Finite Group Databasebeta

← #8429490

Subgroups — #8429490

Order 512.

4247 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59655C212yesmaximal
3#59437C212yesmaximal
4#59321C212yesmaximal, complemented
5#53717C218yesmaximal, complemented
6#53034C214yesmaximal, complemented
7#53002C214yesmaximal, complemented
8#53002C214yesmaximal, complemented
9#42848C214yesmaximal, complemented
10#42639C214yesmaximal
11#42610C214yesmaximal, complemented
12#39753C212yesmaximal, complemented
13#39633C212yesmaximal
14#39619C212yesmaximal, complemented
15#39173C212yesmaximal
16#39159C212yesmaximal, complemented
17#39149C212yesmaximal, complemented
18#37638C212yesmaximal, complemented
19#37630C212yesmaximal, complemented
20#37623C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
23#36180C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic
26#34945C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#557C2212yes—
29C2×#554C2212yes—
30#2868C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2857C2212yes—
34#2843C2218yes—
35#2839C2218yes—
36#2839C2218yes—
37#2835C2218yes—
38#2833C2218yes—
39#2833C2218yes—
40#2833C2218yes—
41#2791C2218yes—
42#2791C2218yes—
43#2790C2218yes—
44#2787C2218yes—
45#2787C2218yes—
46#2776C2218yes—
47#2776C2218yes—
48#2758C2218yes—
49#2745C2218yes—
50#2739C2218yes—
51#2729C2218yes—
52#2729C2218yes—
53#2726C2214yes—
54#2713C2218yes—
55#2713C2218yes—
56#2713C2218yes—
57#2690C2218yes—
58#2690C2218yes—
59#2690C2218yes—
60#2660C2214yes—
61#2660C2214yes—
62#2655C2218yes—
63#2652C2218yes—
64#2647C2214yes—
65#2647C2214yes—
66#2647C2214yes—
67#2645C2214yes—
68#2645C2214yes—
69#2645C2214yes—
70#2642C2214yes—
71#2634C2218yes—
72#2627C2218yes—
73#2585C2214yes—
74#2582C2212yes—
75#2582C2211yescharacteristic
76#2582C2212yes—
77#2577C2218yes—
78#2573C2214yes—
79#2573C2214yes—
80#2571C2211yescharacteristic
81#2571C2211yescharacteristic
82#2571C2212yes—
83#2570C2214yes—
84#2570C2214yes—
85#2568C2212yes—
86#2568C2214yes—
87#2568C2211yescharacteristic
88#2568C2211yescharacteristic
89#2568C2211yescharacteristic
90#2567C2212yes—
91#2567C2212yes—
92#2567C2214yes—
93#2565C2214yes—
94#2565C2214yes—
95#2552C2212yes—
96#2552C2212yes—
97#2552C2214yes—
98#2552C2211yescharacteristic
99#2552C2212yes—
100#2551C2212yes—
101#2551C2214yes—
102#2551C2214yes—
103#2551C2212yes—
104#2550C2214yes—
105#2547C2211yescharacteristic
106#2547C2214yes—
107#2547C2211yescharacteristic
108#2546C2212yes—
109#2546C2211yescharacteristic
110#2538C2211yescharacteristic
111#2538C2211yescharacteristic
112#2514C2214yes—
113#2514C2214yes—
114#2514C2212yes—
115#2514C2212yes—
116#2511C2212yes—
117#2511C2214yes—
118#2511C2214yes—
119#2509C2212yes—
120#2509C2214yes—
121#2506C2214yes—
122#2506C2214yes—
123#2506C2214yes—
124#2502C2214yes—
125#2502C2214yes—
126#2497C2214yes—
127#2495C2214yes—
128#2494C2212yes—
129#2494C2214yes—
130#2494C2212yes—
131#2492C2214yes—
132#2492C2214yes—
133#2473C2218yes—
134#2453C2214yes—
135#2453C2212yes—
136#2453C2214yes—
137#2452C2214yes—
138#2451C2214yes—
139#2451C2214yes—
140#2447C2212yes—
141#2447C2212yes—
142#2446C2214yes—
143#2446C2214yes—
144#2446C2212yes—
145#2446C2214yes—
146#2446C2214yes—
147#2442C2214yes—
148#2442C2214yes—
149#2442C2214yes—
150#2440C2214yes—
151#2440C2214yes—
152#2440C2214yes—
153#2440C2214yes—
154#2429C2214yes—
155#2429C2218yes—
156#2421C2214yes—
157#2421C2214yes—
158#2421C2212yes—
159#2421C2212yes—
160#2402C2214yes—
161#2401C2214yes—
162#2401C2214yes—
163#2367C2214yes—
164#2365C2212yes—
165#2365C2212yes—
166#2360C2214yes—
167#2355C2212yes—
168#2355C2212yes—
169Q8×C4⋊C4C2212yes—
170Q8×C4⋊C4C2212yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174#2345C2214yes—
175#2331C2214yes—
176#2327C2214yes—
177#2326C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193C2×#384C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199Q82—48no—
200#557—48no—
201#554—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2318yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#125C2318yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C42C2312yes—
249#401C2314yes—
250#401C2318yes—
251#401C2314yes—
252#401C2318yes—
253#400C2318yes—
254#400C2314yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2314yes—
259#400C2318yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2318yes—
304#397C2314yes—
305#397C2314yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#396C2314yes—
310#396C2314yes—
311#396C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#393C2318yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2314yes—
333#391C2318yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2318yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#390C2312yes—
351#390C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2318yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2312yes—
391#389C2312yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2314yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2318yes—
423#387C2314yes—
424#387C2314yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#385C2314yes—
429#385C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2312yes—
441#384C2314yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2314yes—
446#384C2312yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2314yes—
451#383C2314yes—
452#383C2314yes—
453#383C2318yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2312yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#382C2312yes—
464#381C2314yes—
465#381C2314yes—
466#380C2318yes—
467#380C2312yes—
468#380C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2314yes—
518#376C2314yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C43C2312yes—
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2414yes—
528C22×Q8C2418yes—
529C22×D4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2418yes—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—24no—
538C4⋊Q8—24no—
539C4⋊Q8—44no—
540C4⋊Q8—48no—
541C4⋊Q8—48no—
542C4⋊Q8—48no—
543C4⋊Q8—48no—
544C4⋊Q8—416no—
545C4⋊Q8—82no—
546C4⋊Q8—84no—
547#125—44no—
548#125—48no—
549#125—48no—
550#125—416no—
551#125—88no—
552#124—28no—
553#124—28no—
554C22⋊Q8—28no—
555C22⋊Q8—416no—
556C22⋊Q8—44no—
557C22⋊Q8—48no—
558C22⋊Q8—88no—
559C4×Q8—24no—
560C4×Q8—28no—
561C4×Q8—28no—
562C4×Q8—24no—
563C4×Q8—24no—
564C4×Q8—24no—
565C4×Q8—28no—
566C4×Q8—24no—
567C4×Q8—42no—
568C4×Q8—48no—
569C4×Q8—48no—
570C4×Q8—48no—
571C4×Q8—48no—
572C4×Q8—84no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—48no—
577C2×C4⋊C4—48no—
578C2×C4⋊C4—48no—
579C2×C4⋊C4—84no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C42—28no—
655C2×C42C2414yes—
656C2×C42C2411yescharacteristic
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2418yes—
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2412yes—
696#95C2412yes—
697#95C2414yes—
698#95C2412yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2418yes—
715#95C2414yes—
716#95C2418yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741C24C2512yes—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—28no—
747C2×Q8—22no—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—48no—
760C2×Q8—48no—
761C2×Q8—48no—
762C2×Q82−1+414yes—
763C2×D4—22no—
764C2×D4—22no—
765C2×D42−1+414yes—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—42no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2518yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C4⋊C4—24no—
804C4⋊C4—28no—
805C4⋊C4—22no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—22no—
837C4⋊C4—24no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—42no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C4⋊C4—42no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—42no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—42no—
865C22⋊C4—24no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C42—28no—
878C42—28no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—22no—
884C42—24no—
885C42—22no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—28no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—22no—
894C42—24no—
895C42—42no—
896C42—48no—
897C42—48no—
898C42—42no—
899C42—48no—
900C42—41no—
901C42—42no—
902C42H(5,𝔽2)14yes—
903C422−1+414yes—
904C422−1+414yes—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23C2×2−1+414yes—
912C23C2611yescharacteristic
913Q8—28no—
914Q8—48no—
915Q8—48no—
916Q8—48no—
917Q8—44no—
918Q8—88no—
919Q8—168no—
920D4—28no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—28no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—48no—
986C2×C4—168no—
987C2×C4C2×H(5,𝔽2)12yes—
988C2×C4C2×H(5,𝔽2)12yes—
989C2×C4C2×H(5,𝔽2)12yes—
990C2×C4C2×2−1+412yes—
991C2×C4C2×2−1+414yes—
992C2×C4C2×2−1+412yes—
993C2×C4C2×2−1+412yes—
994C2×C4C2×2−1+412yes—
995C2×C4C2×2−1+412yes—
996C2×C4C2×2−1+412yes—
997C2×C4C2×2−1+412yes—
998C2×C4C2×2−1+412yes—
999C2×C4#58512yes—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22C22×H(5,𝔽2)11yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C22×2−1+411yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C22×2−1+411yescharacteristic
1012C22C2×#58511yescharacteristic
1013C22H(7,𝔽2)11yescharacteristic
1014C4—24no—
1015C4—22no—
1016C4—22no—
1017C4—22no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—44no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—44no—
1033C4—48no—
1034C4—44no—
1035C4—42no—
1036C4#355214yes—
1037C4#355214yes—
1038C4#355514yes—
1039C2—44no—
1040C2C2×#355211yescharacteristic
1041C2C2×#355211yescharacteristic
1042C2C2×#355511yescharacteristic
1043C2#6294311yescharacteristic
1044C2#6294511yescharacteristic
1045C2#6296111yescharacteristic
1046C2#6303211yescharacteristic
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. #59828C2semidirect
4. #59321C2semidirect
5. #53717C2semidirect
6. #53034C2semidirect
7. #53002C2semidirect
8. #53002C2semidirect
9. #42848C2semidirect
11. #42610C2semidirect
12. #39753C2semidirect
14. #39619C2semidirect
16. #39159C2semidirect
17. #39149C2semidirect
18. #37638C2semidirect
19. #37630C2semidirect
20. #37623C2semidirect
21. #36598C2semidirect
22. Q8×C4⋊Q8C2semidirect
24. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#596552
#594372
#593212
#537172
#530342
#530022
#428482
#426392
#426102
#397532
#396332
#396192
#391732
#391592
#391492
#376382
#376302
#376232
#365982
Q8×C4⋊Q82
#361802
#349512
#349452