Finite Group Databasebeta

← #7688152

Subgroups — #7688152

Order 512.

5355 conjugacy classes of subgroups.

The subgroup lattice has 1165 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59415C214yesmaximal, complemented
3#59398C214yesmaximal, complemented
4#59234C212yesmaximal, complemented
5#59125C212yesmaximal, complemented
6#59042C212yesmaximal, complemented
7#44917C214yesmaximal, complemented
8#44441C218yesmaximal, complemented
9#40190C214yesmaximal, complemented
10#40078C214yesmaximal, complemented
11#39481C212yesmaximal, complemented
12#38922C212yesmaximal, complemented
13#36564C212yesmaximal, complemented
14#36481C212yesmaximal, complemented
15#36449C212yesmaximal, complemented
16#36444C212yesmaximal, complemented
17#36188C211yesmaximal, characteristic, complemented
18#36134C211yesmaximal, characteristic, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35989C214yesmaximal, complemented
21#34979C212yesmaximal, complemented
22#34932C211yesmaximal, characteristic, complemented
23#34243C212yesmaximal, complemented
24#34216C212yesmaximal, complemented
25C4×#555C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#555C2211yescharacteristic
29C2×D4×Q8C2212yes—
30C2×#548C2214yes—
31C2×#547C2211yescharacteristic
32C2×#533C2212yes—
33C22×C4⋊Q8C2212yes—
34C2×#529C2212yes—
35C2×C4×#41C2212yes—
36#2868C2211yescharacteristic
37#2863C2214yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2214yes—
42#2805C2214yes—
43#2775C2218yes—
44#2774C2218yes—
45#2773C2218yes—
46#2770C2218yes—
47#2741C2218yes—
48#2715C2218yes—
49#2698C2218yes—
50#2690C2218yes—
51#2674C2218yes—
52#2672C2218yes—
53#2650C2218yes—
54#2624C2214yes—
55#2611C2218yes—
56#2606C2218yes—
57#2597C2218yes—
58#2586C2218yes—
59#2581C2214yes—
60#2578C2218yes—
61#2571C2212yes—
62#2568C2212yes—
63#2568C2212yes—
64#2567C2212yes—
65#2559C2218yes—
66#2553C2214yes—
67#2552C2212yes—
68#2552C2211yescharacteristic
69#2551C2212yes—
70#2551C2212yes—
71#2549C2218yes—
72#2547C2212yes—
73#2547C2212yes—
74#2547C2214yes—
75#2547C2211yescharacteristic
76#2546C2212yes—
77#2542C2212yes—
78#2542C2211yescharacteristic
79#2538C2212yes—
80#2537C2214yes—
81#2537C2211yescharacteristic
82#2536C2214yes—
83#2530C2218yes—
84#2522C2218yes—
85#2521C2218yes—
86#2513C2214yes—
87#2511C2214yes—
88#2509C2214yes—
89#2507C2214yes—
90#2507C2214yes—
91#2499C2214yes—
92#2499C2214yes—
93#2496C2214yes—
94#2496C2214yes—
95#2496C2212yes—
96#2495C2214yes—
97#2492C2214yes—
98#2491C2214yes—
99#2489C2212yes—
100#2485C2214yes—
101#2477C2218yes—
102#2474C2218yes—
103#2468C2218yes—
104#2451C2214yes—
105#2443C2218yes—
106#2441C2214yes—
107#2441C2214yes—
108#2440C2214yes—
109#2440C2214yes—
110#2440C2214yes—
111#2434C2214yes—
112#2432C2214yes—
113#2429C2214yes—
114#2429C2214yes—
115#2427C2212yes—
116#2427C2214yes—
117#2427C2214yes—
118#2427C2218yes—
119#2423C2214yes—
120#2423C2214yes—
121#2422C2212yes—
122#2421C2214yes—
123#2416C2214yes—
124#2415C2214yes—
125#2415C2214yes—
126#2415C2214yes—
127#2415C2218yes—
128#2409C2214yes—
129#2395C2214yes—
130#2395C2218yes—
131#2372C2214yes—
132#2370C2214yes—
133#2369C2214yes—
134#2369C2211yescharacteristic
135#2369C2214yes—
136#2367C2214yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2212yes—
140#2365C2211yescharacteristic
141#2365C2212yes—
142#2363C2212yes—
143#2363C2212yes—
144#2362C2212yes—
145#2361C2212yes—
146#2359C2218yes—
147#2359C2214yes—
148#2355C2212yes—
149#2354C2212yes—
150#2354C2211yescharacteristic
151#2354C2211yescharacteristic
152#2354C2211yescharacteristic
153#2352C2214yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2211yescharacteristic
159D4×C4⋊C4C2214yes—
160#2347C2214yes—
161#2346C2212yes—
162#2346C2212yes—
163#2345C2218yes—
164#2345C2214yes—
165#2344C2212yes—
166Q8×C22⋊C4C2214yes—
167Q8×C22⋊C4C2214yes—
168#2339C2212yes—
169#2334C2218yes—
170#2331C2218yes—
171#2316C2214yes—
172#2314C2214yes—
173C4×C4⋊Q8C2214yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×C4⋊Q8C2214yes—
178C4×#124C2214yes—
179C4×#124C2214yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×#123C2214yes—
185C4×#121C2214yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192#2274C2214yes—
193C42×D4C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C4×#117C2212yes—
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#556—48no—
202#555—28no—
203D4×Q8—48no—
204#548—416no—
205#547—28no—
206#533—48no—
207C2×C4⋊Q8—216no—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2311yescharacteristic
218#529—216no—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2318yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2318yes—
245C4×#41—48no—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2311yescharacteristic
270C2×#117C2314yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2314yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2314yes—
292#400C2318yes—
293#399C2314yes—
294#399C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2314yes—
322#394C2318yes—
323#394C2318yes—
324#394C2314yes—
325#393C2318yes—
326#391C2312yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2318yes—
340#391C2318yes—
341#391C2318yes—
342#391C2314yes—
343#391C2312yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#390C2312yes—
350#389C2318yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2318yes—
355#389C2318yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2314yes—
380#389C2318yes—
381#389C2312yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2314yes—
399#388C2314yes—
400#388C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#386C2314yes—
419#386C2318yes—
420#386C2314yes—
421#386C2314yes—
422#386C2318yes—
423#386C2314yes—
424#386C2314yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2314yes—
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#383C2318yes—
445#382C2314yes—
446#382C2314yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#381C2314yes—
451#380C2312yes—
452#380C2314yes—
453#380C2318yes—
454#380C2318yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2314yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2314yes—
469#380C2312yes—
470#380C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523#376C2314yes—
524#376C2314yes—
525C2×#95C2314yes—
526C43C2311yescharacteristic
527C43C2314yes—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—44no—
531C22×Q8—216no—
532C22×Q8—48no—
533C22×Q8—48no—
534C22×Q8C2412yes—
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2418yes—
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2411yescharacteristic
543C22×D4C2411yescharacteristic
544C22×D4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2418yes—
556C23×C4C2414yes—
557C4⋊Q8—216no—
558C4⋊Q8—216no—
559C4⋊Q8—216no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—28no—
564C4⋊Q8—48no—
565C4⋊Q8—44no—
566C4⋊Q8#4118yes—
567#126—216no—
568#126—416no—
569#125—28no—
570#125—48no—
571#124—28no—
572#124—216no—
573#124—216no—
574#124—416no—
575#123—216no—
576#123—216no—
577C22⋊Q8—28no—
578C22⋊Q8—28no—
579C22⋊Q8—28no—
580C22⋊Q8—416no—
581C22⋊Q8—48no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587#121—28no—
588#121—28no—
589#121—28no—
590#121—28no—
591#121—28no—
592#121—416no—
593C4×Q8—28no—
594C4×Q8—28no—
595C4×Q8—44no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×D4—24no—
602C4×D4—216no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—416no—
616C4×D4#4118yescomplemented
617#117—216no—
618#117—28no—
619#117—28no—
620#117—28no—
621#117—28no—
622#117—48no—
623#117—48no—
624#117—44no—
625#117—48no—
626C2×C4⋊C4—216no—
627C2×C4⋊C4—216no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2412yes—
711C2×C42—28no—
712C2×C42—28no—
713C2×C42—28no—
714C2×C42—48no—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2414yes—
734C2×C42C2418yes—
735C2×C42C2418yes—
736C2×C42C2418yes—
737C2×C42C2414yes—
738C2×C42C2411yescharacteristic
739C2×C42C2414yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779#95C2414yes—
780#95C2418yes—
781#95C2414yes—
782#95C2418yes—
783C24C2512yes—
784C24C2512yes—
785C24C2512yes—
786#41—432no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—24no—
790C2×Q8—216no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—28no—
795C2×Q8—28no—
796C2×Q8—24no—
797C2×Q8—42no—
798C2×Q8—48no—
799C2×Q8—48no—
800C2×Q8—42no—
801C2×Q8—832no—
802C2×Q8C2×#4118yes—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—28no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4C2×#4114yes—
820C2×D4H(5,𝔽2)14yes—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—216no—
847C22×C4—28no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—44no—
856C22×C4C2×#4118yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2518yes—
870C22×C4C2511yescharacteristic
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2514yes—
874C22×C4C2511yescharacteristic
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—216no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—22no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—48no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4C2×#4118yes—
927C4⋊C4C2×#4118yes—
928C4⋊C4C2×#4114yes—
929C4⋊C42−1+414yes—
930C4⋊C42−1+414yes—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—28no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4C2×#4118yes—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—22no—
974C42—28no—
975C42—28no—
976C42—28no—
977C42—22no—
978C42—22no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—41no—
983C42—48no—
984C42—48no—
985C42—48no—
986C42C2×#4114yes—
987C42C2×#4114yes—
988C42H(5,𝔽2)14yes—
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—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23C22×#4114yes—
1009C23C2×H(5,𝔽2)14yes—
1010C23C2611yescharacteristic
1011Q8—216no—
1012Q8—48no—
1013Q8—416no—
1014Q8—84no—
1015Q8—816no—
1016D4—28no—
1017D4—28no—
1018D4—416no—
1019D4—416no—
1020D4—44no—
1021D4—88no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—216no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—21no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—416no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—88no—
1086C2×C4—816no—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4114yes—
1090C2×C4C22×#4118yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×2−1+414yes—
1100C2×C4C2×2−1+414yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4C2×2−1+412yes—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22C23×#4111yescharacteristic
1125C22C23×#4111yescharacteristic
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×2−1+411yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C222−1+611yescharacteristic
1131C4—22no—
1132C4—22no—
1133C4—24no—
1134C4—28no—
1135C4—22no—
1136C4—24no—
1137C4—24no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C4—42no—
1142C4—42no—
1143C4—48no—
1144C4—44no—
1145C4—41no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—44no—
1150C4—42no—
1151C4#348214yes—
1152C4#351114yes—
1153C4#351914yes—
1154C2—44no—
1155C2—44no—
1156C2—82no—
1157C2C2×#348211yescharacteristic
1158C2C2×#351911yescharacteristic
1159C2C2×#351111yescharacteristic
1160C2#6294211yescharacteristic
1161C2#6298511yescharacteristic
1162C2#6299811yescharacteristic
1163C2#6303711yescharacteristic
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. #59870C2semidirect
2. #59415C2semidirect
3. #59398C2semidirect
4. #59234C2semidirect
5. #59125C2semidirect
6. #59042C2semidirect
7. #44917C2semidirect
8. #44441C2semidirect
9. #40190C2semidirect
10. #40078C2semidirect
11. #39481C2semidirect
12. #38922C2semidirect
13. #36564C2semidirect
14. #36481C2semidirect
15. #36449C2semidirect
16. #36444C2semidirect
17. #36188C2semidirect
18. #36134C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35989C2semidirect
21. #34979C2semidirect
22. #34932C2semidirect
23. #34243C2semidirect
24. #34216C2semidirect
25. C4×#555C2semidirect
26. C4×#547C2semidirect
616. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598702
#594152
#593982
#592342
#591252
#590422
#449172
#444412
#401902
#400782
#394812
#389222
#365642
#364812
#364492
#364442
#361882
#361342
D4×C4⋊Q82
#359892
#349792
#349322
#342432
#342162
C4×#5552
C4×#5472