Subgroups — #14520960

Order 1984.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×(C₂×D₃₁)⋊C₄	C₂	1	3	yes	maximal
3	C₃₁⋊#95	C₂	1	3	yes	maximal, complemented
4	C₂³×D₃₁	C₂²	1	1	yes	characteristic
5	C₂×Q₈×C₃₁	—	2	6	no	—
6	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
7	C₂²×Dic₃₁	C₂²	1	3	yes	—
8	(C₂×D₃₁)⋊C₄	—	2	6	no	—
9	C₂³×C₃₁	C₂³	1	1	yes	characteristic
10	C₂²×D₃₁	—	2	3	no	—
11	C₂²×D₃₁	—	2	3	no	—
12	C₂²×D₃₁	Q₈	1	2	yes	complemented
13	Q₈×C₃₁	—	2	8	no	—
14	C₂×C₄×C₃₁	—	2	6	no	—
15	C₂×C₄×C₃₁	D₄	1	6	yes	—
16	C₂×Dic₃₁	—	2	3	no	—
17	C₂×Dic₃₁	—	2	6	no	—
18	C₂²×C₃₁	C₂×D₄	1	3	yes	—
19	C₂²×C₃₁	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₃₁	#41	1	3	yes	—
21	C₂×D₃₁	—	2	6	no	—
22	C₂×D₃₁	—	4	1	no	—
23	C₂×D₃₁	—	4	3	no	—
24	C₄×C₃₁	—	2	6	no	—
25	Dic₃₁	—	4	3	no	—
26	#393	—	31	1	no	maximal, Sylow
27	C₂×C₃₁	#120	1	1	yes	characteristic
28	C₂×C₃₁	C₂²⋊Q₈	1	3	yes	—
29	C₂×C₃₁	#124	1	3	yes	—
30	D₃₁	—	4	2	no	—
31	C₂²×Q₈	D₃₁	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊C₄	—	31	3	no	—
33	#95	—	31	3	no	—
34	C₃₁	#393	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	31	1	no	—
36	C₂×Q₈	—	2	6	no	—
37	C₂²×C₄	—	31	3	no	—
38	C₂²×C₄	C₂×D₃₁	1	3	yes	—
39	C₂²⋊C₄	—	62	6	no	—
40	C₂³	—	31	2	no	—
41	C₂³	—	62	3	no	—
42	C₂³	—	62	3	no	—
43	C₂³	C₂²×D₃₁	1	1	yes	characteristic
44	Q₈	—	2	8	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	62	6	no	—
47	C₂×C₄	—	62	3	no	—
48	C₂×C₄	C₂²⋊D₃₁	1	6	yes	—
49	C₂²	—	62	6	no	—
50	C₂²	—	124	3	no	—
51	C₂²	—	124	1	no	—
52	C₂²	Q₈×D₃₁	1	1	yes	characteristic
53	C₂²	#92499	1	3	yes	—
54	C₂²	C₂×C₂²⋊D₃₁	1	3	yes	—
55	C₄	—	2	6	no	—
56	C₄	—	124	3	no	—
57	C₂	—	124	2	no	—
58	C₂	#11758523	1	3	yes	—
59	C₂	#11758524	1	3	yes	—
60	C₂	#11758530	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁
commutator, socle, cosocle	C₂³×C₃₁	C₂³
Fitting	C₂²×Q₈×C₃₁	C₂
prime radical	C₂³×D₃₁	C₂²
hypercenter	C₂²×Q₈	D₃₁
hypocenter	C₃₁	#393
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈×C₃₁	C₂	semidirect
3. C₃₁⋊#95	C₂	semidirect
12. C₂²×D₃₁	Q₈	semidirect
31. C₂²×Q₈	D₃₁	semidirect
34. C₃₁	#393	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₃₁	2
C₂×(C₂×D₃₁)⋊C₄	2
C₃₁⋊#95	2
#393	31