Subgroups — #14521428

Order 1984.

122 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	C₂×#92482	C₂	1	4	yes	maximal
3	#11758446	C₂	1	1	yes	maximal, characteristic
4	C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
6	C₂×Dic₆₂	C₂²	1	2	yes	—
7	C₄⋊C₄×C₃₁	—	2	2	no	—
8	C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	#92482	—	2	8	no	—
10	C₄⋊Dic₃₁	—	2	2	no	—
11	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
12	Q₈×C₃₁	—	2	4	no	—
13	C₂×C₄×C₃₁	—	2	2	no	—
14	C₂×C₄×C₃₁	D₄	1	2	yes	—
15	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₃₁	—	2	2	no	—
17	Dic₆₂	—	2	4	no	—
18	C₃₁⋊C₈	D₄	1	4	yes	—
19	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
20	C₄×C₃₁	—	4	2	no	—
21	C₄×C₃₁	Q₁₆	1	4	yes	complemented
22	C₄×C₃₁	C₂×D₄	1	2	yes	—
23	Dic₃₁	—	4	2	no	—
24	#494	—	31	1	no	maximal, Sylow
25	C₂×C₃₁	#127	1	1	yes	characteristic
26	C₂×C₃₁	C₂×Q₁₆	1	2	yes	—
27	C₂×Q₁₆	—	31	4	no	—
28	C₄⋊Q₈	—	31	1	no	—
29	C₄⋊Q₈	D₃₁	1	1	yes	characteristic
30	C₄×C₈	—	31	1	no	—
31	C₃₁	#494	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₈	—	31	2	no	—
33	C₂×Q₈	C₂×D₃₁	1	2	yes	—
34	Q₁₆	—	62	8	no	—
35	C₂×C₈	—	31	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	62	2	no	—
38	C₄²	C₂×D₃₁	1	1	yes	characteristic
39	Q₈	—	2	4	no	—
40	Q₈	—	62	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	62	2	no	—
43	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
44	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
45	C₈	—	31	4	no	—
46	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
47	C₄	—	4	2	no	—
48	C₄	—	124	2	no	—
49	C₄	#92482	1	4	yes	complemented
50	C₄	D₄×D₃₁	1	2	yes	—
51	C₂	#11758517	1	1	yes	characteristic
52	C₂	C₂×#92482	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	C₄⋊Q₈	D₃₁
hypocenter	C₃₁	#494
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
21. C₄×C₃₁	Q₁₆	semidirect
31. C₃₁	#494	semidirect
49. C₄	#92482	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×C₄⋊Q₈	2
C₂×#92482	2
#11758446	2
C₄×C₃₁⋊C₈	2
#494	31