88no—
997Q8—84no—
998Q8—88no—
999D4—28no—
1000D4—216no—
1001D4—216no—
1002D4—416no—
1003D4—48no—
1004D4—416no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—216no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—28no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—416no—
1062C2×C4—416no—
1063C2×C4—416no—
1064C2×C4—48no—
1065C2×C4—816no—
1066C2×C4—84no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4—168no—
1070C2×C4C23×Q812yes—
1071C2×C4C23×Q814yes—
1072C2×C4C23×Q814yes—
1073C2×C4C23×Q814yes—
1074C2×C4C23×Q812yes—
1075C2×C4C23×Q812yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4114yes—
1078C2×C4C22×#4114yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4#58512yes—
1085C2×C4#58512yes—
1086C2×C4#58512yes—
1087C22—28no—
1088C22—24no—
1089C22—24no—
1090C22—28no—
1091C22—24no—
1092C22—28no—
1093C22—44no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—42no—
1098C22—44no—
1099C22—42no—
1100C22—44no—
1101C22C24×Q811yescharacteristic
1102C22C23×#4111yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C2×#58511yescharacteristic
1105C22C2×#58511yescharacteristic
1106C22C2×#58511yescharacteristic
1107C22H(7,𝔽2)11yescharacteristic
1108C4—22no—
1109C4—24no—
1110C4—24no—
1111C4—22no—
1112C4—24no—
1113C4—24no—
1114C4—24no—
1115C4—22no—
1116C4—48no—
1117C4—44no—
1118C4—42no—
1119C4—44no—
1120C4—41no—
1121C4—44no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—44no—
1128C4—44no—
1129C4Q8×#4114yes—
1130C4#350114yes—
1131C4#350614yes—
1132C2—44no—
1133C2—48no—
1134C2C2×Q8×#4111yescharacteristic
1135C2C2×#350111yescharacteristic
1136C2C2×#350611yescharacteristic
1137C2#6293011yescharacteristic
1138C2#6298911yescharacteristic
1139C2#6301011yescharacteristic
1140C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59919C2semidirect
2. #59864C2semidirect
3. #59864C2semidirect
4. #59856C2semidirect
5. #59823C2semidirect
6. #59230C2semidirect
7. #45362C2semidirect
8. #43143C2semidirect
9. #39984C2semidirect
10. #39754C2semidirect
11. #39666C2semidirect
12. #39618C2semidirect
13. #36598C2semidirect
14. #36559C2semidirect
15. #36544C2semidirect
16. #36476C2semidirect
17. #36416C2semidirect
18. #36275C2semidirect
19. #36194C2semidirect
20. #35952C2semidirect
21. #34952C2semidirect
22. #34950C2semidirect
23. #34332C2semidirect
25. C4×D4×Q8C2semidirect
203. #550Q8semidirect
527. C2×#41C2×Q8semidirect
563. #127C2×Q8semidirect
574. #121C2×Q8semidirect
575. #121C2×Q8semidirect
589. C4×Q8C2×Q8semidirect
590. C4×Q8#41semidirect
610. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599192
#598642
#598562
#598232
#592302
#453622
#431432
#399842
#397542
#396662
#396182
#365982
#365592
#365442
#364762
#364162
#362752
#361942
#359522
#349522
#349502
#343322
#343302
C4×D4×Q82
C4×#5502