Subgroups — #14521017

Order 1984.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92495	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃₁)⋊C₈	C₂	1	4	yes	maximal, complemented
5	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×C₂²⋊D₃₁	C₄	1	2	yes	—
7	#92495	—	2	2	no	—
8	#92495	—	2	2	no	—
9	C₂×D₁₂₄	C₄	1	1	yes	characteristic
10	C₂×C₄×D₃₁	C₂²	1	2	yes	—
11	C₂×Dic₆₂	C₄	1	1	yes	characteristic
12	M₁₆×C₃₁	—	2	2	no	—
13	C₂×C₈×C₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁⋊C₈	—	2	2	no	—
15	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₃₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	D₄	1	2	yes	—
20	C₂×C₄×C₃₁	D₄	1	2	yes	—
21	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
22	C₂²⋊D₃₁	—	2	4	no	—
23	C₂×Dic₃₁	C₂×C₄	1	2	yes	—
24	D₁₂₄	—	2	2	no	—
25	C₄×D₃₁	—	2	2	no	—
26	C₄×D₃₁	—	2	2	no	—
27	Dic₆₂	—	2	2	no	—
28	C₈×C₃₁	—	2	2	no	—
29	C₃₁⋊C₈	—	2	2	no	—
30	C₂²×C₃₁	—	2	2	no	—
31	C₂²×C₃₁	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₃₁	—	2	2	no	—
34	C₂×D₃₁	—	2	4	no	—
35	C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
36	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
38	Dic₃₁	—	2	2	no	—
39	#408	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	—	2	2	no	—
41	C₂×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₃₁	#131	1	2	yes	—
43	D₃₁	—	4	2	no	—
44	C₂×#41	—	31	1	no	—
45	C₂×M₁₆	D₃₁	1	1	yes	characteristic, complemented
46	C₂²×C₈	—	31	1	no	—
47	C₂²⋊C₈	—	31	4	no	—
48	C₃₁	#408	1	1	yes	characteristic, complemented, Sylow
49	#41	—	62	2	no	—
50	#41	—	62	2	no	—
51	C₂×Q₈	—	31	1	no	—
52	C₂×D₄	—	31	2	no	—
53	C₂×D₄	—	31	1	no	—
54	C₂²×C₄	—	31	2	no	—
55	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
56	M₁₆	—	2	2	no	—
57	C₂×C₈	—	31	2	no	—
58	C₂×C₈	—	62	2	no	—
59	C₂×C₈	C₂×D₃₁	1	2	yes	—
60	C₂³	—	31	2	no	—
61	C₂³	C₄×D₃₁	1	1	yes	characteristic
62	Q₈	—	62	2	no	—
63	D₄	—	62	4	no	—
64	D₄	—	62	2	no	—
65	C₂×C₄	—	31	2	no	—
66	C₂×C₄	—	62	2	no	—
67	C₂×C₄	—	62	2	no	—
68	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
69	C₂×C₄	D₁₂₄	1	2	yes	—
70	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
71	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	62	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	62	4	no	—
76	C₂²	—	62	2	no	—
77	C₂²	(C₂×D₃₁)⋊C₄	1	2	yes	—
78	C₂²	C₂×C₄×D₃₁	1	1	yes	characteristic
79	C₄	—	62	2	no	—
80	C₄	(C₂×D₃₁)⋊C₄	1	2	yes	—
81	C₄	C₂×D₁₂₄	1	1	yes	characteristic
82	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	124	2	no	—
85	C₂	#11758484	1	2	yes	—
86	C₂	C₂×(C₂×D₃₁)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₁
commutator, socle	C₂²×C₃₁	C₂²×C₄
Fitting	C₂×M₁₆×C₃₁	C₂
prime radical	C₂×#92495	C₂
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₂×M₁₆	D₃₁
hypocenter	C₃₁	#408
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×C₃₁	C₂	semidirect
3. C₂²×C₃₁⋊C₈	C₂	semidirect
4. (C₂×D₃₁)⋊C₈	C₂	semidirect
45. C₂×M₁₆	D₃₁	semidirect
48. C₃₁	#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92495	2
C₂×M₁₆×C₃₁	2
C₂²×C₃₁⋊C₈	2
(C₂×D₃₁)⋊C₈	2
#408	31