Finite Group Databasebeta

← #7687894

Subgroups — #7687894

Order 512.

5141 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59593C214yesmaximal, complemented
3#59377C214yesmaximal, complemented
4#59249C212yesmaximal, complemented
5#59218C212yesmaximal, complemented
6#59034C212yesmaximal, complemented
7#45253C214yesmaximal, complemented
8#43439C218yesmaximal, complemented
9#40195C214yesmaximal, complemented
10#40076C214yesmaximal, complemented
11#39479C212yesmaximal, complemented
12#38920C212yesmaximal, complemented
13#36599C212yesmaximal, complemented
14#36551C212yesmaximal, complemented
15#36505C212yesmaximal, complemented
16#36445C212yesmaximal, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20#35725C214yesmaximal, complemented
21#34976C212yesmaximal, complemented
22#34932C211yesmaximal, characteristic, complemented
23#34243C212yesmaximal, complemented
24#34213C212yesmaximal, complemented
25C4×#547C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#547C2211yescharacteristic
29C2×#547C2211yescharacteristic
30C2×#533C2212yes—
31C2×#529C2212yes—
32C2×C4×#41C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2851C2214yes—
40#2794C2218yes—
41#2783C2218yes—
42#2771C2218yes—
43#2767C2218yes—
44#2754C2218yes—
45#2743C2218yes—
46#2726C2214yes—
47#2718C2218yes—
48#2706C2218yes—
49#2702C2218yes—
50#2696C2218yes—
51#2649C2218yes—
52#2624C2214yes—
53#2609C2218yes—
54#2601C2218yes—
55#2597C2218yes—
56#2596C2218yes—
57#2589C2218yes—
58#2585C2218yes—
59#2582C2212yes—
60#2575C2218yes—
61#2571C2212yes—
62#2571C2212yes—
63#2569C2218yes—
64#2563C2212yes—
65#2563C2212yes—
66#2562C2214yes—
67#2553C2214yes—
68#2552C2212yes—
69#2552C2212yes—
70#2552C2211yescharacteristic
71#2547C2211yescharacteristic
72#2546C2212yes—
73#2542C2214yes—
74#2542C2212yes—
75#2542C2211yescharacteristic
76#2538C2212yes—
77#2538C2212yes—
78#2538C2214yes—
79#2538C2212yes—
80#2537C2211yescharacteristic
81#2536C2214yes—
82#2512C2214yes—
83#2511C2214yes—
84#2509C2214yes—
85#2509C2214yes—
86#2506C2214yes—
87#2497C2214yes—
88#2497C2214yes—
89#2497C2214yes—
90#2496C2212yes—
91#2496C2214yes—
92#2496C2214yes—
93#2492C2214yes—
94#2492C2214yes—
95#2490C2214yes—
96#2489C2214yes—
97#2489C2212yes—
98#2487C2214yes—
99#2485C2214yes—
100#2485C2214yes—
101#2478C2218yes—
102#2475C2218yes—
103#2467C2218yes—
104#2460C2218yes—
105#2458C2218yes—
106#2454C2218yes—
107#2454C2214yes—
108#2453C2214yes—
109#2450C2218yes—
110#2446C2214yes—
111#2446C2214yes—
112#2442C2214yes—
113#2441C2214yes—
114#2441C2214yes—
115#2441C2218yes—
116#2439C2214yes—
117#2439C2214yes—
118#2432C2214yes—
119#2429C2214yes—
120#2427C2212yes—
121#2423C2214yes—
122#2422C2212yes—
123#2421C2214yes—
124#2414C2214yes—
125#2407C2214yes—
126#2407C2214yes—
127#2395C2214yes—
128#2392C2218yes—
129#2370C2214yes—
130#2370C2214yes—
131#2370C2214yes—
132#2369C2212yes—
133#2369C2212yes—
134#2367C2214yes—
135#2365C2212yes—
136#2365C2211yescharacteristic
137#2365C2211yescharacteristic
138#2365C2212yes—
139#2362C2212yes—
140#2362C2214yes—
141#2362C2212yes—
142#2361C2212yes—
143#2361C2212yes—
144#2359C2214yes—
145#2359C2214yes—
146#2359C2218yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2214yes—
150#2355C2218yes—
151#2354C2212yes—
152#2354C2211yescharacteristic
153#2354C2211yescharacteristic
154#2354C2212yes—
155#2354C2212yes—
156#2352C2214yes—
157Q8×C4⋊C4C2214yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2214yes—
163#2345C2214yes—
164#2344C2212yes—
165#2344C2212yes—
166#2341C2214yes—
167#2339C2212yes—
168#2339C2212yes—
169#2334C2218yes—
170#2329C2218yes—
171#2317C2214yes—
172#2314C2214yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×#123C2214yes—
184C4×#123C2214yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2214yes—
189C4×#121C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2274C2214yes—
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201#557—48no—
202#547—28no—
203#547—28no—
204#533—216no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212#529—216no—
213C2×#126C2314yes—
214C2×#126C2318yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2312yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C4×#41—48no—
237C4×#41—48no—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2314yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2318yes—
263C2×C4×D4C2311yescharacteristic
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2312yes—
279C22×C42C2314yes—
280C22×C42C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#399C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#397C2314yes—
301#397C2318yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2318yes—
316#394C2314yes—
317#393C2318yes—
318#393C2318yes—
319#392C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#390C2314yes—
334#390C2314yes—
335#390C2312yes—
336#390C2318yes—
337#390C2318yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2318yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2314yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2314yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2314yes—
434#384C2312yes—
435#384C2312yes—
436#384C2318yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2318yes—
447#382C2314yes—
448#381C2314yes—
449#381C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C2×#95C2314yes—
524C2×#95C2314yes—
525C43C2311yescharacteristic
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2414yes—
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C4⋊Q8—28no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—44no—
559C4⋊Q8—48no—
560C4⋊Q8—82no—
561C4⋊Q8#4118yescomplemented
562#126—216no—
563#126—88no—
564#125—28no—
565#125—216no—
566#125—48no—
567#125—416no—
568#124—28no—
569#123—216no—
570#123—216no—
571#123—216no—
572C22⋊Q8—216no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—28no—
577C22⋊Q8—44no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—84no—
581#121—28no—
582#121—28no—
583#121—28no—
584#121—28no—
585C4×Q8—216no—
586C4×Q8—216no—
587C4×Q8—28no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—44no—
591C4×Q8—44no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×D4—24no—
595C4×D4—216no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—42no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—88no—
610C4×D4#4118yescomplemented
611#117—216no—
612#117—216no—
613#117—48no—
614#117—48no—
615#117—44no—
616#117—44no—
617#117—84no—
618#117—84no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2412yes—
705C2×C42—28no—
706C2×C42—28no—
707C2×C42—28no—
708C2×C42—48no—
709C2×C42—48no—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2418yes—
729C2×C42C2418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2418yes—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#95C2412yes—
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2418yes—
775#95C2414yes—
776#95C2418yes—
777C24C2512yes—
778C24C2512yes—
779C24C2512yes—
780#41—432no—
781#41—432no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8C2×#4118yes—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—28no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4C2×#4114yes—
811C2×D42−1+414yes—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—28no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4C2×#4118yes—
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2518yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—216no—
886C4⋊C4—216no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—28no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—42no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4C2×#4118yes—
924C4⋊C4C2×#4114yes—
925C4⋊C4C2×#4118yes—
926C4⋊C42−1+414yes—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—42no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4C2×#4118yes—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—216no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—22no—
970C42—22no—
971C42—22no—
972C42—44no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—48no—
977C42—48no—
978C42—48no—
979C42—41no—
980C42C2×#4114yes—
981C42C2×#4114yes—
982C42H(5,𝔽2)14yes—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23C22×#4114yes—
1003C23C2×2−1+414yes—
1004C23C2611yescharacteristic
1005Q8—216no—
1006Q8—48no—
1007Q8—48no—
1008Q8—88no—
1009D4—28no—
1010D4—28no—
1011D4—416no—
1012D4—416no—
1013D4—416no—
1014D4—44no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—216no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—28no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—48no—
1071C2×C4—48no—
1072C2×C4—416no—
1073C2×C4—416no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—84no—
1080C2×C4—88no—
1081C2×C4—88no—
1082C2×C4C22×#4112yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4118yes—
1085C2×C4C22×#4114yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×2−1+414yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4#58512yes—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C23×#4111yescharacteristic
1119C22C23×#4111yescharacteristic
1120C22C22×H(5,𝔽2)11yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C22H(7,𝔽2)11yescharacteristic
1125C4—22no—
1126C4—22no—
1127C4—28no—
1128C4—22no—
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—44no—
1133C4—42no—
1134C4—48no—
1135C4—42no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4—42no—
1141C4—41no—
1142C4—44no—
1143C4—44no—
1144C4—42no—
1145C4#348214yes—
1146C4#350614yes—
1147C4#352014yes—
1148C2—44no—
1149C2—44no—
1150C2—82no—
1151C2C2×#348211yescharacteristic
1152C2C2×#350611yescharacteristic
1153C2C2×#352011yescharacteristic
1154C2#6294411yescharacteristic
1155C2#6300011yescharacteristic
1156C2#6300611yescharacteristic
1157C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59828C2semidirect
2. #59593C2semidirect
3. #59377C2semidirect
4. #59249C2semidirect
5. #59218C2semidirect
6. #59034C2semidirect
7. #45253C2semidirect
8. #43439C2semidirect
9. #40195C2semidirect
10. #40076C2semidirect
11. #39479C2semidirect
12. #38920C2semidirect
13. #36599C2semidirect
14. #36551C2semidirect
15. #36505C2semidirect
16. #36445C2semidirect
17. #36194C2semidirect
18. #36194C2semidirect
19. #36134C2semidirect
20. #35725C2semidirect
21. #34976C2semidirect
22. #34932C2semidirect
23. #34243C2semidirect
24. #34213C2semidirect
25. C4×#547C2semidirect
26. C4×#547C2semidirect
561. C4⋊Q8#41semidirect
610. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598282
#595932
#593772
#592492
#592182
#590342
#452532
#434392
#401952
#400762
#394792
#389202
#365992
#365512
#365052
#364452
#361942
#361342
#357252
#349762
#349322
#342432
#342132
C4×#5472