Finite Group Databasebeta

← #7987164

Subgroups — #7987164

Order 512.

4275 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59445C212yesmaximal, complemented
3#59436C212yesmaximal
4#59329C212yesmaximal, complemented
5#50442C218yesmaximal, complemented
6#46069C214yesmaximal, complemented
7#45381C214yesmaximal
8#45328C214yesmaximal, complemented
9#42938C214yesmaximal, complemented
10#42774C214yesmaximal, complemented
11#40051C214yesmaximal, complemented
12#39734C212yesmaximal, complemented
13#39490C212yesmaximal
14#38986C212yesmaximal, complemented
15#38977C212yesmaximal
16#36600C212yesmaximal, complemented
17#36598C211yesmaximal, characteristic, complemented
18#36563C211yesmaximal, characteristic, complemented
19#36450C212yesmaximal, complemented
20#36180C211yesmaximal, characteristic
21#35286C212yesmaximal, complemented
22#35208C212yesmaximal, complemented
23#34951C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic
25#34484C212yesmaximal
26C4×#556C211yesmaximal, characteristic
27C2×#556C2211yescharacteristic
28C2×#554C2212yes—
29#2868C2211yescharacteristic
30#2863C2214yes—
31#2862C2212yes—
32#2859C2212yes—
33#2859C2214yes—
34#2859C2214yes—
35#2857C2212yes—
36#2839C2218yes—
37#2805C2214yes—
38#2794C2218yes—
39#2789C2218yes—
40#2776C2218yes—
41#2774C2218yes—
42#2771C2218yes—
43#2769C2218yes—
44#2766C2218yes—
45#2765C2218yes—
46#2758C2218yes—
47#2747C2218yes—
48#2745C2218yes—
49#2744C2218yes—
50#2739C2218yes—
51#2738C2218yes—
52#2689C2218yes—
53#2689C2218yes—
54#2666C2218yes—
55#2655C2218yes—
56#2647C2218yes—
57#2645C2214yes—
58#2621C2214yes—
59#2599C2218yes—
60#2585C2214yes—
61#2585C2218yes—
62#2585C2218yes—
63#2582C2212yes—
64#2582C2211yescharacteristic
65#2582C2212yes—
66#2581C2214yes—
67#2577C2218yes—
68#2574C2214yes—
69#2571C2212yes—
70#2571C2214yes—
71#2571C2212yes—
72#2570C2214yes—
73#2570C2214yes—
74#2570C2214yes—
75#2570C2214yes—
76#2570C2214yes—
77#2568C2212yes—
78#2568C2211yescharacteristic
79#2568C2212yes—
80#2567C2212yes—
81#2567C2212yes—
82#2567C2212yes—
83#2567C2211yescharacteristic
84#2563C2211yescharacteristic
85#2552C2214yes—
86#2552C2212yes—
87#2552C2212yes—
88#2552C2212yes—
89#2552C2211yescharacteristic
90#2552C2211yescharacteristic
91#2550C2214yes—
92#2546C2211yescharacteristic
93#2538C2211yescharacteristic
94#2528C2218yes—
95#2514C2214yes—
96#2514C2214yes—
97#2514C2214yes—
98#2511C2212yes—
99#2511C2214yes—
100#2511C2214yes—
101#2511C2214yes—
102#2511C2214yes—
103#2509C2212yes—
104#2509C2214yes—
105#2508C2212yes—
106#2508C2214yes—
107#2507C2214yes—
108#2507C2214yes—
109#2506C2214yes—
110#2503C2214yes—
111#2503C2214yes—
112#2502C2214yes—
113#2499C2214yes—
114#2497C2212yes—
115#2495C2214yes—
116#2494C2214yes—
117#2494C2214yes—
118#2489C2214yes—
119#2484C2218yes—
120#2475C2218yes—
121#2462C2218yes—
122#2462C2218yes—
123#2454C2212yes—
124#2453C2214yes—
125#2453C2214yes—
126#2453C2214yes—
127#2453C2212yes—
128#2451C2214yes—
129#2447C2214yes—
130#2447C2214yes—
131#2446C2214yes—
132#2446C2214yes—
133#2446C2212yes—
134#2442C2218yes—
135#2442C2214yes—
136#2442C2214yes—
137#2440C2214yes—
138#2440C2214yes—
139#2423C2212yes—
140#2402C2214yes—
141#2396C2214yes—
142#2378C2218yes—
143#2373C2214yes—
144#2370C2214yes—
145#2370C2214yes—
146#2369C2212yes—
147#2367C2212yes—
148#2365C2212yes—
149#2365C2211yescharacteristic
150#2365C2212yes—
151#2362C2214yes—
152#2362C2212yes—
153#2356C2212yes—
154#2355C2214yes—
155#2355C2212yes—
156#2355C2211yescharacteristic
157#2355C2212yes—
158#2355C2212yes—
159#2355C2212yes—
160#2354C2214yes—
161#2354C2211yescharacteristic
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166#2347C2212yes—
167#2344C2214yes—
168#2344C2214yes—
169#2330C2214yes—
170#2323C2218yes—
171#2323C2214yes—
172#2320C2214yes—
173#2319C2214yes—
174#2317C2214yes—
175#2316C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#125C2212yes—
183C4×#125C2212yes—
184C4×#125C2214yes—
185C4×#126C2214yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193C2×#384C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#556—28no—
200#554—216no—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×#126C2314yes—
209C2×#125C2312yes—
210C2×#125C2314yes—
211C2×#125C2312yes—
212C2×#125C2314yes—
213C2×#125C2318yes—
214C2×#124C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2314yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2314yes—
240C2×#117C2318yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2314yes—
243C22×C4⋊C4C2314yes—
244C22×C42C2312yes—
245#401C2318yes—
246#401C2318yes—
247#400C2318yes—
248#400C2314yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2318yes—
267#399C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2318yes—
274#398C2318yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#396C2314yes—
290#396C2314yes—
291#395C2314yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#393C2314yes—
296#391C2312yes—
297#391C2314yes—
298#391C2312yes—
299#391C2312yes—
300#391C2314yes—
301#391C2312yes—
302#391C2312yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2314yes—
312#391C2312yes—
313#391C2314yes—
314#391C2312yes—
315#391C2318yes—
316#391C2312yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#389C2312yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2314yes—
329#389C2312yes—
330#389C2314yes—
331#389C2312yes—
332#389C2314yes—
333#389C2314yes—
334#389C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2312yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#387C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2314yes—
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2314yes—
438#383C2314yes—
439#383C2318yes—
440#383C2318yes—
441#382C2312yes—
442#382C2312yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#382C2318yes—
451#382C2314yes—
452#382C2318yes—
453#381C2318yes—
454#381C2318yes—
455#381C2318yes—
456#380C2312yes—
457#380C2312yes—
458#380C2318yes—
459#380C2318yes—
460#380C2314yes—
461#380C2314yes—
462#380C2312yes—
463#380C2314yes—
464#380C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515#376C2314yes—
516#376C2314yes—
517C43C2314yes—
518C43C2312yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2414yes—
527C22×D4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2418yes—
532C4⋊Q8—28no—
533C4⋊Q8—24no—
534C4⋊Q8—24no—
535C4⋊Q8—24no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538C4⋊Q8—82no—
539#126—216no—
540#125—216no—
541#125—28no—
542#125—44no—
543#125—48no—
544#125—88no—
545#124—28no—
546C22⋊Q8—216no—
547C22⋊Q8—28no—
548C22⋊Q8—232no—
549C22⋊Q8—44no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—24no—
556C4×Q8—28no—
557C4×Q8—24no—
558C4×Q8—44no—
559C4×Q8—48no—
560C4×Q8—42no—
561C4×Q8—42no—
562C4×Q8—84no—
563C4×Q8—84no—
564C4×D4—216no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4#4118yes—
568#117—28no—
569#117—48no—
570#117—44no—
571#117—88no—
572C2×C4⋊C4—216no—
573C2×C4⋊C4—48no—
574C2×C4⋊C4—84no—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C42—28no—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2412yes—
658C2×C42C2411yescharacteristic
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2418yes—
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2418yes—
678C2×C42C2414yes—
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2412yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2412yes—
703#95C2414yes—
704#95C2412yes—
705#95C2412yes—
706#95C2412yes—
707#95C2418yes—
708#95C2414yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2418yes—
713#95C2414yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737C24C2512yes—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—28no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4C2×#4114yes—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—216no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—42no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4C2×#4118yes—
771C22×C4C2514yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2514yes—
778C22×C4C2512yes—
779C22×C4C2511yescharacteristic
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C4⋊C4—24no—
797C4⋊C4—216no—
798C4⋊C4—28no—
799C4⋊C4—22no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—216no—
806C4⋊C4—24no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—22no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—48no—
831C4⋊C4—42no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—48no—
841C4⋊C4—42no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4C2×#4114yes—
858C4⋊C42−1+414yes—
859C22⋊C4—28no—
860C22⋊C4—216no—
861C22⋊C4—28no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4C2×#4118yes—
871C42—28no—
872C42—28no—
873C42—24no—
874C42—24no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—24no—
879C42—28no—
880C42—24no—
881C42—24no—
882C42—28no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—22no—
888C42—22no—
889C42—24no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—42no—
894C42—42no—
895C42—48no—
896C42—42no—
897C42—42no—
898C42—44no—
899C42—41no—
900C42C2×#4114yes—
901C422−1+414yes—
902C422−1+414yes—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23C22×#4114yes—
910C23C2611yescharacteristic
911Q8—48no—
912Q8—48no—
913Q8—44no—
914Q8—48no—
915Q8—44no—
916Q8—88no—
917D4—28no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—216no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—28no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—48no—
981C2×C4—48no—
982C2×C4—816no—
983C2×C4C22×#4114yes—
984C2×C4C22×#4112yes—
985C2×C4C22×#4112yes—
986C2×C4C22×#4112yes—
987C2×C4C2×2−1+412yes—
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×C4#58512yes—
996C2×C4#58512yes—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—42no—
1001C22—42no—
1002C22—42no—
1003C22—42no—
1004C22C23×#4111yescharacteristic
1005C22C22×2−1+411yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C22C22×2−1+411yescharacteristic
1008C22C2×#58511yescharacteristic
1009C22C2×#58511yescharacteristic
1010C22H(7,𝔽2)11yescharacteristic
1011C4—22no—
1012C4—24no—
1013C4—22no—
1014C4—22no—
1015C4—24no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4—48no—
1021C4—42no—
1022C4—41no—
1023C4—42no—
1024C4—44no—
1025C4—42no—
1026C4—44no—
1027C4—44no—
1028C4—42no—
1029C4—44no—
1030C4—44no—
1031C4—42no—
1032C4—42no—
1033C4#350914yes—
1034C4#351514yes—
1035C4#355514yes—
1036C2—44no—
1037C2C2×#355511yescharacteristic
1038C2C2×#351511yescharacteristic
1039C2C2×#350911yescharacteristic
1040C2#6292611yescharacteristic
1041C2#6294511yescharacteristic
1042C2#6301011yescharacteristic
1043C2#6303411yescharacteristic
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. #59870C2semidirect
2. #59445C2semidirect
4. #59329C2semidirect
5. #50442C2semidirect
6. #46069C2semidirect
8. #45328C2semidirect
9. #42938C2semidirect
10. #42774C2semidirect
11. #40051C2semidirect
12. #39734C2semidirect
14. #38986C2semidirect
16. #36600C2semidirect
17. #36598C2semidirect
18. #36563C2semidirect
19. #36450C2semidirect
21. #35286C2semidirect
22. #35208C2semidirect
23. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#594452
#594362
#593292
#504422
#460692
#453812
#453282
#429382
#427742
#400512
#397342
#394902
#389862
#389772
#366002
#365982
#365632
#364502
#361802
#352862
#352082
#349512
#349412
#344842
C4×#5562