Finite Group Databasebeta

← #7688364

Subgroups — #7688364

Order 512.

4565 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#59876C214yesmaximal, complemented
2#59875C212yesmaximal, complemented
3#59863C211yesmaximal, characteristic
4#59434C212yesmaximal, complemented
5#59427C212yesmaximal, complemented
6#59296C214yesmaximal, complemented
7#45156C214yesmaximal, complemented
8#43717C218yesmaximal, complemented
9#40022C214yesmaximal, complemented
10#39771C212yesmaximal
11#39239C214yesmaximal, complemented
12#39172C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36594C211yesmaximal, characteristic
15#36590C212yesmaximal, complemented
16#36560C211yesmaximal, characteristic, complemented
17#36538C212yesmaximal
18#36416C212yesmaximal, complemented
19#36175C212yesmaximal, complemented
20#35974C214yesmaximal, complemented
21#34951C211yesmaximal, characteristic, complemented
22#34945C212yesmaximal, complemented
23#34328C212yesmaximal, complemented
24#34324C212yesmaximal, complemented
25C4×Q82C211yesmaximal, characteristic, complemented
26C4×#559C211yesmaximal, characteristic
27C2×#559C2211yescharacteristic
28C2×Q82C2211yescharacteristic
29C2×#557C2212yes—
30C2×#556C2212yes—
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2861C2214yes—
34#2859C2212yes—
35#2858C2212yes—
36#2851C2214yes—
37#2810C2218yes—
38#2808C2214yes—
39#2796C2218yes—
40#2793C2218yes—
41#2790C2218yes—
42#2783C2218yes—
43#2777C2218yes—
44#2765C2218yes—
45#2751C2218yes—
46#2716C2218yes—
47#2716C2218yes—
48#2654C2218yes—
49#2640C2214yes—
50#2594C2218yes—
51#2594C2218yes—
52#2592C2214yes—
53#2592C2214yes—
54#2589C2218yes—
55#2587C2218yes—
56#2585C2214yes—
57#2582C2212yes—
58#2582C2211yescharacteristic
59#2580C2214yes—
60#2573C2218yes—
61#2573C2218yes—
62#2571C2212yes—
63#2570C2214yes—
64#2568C2214yes—
65#2568C2214yes—
66#2568C2212yes—
67#2568C2211yescharacteristic
68#2568C2212yes—
69#2566C2214yes—
70#2565C2214yes—
71#2563C2212yes—
72#2558C2218yes—
73#2558C2218yes—
74#2552C2211yescharacteristic
75#2548C2212yes—
76#2547C2212yes—
77#2547C2212yes—
78#2546C2212yes—
79#2546C2211yescharacteristic
80#2546C2212yes—
81#2545C2214yes—
82#2545C2214yes—
83#2545C2214yes—
84#2545C2214yes—
85#2538C2212yes—
86#2538C2212yes—
87#2532C2218yes—
88#2532C2218yes—
89#2527C2218yes—
90#2527C2218yes—
91#2525C2218yes—
92#2525C2218yes—
93#2523C2218yes—
94#2514C2214yes—
95#2514C2214yes—
96#2514C2214yes—
97#2514C2214yes—
98#2514C2218yes—
99#2513C2214yes—
100#2513C2214yes—
101#2512C2214yes—
102#2512C2214yes—
103#2511C2212yes—
104#2511C2214yes—
105#2509C2212yes—
106#2506C2214yes—
107#2506C2214yes—
108#2497C2214yes—
109#2495C2214yes—
110#2494C2214yes—
111#2494C2214yes—
112#2485C2214yes—
113#2453C2212yes—
114#2448C2214yes—
115#2447C2214yes—
116#2447C2214yes—
117#2446C2212yes—
118#2446C2214yes—
119#2441C2214yes—
120#2439C2214yes—
121#2439C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2402C2214yes—
125#2401C2218yes—
126#2374C2214yes—
127#2373C2218yes—
128#2371C2218yes—
129#2370C2214yes—
130#2369C2211yescharacteristic
131#2369C2212yes—
132#2369C2212yes—
133#2369C2214yes—
134#2367C2214yes—
135#2367C2214yes—
136#2367C2212yes—
137#2367C2212yes—
138#2366C2211yescharacteristic
139#2365C2212yes—
140#2365C2214yes—
141#2365C2212yes—
142#2365C2212yes—
143#2362C2214yes—
144#2357C2212yes—
145#2357C2212yes—
146#2356C2214yes—
147#2356C2214yes—
148#2355C2214yes—
149#2355C2211yescharacteristic
150#2355C2212yes—
151#2355C2212yes—
152#2355C2214yes—
153#2355C2211yescharacteristic
154#2355C2212yes—
155#2354C2212yes—
156#2354C2212yes—
157#2354C2212yes—
158#2354C2212yes—
159Q8×C4⋊C4C2211yescharacteristic
160Q8×C4⋊C4C2211yescharacteristic
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163#2347C2214yes—
164#2346C2214yes—
165#2336C2218yes—
166#2334C2218yes—
167#2327C2214yes—
168#2326C2214yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2214yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×#127C2211yescharacteristic
179C4×#125C2214yes—
180C4×#125C2212yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×C22⋊Q8C2214yes—
185C4×#123C2214yes—
186#2296C2214yes—
187#2295C2212yes—
188#2295C2214yes—
189#2295C2212yes—
190#2283C2214yes—
191#2276C2214yes—
192C42×Q8C2212yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2212yes—
198C42×D4C2212yes—
199#559—28no—
200Q82—28no—
201#557—216no—
202#556—216no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2311yescharacteristic
214C2×#126C2318yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#125C2312yes—
218C2×#124C2314yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#123C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C22×C42C2314yes—
255#401C2318yes—
256#401C2318yes—
257#400C2318yes—
258#400C2314yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#399C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#398C2314yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#394C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#391C2312yes—
295#391C2314yes—
296#391C2314yes—
297#391C2312yes—
298#391C2312yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2314yes—
307#391C2312yes—
308#391C2314yes—
309#391C2318yes—
310#391C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2312yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#386C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#383C2318yes—
435#383C2318yes—
436#383C2318yes—
437#382C2312yes—
438#382C2312yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2312yes—
443#382C2318yes—
444#382C2314yes—
445#382C2314yes—
446#381C2314yes—
447#381C2318yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515#376C2314yes—
516#376C2318yes—
517#376C2318yes—
518C43C2314yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C43C2312yes—
522C43C2312yes—
523C22×Q8C2414yes—
524C22×Q8C2412yes—
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C22×Q8C2411yescharacteristic
528C22×Q8C2414yes—
529C22×Q8C2412yes—
530C22×D4C2412yes—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C23×C4C2414yes—
534C23×C4C2414yes—
535C23×C4C2414yes—
536C4⋊Q8—216no—
537C4⋊Q8—28no—
538C4⋊Q8—216no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—24no—
542C4⋊Q8—28no—
543C4⋊Q8—24no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546#127—24no—
547#126—232no—
548#125—232no—
549#125—216no—
550#125—44no—
551#124—28no—
552#124—216no—
553#124—28no—
554#124—48no—
555#124—48no—
556#123—216no—
557C22⋊Q8—216no—
558C4×Q8—28no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—28no—
563C4×Q8—24no—
564C4×Q8—28no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—48no—
569C4×Q8—44no—
570C4×Q8—44no—
571C4×Q8—42no—
572C4×Q8—48no—
573C4×Q8—42no—
574C4×Q8—44no—
575C4×Q8—42no—
576C4×Q8#4118yes—
577C4×Q8#4118yes—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—44no—
583C4×D4—44no—
584C4×D4—44no—
585#117—216no—
586#117—48no—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
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×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C42—48no—
662C2×C42C2418yes—
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2418yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2411yescharacteristic
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2412yes—
711#95C2412yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2412yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747C24C2514yes—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—28no—
752C2×Q8—28no—
753C2×Q8—28no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—24no—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—28no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—42no—
764C2×Q8—44no—
765C2×Q8—42no—
766C2×Q8—44no—
767C2×Q8C2×#4114yes—
768C2×Q8C2×#4114yes—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—24no—
776C2×D4—42no—
777C2×D4—42no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2518yes—
799C22×C4C2514yes—
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2512yes—
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C4⋊C4—28no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—216no—
820C4⋊C4—216no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—22no—
827C4⋊C4—24no—
828C4⋊C4—216no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—42no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—42no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4C2×#4114yes—
866C4⋊C4C2×#4114yes—
867C4⋊C4C2×#4118yes—
868C4⋊C4C2×#4118yes—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—216no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C42—216no—
887C42—24no—
888C42—216no—
889C42—28no—
890C42—24no—
891C42—28no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—22no—
897C42—24no—
898C42—24no—
899C42—22no—
900C42—28no—
901C42—24no—
902C42—24no—
903C42—22no—
904C42—44no—
905C42—44no—
906C42—42no—
907C42—41no—
908C42—44no—
909C42—42no—
910C42—42no—
911C42—48no—
912C42—44no—
913C42—42no—
914C42—42no—
915C42—42no—
916C42—44no—
917C42—48no—
918C42C2×#4114yes—
919C42C2×#4118yes—
920C42C2×#4118yes—
921C42C2×#4114yes—
922C422−1+414yes—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23C2611yescharacteristic
931Q8—28no—
932Q8—28no—
933Q8—416no—
934Q8—48no—
935Q8—44no—
936Q8—84no—
937Q8—88no—
938D4—48no—
939D4—48no—
940D4—84no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—28no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—416no—
1001C2×C4—88no—
1002C2×C4—88no—
1003C2×C4C22×#4114yes—
1004C2×C4C22×#4114yes—
1005C2×C4C22×#4114yes—
1006C2×C4C22×#4114yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4#58512yes—
1017C2×C4#58512yes—
1018C2×C4#58512yes—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22C23×#4111yescharacteristic
1027C22C23×#4111yescharacteristic
1028C22C22×2−1+411yescharacteristic
1029C22C2×#58511yescharacteristic
1030C22C2×#58511yescharacteristic
1031C22C2×#58511yescharacteristic
1032C222−1+611yescharacteristic
1033C4—24no—
1034C4—22no—
1035C4—22no—
1036C4—24no—
1037C4—24no—
1038C4—22no—
1039C4—24no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—41no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—48no—
1055C4#348014yes—
1056C4#350714yes—
1057C4#351814yes—
1058C2—84no—
1059C2C2×#348011yescharacteristic
1060C2C2×#350711yescharacteristic
1061C2C2×#351811yescharacteristic
1062C2#6295611yescharacteristic
1063C2#6299511yescharacteristic
1064C2#6299511yescharacteristic
1065C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59876C2semidirect
2. #59875C2semidirect
4. #59434C2semidirect
5. #59427C2semidirect
6. #59296C2semidirect
7. #45156C2semidirect
8. #43717C2semidirect
9. #40022C2semidirect
11. #39239C2semidirect
12. #39172C2semidirect
13. #36598C2semidirect
15. #36590C2semidirect
16. #36560C2semidirect
18. #36416C2semidirect
19. #36175C2semidirect
20. #35974C2semidirect
21. #34951C2semidirect
22. #34945C2semidirect
23. #34328C2semidirect
24. #34324C2semidirect
25. C4×Q82C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#598752
#598632
#594342
#594272
#592962
#451562
#437172
#400222
#397712
#392392
#391722
#365982
#365942
#365902
#365602
#365382
#364162
#361752
#359742
#349512
#349452
#343282
#343242
C4×Q822
C4×#5592