Finite Group Databasebeta

← #7678780

Subgroups — #7678780

Order 512.

6742 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C212yesmaximal, complemented
2#59155C214yesmaximal, complemented
3#59154C214yesmaximal, complemented
4#59153C214yesmaximal, complemented
5#59152C214yesmaximal, complemented
6#45274C214yesmaximal, complemented
7#45272C214yesmaximal, complemented
8#44941C214yesmaximal, complemented
9#44939C214yesmaximal, complemented
10#39614C214yesmaximal, complemented
11#39610C214yesmaximal, complemented
12#39610C214yesmaximal, complemented
13#36561C214yesmaximal, complemented
14#35575C212yesmaximal, complemented
15#35575C212yesmaximal, complemented
16#35173C211yesmaximal, characteristic, complemented
17#35167C211yesmaximal, characteristic, complemented
18#35167C211yesmaximal, characteristic, complemented
19#34947C212yesmaximal, complemented
20#34274C211yesmaximal, characteristic
21#34274C211yesmaximal, characteristic
22C2×#2370C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic
24#3504—232no—
25C2×#557C2214yes—
26C2×#557C2214yes—
27C2×#554C2214yes—
28C2×#554C2214yes—
29C2×#554C2218yes—
30C2×#554C2218yes—
31C2×#544C2212yes—
32C2×#544C2212yes—
33C2×#544C2214yes—
34C2×#544C2214yes—
35C2×#537C2211yescharacteristic
36C2×#533C2214yes—
37C2×#533C2212yes—
38C22×#125C2214yes—
39C22×#125C2211yescharacteristic
40C2×#520C2212yes—
41C2×#520C2212yes—
42C2×C4×#41C2212yes—
43#2857C2214yes—
44#2857C2214yes—
45#2857C2214yes—
46#2726C2218yes—
47#2720C2218yes—
48#2720C2218yes—
49#2713C2218yes—
50#2713C2218yes—
51#2704C2218yes—
52#2704C2218yes—
53#2692C2218yes—
54#2692C2218yes—
55#2683C2218yes—
56#2677C2218yes—
57#2677C2218yes—
58#2659C2214yes—
59#2659C2214yes—
60#2659C2214yes—
61#2584C2214yes—
62#2584C2214yes—
63#2568C2212yes—
64#2567C2214yes—
65#2567C2212yes—
66#2566C2212yes—
67#2566C2212yes—
68#2565C2212yes—
69#2565C2212yes—
70#2564C2214yes—
71#2564C2214yes—
72#2564C2218yes—
73#2564C2218yes—
74#2563C2212yes—
75#2556C2218yes—
76#2556C2218yes—
77#2552C2214yes—
78#2552C2214yes—
79#2551C2214yes—
80#2551C2214yes—
81#2551C2214yes—
82#2550C2214yes—
83#2550C2214yes—
84#2550C2214yes—
85#2550C2214yes—
86#2546C2214yes—
87#2542C2212yes—
88#2542C2214yes—
89#2506C2214yes—
90#2506C2214yes—
91#2492C2218yes—
92#2473C2218yes—
93#2473C2218yes—
94#2465C2218yes—
95#2465C2218yes—
96#2462C2218yes—
97#2462C2218yes—
98#2454C2214yes—
99#2454C2214yes—
100#2453C2214yes—
101#2453C2214yes—
102#2452C2214yes—
103#2452C2214yes—
104#2452C2214yes—
105#2452C2214yes—
106#2451C2218yes—
107#2451C2214yes—
108#2451C2214yes—
109#2449C2218yes—
110#2449C2218yes—
111#2442C2214yes—
112#2442C2214yes—
113#2441C2214yes—
114#2441C2214yes—
115#2440C2218yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2429C2218yes—
121#2417C2218yes—
122#2417C2214yes—
123#2417C2214yes—
124#2417C2218yes—
125#2417C2218yes—
126#2396C2214yes—
127#2396C2214yes—
128#2370C2214yes—
129#2370C2214yes—
130#2370C2214yes—
131#2370C2214yes—
132#2365C2214yes—
133#2363C2214yes—
134#2363C2214yes—
135#2362C2214yes—
136#2362C2214yes—
137#2361C2214yes—
138#2361C2214yes—
139#2360C2218yes—
140#2360C2214yes—
141#2360C2214yes—
142D4×C4⋊C4C2214yes—
143#2325C2214yes—
144#2325C2214yes—
145#2325C2214yes—
146#2324C2214yes—
147#2323C2214yes—
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2316C2211yescharacteristic
151#2316C2212yes—
152#2311C2212yes—
153C4×C22⋊Q8C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2214yes—
156C4×#121C2214yes—
157C4×#121C2214yes—
158C4×#121C2214yes—
159C4×#121C2214yes—
160#2297C2212yes—
161#2297C2212yes—
162C2×#389C2212yes—
163C2×#389C2211yescharacteristic
164C2×#389C2211yescharacteristic
165C2×#387C2212yes—
166C2×#387C2212yes—
167#2285C2212yes—
168#2285C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C4⋊C4C2211yescharacteristic
173C2×C4×C4⋊C4C2212yes—
174C22×#41C2312yes—
175#557—232no—
176#557—232no—
177#554—232no—
178#554—232no—
179#554—264no—
180#554—264no—
181#544—232no—
182#544—232no—
183#544—216no—
184#544—216no—
185#537Q8116yescomplemented
186#533—232no—
187#533—216no—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2318yes—
193C2×C4⋊Q8C2318yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×#125—232no—
200C2×#125D4116yescomplemented
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2314yes—
204C2×#125C2314yes—
205C2×#125C2318yes—
206C2×#125C2318yes—
207C2×#125C2314yes—
208C2×#125C2314yes—
209C2×#125C2318yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230#520—216no—
231#520—216no—
232C4×#41—216no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2318yes—
240C2×C4×Q8C2318yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2318yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2318yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2318yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C42C2314yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#399C2314yes—
284#399C2314yes—
285#399C2318yes—
286#399C2318yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2314yes—
304#396C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2314yes—
310#395C2314yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#393C2314yes—
320#393C2314yes—
321#393C2318yes—
322#393C2318yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#386C2314yes—
397#386C2314yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#384C2312yes—
416#384C2312yes—
417#384C2312yes—
418#384C2312yes—
419#384C2314yes—
420#384C2314yes—
421#384C2314yes—
422#382C2312yes—
423#382C2312yes—
424#382C2312yes—
425#382C2312yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2318yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2318yes—
439#380C2318yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2318yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2312yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#41—28no—
476C2×#41—28no—
477C2×#41C2×Q8116yes—
478C22×Q8C2412yes—
479C22×Q8C2414yes—
480C22×Q8C2418yes—
481C22×Q8C2418yes—
482C22×Q8C2414yes—
483C22×D4C2414yes—
484C22×D4C2412yes—
485C22×D4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2414yes—
489C23×C4C2418yes—
490C23×C4C2418yes—
491C23×C4C2411yescharacteristic
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C4⋊Q8—216no—
503C4⋊Q8—216no—
504C4⋊Q8—232no—
505C4⋊Q8—232no—
506C4⋊Q8—216no—
507C4⋊Q8—216no—
508C4⋊Q8—28no—
509C4⋊Q8—28no—
510C4⋊Q8—48no—
511C4⋊Q8—84no—
512C4⋊Q8—84no—
513#125—216no—
514#125—216no—
515#125—232no—
516#125—232no—
517#125—232no—
518#125—232no—
519#125—216no—
520#125—216no—
521#125—28no—
522#125—28no—
523#125C2×D4132yes—
524#125C2×D4132yes—
525C22⋊Q8—216no—
526C22⋊Q8—216no—
527C22⋊Q8—232no—
528C22⋊Q8—232no—
529C22⋊Q8—232no—
530C22⋊Q8—232no—
531C22⋊Q8—232no—
532C22⋊Q8—232no—
533C22⋊Q8—232no—
534C22⋊Q8—232no—
535C22⋊Q8—48no—
536C22⋊Q8—416no—
537C22⋊Q8—48no—
538C22⋊Q8—88no—
539C22⋊Q8C2×Q8132yes—
540#121C2×Q8132yes—
541#121C2×Q8132yes—
542C4×Q8—216no—
543C4×Q8—216no—
544C4×Q8—232no—
545C4×Q8—232no—
546C4×Q8—28no—
547C4×Q8—28no—
548C4×Q8—216no—
549C4×Q8—216no—
550C4×D4—216no—
551C4×D4—216no—
552C4×D4—232no—
553C4×D4—232no—
554C4×D4—216no—
555C4×D4—216no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—48no—
559C4×D4—84no—
560C4×D4—84no—
561#117—28no—
562#117—28no—
563#117—28no—
564#117—216no—
565#117—216no—
566#117—216no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—216no—
569C2×C4⋊C4—216no—
570C2×C4⋊C4—232no—
571C2×C4⋊C4—232no—
572C2×C4⋊C4—42no—
573C2×C4⋊C4—42no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4—82no—
576C2×C4⋊C4C2×D418yes—
577C2×C4⋊C4C2×D418yes—
578C2×C4⋊C4C2×D4116yes—
579C2×C4⋊C4C2×D4116yes—
580C2×C4⋊C4C2×Q818yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C42—24no—
653C2×C42—24no—
654C2×C42—216no—
655C2×C42—44no—
656C2×C42—82no—
657C2×C42—82no—
658C2×C42C2×D418yes—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678#95C2411yescharacteristic
679#95C2411yescharacteristic
680#95C2411yescharacteristic
681#95C2411yescharacteristic
682#95C2412yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2412yes—
689#95C2418yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713C24C2514yes—
714C24C2511yescharacteristic
715#41—264no—
716C2×Q8—24no—
717C2×Q8—216no—
718C2×Q8—216no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—24no—
722C2×Q8—44no—
723C2×Q8—48no—
724C2×Q8—44no—
725C2×Q8—48no—
726C2×Q8—48no—
727C2×Q8—44no—
728C2×Q8—48no—
729C2×Q8—44no—
730C2×Q8C22×Q818yes—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4C22×Q8116yes—
738C2×D4C22×Q818yes—
739C2×D4C22×Q8116yes—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—216no—
752C22×C4—216no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—41no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—41no—
760C22×C4—42no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—48no—
771C22×C4—44no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—41no—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D418yes—
782C22×C4C22×D418yes—
783C22×C4C22×D414yes—
784C22×C4C22×Q8116yes—
785C22×C4C22×Q818yes—
786C22×C4C22×Q814yes—
787C22×C42−1+414yes—
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—216no—
817C4⋊C4—216no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4C22×D4116yes—
856C4⋊C4C22×D4116yes—
857C4⋊C4C22×D4116yes—
858C4⋊C4C22×D4132yes—
859C4⋊C4C22×D4116yes—
860C4⋊C4C22×Q8116yes—
861C4⋊C4C22×Q8116yes—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—216no—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4C22×Q8132yes—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—216no—
884C42—216no—
885C42—28no—
886C42—28no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—44no—
893C42—44no—
894C42—44no—
895C42—44no—
896C42—44no—
897C42C22×D418yes—
898C42C22×D418yes—
899C23—21no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23C23×D412yes—
910C23C23×Q818yes—
911C23C23×Q812yes—
912C23C2×2−1+412yes—
913C23C2611yescharacteristic
914Q8—216no—
915Q8—88no—
916Q8—816no—
917Q8—816no—
918Q8—88no—
919D4—232no—
920D4—216no—
921D4—416no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—24no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—24no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—24no—
939C2×C4—21no—
940C2×C4—232no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—21no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—21no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—48no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—48no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—816no—
982C2×C4—88no—
983C2×C4—88no—
984C2×C4—816no—
985C2×C4—82no—
986C2×C4—82no—
987C2×C4—84no—
988C2×C4D4×Q8116yes—
989C2×C4C23×D412yes—
990C2×C4C23×D414yes—
991C2×C4C23×D418yes—
992C2×C4C23×D418yes—
993C2×C4C23×D412yes—
994C2×C4C23×D414yes—
995C2×C4C23×Q818yes—
996C2×C4C23×Q818yes—
997C2×C4C23×Q814yes—
998C2×C4C2×2−1+414yes—
999C2×C4#58512yes—
1000C2×C4#58512yes—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—28no—
1008C22—28no—
1009C22—28no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22C2×D4×Q814yes—
1015C22C24×D411yescharacteristic
1016C22C24×Q811yescharacteristic
1017C22C22×2−1+411yescharacteristic
1018C22C2×#58511yescharacteristic
1019C22C2×#58511yescharacteristic
1020C22H(7,𝔽2)11yescharacteristic
1021C222−1+611yescharacteristic
1022C4—28no—
1023C4—28no—
1024C4—24no—
1025C4—22no—
1026C4—28no—
1027C4—22no—
1028C4—22no—
1029C4—28no—
1030C4—22no—
1031C4—44no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4—41no—
1038C4—42no—
1039C4—41no—
1040C4—42no—
1041C4—44no—
1042C4C2×D4×Q818yes—
1043C2—24no—
1044C2—48no—
1045C2C22×D4×Q811yescharacteristic
1046C2#6281211yescharacteristic
1047C2#6285311yescharacteristic
1048C2#6292811yescharacteristic
1049C2#6295811yescharacteristic
1050C2#6298911yescharacteristic
1051C2#6300411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3504C2semidirect
2. #59155C2semidirect
3. #59154C2semidirect
4. #59153C2semidirect
5. #59152C2semidirect
6. #45274C2semidirect
7. #45272C2semidirect
8. #44941C2semidirect
9. #44939C2semidirect
10. #39614C2semidirect
11. #39610C2semidirect
12. #39610C2semidirect
13. #36561C2semidirect
14. #35575C2semidirect
15. #35575C2semidirect
16. #35173C2semidirect
17. #35167C2semidirect
18. #35167C2semidirect
19. #34947C2semidirect
22. C2×#2370C2semidirect
185. #537Q8semidirect
200. C2×#125D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
#591552
#591542
#591532
#591522
#452742
#452722
#449412
#449392
#396142
#396102
#365612
#355752
#351732
#351672
#349472
#342742
C2×#23702
C4×#5372