Group #22618648 — subgroups

Subgroups — #22618648

Order 9344.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14556599	C₂	1	2	yes	maximal, complemented
2	#17989137	C₂	1	1	yes	maximal, characteristic
3	#17988657	C₂	1	8	yes	maximal, complemented
4	#17988555	C₂	1	2	yes	maximal, complemented
5	C₂×#14556502	C₂	1	1	yes	maximal, characteristic, complemented
6	#423×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11924028	C₂²	1	2	yes	—
8	#14556599	—	2	8	no	—
9	C₂×#11924011	C₂²	1	4	yes	—
10	C₂²×#10596831	C₂²	1	1	yes	characteristic
11	C₂²×#10596831	C₂²	1	1	yes	characteristic
12	C₂×C₈×D₇₃	C₂²	1	4	yes	—
13	#14556591	C₄	1	1	yes	characteristic
14	#14556588	C₄	1	1	yes	characteristic
15	#14556579	C₄	1	2	yes	—
16	#14556565	C₄	1	4	yes	—
17	C₄×D₂₉₂	C₂²	1	4	yes	—
18	#14556503	C₂²	1	8	yes	—
19	#14556502	C₂²	1	4	yes	—
20	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₇₃	C₂²	1	4	yes	—
23	#11924028	—	2	4	no	—
24	#11924028	—	2	4	no	—
25	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
26	C₂×D₂₉₂	C₂×C₄	1	2	yes	—
27	C₂×D₂₉₂	C₂×C₄	1	4	yes	—
28	C₂×C₂²⋊D₇₃	C₂×C₄	1	4	yes	—
29	C₂×C₄×D₇₃	C₂³	1	4	yes	—
30	#11924011	—	2	8	no	—
31	C₂×#10596831	—	2	2	no	—
32	C₂×#10596831	D₄	1	4	yes	complemented
33	C₂×#10596831	C₂³	1	2	yes	—
34	C₂×#10596831	C₂³	1	2	yes	—
35	C₈×D₇₃	—	2	8	no	—
36	C₄⋊Dic₇₃	C₂×C₄	1	4	yes	—
37	#11924005	C₂×C₄	1	8	yes	—
38	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
40	M₁₆×C₇₃	—	2	4	no	—
41	C₂×C₈×C₇₃	C₂³	1	4	yes	—
42	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
43	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
44	C₄²×C₇₃	C₂³	1	2	yes	—
45	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×D₇₃	C₂²×C₄	1	4	yes	—
47	C₂×C₄×C₇₃	—	4	2	no	—
48	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₇₃	#41	1	2	yes	—
53	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
54	C₂²⋊D₇₃	—	2	8	no	—
55	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
56	D₂₉₂	—	2	4	no	—
57	D₂₉₂	—	4	4	no	—
58	C₄×D₇₃	—	2	4	no	—
59	C₄×D₇₃	—	2	4	no	—
60	Dic₁₄₆	—	2	4	no	—
61	C₈×C₇₃	—	2	4	no	—
62	#10596831	—	2	2	no	—
63	#10596831	C₂×D₄	1	4	yes	—
64	C₂²×C₇₃	—	2	2	no	—
65	C₂²×C₇₃	C₄×D₄	1	2	yes	—
66	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
67	C₂×D₇₃	—	2	4	no	—
68	C₂×D₇₃	—	2	8	no	—
69	C₄×C₇₃	—	2	2	no	—
70	C₄×C₇₃	—	2	2	no	—
71	C₄×C₇₃	C₄×D₄	1	2	yes	—
72	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
73	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
74	Dic₇₃	—	2	4	no	—
75	C₂×C₇₃	—	2	2	no	—
76	C₂×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
77	C₂×C₇₃	#568	1	2	yes	—
78	D₇₃	—	4	4	no	—
79	#2932	—	73	1	no	maximal, Sylow
80	C₇₃	#2932	1	1	yes	characteristic, complemented, Sylow
81	C₂×#131	—	73	2	no	—
82	#532	—	73	1	no	—
83	#435	—	73	8	no	—
84	#423	D₇₃	1	1	yes	characteristic, complemented
85	#408	—	73	2	no	—
86	C₂×#97	—	73	1	no	—
87	C₂×#41	—	73	2	no	—
88	#131	—	146	8	no	—
89	C₂×M₁₆	—	73	4	no	—
90	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
91	C₂²×C₈	—	73	1	no	—
92	C₂²×C₈	—	73	1	no	—
93	C₂²×C₈	—	73	4	no	—
94	C₄⋊Q₈	—	73	1	no	—
95	#127	—	73	1	no	—
96	#124	—	73	2	no	—
97	#121	—	73	4	no	—
98	C₄×D₄	—	73	4	no	—
99	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
100	C₄⋊C₈	C₂×D₇₃	1	4	yes	—
101	C₂²⋊C₈	—	73	8	no	—
102	#97	—	73	4	no	—
103	#41	—	146	4	no	—
104	#41	—	146	4	no	—
105	C₂×Q₈	—	73	2	no	—
106	C₂×D₄	—	73	4	no	—
107	C₂×D₄	—	73	4	no	—
108	C₂×D₄	—	73	2	no	—
109	C₂²×C₄	—	73	4	no	—
110	C₂²×C₄	C₄×D₇₃	1	2	yes	—
111	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
112	M₁₆	—	2	4	no	—
113	M₁₆	—	146	8	no	—
114	C₂×C₈	—	73	4	no	—
115	C₂×C₈	—	73	2	no	—
116	C₂×C₈	—	73	2	no	—
117	C₂×C₈	—	146	8	no	—
118	C₂×C₈	—	146	2	no	—
119	C₂×C₈	C₂²×D₇₃	1	4	yes	—
120	C₄⋊C₄	—	73	4	no	—
121	C₂²⋊C₄	—	73	8	no	—
122	C₄²	C₄×D₇₃	1	1	yes	characteristic
123	C₄²	C₄×D₇₃	1	1	yes	characteristic
124	C₄²	C₂²×D₇₃	1	2	yes	—
125	C₂³	—	73	4	no	—
126	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
127	Q₈	—	146	4	no	—
128	D₄	—	292	4	no	—
129	D₄	—	146	8	no	—
130	D₄	—	146	4	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	73	4	no	—
133	C₂×C₄	—	146	4	no	—
134	C₂×C₄	—	146	4	no	—
135	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
136	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
137	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
138	C₂×C₄	D₄×D₇₃	1	2	yes	—
139	C₂×C₄	#11924029	1	2	yes	—
140	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
141	C₈	—	2	4	no	—
142	C₈	—	73	4	no	—
143	C₈	—	146	2	no	—
144	C₂²	—	2	2	no	—
145	C₂²	—	146	4	no	—
146	C₂²	—	146	8	no	—
147	C₂²	#14556553	1	2	yes	—
148	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
149	C₄	—	2	2	no	—
150	C₄	—	2	2	no	—
151	C₄	—	146	4	no	—
152	C₄	#14556553	1	2	yes	—
153	C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
154	C₄	C₂×#11924029	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	292	4	no	—
157	C₂	C₂×#14556553	1	1	yes	characteristic
158	C₂	#17989353	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556599

C₂

yes

maximal, complemented

#17989137

C₂

yes

maximal, characteristic

#17988657

C₂

yes

maximal, complemented

#17988555

C₂

yes

maximal, complemented

C₂×#14556502

C₂

yes

maximal, characteristic, complemented

#423×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924028

C₂²

yes

—

#14556599

—

C₂×#11924011

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

—

#14556591

C₄

yes

characteristic

#14556588

C₄

yes

characteristic

#14556579

C₄

yes

—

#14556565

C₄

yes

—

C₄×D₂₉₂

C₂²

yes

—

#14556503

C₂²

yes

—

#14556502

C₂²

yes

—

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂×D₂₉₂

C₂×C₄

yes

—

C₂×D₂₉₂

C₂×C₄

yes

—

C₂×C₂²⋊D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

—

#11924011

—

C₂×#10596831

—

C₂×#10596831

D₄

yes

complemented

C₂×#10596831

C₂³

yes

—

C₂×#10596831

C₂³

yes

—

C₈×D₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924005

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂³

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

C₂²×C₄

yes

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

C₂×#41

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄×D₄

yes

characteristic

C₂×C₇₃

#568

yes

—

D₇₃

—

#2932

—

maximal, Sylow

C₇₃

#2932

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#408

—

C₂×#97

—

C₂×#41

—

#131

—

146

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

100

C₄⋊C₈

C₂×D₇₃

yes

—

101

C₂²⋊C₈

—

102

#97

—

103

#41

—

146

—

104

#41

—

146

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₄×D₇₃

yes

—

111

C₂²×C₄

C₂²×D₇₃

yes

characteristic

112

M₁₆

—

113

M₁₆

—

146

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

146

—

118

C₂×C₈

—

146

—

119

C₂×C₈

C₂²×D₇₃

yes

—

120

C₄⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

C₄×D₇₃

yes

characteristic

123

C₄²

C₄×D₇₃

yes

characteristic

124

C₄²

C₂²×D₇₃

yes

—

125

C₂³

—

126

C₂³

C₂×C₄×D₇₃

yes

characteristic

127

Q₈

—

146

—

128

D₄

—

292

—

129

D₄

—

146

—

130

D₄

—

146

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

146

—

134

C₂×C₄

—

146

—

135

C₂×C₄

C₂×C₄×D₇₃

yes

—

136

C₂×C₄

C₂×C₄×D₇₃

yes

—

137

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

138

C₂×C₄

D₄×D₇₃

yes

—

139

C₂×C₄

#11924029

yes

—

140

C₂×C₄

C₂³×D₇₃

yes

characteristic

141

C₈

—

142

C₈

—

143

C₈

—

146

—

144

C₂²

—

145

C₂²

—

146

—

146

C₂²

—

146

—

147

C₂²

#14556553

yes

—

148

C₂²

C₂²×C₄×D₇₃

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

146

—

152

C₄

#14556553

yes

—

153

C₄

C₂×D₄×D₇₃

yes

characteristic

154

C₄

C₂×#11924029

yes

characteristic

155

C₂

—

156

C₂

—

292

—

157

C₂

C₂×#14556553

yes

characteristic

158

C₂

#17989353

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	#423×C₇₃	C₂
hypercenter	#423	D₇₃
hypocenter	C₇₃	#2932
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₇₃

commutator, socle

C₂²×C₇₃

C₂³×C₄

Fitting

#423×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #423

N	H ≅ G/N	type
1. C₂×#14556599	C₂	semidirect
3. #17988657	C₂	semidirect
4. #17988555	C₂	semidirect
5. C₂×#14556502	C₂	semidirect
6. #423×C₇₃	C₂	semidirect
32. C₂×#10596831	D₄	semidirect
80. C₇₃	#2932	semidirect
84. #423	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556599

C₂

semidirect

3. #17988657

C₂

semidirect

4. #17988555

C₂

semidirect

5. C₂×#14556502

C₂

semidirect

6. #423×C₇₃

C₂

semidirect

32. C₂×#10596831

D₄

semidirect

80. C₇₃

#2932

semidirect

84. #423

D₇₃

semidirect

Subgroups — #22618648

Conjugacy classes of subgroups

Complements