Group #18011506 — subgroups

Subgroups — #18011506

Order 4736.

330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558585	C₂	1	4	yes	maximal, complemented
2	#14558582	C₂	1	4	yes	maximal, complemented
3	#14558558	C₂	1	4	yes	maximal
4	#14558551	C₂	1	2	yes	maximal
5	#14558089	C₂	1	1	yes	maximal, characteristic
6	#11924603	C₂²	1	2	yes	—
7	#11924603	C₂²	1	2	yes	—
8	#11924603	C₂²	1	4	yes	—
9	C₄⋊#64438	C₂²	1	4	yes	—
10	#11924593	C₂²	1	4	yes	—
11	#11924591	C₂²	1	4	yes	—
12	C₄×#64438	C₂²	1	4	yes	—
13	C₄×#64438	C₂²	1	4	yes	—
14	#11924535	C₄	1	2	yes	—
15	#11924528	C₄	1	1	yes	characteristic
16	#11924514	C₄	1	4	yes	—
17	#11924501	C₂²	1	4	yes	—
18	#11924494	C₂²	1	2	yes	—
19	C₄²×D₃₇	C₂²	1	1	yes	characteristic
20	#125×C₃₇	C₄	1	1	yes	characteristic
21	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₇₄	C₂×C₄	1	4	yes	—
24	C₂×#64438	C₂³	1	4	yes	—
25	C₂×#64438	C₂³	1	4	yes	—
26	C₄⋊C₄×C₃₇	C₂×C₄	1	2	yes	—
27	C₄⋊C₄×C₃₇	C₂×C₄	1	4	yes	—
28	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
29	#10596938	C₂×C₄	1	4	yes	—
30	C₄⋊Dic₃₇	C₂×C₄	1	2	yes	—
31	#10596936	C₂×C₄	1	4	yes	—
32	#10596936	C₂×C₄	1	4	yes	—
33	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₃₇	C₂³	1	2	yes	—
35	C₄×Dic₃₇	C₂³	1	4	yes	—
36	C₂²×D₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₃₇	C₂²×C₄	1	4	yes	—
40	C₂×Dic₃₇	C₂²×C₄	1	4	yes	—
41	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
42	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
43	C₄×D₃₇	—	2	4	no	—
44	C₄×D₃₇	—	2	2	no	—
45	Dic₇₄	—	2	8	no	—
46	#64438	—	2	4	no	—
47	#64438	—	2	4	no	—
48	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
49	C₂×D₃₇	—	2	1	no	—
50	C₂×D₃₇	—	2	2	no	—
51	C₄×C₃₇	—	2	1	no	—
52	C₄×C₃₇	—	2	4	no	—
53	C₄×C₃₇	—	2	2	no	—
54	Dic₃₇	—	2	4	no	—
55	Dic₃₇	#131	1	4	yes	—
56	Dic₃₇	2₋¹⁺⁴	1	2	yes	—
57	#2986	—	37	1	no	maximal, Sylow
58	C₂×C₃₇	#519	1	1	yes	characteristic
59	C₂×C₃₇	C₂×#131	1	2	yes	—
60	D₃₇	—	4	1	no	—
61	#533	—	37	1	no	—
62	#446	—	37	4	no	—
63	C₈×Q₈	—	37	4	no	—
64	#433	—	37	4	no	—
65	#431	—	37	2	no	—
66	C₃₇	#2986	1	1	yes	characteristic, complemented, Sylow
67	C₄⋊Q₈	—	37	2	no	—
68	#125	—	37	1	no	—
69	#125	#3866	1	1	yes	characteristic
70	C₂²⋊Q₈	—	37	4	no	—
71	C₄×Q₈	—	37	4	no	—
72	#117	—	37	2	no	—
73	C₂×C₄²	—	37	1	no	—
74	C₄⋊C₈	—	37	4	no	—
75	C₄⋊C₈	—	37	2	no	—
76	C₄⋊C₈	—	37	2	no	—
77	C₄⋊C₈	—	37	4	no	—
78	C₂²⋊C₈	—	37	4	no	—
79	#97	—	37	4	no	—
80	C₄×C₈	—	37	4	no	—
81	C₄×C₈	—	37	4	no	—
82	C₂×Q₈	—	37	4	no	—
83	C₂²×C₄	—	37	2	no	—
84	C₂²×C₄	—	37	1	no	—
85	C₂×C₈	—	37	4	no	—
86	C₂×C₈	—	37	4	no	—
87	C₄⋊C₄	—	37	4	no	—
88	C₄⋊C₄	—	37	4	no	—
89	C₄⋊C₄	—	37	2	no	—
90	C₄⋊C₄	C₂×#3866	1	2	yes	—
91	C₄⋊C₄	C₂×#3866	1	4	yes	—
92	C₂²⋊C₄	—	37	4	no	—
93	C₄²	—	37	1	no	—
94	C₄²	—	37	2	no	—
95	C₄²	—	37	4	no	—
96	C₄²	C₂×#3866	1	1	yes	characteristic
97	C₂³	—	37	1	no	—
98	Q₈	—	74	8	no	—
99	C₂×C₄	—	37	1	no	—
100	C₂×C₄	—	37	2	no	—
101	C₂×C₄	—	37	4	no	—
102	C₂×C₄	—	74	2	no	—
103	C₂×C₄	—	74	4	no	—
104	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
105	C₂×C₄	C₂²×#3866	1	2	yes	—
106	C₂×C₄	C₂²×#3866	1	4	yes	—
107	C₈	—	74	4	no	—
108	C₈	—	74	4	no	—
109	C₂²	—	74	1	no	—
110	C₂²	—	74	2	no	—
111	C₂²	C₂³×#3866	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	2	no	—
114	C₄	—	2	4	no	—
115	C₄	—	37	2	no	—
116	C₄	—	37	4	no	—
117	C₄	—	74	4	no	—
118	C₂	—	148	1	no	—
119	C₂	#14558601	1	1	yes	characteristic
120	C₂	D₃₇⋊#131	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14558585

C₂

yes

maximal, complemented

#14558582

C₂

yes

maximal, complemented

#14558558

C₂

yes

maximal

#14558551

C₂

yes

maximal

#14558089

C₂

yes

maximal, characteristic

#11924603

C₂²

yes

—

#11924603

C₂²

yes

—

#11924603

C₂²

yes

—

C₄⋊#64438

C₂²

yes

—

#11924593

C₂²

yes

—

#11924591

C₂²

yes

—

C₄×#64438

C₂²

yes

—

C₄×#64438

C₂²

yes

—

#11924535

C₄

yes

—

#11924528

C₄

yes

characteristic

#11924514

C₄

yes

—

#11924501

C₂²

yes

—

#11924494

C₂²

yes

—

C₄²×D₃₇

C₂²

yes

characteristic

#125×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

—

C₂×C₄×D₃₇

C₂³

yes

characteristic

C₂×Dic₇₄

C₂×C₄

yes

—

C₂×#64438

C₂³

yes

—

C₂×#64438

C₂³

yes

—

C₄⋊C₄×C₃₇

C₂×C₄

yes

—

C₄⋊C₄×C₃₇

C₂×C₄

yes

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

#10596938

C₂×C₄

yes

—

C₄⋊Dic₃₇

C₂×C₄

yes

—

#10596936

C₂×C₄

yes

—

#10596936

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂³

yes

—

C₄×Dic₃₇

C₂³

yes

—

C₂²×D₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

C₂⁴

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

Dic₇₄

—

#64438

—

#64438

—

C₂²×C₃₇

C₂³×C₄

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

#131

yes

—

Dic₃₇

2₋¹⁺⁴

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

—

D₃₇

—

#533

—

#446

—

C₈×Q₈

—

#433

—

#431

—

C₃₇

#2986

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#3866

yes

—

C₄⋊C₄

C₂×#3866

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂²×#3866

yes

characteristic

105

C₂×C₄

C₂²×#3866

yes

—

106

C₂×C₄

C₂²×#3866

yes

—

107

C₈

—

108

C₈

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂³×#3866

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₂

—

148

—

119

C₂

#14558601

yes

characteristic

120

C₂

D₃₇⋊#131

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#3866
commutator, socle	C₂²×C₃₇	C₂³×C₄
Fitting	#125×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂²×C₄
cosocle	C₂×Dic₃₇	C₂⁴
hypercenter	#125	#3866
hypocenter	C₃₇	#2986
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#3866

commutator, socle

C₂²×C₃₇

C₂³×C₄

Fitting

#125×C₃₇

C₄

prime radical

C₂²×D₃₇

C₂²×C₄

cosocle

C₂×Dic₃₇

C₂⁴

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #14558585	C₂	semidirect
2. #14558582	C₂	semidirect
66. C₃₇	#2986	semidirect

H ≅ G/N

type

1. #14558585

C₂

semidirect

2. #14558582

C₂

semidirect

66. C₃₇

#2986

semidirect

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

subgroup	index
#14558585	2
#14558582	2
#14558558	2
#14558551	2
#14558089	2
#2986	37

subgroup

index

Subgroups — #18011506

Conjugacy classes of subgroups

Complements

Maximal subgroups