Group #22627139 — subgroups

Subgroups — #22627139

Order 9344.

174 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556686	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924040	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989690	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989684	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊#11924040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11924040	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989614	C₂	1	1	yes	maximal, characteristic
8	#14556686	—	2	2	no	—
9	C₂×#11924040	—	2	2	no	—
10	C₂×#11924040	C₂²	1	1	yes	characteristic
11	C₂×#11924040	C₂²	1	1	yes	characteristic
12	C₂×#11924040	C₂²	1	1	yes	characteristic
13	C₂×#11924040	C₂²	1	1	yes	characteristic
14	C₂×#11924036	C₂²	1	1	yes	characteristic
15	C₂²×#10596833	C₂²	1	1	yes	characteristic
16	#14556658	C₄	1	1	yes	characteristic
17	#14556648	C₄	1	1	yes	characteristic
18	C₂²⋊#10596833	C₄	1	1	yes	characteristic
19	C₄×#10596833	C₂²	1	1	yes	characteristic
20	#14556551	C₄	1	1	yes	characteristic
21	#11924040	—	2	1	no	—
22	#11924040	—	2	1	no	—
23	#11924040	—	2	1	no	—
24	#11924040	D₄	1	2	yes	complemented
25	#11924036	—	2	1	no	—
26	#11924036	—	2	1	no	—
27	C₂×#10596833	—	2	1	no	—
28	C₂×#10596833	—	2	1	no	—
29	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
30	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
31	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
32	C₂×#10596833	C₂³	1	1	yes	characteristic
33	C₂×C₂²⋊D₇₃	C₈	1	1	yes	characteristic
34	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
36	#11924007	C₈	1	1	yes	characteristic
37	#11924005	C₈	1	1	yes	characteristic
38	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂²⋊C₄×C₇₃	C₈	1	1	yes	characteristic
40	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
41	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
44	C₂²⋊D₇₃	C₁₆	1	4	yes	complemented
45	C₂×Dic₇₃	—	2	1	no	—
46	C₂×Dic₇₃	—	2	1	no	—
47	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
48	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
49	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
50	C₄×D₇₃	—	2	1	no	—
51	C₄×D₇₃	—	2	1	no	—
52	#10596833	—	2	1	no	—
53	#10596833	—	2	1	no	—
54	#10596833	—	2	1	no	—
55	#10596833	C₂×D₄	1	1	yes	characteristic
56	#10596833	#41	1	1	yes	characteristic
57	C₂²×C₇₃	—	2	1	no	—
58	C₂²×C₇₃	—	2	1	no	—
59	C₂²×C₇₃	C₂×C₁₆	1	2	yes	complemented
60	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
61	C₂×D₇₃	—	2	1	no	—
62	C₂×D₇₃	—	2	1	no	—
63	C₂×D₇₃	C₂×C₁₆	1	2	yes	complemented
64	C₄×C₇₃	—	2	1	no	—
65	C₄×C₇₃	—	2	1	no	—
66	Dic₇₃	—	2	1	no	—
67	Dic₇₃	C₂×C₁₆	1	2	yes	complemented
68	Dic₇₃	C₄×D₄	1	1	yes	characteristic
69	Dic₇₃	#131	1	1	yes	characteristic
70	C₂×C₇₃	—	2	2	no	—
71	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
72	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
73	C₂×C₇₃	#504	1	1	yes	characteristic
74	D₇₃	—	2	2	no	—
75	D₄×C₁₆	—	73	1	no	maximal, Sylow
76	C₇₃	D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₁₆	—	73	1	no	—
78	C₂²×C₁₆	—	73	1	no	—
79	C₈×D₄	—	73	1	no	—
80	C₄⋊C₁₆	—	73	1	no	—
81	C₂²⋊C₁₆	—	73	1	no	—
82	C₂²⋊C₁₆	—	73	1	no	—
83	C₄×C₁₆	—	73	1	no	—
84	C₂²×C₈	—	73	1	no	—
85	C₂²×C₈	—	73	1	no	—
86	C₄×D₄	—	73	1	no	—
87	C₂×C₁₆	—	73	1	no	—
88	C₂×C₁₆	—	73	1	no	—
89	C₂×C₁₆	—	73	1	no	—
90	C₂×C₁₆	—	73	1	no	—
91	C₂×C₁₆	—	146	2	no	—
92	C₂×C₁₆	—	146	2	no	—
93	C₄⋊C₈	—	73	1	no	—
94	C₂²⋊C₈	—	73	1	no	—
95	C₂²⋊C₈	—	73	1	no	—
96	C₄×C₈	—	73	1	no	—
97	C₂×D₄	—	73	1	no	—
98	C₂²×C₄	—	73	1	no	—
99	C₂²×C₄	—	73	1	no	—
100	C₂×C₈	—	73	1	no	—
101	C₂×C₈	—	73	1	no	—
102	C₂×C₈	—	73	1	no	—
103	C₂×C₈	—	73	1	no	—
104	C₂×C₈	—	146	1	no	—
105	C₂×C₈	—	146	1	no	—
106	C₂×C₈	—	146	1	no	—
107	C₂×C₈	—	146	1	no	—
108	C₄⋊C₄	—	73	1	no	—
109	C₂²⋊C₄	—	73	1	no	—
110	C₂²⋊C₄	#10596842	1	1	yes	characteristic
111	C₄²	—	73	1	no	—
112	C₁₆	—	73	2	no	—
113	C₁₆	—	146	1	no	—
114	C₁₆	—	146	1	no	—
115	C₁₆	—	146	1	no	—
116	C₂³	—	73	1	no	—
117	C₂³	C₂×#10596842	1	1	yes	characteristic
118	D₄	—	73	4	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	1	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	146	1	no	—
123	C₂×C₄	—	146	1	no	—
124	C₂×C₄	—	146	1	no	—
125	C₂×C₄	—	146	1	no	—
126	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
127	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
128	C₈	—	73	1	no	—
129	C₈	—	73	1	no	—
130	C₈	—	146	1	no	—
131	C₈	—	146	1	no	—
132	C₈	—	146	1	no	—
133	C₂²	—	2	1	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	73	2	no	—
136	C₂²	—	146	1	no	—
137	C₂²	—	146	1	no	—
138	C₂²	#14556686	1	2	yes	complemented
139	C₂²	C₂²×#10596842	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	73	1	no	—
143	C₄	—	73	1	no	—
144	C₄	—	73	2	no	—
145	C₄	—	146	1	no	—
146	C₂	—	2	2	no	—
147	C₂	—	146	2	no	—
148	C₂	D₄×#10596842	1	1	yes	characteristic
149	C₂	C₂×#14556686	1	1	yes	characteristic
150	C₂	#17989708	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556686

C₂

yes

maximal, characteristic, complemented

C₂²×#11924040

C₂

yes

maximal, characteristic, complemented

#17989690

C₂

yes

maximal, characteristic, complemented

#17989684

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11924040

C₂

yes

maximal, characteristic, complemented

C₄×#11924040

C₂

yes

maximal, characteristic, complemented

#17989614

C₂

yes

maximal, characteristic

#14556686

—

C₂×#11924040

—

C₂×#11924040

C₂²

yes

characteristic

C₂×#11924040

C₂²

yes

characteristic

C₂×#11924040

C₂²

yes

characteristic

C₂×#11924040

C₂²

yes

characteristic

C₂×#11924036

C₂²

yes

characteristic

C₂²×#10596833

C₂²

yes

characteristic

#14556658

C₄

yes

characteristic

#14556648

C₄

yes

characteristic

C₂²⋊#10596833

C₄

yes

characteristic

C₄×#10596833

C₂²

yes

characteristic

#14556551

C₄

yes

—

—

—

D₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂³

yes

characteristic

C₂×C₂²⋊D₇₃

C₈

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924007

C₈

yes

characteristic

#11924005

C₈

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂²⋊C₄×C₇₃

C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂²⋊D₇₃

C₁₆

yes

complemented

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

—

—

—

C₂×D₄

yes

yes

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₁₆

yes

complemented

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₁₆

yes

complemented

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

C₂×C₁₆

yes

complemented

Dic₇₃

C₄×D₄

yes

characteristic

Dic₇₃

#131

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

C₂×C₇₃

C₂²×C₁₆

yes

characteristic

C₂×C₇₃

#504

yes

characteristic

D₇₃

—

D₄×C₁₆

—

maximal, Sylow

C₇₃

D₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₂×C₈

—

146

—

107

C₂×C₈

—

146

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

#10596842

yes

characteristic

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

146

—

114

C₁₆

—

146

—

115

C₁₆

—

146

—

116

C₂³

—

117

C₂³

C₂×#10596842

yes

characteristic

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

146

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

C₂×#10596842

yes

characteristic

127

C₂×C₄

C₂×#10596842

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

146

—

131

C₈

—

146

—

132

C₈

—

146

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

146

—

137

C₂²

—

146

—

138

C₂²

#14556686

yes

complemented

139

C₂²

C₂²×#10596842

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

—

146

C₂

—

147

C₂

—

146

—

148

C₂

D₄×#10596842

yes

characteristic

149

C₂

C₂×#14556686

yes

characteristic

150

C₂

#17989708

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator	C₂×C₇₃	C₂²×C₁₆
Fitting	C₂²⋊C₄×C₇₃	C₈
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₂²⋊C₄	#10596842
hypocenter	C₇₃	D₄×C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂²

C₂²×#10596842

commutator

C₂×C₇₃

C₂²×C₁₆

Fitting

C₂²⋊C₄×C₇₃

C₈

socle

C₂²×C₇₃

C₂²×C₈

hypercenter

C₂²⋊C₄

#10596842

hypocenter

C₇₃

D₄×C₁₆

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²⋊C₄

N	H ≅ G/N	type
1. C₂×#14556686	C₂	semidirect
2. C₂²×#11924040	C₂	semidirect
3. #17989690	C₂	semidirect
4. #17989684	C₂	semidirect
5. C₂²⋊#11924040	C₂	semidirect
6. C₄×#11924040	C₂	semidirect
24. #11924040	D₄	semidirect
44. C₂²⋊D₇₃	C₁₆	semidirect
59. C₂²×C₇₃	C₂×C₁₆	semidirect
63. C₂×D₇₃	C₂×C₁₆	semidirect
67. Dic₇₃	C₂×C₁₆	semidirect
76. C₇₃	D₄×C₁₆	semidirect
138. C₂²	#14556686	semidirect

H ≅ G/N

type

1. C₂×#14556686

C₂

semidirect

2. C₂²×#11924040

C₂

semidirect

3. #17989690

C₂

semidirect

4. #17989684

C₂

semidirect

5. C₂²⋊#11924040

C₂

semidirect

6. C₄×#11924040

C₂

semidirect

24. #11924040

D₄

semidirect

44. C₂²⋊D₇₃

C₁₆

semidirect

59. C₂²×C₇₃

C₂×C₁₆

semidirect

63. C₂×D₇₃

C₂×C₁₆

semidirect

67. Dic₇₃

C₂×C₁₆

semidirect

76. C₇₃

D₄×C₁₆

semidirect

138. C₂²

#14556686

semidirect

Subgroups — #22627139

Conjugacy classes of subgroups

Complements