Group #18010960 — subgroups

Subgroups — #18010960

Order 4736.

152 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 70 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	C₄⋊#10596927	C₂	1	2	yes	maximal, complemented
2	#14558428	C₂	1	2	yes	maximal
3	#14558422	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596927	C₂²	1	4	yes	—
6	C₂×C₈×D₃₇	C₄	1	1	yes	characteristic
7	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
8	C₄²×D₃₇	C₄	1	1	yes	characteristic
9	C₄×#64436	C₂²	1	1	yes	characteristic
10	C₈×Dic₃₇	C₄	1	1	yes	characteristic
11	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₇	C₈	1	1	yes	characteristic
14	C₂×C₄×D₃₇	C₈	1	1	yes	characteristic
15	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₃₇	C₈	1	1	yes	characteristic
20	C₄×Dic₃₇	C₈	1	1	yes	characteristic
21	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#64436	C₂×C₄	1	1	yes	characteristic
23	C₂×#64436	C₂³	1	1	yes	characteristic
24	C₈×D₃₇	—	2	2	no	—
25	C₈×D₃₇	—	2	2	no	—
26	#10596927	—	2	4	no	—
27	C₂²×D₃₇	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₃₇	C₂×C₈	1	1	yes	characteristic
34	C₄×D₃₇	—	2	2	no	—
35	C₄×D₃₇	—	2	2	no	—
36	C₄×D₃₇	—	2	1	no	—
37	C₄×D₃₇	—	2	1	no	—
38	C₈×C₃₇	—	2	1	no	—
39	C₈×C₃₇	M₁₆	1	2	yes	—
40	#64436	—	2	1	no	—
41	#64436	#41	1	2	yes	—
42	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
43	C₂×D₃₇	—	2	1	no	—
44	C₂×D₃₇	—	2	1	no	—
45	C₂×D₃₇	M₃₂	1	2	yes	—
46	C₄×C₃₇	—	2	1	no	—
47	C₄×C₃₇	M₃₂	1	2	yes	—
48	C₄×C₃₇	#117	1	1	yes	characteristic
49	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
50	Dic₃₇	—	2	1	no	—
51	Dic₃₇	—	2	1	no	—
52	Dic₃₇	—	2	1	no	—
53	#2163	—	37	1	no	maximal, Sylow
54	C₂×C₃₇	#431	1	1	yes	characteristic
55	C₂×C₃₇	C₂×M₃₂	1	1	yes	characteristic
56	C₂×C₃₇	C₂×M₃₂	1	1	yes	characteristic
57	D₃₇	—	2	2	no	—
58	C₂×C₄×C₈	—	37	1	no	—
59	C₄⋊C₁₆	—	37	2	no	—
60	C₂²⋊C₁₆	—	37	2	no	—
61	#346	—	37	2	no	—
62	C₃₇	#2163	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	—	37	1	no	—
64	C₂²×C₈	—	37	1	no	—
65	C₂×C₄²	—	37	1	no	—
66	C₂×C₁₆	—	37	4	no	—
67	C₄×C₈	—	37	1	no	—
68	C₄×C₈	—	37	1	no	—
69	C₄×C₈	—	37	1	no	—
70	C₄×C₈	#3866	1	1	yes	characteristic
71	C₂²×C₄	—	37	1	no	—
72	C₂²×C₄	—	37	1	no	—
73	C₂²×C₄	—	37	1	no	—
74	C₂×C₈	—	37	1	no	—
75	C₂×C₈	—	37	1	no	—
76	C₂×C₈	—	74	2	no	—
77	C₂×C₈	—	74	2	no	—
78	C₂×C₈	C₂×#3866	1	1	yes	characteristic
79	C₂×C₈	C₂×#3866	1	1	yes	characteristic
80	C₄²	—	37	1	no	—
81	C₄²	—	37	1	no	—
82	C₄²	—	37	1	no	—
83	C₄²	C₂×#3866	1	1	yes	characteristic
84	C₁₆	—	74	4	no	—
85	C₂³	—	37	1	no	—
86	C₂×C₄	—	37	1	no	—
87	C₂×C₄	—	37	1	no	—
88	C₂×C₄	—	37	1	no	—
89	C₂×C₄	—	74	2	no	—
90	C₂×C₄	—	74	2	no	—
91	C₂×C₄	—	74	1	no	—
92	C₂×C₄	—	74	1	no	—
93	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
94	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
95	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	37	2	no	—
98	C₈	—	74	1	no	—
99	C₈	#10596953	1	2	yes	—
100	C₂²	—	37	2	no	—
101	C₂²	—	74	1	no	—
102	C₂²	—	74	1	no	—
103	C₂²	C₂×D₃₇⋊C₈	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	74	1	no	—
106	C₄	—	74	1	no	—
107	C₄	—	74	1	no	—
108	C₄	#11924611	1	2	yes	—
109	C₄	#11924615	1	1	yes	characteristic
110	C₄	C₂×#10596953	1	1	yes	characteristic
111	C₂	—	74	2	no	—
112	C₂	#14558552	1	1	yes	characteristic
113	C₂	D₃₇⋊M₃₂	1	1	yes	characteristic
114	C₂	C₂×#11924611	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#10596927

C₂

yes

maximal, complemented

#14558428

C₂

yes

maximal

#14558422

C₂

yes

maximal, complemented

C₄×C₈×D₃₇

C₂

yes

maximal, characteristic

C₂×#10596927

C₂²

yes

—

C₂×C₈×D₃₇

C₄

yes

characteristic

C₂×C₈×D₃₇

C₂²

yes

characteristic

C₄²×D₃₇

C₄

yes

characteristic

C₄×#64436

C₂²

yes

characteristic

C₈×Dic₃₇

C₄

yes

characteristic

C₈×Dic₃₇

C₂²

yes

characteristic

C₄×C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₈

yes

characteristic

C₂×C₄×D₃₇

C₈

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₂×C₈×C₃₇

C₂×C₄

yes

characteristic

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₈

yes

characteristic

C₄×Dic₃₇

C₈

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₂×#64436

C₂×C₄

yes

characteristic

C₂×#64436

C₂³

yes

characteristic

C₈×D₃₇

—

C₈×D₃₇

—

#10596927

—

C₂²×D₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂×C₈

yes

characteristic

C₂×C₄×C₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₂×Dic₃₇

C₂×C₈

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

—

C₈×C₃₇

—

C₈×C₃₇

M₁₆

yes

—

#64436

—

#64436

#41

yes

—

C₂²×C₃₇

C₂²×C₈

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

M₃₂

yes

—

C₄×C₃₇

—

C₄×C₃₇

M₃₂

yes

—

C₄×C₃₇

#117

yes

characteristic

C₄×C₃₇

C₂×M₁₆

yes

characteristic

Dic₃₇

—

Dic₃₇

—

Dic₃₇

—

—

C₂×C₃₇

yes

C₂×C₃₇

C₂×M₃₂

yes

characteristic

C₂×C₃₇

C₂×M₃₂

yes

characteristic

D₃₇

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₃₇

#2163

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3866

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₃₇⋊C₈

yes

characteristic

C₂×C₄

D₃₇⋊C₈

yes

characteristic

C₂×C₄

C₂²×#3866

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10596953

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₂×D₃₇⋊C₈

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#11924611

yes

—

109

C₄

#11924615

yes

characteristic

110

C₄

C₂×#10596953

yes

characteristic

111

C₂

—

112

C₂

#14558552

yes

characteristic

113

C₂

D₃₇⋊M₃₂

yes

characteristic

114

C₂

C₂×#11924611

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	C₄×C₈×C₃₇	C₄
prime radical	C₂²×D₃₇	C₂×C₈
cosocle	C₂×#64436	C₂³
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#2163
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#3866

commutator, socle

C₂²×C₃₇

C₂²×C₈

Fitting

C₄×C₈×C₃₇

C₄

prime radical

C₂²×D₃₇

C₂×C₈

C₂³

C₄×C₈

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
1. C₄⋊#10596927	C₂	semidirect
3. #14558422	C₂	semidirect
62. C₃₇	#2163	semidirect

H ≅ G/N

type

1. C₄⋊#10596927

C₂

semidirect

3. #14558422

C₂

semidirect

62. C₃₇

#2163

semidirect

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

subgroup	index
C₄⋊#10596927	2
#14558428	2
#14558422	2
C₄×C₈×D₃₇	2
#2163	37

subgroup

index

C₄×C₈×D₃₇

Subgroups — #18010960

Conjugacy classes of subgroups

Complements

Maximal subgroups