Group #22626166 — subgroups

Subgroups — C₂×#17989484 #22626166

Order 9344.

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

normal subgroups only

This group has 236 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×#14556665	C₂	1	2	yes	maximal, complemented
2	#17989484	C₂	1	4	yes	maximal, direct product factor
3	C₂²×#11924011	C₂	1	1	yes	maximal, characteristic
4	#14556665	—	2	2	no	—
5	#14556665	C₂²	1	4	yes	complemented
6	C₂×#11924031	—	2	2	no	—
7	C₂²×C₄×D₇₃	C₄	1	1	yes	characteristic
8	C₂×#11924011	—	2	2	no	—
9	C₂×#11924011	—	2	2	no	—
10	C₂×#11924011	C₄	1	2	yes	—
11	C₂×#11924011	C₂²	1	2	yes	—
12	C₂²×#10596831	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
14	#11924031	—	2	4	no	—
15	C₂³×D₇₃	C₈	1	1	yes	characteristic
16	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
17	C₂×C₄×D₇₃	—	2	1	no	—
18	C₂×C₄×D₇₃	—	2	1	no	—
19	C₂×C₄×D₇₃	—	2	1	no	—
20	C₂×C₄×D₇₃	—	2	1	no	—
21	C₂×C₄×D₇₃	C₈	1	2	yes	—
22	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
23	#11924011	—	2	4	no	—
24	#11924011	—	2	4	no	—
25	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596831	D₄	1	2	yes	—
27	C₂×#10596831	D₄	1	2	yes	—
28	C₂×#10596831	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	—	2	1	no	—
31	C₂×C₈×C₇₃	—	2	1	no	—
32	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
33	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×D₇₃	—	2	1	no	—
35	C₂²×D₇₃	—	2	1	no	—
36	C₂²×D₇₃	—	4	2	no	—
37	C₂²×D₇₃	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
42	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₇₃	—	2	1	no	—
45	C₂×Dic₇₃	—	2	1	no	—
46	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
47	C₄×D₇₃	—	2	2	no	—
48	C₄×D₇₃	—	2	2	no	—
49	C₄×D₇₃	—	2	2	no	—
50	C₄×D₇₃	—	2	2	no	—
51	C₈×C₇₃	—	2	2	no	—
52	#10596831	C₂²⋊C₄	1	2	yes	—
53	#10596831	C₂×D₄	1	2	yes	—
54	C₂²×C₇₃	—	2	2	no	—
55	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
56	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
57	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
58	C₂×D₇₃	—	2	2	no	—
59	C₂×D₇₃	—	4	2	no	—
60	C₂×D₇₃	—	4	2	no	—
61	C₂×D₇₃	—	4	2	no	—
62	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
63	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
64	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
66	Dic₇₃	—	2	2	no	—
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	—	2	1	no	—
69	C₂×C₇₃	#349	1	2	yes	complemented
70	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
71	D₇₃	—	4	2	no	—
72	C₂×#349	—	73	1	no	maximal, Sylow
73	C₇₃	C₂×#349	1	1	yes	characteristic, complemented, Sylow
74	C₂²×M₁₆	—	73	1	no	—
75	C₂×M₃₂	—	73	2	no	—
76	#349	—	73	4	no	—
77	C₂³×C₄	—	73	1	no	—
78	C₂×M₁₆	—	73	2	no	—
79	C₂×M₁₆	—	73	2	no	—
80	C₂×M₁₆	—	146	2	no	—
81	C₂×M₁₆	—	146	2	no	—
82	C₂²×C₈	—	73	1	no	—
83	C₂²×C₈	#64408	1	1	yes	characteristic
84	M₃₂	—	73	4	no	—
85	M₃₂	—	146	2	no	—
86	C₂×C₁₆	—	146	2	no	—
87	C₂⁴	—	73	1	no	—
88	C₂²×C₄	—	73	1	no	—
89	C₂²×C₄	—	73	2	no	—
90	C₂²×C₄	—	73	2	no	—
91	C₂²×C₄	—	146	1	no	—
92	C₂²×C₄	—	146	1	no	—
93	C₂²×C₄	—	146	1	no	—
94	C₂²×C₄	—	146	1	no	—
95	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
96	M₁₆	—	146	4	no	—
97	M₁₆	—	146	4	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	73	2	no	—
101	C₂×C₈	—	73	2	no	—
102	C₂×C₈	—	73	1	no	—
103	C₂×C₈	—	73	1	no	—
104	C₂×C₈	C₂×#64408	1	2	yes	—
105	C₁₆	—	146	4	no	—
106	C₂³	—	292	2	no	—
107	C₂³	—	73	2	no	—
108	C₂³	—	146	1	no	—
109	C₂³	—	146	1	no	—
110	C₂³	#11924036	1	1	yes	characteristic
111	C₂×C₄	—	73	2	no	—
112	C₂×C₄	—	146	1	no	—
113	C₂×C₄	—	146	1	no	—
114	C₂×C₄	—	146	2	no	—
115	C₂×C₄	—	146	2	no	—
116	C₂×C₄	—	146	2	no	—
117	C₂×C₄	—	146	2	no	—
118	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
119	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
120	C₂×C₄	#11924036	1	1	yes	characteristic
121	C₂×C₄	#11924038	1	1	yes	characteristic
122	C₂×C₄	#11924038	1	1	yes	characteristic
123	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
124	C₈	—	2	2	no	—
125	C₈	—	73	2	no	—
126	C₈	—	73	2	no	—
127	C₂²	—	2	2	no	—
128	C₂²	—	292	2	no	—
129	C₂²	—	292	2	no	—
130	C₂²	—	292	2	no	—
131	C₂²	—	146	2	no	—
132	C₂²	#14556648	1	1	yes	characteristic
133	C₂²	#14556648	1	1	yes	characteristic
134	C₂²	C₂×#11924036	1	1	yes	characteristic
135	C₄	—	146	2	no	—
136	C₄	#14556648	1	1	yes	characteristic
137	C₄	#14556648	1	1	yes	characteristic
138	C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
139	C₄	C₂×#11924038	1	1	yes	characteristic
140	C₂	—	2	1	no	—
141	C₂	—	2	1	no	—
142	C₂	—	292	2	no	—
143	C₂	#17989484	1	2	yes	direct product factor
144	C₂	C₂×#14556648	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556665

C₂

yes

maximal, complemented

#17989484

C₂

yes

maximal, direct product factor

C₂²×#11924011

C₂

yes

maximal, characteristic

#14556665

—

#14556665

C₂²

yes

complemented

C₂×#11924031

—

C₂²×C₄×D₇₃

C₄

yes

—

—

C₄

yes

—

C₂×#11924011

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₄

yes

characteristic

#11924031

—

C₂³×D₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₈

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₈

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

#11924011

—

#11924011

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₂×#10596831

D₄

yes

—

C₂×#10596831

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×C₈

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#349

yes

complemented

C₂×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

D₇₃

—

C₂×#349

—

maximal, Sylow

C₇₃

C₂×#349

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂×M₃₂

—

#349

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

146

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²×C₈

#64408

yes

characteristic

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#64408

yes

—

105

C₁₆

—

146

—

106

C₂³

—

292

—

107

C₂³

—

108

C₂³

—

146

—

109

C₂³

—

146

—

110

C₂³

#11924036

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

146

—

113

C₂×C₄

—

146

—

114

C₂×C₄

—

146

—

115

C₂×C₄

—

146

—

116

C₂×C₄

—

146

—

117

C₂×C₄

—

146

—

118

C₂×C₄

C₂²⋊#64408

yes

characteristic

119

C₂×C₄

C₂²⋊#64408

yes

characteristic

120

C₂×C₄

#11924036

yes

characteristic

121

C₂×C₄

#11924038

yes

characteristic

122

C₂×C₄

#11924038

yes

characteristic

123

C₂×C₄

C₂²×#64408

yes

characteristic

124

C₈

—

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

292

—

129

C₂²

—

292

—

130

C₂²

—

292

—

131

C₂²

—

146

—

132

C₂²

#14556648

yes

characteristic

133

C₂²

#14556648

yes

characteristic

134

C₂²

C₂×#11924036

yes

characteristic

135

C₄

—

146

—

136

C₄

#14556648

yes

characteristic

137

C₄

#14556648

yes

characteristic

138

C₄

C₂×C₂²⋊#64408

yes

characteristic

139

C₄

C₂×#11924038

yes

characteristic

140

C₂

—

141

C₂

—

142

C₂

—

292

—

143

C₂

#17989484

yes

direct product factor

144

C₂

C₂×#14556648

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#64408
commutator	C₂²×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	C₂×#349
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#64408

commutator

C₂²×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂²⋊C₈

C₂²×C₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
1. C₂×#14556665	C₂	semidirect
2. #17989484	C₂	direct (N × H)
5. #14556665	C₂²	semidirect
69. C₂×C₇₃	#349	semidirect
73. C₇₃	C₂×#349	semidirect
143. C₂	#17989484	direct (N × H)

H ≅ G/N

type

1. C₂×#14556665

C₂

semidirect

2. #17989484

C₂

direct (N × H)

5. #14556665

C₂²

semidirect

69. C₂×C₇₃

#349

semidirect

73. C₇₃

C₂×#349

semidirect

143. C₂

#17989484

direct (N × H)

Subgroups — C₂×#17989484 #22626166

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989484 #22626166

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989484 #22626166