Finite Group Databasebeta

← #7699931

Subgroups — #7699931

Order 512.

5579 conjugacy classes of subgroups.

The subgroup lattice has 1153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59775C218yesmaximal, complemented
3#59754C214yesmaximal, complemented
4#59700C214yesmaximal, complemented
5#59683C214yesmaximal, complemented
6#59679C212yesmaximal, complemented
7#59647C212yesmaximal, complemented
8#59078C212yesmaximal, complemented
9#36595C211yesmaximal, characteristic, complemented
10#36595C211yesmaximal, characteristic, complemented
11#36591C212yesmaximal, complemented
12#36587C212yesmaximal, complemented
13#36496C212yesmaximal, complemented
14#36495C214yesmaximal, complemented
15#36460C212yesmaximal, complemented
16#36437C214yesmaximal, complemented
17#36419C212yesmaximal, complemented
18#36300C212yesmaximal, complemented
19#36253C214yesmaximal, complemented
20#36128C211yesmaximal, characteristic
21C4×#557C211yesmaximal, characteristic, complemented
22C4×#559C212yesmaximal, complemented
23C4×#554C211yesmaximal, characteristic, complemented
24C4×#556C211yesmaximal, characteristic, complemented
25C4×#550C212yesmaximal, complemented
26#34141C212yesmaximal, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#557C2211yescharacteristic
30C2×#556C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#550C2212yes—
33C2×#532C2212yes—
34C2×C4×#41C2214yes—
35#2867C2211yescharacteristic
36#2861C2214yes—
37#2860C2214yes—
38#2858C2212yes—
39#2858C2212yes—
40#2856C2212yes—
41#2853C2218yes—
42#2850C2214yes—
43#2805C2214yes—
44#2800C2218yes—
45#2797C2218yes—
46#2753C2218yes—
47#2711C2218yes—
48#2602C2218yes—
49#2600C2218yes—
50#2597C2218yes—
51#2595C2218yes—
52#2581C2214yes—
53#2578C2218yes—
54#2571C2212yes—
55#2568C2212yes—
56#2567C2212yes—
57#2566C2214yes—
58#2559C2218yes—
59#2559C2218yes—
60#2559C2218yes—
61#2548C2212yes—
62#2548C2212yes—
63#2548C2212yes—
64#2548C2212yes—
65#2548C2212yes—
66#2548C2212yes—
67#2548C2212yes—
68#2545C2214yes—
69#2544C2214yes—
70#2544C2214yes—
71#2544C2214yes—
72#2544C2214yes—
73#2541C2212yes—
74#2541C2212yes—
75#2526C2218yes—
76#2521C2218yes—
77#2518C2218yes—
78#2516C2218yes—
79#2513C2214yes—
80#2513C2214yes—
81#2513C2214yes—
82#2512C2214yes—
83#2512C2214yes—
84#2511C2214yes—
85#2509C2214yes—
86#2504C2214yes—
87#2500C2214yes—
88#2490C2214yes—
89#2474C2218yes—
90#2470C2218yes—
91#2467C2218yes—
92#2466C2218yes—
93#2461C2218yes—
94#2461C2218yes—
95#2460C2218yes—
96#2457C2218yes—
97#2454C2214yes—
98#2448C2214yes—
99#2448C2214yes—
100#2447C2214yes—
101#2447C2214yes—
102#2445C2214yes—
103#2445C2214yes—
104#2445C2214yes—
105#2445C2214yes—
106#2444C2218yes—
107#2432C2214yes—
108#2431C2214yes—
109#2428C2214yes—
110#2428C2214yes—
111#2426C2214yes—
112#2426C2214yes—
113#2420C2214yes—
114#2374C2218yes—
115#2373C2214yes—
116#2370C2212yes—
117#2370C2214yes—
118#2370C2212yes—
119#2369C2211yescharacteristic
120#2368C2214yes—
121#2367C2214yes—
122#2367C2212yes—
123#2367C2214yes—
124#2367C2214yes—
125#2367C2214yes—
126#2367C2214yes—
127#2366C2212yes—
128#2366C2212yes—
129#2366C2214yes—
130#2366C2212yes—
131#2366C2212yes—
132#2366C2212yes—
133#2366C2212yes—
134#2365C2212yes—
135#2365C2211yescharacteristic
136#2365C2212yes—
137#2365C2211yescharacteristic
138#2364C2218yes—
139#2363C2218yes—
140#2363C2214yes—
141#2362C2212yes—
142#2361C2214yes—
143#2361C2214yes—
144#2361C2214yes—
145#2360C2212yes—
146#2357C2214yes—
147#2357C2214yes—
148#2357C2214yes—
149#2356C2212yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2355C2211yescharacteristic
153#2355C2212yes—
154#2355C2211yescharacteristic
155#2354C2211yescharacteristic
156#2354C2214yes—
157#2351C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2211yescharacteristic
160#2349C2212yes—
161D4×C4⋊C4C2211yescharacteristic
162#2347C2212yes—
163#2345C2212yes—
164#2341C2214yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2211yescharacteristic
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×#127C2212yes—
170C4×#127C2214yes—
171C4×#127C2212yes—
172C4×#125C2212yes—
173C4×#125C2214yes—
174C4×#125C2212yes—
175C4×#126C2214yes—
176C4×#124C2214yes—
177C4×#124C2214yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×#123C2218yes—
183C4×#121C2214yes—
184C4×#121C2218yes—
185#2297C2214yes—
186#2293C2214yes—
187#2290C2218yes—
188C42×Q8C2212yes—
189C42×Q8C2212yes—
190C42×Q8C2211yescharacteristic
191C42×Q8C2211yescharacteristic
192C42×Q8C2212yes—
193C42×D4C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2214yes—
196C42×D4C2214yes—
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2314yes—
200#559—216no—
201#559—48no—
202#557—28no—
203#556—28no—
204#554—28no—
205#550—216no—
206#532—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#127C2314yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#123C2318yes—
233C2×#123C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2318yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C4×#41—416no—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2318yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2312yes—
281C2×#117C2318yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C42C2312yes—
285C22×C42C2314yes—
286C22×C42C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#395C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#392C2318yes—
313#392C2318yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#390C2312yes—
327#390C2318yes—
328#390C2314yes—
329#390C2318yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2318yes—
391#388C2314yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2318yes—
415#387C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2314yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2314yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#383C2314yes—
443#382C2312yes—
444#382C2314yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2314yes—
449#381C2318yes—
450#381C2318yes—
451#380C2318yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2312yes—
520#376C2314yes—
521C2×#95C2314yes—
522C43C2314yes—
523C43C2312yes—
524C43C2312yes—
525C43C2314yes—
526C43C2311yescharacteristic
527C2×#41—216no—
528C2×#41—216no—
529C2×#41—48no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2418yes—
539C22×D4C2411yescharacteristic
540C22×D4C2418yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2418yes—
550C23×C4C2418yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8#4118yes—
557#127—216no—
558#127—28no—
559#127—28no—
560#127—28no—
561#127—44no—
562#127—44no—
563#127—44no—
564#127—82no—
565#126—216no—
566#126—88no—
567#125—216no—
568#125—28no—
569#125—28no—
570#124—216no—
571#124—216no—
572#124—28no—
573#124—216no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—84no—
578#123—232no—
579#123—416no—
580C22⋊Q8—28no—
581C22⋊Q8—28no—
582C22⋊Q8—216no—
583#121—216no—
584#121—216no—
585#121—216no—
586#121—232no—
587#121—48no—
588#121—84no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—28no—
593C4×Q8—24no—
594C4×Q8—28no—
595C4×Q8—24no—
596C4×Q8—24no—
597C4×Q8—24no—
598C4×Q8—28no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—42no—
603C4×Q8—48no—
604C4×Q8#4118yescomplemented
605C4×D4—216no—
606C4×D4—216no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—28no—
611C4×D4—24no—
612C4×D4—216no—
613C4×D4—416no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—44no—
617C4×D4—42no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—416no—
621C4×D4—88no—
622C4×D4—84no—
623C4×D4#4118yes—
624#117—28no—
625#117—28no—
626#117—416no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4—44no—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2412yes—
704C2×C42—28no—
705C2×C42—416no—
706C2×C42—48no—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2414yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2412yes—
731C2×C42C2418yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2414yes—
737C2×C42C2411yescharacteristic
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2412yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2412yes—
760#95C2418yes—
761#95C2414yes—
762#95C2412yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2412yes—
768#95C2412yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2412yes—
773#95C2414yes—
774#95C2412yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781C24C2518yes—
782C24C2512yes—
783#41—464no—
784C2×Q8—22no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—24no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8C2×#4118yes—
798C2×Q8C2×#4114yes—
799C2×D4—216no—
800C2×D4—216no—
801C2×D4—22no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—216no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—22no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—48no—
817C2×D4—44no—
818C2×D4—48no—
819C2×D4—44no—
820C2×D4—48no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4C2×#4114yes—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—216no—
834C22×C4—216no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—216no—
839C22×C4—216no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—42no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—42no—
852C22×C4C2×#4118yes—
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2511yescharacteristic
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—22no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—24no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4C2×#4114yes—
919C4⋊C4C2×#4114yes—
920C4⋊C4C2×#4118yes—
921C4⋊C4C2×#4118yes—
922C4⋊C4C2×#4118yes—
923C4⋊C4H(5,𝔽2)14yes—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—216no—
927C22⋊C4—216no—
928C22⋊C4—216no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—216no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—42no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4C2×#4118yes—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—28no—
956C42—28no—
957C42—28no—
958C42—24no—
959C42—28no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—28no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—22no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—22no—
972C42—22no—
973C42—44no—
974C42—44no—
975C42—48no—
976C42—42no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—42no—
981C42—42no—
982C42—44no—
983C42—41no—
984C42C2×#4114yes—
985C42C2×#4118yes—
986C42C2×#4114yes—
987C42C2×#4114yes—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—28no—
995C23—28no—
996C23—28no—
997C23—28no—
998C23—28no—
999C23—28no—
1000C23—28no—
1001C23C22×#4114yes—
1002C23C2611yescharacteristic
1003Q8—28no—
1004Q8—216no—
1005Q8—48no—
1006Q8—44no—
1007Q8—84no—
1008D4—28no—
1009D4—432no—
1010D4—416no—
1011D4—416no—
1012D4—416no—
1013D4—88no—
1014D4—88no—
1015D4—88no—
1016D4—816no—
1017D4—164no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—216no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—432no—
1075C2×C4—48no—
1076C2×C4—816no—
1077C2×C4—88no—
1078C2×C4—84no—
1079C2×C4—816no—
1080C2×C4—88no—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4114yes—
1083C2×C4C22×#4118yes—
1084C2×C4C22×#4114yes—
1085C2×C4C22×#4114yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C2×H(5,𝔽2)14yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4#58512yes—
1097C2×C4#58512yes—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—48no—
1106C22—48no—
1107C22—48no—
1108C22—48no—
1109C22—48no—
1110C22—48no—
1111C22—48no—
1112C22C23×#4111yescharacteristic
1113C22C23×#4111yescharacteristic
1114C22C23×#4111yescharacteristic
1115C22C22×H(5,𝔽2)11yescharacteristic
1116C22C2×#58511yescharacteristic
1117C22C2×#58511yescharacteristic
1118C22H(7,𝔽2)11yescharacteristic
1119C4—24no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—24no—
1124C4—24no—
1125C4—24no—
1126C4—28no—
1127C4—44no—
1128C4—44no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—41no—
1137C4—42no—
1138C4—44no—
1139C4—42no—
1140C4#348014yes—
1141C4#348014yes—
1142C4#348114yes—
1143C2—44no—
1144C2—88no—
1145C2C2×#348011yescharacteristic
1146C2C2×#348011yescharacteristic
1147C2C2×#348111yescharacteristic
1148C2#6298611yescharacteristic
1149C2#6300611yescharacteristic
1150C2#6301011yescharacteristic
1151C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36128C2
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. #59775C2semidirect
3. #59754C2semidirect
4. #59700C2semidirect
5. #59683C2semidirect
6. #59679C2semidirect
7. #59647C2semidirect
8. #59078C2semidirect
9. #36595C2semidirect
10. #36595C2semidirect
11. #36591C2semidirect
12. #36587C2semidirect
13. #36496C2semidirect
14. #36495C2semidirect
15. #36460C2semidirect
16. #36437C2semidirect
17. #36419C2semidirect
18. #36300C2semidirect
19. #36253C2semidirect
21. C4×#557C2semidirect
22. C4×#559C2semidirect
23. C4×#554C2semidirect
24. C4×#556C2semidirect
25. C4×#550C2semidirect
26. #34141C2semidirect
604. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598702
#597752
#597542
#597002
#596832
#596792
#596472
#590782
#365952
#365912
#365872
#364962
#364952
#364602
#364372
#364192
#363002
#362532
#361282
C4×#5572
C4×#5592
C4×#5542
C4×#5562
C4×#5502
#341412