Finite Group Databasebeta

← #8094880

Subgroups — #8094880

Order 512.

4970 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53118C214yesmaximal, complemented
2#53082C214yesmaximal, complemented
3#53001C214yesmaximal, complemented
4#52997C214yesmaximal, complemented
5#52426C218yesmaximal, complemented
6#46109C214yesmaximal, complemented
7#46105C214yesmaximal, complemented
8#45998C214yesmaximal, complemented
9#45993C214yesmaximal, complemented
10#45446C218yesmaximal, complemented
11#35576C211yesmaximal, characteristic, complemented
12#35574C211yesmaximal, characteristic, complemented
13#35558C211yesmaximal, characteristic, complemented
14#35557C211yesmaximal, characteristic, complemented
15#35532C211yesmaximal, characteristic, complemented
16#35531C211yesmaximal, characteristic
17#35286C211yesmaximal, characteristic, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35266C211yesmaximal, characteristic, complemented
20#35264C211yesmaximal, characteristic
21#35174C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic
23C2×#2542C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34815C211yesmaximal, characteristic, complemented
26C2×#563C2218yescomplemented
27C2×#544C2211yescharacteristic
28C2×#544C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2214yes—
32C2×#520C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34#2868C2212yescomplemented
35#2861C2212yes—
36#2860C2214yes—
37#2859C2214yescomplemented
38#2859C2212yescomplemented
39#2858C2212yes—
40#2849C2214yes—
41#2848C2214yes—
42#2838C2218yescomplemented
43#2838C2218yescomplemented
44#2837C2218yescomplemented
45#2837C2218yescomplemented
46#2836C2218yescomplemented
47#2827C2218yescomplemented
48#2821C2218yescomplemented
49#2820C2218yescomplemented
50#2817C2218yescomplemented
51#2814C2218yescomplemented
52#2777C2218yescomplemented
53#2773C2218yescomplemented
54#2773C2218yescomplemented
55#2729C2218yescomplemented
56#2728C2218yescomplemented
57#2727C2218yescomplemented
58#2723C2218yescomplemented
59#2723C2218yescomplemented
60#2721C2218yescomplemented
61#2720C2218yescomplemented
62#2718C2218yescomplemented
63#2702C2218yescomplemented
64#2698C2218yescomplemented
65#2690C2218yescomplemented
66#2689C2218yescomplemented
67#2683C2218yescomplemented
68#2680C2218yescomplemented
69#2677C2218yescomplemented
70#2674C2218yescomplemented
71#2674C2218yescomplemented
72#2660C2212yescomplemented
73#2660C2212yescomplemented
74#2647C2214yescomplemented
75#2644C2214yes—
76#2641C2212yes—
77#2640C2212yes—
78#2626C2214yes—
79#2622C2214yes—
80#2583C2214yes—
81#2579C2214yes—
82#2571C2214yescomplemented
83#2567C2212yescomplemented
84#2566C2212yescomplemented
85#2565C2212yescomplemented
86#2552C2214yescomplemented
87#2552C2214yescomplemented
88#2551C2214yescomplemented
89#2551C2214yescomplemented
90#2551C2214yescomplemented
91#2550C2214yescomplemented
92#2550C2214yescomplemented
93#2542C2214yes—
94#2542C2214yes—
95#2542C2214yes—
96#2542C2214yes—
97#2542C2212yescomplemented
98#2514C2212yescomplemented
99#2513C2214yes—
100#2513C2214yes—
101#2513C2214yes—
102#2513C2212yescomplemented
103#2512C2214yes—
104#2512C2214yes—
105#2512C2214yes—
106#2512C2212yescomplemented
107#2512C2214yescomplemented
108#2511C2212yescomplemented
109#2511C2214yescomplemented
110#2510C2214yes—
111#2509C2212yescomplemented
112#2508C2212yescomplemented
113#2507C2212yescomplemented
114#2506C2212yescomplemented
115#2505C2214yes—
116#2504C2212yes—
117#2501C2212yes—
118#2500C2212yes—
119#2500C2212yes—
120#2497C2214yescomplemented
121#2496C2214yescomplemented
122#2491C2214yes—
123#2490C2214yes—
124#2481C2214yes—
125#2481C2218yes—
126#2480C2218yes—
127#2480C2218yes—
128#2473C2214yes—
129#2472C2218yes—
130#2454C2214yes—
131#2454C2214yes—
132#2452C2214yes—
133#2452C2214yes—
134#2452C2214yescomplemented
135#2451C2214yescomplemented
136#2449C2218yes—
137#2448C2214yes—
138#2447C2214yes—
139#2445C2214yes—
140#2445C2214yes—
141#2442C2218yes—
142#2441C2214yescomplemented
143#2440C2218yes—
144#2440C2214yescomplemented
145#2440C2214yescomplemented
146#2439C2214yescomplemented
147#2434C2214yes—
148#2422C2214yes—
149#2420C2214yes—
150#2418C2218yes—
151#2409C2214yes—
152#2402C2214yescomplemented
153#2401C2214yescomplemented
154C2×#399C2214yes—
155#2378C2218yescomplemented
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2317C2211yescharacteristic
160#2316C2211yescharacteristic
161#2316C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166#2309C2211yescharacteristic
167C4×#125C2214yescomplemented
168C4×#126C2214yescomplemented
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177C2×#390C2211yescharacteristic
178C2×#390C2211yescharacteristic
179#2285C2211yescharacteristic
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2312yes—
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#563—432no—
192#544—44no—
193#544—44no—
194#535—44no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2318yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2318yes—
204C2×#127C2312yes—
205C2×#126C2314yes—
206C2×#126C2318yes—
207C2×#126C2318yes—
208C2×#126C2318yes—
209C2×#125C2314yes—
210C2×#125C2318yes—
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#124C2318yes—
216C2×#124C2312yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×C22⋊Q8—416no—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#120C2314yes—
232#520—44no—
233C2×C4×Q8C2312yes—
234C2×C4×D4—44no—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2314yes—
257C22×C22⋊C4C2314yes—
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261#401C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2318yes—
279#399C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2314yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#391C2311yescharacteristic
330#391C2312yes—
331#391C2312yes—
332#391C2311yescharacteristic
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2314yes—
342#390C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2311yescharacteristic
346#390C2312yes—
347#390C2312yes—
348#390C2311yescharacteristic
349#390C2312yes—
350#390C2318yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2314yes—
357#390C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#387C2314yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2318yes—
413#386C2312yes—
414#386C2312yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2312yes—
425#385C2312yes—
426#385C2312yes—
427#385C2312yes—
428#385C2312yes—
429#385C2318yes—
430#385C2318yes—
431#385C2312yes—
432#385C2318yes—
433#385C2314yes—
434#385C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2318yes—
447#384C2312yes—
448#384C2314yes—
449#383C2314yes—
450#382C2314yes—
451#382C2312yes—
452#382C2312yes—
453#382C2312yes—
454#382C2318yes—
455#382C2312yes—
456#382C2312yes—
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2314yes—
466#380C2314yes—
467#379C2314yes—
468#379C2314yes—
469#379C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495#376C2312yes—
496#376C2312yes—
497C2×#95C2312yes—
498C43C2312yes—
499C43C2312yes—
500C25C2412yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8—44no—
505C22×Q8—48no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2418yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2411yescharacteristic
517C22×D4C2414yes—
518C22×D4C2414yes—
519C23×C4—48no—
520C23×C4—44no—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2418yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—48no—
533C4⋊Q8—48no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—416no—
539C4⋊Q8—416no—
540#127—44no—
541#126—216no—
542#126—416no—
543#126—416no—
544#126—416no—
545#125—216no—
546#125—44no—
547#125—44no—
548#125—44no—
549#125—44no—
550#125—416no—
551#124—416no—
552#124—44no—
553#123—416no—
554#123—416no—
555C22⋊Q8—232no—
556C22⋊Q8—48no—
557C22⋊Q8—48no—
558C22⋊Q8—416no—
559C22⋊Q8—416no—
560C22⋊Q8—416no—
561C22⋊Q8—416no—
562C22⋊Q8—416no—
563C22⋊Q8—416no—
564#121—44no—
565#121—44no—
566#120—48no—
567C4×Q8—44no—
568C4×D4—48no—
569C4×D4—48no—
570C4×D4—44no—
571C4×D4—48no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—44no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—28no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—48no—
586C2×C4⋊C4—48no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C22⋊C4—48no—
641C2×C22⋊C4—48no—
642C2×C22⋊C4—44no—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C42—24no—
673C2×C42—24no—
674C2×C42—24no—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733C24—24no—
734C24—24no—
735C24—24no—
736C24—44no—
737C24—44no—
738C24C2514yes—
739C24C2512yes—
740C24C2511yescharacteristic
741#41—416no—
742C2×Q8—22no—
743C2×Q8—216no—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—48no—
747C2×Q8—48no—
748C2×Q8—48no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—48no—
752C2×Q8—816no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—416no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—216no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—44no—
793C22×C4—48no—
794C22×C4—816no—
795C22×C4H(5,𝔽2)14yes—
796C22×C42−1+414yes—
797C22×C42−1+414yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—22no—
830C4⋊C4—216no—
831C4⋊C4—216no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4H(5,𝔽2)18yes—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—28no—
907C42—28no—
908C42—22no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—22no—
913C42—22no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—44no—
919C42—44no—
920C42—44no—
921C42—48no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—28no—
926C23—24no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—28no—
934C23—416no—
935C23—48no—
936C23—84no—
937C23—84no—
938C23—88no—
939C23C2×H(5,𝔽2)12yes—
940C23C2×2−1+412yes—
941C23C2×2−1+412yes—
942C23C2611yescharacteristic
943Q8—44no—
944Q8—816no—
945Q8—164no—
946Q8—164no—
947D4—48no—
948D4—48no—
949D4—48no—
950D4—44no—
951D4—164no—
952D4—164no—
953C2×C4—28no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—44no—
1005C2×C4—48no—
1006C2×C4—816no—
1007C2×C4—84no—
1008C2×C4—84no—
1009C2×C4—84no—
1010C2×C4—164no—
1011C2×C4#563116yescomplemented
1012C2×C4C2×H(5,𝔽2)14yes—
1013C2×C4C2×H(5,𝔽2)14yes—
1014C2×C4C2×H(5,𝔽2)14yes—
1015C2×C4C2×H(5,𝔽2)12yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×2−1+412yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+412yes—
1021C22—22no—
1022C22—22no—
1023C22—24no—
1024C22—24no—
1025C22—44no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—48no—
1031C22—44no—
1032C22—48no—
1033C22—42no—
1034C22—44no—
1035C22—816no—
1036C22C2×#56314yes—
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C22×H(5,𝔽2)12yes—
1039C22C22×2−1+411yescharacteristic
1040C22C22×2−1+411yescharacteristic
1041C222−1+612yes—
1042C4—24no—
1043C4—24no—
1044C4—24no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4C2×#56314yes—
1063C4C2×#56314yes—
1064C2—24no—
1065C2—82no—
1066C2—84no—
1067C2C22×#56311yescharacteristic
1068C2#6283211yescharacteristic
1069C2#6288711yescharacteristic
1070C2#6291312yes—
1071C2#6291512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53118C2semidirect
2. #53082C2semidirect
3. #53001C2semidirect
4. #52997C2semidirect
5. #52426C2semidirect
6. #46109C2semidirect
7. #46105C2semidirect
8. #45998C2semidirect
9. #45993C2semidirect
10. #45446C2semidirect
11. #35576C2semidirect
12. #35574C2semidirect
13. #35558C2semidirect
14. #35557C2semidirect
15. #35532C2semidirect
17. #35286C2semidirect
18. #35275C2semidirect
19. #35266C2semidirect
21. #35174C2semidirect
23. C2×#2542C2semidirect
24. #34816C2semidirect
25. #34815C2semidirect
26. C2×#563C22semidirect
34. #2868C22semidirect
37. #2859C22semidirect
38. #2859C22semidirect
42. #2838C22semidirect
43. #2838C22semidirect
44. #2837C22semidirect
45. #2837C22semidirect
46. #2836C22semidirect
47. #2827C22semidirect
48. #2821C22semidirect
49. #2820C22semidirect
50. #2817C22semidirect
51. #2814C22semidirect
52. #2777C22semidirect
53. #2773C22semidirect
54. #2773C22semidirect
55. #2729C22semidirect
56. #2728C22semidirect
57. #2727C22semidirect
58. #2723C22semidirect
59. #2723C22semidirect
60. #2721C22semidirect
61. #2720C22semidirect
62. #2718C22semidirect
63. #2702C22semidirect
64. #2698C22semidirect
65. #2690C22semidirect
66. #2689C22semidirect
67. #2683C22semidirect
68. #2680C22semidirect
69. #2677C22semidirect
70. #2674C22semidirect
71. #2674C22semidirect
72. #2660C22semidirect
73. #2660C22semidirect
74. #2647C22semidirect
82. #2571C22semidirect
83. #2567C22semidirect
84. #2566C22semidirect
85. #2565C22semidirect
86. #2552C22semidirect
87. #2552C22semidirect
88. #2551C22semidirect
89. #2551C22semidirect
90. #2551C22semidirect
91. #2550C22semidirect
92. #2550C22semidirect
97. #2542C22semidirect
98. #2514C22semidirect
102. #2513C22semidirect
106. #2512C22semidirect
107. #2512C22semidirect
108. #2511C22semidirect
109. #2511C22semidirect
111. #2509C22semidirect
112. #2508C22semidirect
113. #2507C22semidirect
114. #2506C22semidirect
120. #2497C22semidirect
121. #2496C22semidirect
134. #2452C22semidirect
135. #2451C22semidirect
142. #2441C22semidirect
144. #2440C22semidirect
145. #2440C22semidirect
146. #2439C22semidirect
152. #2402C22semidirect
153. #2401C22semidirect
155. #2378C22semidirect
167. C4×#125C22semidirect
168. C4×#126C22semidirect
1011. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#531182
#530822
#530012
#529972
#524262
#461092
#461052
#459982
#459932
#454462
#355762
#355742
#355582
#355572
#355322
#355312
#352862
#352752
#352662
#352642
#351742
#351522
C2×#25422
#348162
#348152