Finite Group Databasebeta

← #7985286

Subgroups — #7985286

Order 512.

5103 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59864C212yesmaximal, complemented
3#59458C212yesmaximal, complemented
4#59136C212yesmaximal, complemented
5#47965C218yesmaximal, complemented
6#45498C214yesmaximal, complemented
7#45357C214yesmaximal, complemented
8#44908C214yesmaximal, complemented
9#42930C214yesmaximal, complemented
10#42493C214yesmaximal, complemented
11#39634C212yesmaximal, complemented
12#39631C214yesmaximal, complemented
13#39608C212yesmaximal, complemented
14#39498C212yesmaximal, complemented
15#39182C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36559C211yesmaximal, characteristic, complemented
18#36275C212yesmaximal, complemented
19#36261C212yesmaximal, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35279C212yesmaximal, complemented
22#35177C212yesmaximal, complemented
23#34950C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic, complemented
25#34494C212yesmaximal
26C4×#550C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×#554C2214yes—
29C2×#550C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×C4×#41C2212yes—
33#2868C2211yescharacteristic
34#2859C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2214yes—
38#2857C2214yes—
39#2855C2214yes—
40#2841C2218yes—
41#2807C2218yes—
42#2807C2218yes—
43#2805C2218yes—
44#2804C2214yes—
45#2804C2218yes—
46#2788C2218yes—
47#2780C2218yes—
48#2780C2218yes—
49#2768C2218yes—
50#2763C2218yes—
51#2755C2218yes—
52#2732C2218yes—
53#2732C2218yes—
54#2729C2218yes—
55#2692C2218yes—
56#2692C2218yes—
57#2692C2218yes—
58#2665C2218yes—
59#2647C2214yes—
60#2646C2218yes—
61#2628C2214yes—
62#2628C2218yes—
63#2586C2214yes—
64#2584C2214yes—
65#2583C2218yes—
66#2582C2211yescharacteristic
67#2582C2212yes—
68#2580C2214yes—
69#2580C2214yes—
70#2580C2214yes—
71#2580C2218yes—
72#2580C2214yes—
73#2574C2214yes—
74#2571C2212yes—
75#2571C2214yes—
76#2568C2214yes—
77#2567C2211yescharacteristic
78#2567C2211yescharacteristic
79#2567C2211yescharacteristic
80#2567C2212yes—
81#2566C2214yes—
82#2563C2212yes—
83#2563C2212yes—
84#2563C2211yescharacteristic
85#2563C2214yes—
86#2563C2212yes—
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2551C2212yes—
90#2551C2212yes—
91#2551C2211yescharacteristic
92#2550C2214yes—
93#2550C2214yes—
94#2550C2214yes—
95#2549C2218yes—
96#2546C2212yes—
97#2542C2214yes—
98#2538C2212yes—
99#2538C2211yescharacteristic
100#2538C2212yes—
101#2509C2214yes—
102#2508C2214yes—
103#2508C2212yes—
104#2507C2212yes—
105#2507C2212yes—
106#2507C2214yes—
107#2497C2214yes—
108#2497C2212yes—
109#2492C2214yes—
110#2487C2214yes—
111#2487C2214yes—
112#2487C2214yes—
113#2487C2214yes—
114#2487C2214yes—
115#2465C2218yes—
116#2454C2212yes—
117#2454C2214yes—
118#2454C2214yes—
119#2453C2214yes—
120#2452C2214yes—
121#2452C2214yes—
122#2452C2214yes—
123#2452C2214yes—
124#2452C2214yes—
125#2451C2214yes—
126#2451C2212yes—
127#2451C2212yes—
128#2449C2218yes—
129#2449C2218yes—
130#2449C2218yes—
131#2442C2214yes—
132#2441C2214yes—
133#2440C2214yes—
134#2440C2214yes—
135#2440C2214yes—
136#2440C2214yes—
137#2438C2218yes—
138#2434C2214yes—
139#2423C2212yes—
140#2417C2214yes—
141#2417C2214yes—
142#2409C2218yes—
143#2409C2218yes—
144#2399C2214yes—
145#2396C2214yes—
146#2377C2218yes—
147#2369C2212yes—
148#2366C2212yes—
149#2366C2214yes—
150#2366C2211yescharacteristic
151#2366C2212yes—
152#2363C2214yes—
153#2363C2212yes—
154#2361C2214yes—
155#2355C2212yes—
156#2354C2211yescharacteristic
157#2354C2212yes—
158Q8×C4⋊C4C2211yescharacteristic
159Q8×C4⋊C4C2212yes—
160#2349C2214yes—
161D4×C4⋊C4C2214yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2214yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2212yes—
169#2341C2212yes—
170#2339C2214yes—
171#2331C2214yes—
172#2328C2214yes—
173#2325C2218yes—
174#2324C2214yes—
175#2319C2214yes—
176#2317C2214yes—
177#2311C2214yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#127C2212yes—
186C4×#125C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2214yes—
190#2295C2212yes—
191#2295C2212yes—
192#2293C2212yes—
193C2×#389C2214yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#554—48no—
202#554—416no—
203#550Q8116yescomplemented
204D4×Q8—48no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×#127C2312yes—
218C2×#127C2311yescharacteristic
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C4×#41—48no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2318yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×#117C2314yes—
265C2×#117C2312yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2318yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2314yes—
304#396C2318yes—
305#396C2314yes—
306#396C2318yes—
307#396C2318yes—
308#395C2314yes—
309#395C2314yes—
310#395C2314yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2314yes—
316#395C2314yes—
317#395C2318yes—
318#393C2314yes—
319#393C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2318yes—
323#393C2318yes—
324#393C2318yes—
325#391C2312yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2318yes—
335#391C2318yes—
336#391C2312yes—
337#391C2312yes—
338#391C2318yes—
339#391C2314yes—
340#391C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2314yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#390C2312yes—
355#390C2312yes—
356#390C2314yes—
357#390C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2312yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2318yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2312yes—
398#389C2318yes—
399#389C2312yes—
400#389C2318yes—
401#389C2312yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2312yes—
456#384C2314yes—
457#384C2312yes—
458#384C2312yes—
459#384C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2318yes—
465#382C2314yes—
466#382C2314yes—
467#381C2318yes—
468#380C2312yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2318yes—
477#380C2318yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2318yes—
483#380C2318yes—
484#380C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—44no—
526C2×#41—44no—
527C2×#41C2×Q8116yescomplemented
528C22×Q8—48no—
529C22×Q8—48no—
530C22×Q8—84no—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2418yes—
536C22×Q8C2414yes—
537C22×Q8C2414yes—
538C22×D4C2411yescharacteristic
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2418yes—
550C23×C4C2418yes—
551C23×C4C2418yes—
552C23×C4C2414yes—
553C4⋊Q8—216no—
554C4⋊Q8—24no—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—48no—
563C4⋊Q8—82no—
564#127C2×Q8116yes—
565#127C2×Q818yescomplemented
566#125—28no—
567#125—48no—
568#125—48no—
569C22⋊Q8—416no—
570C22⋊Q8—416no—
571C22⋊Q8—416no—
572C22⋊Q8—416no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—48no—
576C22⋊Q8—416no—
577C22⋊Q8—88no—
578#121C2×Q8132yescomplemented
579#121C2×Q8116yescomplemented
580C4×Q8—24no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—48no—
586C4×Q8—42no—
587C4×Q8—42no—
588C4×Q8—44no—
589C4×Q8—84no—
590C4×Q8C2×Q818yescomplemented
591C4×D4—24no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—24no—
596C4×D4—48no—
597C4×D4—44no—
598C4×D4—48no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—44no—
603C4×D4—48no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—84no—
607C4×D4—88no—
608C4×D4C2×Q818yes—
609C4×D4C2×Q8116yescomplemented
610#117—48no—
611#117—48no—
612#117—44no—
613C2×C4⋊C4—48no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—48no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—416no—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2414yes—
701C2×C42—28no—
702C2×C42—48no—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2414yes—
740#95C2412yes—
741#95C2412yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24C2514yes—
771C24C2512yes—
772#41—432no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—24no—
776C2×Q8—216no—
777C2×Q8—28no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—48no—
789C2×Q8—48no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—832no—
794C2×Q8C22×Q814yes—
795C2×D4—22no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—44no—
802C2×D4—42no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—42no—
806C2×D4—44no—
807C2×D4C22×Q814yes—
808C2×D4C22×Q818yes—
809C2×D4C22×Q818yes—
810C2×D4C22×Q8116yes—
811C2×D4C22×Q818yes—
812C2×D4C22×Q8116yes—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—44no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4C22×Q818yes—
839C22×C4C22×Q8116yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2518yes—
852C22×C4C2511yescharacteristic
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C4⋊C4—22no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—28no—
870C4⋊C4—216no—
871C4⋊C4—24no—
872C4⋊C4—22no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—42no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4C22×Q814yes—
921C4⋊C4C22×Q818yes—
922C4⋊C4C22×Q814yes—
923C4⋊C4H(5,𝔽2)14yes—
924C22⋊C4—28no—
925C22⋊C4—24no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—28no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4C22×Q818yes—
946C22⋊C4C22×Q8116yes—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—22no—
953C42—24no—
954C42—24no—
955C42—28no—
956C42—24no—
957C42—24no—
958C42—28no—
959C42—22no—
960C42—24no—
961C42—22no—
962C42—44no—
963C42—44no—
964C42—42no—
965C42—48no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—41no—
970C42C22×Q814yes—
971C42C22×Q818yes—
972C42H(5,𝔽2)14yes—
973C422−1+414yes—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23C23×Q814yes—
987C23C23×Q818yes—
988C23C2611yescharacteristic
989Q8—28no—
990Q8—48no—
991Q8—48no—
992Q8—44no—
993Q8—88no—
994Q8—816no—
995Q8—88no—
996D4—216no—
997D4—28no—
998D4—216no—
999D4—416no—
1000D4—48no—
1001D4—416no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—216no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—28no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—416no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—416no—
1063C2×C4—88no—
1064C2×C4—816no—
1065C2×C4—816no—
1066C2×C4—168no—
1067C2×C4C23×Q812yes—
1068C2×C4C23×Q814yes—
1069C2×C4C23×Q814yes—
1070C2×C4C23×Q814yes—
1071C2×C4C23×Q812yes—
1072C2×C4C23×Q812yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)14yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×2−1+412yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4#58512yes—
1082C2×C4#58512yes—
1083C22—24no—
1084C22—28no—
1085C22—24no—
1086C22—28no—
1087C22—24no—
1088C22—28no—
1089C22—44no—
1090C22—42no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—44no—
1095C22—42no—
1096C22—44no—
1097C22C24×Q811yescharacteristic
1098C22C22×H(5,𝔽2)11yescharacteristic
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×2−1+411yescharacteristic
1101C22C2×#58511yescharacteristic
1102C22C2×#58511yescharacteristic
1103C22H(7,𝔽2)11yescharacteristic
1104C4—22no—
1105C4—24no—
1106C4—24no—
1107C4—24no—
1108C4—22no—
1109C4—24no—
1110C4—22no—
1111C4—42no—
1112C4—44no—
1113C4—42no—
1114C4—41no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—44no—
1121C4—48no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4#350114yes—
1126C4#350314yes—
1127C4#355414yes—
1128C2—44no—
1129C2—48no—
1130C2C2×#355411yescharacteristic
1131C2C2×#350111yescharacteristic
1132C2C2×#350311yescharacteristic
1133C2#6291211yescharacteristic
1134C2#6292611yescharacteristic
1135C2#6298911yescharacteristic
1136C2#6302211yescharacteristic
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. #59864C2semidirect
2. #59864C2semidirect
3. #59458C2semidirect
4. #59136C2semidirect
5. #47965C2semidirect
6. #45498C2semidirect
7. #45357C2semidirect
8. #44908C2semidirect
9. #42930C2semidirect
10. #42493C2semidirect
11. #39634C2semidirect
12. #39631C2semidirect
13. #39608C2semidirect
14. #39498C2semidirect
15. #39182C2semidirect
16. #36563C2semidirect
17. #36559C2semidirect
18. #36275C2semidirect
19. #36261C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35279C2semidirect
22. #35177C2semidirect
23. #34950C2semidirect
24. #34941C2semidirect
203. #550Q8semidirect
527. C2×#41C2×Q8semidirect
565. #127C2×Q8semidirect
578. #121C2×Q8semidirect
579. #121C2×Q8semidirect
590. C4×Q8C2×Q8semidirect
609. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598642
#594582
#591362
#479652
#454982
#453572
#449082
#429302
#424932
#396342
#396312
#396082
#394982
#391822
#365632
#365592
#362752
#362612
D4×C4⋊Q82
#352792
#351772
#349502
#349412
#344942
C4×#5502