Subgroups — #14521054

Order 1984.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	#11758503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#92474	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758420	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₃₁	—	2	1	no	—
6	C₂×D₄×C₃₁	—	2	1	no	—
7	C₂×D₄×C₃₁	—	2	2	no	—
8	C₂×D₄×C₃₁	C₄	1	4	yes	complemented
9	C₂×D₄×C₃₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₃₁	—	2	1	no	—
12	C₄⋊Dic₃₁	C₂²	1	2	yes	complemented
13	C₄×Dic₃₁	—	2	1	no	—
14	#92474	—	2	2	no	—
15	C₂×C₃₁⋊C₈	C₂²	1	2	yes	complemented
16	C₂³×C₃₁	—	2	4	no	—
17	C₂³×C₃₁	—	2	2	no	—
18	C₂³×C₃₁	—	4	4	no	—
19	C₂³×C₃₁	D₄	1	1	yes	characteristic
20	D₄×C₃₁	—	2	4	no	—
21	D₄×C₃₁	—	2	2	no	—
22	D₄×C₃₁	C₂×C₄	1	4	yes	—
23	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	D₄	1	2	yes	—
26	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂×Dic₃₁	—	2	2	no	—
28	C₃₁⋊C₈	—	2	2	no	—
29	C₂²×C₃₁	—	2	2	no	—
30	C₂²×C₃₁	—	2	4	no	—
31	C₂²×C₃₁	—	4	8	no	—
32	C₂²×C₃₁	—	4	4	no	—
33	C₂²×C₃₁	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
35	C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
36	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
38	Dic₃₁	—	4	2	no	—
39	#418	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	—	2	2	no	—
41	C₂×C₃₁	—	4	4	no	—
42	C₂×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
44	C₂²×D₄	D₃₁	1	1	yes	characteristic
45	C₂×M₁₆	—	31	1	no	—
46	#117	—	31	1	no	—
47	#102	—	31	4	no	—
48	C₃₁	#418	1	1	yes	characteristic, complemented, Sylow
49	C₂⁴	—	2	1	no	—
50	C₂×D₄	—	2	1	no	—
51	C₂×D₄	—	2	2	no	—
52	C₂×D₄	Dic₃₁	1	4	yes	complemented
53	C₂×D₄	C₂×D₃₁	1	2	yes	—
54	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
55	M₁₆	—	62	2	no	—
56	C₂×C₈	—	31	2	no	—
57	C₄⋊C₄	—	31	2	no	—
58	C₂²⋊C₄	—	62	1	no	—
59	C₄²	—	62	1	no	—
60	C₂³	—	2	4	no	—
61	C₂³	—	2	2	no	—
62	C₂³	—	4	4	no	—
63	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
64	D₄	—	2	4	no	—
65	D₄	—	2	2	no	—
66	D₄	C₂×Dic₃₁	1	4	yes	—
67	C₂×C₄	—	62	2	no	—
68	C₂×C₄	C₂×Dic₃₁	1	2	yes	—
69	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
71	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
72	C₈	—	62	2	no	—
73	C₂²	—	2	2	no	—
74	C₂²	—	2	4	no	—
75	C₂²	—	4	8	no	—
76	C₂²	—	4	4	no	—
77	C₂²	C₂²⋊Dic₃₁	1	2	yes	—
78	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
79	C₄	—	124	2	no	—
80	C₄	C₂²⋊Dic₃₁	1	2	yes	—
81	C₄	C₂²×Dic₃₁	1	1	yes	characteristic
82	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	4	4	no	—
85	C₂	#11758509	1	2	yes	—
86	C₂	C₂×C₂²⋊Dic₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator	C₄×C₃₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₁
Fitting, prime radical	C₂²×D₄×C₃₁	C₂
socle	C₂²×C₃₁	C₂×D₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₂²×D₄	D₃₁
hypocenter	C₃₁	#418
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. #11758503	C₂	semidirect
3. C₂×#92474	C₂	semidirect
4. #11758420	C₂	semidirect
8. C₂×D₄×C₃₁	C₄	semidirect
12. C₄⋊Dic₃₁	C₂²	semidirect
15. C₂×C₃₁⋊C₈	C₂²	semidirect
48. C₃₁	#418	semidirect
52. C₂×D₄	Dic₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×C₃₁	2
#11758503	2
C₂×#92474	2
#11758420	2
#418	31