Finite Group Databasebeta

← #8424622

Subgroups — #8424622

Order 512.

5635 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59660C211yesmaximal, characteristic, complemented
2#59322C211yesmaximal, characteristic, complemented
3#59313C211yesmaximal, characteristic, complemented
4#59015C214yesmaximal, complemented
5#58310C214yesmaximal, complemented
6#56487C214yesmaximal, complemented
7#53016C214yesmaximal, complemented
8#52972C214yesmaximal, complemented
9#52411C214yesmaximal, complemented
10#42615C214yesmaximal, complemented
11#42428C214yesmaximal, complemented
12#40592C214yesmaximal, complemented
13#39377C212yesmaximal, complemented
14#39126C212yesmaximal, complemented
15#38928C214yesmaximal, complemented
16#37664C214yesmaximal, complemented
17#37636C211yesmaximal, characteristic, complemented
18#37620C211yesmaximal, characteristic, complemented
19#37477C214yesmaximal, complemented
20#36180C211yesmaximal, characteristic, complemented
21#36154C212yesmaximal, complemented
22C2×#2537C211yesmaximal, characteristic, complemented
23#34700C212yesmaximal, complemented
24C2×#554C2212yes—
25C2×#554C2212yescomplemented
26C2×#547C2214yescomplemented
27C2×#546C2214yes—
28C2×#542C2214yescomplemented
29C2×#529C2212yescomplemented
30C22×#121C2214yes—
31C22×C4×D4C2212yes—
32#2868C2211yescharacteristic, complemented
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic, complemented
35#2848C2214yes—
36#2841C2218yescomplemented
37#2841C2218yescomplemented
38#2837C2218yescomplemented
39#2832C2214yescomplemented
40#2827C2218yescomplemented
41#2823C2214yescomplemented
42#2820C2214yescomplemented
43#2816C2214yescomplemented
44#2814C2218yescomplemented
45#2792C2214yescomplemented
46#2770C2218yescomplemented
47#2768C2218yescomplemented
48#2750C2218yescomplemented
49#2728C2214yescomplemented
50#2718C2218yescomplemented
51#2702C2218yescomplemented
52#2701C2218yescomplemented
53#2695C2218yescomplemented
54#2695C2218yescomplemented
55#2694C2218yescomplemented
56#2691C2218yescomplemented
57#2686C2218yescomplemented
58#2681C2218yescomplemented
59#2680C2214yescomplemented
60#2674C2218yescomplemented
61#2672C2218yescomplemented
62#2672C2218yescomplemented
63#2672C2218yescomplemented
64#2671C2218yescomplemented
65#2659C2214yes—
66#2659C2218yescomplemented
67#2646C2218yes—
68#2646C2218yescomplemented
69#2633C2214yescomplemented
70#2632C2214yescomplemented
71#2629C2214yescomplemented
72#2629C2214yescomplemented
73#2628C2214yescomplemented
74#2628C2214yescomplemented
75#2624C2214yescomplemented
76#2620C2214yescomplemented
77#2618C2214yescomplemented
78#2616C2214yescomplemented
79#2583C2214yes—
80#2582C2211yescharacteristic, complemented
81#2567C2214yescomplemented
82#2567C2212yescomplemented
83#2563C2212yescomplemented
84#2562C2214yescomplemented
85#2552C2214yescomplemented
86#2551C2211yescharacteristic, complemented
87#2538C2212yescomplemented
88#2537C2211yescharacteristic
89#2537C2211yescharacteristic
90#2537C2214yes—
91#2537C2214yes—
92#2537C2214yes—
93#2537C2212yes—
94#2537C2214yescomplemented
95#2536C2214yescomplemented
96#2536C2214yescomplemented
97#2507C2214yescomplemented
98#2502C2212yes—
99#2502C2212yescomplemented
100#2501C2214yescomplemented
101#2496C2214yescomplemented
102#2495C2214yescomplemented
103#2491C2214yescomplemented
104#2491C2214yescomplemented
105#2489C2214yescomplemented
106#2487C2214yescomplemented
107#2486C2214yescomplemented
108#2480C2218yes—
109#2480C2214yes—
110#2468C2214yescomplemented
111#2457C2214yescomplemented
112#2454C2214yescomplemented
113#2454C2212yescomplemented
114#2450C2218yescomplemented
115#2447C2212yescomplemented
116#2442C2214yes—
117#2442C2212yes—
118#2442C2214yescomplemented
119#2442C2214yescomplemented
120#2440C2214yes—
121#2440C2214yes—
122#2440C2214yescomplemented
123#2440C2214yescomplemented
124#2440C2214yescomplemented
125#2437C2218yes—
126#2437C2218yes—
127#2437C2218yes—
128#2435C2212yes—
129#2435C2214yes—
130#2430C2218yescomplemented
131#2427C2214yescomplemented
132#2427C2212yescomplemented
133#2426C2214yescomplemented
134#2425C2218yescomplemented
135#2423C2214yescomplemented
136#2422C2214yescomplemented
137#2422C2214yescomplemented
138#2420C2212yescomplemented
139#2418C2218yes—
140#2418C2214yes—
141#2417C2212yes—
142#2417C2214yescomplemented
143#2417C2214yescomplemented
144#2416C2214yescomplemented
145#2416C2214yescomplemented
146#2408C2212yes—
147#2406C2214yescomplemented
148#2405C2218yes—
149#2395C2214yescomplemented
150#2392C2214yescomplemented
151C2×#394C2214yes—
152#2361C2214yescomplemented
153#2360C2214yes—
154Q8×C4⋊C4C2212yescomplemented
155#2349C2214yescomplemented
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2212yescomplemented
158D4×C22⋊C4C2214yes—
159#2324C2214yescomplemented
160#2318C2214yes—
161C4×C4⋊Q8C2211yescharacteristic, complemented
162C4×#124C2212yescomplemented
163C4×C22⋊Q8C2212yes—
164C4×#121C2212yescomplemented
165C4×#120C2214yes—
166#2293C2212yescomplemented
167C2×#384C2211yescharacteristic
168C2×#384C2211yescharacteristic, complemented
169#2280C2214yes—
170C2×#380C2214yes—
171C2×#380C2214yes—
172C42×D4C2211yescharacteristic
173C22×#41C2314yes—
174C23×D4C2312yes—
175C23×D4C2314yes—
176C24×C4C2314yes—
177#554—48no—
178#554—48no—
179#547—416no—
180#546—416no—
181#542—416no—
182C2×C4⋊Q8C2311yescharacteristic
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2314yes—
186#529—48no—
187C2×#126C2314yes—
188C2×#126C2318yes—
189C2×#125C2314yes—
190C2×#125C2314yes—
191C2×#125C2312yes—
192C2×#124C2312yes—
193C2×#124C2314yes—
194C2×#124C2312yes—
195C2×#124C2318yes—
196C2×#123C2314yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2318yes—
213C2×#121—416no—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2312yes—
220C2×#121C2318yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#120C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×D4—48no—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C22⋊C4C2318yes—
253C22×C22⋊C4C2314yes—
254C22×C22⋊C4C2318yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2314yes—
262#400C2318yes—
263#399C2318yes—
264#399C2318yes—
265#399C2318yes—
266#399C2318yes—
267#399C2314yes—
268#398C2314yes—
269#398C2314yes—
270#398C2314yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2318yes—
282#398C2314yes—
283#397C2314yes—
284#397C2314yes—
285#397C2318yes—
286#397C2318yes—
287#397C2314yes—
288#397C2318yes—
289#397C2314yes—
290#397C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2314yes—
297#396C2318yes—
298#396C2318yes—
299#396C2314yes—
300#395C2314yes—
301#395C2314yes—
302#395C2318yes—
303#395C2318yes—
304#395C2314yes—
305#395C2318yes—
306#395C2314yes—
307#394C2314yes—
308#394C2318yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2314yes—
320#394C2318yes—
321#394C2314yes—
322#394C2314yes—
323#394C2318yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2318yes—
328#393C2318yes—
329#393C2318yes—
330#393C2318yes—
331#392C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2314yes—
339#390C2312yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#387C2318yes—
373#387C2318yes—
374#387C2314yes—
375#386C2318yes—
376#386C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#386C2314yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2314yes—
399#385C2314yes—
400#384C2311yescharacteristic
401#384C2312yes—
402#384C2314yes—
403#384C2314yes—
404#384C2312yes—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2314yes—
408#384C2312yes—
409#384C2314yes—
410#383C2314yes—
411#382C2314yes—
412#382C2314yes—
413#382C2312yes—
414#381C2314yes—
415#381C2314yes—
416#381C2314yes—
417#380C2312yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2318yes—
424#380C2318yes—
425#380C2314yes—
426#380C2314yes—
427#380C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2318yes—
432#380C2314yes—
433#380C2318yes—
434#380C2314yes—
435#380C2314yes—
436#380C2318yes—
437#380C2318yes—
438#380C2312yes—
439#380C2314yes—
440#380C2314yes—
441#379C2318yes—
442#379C2314yes—
443#379C2314yes—
444#379C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2312yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C2×#95C2314yes—
462C2×#95C2318yes—
463C43C2311yescharacteristic
464C25C2414yes—
465C2×#41—48no—
466C2×#41—416no—
467C22×Q8C2412yes—
468C22×Q8C2412yes—
469C22×Q8C2414yes—
470C22×Q8C2414yes—
471C22×D4—28no—
472C22×D4—28no—
473C22×D4—44no—
474C22×D4—48no—
475C22×D4—416no—
476C22×D4C2412yes—
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2411yescharacteristic
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2418yes—
484C22×D4C2414yes—
485C23×C4—216no—
486C23×C4—48no—
487C23×C4—48no—
488C23×C4C2412yes—
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2414yes—
495C23×C4C2414yes—
496C23×C4C2418yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2418yes—
501C4⋊Q8—24no—
502C4⋊Q8—48no—
503C4⋊Q8—48no—
504C4⋊Q8—44no—
505#126—48no—
506#126—416no—
507#125—44no—
508#125—48no—
509#125—48no—
510#124—28no—
511#124—48no—
512#124—44no—
513#124—416no—
514#123—416no—
515#123—416no—
516#123—416no—
517#123—48no—
518#123—416no—
519C22⋊Q8—28no—
520C22⋊Q8—416no—
521C22⋊Q8—48no—
522C22⋊Q8—416no—
523C22⋊Q8—44no—
524C22⋊Q8—48no—
525C22⋊Q8—44no—
526C22⋊Q8—48no—
527C22⋊Q8—416no—
528C22⋊Q8—44no—
529C22⋊Q8—48no—
530C22⋊Q8—48no—
531#121—216no—
532#121—216no—
533#121—28no—
534#121—416no—
535#121—416no—
536#121—416no—
537#121—48no—
538#121—48no—
539#121—44no—
540#121—48no—
541#120—216no—
542C4×Q8—28no—
543C4×Q8—44no—
544C4×Q8—48no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—24no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—28no—
551C4×D4—48no—
552C4×D4—48no—
553C4×D4—44no—
554C4×D4—44no—
555C4×D4—48no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—48no—
559#117—48no—
560#117—48no—
561C2×C4⋊C4—44no—
562C2×C4⋊C4—48no—
563C2×C4⋊C4—48no—
564C2×C4⋊C4—48no—
565C2×C4⋊C4—48no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C22⋊C4—48no—
610C2×C22⋊C4—416no—
611C2×C22⋊C4—416no—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2411yescharacteristic
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C42—24no—
651C2×C42—24no—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2411yescharacteristic
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2411yescharacteristic
662C2×C42C2418yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695C24—28no—
696C24—28no—
697C24—28no—
698C24—28no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24C2514yes—
703C24C2514yes—
704C24C2511yescharacteristic
705C24C2511yescharacteristic
706#41—832no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—42no—
712C2×Q8—44no—
713C2×Q8—48no—
714C2×Q8—42no—
715C2×Q8—44no—
716C2×Q8—48no—
717C2×D4—24no—
718C2×D4—28no—
719C2×D4—216no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—432no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—832no—
741C2×D4H(5,𝔽2)14yes—
742C2×D4H(5,𝔽2)18yes—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—216no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—24no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—832no—
780C22×C42−1+418yes—
781C22×C4C2514yes—
782C22×C4C2512yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C22×C4C2512yes—
800C4⋊C4—28no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—22no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—42no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—216no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—24no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—24no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C42—24no—
880C42—22no—
881C42—24no—
882C42—22no—
883C42—24no—
884C42—28no—
885C42—28no—
886C42—28no—
887C42—22no—
888C42—24no—
889C42—41no—
890C42—48no—
891C42H(5,𝔽2)14yes—
892C23—21no—
893C23—22no—
894C23—21no—
895C23—24no—
896C23—24no—
897C23—21no—
898C23—22no—
899C23—24no—
900C23—22no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—21no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—416no—
913C23—416no—
914C23—416no—
915C23—416no—
916C23—88no—
917C23—88no—
918C23—88no—
919C23C2×H(5,𝔽2)18yes—
920C23C2×H(5,𝔽2)12yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2×2−1+414yes—
923C23C2611yescharacteristic
924Q8—48no—
925Q8—84no—
926Q8—88no—
927Q8—164no—
928D4—28no—
929D4—216no—
930D4—416no—
931D4—416no—
932D4—416no—
933D4—48no—
934D4—88no—
935D4—816no—
936D4—88no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—216no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—21no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—48no—
987C2×C4—416no—
988C2×C4—416no—
989C2×C4—88no—
990C2×C4—88no—
991C2×C4—88no—
992C2×C4—88no—
993C2×C4—88no—
994C2×C4—816no—
995C2×C4—168no—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×H(5,𝔽2)12yes—
998C2×C4C2×H(5,𝔽2)14yes—
999C2×C4C2×H(5,𝔽2)14yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+414yes—
1002C22—24no—
1003C22—22no—
1004C22—22no—
1005C22—24no—
1006C22—28no—
1007C22—22no—
1008C22—22no—
1009C22—28no—
1010C22—22no—
1011C22—28no—
1012C22—44no—
1013C22—42no—
1014C22—44no—
1015C22—44no—
1016C22—42no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—832no—
1026C22#354414yes—
1027C22C22×H(5,𝔽2)11yescharacteristic
1028C22C22×H(5,𝔽2)12yes—
1029C22C22×H(5,𝔽2)11yescharacteristic
1030C22C22×2−1+412yes—
1031C222−1+611yescharacteristic
1032C4—24no—
1033C4—22no—
1034C4—22no—
1035C4—42no—
1036C4—44no—
1037C4—44no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—42no—
1050C4#353618yes—
1051C2—24no—
1052C2—42no—
1053C2—48no—
1054C2—84no—
1055C2C2×#353612yes—
1056C2C2×#354411yescharacteristic
1057C2#6291411yescharacteristic
1058C2#6291512yes—
1059C2#6301111yescharacteristic
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. #59660C2semidirect
2. #59322C2semidirect
3. #59313C2semidirect
4. #59015C2semidirect
5. #58310C2semidirect
6. #56487C2semidirect
7. #53016C2semidirect
8. #52972C2semidirect
9. #52411C2semidirect
10. #42615C2semidirect
11. #42428C2semidirect
12. #40592C2semidirect
13. #39377C2semidirect
14. #39126C2semidirect
15. #38928C2semidirect
16. #37664C2semidirect
17. #37636C2semidirect
18. #37620C2semidirect
19. #37477C2semidirect
20. #36180C2semidirect
21. #36154C2semidirect
22. C2×#2537C2semidirect
23. #34700C2semidirect
25. C2×#554C22semidirect
26. C2×#547C22semidirect
28. C2×#542C22semidirect
29. C2×#529C22semidirect
32. #2868C22semidirect
34. #2857C22semidirect
36. #2841C22semidirect
37. #2841C22semidirect
38. #2837C22semidirect
39. #2832C22semidirect
40. #2827C22semidirect
41. #2823C22semidirect
42. #2820C22semidirect
43. #2816C22semidirect
44. #2814C22semidirect
45. #2792C22semidirect
46. #2770C22semidirect
47. #2768C22semidirect
48. #2750C22semidirect
49. #2728C22semidirect
50. #2718C22semidirect
51. #2702C22semidirect
52. #2701C22semidirect
53. #2695C22semidirect
54. #2695C22semidirect
55. #2694C22semidirect
56. #2691C22semidirect
57. #2686C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
60. #2674C22semidirect
61. #2672C22semidirect
62. #2672C22semidirect
63. #2672C22semidirect
64. #2671C22semidirect
66. #2659C22semidirect
68. #2646C22semidirect
69. #2633C22semidirect
70. #2632C22semidirect
71. #2629C22semidirect
72. #2629C22semidirect
73. #2628C22semidirect
74. #2628C22semidirect
75. #2624C22semidirect
76. #2620C22semidirect
77. #2618C22semidirect
78. #2616C22semidirect
80. #2582C22semidirect
81. #2567C22semidirect
82. #2567C22semidirect
83. #2563C22semidirect
84. #2562C22semidirect
85. #2552C22semidirect
86. #2551C22semidirect
87. #2538C22semidirect
94. #2537C22semidirect
95. #2536C22semidirect
96. #2536C22semidirect
97. #2507C22semidirect
99. #2502C22semidirect
100. #2501C22semidirect
101. #2496C22semidirect
102. #2495C22semidirect
103. #2491C22semidirect
104. #2491C22semidirect
105. #2489C22semidirect
106. #2487C22semidirect
107. #2486C22semidirect
110. #2468C22semidirect
111. #2457C22semidirect
112. #2454C22semidirect
113. #2454C22semidirect
114. #2450C22semidirect
115. #2447C22semidirect
118. #2442C22semidirect
119. #2442C22semidirect
122. #2440C22semidirect
123. #2440C22semidirect
124. #2440C22semidirect
130. #2430C22semidirect
131. #2427C22semidirect
132. #2427C22semidirect
133. #2426C22semidirect
134. #2425C22semidirect
135. #2423C22semidirect
136. #2422C22semidirect
137. #2422C22semidirect
138. #2420C22semidirect
142. #2417C22semidirect
143. #2417C22semidirect
144. #2416C22semidirect
145. #2416C22semidirect
147. #2406C22semidirect
149. #2395C22semidirect
150. #2392C22semidirect
152. #2361C22semidirect
154. Q8×C4⋊C4C22semidirect
155. #2349C22semidirect
157. D4×C4⋊C4C22semidirect
159. #2324C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×#124C22semidirect
164. C4×#121C22semidirect
166. #2293C22semidirect
168. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#596602
#593222
#593132
#590152
#583102
#564872
#530162
#529722
#524112
#426152
#424282
#405922
#393772
#391262
#389282
#376642
#376362
#376202
#374772
#361802
#361542
C2×#25372
#347002