Finite Group Databasebeta

← #8429321

Subgroups — #8429321

Order 512.

4443 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C212yesmaximal, complemented
2#59870C211yesmaximal, characteristic, complemented
3#59464C212yesmaximal, complemented
4#59071C212yesmaximal, complemented
5#55146C218yesmaximal, complemented
6#53140C214yesmaximal, complemented
7#53121C214yesmaximal, complemented
8#53107C214yesmaximal, complemented
9#42840C214yesmaximal, complemented
10#42791C214yesmaximal, complemented
11#42626C214yesmaximal
12#39641C212yesmaximal, complemented
13#39599C212yesmaximal, complemented
14#39385C212yesmaximal
15#39353C212yesmaximal, complemented
16#39192C212yesmaximal
17#39180C212yesmaximal, complemented
18#37641C212yesmaximal, complemented
19#37637C212yesmaximal
20#37628C212yesmaximal
21#36593C211yesmaximal, characteristic, complemented
22#36560C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34941C211yesmaximal, characteristic
26#34929C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#541C2214yes—
30C2×#533C2212yes—
31C2×#533C2212yes—
32#2868C2211yescharacteristic
33#2868C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2839C2218yes—
37#2839C2218yes—
38#2836C2218yes—
39#2831C2218yes—
40#2831C2218yes—
41#2822C2218yes—
42#2822C2218yes—
43#2806C2218yes—
44#2805C2214yes—
45#2798C2218yes—
46#2791C2218yes—
47#2791C2218yes—
48#2774C2218yes—
49#2772C2218yes—
50#2755C2218yes—
51#2726C2218yes—
52#2726C2218yes—
53#2726C2218yes—
54#2725C2218yes—
55#2725C2218yes—
56#2722C2218yes—
57#2721C2218yes—
58#2721C2218yes—
59#2719C2218yes—
60#2719C2218yes—
61#2704C2218yes—
62#2664C2218yes—
63#2654C2218yes—
64#2647C2214yes—
65#2647C2214yes—
66#2644C2214yes—
67#2637C2218yes—
68#2629C2214yes—
69#2625C2214yes—
70#2625C2214yes—
71#2625C2218yes—
72#2625C2214yes—
73#2621C2214yes—
74#2621C2214yes—
75#2588C2218yes—
76#2585C2214yes—
77#2584C2214yes—
78#2584C2218yes—
79#2582C2214yes—
80#2582C2214yes—
81#2582C2214yes—
82#2582C2211yescharacteristic
83#2581C2214yes—
84#2574C2214yes—
85#2571C2212yes—
86#2568C2211yescharacteristic
87#2568C2214yes—
88#2568C2212yes—
89#2568C2212yes—
90#2567C2212yes—
91#2567C2211yescharacteristic
92#2565C2214yes—
93#2563C2211yescharacteristic
94#2556C2214yes—
95#2552C2212yes—
96#2552C2211yescharacteristic
97#2552C2214yes—
98#2552C2212yes—
99#2552C2214yes—
100#2552C2212yes—
101#2552C2214yes—
102#2552C2214yes—
103#2552C2214yes—
104#2552C2211yescharacteristic
105#2551C2211yescharacteristic
106#2550C2214yes—
107#2546C2214yes—
108#2546C2212yes—
109#2546C2212yes—
110#2546C2214yes—
111#2546C2214yes—
112#2546C2211yescharacteristic
113#2546C2211yescharacteristic
114#2546C2212yes—
115#2542C2212yes—
116#2542C2211yescharacteristic
117#2538C2212yes—
118#2538C2211yescharacteristic
119#2538C2211yescharacteristic
120#2513C2214yes—
121#2512C2214yes—
122#2512C2214yes—
123#2511C2214yes—
124#2511C2212yes—
125#2509C2214yes—
126#2509C2214yes—
127#2509C2212yes—
128#2508C2214yes—
129#2508C2212yes—
130#2507C2214yes—
131#2507C2214yes—
132#2507C2214yes—
133#2506C2214yes—
134#2506C2214yes—
135#2506C2212yes—
136#2506C2214yes—
137#2497C2212yes—
138#2496C2214yes—
139#2496C2214yes—
140#2492C2212yes—
141#2489C2214yes—
142#2475C2218yes—
143#2454C2212yes—
144#2453C2214yes—
145#2453C2212yes—
146#2453C2214yes—
147#2452C2212yes—
148#2451C2214yes—
149#2446C2212yes—
150#2446C2214yes—
151#2446C2214yes—
152#2441C2214yes—
153#2429C2214yes—
154#2429C2214yes—
155#2429C2212yes—
156#2429C2214yes—
157#2429C2214yes—
158#2429C2214yes—
159#2423C2214yes—
160#2423C2212yes—
161#2421C2214yes—
162#2402C2214yes—
163#2396C2214yes—
164#2396C2214yes—
165#2369C2214yes—
166#2365C2212yes—
167#2365C2212yes—
168#2365C2214yes—
169#2365C2212yes—
170#2365C2212yes—
171#2355C2212yes—
172#2354C2212yes—
173#2351C2214yes—
174Q8×C4⋊C4C2212yes—
175Q8×C4⋊C4C2212yes—
176Q8×C4⋊C4C2212yes—
177Q8×C4⋊C4C2212yes—
178#2330C2214yes—
179#2323C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2212yes—
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2211yescharacteristic
187C4×#125C2212yes—
188C4×#125C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#557—48no—
200#557—48no—
201#541—416no—
202#533—48no—
203#533—48no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×#126C2318yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#125C2314yes—
227C2×#125C2318yes—
228C2×#125C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C22×C42C2312yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#400C2318yes—
278#399C2318yes—
279#399C2314yes—
280#399C2314yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2314yes—
304#398C2314yes—
305#398C2318yes—
306#398C2314yes—
307#398C2314yes—
308#398C2318yes—
309#398C2314yes—
310#398C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#396C2314yes—
319#396C2318yes—
320#396C2314yes—
321#396C2318yes—
322#396C2314yes—
323#396C2318yes—
324#396C2314yes—
325#396C2318yes—
326#395C2314yes—
327#395C2318yes—
328#395C2318yes—
329#395C2314yes—
330#393C2314yes—
331#393C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2314yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2312yes—
342#391C2314yes—
343#391C2318yes—
344#391C2314yes—
345#391C2312yes—
346#391C2318yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#391C2318yes—
351#391C2312yes—
352#391C2314yes—
353#391C2312yes—
354#391C2312yes—
355#390C2312yes—
356#390C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2312yes—
386#389C2314yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2314yes—
391#389C2314yes—
392#389C2318yes—
393#389C2318yes—
394#389C2312yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2314yes—
401#389C2318yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2318yes—
406#389C2312yes—
407#389C2318yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2314yes—
422#388C2318yes—
423#388C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2314yes—
440#387C2314yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2314yes—
447#385C2314yes—
448#385C2314yes—
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#384C2314yes—
458#384C2312yes—
459#384C2314yes—
460#384C2312yes—
461#384C2314yes—
462#384C2314yes—
463#384C2314yes—
464#384C2312yes—
465#384C2314yes—
466#382C2312yes—
467#382C2312yes—
468#382C2314yes—
469#382C2314yes—
470#382C2318yes—
471#382C2314yes—
472#382C2314yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2311yescharacteristic
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×D4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C4⋊Q8—28no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547C4⋊Q8—48no—
548#126—416no—
549#126—416no—
550#125—28no—
551#125—28no—
552#125—48no—
553#125—48no—
554#125—416no—
555#125—48no—
556#125—48no—
557#125—416no—
558#125—416no—
559#125—416no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—48no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568C4×Q8—24no—
569C4×Q8—216no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—28no—
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—48no—
578C4×Q8—44no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588#117—48no—
589#117—48no—
590#117—48no—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C42—28no—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2418yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2418yes—
697C2×C42C2418yes—
698C2×C42C2418yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2412yes—
717#95C2412yes—
718#95C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753C24C2512yes—
754C2×Q8—22no—
755C2×Q8—22no—
756C2×Q8—28no—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—28no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—24no—
767C2×Q8—28no—
768C2×Q8—24no—
769C2×Q8—28no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q82−1+414yes—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—42no—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2514yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2518yes—
802C22×C4C2512yes—
803C22×C4C2511yescharacteristic
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—216no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—42no—
854C4⋊C4—42no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4H(5,𝔽2)14yes—
882C4⋊C42−1+414yes—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—28no—
902C42—28no—
903C42—24no—
904C42—22no—
905C42—24no—
906C42—216no—
907C42—22no—
908C42—24no—
909C42—22no—
910C42—24no—
911C42—28no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—41no—
917C42—42no—
918C42—42no—
919C42—48no—
920C42—48no—
921C42—48no—
922C42H(5,𝔽2)14yes—
923C422−1+414yes—
924C422−1+414yes—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23C2611yescharacteristic
933Q8—28no—
934Q8—48no—
935Q8—44no—
936Q8—48no—
937Q8—416no—
938Q8—48no—
939Q8—88no—
940D4—44no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C2×C4C2×H(5,𝔽2)12yes—
1006C2×C4C2×H(5,𝔽2)12yes—
1007C2×C4C2×H(5,𝔽2)12yes—
1008C2×C4C2×H(5,𝔽2)12yes—
1009C2×C4C2×2−1+414yes—
1010C2×C4C2×2−1+412yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4C2×2−1+414yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4C2×2−1+412yes—
1017C2×C4C2×2−1+412yes—
1018C2×C4C2×2−1+412yes—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22C22×H(5,𝔽2)11yescharacteristic
1027C22C22×H(5,𝔽2)11yescharacteristic
1028C22C22×2−1+411yescharacteristic
1029C22C22×2−1+411yescharacteristic
1030C22C22×2−1+411yescharacteristic
1031C22C22×2−1+411yescharacteristic
1032C222−1+611yescharacteristic
1033C4—24no—
1034C4—24no—
1035C4—22no—
1036C4—22no—
1037C4—24no—
1038C4—22no—
1039C4—42no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—48no—
1045C4—44no—
1046C4—42no—
1047C4—41no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4—42no—
1052C4—44no—
1053C4—42no—
1054C4—42no—
1055C4#354814yes—
1056C4#355214yes—
1057C4#355614yes—
1058C2—82no—
1059C2C2×#355211yescharacteristic
1060C2C2×#354811yescharacteristic
1061C2C2×#355611yescharacteristic
1062C2#6291311yescharacteristic
1063C2#6294211yescharacteristic
1064C2#6294711yescharacteristic
1065C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59870C2semidirect
3. #59464C2semidirect
4. #59071C2semidirect
5. #55146C2semidirect
6. #53140C2semidirect
7. #53121C2semidirect
8. #53107C2semidirect
9. #42840C2semidirect
10. #42791C2semidirect
12. #39641C2semidirect
13. #39599C2semidirect
15. #39353C2semidirect
17. #39180C2semidirect
18. #37641C2semidirect
21. #36593C2semidirect
22. #36560C2semidirect
24. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598702
#594642
#590712
#551462
#531402
#531212
#531072
#428402
#427912
#426262
#396412
#395992
#393852
#393532
#391922
#391802
#376412
#376372
#376282
#365932
#365602
#361342
#349512
#349412
#349292