Subgroups — C₃₁×Q₆₄ #14520554

Order 1984.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×Q₃₂	C₂	1	2	yes	maximal
2	C₃₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₃₁	—	2	2	no	—
4	C₁₆×C₃₁	C₂²	1	1	yes	characteristic
5	Q₈×C₃₁	—	4	2	no	—
6	C₈×C₃₁	D₄	1	1	yes	characteristic
7	C₄×C₃₁	—	8	2	no	—
8	C₄×C₃₁	D₈	1	1	yes	characteristic
9	Q₆₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃₁	D₁₆	1	1	yes	characteristic
11	Q₃₂	C₂×C₃₁	1	2	yes	—
12	C₃₂	C₂×C₃₁	1	1	yes	characteristic
13	C₃₁	Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
14	Q₁₆	—	2	2	no	—
15	C₁₆	C₂²×C₃₁	1	1	yes	characteristic
16	Q₈	—	4	2	no	—
17	C₈	D₄×C₃₁	1	1	yes	characteristic
18	C₄	—	8	2	no	—
19	C₄	D₈×C₃₁	1	1	yes	characteristic
20	C₂	C₃₁×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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.

N	H ≅ G/N	type
9. Q₆₄	C₃₁	direct (N × H)
13. C₃₁	Q₆₄	direct (N × H)

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