Subgroups — D₁₅₆₃₂ #44530608

Order 31264.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₈₁₆	C₂	1	2	yes	maximal, complemented
2	C₁₆×C₉₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₉₀₈	—	2	2	no	—
4	C₈×C₉₇₇	C₂²	1	1	yes	characteristic
5	C₂×D₉₇₇	—	4	2	no	—
6	C₄×C₉₇₇	D₄	1	1	yes	characteristic
7	C₂×C₉₇₇	D₈	1	1	yes	characteristic
8	D₉₇₇	—	8	2	no	—
9	C₉₇₇	D₁₆	1	1	yes	characteristic, complemented, Sylow
10	D₁₆	—	977	1	no	maximal, Sylow
11	D₈	—	977	2	no	—
12	C₁₆	D₉₇₇	1	1	yes	characteristic, complemented
13	D₄	—	1954	2	no	—
14	C₈	C₂×D₉₇₇	1	1	yes	characteristic
15	C₂²	—	3908	2	no	—
16	C₄	D₃₉₀₈	1	1	yes	characteristic
17	C₂	—	7816	2	no	—
18	C₂	D₇₈₁₆	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.