Group #18011380 — subgroups

Subgroups — C₂×#14558583 #18011380

Order 4736.

400 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 194 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	#14558583	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊#64438	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#64438	C₂	1	2	yes	maximal
4	C₂×#11924591	C₂	1	2	yes	maximal
5	C₂×C₄×#64438	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924501	C₂	1	1	yes	maximal, characteristic
7	C₂²×#64438	C₂²	1	1	yes	characteristic
8	C₂²×#64438	C₂²	1	2	yes	—
9	C₂²×#64438	C₂²	1	1	yes	characteristic
10	C₄⋊#64438	C₂²	1	4	yes	—
11	C₄⋊#64438	C₂²	1	8	yes	—
12	#11924591	C₂²	1	8	yes	—
13	C₄×#64438	C₂²	1	4	yes	—
14	C₂²×Dic₇₄	C₄	1	1	yes	characteristic
15	#11924501	C₄	1	4	yes	—
16	#11924501	C₂²	1	4	yes	—
17	C₂×#10596936	C₄	1	2	yes	—
18	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
21	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
25	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₇₄	—	2	4	no	—
27	C₂×Dic₇₄	C₂×C₄	1	4	yes	—
28	C₂×#64438	—	2	2	no	—
29	C₂×#64438	—	2	4	no	—
30	C₂×#64438	Q₈	1	4	yes	complemented
31	C₂×#64438	C₂³	1	2	yes	—
32	C₂×#64438	C₂³	1	4	yes	—
33	C₂×#64438	C₂³	1	2	yes	—
34	C₄⋊C₄×C₃₇	C₂×C₄	1	4	yes	—
35	#10596936	C₂×C₄	1	8	yes	—
36	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
37	C₄×Dic₃₇	C₂×C₄	1	4	yes	—
38	C₄×Dic₃₇	C₂³	1	2	yes	—
39	C₄×Dic₃₇	C₂³	1	4	yes	—
40	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₃₇	—	2	4	no	—
42	C₂×C₄×C₃₇	M₁₆	1	4	yes	—
43	C₂×C₄×C₃₇	C₂²×C₄	1	4	yes	—
44	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
45	C₂×Dic₃₇	—	2	4	no	—
46	C₂×Dic₃₇	—	2	2	no	—
47	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
48	C₂×Dic₃₇	C₂²×C₄	1	4	yes	—
49	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
50	C₂×Dic₃₇	C₂×Q₈	1	2	yes	—
51	C₂×Dic₃₇	#41	1	2	yes	—
52	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
53	Dic₇₄	—	2	8	no	—
54	#64438	—	2	2	no	—
55	#64438	—	2	4	no	—
56	#64438	C₂×Q₈	1	4	yes	complemented
57	C₂²×C₃₇	C₄×Q₈	1	2	yes	—
58	C₂²×C₃₇	C₂×M₁₆	1	2	yes	—
59	C₂²×C₃₇	#131	1	2	yes	—
60	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
61	C₄×C₃₇	—	2	4	no	—
62	C₄×C₃₇	C₂×M₁₆	1	4	yes	—
63	Dic₃₇	—	2	4	no	—
64	Dic₃₇	—	2	2	no	—
65	Dic₃₇	C₄×Q₈	1	2	yes	—
66	Dic₃₇	C₂²×Q₈	1	1	yes	characteristic
67	Dic₃₇	C₂×#41	1	1	yes	characteristic
68	C₂×#446	—	37	1	no	maximal, Sylow
69	C₂×C₃₇	#446	1	4	yes	complemented
70	C₂×C₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
71	C₂×C₃₇	C₂²×M₁₆	1	1	yes	characteristic
72	C₂×C₃₇	C₂×#131	1	1	yes	characteristic
73	C₂×C₄×Q₈	—	37	1	no	—
74	#446	—	37	8	no	—
75	C₂×C₄⋊C₈	—	37	1	no	—
76	C₂×C₄⋊C₈	—	37	2	no	—
77	C₂×#97	—	37	2	no	—
78	C₂×C₄×C₈	—	37	1	no	—
79	C₃₇	C₂×#446	1	1	yes	characteristic, complemented, Sylow
80	C₂²×Q₈	—	37	1	no	—
81	C₂²×C₈	—	37	1	no	—
82	C₂²×C₈	—	37	1	no	—
83	C₂²×C₈	—	37	2	no	—
84	C₄×Q₈	—	37	4	no	—
85	C₄×Q₈	—	37	4	no	—
86	C₂×C₄⋊C₄	—	37	2	no	—
87	C₂×C₄⋊C₄	#3866	1	1	yes	characteristic
88	C₂×C₄²	—	37	1	no	—
89	C₂×C₄²	—	37	2	no	—
90	C₄⋊C₈	—	37	4	no	—
91	C₄⋊C₈	—	37	8	no	—
92	#97	—	37	8	no	—
93	C₄×C₈	—	37	4	no	—
94	C₂×Q₈	—	37	4	no	—
95	C₂×Q₈	—	74	4	no	—
96	C₂²×C₄	—	37	1	no	—
97	C₂²×C₄	—	37	1	no	—
98	C₂²×C₄	—	37	2	no	—
99	C₂²×C₄	C₂×#3866	1	2	yes	—
100	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
101	C₂×C₈	—	37	4	no	—
102	C₂×C₈	—	37	2	no	—
103	C₂×C₈	—	37	2	no	—
104	C₂×C₈	—	37	4	no	—
105	C₂×C₈	—	74	2	no	—
106	C₂×C₈	—	74	4	no	—
107	C₄⋊C₄	—	37	8	no	—
108	C₄⋊C₄	C₂×#3866	1	4	yes	—
109	C₄²	—	37	2	no	—
110	C₄²	—	37	4	no	—
111	C₄²	—	37	2	no	—
112	C₄²	—	37	4	no	—
113	C₂³	C₂²×#3866	1	1	yes	characteristic
114	Q₈	—	74	8	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	37	2	no	—
117	C₂×C₄	—	37	2	no	—
118	C₂×C₄	—	37	1	no	—
119	C₂×C₄	—	37	1	no	—
120	C₂×C₄	—	37	2	no	—
121	C₂×C₄	—	37	4	no	—
122	C₂×C₄	—	74	4	no	—
123	C₂×C₄	—	74	2	no	—
124	C₂×C₄	#10596953	1	4	yes	—
125	C₂×C₄	C₂²×#3866	1	4	yes	—
126	C₂×C₄	C₂²×#3866	1	2	yes	—
127	C₈	—	37	4	no	—
128	C₈	—	74	2	no	—
129	C₈	—	74	4	no	—
130	C₂²	Q₈×#3866	1	2	yes	—
131	C₂²	C₂×#10596953	1	2	yes	—
132	C₂²	#11924623	1	2	yes	—
133	C₂²	C₂³×#3866	1	1	yes	characteristic
134	C₄	—	2	4	no	—
135	C₄	—	37	1	no	—
136	C₄	—	37	1	no	—
137	C₄	—	37	2	no	—
138	C₄	—	74	4	no	—
139	C₄	—	74	2	no	—
140	C₄	C₂×#10596953	1	4	yes	—
141	C₂	#14558583	1	4	yes	direct product factor
142	C₂	C₂×Q₈×#3866	1	1	yes	characteristic
143	C₂	C₂²×#10596953	1	1	yes	characteristic
144	C₂	C₂×#11924623	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14558583

C₂

yes

maximal, direct product factor

C₂×C₄⋊#64438

C₂

yes

maximal, characteristic

C₂×C₄⋊#64438

C₂

yes

maximal

C₂×#11924591

C₂

yes

maximal

C₂×C₄×#64438

C₂

yes

maximal, characteristic

C₂×#11924501

C₂

yes

maximal, characteristic

C₂²×#64438

C₂²

yes

characteristic

C₂²×#64438

C₂²

yes

—

C₂²×#64438

C₂²

yes

characteristic

C₄⋊#64438

C₂²

yes

—

C₄⋊#64438

C₂²

yes

—

#11924591

C₂²

yes

—

C₄×#64438

C₂²

yes

—

C₂²×Dic₇₄

C₄

yes

characteristic

#11924501

C₄

yes

—

#11924501

C₂²

yes

—

C₂×#10596936

C₄

yes

—

C₂×C₄×Dic₃₇

C₂²

yes

characteristic

C₂×C₄×Dic₃₇

C₂²

yes

—

C₂×C₄⋊C₄×C₃₇

C₄

yes

characteristic

C₂²×C₄×C₃₇

C₂×C₄

yes

—

C₂²×C₄×C₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

characteristic

C₂²×Dic₃₇

C₂×C₄

yes

—

C₂²×Dic₃₇

C₂³

yes

characteristic

C₂×Dic₇₄

—

C₂×Dic₇₄

C₂×C₄

yes

—

C₂×#64438

—

C₂×#64438

—

C₂×#64438

Q₈

yes

complemented

C₂×#64438

C₂³

yes

—

C₂×#64438

C₂³

yes

—

C₂×#64438

C₂³

yes

—

C₄⋊C₄×C₃₇

C₂×C₄

yes

—

#10596936

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂×C₄

yes

—

C₄×Dic₃₇

C₂³

yes

—

C₄×Dic₃₇

C₂³

yes

—

C₂³×C₃₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₇

—

C₂×C₄×C₃₇

M₁₆

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×C₄×C₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

—

C₂×Dic₃₇

—

C₂×Dic₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

—

C₂×Dic₃₇

C₂²×C₄

yes

characteristic

C₂×Dic₃₇

C₂×Q₈

yes

—

C₂×Dic₃₇

#41

yes

—

C₂×Dic₃₇

C₂⁴

yes

characteristic

Dic₇₄

—

#64438

—

#64438

—

#64438

C₂×Q₈

yes

complemented

C₂²×C₃₇

C₄×Q₈

yes

—

C₂²×C₃₇

C₂×M₁₆

yes

—

C₂²×C₃₇

#131

yes

—

C₂²×C₃₇

C₂³×C₄

yes

characteristic

C₄×C₃₇

—

C₄×C₃₇

C₂×M₁₆

yes

—

Dic₃₇

—

Dic₃₇

—

Dic₃₇

C₄×Q₈

yes

—

Dic₃₇

C₂²×Q₈

yes

characteristic

Dic₃₇

C₂×#41

yes

—

C₂×C₃₇

yes

C₂×C₃₇

C₂×C₄×Q₈

yes

characteristic

C₂×C₃₇

C₂²×M₁₆

yes

characteristic

C₂×C₃₇

C₂×#131

yes

characteristic

C₂×C₄×Q₈

—

#446

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

—

C₃₇

C₂×#446

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#3866

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#3866

yes

—

100

C₂²×C₄

C₂×#3866

yes

characteristic

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₄⋊C₄

—

108

C₄⋊C₄

C₂×#3866

yes

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₂³

C₂²×#3866

yes

characteristic

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#10596953

yes

—

125

C₂×C₄

C₂²×#3866

yes

—

126

C₂×C₄

C₂²×#3866

yes

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₂²

Q₈×#3866

yes

—

131

C₂²

C₂×#10596953

yes

—

132

C₂²

#11924623

yes

—

133

C₂²

C₂³×#3866

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

C₂×#10596953

yes

—

141

C₂

#14558583

yes

direct product factor

142

C₂

C₂×Q₈×#3866

yes

characteristic

143

C₂

C₂²×#10596953

yes

characteristic

144

C₂

C₂×#11924623

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²×#3866
commutator	C₂²×C₃₇	C₂³×C₄
Frattini	C₂²	C₂³×#3866
Fitting	C₂×C₄⋊C₄×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂×Dic₃₇	C₂⁴
hypercenter	C₂×C₄⋊C₄	#3866
hypocenter	C₃₇	C₂×#446
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²×#3866

commutator

C₂²×C₃₇

C₂³×C₄

Frattini

C₂²

C₂³×#3866

Fitting

C₂×C₄⋊C₄×C₃₇

C₄

socle, prime radical

C₂³×C₃₇

C₂²×C₄

cosocle

C₂×Dic₃₇

C₂⁴

C₂×C₄⋊C₄

C₃₇

G ▷ C₂²×C₃₇ ▷ C₃₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
1. #14558583	C₂	direct (N × H)
30. C₂×#64438	Q₈	semidirect
56. #64438	C₂×Q₈	semidirect
69. C₂×C₃₇	#446	semidirect
79. C₃₇	C₂×#446	semidirect
141. C₂	#14558583	direct (N × H)

H ≅ G/N

type

1. #14558583

C₂

direct (N × H)

30. C₂×#64438

Q₈

semidirect

56. #64438

C₂×Q₈

semidirect

69. C₂×C₃₇

#446

semidirect

79. C₃₇

C₂×#446

semidirect

141. C₂

#14558583

direct (N × H)

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

subgroup	index
#14558583	2
C₂×C₄⋊#64438	2
C₂×#11924591	2
C₂×C₄×#64438	2
C₂×#11924501	2
C₂×#446	37

subgroup

index

C₂×C₄⋊#64438

C₂×C₄×#64438

Subgroups — C₂×#14558583 #18011380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14558583 #18011380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558583 #18011380