Group #18009486 — subgroups

Subgroups — #18009486

Order 4736.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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	#14558551	C₂	1	1	yes	maximal, characteristic
2	D₃₇⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14557555	C₂	1	1	yes	maximal, characteristic
4	C₂×D₃₇⋊C₈	—	2	1	no	—
5	#11924603	—	2	1	no	—
6	#11924603	C₄	1	2	yes	—
7	C₄⋊#64438	—	2	1	no	—
8	#11924593	C₄	1	2	yes	—
9	C₄×#64438	—	2	1	no	—
10	C₂×#10596929	—	2	1	no	—
11	C₄²×D₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊#64436	C₄	1	1	yes	characteristic
13	#11924465	—	2	1	no	—
14	C₄⋊C₈×C₃₇	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
17	C₂×C₄×D₃₇	Q₈	1	1	yes	characteristic
18	C₂×#64438	—	2	2	no	—
19	C₂×#64438	—	2	2	no	—
20	D₃₇⋊C₈	—	4	1	no	—
21	D₃₇⋊C₈	—	4	1	no	—
22	C₂×C₈×C₃₇	—	2	1	no	—
23	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₃₇	D₄	1	1	yes	characteristic
26	C₄×Dic₃₇	D₄	1	1	yes	characteristic
27	C₂×#64436	—	2	1	no	—
28	#10596929	—	4	1	no	—
29	#10596929	—	4	1	no	—
30	C₂²×D₃₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₃₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₃₇	—	2	2	no	—
38	C₄×D₃₇	—	4	1	no	—
39	C₄×D₃₇	D₈	1	1	yes	characteristic
40	C₄×D₃₇	SD₁₆	1	1	yes	characteristic
41	C₄×D₃₇	SD₁₆	1	1	yes	characteristic
42	C₄×D₃₇	Q₁₆	1	1	yes	characteristic
43	#64438	—	4	2	no	—
44	#64438	—	4	2	no	—
45	C₈×C₃₇	—	4	1	no	—
46	#64436	—	4	1	no	—
47	C₂²×C₃₇	#95	1	1	yes	characteristic
48	C₂×D₃₇	—	2	1	no	—
49	C₂×D₃₇	—	2	1	no	—
50	C₂×D₃₇	#106	1	1	yes	characteristic
51	C₂×D₃₇	#107	1	1	yes	characteristic
52	C₄×C₃₇	—	2	1	no	—
53	C₄×C₃₇	—	2	1	no	—
54	C₄×C₃₇	#102	1	1	yes	characteristic
55	C₄×C₃₇	#103	1	1	yes	characteristic
56	Dic₃₇	—	2	1	no	—
57	Dic₃₇	#102	1	1	yes	characteristic
58	Dic₃₇	#103	1	1	yes	characteristic
59	Dic₃₇	#108	1	2	yes	—
60	#1301	—	37	1	no	maximal, Sylow
61	C₂×C₃₇	#340	1	1	yes	characteristic
62	C₂×C₃₇	#341	1	1	yes	characteristic
63	C₂×C₃₇	#344	1	1	yes	characteristic
64	D₃₇	—	2	1	no	—
65	D₃₇	—	2	1	no	—
66	#431	—	37	1	no	—
67	#423	—	37	1	no	—
68	C₂×C₄⋊C₈	—	37	1	no	—
69	C₃₇	#1301	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	74	1	no	—
71	C₂²×C₈	—	74	1	no	—
72	C₂×C₄²	—	37	1	no	—
73	C₄⋊C₈	—	37	2	no	—
74	C₄⋊C₈	—	37	1	no	—
75	C₄⋊C₈	—	74	1	no	—
76	C₄⋊C₈	—	74	1	no	—
77	C₄⋊C₈	—	74	1	no	—
78	C₄⋊C₈	#3866	1	1	yes	characteristic
79	C₂²⋊C₈	—	37	2	no	—
80	C₄×C₈	—	74	1	no	—
81	C₂²×C₄	—	37	1	no	—
82	C₂²×C₄	—	37	1	no	—
83	C₂²×C₄	—	37	1	no	—
84	M₁₆	—	148	1	no	—
85	M₁₆	—	148	1	no	—
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	74	2	no	—
88	C₂×C₈	—	74	2	no	—
89	C₂×C₈	—	74	1	no	—
90	C₂×C₈	—	148	1	no	—
91	C₂×C₈	—	148	1	no	—
92	C₄²	—	37	1	no	—
93	C₄²	—	37	1	no	—
94	C₄²	—	37	1	no	—
95	C₄²	C₂×#3866	1	1	yes	characteristic
96	C₂³	—	37	1	no	—
97	C₂×C₄	—	37	1	no	—
98	C₂×C₄	—	37	1	no	—
99	C₂×C₄	—	37	1	no	—
100	C₂×C₄	—	37	1	no	—
101	C₂×C₄	—	37	1	no	—
102	C₂×C₄	—	37	1	no	—
103	C₂×C₄	—	37	1	no	—
104	C₂×C₄	—	74	2	no	—
105	C₂×C₄	—	148	1	no	—
106	C₂×C₄	C₄×#3866	1	1	yes	characteristic
107	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
108	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
109	C₈	—	4	1	no	—
110	C₈	—	148	2	no	—
111	C₈	—	148	2	no	—
112	C₈	—	148	1	no	—
113	C₂²	—	37	1	no	—
114	C₂²	—	37	1	no	—
115	C₂²	—	74	1	no	—
116	C₂²	—	74	1	no	—
117	C₂²	(C₂×#3866)⋊C₄	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	1	no	—
120	C₄	—	37	1	no	—
121	C₄	—	37	1	no	—
122	C₄	—	37	2	no	—
123	C₄	—	74	1	no	—
124	C₄	#11924598	1	1	yes	characteristic
125	C₄	#11924599	1	1	yes	characteristic
126	C₂	—	74	1	no	—
127	C₂	—	74	1	no	—
128	C₂	#14558406	1	1	yes	characteristic
129	C₂	#14558408	1	1	yes	characteristic
130	C₂	#14558415	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558551

C₂

yes

maximal, characteristic

D₃₇⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

#14557555

C₂

yes

maximal, characteristic

C₂×D₃₇⋊C₈

—

#11924603

—

#11924603

C₄

yes

—

C₄⋊#64438

—

#11924593

C₄

yes

—

C₄×#64438

—

C₂×#10596929

—

C₄²×D₃₇

C₂²

yes

characteristic

C₄⋊#64436

C₄

yes

characteristic

#11924465

—

C₄⋊C₈×C₃₇

C₄

yes

characteristic

C₂×C₄×D₃₇

C₂×C₄

yes

characteristic

C₂×C₄×D₃₇

D₄

yes

characteristic

C₂×C₄×D₃₇

Q₈

yes

characteristic

C₂×#64438

—

C₂×#64438

—

D₃₇⋊C₈

—

D₃₇⋊C₈

—

C₂×C₈×C₃₇

—

C₄²×C₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

C₂×C₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

characteristic

C₄×Dic₃₇

D₄

yes

—

—

—

C₂²×D₃₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₄²

yes

characteristic

C₂×C₄×C₃₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₃₇

C₄⋊C₄

yes

characteristic

C₂×Dic₃₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₃₇

C₄⋊C₄

yes

characteristic

C₄×D₃₇

—

C₄×D₃₇

—

C₄×D₃₇

D₈

yes

characteristic

C₄×D₃₇

SD₁₆

yes

characteristic

C₄×D₃₇

SD₁₆

yes

characteristic

C₄×D₃₇

Q₁₆

yes

characteristic

#64438

—

#64438

—

C₈×C₃₇

—

#64436

—

C₂²×C₃₇

#95

yes

characteristic

C₂×D₃₇

—

C₂×D₃₇

—

C₂×D₃₇

yes

C₂×D₃₇

yes

C₄×C₃₇

—

C₄×C₃₇

—

C₄×C₃₇

yes

C₄×C₃₇

yes

Dic₃₇

—

Dic₃₇

yes

Dic₃₇

yes

Dic₃₇

yes

—

—

C₂×C₃₇

yes

C₂×C₃₇

yes

C₂×C₃₇

yes

D₃₇

—

D₃₇

—

#431

—

#423

—

C₂×C₄⋊C₈

—

C₃₇

#1301

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#3866

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

148

—

M₁₆

—

148

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

148

—

C₂×C₈

—

148

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#3866

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

148

—

106

C₂×C₄

C₄×#3866

yes

characteristic

107

C₂×C₄

C₄⋊#3866

yes

characteristic

108

C₂×C₄

C₂²⋊#3866

yes

characteristic

109

C₈

—

110

C₈

—

148

—

111

C₈

—

148

—

112

C₈

—

148

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

(C₂×#3866)⋊C₄

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11924598

yes

characteristic

125

C₄

#11924599

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#14558406

yes

characteristic

129

C₂

#14558408

yes

characteristic

130

C₂

#14558415

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₄²
Frattini	C₄²	C₂×#3866
Fitting	C₄⋊C₈×C₃₇	C₄
socle	C₂²×C₃₇	#95
prime radical	C₂²×D₃₇	C₄⋊C₄
cosocle	C₄²×D₃₇	C₂²
hypercenter	C₄⋊C₈	#3866
hypocenter	C₃₇	#1301
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#3866

commutator

C₂×C₄×C₃₇

C₄²

Frattini

C₄²

C₂×#3866

Fitting

C₄⋊C₈×C₃₇

C₄

socle

C₂²×C₃₇

#95

prime radical

C₂²×D₃₇

C₄⋊C₄

cosocle

C₄²×D₃₇

C₂²

C₄⋊C₈

C₃₇

G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
69. C₃₇	#1301	semidirect

H ≅ G/N

type

69. C₃₇

#1301

semidirect

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

subgroup	index
#14558551	2
D₃₇⋊(C₄⋊C₈)	2
#14557555	2
#1301	37

subgroup

index

#14558551

D₃₇⋊(C₄⋊C₈)

#14557555

#1301

Subgroups — #18009486

Conjugacy classes of subgroups

Complements

Maximal subgroups