Subgroups — Q₈×#16840926 #44530747

Order 31264.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16840926	C₂	1	3	yes	maximal
2	C₄×#16840926	C₂	1	3	yes	maximal
3	Q₈×D₉₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#16840926	C₂²	1	3	yes	—
5	C₂×#16840926	C₂²	1	1	yes	characteristic
6	Dic₁₉₅₄	C₄	1	3	yes	complemented
7	C₄×D₉₇₇	C₂²	1	3	yes	—
8	Q₈×C₉₇₇	C₄	1	1	yes	characteristic, complemented
9	C₂×D₉₇₇	C₂³	1	1	yes	characteristic
10	#16840926	—	2	3	no	—
11	#16840926	Q₈	1	2	yes	direct product factor
12	C₄×C₉₇₇	C₂×C₄	1	3	yes	—
13	Dic₉₇₇	C₂×C₄	1	3	yes	—
14	C₂×C₉₇₇	C₂²×C₄	1	1	yes	characteristic
15	D₉₇₇	C₂×Q₈	1	1	yes	characteristic
16	D₉₇₇	#41	1	1	yes	characteristic
17	C₉₇₇	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×Q₈	—	977	1	no	maximal, Sylow
19	C₂×Q₈	—	977	1	no	—
20	C₄⋊C₄	—	977	3	no	—
21	C₄²	—	977	3	no	—
22	Q₈	—	977	3	no	—
23	Q₈	#16840926	1	1	yes	characteristic, direct product factor
24	C₂×C₄	—	977	3	no	—
25	C₂×C₄	—	977	1	no	—
26	C₂×C₄	—	977	3	no	—
27	C₂²	—	977	1	no	—
28	C₄	—	1954	3	no	—
29	C₄	—	977	2	no	—
30	C₄	—	977	3	no	—
31	C₄	C₂×#16840926	1	3	yes	—
32	C₂	—	977	1	no	—
33	C₂	—	977	1	no	—
34	C₂	C₂²×#16840926	1	1	yes	characteristic

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

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