Finite Group Databasebeta

← #7987067

Subgroups — #7987067

Order 512.

4589 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59450C212yesmaximal, complemented
3#59329C212yesmaximal, complemented
4#59257C212yesmaximal, complemented
5#49129C218yesmaximal, complemented
6#45618C214yesmaximal, complemented
7#45014C214yesmaximal, complemented
8#45005C214yesmaximal, complemented
9#42543C214yesmaximal, complemented
10#42452C214yesmaximal, complemented
11#39880C214yesmaximal, complemented
12#39478C212yesmaximal, complemented
13#39183C212yesmaximal, complemented
14#38931C212yesmaximal, complemented
15#38921C212yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36180C211yesmaximal, characteristic, complemented
19#36116C212yesmaximal, complemented
20#36114C212yesmaximal
21#35206C212yesmaximal, complemented
22#35181C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic
25#34384C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#554C2211yescharacteristic
28C2×#554C2212yes—
29C2×#529C2212yes—
30C2×#529C2214yes—
31#2868C2211yescharacteristic
32#2859C2212yes—
33#2857C2212yes—
34#2857C2212yes—
35#2855C2214yes—
36#2851C2214yes—
37#2851C2214yes—
38#2835C2218yes—
39#2805C2218yes—
40#2805C2214yes—
41#2802C2218yes—
42#2794C2218yes—
43#2791C2218yes—
44#2771C2218yes—
45#2767C2218yes—
46#2762C2218yes—
47#2758C2218yes—
48#2750C2218yes—
49#2747C2218yes—
50#2745C2218yes—
51#2698C2218yes—
52#2698C2218yes—
53#2689C2218yes—
54#2687C2218yes—
55#2680C2218yes—
56#2652C2218yes—
57#2647C2214yes—
58#2646C2218yes—
59#2638C2218yes—
60#2625C2214yes—
61#2582C2212yes—
62#2581C2214yes—
63#2575C2218yes—
64#2573C2218yes—
65#2573C2214yes—
66#2571C2212yes—
67#2571C2214yes—
68#2571C2211yescharacteristic
69#2571C2212yes—
70#2570C2214yes—
71#2570C2214yes—
72#2570C2214yes—
73#2570C2218yes—
74#2568C2211yescharacteristic
75#2568C2212yes—
76#2567C2212yes—
77#2567C2212yes—
78#2567C2212yes—
79#2565C2214yes—
80#2563C2212yes—
81#2553C2214yes—
82#2552C2214yes—
83#2552C2211yescharacteristic
84#2552C2212yes—
85#2552C2214yes—
86#2552C2212yes—
87#2552C2212yes—
88#2550C2214yes—
89#2547C2211yescharacteristic
90#2547C2211yescharacteristic
91#2542C2211yescharacteristic
92#2538C2212yes—
93#2538C2211yescharacteristic
94#2537C2211yescharacteristic
95#2515C2218yes—
96#2514C2212yes—
97#2511C2214yes—
98#2511C2214yes—
99#2511C2214yes—
100#2511C2214yes—
101#2509C2214yes—
102#2509C2214yes—
103#2508C2214yes—
104#2507C2214yes—
105#2503C2214yes—
106#2503C2214yes—
107#2502C2214yes—
108#2499C2218yes—
109#2497C2214yes—
110#2496C2214yes—
111#2496C2214yes—
112#2496C2212yes—
113#2495C2214yes—
114#2495C2214yes—
115#2494C2212yes—
116#2492C2214yes—
117#2489C2214yes—
118#2489C2214yes—
119#2489C2212yes—
120#2486C2214yes—
121#2484C2218yes—
122#2478C2218yes—
123#2470C2218yes—
124#2466C2218yes—
125#2453C2214yes—
126#2451C2214yes—
127#2447C2214yes—
128#2447C2214yes—
129#2447C2212yes—
130#2440C2214yes—
131#2440C2214yes—
132#2439C2214yes—
133#2427C2212yes—
134#2422C2214yes—
135#2422C2212yes—
136#2421C2214yes—
137#2421C2214yes—
138#2421C2212yes—
139#2420C2214yes—
140#2419C2218yes—
141#2415C2214yes—
142#2401C2214yes—
143#2395C2214yes—
144#2383C2218yes—
145#2370C2212yes—
146#2369C2211yescharacteristic
147#2369C2212yes—
148#2369C2212yes—
149#2368C2214yes—
150#2365C2212yes—
151#2361C2214yes—
152#2360C2214yes—
153#2360C2212yes—
154#2357C2214yes—
155#2355C2212yes—
156#2355C2212yes—
157#2355C2212yes—
158#2355C2211yescharacteristic
159#2354C2212yes—
160#2352C2214yes—
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163#2349C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2214yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2345C2212yes—
169#2344C2214yes—
170#2344C2214yes—
171#2330C2214yes—
172#2326C2214yes—
173#2322C2218yes—
174#2320C2214yes—
175#2317C2214yes—
176#2317C2214yes—
177#2314C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#125C2212yes—
183C4×#124C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2214yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189#2295C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199#554—28no—
200#554—48no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207#529—216no—
208#529—416no—
209C2×#126C2314yes—
210C2×#126C2318yes—
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#123C2314yes—
218C2×#123C2318yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2314yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2318yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2318yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C42C2312yes—
257C22×C42C2312yes—
258C22×C42C2314yes—
259#401C2314yes—
260#400C2314yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2318yes—
277#400C2318yes—
278#399C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#397C2314yes—
290#397C2318yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2314yes—
299#397C2314yes—
300#397C2314yes—
301#396C2314yes—
302#396C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#394C2314yes—
307#394C2318yes—
308#394C2314yes—
309#393C2318yes—
310#391C2312yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2314yes—
327#391C2318yes—
328#391C2318yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2318yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2312yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#387C2314yes—
380#387C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2314yes—
404#387C2318yes—
405#387C2314yes—
406#386C2318yes—
407#386C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2314yes—
427#384C2314yes—
428#384C2314yes—
429#384C2314yes—
430#384C2318yes—
431#384C2314yes—
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#383C2318yes—
437#383C2314yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2312yes—
442#382C2314yes—
443#382C2312yes—
444#382C2314yes—
445#382C2314yes—
446#382C2318yes—
447#382C2314yes—
448#382C2312yes—
449#382C2318yes—
450#381C2314yes—
451#381C2318yes—
452#381C2318yes—
453#381C2318yes—
454#381C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519#376C2314yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2412yes—
527C22×Q8C2414yes—
528C22×D4C2414yes—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2418yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2414yes—
540C4⋊Q8—24no—
541C4⋊Q8—24no—
542C4⋊Q8—24no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546#126—216no—
547#126—416no—
548#125—28no—
549#125—28no—
550#125—48no—
551#125—48no—
552#124—28no—
553#124—28no—
554#123—216no—
555#123—416no—
556C22⋊Q8—28no—
557C22⋊Q8—28no—
558C22⋊Q8—216no—
559C22⋊Q8—416no—
560C22⋊Q8—48no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—48no—
564#121—28no—
565#121—28no—
566C4×Q8—28no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—28no—
570C4×Q8—44no—
571C4×Q8—48no—
572C4×Q8—42no—
573C4×Q8—48no—
574C4×D4—28no—
575C4×D4—216no—
576C4×D4—24no—
577C4×D4—216no—
578C4×D4—24no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—44no—
582C4×D4—42no—
583C4×D4—416no—
584C4×D4#4118yes—
585#117—216no—
586#117—416no—
587#117—48no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—48no—
591C2×C4⋊C4—48no—
592C2×C4⋊C4—48no—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C42—28no—
672C2×C42—28no—
673C2×C42—48no—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2414yes—
691C2×C42C2418yes—
692C2×C42C2418yes—
693C2×C42C2412yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2412yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2414yes—
715#95C2412yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751C24C2512yes—
752C24C2512yes—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—44no—
775C2×D4C2×#4114yes—
776C2×D4H(5,𝔽2)14yes—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—216no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4C2×#4118yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2511yescharacteristic
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2518yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C4⋊C4—22no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—22no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—42no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—42no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4C2×#4114yes—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—24no—
892C22⋊C4—216no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—42no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4C2×#4118yes—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—28no—
910C42—24no—
911C42—24no—
912C42—28no—
913C42—22no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—22no—
921C42—22no—
922C42—44no—
923C42—44no—
924C42—41no—
925C42—42no—
926C42—48no—
927C42—48no—
928C42—42no—
929C42—48no—
930C42C2×#4114yes—
931C422−1+414yes—
932C422−1+414yes—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23C22×#4114yes—
946C23C2×H(5,𝔽2)14yes—
947C23C2611yescharacteristic
948Q8—48no—
949Q8—44no—
950Q8—48no—
951Q8—84no—
952Q8—164no—
953D4—28no—
954D4—28no—
955D4—416no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—216no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—28no—
1002C2×C4—22no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—48no—
1020C2×C4—84no—
1021C2×C4—88no—
1022C2×C4—816no—
1023C2×C4—88no—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4114yes—
1026C2×C4C22×#4112yes—
1027C2×C4C22×#4112yes—
1028C2×C4C2×H(5,𝔽2)12yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4C2×2−1+412yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4C2×2−1+412yes—
1034C2×C4C2×2−1+412yes—
1035C2×C4#58512yes—
1036C2×C4#58512yes—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22C23×#4111yescharacteristic
1052C22C22×H(5,𝔽2)11yescharacteristic
1053C22C22×2−1+411yescharacteristic
1054C22C22×2−1+411yescharacteristic
1055C22C2×#58511yescharacteristic
1056C22C2×#58511yescharacteristic
1057C222−1+611yescharacteristic
1058C4—22no—
1059C4—24no—
1060C4—22no—
1061C4—22no—
1062C4—42no—
1063C4—42no—
1064C4—44no—
1065C4—44no—
1066C4—42no—
1067C4—44no—
1068C4—42no—
1069C4—44no—
1070C4—48no—
1071C4—41no—
1072C4—42no—
1073C4—44no—
1074C4—42no—
1075C4—42no—
1076C4—44no—
1077C4—42no—
1078C4—42no—
1079C4#350714yes—
1080C4#351514yes—
1081C4#354414yes—
1082C2—44no—
1083C2—44no—
1084C2C2×#354411yescharacteristic
1085C2C2×#350711yescharacteristic
1086C2C2×#351511yescharacteristic
1087C2#6295611yescharacteristic
1088C2#6295911yescharacteristic
1089C2#6298511yescharacteristic
1090C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
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. #59450C2semidirect
3. #59329C2semidirect
4. #59257C2semidirect
5. #49129C2semidirect
6. #45618C2semidirect
7. #45014C2semidirect
8. #45005C2semidirect
9. #42543C2semidirect
10. #42452C2semidirect
11. #39880C2semidirect
12. #39478C2semidirect
13. #39183C2semidirect
14. #38931C2semidirect
15. #38921C2semidirect
16. #36563C2semidirect
17. #36194C2semidirect
18. #36180C2semidirect
19. #36116C2semidirect
21. #35206C2semidirect
22. #35181C2semidirect
23. #34945C2semidirect
25. #34384C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#594502
#593292
#592572
#491292
#456182
#450142
#450052
#425432
#424522
#398802
#394782
#391832
#389312
#389212
#365632
#361942
#361802
#361162
#361142
#352062
#351812
#349452
#349322
#343842
C4×#5542