Finite Group Databasebeta

← #7986719

Subgroups — #7986719

Order 512.

4745 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C212yesmaximal, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59459C212yesmaximal, complemented
4#59067C212yesmaximal, complemented
5#51594C218yesmaximal, complemented
6#45500C214yesmaximal, complemented
7#45025C214yesmaximal, complemented
8#44982C214yesmaximal, complemented
9#42494C214yesmaximal
10#42489C214yesmaximal, complemented
11#39641C212yesmaximal, complemented
12#39599C214yesmaximal, complemented
13#39599C212yesmaximal, complemented
14#39180C212yesmaximal, complemented
15#38965C212yesmaximal
16#36593C211yesmaximal, characteristic, complemented
17#36560C211yesmaximal, characteristic, complemented
18#36134C212yesmaximal
19#36134C211yesmaximal, characteristic
20#36133C212yesmaximal, complemented
21#35176C212yesmaximal
22#35173C212yesmaximal, complemented
23#34950C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic
25#34484C212yesmaximal
26C4×#554C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#554C2211yescharacteristic
30C2×#533C2214yes—
31C2×#533C2212yes—
32C2×#533C2212yes—
33#2868C2211yescharacteristic
34#2868C2212yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2214yes—
38#2857C2214yes—
39#2855C2214yes—
40#2841C2218yes—
41#2806C2214yes—
42#2806C2218yes—
43#2802C2218yes—
44#2802C2218yes—
45#2792C2218yes—
46#2791C2218yes—
47#2791C2218yes—
48#2788C2218yes—
49#2768C2218yes—
50#2755C2218yes—
51#2726C2218yes—
52#2726C2218yes—
53#2726C2218yes—
54#2720C2218yes—
55#2704C2218yes—
56#2704C2218yes—
57#2704C2218yes—
58#2667C2218yes—
59#2659C2218yes—
60#2647C2214yes—
61#2629C2214yes—
62#2629C2218yes—
63#2586C2218yes—
64#2586C2214yes—
65#2584C2214yes—
66#2584C2214yes—
67#2584C2218yes—
68#2584C2214yes—
69#2584C2218yes—
70#2584C2214yes—
71#2584C2214yes—
72#2582C2214yes—
73#2582C2211yescharacteristic
74#2582C2218yes—
75#2582C2214yes—
76#2568C2212yes—
77#2567C2214yes—
78#2567C2214yes—
79#2567C2211yescharacteristic
80#2567C2212yes—
81#2567C2211yescharacteristic
82#2565C2214yes—
83#2556C2214yes—
84#2552C2214yes—
85#2552C2212yes—
86#2552C2212yes—
87#2552C2212yes—
88#2552C2212yes—
89#2552C2214yes—
90#2552C2214yes—
91#2552C2214yes—
92#2552C2212yes—
93#2551C2211yescharacteristic
94#2551C2211yescharacteristic
95#2550C2214yes—
96#2546C2212yes—
97#2546C2212yes—
98#2546C2214yes—
99#2546C2212yes—
100#2546C2211yescharacteristic
101#2546C2214yes—
102#2546C2214yes—
103#2542C2212yes—
104#2542C2211yescharacteristic
105#2538C2214yes—
106#2538C2212yes—
107#2538C2211yescharacteristic
108#2522C2218yes—
109#2507C2214yes—
110#2507C2214yes—
111#2507C2212yes—
112#2507C2212yes—
113#2507C2214yes—
114#2507C2214yes—
115#2506C2214yes—
116#2506C2212yes—
117#2506C2214yes—
118#2506C2214yes—
119#2492C2212yes—
120#2462C2218yes—
121#2462C2218yes—
122#2454C2214yes—
123#2453C2214yes—
124#2452C2212yes—
125#2451C2214yes—
126#2451C2214yes—
127#2451C2212yes—
128#2451C2212yes—
129#2446C2214yes—
130#2446C2214yes—
131#2441C2218yes—
132#2441C2214yes—
133#2441C2214yes—
134#2440C2214yes—
135#2438C2218yes—
136#2429C2214yes—
137#2429C2214yes—
138#2429C2214yes—
139#2429C2214yes—
140#2429C2212yes—
141#2423C2214yes—
142#2423C2218yes—
143#2423C2214yes—
144#2399C2214yes—
145#2396C2214yes—
146#2378C2218yes—
147#2370C2214yes—
148#2370C2212yes—
149#2369C2211yescharacteristic
150#2369C2212yes—
151#2368C2214yes—
152#2365C2212yes—
153#2365C2214yes—
154#2365C2212yes—
155#2365C2212yes—
156#2365C2212yes—
157#2362C2214yes—
158#2360C2212yes—
159#2355C2211yescharacteristic
160#2354C2212yes—
161#2354C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2214yes—
166Q8×C4⋊C4C2214yes—
167Q8×C4⋊C4C2212yes—
168#2349C2212yes—
169D4×C4⋊C4C2211yescharacteristic
170#2345C2212yes—
171#2344C2214yes—
172#2330C2214yes—
173#2330C2214yes—
174#2323C2218yes—
175#2323C2214yes—
176#2319C2214yes—
177#2316C2214yes—
178#2316C2214yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2212yes—
187C4×#125C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2214yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199#557—48no—
200#557—48no—
201#554Q8116yescomplemented
202#533—48no—
203#533—48no—
204#533—416no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#125C2318yes—
227C2×#125C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2318yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2318yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C42C2312yes—
268C22×C42C2314yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#399C2318yes—
274#399C2314yes—
275#399C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#395C2318yes—
310#395C2314yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2314yes—
315#395C2318yes—
316#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#393C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2318yes—
336#391C2312yes—
337#391C2314yes—
338#391C2318yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2318yes—
375#389C2314yes—
376#389C2318yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2314yes—
385#389C2318yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2312yes—
390#389C2318yes—
391#389C2318yes—
392#389C2314yes—
393#389C2312yes—
394#389C2314yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2314yes—
401#389C2312yes—
402#389C2314yes—
403#389C2318yes—
404#389C2312yes—
405#389C2312yes—
406#389C2314yes—
407#389C2314yes—
408#389C2312yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2314yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2318yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2314yes—
437#387C2318yes—
438#387C2314yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#384C2311yescharacteristic
445#384C2312yes—
446#384C2312yes—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#384C2318yes—
454#384C2314yes—
455#384C2314yes—
456#384C2314yes—
457#384C2314yes—
458#384C2312yes—
459#384C2312yes—
460#384C2314yes—
461#384C2314yes—
462#382C2312yes—
463#382C2314yes—
464#381C2318yes—
465#380C2318yes—
466#380C2318yes—
467#380C2318yes—
468#380C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2314yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2411yescharacteristic
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2412yes—
533C22×D4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2414yes—
537C23×C4C2412yes—
538C23×C4C2414yes—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—28no—
543C4⋊Q8—28no—
544C4⋊Q8—24no—
545C4⋊Q8—44no—
546C4⋊Q8—44no—
547C4⋊Q8—44no—
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—44no—
551C4⋊Q8—48no—
552C4⋊Q8C2×Q818yes—
553#125—48no—
554#125—48no—
555#125—48no—
556#125—48no—
557#125—416no—
558#125—48no—
559#125—416no—
560#125—416no—
561#125C2×Q8116yes—
562C22⋊Q8—28no—
563C22⋊Q8—416no—
564C22⋊Q8—48no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—48no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C22⋊Q8C2×Q8132yes—
571C22⋊Q8C2×Q8116yes—
572C4×Q8—216no—
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—24no—
576C4×Q8—28no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—44no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—44no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—416no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8C2×Q818yes—
591C4×D4—24no—
592C4×D4—44no—
593C4×D4—42no—
594C4×D4C2×Q8116yes—
595C4×D4C2×Q818yes—
596#117—48no—
597#117—416no—
598#117—48no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4C2×Q8116yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C42—28no—
685C2×C42—48no—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2418yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2418yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2414yes—
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2412yes—
729#95C2414yes—
730#95C2412yes—
731#95C2414yes—
732#95C2414yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2412yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24C2512yes—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—28no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—42no—
777C2×Q8—44no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8C22×Q814yes—
785C2×Q8C22×Q818yes—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4C22×Q814yes—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—28no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4C22×Q818yes—
803C22×C4C22×Q8116yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2514yes—
809C22×C4C2511yescharacteristic
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2518yes—
817C22×C4C2512yes—
818C22×C4C2511yescharacteristic
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—22no—
835C4⋊C4—28no—
836C4⋊C4—216no—
837C4⋊C4—24no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—42no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—42no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4C22×Q814yes—
893C4⋊C4C22×Q8116yes—
894C4⋊C4C22×Q818yes—
895C4⋊C4C22×Q814yes—
896C4⋊C4C22×Q818yes—
897C4⋊C4C22×Q818yes—
898C4⋊C4C22×Q8116yes—
899C4⋊C4H(5,𝔽2)14yes—
900C4⋊C42−1+414yes—
901C22⋊C4—28no—
902C22⋊C4—24no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—44no—
909C22⋊C4—42no—
910C22⋊C4C22×Q8116yes—
911C22⋊C4C22×Q818yes—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—24no—
918C42—216no—
919C42—28no—
920C42—24no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—22no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—22no—
929C42—28no—
930C42—24no—
931C42—44no—
932C42—44no—
933C42—41no—
934C42—42no—
935C42—42no—
936C42—48no—
937C42—48no—
938C42—48no—
939C42C22×Q818yes—
940C42C22×Q814yes—
941C42H(5,𝔽2)14yes—
942C422−1+414yes—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23C23×Q814yes—
950C23C2611yescharacteristic
951Q8—28no—
952Q8—48no—
953Q8—416no—
954Q8—48no—
955Q8—44no—
956Q8—48no—
957Q8—416no—
958Q8—88no—
959D4—28no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—216no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—416no—
1019C2×C4—48no—
1020C2×C4—88no—
1021C2×C4—84no—
1022C2×C4C23×Q814yes—
1023C2×C4C23×Q812yes—
1024C2×C4C23×Q814yes—
1025C2×C4C23×Q814yes—
1026C2×C4C23×Q818yes—
1027C2×C4C23×Q812yes—
1028C2×C4C23×Q812yes—
1029C2×C4C2×H(5,𝔽2)14yes—
1030C2×C4C2×H(5,𝔽2)12yes—
1031C2×C4C2×H(5,𝔽2)12yes—
1032C2×C4C2×H(5,𝔽2)12yes—
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×2−1+414yes—
1035C2×C4C2×2−1+412yes—
1036C2×C4C2×2−1+412yes—
1037C2×C4C2×2−1+412yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4#58512yes—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22C24×Q811yescharacteristic
1048C22C22×H(5,𝔽2)11yescharacteristic
1049C22C22×H(5,𝔽2)11yescharacteristic
1050C22C22×2−1+411yescharacteristic
1051C22C22×2−1+411yescharacteristic
1052C22C2×#58511yescharacteristic
1053C222−1+611yescharacteristic
1054C4—24no—
1055C4—28no—
1056C4—22no—
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—24no—
1061C4—22no—
1062C4—22no—
1063C4—42no—
1064C4—42no—
1065C4—44no—
1066C4—48no—
1067C4—41no—
1068C4—44no—
1069C4—44no—
1070C4—42no—
1071C4—42no—
1072C4—44no—
1073C4—44no—
1074C4—42no—
1075C4—42no—
1076C4#350214yes—
1077C4#350314yes—
1078C4#354814yes—
1079C2—44no—
1080C2C2×#354811yescharacteristic
1081C2C2×#350211yescharacteristic
1082C2C2×#350311yescharacteristic
1083C2#6292511yescharacteristic
1084C2#6294711yescharacteristic
1085C2Q8×H(5,𝔽2)11yescharacteristic
1086C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59871C2semidirect
3. #59459C2semidirect
4. #59067C2semidirect
5. #51594C2semidirect
6. #45500C2semidirect
7. #45025C2semidirect
8. #44982C2semidirect
10. #42489C2semidirect
11. #39641C2semidirect
12. #39599C2semidirect
13. #39599C2semidirect
14. #39180C2semidirect
16. #36593C2semidirect
17. #36560C2semidirect
20. #36133C2semidirect
22. #35173C2semidirect
23. #34950C2semidirect
201. #554Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#594592
#590672
#515942
#455002
#450252
#449822
#424942
#424892
#396412
#395992
#391802
#389652
#365932
#365602
#361342
#361332
#351762
#351732
#349502
#349292
#344842
C4×#5542