Finite Group Databasebeta

← #7699631

Subgroups — #7699631

Order 512.

5121 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59708C218yesmaximal, complemented
3#59557C214yesmaximal, complemented
4#59426C212yesmaximal, complemented
5#59333C214yesmaximal, complemented
6#59302C212yesmaximal, complemented
7#59249C212yesmaximal, complemented
8#59239C214yesmaximal, complemented
9#36598C211yesmaximal, characteristic, complemented
10#36579C212yesmaximal, complemented
11#36489C214yesmaximal, complemented
12#36450C212yesmaximal, complemented
13#36286C212yesmaximal, complemented
14#36274C212yesmaximal, complemented
15#36255C214yesmaximal, complemented
16#36241C214yesmaximal, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36180C211yesmaximal, characteristic, complemented
19#36177C212yesmaximal, complemented
20#36164C212yesmaximal
21C4×#554C212yesmaximal, complemented
22C4×#556C211yesmaximal, characteristic, complemented
23C4×D4×Q8C211yesmaximal, characteristic, complemented
24C4×#547C211yesmaximal, characteristic
25#34127C212yesmaximal, complemented
26C2×#2355C212yesmaximal, complemented
27C2×#556C2211yescharacteristic
28C2×#554C2212yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#547C2211yescharacteristic
31C2×C4×#41C2212yes—
32C22×C4×Q8C2212yes—
33#2868C2211yescharacteristic
34#2863C2214yes—
35#2862C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2852C2218yes—
40#2850C2214yes—
41#2810C2214yes—
42#2793C2218yes—
43#2767C2218yes—
44#2762C2218yes—
45#2759C2218yes—
46#2605C2218yes—
47#2594C2218yes—
48#2592C2214yes—
49#2588C2218yes—
50#2582C2212yes—
51#2581C2214yes—
52#2577C2218yes—
53#2571C2212yes—
54#2571C2212yes—
55#2570C2214yes—
56#2570C2214yes—
57#2568C2212yes—
58#2568C2212yes—
59#2568C2212yes—
60#2568C2212yes—
61#2567C2212yes—
62#2563C2212yes—
63#2552C2212yes—
64#2552C2212yes—
65#2538C2212yes—
66#2533C2218yes—
67#2532C2218yes—
68#2528C2218yes—
69#2524C2218yes—
70#2514C2214yes—
71#2514C2214yes—
72#2514C2214yes—
73#2514C2214yes—
74#2514C2214yes—
75#2512C2214yes—
76#2511C2214yes—
77#2511C2214yes—
78#2510C2218yes—
79#2509C2214yes—
80#2504C2214yes—
81#2503C2214yes—
82#2502C2214yes—
83#2499C2214yes—
84#2497C2214yes—
85#2496C2214yes—
86#2496C2214yes—
87#2494C2214yes—
88#2493C2218yes—
89#2493C2218yes—
90#2493C2218yes—
91#2492C2214yes—
92#2489C2214yes—
93#2489C2214yes—
94#2488C2218yes—
95#2488C2218yes—
96#2481C2218yes—
97#2481C2218yes—
98#2478C2218yes—
99#2469C2218yes—
100#2469C2218yes—
101#2451C2214yes—
102#2450C2218yes—
103#2446C2214yes—
104#2440C2214yes—
105#2440C2214yes—
106#2439C2214yes—
107#2439C2214yes—
108#2438C2218yes—
109#2421C2214yes—
110#2417C2214yes—
111#2409C2214yes—
112#2373C2214yes—
113#2370C2214yes—
114#2369C2212yes—
115#2368C2218yes—
116#2367C2212yes—
117#2365C2211yescharacteristic
118#2365C2211yescharacteristic
119#2365C2211yescharacteristic
120#2365C2212yes—
121#2365C2212yes—
122#2362C2214yes—
123#2362C2212yes—
124#2362C2212yes—
125#2361C2212yes—
126#2360C2214yes—
127#2360C2214yes—
128#2360C2212yes—
129#2359C2214yes—
130#2356C2214yes—
131#2356C2212yes—
132#2355C2214yes—
133#2355C2212yes—
134#2355C2218yes—
135#2355C2211yescharacteristic
136#2355C2212yes—
137#2355C2214yes—
138#2355C2214yes—
139#2355C2214yes—
140#2355C2212yes—
141#2355C2212yes—
142#2355C2212yes—
143#2355C2212yes—
144#2354C2211yescharacteristic
145#2354C2212yes—
146#2354C2211yescharacteristic
147#2352C2214yes—
148#2352C2214yes—
149Q8×C4⋊C4C2211yescharacteristic
150#2349C2214yes—
151D4×C4⋊C4C2211yescharacteristic
152D4×C4⋊C4C2212yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2211yescharacteristic
155D4×C4⋊C4C2212yes—
156#2347C2214yes—
157#2347C2212yes—
158#2345C2214yes—
159#2344C2212yes—
160#2343C2218yes—
161Q8×C22⋊C4C2212yes—
162#2339C2214yes—
163#2339C2214yes—
164#2339C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×C4⋊Q8C2211yescharacteristic
170C4×#125C2214yes—
171C4×#126C2214yes—
172C4×#124C2212yes—
173C4×C22⋊Q8C2218yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2214yes—
179C4×#123C2214yes—
180C4×#121C2212yes—
181#2295C2214yes—
182C2×#391C2214yes—
183#2290C2218yes—
184C2×#387C2218yes—
185#2285C2212yes—
186C2×#384C2212yes—
187#2283C2214yes—
188C2×#382C2214yes—
189C42×Q8C2211yescharacteristic
190C42×Q8C2212yes—
191C42×D4C2212yes—
192C42×D4C2214yes—
193C42×D4C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C4×#117C2212yes—
196C2×C4×C4⋊C4C2214yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2214yes—
199C22×#41C2312yes—
200C23×Q8C2312yes—
201#556—28no—
202#554—216no—
203D4×Q8—28no—
204#547—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#126C2314yes—
213C2×#126C2318yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×#123C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×#121C2312yes—
225C4×#41—216no—
226C2×C4×Q8—216no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2314yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2314yes—
266C22×C42C2314yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2318yes—
270#401C2318yes—
271#401C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#395C2318yes—
294#395C2318yes—
295#393C2318yes—
296#393C2318yes—
297#391C2314yes—
298#391C2312yes—
299#391C2314yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2312yes—
321#391C2318yes—
322#391C2312yes—
323#390C2314yes—
324#390C2312yes—
325#390C2312yes—
326#389C2312yes—
327#389C2314yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2312yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2314yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2314yes—
379#387C2318yes—
380#387C2318yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2314yes—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2312yes—
416#384C2311yescharacteristic
417#384C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#384C2312yes—
422#384C2314yes—
423#384C2314yes—
424#383C2314yes—
425#383C2318yes—
426#383C2318yes—
427#383C2318yes—
428#382C2314yes—
429#382C2314yes—
430#382C2314yes—
431#382C2314yes—
432#382C2314yes—
433#382C2314yes—
434#382C2314yes—
435#382C2314yes—
436#382C2312yes—
437#382C2318yes—
438#382C2318yes—
439#381C2318yes—
440#381C2318yes—
441#381C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2314yes—
448#380C2314yes—
449#380C2312yes—
450#380C2318yes—
451#380C2314yes—
452#380C2312yes—
453#380C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2318yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2318yes—
518C2×#95C2318yes—
519C2×#95C2314yes—
520C2×#95C2318yes—
521C2×#95C2318yes—
522C43C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C2×#41—28no—
526C2×#41—28no—
527C2×#41—28no—
528C22×Q8—28no—
529C22×Q8—28no—
530C22×Q8—44no—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2411yescharacteristic
540C23×C4C2414yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2418yes—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—44no—
557C4⋊Q8—82no—
558#126—216no—
559#126—88no—
560#125—216no—
561#124—28no—
562#123—216no—
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—216no—
566C22⋊Q8—28no—
567C22⋊Q8—216no—
568C22⋊Q8—232no—
569C22⋊Q8—48no—
570#121—28no—
571C4×Q8—28no—
572C4×Q8—28no—
573C4×Q8—216no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—216no—
578C4×Q8—28no—
579C4×Q8—24no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—42no—
583C4×Q8—84no—
584C4×Q8#4118yescomplemented
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—216no—
588C4×D4—24no—
589C4×D4—28no—
590C4×D4—216no—
591C4×D4—24no—
592C4×D4—216no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4#4118yes—
596C4×D4#4118yes—
597#117—28no—
598#117—28no—
599#117—216no—
600#117—44no—
601#117—84no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—216no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—216no—
606C2×C4⋊C4—28no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—84no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C42—216no—
681C2×C42—28no—
682C2×C42—216no—
683C2×C42—28no—
684C2×C42—88no—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2418yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2418yes—
711C2×C42C2418yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718#95C2414yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2412yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2412yes—
742#95C2418yes—
743#95C2412yes—
744#95C2418yes—
745#95C2418yes—
746#95C2412yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2412yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2412yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766C24C2512yes—
767C24C2512yes—
768#41—432no—
769C2×Q8—22no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—28no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—432no—
787C2×Q8C2×#4114yes—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4C2×#4114yes—
795C2×D4C2×#4114yes—
796C2×D42−1+414yes—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—216no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4C2×#4118yes—
829C22×C4C2×#4118yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2511yescharacteristic
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2518yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2512yes—
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—216no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—22no—
889C4⋊C4—48no—
890C4⋊C4—42no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4C2×#4114yes—
902C4⋊C4C2×#4118yes—
903C4⋊C4C2×#4114yes—
904C4⋊C4C2×#4114yes—
905C4⋊C42−1+414yes—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—216no—
909C22⋊C4—28no—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4C2×#4118yes—
924C22⋊C4C2×#4118yes—
925C42—24no—
926C42—28no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—28no—
931C42—24no—
932C42—28no—
933C42—24no—
934C42—28no—
935C42—24no—
936C42—28no—
937C42—28no—
938C42—28no—
939C42—24no—
940C42—24no—
941C42—22no—
942C42—22no—
943C42—24no—
944C42—28no—
945C42—22no—
946C42—44no—
947C42—48no—
948C42—48no—
949C42—48no—
950C42—44no—
951C42—42no—
952C42—42no—
953C42—41no—
954C42C2×#4114yes—
955C42C2×#4114yes—
956C42C2×#4118yes—
957C42C2×#4114yes—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23C22×#4114yes—
970C23C22×#4114yes—
971C23C2×2−1+414yes—
972C23C2611yescharacteristic
973Q8—28no—
974Q8—416no—
975Q8—48no—
976Q8—48no—
977Q8—48no—
978Q8—88no—
979D4—416no—
980D4—44no—
981D4#556116yescomplemented
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—216no—
999C2×C4—216no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—28no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—48no—
1040C2×C4—416no—
1041C2×C4—416no—
1042C2×C4—48no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—48no—
1046C2×C4—48no—
1047C2×C4—816no—
1048C2×C4C22×#4114yes—
1049C2×C4C22×#4114yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4114yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4114yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C2×2−1+414yes—
1062C2×C4C2×2−1+412yes—
1063C2×C4C2×2−1+412yes—
1064C2×C4#58512yes—
1065C22—24no—
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22C2×#55618yes—
1079C22C23×#4111yescharacteristic
1080C22C23×#4111yescharacteristic
1081C22C23×#4111yescharacteristic
1082C22C22×2−1+411yescharacteristic
1083C22C22×2−1+411yescharacteristic
1084C22C2×#58511yescharacteristic
1085C22H(7,𝔽2)11yescharacteristic
1086C4—24no—
1087C4—24no—
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—24no—
1092C4—24no—
1093C4—24no—
1094C4—42no—
1095C4—44no—
1096C4—44no—
1097C4—42no—
1098C4—44no—
1099C4—48no—
1100C4—42no—
1101C4—41no—
1102C4—42no—
1103C4—44no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4C2×#55614yes—
1108C4#347514yes—
1109C4#348214yes—
1110C2—28no—
1111C2—82no—
1112C2C22×#55611yescharacteristic
1113C2C2×#347511yescharacteristic
1114C2C2×#348211yescharacteristic
1115C2#6300011yescharacteristic
1116C2#6300011yescharacteristic
1117C2#6301011yescharacteristic
1118C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59708C2semidirect
3. #59557C2semidirect
4. #59426C2semidirect
5. #59333C2semidirect
6. #59302C2semidirect
7. #59249C2semidirect
8. #59239C2semidirect
9. #36598C2semidirect
10. #36579C2semidirect
11. #36489C2semidirect
12. #36450C2semidirect
13. #36286C2semidirect
14. #36274C2semidirect
15. #36255C2semidirect
16. #36241C2semidirect
17. #36194C2semidirect
18. #36180C2semidirect
19. #36177C2semidirect
21. C4×#554C2semidirect
22. C4×#556C2semidirect
23. C4×D4×Q8C2semidirect
25. #34127C2semidirect
26. C2×#2355C2semidirect
584. C4×Q8#41semidirect
981. D4#556semidirect

Maximal subgroups

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

subgroupindex
#598752
#597082
#595572
#594262
#593332
#593022
#592492
#592392
#365982
#365792
#364892
#364502
#362862
#362742
#362552
#362412
#361942
#361802
#361772
#361642
C4×#5542
C4×#5562
C4×D4×Q82
C4×#5472
#341272
C2×#23552