Subgroups — #14521226

Order 1984.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758561	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758519	C₂	1	2	yes	maximal, complemented
4	#11758421	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758393	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
7	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₃₁	—	2	2	no	—
9	#92497	—	2	2	no	—
10	D₄×D₃₁	—	2	2	no	—
11	#92495	C₂²	1	2	yes	—
12	C₂²⋊C₄×C₃₁	—	2	2	no	—
13	C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
14	#92482	—	2	2	no	—
15	#92481	—	2	2	no	—
16	#92474	C₂²	1	2	yes	complemented
17	C₂³×C₃₁	D₄	1	2	yes	—
18	C₂²×D₃₁	—	2	2	no	—
19	Q₈×C₃₁	—	2	2	no	—
20	D₄×C₃₁	—	2	2	no	—
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂²⋊D₃₁	—	2	4	no	—
25	C₂²⋊D₃₁	—	2	2	no	—
26	C₂×Dic₃₁	—	2	2	no	—
27	D₁₂₄	D₄	1	2	yes	—
28	C₄×D₃₁	—	2	2	no	—
29	Dic₆₂	D₄	1	2	yes	—
30	C₃₁⋊C₈	—	2	2	no	—
31	C₂²×C₃₁	—	2	2	no	—
32	C₂²×C₃₁	—	4	2	no	—
33	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₂×D₃₁	—	2	2	no	—
35	C₂×D₃₁	—	8	2	no	—
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	C₂×D₄	1	2	yes	—
39	Dic₃₁	—	2	2	no	—
40	#455	—	31	1	no	maximal, Sylow
41	C₂×C₃₁	—	2	1	no	—
42	C₂×C₃₁	—	4	2	no	—
43	C₂×C₃₁	#120	1	1	yes	characteristic
44	D₃₁	—	4	2	no	—
45	H(5,𝔽₂)	—	31	1	no	—
46	#137	—	31	2	no	—
47	#124	D₃₁	1	1	yes	characteristic, complemented
48	#104	—	31	2	no	—
49	#100	—	31	1	no	—
50	C₃₁	#455	1	1	yes	characteristic, complemented, Sylow
51	#41	—	31	2	no	—
52	#41	—	62	2	no	—
53	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
54	C₂×D₄	—	62	2	no	—
55	C₂×D₄	—	62	2	no	—
56	C₂×D₄	C₂×D₃₁	1	1	yes	characteristic
57	Q₁₆	—	62	2	no	—
58	SD₁₆	—	62	2	no	—
59	M₁₆	—	31	2	no	—
60	C₂²⋊C₄	—	2	2	no	—
61	C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
62	C₂³	—	62	2	no	—
63	C₂³	C₂²⋊D₃₁	1	2	yes	—
64	Q₈	—	2	2	no	—
65	Q₈	—	31	2	no	—
66	D₄	—	2	2	no	—
67	D₄	—	31	2	no	—
68	D₄	—	62	4	no	—
69	D₄	—	62	2	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	62	2	no	—
73	C₂×C₄	—	62	2	no	—
74	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
75	C₈	—	62	2	no	—
76	C₂²	—	2	2	no	—
77	C₂²	—	4	2	no	—
78	C₂²	—	62	2	no	—
79	C₂²	—	248	2	no	—
80	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
81	C₄	—	4	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	62	2	no	—
84	C₄	D₄×D₃₁	1	2	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	4	2	no	—
87	C₂	—	124	2	no	—
88	C₂	#11758514	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758514
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#124	C₂
socle	C₂×C₃₁	#120
prime radical	#11758561	C₂
hypercenter	#124	D₃₁
hypocenter	C₃₁	#455
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #124

Complements

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

N	H ≅ G/N	type
2. C₃₁×#124	C₂	semidirect
3. #11758519	C₂	semidirect
4. #11758421	C₂	semidirect
5. #11758393	C₂	semidirect
6. C₂×Q₈×C₃₁	C₂²	semidirect
13. C₄²×C₃₁	C₂²	semidirect
16. #92474	C₂²	semidirect
47. #124	D₃₁	semidirect
50. C₃₁	#455	semidirect
53. C₂×Q₈	C₂×D₃₁	semidirect
61. C₄²	C₂×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
#11758561	2
C₃₁×#124	2
#11758519	2
#11758421	2
#11758393	2
#455	31