Finite Group Databasebeta

← #7699945

Subgroups — #7699945

Order 512.

4843 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59931C218yesmaximal, complemented
2#59922C214yesmaximal, complemented
3#59832C211yesmaximal, characteristic, complemented
4#59655C212yesmaximal
5#59499C214yesmaximal, complemented
6#59467C212yesmaximal, complemented
7#59461C214yesmaximal
8#59067C212yesmaximal, complemented
9#36564C212yesmaximal, complemented
10#36563C211yesmaximal, characteristic, complemented
11#36563C211yesmaximal, characteristic, complemented
12#36555C212yesmaximal
13#36554C214yesmaximal, complemented
14#36497C212yesmaximal, complemented
15#36481C214yesmaximal, complemented
16#36480C212yesmaximal, complemented
17#36407C212yesmaximal
18#36285C212yesmaximal, complemented
19#36283C214yesmaximal, complemented
20#36134C211yesmaximal, characteristic
21C4×Q82C212yesmaximal, complemented
22C4×#557C211yesmaximal, characteristic, complemented
23C4×#554C211yesmaximal, characteristic
24C4×#556C212yesmaximal
25C4×#556C211yesmaximal, characteristic
26#34145C212yesmaximal, complemented
27C2×Q82C2212yes—
28C2×#557C2211yescharacteristic
29C2×#556C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×#533C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2863C2214yes—
35#2863C2218yes—
36#2859C2212yes—
37#2859C2212yes—
38#2857C2212yes—
39#2857C2214yes—
40#2791C2218yes—
41#2768C2218yes—
42#2734C2214yes—
43#2729C2218yes—
44#2720C2218yes—
45#2606C2218yes—
46#2606C2218yes—
47#2605C2218yes—
48#2590C2218yes—
49#2590C2218yes—
50#2589C2218yes—
51#2587C2218yes—
52#2586C2218yes—
53#2585C2218yes—
54#2582C2212yes—
55#2582C2212yes—
56#2582C2212yes—
57#2574C2218yes—
58#2570C2214yes—
59#2567C2212yes—
60#2567C2212yes—
61#2565C2214yes—
62#2556C2218yes—
63#2552C2212yes—
64#2552C2212yes—
65#2552C2214yes—
66#2552C2212yes—
67#2551C2212yes—
68#2551C2212yes—
69#2550C2214yes—
70#2550C2214yes—
71#2550C2214yes—
72#2549C2218yes—
73#2546C2214yes—
74#2542C2212yes—
75#2538C2212yes—
76#2522C2218yes—
77#2522C2218yes—
78#2520C2218yes—
79#2520C2218yes—
80#2509C2214yes—
81#2507C2214yes—
82#2507C2214yes—
83#2507C2214yes—
84#2507C2214yes—
85#2497C2214yes—
86#2492C2214yes—
87#2465C2218yes—
88#2462C2218yes—
89#2462C2218yes—
90#2454C2214yes—
91#2453C2214yes—
92#2453C2214yes—
93#2453C2214yes—
94#2452C2214yes—
95#2451C2214yes—
96#2451C2214yes—
97#2451C2214yes—
98#2451C2214yes—
99#2451C2214yes—
100#2446C2214yes—
101#2441C2214yes—
102#2441C2214yes—
103#2440C2214yes—
104#2439C2214yes—
105#2429C2218yes—
106#2429C2214yes—
107#2429C2214yes—
108#2423C2214yes—
109#2423C2218yes—
110#2423C2214yes—
111#2373C2214yes—
112#2373C2218yes—
113#2370C2214yes—
114#2370C2214yes—
115#2370C2214yes—
116#2370C2214yes—
117#2370C2212yes—
118#2370C2212yes—
119#2369C2218yes—
120#2369C2214yes—
121#2369C2212yes—
122#2369C2212yes—
123#2369C2211yescharacteristic
124#2369C2214yes—
125#2368C2214yes—
126#2368C2218yes—
127#2367C2214yes—
128#2367C2212yes—
129#2365C2212yes—
130#2365C2211yescharacteristic
131#2365C2212yes—
132#2365C2211yescharacteristic
133#2365C2212yes—
134#2365C2212yes—
135#2365C2214yes—
136#2362C2212yes—
137#2362C2214yes—
138#2360C2214yes—
139#2360C2214yes—
140#2360C2212yes—
141#2356C2212yes—
142#2356C2214yes—
143#2355C2212yes—
144#2355C2211yescharacteristic
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2211yescharacteristic
148#2355C2212yes—
149#2354C2212yes—
150#2354C2211yescharacteristic
151#2351C2212yes—
152Q8×C4⋊C4C2212yes—
153Q8×C4⋊C4C2214yes—
154Q8×C4⋊C4C2214yes—
155Q8×C4⋊C4C2211yescharacteristic
156Q8×C4⋊C4C2212yes—
157Q8×C4⋊C4C2212yes—
158#2349C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160#2347C2214yes—
161#2347C2212yes—
162#2345C2212yes—
163#2345C2214yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2218yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2214yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×#125C2212yes—
174C4×#125C2214yes—
175C4×#125C2212yes—
176C4×#126C2218yes—
177C4×#126C2214yes—
178C4×#124C2212yes—
179C4×#124C2214yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2212yes—
184#2296C2214yes—
185#2295C2218yes—
186#2295C2214yes—
187C42×Q8C2214yes—
188C42×Q8C2212yes—
189C42×Q8C2211yescharacteristic
190C42×Q8C2214yes—
191C42×Q8C2212yes—
192C42×Q8C2211yescharacteristic
193C42×Q8C2212yes—
194C42×D4C2211yescharacteristic
195C42×D4C2212yes—
196C4×#117C2212yes—
197C4×#117C2214yes—
198C2×C4×C4⋊C4C2212yes—
199Q82—216no—
200#557—28no—
201#556Q8116yescomplemented
202#554—28no—
203#533—216no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2318yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126C2314yes—
216C2×#125C2312yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2318yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C42C2312yes—
263C22×C42C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#399C2318yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2318yes—
290#393C2318yes—
291#391C2314yes—
292#391C2314yes—
293#391C2318yes—
294#391C2314yes—
295#391C2318yes—
296#391C2318yes—
297#391C2312yes—
298#391C2312yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2318yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#390C2312yes—
315#390C2314yes—
316#389C2312yes—
317#389C2314yes—
318#389C2314yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2314yes—
333#389C2312yes—
334#389C2318yes—
335#389C2314yes—
336#389C2318yes—
337#389C2318yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2318yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#388C2314yes—
366#388C2318yes—
367#388C2314yes—
368#388C2318yes—
369#388C2314yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#387C2314yes—
376#387C2318yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#385C2318yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#384C2314yes—
417#384C2314yes—
418#384C2311yescharacteristic
419#384C2312yes—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2318yes—
424#384C2312yes—
425#384C2314yes—
426#384C2312yes—
427#384C2312yes—
428#383C2318yes—
429#383C2314yes—
430#382C2312yes—
431#382C2312yes—
432#382C2314yes—
433#382C2314yes—
434#382C2314yes—
435#382C2312yes—
436#380C2318yes—
437#380C2314yes—
438#380C2312yes—
439#380C2314yes—
440#380C2314yes—
441#380C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2318yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515#376C2314yes—
516#376C2318yes—
517C2×#95C2314yes—
518C43C2318yes—
519C43C2314yes—
520C43C2312yes—
521C43C2314yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×Q8C2412yes—
531C22×D4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2414yes—
536C23×C4C2412yes—
537C4⋊Q8—28no—
538C4⋊Q8—232no—
539C4⋊Q8—216no—
540C4⋊Q8—216no—
541C4⋊Q8—28no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544C4⋊Q8—82no—
545C4⋊Q8C2×Q818yes—
546C4⋊Q8#4118yes—
547C4⋊Q8#4118yes—
548#126C2×Q8132yes—
549#125—216no—
550#125—28no—
551#125—216no—
552#125—28no—
553#125—48no—
554#125—84no—
555#124C2×Q8116yes—
556C22⋊Q8—216no—
557C22⋊Q8—216no—
558C22⋊Q8—216no—
559C22⋊Q8—28no—
560C22⋊Q8—84no—
561C22⋊Q8—88no—
562C22⋊Q8C2×Q8116yes—
563C4×Q8—216no—
564C4×Q8—28no—
565C4×Q8—216no—
566C4×Q8—28no—
567C4×Q8—216no—
568C4×Q8—216no—
569C4×Q8—28no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—44no—
577C4×Q8—44no—
578C4×Q8—48no—
579C4×Q8—42no—
580C4×Q8—44no—
581C4×Q8—88no—
582C4×Q8—84no—
583C4×Q8C2×Q8116yes—
584C4×Q8C2×Q818yes—
585C4×D4—28no—
586C4×D4—24no—
587C4×D4—44no—
588C4×D4—42no—
589C4×D4C2×Q818yes—
590#117—216no—
591#117—44no—
592#117C2×Q8116yes—
593C2×C4⋊C4—28no—
594C2×C4⋊C4—28no—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2411yescharacteristic
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C42—28no—
670C2×C42—48no—
671C2×C42C2418yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2412yes—
697C2×C42C2418yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#95C2412yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2412yes—
716#95C2418yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2412yes—
723#95C2414yes—
724#95C2412yes—
725#95C2414yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2412yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2512yes—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—28no—
763C2×Q8—216no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—48no—
771C2×Q8—44no—
772C2×Q8—48no—
773C2×Q8—44no—
774C2×Q8C22×Q814yes—
775C2×Q8C22×Q818yes—
776C2×Q8C2×#4118yes—
777C2×Q8C2×#4118yes—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4C22×Q814yes—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—44no—
794C22×C4—42no—
795C22×C4C22×Q818yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2518yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2511yescharacteristic
817C22×C4C2512yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C4⋊C4—22no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—22no—
834C4⋊C4—28no—
835C4⋊C4—216no—
836C4⋊C4—216no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—42no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—42no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—42no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4C22×Q814yes—
874C4⋊C4C22×Q818yes—
875C4⋊C4C22×Q814yes—
876C4⋊C4C22×Q8116yes—
877C4⋊C4C22×Q818yes—
878C4⋊C4C22×Q818yes—
879C4⋊C4C2×#4118yes—
880C4⋊C4C2×#4118yes—
881C4⋊C4C2×#4118yes—
882C4⋊C4C2×#4118yes—
883C4⋊C42−1+414yes—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—44no—
888C22⋊C4—42no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4C22×Q8116yes—
893C22⋊C4C22×Q818yes—
894C22⋊C4C22×Q8116yes—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—216no—
899C42—24no—
900C42—28no—
901C42—24no—
902C42—216no—
903C42—24no—
904C42—28no—
905C42—28no—
906C42—28no—
907C42—24no—
908C42—22no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—24no—
913C42—22no—
914C42—22no—
915C42—24no—
916C42—44no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42—44no—
921C42—42no—
922C42—44no—
923C42—42no—
924C42—48no—
925C42—44no—
926C42—44no—
927C42—42no—
928C42—41no—
929C42C22×Q8116yes—
930C42C22×Q814yes—
931C42C22×Q818yes—
932C42C2×#4114yes—
933C42C2×#4114yes—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23C23×Q814yes—
941C23C2611yescharacteristic
942Q8—28no—
943Q8—216no—
944Q8—216no—
945Q8—48no—
946Q8—44no—
947Q8—816no—
948Q8—88no—
949D4—28no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—24no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—216no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—48no—
1008C2×C4—88no—
1009C2×C4—84no—
1010C2×C4—88no—
1011C2×C4C23×Q814yes—
1012C2×C4C23×Q814yes—
1013C2×C4C23×Q812yes—
1014C2×C4C23×Q818yes—
1015C2×C4C23×Q814yes—
1016C2×C4C23×Q812yes—
1017C2×C4C23×Q812yes—
1018C2×C4C22×#4118yes—
1019C2×C4C22×#4112yes—
1020C2×C4C22×#4118yes—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C2×2−1+414yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4#58512yes—
1029C2×C4#58512yes—
1030C22—24no—
1031C22—24no—
1032C22—24no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22C24×Q811yescharacteristic
1038C22C23×#4111yescharacteristic
1039C22C23×#4111yescharacteristic
1040C22C22×2−1+411yescharacteristic
1041C22C2×#58511yescharacteristic
1042C22C2×#58511yescharacteristic
1043C22H(7,𝔽2)11yescharacteristic
1044C4—28no—
1045C4—22no—
1046C4—24no—
1047C4—22no—
1048C4—22no—
1049C4—24no—
1050C4—24no—
1051C4—24no—
1052C4—28no—
1053C4—28no—
1054C4—42no—
1055C4—44no—
1056C4—44no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—48no—
1061C4—42no—
1062C4—41no—
1063C4—44no—
1064C4—42no—
1065C4—42no—
1066C4Q8×#4114yes—
1067C4Q8×#4114yes—
1068C4#348214yes—
1069C2—44no—
1070C2C2×Q8×#4111yescharacteristic
1071C2C2×Q8×#4111yescharacteristic
1072C2C2×#348211yescharacteristic
1073C2#6299211yescharacteristic
1074C2Q8×2−1+411yescharacteristic
1075C2#6300611yescharacteristic
1076C2#6302511yescharacteristic
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. #59931C2semidirect
2. #59922C2semidirect
3. #59832C2semidirect
5. #59499C2semidirect
6. #59467C2semidirect
8. #59067C2semidirect
9. #36564C2semidirect
10. #36563C2semidirect
11. #36563C2semidirect
13. #36554C2semidirect
14. #36497C2semidirect
15. #36481C2semidirect
16. #36480C2semidirect
18. #36285C2semidirect
19. #36283C2semidirect
21. C4×Q82C2semidirect
22. C4×#557C2semidirect
26. #34145C2semidirect
201. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#599312
#599222
#598322
#596552
#594992
#594672
#594612
#590672
#365642
#365632
#365552
#365542
#364972
#364812
#364802
#364072
#362852
#362832
#361342
C4×Q822
C4×#5572
C4×#5542
C4×#5562
#341452