Group #22608819 — subgroups

Subgroups — #22608819

Order 9344.

166 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 67 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	#17988717	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11924016	C₂	1	1	yes	maximal, characteristic
3	#17988337	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988317	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄⋊#10596831	C₂	1	1	yes	maximal, characteristic
6	C₈×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
7	#436×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924016	C₄	1	1	yes	characteristic
9	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
10	#14556522	C₄	1	1	yes	characteristic
11	C₄⋊#10596831	C₂²	1	1	yes	characteristic
12	#14556520	—	2	1	no	—
13	#14556514	C₄	1	1	yes	characteristic
14	#14556512	C₄	1	1	yes	characteristic
15	#14556501	—	2	1	no	—
16	C₄×#10596831	C₂²	1	1	yes	characteristic
17	C₄×#10596831	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₇₃	—	2	1	no	—
19	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²⋊C₈×C₇₃	—	2	1	no	—
22	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
24	#11924016	—	2	2	no	—
25	C₂×#10596831	—	2	1	no	—
26	C₂×#10596831	—	2	1	no	—
27	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
28	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
29	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	#11924007	—	2	1	no	—
31	C₄×Dic₇₃	—	2	1	no	—
32	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₃	—	2	1	no	—
34	M₁₆×C₇₃	—	4	2	no	—
35	C₂×C₈×C₇₃	—	2	1	no	—
36	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
37	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
38	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂²⋊C₄×C₇₃	—	2	1	no	—
40	C₄²×C₇₃	C₂³	1	1	yes	characteristic
41	C₂³×C₇₃	—	2	1	no	—
42	D₄×C₇₃	—	2	1	no	—
43	D₄×C₇₃	—	2	1	no	—
44	C₂×C₄×C₇₃	—	2	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
50	C₂×Dic₇₃	—	2	1	no	—
51	C₂×Dic₇₃	—	2	1	no	—
52	Dic₁₄₆	—	2	1	no	—
53	Dic₁₄₆	—	2	1	no	—
54	C₈×C₇₃	—	2	1	no	—
55	C₈×C₇₃	—	4	1	no	—
56	C₈×C₇₃	SD₁₆	1	2	yes	complemented
57	#10596831	—	2	2	no	—
58	#10596831	—	2	1	no	—
59	#10596831	—	4	1	no	—
60	#10596831	M₁₆	1	2	yes	complemented
61	C₂²×C₇₃	—	4	1	no	—
62	C₂²×C₇₃	—	4	1	no	—
63	C₂²×C₇₃	—	4	1	no	—
64	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
65	C₄×C₇₃	—	2	1	no	—
66	C₄×C₇₃	—	4	1	no	—
67	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
68	C₄×C₇₃	#131	1	1	yes	characteristic
69	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
70	C₄×C₇₃	#135	1	1	yes	characteristic
71	Dic₇₃	—	4	1	no	—
72	Dic₇₃	—	4	1	no	—
73	C₂×C₇₃	—	8	1	no	—
74	C₂×C₇₃	#436	1	1	yes	characteristic
75	C₂×C₇₃	C₄×SD₁₆	1	1	yes	characteristic
76	C₂×C₇₃	#443	1	1	yes	characteristic
77	#1590	—	73	1	no	maximal, Sylow
78	C₇₃	#1590	1	1	yes	characteristic, complemented, Sylow
79	#446	—	73	1	no	—
80	C₄×SD₁₆	—	73	1	no	—
81	#436	D₇₃	1	1	yes	characteristic
82	#334	—	73	1	no	—
83	Q₈⋊C₈	—	73	1	no	—
84	D₄⋊C₈	—	73	1	no	—
85	C₈²	—	73	1	no	—
86	C₂×SD₁₆	—	73	1	no	—
87	C₂×M₁₆	—	2	1	no	—
88	C₄×Q₈	—	73	1	no	—
89	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
90	#106	—	73	1	no	—
91	C₄⋊C₈	—	73	1	no	—
92	C₄⋊C₈	—	146	1	no	—
93	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
94	#103	—	73	1	no	—
95	#102	—	73	1	no	—
96	C₂²⋊C₈	—	2	1	no	—
97	#97	—	146	1	no	—
98	C₄×C₈	—	73	1	no	—
99	C₄×C₈	—	73	1	no	—
100	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
101	C₂×Q₈	—	73	1	no	—
102	C₂×D₄	C₄×D₇₃	1	1	yes	characteristic
103	C₂²×C₄	—	2	1	no	—
104	SD₁₆	—	146	2	no	—
105	M₁₆	—	4	2	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	73	1	no	—
108	C₂×C₈	—	73	1	no	—
109	C₂×C₈	—	146	1	no	—
110	C₂×C₈	—	146	1	no	—
111	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
112	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
113	C₄⋊C₄	—	73	1	no	—
114	C₄⋊C₄	—	146	1	no	—
115	C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
116	C₂²⋊C₄	—	2	1	no	—
117	C₄²	—	146	1	no	—
118	C₄²	C₂²×D₇₃	1	1	yes	characteristic
119	C₂³	—	2	1	no	—
120	Q₈	—	146	1	no	—
121	Q₈	—	146	1	no	—
122	D₄	—	2	1	no	—
123	D₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	—	146	1	no	—
129	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
131	C₂×C₄	#11924028	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	4	1	no	—
134	C₈	—	292	1	no	—
135	C₈	—	73	2	no	—
136	C₈	—	146	2	no	—
137	C₈	—	146	1	no	—
138	C₈	#11924016	1	2	yes	complemented
139	C₂²	—	4	1	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	4	1	no	—
142	C₂²	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	292	1	no	—
146	C₄	—	292	1	no	—
147	C₄	M₁₆×D₇₃	1	1	yes	characteristic
148	C₄	#14556599	1	1	yes	characteristic
149	C₄	C₂×#11924016	1	1	yes	characteristic
150	C₄	#14556611	1	1	yes	characteristic
151	C₂	—	8	1	no	—
152	C₂	#17988663	1	1	yes	characteristic
153	C₂	C₄×#11924016	1	1	yes	characteristic
154	C₂	#17988702	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988717

C₂

yes

maximal, characteristic, complemented

C₄×#11924016

C₂

yes

maximal, characteristic

#17988337

C₂

yes

maximal, characteristic, complemented

#17988317

C₂

yes

maximal, characteristic, complemented

D₄⋊#10596831

C₂

yes

maximal, characteristic

C₈×#10596831

C₂

yes

maximal, characteristic, complemented

#436×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924016

C₄

yes

characteristic

C₄×Dic₁₄₆

C₂²

yes

characteristic

#14556522

C₄

yes

characteristic

C₄⋊#10596831

C₂²

yes

characteristic

#14556520

—

#14556514

C₄

yes

characteristic

#14556512

C₄

yes

characteristic

#14556501

—

C₄×#10596831

C₂²

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

—

C₄×D₄×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

C₂×C₄

yes

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₂×D₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

—

—

—

M₁₆

yes

complemented

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

#131

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

#135

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#436

yes

characteristic

C₂×C₇₃

C₄×SD₁₆

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#446

—

C₄×SD₁₆

—

#436

D₇₃

yes

characteristic

#334

—

Q₈⋊C₈

—

D₄⋊C₈

—

C₈²

—

C₂×SD₁₆

—

C₂×M₁₆

—

C₄×Q₈

—

C₄×D₄

C₂×D₇₃

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

#102

—

C₂²⋊C₈

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₂×D₇₃

yes

characteristic

101

C₂×Q₈

—

102

C₂×D₄

C₄×D₇₃

yes

characteristic

103

C₂²×C₄

—

104

SD₁₆

—

146

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

146

—

110

C₂×C₈

—

146

—

111

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

112

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

113

C₄⋊C₄

—

114

C₄⋊C₄

—

146

—

115

C₄⋊C₄

C₄×D₇₃

yes

characteristic

116

C₂²⋊C₄

—

117

C₄²

—

146

—

118

C₄²

C₂²×D₇₃

yes

characteristic

119

C₂³

—

120

Q₈

—

146

—

121

Q₈

—

146

—

122

D₄

—

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

146

—

128

C₂×C₄

—

146

—

129

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

131

C₂×C₄

#11924028

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

292

—

135

C₈

—

136

C₈

—

146

—

137

C₈

—

146

—

138

C₈

#11924016

yes

complemented

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₄×C₂²⋊D₇₃

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

292

—

146

C₄

—

292

—

147

C₄

M₁₆×D₇₃

yes

characteristic

148

C₄

#14556599

yes

characteristic

149

C₄

C₂×#11924016

yes

characteristic

150

C₄

#14556611

yes

characteristic

151

C₂

—

152

C₂

#17988663

yes

characteristic

153

C₂

C₄×#11924016

yes

characteristic

154

C₂

#17988702

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#436×C₇₃	C₂
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#436	D₇₃
hypocenter	C₇₃	#1590
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #436

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#436×C₇₃

C₂

socle

C₂²×C₇₃

C₄×D₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #436

N	H ≅ G/N	type
1. #17988717	C₂	semidirect
3. #17988337	C₂	semidirect
4. #17988317	C₂	semidirect
6. C₈×#10596831	C₂	semidirect
56. C₈×C₇₃	SD₁₆	semidirect
60. #10596831	M₁₆	semidirect
78. C₇₃	#1590	semidirect
138. C₈	#11924016	semidirect

H ≅ G/N

type

1. #17988717

C₂

semidirect

3. #17988337

C₂

semidirect

4. #17988317

C₂

semidirect

6. C₈×#10596831

C₂

semidirect

56. C₈×C₇₃

SD₁₆

semidirect

60. #10596831

M₁₆

semidirect

78. C₇₃

#1590

semidirect

138. C₈

#11924016

semidirect

Subgroups — #22608819

Conjugacy classes of subgroups

Complements