Subgroups — #14520883

Order 1984.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁⋊C₃₂	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×C₃₁	C₄	1	1	yes	characteristic
4	C₁₆×C₃₁	C₄	1	1	yes	characteristic
5	C₁₆×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₃₁	C₈	1	1	yes	characteristic
7	C₈×C₃₁	C₈	1	1	yes	characteristic
8	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₃₁	C₁₆	1	1	yes	characteristic
10	C₄×C₃₁	C₁₆	1	1	yes	characteristic
11	C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
12	M₆₄	—	31	1	no	maximal, Sylow
13	C₂×C₃₁	—	2	1	no	—
14	C₂×C₃₁	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₆	D₃₁	1	1	yes	characteristic
16	C₃₂	—	31	2	no	—
17	C₃₁	M₆₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₈	Dic₃₁	1	1	yes	characteristic
19	C₁₆	Dic₃₁	1	1	yes	characteristic
20	C₁₆	C₂×D₃₁	1	1	yes	characteristic
21	C₂×C₄	C₃₁⋊C₈	1	1	yes	characteristic
22	C₈	C₃₁⋊C₈	1	1	yes	characteristic
23	C₈	C₂×Dic₃₁	1	1	yes	characteristic
24	C₂²	C₃₁⋊C₁₆	1	1	yes	characteristic
25	C₄	C₃₁⋊C₁₆	1	1	yes	characteristic
26	C₄	C₂×C₃₁⋊C₈	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×C₃₁⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₃₁⋊C₃₂	C₂	semidirect
17. C₃₁	M₆₄	semidirect

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