Subgroups — C₃₁×D₃₂ #14520552

Order 1984.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₃₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×C₃₁	—	2	2	no	—
4	C₁₆×C₃₁	C₂²	1	1	yes	characteristic
5	D₄×C₃₁	—	4	2	no	—
6	C₈×C₃₁	D₄	1	1	yes	characteristic
7	C₂²×C₃₁	—	8	2	no	—
8	C₄×C₃₁	D₈	1	1	yes	characteristic
9	D₃₂	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃₁	—	16	2	no	—
11	C₂×C₃₁	D₁₆	1	1	yes	characteristic
12	D₁₆	C₂×C₃₁	1	2	yes	complemented
13	C₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
14	C₃₁	D₃₂	1	1	yes	characteristic, direct product factor, Sylow
15	D₈	—	2	2	no	—
16	C₁₆	C₂²×C₃₁	1	1	yes	characteristic
17	D₄	—	4	2	no	—
18	C₈	D₄×C₃₁	1	1	yes	characteristic
19	C₂²	—	8	2	no	—
20	C₄	D₈×C₃₁	1	1	yes	characteristic
21	C₂	—	16	2	no	—
22	C₂	C₃₁×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₃₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₄×C₃₁ ◁ C₈×C₃₁ ◁ C₁₆×C₃₁ ◁ G

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.