Finite Group Databasebeta

← #7688141

Subgroups — #7688141

Order 512.

5007 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59434C212yesmaximal, complemented
3#59426C212yesmaximal, complemented
4#59293C214yesmaximal, complemented
5#59242C212yesmaximal, complemented
6#59082C214yesmaximal, complemented
7#45147C214yesmaximal, complemented
8#43846C218yesmaximal, complemented
9#40222C214yesmaximal, complemented
10#40077C214yesmaximal, complemented
11#39726C212yesmaximal, complemented
12#39489C212yesmaximal, complemented
13#36593C211yesmaximal, characteristic, complemented
14#36563C211yesmaximal, characteristic, complemented
15#36464C212yesmaximal, complemented
16#36407C212yesmaximal, complemented
17#36194C212yesmaximal, complemented
18#36187C211yesmaximal, characteristic
19#36117C212yesmaximal, complemented
20#35838C214yesmaximal, complemented
21#34932C212yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23#34321C212yesmaximal, complemented
24#34213C212yesmaximal, complemented
25C4×#559C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#559C2211yescharacteristic
28C2×#557C2212yes—
29C2×#555C2212yes—
30C2×#554C2211yescharacteristic
31C2×#533C2212yes—
32C2×#529C2214yes—
33#2868C2212yes—
34#2868C2211yescharacteristic
35#2859C2212yes—
36#2857C2214yes—
37#2856C2212yes—
38#2854C2214yes—
39#2808C2214yes—
40#2787C2218yes—
41#2777C2218yes—
42#2759C2218yes—
43#2738C2218yes—
44#2707C2218yes—
45#2707C2218yes—
46#2687C2218yes—
47#2681C2218yes—
48#2674C2218yes—
49#2674C2218yes—
50#2653C2218yes—
51#2620C2214yes—
52#2594C2218yes—
53#2592C2214yes—
54#2592C2214yes—
55#2582C2212yes—
56#2574C2218yes—
57#2571C2214yes—
58#2567C2212yes—
59#2563C2212yes—
60#2563C2212yes—
61#2558C2218yes—
62#2556C2218yes—
63#2556C2214yes—
64#2553C2218yes—
65#2552C2212yes—
66#2552C2212yes—
67#2552C2212yes—
68#2552C2214yes—
69#2552C2214yes—
70#2551C2211yescharacteristic
71#2550C2214yes—
72#2548C2212yes—
73#2547C2212yes—
74#2546C2212yes—
75#2546C2211yescharacteristic
76#2546C2214yes—
77#2545C2214yes—
78#2542C2211yescharacteristic
79#2538C2214yes—
80#2538C2211yescharacteristic
81#2537C2212yes—
82#2537C2212yes—
83#2525C2218yes—
84#2524C2218yes—
85#2519C2218yes—
86#2518C2218yes—
87#2514C2214yes—
88#2514C2214yes—
89#2513C2214yes—
90#2512C2214yes—
91#2507C2214yes—
92#2506C2212yes—
93#2501C2214yes—
94#2500C2214yes—
95#2499C2214yes—
96#2497C2214yes—
97#2497C2214yes—
98#2496C2214yes—
99#2495C2214yes—
100#2494C2214yes—
101#2492C2212yes—
102#2492C2218yes—
103#2491C2214yes—
104#2491C2214yes—
105#2489C2214yes—
106#2485C2214yes—
107#2479C2218yes—
108#2475C2218yes—
109#2469C2218yes—
110#2460C2218yes—
111#2454C2214yes—
112#2452C2214yes—
113#2452C2212yes—
114#2451C2214yes—
115#2448C2214yes—
116#2441C2214yes—
117#2441C2214yes—
118#2439C2214yes—
119#2439C2218yes—
120#2429C2212yes—
121#2427C2214yes—
122#2426C2214yes—
123#2425C2218yes—
124#2422C2214yes—
125#2422C2214yes—
126#2396C2214yes—
127#2395C2218yes—
128#2374C2214yes—
129#2370C2214yes—
130#2370C2218yes—
131#2370C2212yes—
132#2369C2212yes—
133#2369C2214yes—
134#2369C2211yescharacteristic
135#2368C2214yes—
136#2367C2218yes—
137#2367C2212yes—
138#2367C2212yes—
139#2366C2211yescharacteristic
140#2365C2214yes—
141#2363C2214yes—
142#2361C2214yes—
143#2360C2212yes—
144#2357C2212yes—
145#2357C2212yes—
146#2355C2211yescharacteristic
147#2355C2214yes—
148#2355C2214yes—
149#2355C2211yescharacteristic
150#2355C2212yes—
151#2355C2211yescharacteristic
152#2355C2212yes—
153#2354C2212yes—
154#2354C2214yes—
155#2354C2212yes—
156#2354C2212yes—
157#2354C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2212yes—
161#2349C2212yes—
162D4×C4⋊C4C2211yescharacteristic
163#2347C2214yes—
164#2347C2214yes—
165#2347C2214yes—
166#2345C2212yes—
167#2337C2218yes—
168#2329C2218yes—
169#2324C2214yes—
170#2317C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2211yescharacteristic
177C4×#125C2212yes—
178C4×#124C2212yes—
179C4×#124C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2214yes—
185C4×#123C2214yes—
186C4×#121C2214yes—
187#2296C2214yes—
188#2293C2212yes—
189#2285C2212yes—
190#2285C2214yes—
191#2274C2214yes—
192C42×Q8C2211yescharacteristic
193C42×Q8C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199#559—28no—
200#557—48no—
201#555—216no—
202#554—28no—
203#533—216no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2311yescharacteristic
215#529—416no—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2318yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2318yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2318yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2318yes—
264C2×C4×D4C2311yescharacteristic
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2318yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274C22×C42C2314yes—
275#401C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#399C2314yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#395C2318yes—
304#395C2314yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2312yes—
323#391C2314yes—
324#391C2318yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2318yes—
411#387C2314yes—
412#387C2314yes—
413#386C2318yes—
414#386C2318yes—
415#386C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2312yes—
429#384C2312yes—
430#384C2314yes—
431#384C2314yes—
432#384C2314yes—
433#384C2312yes—
434#384C2314yes—
435#384C2314yes—
436#384C2312yes—
437#384C2312yes—
438#383C2318yes—
439#383C2318yes—
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#382C2318yes—
444#382C2312yes—
445#382C2314yes—
446#382C2312yes—
447#381C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2318yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2314yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C2×#95C2314yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2411yescharacteristic
534C22×D4C2418yes—
535C22×D4C2412yes—
536C23×C4C2414yes—
537C23×C4C2412yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C4⋊Q8—28no—
545C4⋊Q8—28no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—44no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8—82no—
553C4⋊Q8—84no—
554#127—24no—
555#126—416no—
556#125—216no—
557#125—28no—
558#125—216no—
559#125—416no—
560#125—84no—
561#124—28no—
562#124—232no—
563#124—28no—
564#124—48no—
565#123—216no—
566#123—416no—
567#123—88no—
568C22⋊Q8—28no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—216no—
572C22⋊Q8—28no—
573C22⋊Q8—216no—
574C22⋊Q8—88no—
575#121—216no—
576#121—216no—
577#121—48no—
578#121—84no—
579C4×Q8—24no—
580C4×Q8—24no—
581C4×Q8—216no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8#4118yes—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—28no—
599C4×D4—44no—
600C4×D4—42no—
601C4×D4—44no—
602C4×D4—416no—
603C4×D4#4118yes—
604#117—216no—
605#117—216no—
606#117—216no—
607#117—48no—
608#117—416no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4—28no—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C42—28no—
693C2×C42—48no—
694C2×C42—48no—
695C2×C42C2418yes—
696C2×C42C2414yes—
697C2×C42C2411yescharacteristic
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2411yescharacteristic
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2418yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2412yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2418yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767C24C2514yes—
768C24C2512yes—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—28no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—42no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—42no—
785C2×Q8—44no—
786C2×Q8C2×#4114yes—
787C2×D4—216no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—48no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—48no—
801C2×D4C2×#4114yes—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4C2×#4118yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2511yescharacteristic
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2518yes—
838C22×C4C2514yes—
839C22×C4C2511yescharacteristic
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C4⋊C4—22no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—216no—
870C4⋊C4—216no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4C2×#4114yes—
901C4⋊C4C2×#4114yes—
902C4⋊C4C2×#4118yes—
903C4⋊C4H(5,𝔽2)14yes—
904C4⋊C42−1+414yes—
905C22⋊C4—216no—
906C22⋊C4—28no—
907C22⋊C4—216no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—42no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4C2×#4118yes—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—216no—
935C42—28no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—28no—
940C42—24no—
941C42—22no—
942C42—24no—
943C42—22no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—22no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—44no—
953C42—48no—
954C42—48no—
955C42—48no—
956C42—42no—
957C42—41no—
958C42—42no—
959C42C2×#4114yes—
960C42C2×#4118yes—
961C42C2×#4114yes—
962C422−1+414yes—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23C22×#4114yes—
977C23C2611yescharacteristic
978Q8—28no—
979Q8—44no—
980Q8—48no—
981Q8—84no—
982Q8—88no—
983Q8—88no—
984D4—28no—
985D4—48no—
986D4—48no—
987D4—84no—
988D4—816no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—216no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—28no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—28no—
1045C2×C4—416no—
1046C2×C4—416no—
1047C2×C4—48no—
1048C2×C4—84no—
1049C2×C4—88no—
1050C2×C4—88no—
1051C2×C4—88no—
1052C2×C4C22×#4114yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4114yes—
1055C2×C4C22×#4112yes—
1056C2×C4C22×#4114yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C2×H(5,𝔽2)14yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×2−1+414yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4C2×2−1+412yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4#58512yes—
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22C23×#4111yescharacteristic
1084C22C23×#4111yescharacteristic
1085C22C22×H(5,𝔽2)11yescharacteristic
1086C22C22×2−1+411yescharacteristic
1087C22C22×2−1+411yescharacteristic
1088C22C2×#58511yescharacteristic
1089C22H(7,𝔽2)11yescharacteristic
1090C4—22no—
1091C4—22no—
1092C4—24no—
1093C4—24no—
1094C4—24no—
1095C4—24no—
1096C4—22no—
1097C4—24no—
1098C4—42no—
1099C4—44no—
1100C4—48no—
1101C4—42no—
1102C4—42no—
1103C4—44no—
1104C4—41no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C4—42no—
1110C4—42no—
1111C4#348214yes—
1112C4#350714yes—
1113C4#351114yes—
1114C2—44no—
1115C2—84no—
1116C2C2×#348211yescharacteristic
1117C2C2×#350711yescharacteristic
1118C2C2×#351111yescharacteristic
1119C2#6294311yescharacteristic
1120C2#6298611yescharacteristic
1121C2#6299411yescharacteristic
1122C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36187C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59434C2semidirect
3. #59426C2semidirect
4. #59293C2semidirect
5. #59242C2semidirect
6. #59082C2semidirect
7. #45147C2semidirect
8. #43846C2semidirect
9. #40222C2semidirect
10. #40077C2semidirect
11. #39726C2semidirect
12. #39489C2semidirect
13. #36593C2semidirect
14. #36563C2semidirect
15. #36464C2semidirect
16. #36407C2semidirect
17. #36194C2semidirect
19. #36117C2semidirect
20. #35838C2semidirect
21. #34932C2semidirect
22. #34929C2semidirect
23. #34321C2semidirect
24. #34213C2semidirect
25. C4×#559C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#594342
#594262
#592932
#592422
#590822
#451472
#438462
#402222
#400772
#397262
#394892
#365932
#365632
#364642
#364072
#361942
#361872
#361172
#358382
#349322
#349292
#343212
#342132
C4×#5592
C4×#5542