Subgroups — #14521222

Order 1984.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	#11758526	C₂	1	2	yes	maximal, complemented
3	#11758524	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758425	C₂	1	2	yes	maximal, complemented
5	#11758424	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₃₁	—	2	2	no	—
7	#41×C₃₁	—	2	2	no	—
8	#41×C₃₁	C₂²	1	2	yes	—
9	C₂×Q₈×C₃₁	—	2	2	no	—
10	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
12	#92481	—	2	2	no	—
13	#92479	—	2	2	no	—
14	(C₂×D₃₁)⋊C₄	—	2	2	no	—
15	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
16	#92474	C₂²	1	2	yes	—
17	C₂²×D₃₁	—	2	1	no	—
18	Q₈×C₃₁	—	2	2	no	—
19	Q₈×C₃₁	—	2	2	no	—
20	Q₈×C₃₁	D₄	1	2	yes	—
21	D₄×C₃₁	—	2	2	no	—
22	D₄×C₃₁	—	2	2	no	—
23	D₄×C₃₁	D₄	1	2	yes	—
24	C₂×C₄×C₃₁	—	2	4	no	—
25	C₂×C₄×C₃₁	—	2	2	no	—
26	C₂×C₄×C₃₁	D₄	1	2	yes	—
27	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₁	—	2	1	no	—
29	D₁₂₄	—	2	2	no	—
30	C₃₁⋊C₈	—	2	2	no	—
31	C₂²×C₃₁	—	2	2	no	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₁	—	4	2	no	—
34	C₂×D₃₁	—	4	1	no	—
35	C₄×C₃₁	—	2	2	no	—
36	C₄×C₃₁	—	2	2	no	—
37	C₄×C₃₁	C₂×D₄	1	2	yes	—
38	Dic₃₁	—	4	1	no	—
39	#454	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	—	2	1	no	—
41	C₂×C₃₁	—	4	2	no	—
42	C₂×C₃₁	#120	1	1	yes	characteristic
43	D₃₁	—	8	1	no	—
44	2₋¹⁺⁴	D₃₁	1	1	yes	characteristic, complemented
45	AGL(1,ℤ/8)	—	31	2	no	—
46	#124	—	31	1	no	—
47	#104	—	31	2	no	—
48	#101	—	31	1	no	—
49	C₃₁	#454	1	1	yes	characteristic, complemented, Sylow
50	#41	—	2	2	no	—
51	#41	—	2	2	no	—
52	#41	C₂×D₃₁	1	2	yes	—
53	C₂×Q₈	—	2	2	no	—
54	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
55	C₂×D₄	—	31	1	no	—
56	SD₁₆	—	62	2	no	—
57	D₈	—	62	2	no	—
58	M₁₆	—	31	2	no	—
59	C₂²⋊C₄	—	62	2	no	—
60	C₄²	—	31	1	no	—
61	C₂³	—	62	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	2	2	no	—
64	Q₈	C₂²⋊D₃₁	1	2	yes	—
65	D₄	—	2	2	no	—
66	D₄	—	2	2	no	—
67	D₄	—	62	2	no	—
68	D₄	C₂²⋊D₃₁	1	2	yes	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	2	2	no	—
71	C₂×C₄	—	62	1	no	—
72	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
73	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
74	C₈	—	62	2	no	—
75	C₂²	—	2	2	no	—
76	C₂²	—	124	2	no	—
77	C₂²	—	124	1	no	—
78	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	2	2	no	—
81	C₄	—	124	1	no	—
82	C₄	C₂×C₂²⋊D₃₁	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	4	2	no	—
85	C₂	—	248	1	no	—
86	C₂	#11758530	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758530
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×2₋¹⁺⁴	C₂
socle	C₂×C₃₁	#120
hypercenter	2₋¹⁺⁴	D₃₁
hypocenter	C₃₁	#454
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ 2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₃₁×2₋¹⁺⁴	C₂	semidirect
2. #11758526	C₂	semidirect
3. #11758524	C₂	semidirect
4. #11758425	C₂	semidirect
5. #11758424	C₂	semidirect
44. 2₋¹⁺⁴	D₃₁	semidirect
49. C₃₁	#454	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×2₋¹⁺⁴	2
#11758526	2
#11758524	2
#11758425	2
#11758424	2
#454	31