Finite Group Databasebeta

← #8429502

Subgroups — #8429502

Order 512.

4233 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59870C212yesmaximal, complemented
3#59451C212yesmaximal
4#59081C212yesmaximal, complemented
5#55136C218yesmaximal, complemented
6#53124C214yesmaximal, complemented
7#53118C214yesmaximal
8#53091C214yesmaximal, complemented
9#42856C214yesmaximal, complemented
10#42717C214yesmaximal, complemented
11#42600C214yesmaximal, complemented
12#39761C212yesmaximal
13#39625C212yesmaximal, complemented
14#39597C212yesmaximal, complemented
15#39192C212yesmaximal
16#39181C212yesmaximal, complemented
17#39157C212yesmaximal, complemented
18#37635C212yesmaximal, complemented
19#37631C212yesmaximal
20#37630C212yesmaximal, complemented
21#36563C211yesmaximal, characteristic, complemented
22Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic
26#34929C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#533C2212yes—
29C2×#533C2212yes—
30#2868C2211yescharacteristic
31#2868C2212yes—
32#2859C2212yes—
33#2857C2212yes—
34#2839C2218yes—
35#2838C2218yes—
36#2838C2218yes—
37#2838C2218yes—
38#2833C2218yes—
39#2821C2218yes—
40#2817C2218yes—
41#2810C2214yes—
42#2805C2218yes—
43#2793C2218yes—
44#2792C2218yes—
45#2777C2218yes—
46#2776C2218yes—
47#2774C2218yes—
48#2773C2218yes—
49#2772C2218yes—
50#2762C2218yes—
51#2762C2218yes—
52#2734C2218yes—
53#2729C2218yes—
54#2725C2218yes—
55#2716C2218yes—
56#2713C2218yes—
57#2713C2218yes—
58#2689C2218yes—
59#2677C2218yes—
60#2660C2214yes—
61#2655C2218yes—
62#2655C2218yes—
63#2650C2218yes—
64#2647C2214yes—
65#2645C2214yes—
66#2645C2214yes—
67#2642C2214yes—
68#2640C2214yes—
69#2634C2218yes—
70#2628C2214yes—
71#2625C2214yes—
72#2625C2214yes—
73#2596C2218yes—
74#2585C2214yes—
75#2582C2212yes—
76#2582C2211yescharacteristic
77#2581C2214yes—
78#2581C2214yes—
79#2581C2214yes—
80#2573C2214yes—
81#2571C2211yescharacteristic
82#2571C2214yes—
83#2570C2214yes—
84#2568C2211yescharacteristic
85#2568C2212yes—
86#2568C2212yes—
87#2568C2211yescharacteristic
88#2568C2212yes—
89#2567C2212yes—
90#2567C2212yes—
91#2567C2214yes—
92#2567C2214yes—
93#2556C2214yes—
94#2552C2212yes—
95#2552C2212yes—
96#2552C2211yescharacteristic
97#2551C2214yes—
98#2551C2212yes—
99#2551C2214yes—
100#2551C2214yes—
101#2551C2214yes—
102#2551C2211yescharacteristic
103#2551C2212yes—
104#2550C2214yes—
105#2550C2214yes—
106#2547C2211yescharacteristic
107#2546C2214yes—
108#2546C2211yescharacteristic
109#2546C2211yescharacteristic
110#2542C2212yes—
111#2542C2211yescharacteristic
112#2538C2211yescharacteristic
113#2538C2212yes—
114#2538C2211yescharacteristic
115#2514C2214yes—
116#2514C2212yes—
117#2514C2214yes—
118#2514C2214yes—
119#2513C2214yes—
120#2512C2214yes—
121#2511C2214yes—
122#2511C2214yes—
123#2511C2212yes—
124#2509C2214yes—
125#2509C2214yes—
126#2509C2218yes—
127#2509C2212yes—
128#2507C2214yes—
129#2507C2214yes—
130#2506C2212yes—
131#2499C2214yes—
132#2499C2214yes—
133#2496C2214yes—
134#2496C2214yes—
135#2494C2214yes—
136#2494C2212yes—
137#2492C2214yes—
138#2492C2212yes—
139#2492C2214yes—
140#2489C2214yes—
141#2453C2214yes—
142#2453C2212yes—
143#2452C2212yes—
144#2451C2214yes—
145#2451C2214yes—
146#2451C2214yes—
147#2448C2214yes—
148#2447C2212yes—
149#2446C2218yes—
150#2446C2212yes—
151#2446C2214yes—
152#2441C2214yes—
153#2439C2214yes—
154#2429C2214yes—
155#2429C2214yes—
156#2429C2212yes—
157#2423C2214yes—
158#2423C2214yes—
159#2421C2212yes—
160#2402C2214yes—
161#2401C2214yes—
162#2396C2214yes—
163#2369C2212yes—
164#2365C2212yes—
165#2365C2214yes—
166#2362C2214yes—
167#2355C2212yes—
168#2355C2214yes—
169#2355C2212yes—
170#2355C2212yes—
171#2355C2212yes—
172#2354C2212yes—
173Q8×C4⋊C4C2212yes—
174Q8×C4⋊C4C2212yes—
175Q8×C4⋊C4C2212yes—
176Q8×C4⋊C4C2212yes—
177#2331C2214yes—
178#2330C2214yes—
179#2323C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2212yes—
187C4×#125C2212yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199Q82—48no—
200#533—48no—
201#533—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2318yes—
215C2×C4⋊Q8C2318yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2314yes—
218C2×#126C2318yes—
219C2×#125C2312yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#124C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2314yes—
251C2×#117C2314yes—
252C22×C42C2312yes—
253#401C2314yes—
254#401C2318yes—
255#401C2318yes—
256#400C2314yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2314yes—
261#400C2318yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#399C2318yes—
280#399C2318yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2318yes—
304#397C2314yes—
305#397C2318yes—
306#396C2314yes—
307#396C2314yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2314yes—
321#393C2314yes—
322#393C2318yes—
323#393C2318yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2314yes—
343#391C2312yes—
344#391C2318yes—
345#391C2312yes—
346#391C2318yes—
347#391C2314yes—
348#391C2318yes—
349#391C2312yes—
350#391C2312yes—
351#391C2318yes—
352#391C2312yes—
353#390C2314yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2318yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2312yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2318yes—
392#389C2318yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2318yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#388C2314yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#387C2318yes—
429#387C2318yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2314yes—
441#385C2314yes—
442#385C2314yes—
443#384C2312yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2312yes—
448#384C2312yes—
449#384C2311yescharacteristic
450#384C2314yes—
451#384C2312yes—
452#384C2314yes—
453#384C2314yes—
454#384C2314yes—
455#384C2312yes—
456#384C2314yes—
457#383C2318yes—
458#383C2314yes—
459#382C2312yes—
460#382C2314yes—
461#382C2312yes—
462#382C2314yes—
463#382C2314yes—
464#382C2312yes—
465#382C2312yes—
466#382C2318yes—
467#382C2314yes—
468#381C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517#376C2314yes—
518#376C2314yes—
519C43C2312yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2418yes—
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—28no—
535C4⋊Q8—24no—
536C4⋊Q8—28no—
537C4⋊Q8—24no—
538C4⋊Q8—24no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—48no—
542C4⋊Q8—44no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545C4⋊Q8—44no—
546C4⋊Q8—416no—
547C4⋊Q8—88no—
548C4⋊Q8—82no—
549C4⋊Q8—84no—
550#126—88no—
551#125—28no—
552#125—48no—
553#125—48no—
554#125—84no—
555#124—44no—
556C22⋊Q8—28no—
557C22⋊Q8—28no—
558C22⋊Q8—48no—
559C22⋊Q8—44no—
560C22⋊Q8—44no—
561C22⋊Q8—48no—
562C22⋊Q8—48no—
563C22⋊Q8—84no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—28no—
571C4×Q8—28no—
572C4×Q8—24no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×Q8—48no—
576C4×Q8—48no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—42no—
582#117—48no—
583#117—48no—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C42—28no—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2411yescharacteristic
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2418yes—
684C2×C42C2412yes—
685C2×C42C2418yes—
686C2×C42C2411yescharacteristic
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24C2512yes—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—28no—
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—44no—
762C2×Q8—44no—
763C2×Q8—44no—
764C2×Q8—44no—
765C2×Q8—44no—
766C2×Q8—48no—
767C2×Q8—48no—
768C2×Q8—48no—
769C2×Q82−1+414yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2514yes—
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2518yes—
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—22no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—42no—
856C4⋊C4—48no—
857C4⋊C4—42no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—42no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C42−1+414yes—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—42no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—28no—
889C42—24no—
890C42—24no—
891C42—22no—
892C42—22no—
893C42—24no—
894C42—24no—
895C42—28no—
896C42—28no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—48no—
904C42—48no—
905C42—48no—
906C42—42no—
907C42—48no—
908C42—41no—
909C42—42no—
910C42H(5,𝔽2)14yes—
911C422−1+414yes—
912C422−1+414yes—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23C2611yescharacteristic
921Q8—28no—
922Q8—48no—
923Q8—44no—
924Q8—48no—
925Q8—48no—
926Q8—88no—
927Q8—88no—
928Q8—168no—
929D4—44no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—28no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—28no—
990C2×C4—22no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—84no—
994C2×C4C2×H(5,𝔽2)12yes—
995C2×C4C2×H(5,𝔽2)12yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×2−1+414yes—
998C2×C4C2×2−1+414yes—
999C2×C4C2×2−1+412yes—
1000C2×C4C2×2−1+412yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4C2×2−1+412yes—
1007C2×C4#58512yes—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22C22×H(5,𝔽2)11yescharacteristic
1016C22C22×2−1+411yescharacteristic
1017C22C22×2−1+411yescharacteristic
1018C22C22×2−1+411yescharacteristic
1019C22C22×2−1+411yescharacteristic
1020C22C2×#58511yescharacteristic
1021C22H(7,𝔽2)11yescharacteristic
1022C4—24no—
1023C4—24no—
1024C4—22no—
1025C4—22no—
1026C4—22no—
1027C4—42no—
1028C4—44no—
1029C4—44no—
1030C4—42no—
1031C4—44no—
1032C4—42no—
1033C4—41no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—42no—
1040C4—42no—
1041C4—48no—
1042C4—44no—
1043C4—42no—
1044C4#355014yes—
1045C4#355214yes—
1046C4#355514yes—
1047C2—82no—
1048C2C2×#355211yescharacteristic
1049C2C2×#355511yescharacteristic
1050C2C2×#355011yescharacteristic
1051C2#6294311yescharacteristic
1052C2#6294311yescharacteristic
1053C2#6295511yescharacteristic
1054C2#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. #59875C2semidirect
2. #59870C2semidirect
4. #59081C2semidirect
5. #55136C2semidirect
6. #53124C2semidirect
8. #53091C2semidirect
9. #42856C2semidirect
10. #42717C2semidirect
11. #42600C2semidirect
13. #39625C2semidirect
14. #39597C2semidirect
16. #39181C2semidirect
17. #39157C2semidirect
18. #37635C2semidirect
20. #37630C2semidirect
21. #36563C2semidirect
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
#598752
#598702
#594512
#590812
#551362
#531242
#531182
#530912
#428562
#427172
#426002
#397612
#396252
#395972
#391922
#391812
#391572
#376352
#376312
#376302
#365632
Q8×C4⋊Q82
#361342
#349512
#349452
#349292