Finite Group Databasebeta

← #7672359

Subgroups — #7672359

Order 512.

4696 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59868C214yesmaximal, complemented
2#59855C214yesmaximal
3#59709C214yesmaximal, complemented
4#59496C214yesmaximal, complemented
5#39527C214yesmaximal, complemented
6#39526C214yesmaximal, complemented
7#39186C212yesmaximal, complemented
8#38970C212yesmaximal, complemented
9#38113C214yesmaximal, complemented
10#36635C211yesmaximal, characteristic, complemented
11#36608C211yesmaximal, characteristic, complemented
12#36574C211yesmaximal, characteristic, complemented
13#36209C211yesmaximal, characteristic, complemented
14#36189C212yesmaximal, complemented
15#36178C214yesmaximal, complemented
16#36178C214yesmaximal, complemented
17#36151C211yesmaximal, characteristic, complemented
18#36129C212yesmaximal, complemented
19#35650C214yesmaximal, complemented
20#35291C212yesmaximal, complemented
21#35245C212yesmaximal
22#34225C212yesmaximal, complemented
23#34192C212yesmaximal, complemented
24C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
25C4×#529C211yesmaximal, characteristic
26C2×#533C2212yes—
27C22×C4⋊Q8C2211yescharacteristic
28C2×#529C2211yescharacteristic
29C22×C4×Q8C2212yes—
30#2864C2212yes—
31#2863C2214yes—
32#2862C2211yescharacteristic
33#2862C2212yes—
34#2859C2211yescharacteristic
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2853C2218yes—
41#2851C2212yes—
42#2802C2218yes—
43#2800C2218yes—
44#2798C2218yes—
45#2789C2218yes—
46#2776C2218yes—
47#2774C2218yes—
48#2758C2218yes—
49#2754C2218yes—
50#2645C2214yes—
51#2634C2214yes—
52#2632C2214yes—
53#2625C2214yes—
54#2604C2218yes—
55#2594C2218yes—
56#2591C2214yes—
57#2585C2218yes—
58#2584C2214yes—
59#2583C2214yes—
60#2581C2212yes—
61#2581C2214yes—
62#2581C2212yes—
63#2570C2214yes—
64#2550C2214yes—
65#2536C2212yes—
66#2536C2212yes—
67#2529C2218yes—
68#2529C2218yes—
69#2528C2218yes—
70#2528C2218yes—
71#2525C2218yes—
72#2525C2218yes—
73#2525C2218yes—
74#2524C2218yes—
75#2524C2218yes—
76#2514C2214yes—
77#2514C2214yes—
78#2514C2214yes—
79#2514C2214yes—
80#2511C2214yes—
81#2510C2218yes—
82#2510C2218yes—
83#2509C2218yes—
84#2509C2214yes—
85#2509C2214yes—
86#2508C2214yes—
87#2508C2214yes—
88#2508C2214yes—
89#2507C2214yes—
90#2505C2218yes—
91#2505C2218yes—
92#2497C2214yes—
93#2495C2214yes—
94#2495C2214yes—
95#2494C2214yes—
96#2492C2214yes—
97#2489C2214yes—
98#2489C2214yes—
99#2489C2214yes—
100#2487C2214yes—
101#2485C2214yes—
102#2453C2214yes—
103#2453C2214yes—
104#2453C2214yes—
105#2451C2214yes—
106#2446C2214yes—
107#2442C2214yes—
108#2442C2214yes—
109#2441C2214yes—
110#2439C2214yes—
111#2429C2214yes—
112#2423C2214yes—
113#2421C2214yes—
114#2421C2214yes—
115#2417C2214yes—
116#2417C2214yes—
117#2415C2214yes—
118#2409C2214yes—
119#2370C2214yes—
120#2370C2214yes—
121#2370C2214yes—
122#2362C2214yes—
123#2362C2214yes—
124#2362C2214yes—
125#2360C2214yes—
126#2360C2214yes—
127#2356C2212yes—
128#2356C2214yes—
129#2356C2212yes—
130#2356C2214yes—
131#2356C2214yes—
132#2356C2214yes—
133#2352C2214yes—
134#2352C2214yes—
135#2351C2212yes—
136#2351C2212yes—
137#2351C2214yes—
138#2347C2214yes—
139#2346C2214yes—
140#2346C2214yes—
141#2345C2214yes—
142#2345C2218yes—
143Q8×C22⋊C4C2214yes—
144#2323C2214yes—
145#2323C2214yes—
146#2323C2214yes—
147#2320C2214yes—
148#2320C2214yes—
149#2320C2218yes—
150C4×C4⋊Q8C2212yes—
151C4×C4⋊Q8C2211yescharacteristic
152C4×C4⋊Q8C2212yes—
153C4×C4⋊Q8C2212yes—
154C4×C4⋊Q8C2212yes—
155C4×C4⋊Q8C2211yescharacteristic
156C4×C4⋊Q8C2214yes—
157C4×C4⋊Q8C2212yes—
158C4×C4⋊Q8C2214yes—
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2211yescharacteristic
161C4×#125C2212yes—
162C4×#125C2212yes—
163C4×#126C2212yes—
164C4×#126C2212yes—
165C4×#124C2212yes—
166C4×C22⋊Q8C2214yes—
167C4×C22⋊Q8C2212yes—
168C4×#123C2212yes—
169C4×#123C2212yes—
170C4×#121C2212yes—
171#2298C2212yes—
172#2295C2214yes—
173#2295C2211yescharacteristic
174C2×#391C2212yes—
175#2293C2211yescharacteristic
176C2×#389C2214yes—
177#2290C2212yes—
178#2285C2212yes—
179C2×#384C2211yescharacteristic
180#2283C2212yes—
181#2283C2214yes—
182#2283C2214yes—
183#2283C2211yescharacteristic
184#2276C2214yes—
185C42×Q8C2211yescharacteristic
186C42×D4C2212yes—
187C42×D4C2211yescharacteristic
188C4×#117C2212yes—
189C2×C4×C4⋊C4C2214yes—
190C2×C43C2211yescharacteristic
191C23×Q8C2312yes—
192#533—216no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8C2311yescharacteristic
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2311yescharacteristic
199#529—28no—
200C2×#126C2312yes—
201C2×#125C2311yescharacteristic
202C2×#125C2314yes—
203C2×#125C2312yes—
204C2×#125C2314yes—
205C2×#124C2311yescharacteristic
206C2×#123C2312yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2311yescharacteristic
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×#121C2311yescharacteristic
214C2×C4×Q8—216no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2312yes—
233C2×#117C2312yes—
234C2×#117C2314yes—
235C2×#117C2312yes—
236C2×#117C2314yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2314yes—
241C22×C42C2314yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248#401C2318yes—
249#401C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2314yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#399C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#396C2318yes—
277#396C2318yes—
278#395C2314yes—
279#395C2314yes—
280#395C2318yes—
281#394C2314yes—
282#394C2314yes—
283#393C2318yes—
284#391C2312yes—
285#391C2312yes—
286#391C2312yes—
287#391C2312yes—
288#391C2318yes—
289#391C2314yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C2314yes—
294#391C2318yes—
295#391C2318yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2312yes—
304#390C2312yes—
305#389C2314yes—
306#389C2312yes—
307#389C2312yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2318yes—
338#389C2318yes—
339#388C2312yes—
340#388C2312yes—
341#388C2312yes—
342#388C2312yes—
343#388C2312yes—
344#388C2312yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2312yes—
358#388C2312yes—
359#387C2312yes—
360#387C2312yes—
361#387C2312yes—
362#387C2312yes—
363#387C2312yes—
364#387C2312yes—
365#387C2318yes—
366#387C2312yes—
367#387C2312yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2312yes—
394#386C2312yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2312yes—
399#385C2312yes—
400#384C2311yescharacteristic
401#384C2314yes—
402#384C2311yescharacteristic
403#384C2312yes—
404#384C2312yes—
405#383C2311yescharacteristic
406#383C2311yescharacteristic
407#383C2314yes—
408#383C2318yes—
409#383C2318yes—
410#383C2314yes—
411#383C2314yes—
412#383C2318yes—
413#382C2312yes—
414#382C2312yes—
415#382C2314yes—
416#382C2314yes—
417#382C2318yes—
418#382C2318yes—
419#382C2312yes—
420#382C2312yes—
421#382C2314yes—
422#382C2318yes—
423#382C2314yes—
424#382C2314yes—
425#382C2314yes—
426#381C2314yes—
427#381C2311yescharacteristic
428#381C2311yescharacteristic
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2318yes—
433#380C2314yes—
434#380C2312yes—
435#380C2318yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2312yes—
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2318yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2312yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490#376C2312yes—
491#376C2312yes—
492#376C2318yes—
493#376C2314yes—
494#376C2314yes—
495#376C2314yes—
496C2×#95C2318yes—
497C43C2312yes—
498C43C2311yescharacteristic
499C43C2312yes—
500C43C2311yescharacteristic
501C43C2311yescharacteristic
502C43C2312yes—
503C43C2311yescharacteristic
504C22×Q8—28no—
505C22×Q8—28no—
506C22×Q8—44no—
507C22×Q8C2414yes—
508C22×Q8C2412yes—
509C22×Q8C2414yes—
510C22×Q8C2412yes—
511C22×Q8C2411yescharacteristic
512C22×D4C2412yes—
513C22×D4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2412yes—
521C23×C4C2414yes—
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C4⋊Q8—28no—
525C4⋊Q8—216no—
526C4⋊Q8—24no—
527C4⋊Q8—28no—
528C4⋊Q8#4118yes—
529#126—28no—
530#125—216no—
531#125—24no—
532#125—44no—
533#125—48no—
534#124—24no—
535#123—28no—
536C22⋊Q8—216no—
537C22⋊Q8—24no—
538C22⋊Q8—216no—
539C22⋊Q8—216no—
540C22⋊Q8—48no—
541C22⋊Q8—48no—
542#121—24no—
543C4×Q8—216no—
544C4×Q8—216no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—216no—
550C4×Q8—216no—
551C4×Q8—24no—
552C4×Q8—44no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—24no—
560C4×D4—44no—
561#117—216no—
562#117—28no—
563#117—44no—
564#117—48no—
565C2×C4⋊C4—216no—
566C2×C4⋊C4—28no—
567C2×C4⋊C4—216no—
568C2×C4⋊C4—48no—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C42—216no—
631C2×C42—28no—
632C2×C42—24no—
633C2×C42—28no—
634C2×C42—42no—
635C2×C42—44no—
636C2×C42#4118yes—
637C2×C42C2411yescharacteristic
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2418yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2414yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2418yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2418yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2412yes—
678#95C2411yescharacteristic
679#95C2411yescharacteristic
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2411yescharacteristic
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2411yescharacteristic
711#95C2412yes—
712#95C2412yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724C24C2512yes—
725C24C2511yescharacteristic
726C2×Q8—24no—
727C2×Q8—28no—
728C2×Q8—24no—
729C2×Q8—22no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—24no—
733C2×Q8—28no—
734C2×Q8—24no—
735C2×Q8—28no—
736C2×Q8—24no—
737C2×Q8—42no—
738C2×Q8—44no—
739C2×Q8—432no—
740C2×Q8C2×#4118yes—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—22no—
745C2×D4—42no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—24no—
750C22×C4—22no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—44no—
768C22×C4—48no—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C22×C4C2×#4114yes—
772C22×C42−1+418yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2518yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2518yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2514yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2512yes—
794C22×C4C2511yescharacteristic
795C22×C4C2512yes—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—216no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—216no—
812C4⋊C4—216no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—216no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—48no—
824C4⋊C4—42no—
825C4⋊C4—42no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—48no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4C2×#41116yes—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—216no—
843C22⋊C4—24no—
844C22⋊C4—216no—
845C22⋊C4—24no—
846C22⋊C4—24no—
847C22⋊C4—24no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—48no—
853C22⋊C4—42no—
854C22⋊C4—42no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C42—28no—
858C42—28no—
859C42—24no—
860C42—24no—
861C42—28no—
862C42—28no—
863C42—24no—
864C42—22no—
865C42—24no—
866C42—24no—
867C42—216no—
868C42—24no—
869C42—24no—
870C42—24no—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—22no—
875C42—24no—
876C42—24no—
877C42—22no—
878C42—24no—
879C42—24no—
880C42—24no—
881C42—42no—
882C42—42no—
883C42—42no—
884C42—48no—
885C42—48no—
886C42—48no—
887C42—48no—
888C42C2×#4114yes—
889C42C2×#4114yes—
890C42C2×#4114yes—
891C42C2×#4114yes—
892C42C2×#4114yes—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23C22×#4112yes—
904C23C2×2−1+414yes—
905C23C2611yescharacteristic
906Q8—216no—
907Q8—416no—
908Q8—44no—
909Q8—48no—
910Q8—416no—
911D4—44no—
912D4—48no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—28no—
924C2×C4—28no—
925C2×C4—216no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—44no—
967C2×C4—416no—
968C2×C4—48no—
969C2×C4—48no—
970C2×C4—48no—
971C2×C4—48no—
972C2×C4—88no—
973C2×C4C22×#4112yes—
974C2×C4C22×#4112yes—
975C2×C4C22×#4118yes—
976C2×C4C22×#4112yes—
977C2×C4C22×#4112yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C22×#4112yes—
981C2×C4C22×#4114yes—
982C2×C4C2×2−1+414yes—
983C2×C4C2×2−1+414yes—
984C2×C4#58512yes—
985C2×C4#58514yes—
986C22—24no—
987C22—22no—
988C22—24no—
989C22—22no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22#350914yes—
998C22C23×#4111yescharacteristic
999C22C23×#4111yescharacteristic
1000C22C22×2−1+412yes—
1001C22C2×#58512yes—
1002C22C2×#58511yescharacteristic
1003C4—24no—
1004C4—22no—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—22no—
1009C4—28no—
1010C4—42no—
1011C4—42no—
1012C4—48no—
1013C4—42no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—48no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4#347514yes—
1025C4#351618yes—
1026C2—24no—
1027C2—82no—
1028C2C2×#347511yescharacteristic
1029C2C2×#351612yes—
1030C2C2×#350911yescharacteristic
1031C2#6281511yescharacteristic
1032C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59868C2semidirect
3. #59709C2semidirect
4. #59496C2semidirect
5. #39527C2semidirect
6. #39526C2semidirect
7. #39186C2semidirect
8. #38970C2semidirect
9. #38113C2semidirect
10. #36635C2semidirect
11. #36608C2semidirect
12. #36574C2semidirect
13. #36209C2semidirect
14. #36189C2semidirect
15. #36178C2semidirect
16. #36178C2semidirect
17. #36151C2semidirect
18. #36129C2semidirect
19. #35650C2semidirect
20. #35291C2semidirect
22. #34225C2semidirect
23. #34192C2semidirect
24. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598682
#598552
#597092
#594962
#395272
#395262
#391862
#389702
#381132
#366352
#366082
#365742
#362092
#361892
#361782
#361512
#361292
#356502
#352912
#352452
#342252
#341922
C2×C4×C4⋊Q82
C4×#5292