Finite Group Databasebeta

← #7688592

Subgroups — #7688592

Order 512.

4749 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59435C212yesmaximal, complemented
3#59333C214yesmaximal, complemented
4#59302C212yesmaximal, complemented
5#59242C212yesmaximal, complemented
6#59240C214yesmaximal, complemented
7#45219C214yesmaximal, complemented
8#43648C218yesmaximal, complemented
9#39157C212yesmaximal, complemented
10#39155C214yesmaximal, complemented
11#38986C212yesmaximal, complemented
12#38982C214yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36586C212yesmaximal, complemented
15#36275C212yesmaximal, complemented
16#36194C211yesmaximal, characteristic, complemented
17#36180C211yesmaximal, characteristic, complemented
18#36177C212yesmaximal, complemented
19#36164C212yesmaximal
20#35888C214yesmaximal, complemented
21#34945C211yesmaximal, characteristic, complemented
22C2×#2571C212yesmaximal, complemented
23#34332C212yesmaximal, complemented
24#34191C212yesmaximal, complemented
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27C2×#554C2212yes—
28C2×#554C2211yescharacteristic
29C2×#547C2211yescharacteristic
30C2×C4×#41C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2855C2214yes—
36#2850C2214yes—
37#2805C2214yes—
38#2793C2218yes—
39#2789C2218yes—
40#2787C2218yes—
41#2783C2218yes—
42#2777C2218yes—
43#2775C2218yes—
44#2767C2218yes—
45#2762C2218yes—
46#2758C2218yes—
47#2689C2218yes—
48#2645C2214yes—
49#2643C2218yes—
50#2604C2218yes—
51#2596C2218yes—
52#2582C2212yes—
53#2581C2214yes—
54#2573C2214yes—
55#2571C2214yes—
56#2571C2214yes—
57#2571C2212yes—
58#2571C2214yes—
59#2571C2211yescharacteristic
60#2571C2218yes—
61#2571C2212yes—
62#2571C2212yes—
63#2571C2214yes—
64#2570C2214yes—
65#2570C2214yes—
66#2568C2212yes—
67#2568C2211yescharacteristic
68#2568C2212yes—
69#2567C2212yes—
70#2567C2212yes—
71#2563C2212yes—
72#2552C2212yes—
73#2552C2212yes—
74#2547C2211yescharacteristic
75#2538C2212yes—
76#2538C2211yescharacteristic
77#2533C2218yes—
78#2528C2218yes—
79#2524C2218yes—
80#2514C2214yes—
81#2514C2214yes—
82#2514C2214yes—
83#2514C2214yes—
84#2514C2212yes—
85#2512C2214yes—
86#2511C2214yes—
87#2511C2214yes—
88#2510C2218yes—
89#2509C2214yes—
90#2509C2214yes—
91#2504C2214yes—
92#2503C2214yes—
93#2502C2214yes—
94#2499C2214yes—
95#2497C2214yes—
96#2496C2214yes—
97#2496C2214yes—
98#2495C2214yes—
99#2494C2212yes—
100#2494C2214yes—
101#2493C2218yes—
102#2493C2218yes—
103#2493C2218yes—
104#2492C2214yes—
105#2489C2214yes—
106#2489C2214yes—
107#2488C2218yes—
108#2488C2218yes—
109#2487C2214yes—
110#2481C2218yes—
111#2481C2218yes—
112#2453C2214yes—
113#2449C2218yes—
114#2448C2214yes—
115#2447C2212yes—
116#2446C2214yes—
117#2441C2214yes—
118#2440C2214yes—
119#2440C2214yes—
120#2439C2214yes—
121#2438C2218yes—
122#2421C2212yes—
123#2417C2214yes—
124#2401C2214yes—
125C2×#400C2218yes—
126#2370C2214yes—
127#2370C2212yes—
128#2369C2212yes—
129#2369C2211yescharacteristic
130#2368C2214yes—
131#2365C2211yescharacteristic
132#2365C2212yes—
133#2365C2212yes—
134#2362C2212yes—
135#2361C2212yes—
136#2360C2214yes—
137#2360C2218yes—
138#2360C2212yes—
139#2359C2214yes—
140#2356C2214yes—
141#2355C2212yes—
142#2355C2212yes—
143#2355C2211yescharacteristic
144#2355C2212yes—
145#2355C2212yes—
146#2354C2211yescharacteristic
147#2354C2212yes—
148#2352C2214yes—
149#2352C2214yes—
150Q8×C4⋊C4C2212yes—
151#2349C2212yes—
152D4×C4⋊C4C2211yescharacteristic
153D4×C4⋊C4C2214yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2211yescharacteristic
157#2347C2214yes—
158#2346C2214yes—
159#2345C2214yes—
160#2345C2212yes—
161#2344C2212yes—
162#2343C2218yes—
163#2339C2212yes—
164#2339C2214yes—
165#2339C2214yes—
166#2330C2214yes—
167#2329C2218yes—
168#2320C2214yes—
169#2318C2218yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2211yescharacteristic
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#125C2212yes—
175C4×#124C2212yes—
176C4×C22⋊Q8C2214yes—
177C4×C22⋊Q8C2214yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×#123C2214yes—
182C4×#121C2212yes—
183#2295C2212yes—
184C2×#389C2214yes—
185C2×#389C2214yes—
186#2285C2212yes—
187C2×#384C2212yes—
188#2283C2214yes—
189#2283C2212yes—
190C2×#382C2214yes—
191C2×#382C2214yes—
192#2275C2214yes—
193C42×Q8C2211yescharacteristic
194C42×D4C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200#554—28no—
201#554—216no—
202#547—28no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×#126C2318yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#124C2312yes—
213C2×#123C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×#121C2312yes—
222C4×#41—216no—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2318yes—
254C22×C4⋊C4C2314yes—
255C22×C42C2314yes—
256C22×C42C2312yes—
257C22×C42C2312yes—
258C22×C42C2314yes—
259#401C2318yes—
260#401C2318yes—
261#401C2314yes—
262#400C2318yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#397C2314yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#396C2314yes—
293#396C2318yes—
294#396C2318yes—
295#395C2318yes—
296#395C2318yes—
297#393C2318yes—
298#391C2314yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2314yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#390C2314yes—
321#390C2312yes—
322#390C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2314yes—
327#389C2312yes—
328#389C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2318yes—
349#389C2318yes—
350#389C2312yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#388C2314yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2314yes—
367#388C2314yes—
368#387C2314yes—
369#387C2314yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2314yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2318yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#385C2314yes—
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2314yes—
416#384C2314yes—
417#384C2312yes—
418#384C2312yes—
419#384C2314yes—
420#384C2314yes—
421#384C2312yes—
422#384C2312yes—
423#383C2314yes—
424#383C2318yes—
425#383C2318yes—
426#383C2318yes—
427#382C2312yes—
428#382C2314yes—
429#382C2314yes—
430#382C2314yes—
431#382C2312yes—
432#382C2314yes—
433#382C2314yes—
434#382C2312yes—
435#382C2312yes—
436#382C2318yes—
437#382C2318yes—
438#382C2314yes—
439#382C2314yes—
440#382C2318yes—
441#382C2318yes—
442#381C2314yes—
443#381C2318yes—
444#381C2318yes—
445#381C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2318yes—
450#380C2312yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2318yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514#376C2314yes—
515#376C2318yes—
516C2×#95C2318yes—
517C2×#95C2318yes—
518C2×#95C2314yes—
519C2×#95C2318yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C2×#41—28no—
524C2×#41—28no—
525C2×#41—28no—
526C22×Q8C2411yescharacteristic
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×D4C2411yescharacteristic
532C22×D4C2414yes—
533C22×D4C2411yescharacteristic
534C23×C4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2418yes—
541C23×C4C2414yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C4⋊Q8—24no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—44no—
550C4⋊Q8—82no—
551#126—88no—
552#125—28no—
553#125—216no—
554#124—44no—
555#123—216no—
556C22⋊Q8—28no—
557C22⋊Q8—216no—
558C22⋊Q8—28no—
559C22⋊Q8—216no—
560C22⋊Q8—232no—
561C22⋊Q8—44no—
562C22⋊Q8—84no—
563#121—28no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—44no—
570C4×Q8—48no—
571C4×Q8—42no—
572C4×Q8—84no—
573C4×D4—28no—
574C4×D4—216no—
575C4×D4—28no—
576C4×D4—24no—
577C4×D4—28no—
578C4×D4—216no—
579C4×D4—216no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—42no—
583C4×D4#4118yes—
584C4×D4#4118yes—
585#117—28no—
586#117—216no—
587#117—48no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—48no—
594C2×C4⋊C4—88no—
595C2×C4⋊C4—84no—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C42—216no—
669C2×C42—28no—
670C2×C42—28no—
671C2×C42—48no—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2412yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2414yes—
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2418yes—
691C2×C42C2412yes—
692C2×C42C2418yes—
693C2×C42C2412yes—
694C2×C42C2418yes—
695C2×C42C2411yescharacteristic
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701#95C2414yes—
702#95C2412yes—
703#95C2414yes—
704#95C2414yes—
705#95C2412yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2414yes—
732#95C2412yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2412yes—
739#95C2414yes—
740#95C2412yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24C2512yes—
754C24C2512yes—
755#41—432no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—28no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—42no—
768C2×Q8—44no—
769C2×Q8—42no—
770C2×Q8—44no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4C2×#4114yes—
778C2×D4C2×#4114yes—
779C2×D42−1+414yes—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—216no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—42no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4C2×#4118yes—
812C22×C4C2×#4118yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—216no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—216no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—42no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4C2×#4114yes—
889C4⋊C4C2×#4114yes—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—216no—
893C22⋊C4—28no—
894C22⋊C4—24no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—24no—
899C22⋊C4—48no—
900C22⋊C4—42no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C2×#4118yes—
908C22⋊C4C2×#4118yes—
909C42—24no—
910C42—28no—
911C42—24no—
912C42—24no—
913C42—28no—
914C42—28no—
915C42—24no—
916C42—28no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—22no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—28no—
925C42—22no—
926C42—22no—
927C42—44no—
928C42—44no—
929C42—48no—
930C42—42no—
931C42—48no—
932C42—42no—
933C42—48no—
934C42—41no—
935C42C2×#4114yes—
936C42C2×#4114yes—
937C422−1+414yes—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23C22×#4114yes—
950C23C22×#4114yes—
951C23C2×2−1+414yes—
952C23C2611yescharacteristic
953Q8—48no—
954Q8—44no—
955Q8—48no—
956Q8—84no—
957Q8—88no—
958D4—416no—
959D4—44no—
960D4#556116yes—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—216no—
972C2×C4—216no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—48no—
1022C2×C4—416no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—84no—
1026C2×C4—88no—
1027C2×C4—88no—
1028C2×C4—816no—
1029C2×C4—88no—
1030C2×C4C22×#4114yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4114yes—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2×2−1+412yes—
1042C2×C4#58512yes—
1043C2×C4#58512yes—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22C2×#55618yes—
1058C22C23×#4111yescharacteristic
1059C22C23×#4111yescharacteristic
1060C22C22×2−1+411yescharacteristic
1061C22C22×2−1+411yescharacteristic
1062C22C2×#58511yescharacteristic
1063C22C2×#58511yescharacteristic
1064C22H(7,𝔽2)11yescharacteristic
1065C4—22no—
1066C4—22no—
1067C4—24no—
1068C4—24no—
1069C4—22no—
1070C4—44no—
1071C4—42no—
1072C4—42no—
1073C4—44no—
1074C4—44no—
1075C4—48no—
1076C4—41no—
1077C4—44no—
1078C4—42no—
1079C4—42no—
1080C4—42no—
1081C4—44no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4C2×#55614yes—
1087C4#351514yes—
1088C4#351514yes—
1089C2—28no—
1090C2—82no—
1091C2C22×#55611yescharacteristic
1092C2C2×#351511yescharacteristic
1093C2C2×#351511yescharacteristic
1094C2#6294511yescharacteristic
1095C2#6299411yescharacteristic
1096C2#6301011yescharacteristic
1097C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
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. #59435C2semidirect
3. #59333C2semidirect
4. #59302C2semidirect
5. #59242C2semidirect
6. #59240C2semidirect
7. #45219C2semidirect
8. #43648C2semidirect
9. #39157C2semidirect
10. #39155C2semidirect
11. #38986C2semidirect
12. #38982C2semidirect
13. #36598C2semidirect
14. #36586C2semidirect
15. #36275C2semidirect
16. #36194C2semidirect
17. #36180C2semidirect
18. #36177C2semidirect
20. #35888C2semidirect
21. #34945C2semidirect
22. C2×#2571C2semidirect
23. #34332C2semidirect
24. #34191C2semidirect
25. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#594352
#593332
#593022
#592422
#592402
#452192
#436482
#391572
#391552
#389862
#389822
#365982
#365862
#362752
#361942
#361802
#361772
#361642
#358882
#349452
C2×#25712
#343322
#341912
C4×#5542
C4×#5472