Subgroups — #14520798

Order 1984.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal
3	C₂×Q₈×C₃₁	C₄	1	2	yes	—
4	C₄⋊C₄×C₃₁	—	2	2	no	—
5	C₄²×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×C₃₁⋊C₈	—	2	2	no	—
7	Q₈×C₃₁	—	4	2	no	—
8	C₂×C₄×C₃₁	—	2	2	no	—
9	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₃₁	D₄	1	2	yes	—
11	C₃₁⋊C₈	—	4	2	no	—
12	C₂²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₃₁	—	2	1	no	—
14	C₄×C₃₁	—	4	2	no	—
15	C₄×C₃₁	SD₁₆	1	2	yes	—
16	C₄×C₃₁	Q₁₆	1	2	yes	—
17	#333	—	31	1	no	maximal, Sylow
18	C₂×C₃₁	#100	1	1	yes	characteristic
19	C₂×C₃₁	#103	1	2	yes	—
20	C₄⋊Q₈	D₃₁	1	1	yes	characteristic
21	C₄⋊C₈	—	31	2	no	—
22	C₃₁	#333	1	1	yes	characteristic, complemented, Sylow
23	C₂×Q₈	Dic₃₁	1	2	yes	—
24	C₂×C₈	—	62	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₃₁	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
31	C₈	—	124	2	no	—
32	C₂²	C₂²⋊Dic₃₁	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#92481	1	2	yes	—
36	C₄	#92482	1	2	yes	—
37	C₂	#11758421	1	1	yes	characteristic
38	C₂	#11758423	1	2	yes	—

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

N	H ≅ G/N	type
22. C₃₁	#333	semidirect

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