Subgroups — #44530595

Order 31264.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21463091	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₉₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₇₇	C₄	1	1	yes	characteristic
5	C₂×Dic₉₇₇	C₄	1	1	yes	characteristic
6	#21463091	—	2	1	no	—
7	C₂×C₄×C₉₇₇	C₂²	1	1	yes	characteristic
8	C₈×C₉₇₇	—	2	1	no	—
9	C₂²×C₉₇₇	C₂×C₄	1	1	yes	characteristic
10	C₄×C₉₇₇	D₄	1	1	yes	characteristic
11	C₄×C₉₇₇	Q₈	1	1	yes	characteristic
12	Dic₉₇₇	—	2	1	no	—
13	Dic₉₇₇	C₈	1	2	yes	complemented
14	C₂×C₉₇₇	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₉₇₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₉₇₇	M₁₆	1	1	yes	characteristic
17	C₉₇₇	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
18	C₄⋊C₈	—	977	1	no	maximal, Sylow
19	C₂×C₈	—	977	1	no	—
20	C₂×C₈	D₉₇₇	1	1	yes	characteristic
21	C₄²	—	977	1	no	—
22	C₂×C₄	—	977	1	no	—
23	C₂×C₄	—	977	1	no	—
24	C₂×C₄	C₂×D₉₇₇	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	1954	1	no	—
27	C₂²	C₄×D₉₇₇	1	1	yes	characteristic
28	C₄	—	1954	1	no	—
29	C₄	—	977	2	no	—
30	C₄	C₂²⋊D₉₇₇	1	1	yes	characteristic
31	C₄	Dic₁₉₅₄	1	1	yes	characteristic
32	C₂	#30627586	1	1	yes	characteristic
33	C₂	C₈×D₉₇₇	1	1	yes	characteristic
34	C₂	#30627590	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Dic₉₇₇	C₈	semidirect
17. C₉₇₇	C₄⋊C₈	semidirect

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