Finite Group Databasebeta

← #7687879

Subgroups — #7687879

Order 512.

5201 conjugacy classes of subgroups.

The subgroup lattice has 1171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C212yesmaximal, complemented
2#59857C214yesmaximal, complemented
3#59821C211yesmaximal, characteristic, complemented
4#59630C214yesmaximal, complemented
5#59234C212yesmaximal, complemented
6#59211C212yesmaximal, complemented
7#45254C214yesmaximal, complemented
8#43393C218yesmaximal, complemented
9#40218C214yesmaximal, complemented
10#40068C214yesmaximal, complemented
11#39725C212yesmaximal, complemented
12#39491C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36587C212yesmaximal, complemented
15#36504C212yesmaximal, complemented
16#36476C212yesmaximal, complemented
17#36405C212yesmaximal, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36187C211yesmaximal, characteristic, complemented
20#35785C214yesmaximal, complemented
21#34976C212yesmaximal, complemented
22#34929C211yesmaximal, characteristic, complemented
23#34321C212yesmaximal, complemented
24#34213C212yesmaximal, complemented
25C4×#550C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#555C2212yes—
29C2×#550C2211yescharacteristic
30C2×#547C2211yescharacteristic
31C2×#533C2212yes—
32C2×C4×#41C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2862C2212yes—
36#2857C2212yes—
37#2856C2212yes—
38#2855C2214yes—
39#2850C2214yes—
40#2808C2218yes—
41#2779C2218yes—
42#2775C2218yes—
43#2770C2218yes—
44#2751C2218yes—
45#2750C2218yes—
46#2727C2214yes—
47#2711C2218yes—
48#2710C2218yes—
49#2710C2218yes—
50#2676C2218yes—
51#2648C2218yes—
52#2619C2214yes—
53#2609C2218yes—
54#2607C2218yes—
55#2597C2218yes—
56#2596C2218yes—
57#2595C2218yes—
58#2593C2218yes—
59#2592C2218yes—
60#2589C2218yes—
61#2582C2212yes—
62#2580C2214yes—
63#2571C2212yes—
64#2571C2212yes—
65#2570C2214yes—
66#2570C2214yes—
67#2568C2212yes—
68#2563C2212yes—
69#2563C2212yes—
70#2556C2214yes—
71#2551C2211yescharacteristic
72#2548C2212yes—
73#2548C2214yes—
74#2547C2214yes—
75#2546C2211yescharacteristic
76#2542C2212yes—
77#2542C2211yescharacteristic
78#2540C2214yes—
79#2538C2212yes—
80#2538C2212yes—
81#2538C2211yescharacteristic
82#2537C2212yes—
83#2537C2212yes—
84#2536C2214yes—
85#2525C2218yes—
86#2513C2214yes—
87#2513C2214yes—
88#2513C2214yes—
89#2512C2214yes—
90#2511C2214yes—
91#2506C2212yes—
92#2504C2214yes—
93#2500C2214yes—
94#2500C2214yes—
95#2497C2214yes—
96#2495C2214yes—
97#2492C2214yes—
98#2492C2214yes—
99#2492C2212yes—
100#2491C2214yes—
101#2491C2214yes—
102#2491C2214yes—
103#2485C2214yes—
104#2485C2214yes—
105#2485C2214yes—
106#2479C2218yes—
107#2478C2218yes—
108#2474C2218yes—
109#2468C2218yes—
110#2467C2218yes—
111#2459C2218yes—
112#2452C2212yes—
113#2448C2214yes—
114#2447C2214yes—
115#2446C2214yes—
116#2444C2218yes—
117#2439C2214yes—
118#2432C2214yes—
119#2429C2212yes—
120#2423C2214yes—
121#2415C2214yes—
122#2415C2214yes—
123#2415C2214yes—
124#2407C2214yes—
125#2407C2214yes—
126#2407C2214yes—
127#2396C2214yes—
128#2392C2218yes—
129#2370C2218yes—
130#2369C2212yes—
131#2369C2214yes—
132#2367C2218yes—
133#2366C2212yes—
134#2366C2211yescharacteristic
135#2365C2214yes—
136#2365C2211yescharacteristic
137#2365C2212yes—
138#2363C2214yes—
139#2363C2214yes—
140#2363C2212yes—
141#2362C2214yes—
142#2362C2212yes—
143#2361C2214yes—
144#2361C2212yes—
145#2359C2214yes—
146#2357C2214yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2214yes—
151#2355C2214yes—
152#2354C2212yes—
153#2354C2212yes—
154#2354C2211yescharacteristic
155#2354C2212yes—
156#2354C2212yes—
157#2354C2211yescharacteristic
158#2354C2212yes—
159#2354C2214yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2211yescharacteristic
162D4×C4⋊C4C2211yescharacteristic
163#2347C2214yes—
164#2347C2214yes—
165#2344C2212yes—
166#2341C2212yes—
167#2339C2212yes—
168#2337C2218yes—
169#2329C2218yes—
170#2324C2214yes—
171#2317C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2212yes—
176C4×#127C2212yes—
177C4×#127C2211yescharacteristic
178C4×C22⋊Q8C2214yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2214yes—
182C4×C22⋊Q8C2214yes—
183C4×#123C2214yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187C4×#121C2214yes—
188C4×#121C2214yes—
189#2296C2214yes—
190#2293C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2274C2214yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201#556—48no—
202#555—216no—
203#550—28no—
204#547—28no—
205#533—216no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2311yescharacteristic
215C2×#127C2312yes—
216C2×#126C2318yes—
217C2×#125C2314yes—
218C2×#124C2318yes—
219C2×#124C2314yes—
220C2×#124C2318yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C4×#41—48no—
238C4×#41—48no—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2318yes—
267C2×C4×D4C2311yescharacteristic
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2312yes—
276C2×#117C2314yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2314yes—
282C22×C42C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#399C2318yes—
289#399C2318yes—
290#399C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2314yes—
303#396C2318yes—
304#396C2314yes—
305#396C2318yes—
306#395C2314yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2314yes—
320#392C2318yes—
321#392C2318yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2318yes—
331#391C2318yes—
332#391C2314yes—
333#391C2312yes—
334#391C2314yes—
335#391C2314yes—
336#391C2312yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2318yes—
348#390C2314yes—
349#390C2318yes—
350#390C2314yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2318yes—
373#389C2314yes—
374#389C2318yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2314yes—
406#388C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#386C2318yes—
429#386C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2312yes—
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#383C2318yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2314yes—
454#382C2314yes—
455#382C2314yes—
456#381C2314yes—
457#381C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2312yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2314yes—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—44no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—44no—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2418yes—
544C22×D4C2412yes—
545C22×D4C2414yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2414yes—
556C23×C4C2412yes—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8—82no—
565#127—24no—
566#127—28no—
567#126—416no—
568#125—216no—
569#124—232no—
570#124—48no—
571#124—88no—
572#123—216no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—28no—
577C22⋊Q8—44no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581#121—216no—
582#121—28no—
583#121—216no—
584#121—216no—
585#121—28no—
586#121—48no—
587#121—84no—
588C4×Q8—216no—
589C4×Q8—28no—
590C4×Q8—24no—
591C4×Q8—28no—
592C4×Q8—42no—
593C4×Q8—44no—
594C4×Q8—44no—
595C4×Q8—48no—
596C4×Q8—84no—
597C4×Q8#4118yescomplemented
598C4×D4—24no—
599C4×D4—28no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—24no—
605C4×D4—28no—
606C4×D4—42no—
607C4×D4—44no—
608C4×D4—44no—
609C4×D4—44no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—88no—
616C4×D4#4118yescomplemented
617#117—216no—
618#117—216no—
619#117—216no—
620#117—48no—
621#117—48no—
622#117—44no—
623#117—44no—
624#117—48no—
625#117—84no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2412yes—
710C2×C42—28no—
711C2×C42—28no—
712C2×C42—48no—
713C2×C42—48no—
714C2×C42C2412yes—
715C2×C42C2418yes—
716C2×C42C2414yes—
717C2×C42C2411yescharacteristic
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2418yes—
732C2×C42C2418yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2412yes—
736C2×C42C2418yes—
737C2×C42C2412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2418yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779C24C2514yes—
780C24C2512yes—
781C24C2512yes—
782#41—432no—
783#41—432no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—28no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8C2×#4114yes—
799C2×D4—28no—
800C2×D4—216no—
801C2×D4—22no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—28no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—28no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—42no—
824C2×D4—44no—
825C2×D4C2×#4114yes—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—28no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—28no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—42no—
858C22×C4C2×#4118yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2518yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2514yes—
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2511yescharacteristic
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—22no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—28no—
910C4⋊C4—24no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—42no—
919C4⋊C4—48no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4C2×#4114yes—
928C4⋊C4C2×#4118yes—
929C4⋊C4C2×#4114yes—
930C4⋊C42−1+414yes—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—24no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—42no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4C2×#4118yes—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—216no—
968C42—28no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—22no—
975C42—24no—
976C42—22no—
977C42—24no—
978C42—22no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42—48no—
984C42—48no—
985C42—42no—
986C42—42no—
987C42—48no—
988C42—41no—
989C42C2×#4114yes—
990C42C2×#4118yes—
991C42C2×#4114yes—
992C42H(5,𝔽2)14yes—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23C22×#4114yes—
1014C23C2611yescharacteristic
1015Q8—28no—
1016Q8—48no—
1017Q8—48no—
1018Q8—88no—
1019Q8—88no—
1020D4—28no—
1021D4—416no—
1022D4—416no—
1023D4—44no—
1024D4—48no—
1025D4—48no—
1026D4—84no—
1027D4—88no—
1028D4—816no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—216no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—28no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—48no—
1084C2×C4—416no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—84no—
1091C2×C4—88no—
1092C2×C4—88no—
1093C2×C4C22×#4114yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4114yes—
1097C2×C4C22×#4114yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×2−1+414yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4#58512yes—
1108C2×C4#58512yes—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—44no—
1117C22—42no—
1118C22—44no—
1119C22—42no—
1120C22—44no—
1121C22—42no—
1122C22—42no—
1123C22—44no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—44no—
1128C22—44no—
1129C22—42no—
1130C22C23×#4111yescharacteristic
1131C22C23×#4111yescharacteristic
1132C22C22×H(5,𝔽2)11yescharacteristic
1133C22C22×2−1+411yescharacteristic
1134C22C2×#58511yescharacteristic
1135C22C2×#58511yescharacteristic
1136C22H(7,𝔽2)11yescharacteristic
1137C4—22no—
1138C4—24no—
1139C4—22no—
1140C4—24no—
1141C4—22no—
1142C4—24no—
1143C4—24no—
1144C4—42no—
1145C4—44no—
1146C4—48no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—44no—
1152C4—44no—
1153C4—41no—
1154C4—42no—
1155C4—44no—
1156C4—42no—
1157C4#348214yes—
1158C4#350614yes—
1159C4#350614yes—
1160C2—44no—
1161C2—84no—
1162C2—82no—
1163C2C2×#348211yescharacteristic
1164C2C2×#350611yescharacteristic
1165C2C2×#350611yescharacteristic
1166C2#6294411yescharacteristic
1167C2#6299411yescharacteristic
1168C2#6301011yescharacteristic
1169C2#6303411yescharacteristic
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. #59863C2semidirect
2. #59857C2semidirect
3. #59821C2semidirect
4. #59630C2semidirect
5. #59234C2semidirect
6. #59211C2semidirect
7. #45254C2semidirect
8. #43393C2semidirect
9. #40218C2semidirect
10. #40068C2semidirect
11. #39725C2semidirect
12. #39491C2semidirect
13. #36598C2semidirect
14. #36587C2semidirect
15. #36504C2semidirect
16. #36476C2semidirect
17. #36405C2semidirect
18. #36194C2semidirect
19. #36187C2semidirect
20. #35785C2semidirect
21. #34976C2semidirect
22. #34929C2semidirect
23. #34321C2semidirect
24. #34213C2semidirect
25. C4×#550C2semidirect
26. C4×#547C2semidirect
597. C4×Q8#41semidirect
616. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598632
#598572
#598212
#596302
#592342
#592112
#452542
#433932
#402182
#400682
#397252
#394912
#365982
#365872
#365042
#364762
#364052
#361942
#361872
#357852
#349762
#349292
#343212
#342132
C4×#5502
C4×#5472