Group #18010490 — subgroups

Subgroups — #18010490

Order 4736.

292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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	C₂×#11924593	C₂	1	2	yes	maximal
2	#14558399	C₂	1	4	yes	maximal, complemented
3	C₂×#11924494	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64438	C₂²	1	4	yes	—
5	#11924593	—	2	4	no	—
6	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	#11924494	—	2	4	no	—
8	C₂×C₄⋊Dic₃₇	C₄	1	1	yes	characteristic
9	C₂×#10596938	C₄	1	2	yes	—
10	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
12	C₂³×D₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
16	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₃₇	—	2	4	no	—
18	C₂×C₄×D₃₇	D₄	1	4	yes	—
19	C₂×#64438	—	2	4	no	—
20	C₂×#64438	—	2	8	no	—
21	C₄⋊C₄×C₃₇	—	2	2	no	—
22	#10596938	—	2	4	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄×Dic₃₇	—	2	4	no	—
25	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂²×D₃₇	—	2	2	no	—
27	C₂²×D₃₇	—	2	2	no	—
28	C₂²×D₃₇	—	2	2	no	—
29	C₂²×D₃₇	C₂²⋊C₄	1	2	yes	—
30	C₂×C₄×C₃₇	—	2	2	no	—
31	C₂×C₄×C₃₇	—	2	2	no	—
32	C₂×C₄×C₃₇	—	2	4	no	—
33	C₂×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₃₇	—	2	2	no	—
35	C₂×Dic₃₇	—	2	4	no	—
36	C₂×Dic₃₇	C₂×D₄	1	2	yes	—
37	C₂×Dic₃₇	#41	1	4	yes	—
38	C₄×D₃₇	—	2	8	no	—
39	#64438	—	4	4	no	—
40	C₂²×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₃₇	#117	1	2	yes	—
42	C₂²×C₃₇	#131	1	2	yes	—
43	C₂²×C₃₇	#131	1	2	yes	—
44	C₂×D₃₇	—	2	2	no	—
45	C₂×D₃₇	—	2	2	no	—
46	C₂×D₃₇	—	2	2	no	—
47	C₂×D₃₇	—	4	4	no	—
48	C₄×C₃₇	—	2	2	no	—
49	C₄×C₃₇	—	4	2	no	—
50	Dic₃₇	—	4	2	no	—
51	Dic₃₇	#123	1	4	yes	—
52	#1818	—	37	1	no	maximal, Sylow
53	C₂×C₃₇	#381	1	1	yes	characteristic
54	C₂×C₃₇	#408	1	1	yes	characteristic
55	C₂×C₃₇	#408	1	1	yes	characteristic
56	C₂×C₃₇	#433	1	4	yes	—
57	D₃₇	—	4	2	no	—
58	C₂×#117	—	37	1	no	—
59	C₂×C₂²⋊C₈	—	37	2	no	—
60	#336	—	37	4	no	—
61	C₃₇	#1818	1	1	yes	characteristic, complemented, Sylow
62	C₂³×C₄	—	37	1	no	—
63	C₂²×C₈	—	37	4	no	—
64	#117	—	74	4	no	—
65	C₂×C₄⋊C₄	—	37	1	no	—
66	C₂×C₄⋊C₄	#3866	1	1	yes	characteristic
67	C₂×C₂²⋊C₄	—	37	2	no	—
68	C₂×C₄²	—	37	2	no	—
69	C₂²⋊C₈	—	74	4	no	—
70	C₂⁴	—	37	1	no	—
71	C₂²×C₄	—	37	1	no	—
72	C₂²×C₄	—	37	4	no	—
73	C₂²×C₄	—	37	2	no	—
74	C₂²×C₄	—	74	4	no	—
75	C₂²×C₄	C₂×#3866	1	2	yes	—
76	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
77	C₂×C₈	—	74	4	no	—
78	C₂×C₈	—	74	8	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	74	2	no	—
81	C₂²⋊C₄	—	74	4	no	—
82	C₄²	—	74	4	no	—
83	C₂³	—	37	2	no	—
84	C₂³	—	74	2	no	—
85	C₂³	—	74	2	no	—
86	C₂³	—	74	2	no	—
87	C₂³	C₂²×#3866	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	4	no	—
91	C₂×C₄	—	37	2	no	—
92	C₂×C₄	—	37	4	no	—
93	C₂×C₄	—	74	8	no	—
94	C₂×C₄	—	74	2	no	—
95	C₂×C₄	—	74	4	no	—
96	C₂×C₄	C₂²⋊#3866	1	2	yes	—
97	C₈	—	148	4	no	—
98	C₂²	—	74	2	no	—
99	C₂²	—	74	2	no	—
100	C₂²	—	74	2	no	—
101	C₂²	—	148	4	no	—
102	C₂²	C₂×C₂²⋊#3866	1	1	yes	characteristic
103	C₂²	#11924615	1	2	yes	—
104	C₂²	#11924623	1	2	yes	—
105	C₂²	#11924624	1	2	yes	—
106	C₄	—	2	2	no	—
107	C₄	—	4	2	no	—
108	C₄	—	37	4	no	—
109	C₄	—	148	2	no	—
110	C₂	—	148	2	no	—
111	C₂	#14558476	1	1	yes	characteristic
112	C₂	#14558507	1	1	yes	characteristic
113	C₂	#14558508	1	1	yes	characteristic
114	C₂	#14558558	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11924593

C₂

yes

maximal

#14558399

C₂

yes

maximal, complemented

C₂×#11924494

C₂

yes

maximal, characteristic

C₂²×#64438

C₂²

yes

—

#11924593

—

C₂²×C₄×D₃₇

C₂²

yes

characteristic

#11924494

—

C₂×C₄⋊Dic₃₇

C₄

yes

characteristic

C₂×#10596938

C₄

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

—

C₂×C₄⋊C₄×C₃₇

C₄

yes

characteristic

C₂³×D₃₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂²×Dic₃₇

C₂³

yes

characteristic

C₂×C₄×D₃₇

—

C₂×C₄×D₃₇

D₄

yes

—

C₂×#64438

—

C₂×#64438

—

C₄⋊C₄×C₃₇

—

#10596938

—

C₄⋊Dic₃₇

—

C₄×Dic₃₇

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂²×D₃₇

—

C₂²×D₃₇

—

C₂²×D₃₇

—

C₂²×D₃₇

C₂²⋊C₄

yes

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

C₂²⋊C₄

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₂×D₄

yes

—

C₂×Dic₃₇

#41

yes

—

C₄×D₃₇

—

#64438

—

C₂²×C₃₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₃₇

#117

yes

—

C₂²×C₃₇

#131

yes

—

C₂²×C₃₇

#131

yes

—

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

—

C₄×C₃₇

—

C₄×C₃₇

—

Dic₃₇

—

Dic₃₇

#123

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

—

D₃₇

—

C₂×#117

—

C₂×C₂²⋊C₈

—

#336

—

C₃₇

#1818

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#3866

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

—

C₂²×C₄

C₂×#3866

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²×#3866

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#3866

yes

—

C₈

—

148

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

148

—

102

C₂²

C₂×C₂²⋊#3866

yes

characteristic

103

C₂²

#11924615

yes

—

104

C₂²

#11924623

yes

—

105

C₂²

#11924624

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

148

—

110

C₂

—

148

—

111

C₂

#14558476

yes

characteristic

112

C₂

#14558507

yes

characteristic

113

C₂

#14558508

yes

characteristic

114

C₂

#14558558

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3866
commutator, socle	C₂³×C₃₇	C₂²×C₄
Fitting	C₂×C₄⋊C₄×C₃₇	C₄
prime radical	C₂³×D₃₇	C₂×C₄
cosocle	C₂²×Dic₃₇	C₂³
hypercenter	C₂×C₄⋊C₄	#3866
hypocenter	C₃₇	#1818
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×#3866

commutator, socle

C₂³×C₃₇

C₂²×C₄

Fitting

C₂×C₄⋊C₄×C₃₇

C₄

prime radical

C₂³×D₃₇

C₂×C₄

cosocle

C₂²×Dic₃₇

C₂³

C₂×C₄⋊C₄

C₃₇

G ▷ C₂³×C₃₇ ▷ C₃₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
2. #14558399	C₂	semidirect
61. C₃₇	#1818	semidirect

H ≅ G/N

type

2. #14558399

C₂

semidirect

61. C₃₇

#1818

semidirect

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

subgroup	index
C₂×#11924593	2
#14558399	2
C₂×#11924494	2
#1818	37

subgroup

index

Subgroups — #18010490

Conjugacy classes of subgroups

Complements

Maximal subgroups