Group #22611882 — subgroups

Subgroups — #22611882

Order 9344.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17989027	C₂	1	2	yes	maximal, complemented
2	#17988845	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988397	C₂	1	2	yes	maximal, complemented
4	#17988369	C₂	1	1	yes	maximal, characteristic, complemented
5	#575×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
7	#14556570	—	2	1	no	—
8	#14556537	—	2	2	no	—
9	#14556535	—	2	2	no	—
10	#14556531	C₂²	1	2	yes	complemented
11	#14556523	C₂²	1	1	yes	characteristic, complemented
12	#14556516	—	2	1	no	—
13	C₂×#41×C₇₃	—	2	1	no	—
14	#137×C₇₃	—	2	2	no	—
15	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
16	#135×C₇₃	—	2	1	no	—
17	#135×C₇₃	C₂²	1	2	yes	—
18	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₄₆	—	2	1	no	—
20	Dic₂₉₂	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	1	no	—
22	#11924007	—	4	1	no	—
23	C₂²⋊Dic₇₃	—	4	1	no	—
24	#11924003	—	2	2	no	—
25	#41×C₇₃	—	2	2	no	—
26	#41×C₇₃	—	2	2	no	—
27	#41×C₇₃	—	4	1	no	—
28	#41×C₇₃	—	4	1	no	—
29	C₂×Q₈×C₇₃	—	2	1	no	—
30	C₂×D₄×C₇₃	—	2	1	no	—
31	C₂×D₄×C₇₃	—	4	1	no	—
32	C₂²×C₄×C₇₃	—	4	1	no	—
33	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
34	Q₁₆×C₇₃	—	2	1	no	—
35	Q₁₆×C₇₃	D₄	1	2	yes	—
36	SD₁₆×C₇₃	—	2	2	no	—
37	SD₁₆×C₇₃	—	2	2	no	—
38	D₈×C₇₃	—	2	1	no	—
39	D₈×C₇₃	D₄	1	2	yes	—
40	M₁₆×C₇₃	—	2	2	no	—
41	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂³×C₇₃	—	4	1	no	—
44	C₂³×C₇₃	D₈	1	1	yes	characteristic
45	Q₈×C₇₃	—	2	2	no	—
46	Q₈×C₇₃	—	4	1	no	—
47	D₄×C₇₃	—	2	2	no	—
48	D₄×C₇₃	—	4	1	no	—
49	D₄×C₇₃	—	4	2	no	—
50	D₄×C₇₃	—	4	2	no	—
51	C₂×C₄×C₇₃	—	2	1	no	—
52	C₂×C₄×C₇₃	—	2	1	no	—
53	C₂×C₄×C₇₃	—	4	2	no	—
54	C₂×C₄×C₇₃	—	4	1	no	—
55	C₂×C₄×C₇₃	—	4	2	no	—
56	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
57	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
58	C₂×Dic₇₃	—	4	1	no	—
59	C₂×Dic₇₃	—	4	1	no	—
60	Dic₁₄₆	—	4	1	no	—
61	Dic₁₄₆	—	4	1	no	—
62	C₈×C₇₃	—	2	1	no	—
63	C₈×C₇₃	C₂×D₄	1	2	yes	—
64	C₂²×C₇₃	—	2	1	no	—
65	C₂²×C₇₃	—	4	1	no	—
66	C₂²×C₇₃	—	4	2	no	—
67	C₂²×C₇₃	—	8	2	no	—
68	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
69	C₄×C₇₃	—	2	1	no	—
70	C₄×C₇₃	—	4	2	no	—
71	C₄×C₇₃	#120	1	1	yes	characteristic
72	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
73	Dic₇₃	—	8	1	no	—
74	Dic₇₃	—	8	1	no	—
75	C₂×C₇₃	—	2	1	no	—
76	C₂×C₇₃	—	4	1	no	—
77	C₂×C₇₃	—	8	2	no	—
78	C₂×C₇₃	#447	1	1	yes	characteristic
79	#2191	—	73	1	no	maximal, Sylow
80	C₇₃	#2191	1	1	yes	characteristic, complemented, Sylow
81	#575	D₇₃	1	1	yes	characteristic
82	#510	—	73	2	no	—
83	#470	—	73	1	no	—
84	#360	—	73	2	no	—
85	#349	—	73	1	no	—
86	C₂×#41	—	2	1	no	—
87	#137	—	2	2	no	—
88	AGL(1,ℤ/8)	—	2	2	no	—
89	#135	—	2	1	no	—
90	#135	C₂×D₇₃	1	2	yes	—
91	C₂×Q₁₆	—	73	1	no	—
92	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
93	C₂²⋊Q₈	—	146	1	no	—
94	Q₃₂	—	146	2	no	—
95	SD₃₂	—	146	2	no	—
96	M₃₂	—	73	2	no	—
97	#106	—	73	1	no	—
98	#103	—	146	1	no	—
99	#41	—	2	2	no	—
100	#41	—	2	2	no	—
101	#41	—	4	1	no	—
102	#41	—	4	1	no	—
103	C₂×Q₈	—	2	1	no	—
104	C₂×Q₈	—	146	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	4	1	no	—
107	C₂²×C₄	—	4	1	no	—
108	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
109	Q₁₆	—	2	1	no	—
110	Q₁₆	—	146	2	no	—
111	Q₁₆	C₂²⋊D₇₃	1	2	yes	—
112	SD₁₆	—	2	2	no	—
113	SD₁₆	—	2	2	no	—
114	D₈	—	2	1	no	—
115	D₈	C₂²⋊D₇₃	1	2	yes	—
116	M₁₆	—	2	2	no	—
117	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
118	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
119	C₄⋊C₄	—	292	1	no	—
120	C₄⋊C₄	—	146	1	no	—
121	C₂²⋊C₄	—	292	1	no	—
122	C₁₆	—	146	2	no	—
123	C₂³	—	4	1	no	—
124	C₂³	#11924013	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	Q₈	—	4	1	no	—
127	Q₈	—	292	1	no	—
128	Q₈	—	292	1	no	—
129	D₄	—	2	2	no	—
130	D₄	—	4	1	no	—
131	D₄	—	4	2	no	—
132	D₄	—	4	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	—	4	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	292	1	no	—
139	C₂×C₄	—	292	1	no	—
140	C₂×C₄	#11924013	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	4	2	no	—
147	C₂²	—	8	2	no	—
148	C₂²	C₂×#11924013	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	4	2	no	—
151	C₄	—	584	1	no	—
152	C₄	—	584	1	no	—
153	C₄	#14556560	1	1	yes	characteristic
154	C₄	#14556617	1	1	yes	characteristic
155	C₂	—	2	1	no	—
156	C₂	—	4	1	no	—
157	C₂	—	8	2	no	—
158	C₂	#17988721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989027

C₂

yes

maximal, complemented

#17988845

C₂

yes

maximal, characteristic, complemented

#17988397

C₂

yes

maximal, complemented

#17988369

C₂

yes

maximal, characteristic, complemented

#575×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

characteristic, complemented

—

—

—

C₂²

yes

complemented

#14556523

C₂²

yes

characteristic, complemented

#14556516

—

C₂×#41×C₇₃

—

#137×C₇₃

—

AGL(1,ℤ/8)×C₇₃

—

#135×C₇₃

—

#135×C₇₃

C₂²

yes

—

C₂×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

#11924003

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

D₄

yes

—

SD₁₆×C₇₃

—

SD₁₆×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

D₄

yes

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#575

D₇₃

yes

—

—

—

—

C₂×#41

—

—

—

—

C₂×D₇₃

yes

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

characteristic

C₂²⋊Q₈

—

146

—

Q₃₂

—

146

—

SD₃₂

—

146

—

M₃₂

—

#106

—

#103

—

146

—

#41

—

100

#41

—

101

#41

—

102

#41

—

103

C₂×Q₈

—

104

C₂×Q₈

—

146

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

109

Q₁₆

—

110

Q₁₆

—

146

—

111

Q₁₆

C₂²⋊D₇₃

yes

—

112

SD₁₆

—

113

SD₁₆

—

114

D₈

—

115

D₈

C₂²⋊D₇₃

yes

—

116

M₁₆

—

117

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

118

C₂×C₈

C₂²×D₇₃

yes

characteristic

119

C₄⋊C₄

—

292

—

120

C₄⋊C₄

—

146

—

121

C₂²⋊C₄

—

292

—

122

C₁₆

—

146

—

123

C₂³

—

124

C₂³

#11924013

yes

characteristic

125

Q₈

—

126

Q₈

—

127

Q₈

—

292

—

128

Q₈

—

292

—

129

D₄

—

130

D₄

—

131

D₄

—

132

D₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

292

—

139

C₂×C₄

—

292

—

140

C₂×C₄

#11924013

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

142

C₈

—

143

C₈

C₂×C₂²⋊D₇₃

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

C₂×#11924013

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

584

—

152

C₄

—

584

—

153

C₄

#14556560

yes

characteristic

154

C₄

#14556617

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

—

158

C₂

#17988721

yes

characteristic

	subgroup	G/H
center	C₂	#17988721
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#575×C₇₃	C₂
socle	C₂×C₇₃	#447
hypercenter	#575	D₇₃
hypocenter	C₇₃	#2191
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #575

subgroup

G/H

center

C₂

#17988721

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#575×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #575

N	H ≅ G/N	type
1. #17989027	C₂	semidirect
2. #17988845	C₂	semidirect
3. #17988397	C₂	semidirect
4. #17988369	C₂	semidirect
6. C₂×Dic₂₉₂	C₂²	semidirect
10. #14556531	C₂²	semidirect
11. #14556523	C₂²	semidirect
80. C₇₃	#2191	semidirect

H ≅ G/N

type

1. #17989027

C₂

semidirect

2. #17988845

C₂

semidirect

3. #17988397

C₂

semidirect

4. #17988369

C₂

semidirect

6. C₂×Dic₂₉₂

C₂²

semidirect

10. #14556531

C₂²

semidirect

11. #14556523

C₂²

semidirect

80. C₇₃

#2191

semidirect

Subgroups — #22611882

Conjugacy classes of subgroups

Complements