Finite Group Databasebeta

← #7688366

Subgroups — #7688366

Order 512.

4671 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59960C214yesmaximal, complemented
2#59827C212yesmaximal
3#59827C211yesmaximal, characteristic
4#59437C212yesmaximal, complemented
5#59436C212yesmaximal, complemented
6#59209C214yesmaximal, complemented
7#45153C214yesmaximal, complemented
8#43794C218yesmaximal, complemented
9#40219C214yesmaximal, complemented
10#40080C214yesmaximal, complemented
11#39762C212yesmaximal, complemented
12#39173C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36563C211yesmaximal, characteristic, complemented
15#36559C211yesmaximal, characteristic
16#36299C212yesmaximal, complemented
17#36290C212yesmaximal, complemented
18#36285C212yesmaximal, complemented
19#36175C212yesmaximal, complemented
20#35973C214yesmaximal, complemented
21#34951C211yesmaximal, characteristic, complemented
22#34945C212yesmaximal, complemented
23#34332C212yesmaximal, complemented
24#34331C212yesmaximal
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#559C211yesmaximal, characteristic
27C2×#559C2212yes—
28C2×#559C2211yescharacteristic
29C2×#557C2211yescharacteristic
30C2×#554C2212yes—
31#2868C2211yescharacteristic
32#2863C2214yes—
33#2862C2212yes—
34#2859C2212yes—
35#2859C2212yes—
36#2851C2214yes—
37#2787C2218yes—
38#2776C2218yes—
39#2776C2218yes—
40#2770C2218yes—
41#2765C2218yes—
42#2745C2218yes—
43#2744C2218yes—
44#2724C2214yes—
45#2724C2218yes—
46#2690C2218yes—
47#2690C2218yes—
48#2652C2218yes—
49#2642C2214yes—
50#2606C2218yes—
51#2599C2218yes—
52#2590C2218yes—
53#2585C2214yes—
54#2582C2212yes—
55#2582C2212yes—
56#2582C2211yescharacteristic
57#2582C2212yes—
58#2577C2218yes—
59#2573C2218yes—
60#2573C2218yes—
61#2571C2212yes—
62#2570C2214yes—
63#2570C2214yes—
64#2568C2211yescharacteristic
65#2568C2212yes—
66#2567C2212yes—
67#2566C2214yes—
68#2565C2214yes—
69#2563C2212yes—
70#2552C2212yes—
71#2552C2211yescharacteristic
72#2550C2214yes—
73#2547C2212yes—
74#2547C2214yes—
75#2547C2212yes—
76#2547C2214yes—
77#2546C2211yescharacteristic
78#2538C2212yes—
79#2538C2212yes—
80#2530C2218yes—
81#2527C2218yes—
82#2523C2218yes—
83#2515C2218yes—
84#2514C2214yes—
85#2514C2214yes—
86#2514C2214yes—
87#2514C2214yes—
88#2511C2212yes—
89#2511C2214yes—
90#2509C2214yes—
91#2509C2212yes—
92#2509C2214yes—
93#2507C2214yes—
94#2507C2214yes—
95#2505C2218yes—
96#2495C2214yes—
97#2495C2214yes—
98#2494C2214yes—
99#2494C2214yes—
100#2493C2218yes—
101#2486C2218yes—
102#2486C2214yes—
103#2484C2218yes—
104#2475C2218yes—
105#2473C2218yes—
106#2453C2212yes—
107#2452C2214yes—
108#2452C2214yes—
109#2451C2214yes—
110#2447C2214yes—
111#2447C2214yes—
112#2447C2214yes—
113#2447C2214yes—
114#2447C2214yes—
115#2447C2214yes—
116#2446C2214yes—
117#2446C2214yes—
118#2446C2212yes—
119#2442C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2402C2214yes—
125#2401C2218yes—
126#2374C2214yes—
127#2370C2214yes—
128#2370C2214yes—
129#2370C2212yes—
130#2369C2212yes—
131#2367C2214yes—
132#2367C2214yes—
133#2367C2212yes—
134#2367C2212yes—
135#2366C2211yescharacteristic
136#2365C2212yes—
137#2365C2211yescharacteristic
138#2365C2212yes—
139#2360C2218yes—
140#2360C2214yes—
141#2359C2218yes—
142#2357C2212yes—
143#2357C2212yes—
144#2356C2214yes—
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2355C2212yes—
150#2355C2211yescharacteristic
151#2355C2212yes—
152#2354C2214yes—
153#2351C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2211yescharacteristic
156#2349C2214yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2214yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2345C2214yes—
164#2344C2214yes—
165#2335C2218yes—
166#2330C2214yes—
167#2329C2218yes—
168#2326C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2211yescharacteristic
175C4×#127C2212yes—
176C4×#127C2211yescharacteristic
177C4×#125C2212yes—
178C4×#125C2212yes—
179C4×#125C2214yes—
180C4×#124C2212yes—
181C4×#124C2214yes—
182C4×#124C2212yes—
183C4×C22⋊Q8C2214yes—
184C4×#123C2214yes—
185#2295C2212yes—
186#2295C2212yes—
187#2295C2214yes—
188#2293C2214yes—
189C2×#389C2214yes—
190#2283C2214yes—
191#2275C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2212yes—
199#559—216no—
200#559—28no—
201#557—28no—
202#554—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#125C2314yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#123C2318yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×#117C2318yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2318yes—
257C22×C42C2314yes—
258#401C2318yes—
259#401C2318yes—
260#400C2318yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#400C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2314yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2314yes—
282#398C2314yes—
283#398C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#396C2318yes—
294#396C2318yes—
295#395C2318yes—
296#393C2318yes—
297#391C2314yes—
298#391C2312yes—
299#391C2312yes—
300#391C2314yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2314yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#390C2314yes—
321#390C2312yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2312yes—
328#389C2314yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2318yes—
354#389C2318yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2318yes—
365#389C2312yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#386C2314yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#384C2311yescharacteristic
422#384C2312yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#383C2318yes—
432#383C2318yes—
433#383C2318yes—
434#382C2312yes—
435#382C2312yes—
436#382C2314yes—
437#382C2314yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2312yes—
444#381C2318yes—
445#381C2318yes—
446#381C2318yes—
447#381C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2314yes—
454#380C2314yes—
455#380C2318yes—
456#380C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515#376C2314yes—
516#376C2318yes—
517C2×#95C2318yes—
518C43C2312yes—
519C43C2312yes—
520C43C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×D4C2412yes—
530C22×D4C2412yes—
531C22×D4C2412yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C23×C4C2418yes—
535C23×C4C2414yes—
536C23×C4C2414yes—
537C4⋊Q8—28no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—24no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—82no—
544#127#4118yes—
545#125—28no—
546#125—216no—
547#125—216no—
548#125—44no—
549#125—84no—
550#124—216no—
551#124—28no—
552#124—216no—
553#124—28no—
554#123—232no—
555#123—216no—
556C22⋊Q8—216no—
557C22⋊Q8—232no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—28no—
561C4×Q8—28no—
562C4×Q8—24no—
563C4×Q8—28no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—28no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—44no—
570C4×Q8—42no—
571C4×Q8—48no—
572C4×Q8—42no—
573C4×Q8—84no—
574C4×Q8#4118yes—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—216no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—48no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—84no—
587#117—88no—
588C2×C4⋊C4—216no—
589C2×C4⋊C4—48no—
590C2×C4⋊C4—88no—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C42—48no—
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2411yescharacteristic
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2418yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2412yes—
722#95C2414yes—
723#95C2412yes—
724#95C2414yes—
725#95C2412yes—
726#95C2414yes—
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750C24C2514yes—
751C2×Q8—24no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—28no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—24no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8C2×#4114yes—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4C2×#4118yes—
776C2×D4C2×#4118yes—
777C2×D4C2×#4118yes—
778C22×C4—216no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—216no—
784C22×C4—28no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—48no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2518yes—
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2512yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C4⋊C4—216no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—22no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—216no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—28no—
851C4⋊C4—22no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—42no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—42no—
863C4⋊C4—48no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4C2×#4114yes—
874C4⋊C4C2×#4118yes—
875C4⋊C42−1+414yes—
876C22⋊C4—216no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—216no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C42—24no—
892C42—28no—
893C42—28no—
894C42—24no—
895C42—28no—
896C42—24no—
897C42—24no—
898C42—22no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—28no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—22no—
907C42—24no—
908C42—24no—
909C42—22no—
910C42—44no—
911C42—44no—
912C42—44no—
913C42—48no—
914C42—42no—
915C42—44no—
916C42—48no—
917C42—42no—
918C42—42no—
919C42—42no—
920C42—42no—
921C42—41no—
922C42C2×#4118yes—
923C42C2×#4114yes—
924C42C2×#4114yes—
925C422−1+414yes—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23C22×#4118yes—
933C23C2611yescharacteristic
934Q8—28no—
935Q8—48no—
936Q8—44no—
937Q8—44no—
938Q8—48no—
939Q8—88no—
940D4—216no—
941D4—216no—
942D4—48no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—416no—
1004C2×C4—816no—
1005C2×C4—88no—
1006C2×C4—88no—
1007C2×C4—816no—
1008C2×C4C22×#4114yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4114yes—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4112yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C2×2−1+414yes—
1017C2×C4C2×2−1+412yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+412yes—
1021C2×C4#58512yes—
1022C2×C4#58512yes—
1023C22—28no—
1024C22—28no—
1025C22—28no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22C23×#4111yescharacteristic
1031C22C23×#4111yescharacteristic
1032C22C22×2−1+411yescharacteristic
1033C22C22×2−1+411yescharacteristic
1034C22C2×#58511yescharacteristic
1035C22C2×#58511yescharacteristic
1036C22H(7,𝔽2)11yescharacteristic
1037C4—22no—
1038C4—24no—
1039C4—22no—
1040C4—24no—
1041C4—24no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—44no—
1047C4—42no—
1048C4—48no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—44no—
1053C4—42no—
1054C4—44no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—44no—
1059C4#348214yes—
1060C4#350714yes—
1061C4#351514yes—
1062C2—48no—
1063C2C2×#348211yescharacteristic
1064C2C2×#350711yescharacteristic
1065C2C2×#351511yescharacteristic
1066C2#6294311yescharacteristic
1067C2#6299211yescharacteristic
1068C2#6301011yescharacteristic
1069C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59960C2semidirect
4. #59437C2semidirect
5. #59436C2semidirect
6. #59209C2semidirect
7. #45153C2semidirect
8. #43794C2semidirect
9. #40219C2semidirect
10. #40080C2semidirect
11. #39762C2semidirect
12. #39173C2semidirect
13. #36598C2semidirect
14. #36563C2semidirect
16. #36299C2semidirect
17. #36290C2semidirect
18. #36285C2semidirect
19. #36175C2semidirect
20. #35973C2semidirect
21. #34951C2semidirect
22. #34945C2semidirect
23. #34332C2semidirect
25. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#599602
#598272
#594372
#594362
#592092
#451532
#437942
#402192
#400802
#397622
#391732
#365982
#365632
#365592
#362992
#362902
#362852
#361752
#359732
#349512
#349452
#343322
#343312
C4×#5572
C4×#5592