Finite Group Databasebeta

← #7739335

Subgroups — #7739335

Order 512.

4384 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C212yesmaximal, complemented
2#59642C212yesmaximal, complemented
3#59450C212yesmaximal, complemented
4#59443C212yesmaximal, complemented
5#51619C218yesmaximal, complemented
6#45150C214yesmaximal
7#45145C214yesmaximal, complemented
8#45117C214yesmaximal, complemented
9#45116C214yesmaximal, complemented
10#39643C212yesmaximal, complemented
11#39159C212yesmaximal, complemented
12#38986C212yesmaximal, complemented
13#38933C212yesmaximal, complemented
14#37415C214yesmaximal, complemented
15#36552C212yesmaximal, complemented
16#36476C212yesmaximal, complemented
17#36177C212yesmaximal, complemented
18#36175C212yesmaximal, complemented
19#35648C214yesmaximal, complemented
20#35320C211yesmaximal, characteristic, complemented
21#35279C211yesmaximal, characteristic
22#34979C211yesmaximal, characteristic
23#34978C211yesmaximal, characteristic, complemented
24#34374C211yesmaximal, characteristic, complemented
25#34216C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic
27C2×#533C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30#2862C2212yes—
31#2862C2212yes—
32#2857C2212yes—
33#2857C2212yes—
34#2855C2214yes—
35#2851C2214yes—
36#2810C2218yes—
37#2807C2218yes—
38#2799C2218yes—
39#2789C2218yes—
40#2776C2218yes—
41#2771C2218yes—
42#2766C2218yes—
43#2758C2218yes—
44#2758C2218yes—
45#2755C2218yes—
46#2746C2218yes—
47#2745C2218yes—
48#2743C2218yes—
49#2739C2218yes—
50#2738C2218yes—
51#2738C2218yes—
52#2647C2214yes—
53#2645C2214yes—
54#2642C2214yes—
55#2628C2214yes—
56#2612C2214yes—
57#2611C2214yes—
58#2607C2218yes—
59#2590C2218yes—
60#2589C2218yes—
61#2589C2218yes—
62#2582C2214yes—
63#2580C2214yes—
64#2576C2218yes—
65#2575C2218yes—
66#2572C2218yes—
67#2571C2214yes—
68#2571C2211yescharacteristic
69#2570C2214yes—
70#2570C2214yes—
71#2568C2212yes—
72#2568C2212yes—
73#2568C2212yes—
74#2568C2214yes—
75#2568C2211yescharacteristic
76#2568C2212yes—
77#2568C2214yes—
78#2568C2212yes—
79#2567C2212yes—
80#2565C2214yes—
81#2563C2212yes—
82#2552C2211yescharacteristic
83#2552C2211yescharacteristic
84#2551C2211yescharacteristic
85#2547C2211yescharacteristic
86#2546C2211yescharacteristic
87#2542C2212yes—
88#2542C2211yescharacteristic
89#2533C2218yes—
90#2533C2218yes—
91#2527C2218yes—
92#2527C2218yes—
93#2523C2218yes—
94#2515C2218yes—
95#2514C2214yes—
96#2514C2214yes—
97#2514C2214yes—
98#2514C2214yes—
99#2514C2214yes—
100#2514C2218yes—
101#2514C2214yes—
102#2514C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2509C2214yes—
106#2508C2214yes—
107#2505C2218yes—
108#2503C2214yes—
109#2503C2214yes—
110#2503C2214yes—
111#2502C2214yes—
112#2499C2212yes—
113#2495C2214yes—
114#2494C2214yes—
115#2493C2218yes—
116#2492C2214yes—
117#2492C2214yes—
118#2489C2214yes—
119#2487C2214yes—
120#2453C2214yes—
121#2447C2214yes—
122#2446C2214yes—
123#2441C2212yes—
124#2441C2212yes—
125#2439C2212yes—
126#2439C2212yes—
127#2432C2212yes—
128#2423C2214yes—
129#2423C2214yes—
130#2421C2214yes—
131#2415C2212yes—
132#2415C2212yes—
133#2409C2214yes—
134#2396C2214yes—
135#2395C2214yes—
136#2382C2214yes—
137#2369C2212yes—
138#2369C2212yes—
139#2367C2214yes—
140#2365C2212yes—
141#2365C2212yes—
142#2365C2212yes—
143#2365C2212yes—
144#2360C2214yes—
145#2360C2214yes—
146#2357C2214yes—
147#2356C2214yes—
148#2356C2214yes—
149#2355C2211yescharacteristic
150#2355C2212yes—
151#2355C2214yes—
152#2355C2212yes—
153#2355C2211yescharacteristic
154#2355C2214yes—
155#2352C2212yes—
156#2352C2212yes—
157Q8×C4⋊C4C2212yes—
158Q8×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160D4×C4⋊C4C2211yescharacteristic
161#2347C2212yes—
162#2345C2214yes—
163#2343C2214yes—
164Q8×C22⋊C4C2214yes—
165#2339C2212yes—
166#2331C2214yes—
167#2331C2214yes—
168#2323C2214yes—
169#2323C2214yes—
170#2320C2214yes—
171#2317C2212yes—
172#2316C2212yes—
173#2314C2214yes—
174#2311C2212yes—
175#2310C2212yes—
176#2310C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×#125C2212yes—
183C4×#125C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2214yes—
187C4×C22⋊Q8C2212yes—
188#2295C2212yes—
189#2290C2214yes—
190#2285C2211yescharacteristic
191#2285C2211yescharacteristic
192#2283C2212yes—
193#2283C2214yes—
194#2274C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C23×Q8C2312yes—
201#533—28no—
202C2×C4⋊Q8—28no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#124C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C4×#41—28no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×#117C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C42C2312yes—
252C22×C42C2314yes—
253C22×C42C2311yescharacteristic
254#401C2318yes—
255#401C2318yes—
256#401C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2314yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#399C2318yes—
277#399C2318yes—
278#399C2314yes—
279#399C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#397C2318yes—
289#397C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2318yes—
293#396C2314yes—
294#396C2314yes—
295#395C2318yes—
296#395C2314yes—
297#394C2314yes—
298#394C2314yes—
299#393C2318yes—
300#393C2314yes—
301#393C2318yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2318yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2312yes—
335#390C2314yes—
336#390C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2318yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2314yes—
378#388C2318yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2318yes—
410#386C2318yes—
411#386C2314yes—
412#386C2314yes—
413#385C2318yes—
414#385C2314yes—
415#385C2318yes—
416#385C2318yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2314yes—
428#384C2314yes—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383C2318yes—
432#383C2318yes—
433#383C2314yes—
434#383C2318yes—
435#383C2318yes—
436#382C2312yes—
437#382C2312yes—
438#382C2314yes—
439#382C2312yes—
440#382C2312yes—
441#382C2314yes—
442#382C2312yes—
443#382C2314yes—
444#382C2314yes—
445#382C2318yes—
446#382C2314yes—
447#382C2314yes—
448#382C2318yes—
449#382C2312yes—
450#382C2312yes—
451#381C2318yes—
452#381C2318yes—
453#381C2318yes—
454#381C2314yes—
455#381C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462#380C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2314yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515#376C2314yes—
516#376C2312yes—
517#376C2312yes—
518#376C2318yes—
519C2×#95C2314yes—
520C43C2312yes—
521C43C2312yes—
522C2×#41—24no—
523C2×#41—24no—
524C2×#41—42no—
525C22×Q8—28no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×D4C2412yes—
535C22×D4C2411yescharacteristic
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C4⋊Q8—28no—
546C4⋊Q8—28no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554#125—28no—
555#125—44no—
556#125—44no—
557#124—28no—
558C22⋊Q8—28no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—44no—
562C22⋊Q8—48no—
563C22⋊Q8—48no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—28no—
567C4×Q8—28no—
568C4×Q8—48no—
569C4×Q8—48no—
570C4×Q8—48no—
571C4×Q8—48no—
572C4×Q8—48no—
573C4×D4—28no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—44no—
579#117—24no—
580#117—28no—
581#117—24no—
582#117—28no—
583#117—44no—
584#117—44no—
585#117—42no—
586#117—42no—
587#117—42no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C42—28no—
666C2×C42—48no—
667C2×C42#4118yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2418yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#95C2412yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2412yes—
703#95C2412yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750C24C2511yescharacteristic
751C24C2512yes—
752#41—416no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—28no—
757C2×Q8—28no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—28no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—22no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—816no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—42no—
777C2×D42−1+414yes—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4C2×#4114yes—
803C22×C4C2×#4114yes—
804C22×C4C2×#4114yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2518yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—42no—
863C4⋊C4—42no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C42−1+414yes—
884C22⋊C4—24no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—28no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—28no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—44no—
918C42—44no—
919C42—42no—
920C42—42no—
921C42—42no—
922C42—48no—
923C42—48no—
924C42—48no—
925C42—48no—
926C42C2×#4114yes—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C23—22no—
931C23—22no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—22no—
936C23—22no—
937C23—21no—
938C23—22no—
939C23—21no—
940C23—21no—
941C23—22no—
942C23C22×#4112yes—
943C23C2×2−1+414yes—
944C23C2611yescharacteristic
945Q8—48no—
946Q8—44no—
947Q8—48no—
948Q8—416no—
949Q8—88no—
950Q8—88no—
951D4—28no—
952D4—48no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—28no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—88no—
1019C2×C4—88no—
1020C2×C4—88no—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4112yes—
1027C2×C4C2×2−1+414yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4#58512yes—
1031C2×C4#58512yes—
1032C2×C4#58512yes—
1033C2×C4#58512yes—
1034C22—24no—
1035C22—24no—
1036C22—22no—
1037C22—22no—
1038C22—24no—
1039C22—22no—
1040C22—42no—
1041C22—41no—
1042C22—41no—
1043C22—42no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—42no—
1048C22C23×#4111yescharacteristic
1049C22C22×2−1+411yescharacteristic
1050C22C22×2−1+411yescharacteristic
1051C22C2×#58511yescharacteristic
1052C22C2×#58511yescharacteristic
1053C22C2×#58511yescharacteristic
1054C22C2×#58511yescharacteristic
1055C4—24no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—42no—
1060C4—44no—
1061C4—42no—
1062C4—44no—
1063C4—42no—
1064C4—44no—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—44no—
1074C4—42no—
1075C4—48no—
1076C4#349514yes—
1077C4#350714yes—
1078C4#351014yes—
1079C2—44no—
1080C2—42no—
1081C2C2×#350711yescharacteristic
1082C2C2×#349511yescharacteristic
1083C2C2×#351011yescharacteristic
1084C2#6302511yescharacteristic
1085C2#6302511yescharacteristic
1086C2#6303111yescharacteristic
1087C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59642C2semidirect
3. #59450C2semidirect
4. #59443C2semidirect
5. #51619C2semidirect
7. #45145C2semidirect
8. #45117C2semidirect
9. #45116C2semidirect
10. #39643C2semidirect
11. #39159C2semidirect
12. #38986C2semidirect
13. #38933C2semidirect
14. #37415C2semidirect
15. #36552C2semidirect
16. #36476C2semidirect
17. #36177C2semidirect
18. #36175C2semidirect
19. #35648C2semidirect
20. #35320C2semidirect
23. #34978C2semidirect
24. #34374C2semidirect
25. #34216C2semidirect

Maximal subgroups

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

subgroupindex
#598752
#596422
#594502
#594432
#516192
#451502
#451452
#451172
#451162
#396432
#391592
#389862
#389332
#374152
#365522
#364762
#361772
#361752
#356482
#353202
#352792
#349792
#349782
#343742
#342162
#341272