Finite Group Databasebeta

← #7987095

Subgroups — #7987095

Order 512.

4261 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59427C212yesmaximal
3#59426C212yesmaximal
4#59256C212yesmaximal, complemented
5#51377C218yesmaximal, complemented
6#46051C214yesmaximal, complemented
7#45431C214yesmaximal, complemented
8#45293C214yesmaximal, complemented
9#42597C214yesmaximal, complemented
10#42526C214yesmaximal
11#40155C214yesmaximal, complemented
12#39761C212yesmaximal
13#39643C212yesmaximal, complemented
14#39172C212yesmaximal
15#38931C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36598C212yesmaximal, complemented
18Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
19#36480C212yesmaximal, complemented
20#36194C211yesmaximal, characteristic
21#35192C212yesmaximal, complemented
22#35187C212yesmaximal, complemented
23#34950C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic
25#34491C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#556C2211yescharacteristic
29#2868C2212yes—
30#2868C2211yescharacteristic
31#2864C2214yes—
32#2863C2214yes—
33#2862C2212yes—
34#2862C2214yes—
35#2857C2212yes—
36#2831C2218yes—
37#2809C2214yes—
38#2799C2218yes—
39#2793C2218yes—
40#2783C2218yes—
41#2775C2218yes—
42#2772C2218yes—
43#2770C2218yes—
44#2762C2218yes—
45#2762C2218yes—
46#2759C2218yes—
47#2758C2218yes—
48#2758C2218yes—
49#2755C2218yes—
50#2716C2218yes—
51#2716C2218yes—
52#2716C2218yes—
53#2698C2218yes—
54#2665C2218yes—
55#2655C2218yes—
56#2647C2214yes—
57#2640C2214yes—
58#2637C2218yes—
59#2605C2218yes—
60#2605C2218yes—
61#2592C2214yes—
62#2586C2214yes—
63#2582C2214yes—
64#2582C2212yes—
65#2582C2211yescharacteristic
66#2573C2214yes—
67#2571C2212yes—
68#2571C2212yes—
69#2571C2212yes—
70#2571C2211yescharacteristic
71#2570C2214yes—
72#2570C2214yes—
73#2570C2214yes—
74#2568C2214yes—
75#2568C2214yes—
76#2568C2214yes—
77#2568C2211yescharacteristic
78#2568C2212yes—
79#2567C2211yescharacteristic
80#2567C2214yes—
81#2567C2212yes—
82#2567C2211yescharacteristic
83#2563C2212yes—
84#2551C2212yes—
85#2551C2211yescharacteristic
86#2551C2212yes—
87#2551C2214yes—
88#2551C2214yes—
89#2547C2211yescharacteristic
90#2546C2212yes—
91#2546C2212yes—
92#2545C2214yes—
93#2538C2212yes—
94#2538C2211yescharacteristic
95#2532C2218yes—
96#2528C2218yes—
97#2528C2218yes—
98#2524C2218yes—
99#2514C2214yes—
100#2514C2214yes—
101#2514C2212yes—
102#2512C2214yes—
103#2511C2214yes—
104#2511C2214yes—
105#2511C2218yes—
106#2509C2214yes—
107#2508C2214yes—
108#2508C2214yes—
109#2508C2214yes—
110#2508C2214yes—
111#2507C2212yes—
112#2507C2212yes—
113#2499C2214yes—
114#2497C2214yes—
115#2497C2214yes—
116#2496C2214yes—
117#2496C2214yes—
118#2495C2214yes—
119#2494C2214yes—
120#2494C2212yes—
121#2492C2214yes—
122#2492C2214yes—
123#2469C2218yes—
124#2465C2218yes—
125#2451C2212yes—
126#2451C2212yes—
127#2447C2212yes—
128#2446C2214yes—
129#2446C2218yes—
130#2446C2214yes—
131#2439C2214yes—
132#2439C2214yes—
133#2439C2214yes—
134#2439C2214yes—
135#2439C2214yes—
136#2439C2214yes—
137#2421C2214yes—
138#2421C2214yes—
139#2421C2212yes—
140#2401C2214yes—
141#2399C2214yes—
142#2381C2218yes—
143#2373C2214yes—
144#2369C2212yes—
145#2369C2212yes—
146#2367C2212yes—
147#2365C2214yes—
148#2365C2214yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2362C2212yes—
152#2356C2214yes—
153#2356C2212yes—
154#2356C2214yes—
155#2355C2214yes—
156#2355C2212yes—
157#2355C2212yes—
158#2355C2212yes—
159#2355C2212yes—
160#2355C2211yescharacteristic
161#2355C2212yes—
162#2354C2211yescharacteristic
163#2354C2212yes—
164Q8×C4⋊C4C2212yes—
165Q8×C4⋊C4C2212yes—
166#2347C2214yes—
167#2347C2212yes—
168#2346C2214yes—
169#2331C2214yes—
170#2331C2214yes—
171#2331C2214yes—
172#2327C2214yes—
173#2327C2218yes—
174#2320C2214yes—
175#2320C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2214yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×#126C2214yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199Q82—216no—
200#556—28no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2318yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2318yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C22×C42C2312yes—
245#401C2318yes—
246#401C2314yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#398C2318yes—
270#398C2314yes—
271#398C2318yes—
272#398C2318yes—
273#397C2314yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#396C2314yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#395C2318yes—
286#395C2314yes—
287#395C2314yes—
288#395C2318yes—
289#395C2318yes—
290#395C2314yes—
291#395C2314yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2318yes—
296#391C2312yes—
297#391C2314yes—
298#391C2312yes—
299#391C2318yes—
300#391C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2314yes—
312#391C2314yes—
313#391C2312yes—
314#391C2318yes—
315#391C2318yes—
316#391C2318yes—
317#391C2314yes—
318#391C2312yes—
319#391C2318yes—
320#391C2312yes—
321#391C2314yes—
322#391C2318yes—
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#391C2314yes—
329#391C2318yes—
330#391C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2318yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2314yes—
383#388C2318yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2318yes—
420#385C2314yes—
421#385C2314yes—
422#384C2312yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2312yes—
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#383C2314yes—
435#383C2314yes—
436#383C2318yes—
437#383C2318yes—
438#383C2318yes—
439#382C2314yes—
440#382C2312yes—
441#382C2314yes—
442#382C2318yes—
443#382C2312yes—
444#382C2318yes—
445#382C2312yes—
446#382C2314yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2318yes—
452#382C2312yes—
453#381C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2312yes—
461#380C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513#376C2314yes—
514#376C2314yes—
515#376C2318yes—
516#376C2314yes—
517C43C2314yes—
518C43C2311yescharacteristic
519C43C2312yes—
520C43C2312yes—
521C22×Q8C2411yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×Q8C2418yes—
528C22×Q8C2414yes—
529C22×D4C2411yescharacteristic
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C4⋊Q8—216no—
534C4⋊Q8—232no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—28no—
538C4⋊Q8—216no—
539C4⋊Q8—24no—
540C4⋊Q8—24no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—48no—
544C4⋊Q8—48no—
545C4⋊Q8—82no—
546C4⋊Q8—84no—
547#126—216no—
548#126—88no—
549#124—28no—
550#124—44no—
551C22⋊Q8—28no—
552C22⋊Q8—44no—
553C22⋊Q8—84no—
554C4×Q8—216no—
555C4×Q8—24no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—216no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—28no—
562C4×Q8—24no—
563C4×Q8—44no—
564C4×Q8—48no—
565C4×Q8—44no—
566C4×Q8—42no—
567C4×Q8—84no—
568C4×Q8—88no—
569C4×Q8#4118yes—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—42no—
573#117—28no—
574#117—28no—
575#117—48no—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C42—28no—
648C2×C42C2414yes—
649C2×C42C2414yes—
650C2×C42C2411yescharacteristic
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2418yes—
656C2×C42C2411yescharacteristic
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2414yes—
660C2×C42C2411yescharacteristic
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2418yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2418yes—
672C2×C42C2418yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2412yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681#95C2412yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2412yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737C24C2512yes—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—216no—
741C2×Q8—28no—
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—44no—
754C2×Q8—42no—
755C2×Q8—48no—
756C2×Q8—44no—
757C2×Q8—42no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—48no—
761C2×Q8C2×#4114yes—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—22no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2518yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2511yescharacteristic
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C4⋊C4—24no—
800C4⋊C4—22no—
801C4⋊C4—28no—
802C4⋊C4—216no—
803C4⋊C4—28no—
804C4⋊C4—216no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—24no—
831C4⋊C4—44no—
832C4⋊C4—42no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—42no—
853C4⋊C4—44no—
854C4⋊C4C2×#4114yes—
855C4⋊C4C2×#4118yes—
856C4⋊C42−1+414yes—
857C22⋊C4—28no—
858C22⋊C4—24no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—24no—
862C22⋊C4—48no—
863C22⋊C4—42no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C42—28no—
871C42—216no—
872C42—28no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—28no—
877C42—24no—
878C42—22no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—28no—
883C42—24no—
884C42—22no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—22no—
889C42—24no—
890C42—48no—
891C42—44no—
892C42—42no—
893C42—44no—
894C42—42no—
895C42—48no—
896C42—48no—
897C42—41no—
898C42—42no—
899C42C2×#4114yes—
900C42C2×#4118yes—
901C422−1+414yes—
902C422−1+414yes—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23C2611yescharacteristic
911Q8—28no—
912Q8—48no—
913Q8—48no—
914Q8—44no—
915Q8—88no—
916Q8—816no—
917Q8—88no—
918Q8—84no—
919D4—44no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—28no—
980C2×C4—48no—
981C2×C4—48no—
982C2×C4—84no—
983C2×C4C22×#4114yes—
984C2×C4C22×#4114yes—
985C2×C4C22×#4112yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4112yes—
988C2×C4C2×2−1+414yes—
989C2×C4C2×2−1+412yes—
990C2×C4C2×2−1+412yes—
991C2×C4C2×2−1+412yes—
992C2×C4C2×2−1+412yes—
993C2×C4C2×2−1+412yes—
994C2×C4C2×2−1+412yes—
995C2×C4C2×2−1+412yes—
996C2×C4#58512yes—
997C2×C4#58512yes—
998C22—42no—
999C22—42no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22C23×#4111yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C22C22×2−1+411yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C2×#58511yescharacteristic
1010C22C2×#58511yescharacteristic
1011C22H(7,𝔽2)11yescharacteristic
1012C4—22no—
1013C4—24no—
1014C4—24no—
1015C4—24no—
1016C4—22no—
1017C4—22no—
1018C4—42no—
1019C4—42no—
1020C4—48no—
1021C4—44no—
1022C4—41no—
1023C4—44no—
1024C4—42no—
1025C4—44no—
1026C4—44no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—44no—
1032C4—44no—
1033C4—42no—
1034C4#350914yes—
1035C4#351814yes—
1036C4#355514yes—
1037C2—82no—
1038C2C2×#355511yescharacteristic
1039C2C2×#351811yescharacteristic
1040C2C2×#350911yescharacteristic
1041C2#6292911yescharacteristic
1042C2#6294311yescharacteristic
1043C2#6301011yescharacteristic
1044C2#6302511yescharacteristic
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. #59869C2semidirect
4. #59256C2semidirect
5. #51377C2semidirect
6. #46051C2semidirect
7. #45431C2semidirect
8. #45293C2semidirect
9. #42597C2semidirect
11. #40155C2semidirect
13. #39643C2semidirect
15. #38931C2semidirect
16. #36598C2semidirect
17. #36598C2semidirect
18. Q8×C4⋊Q8C2semidirect
19. #36480C2semidirect
21. #35192C2semidirect
22. #35187C2semidirect
23. #34950C2semidirect
25. #34491C2semidirect

Maximal subgroups

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

subgroupindex
#598692
#594272
#594262
#592562
#513772
#460512
#454312
#452932
#425972
#425262
#401552
#397612
#396432
#391722
#389312
#365982
Q8×C4⋊Q82
#364802
#361942
#351922
#351872
#349502
#349452
#344912
C4×#5562