Group #22611970 — subgroups

Subgroups — #22611970

Order 9344.

174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14556536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556535	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988962	C₂	1	1	yes	maximal, characteristic
4	#17988681	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988405	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988387	C₂	1	1	yes	maximal, characteristic, complemented
7	#357×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×D₅₈₄	C₂²	1	1	yes	characteristic
10	C₂×#11924013	—	2	1	no	—
11	#14556587	—	2	1	no	—
12	#14556556	—	2	1	no	—
13	#14556536	—	2	2	no	—
14	#14556535	—	2	2	no	—
15	C₂×#11924003	C₂²	1	1	yes	characteristic
16	#14556514	—	2	1	no	—
17	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	#107×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₄₆	—	2	1	no	—
22	C₂×D₂₉₂	—	2	1	no	—
23	C₂×C₂²⋊D₇₃	—	4	1	no	—
24	C₂×C₂²⋊D₇₃	—	4	1	no	—
25	Dic₂₉₂	—	2	1	no	—
26	Dic₂₉₂	D₄	1	2	yes	complemented
27	D₅₈₄	—	2	1	no	—
28	D₅₈₄	—	2	1	no	—
29	#11924013	—	4	2	no	—
30	C₂×#10596831	D₄	1	1	yes	characteristic
31	#11924007	—	4	1	no	—
32	C₄×Dic₇₃	—	4	1	no	—
33	C₄×Dic₇₃	D₄	1	1	yes	characteristic
34	#11924003	—	2	1	no	—
35	C₂×D₄×C₇₃	—	2	1	no	—
36	D₈×C₇₃	—	2	1	no	—
37	D₈×C₇₃	—	2	1	no	—
38	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
39	C₄⋊C₄×C₇₃	—	2	1	no	—
40	C₁₆×C₇₃	—	2	1	no	—
41	C₂³×C₇₃	—	4	1	no	—
42	C₂²×D₇₃	—	4	1	no	—
43	D₄×C₇₃	—	4	1	no	—
44	D₄×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₇₃	—	8	2	no	—
48	C₂²⋊D₇₃	—	8	2	no	—
49	C₂×Dic₇₃	—	4	1	no	—
50	C₂×Dic₇₃	D₈	1	1	yes	characteristic
51	C₂×Dic₇₃	D₈	1	1	yes	characteristic
52	D₂₉₂	—	4	1	no	—
53	D₂₉₂	—	4	1	no	—
54	Dic₁₄₆	—	2	2	no	—
55	Dic₁₄₆	—	4	1	no	—
56	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₃	#41	1	1	yes	characteristic
58	#10596831	—	2	1	no	—
59	C₂²×C₇₃	—	8	1	no	—
60	C₂²×C₇₃	—	8	1	no	—
61	C₂²×C₇₃	—	8	1	no	—
62	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
63	C₂×D₇₃	—	8	1	no	—
64	C₂×D₇₃	—	8	1	no	—
65	C₂×D₇₃	—	8	1	no	—
66	C₄×C₇₃	—	8	1	no	—
67	C₄×C₇₃	#121	1	1	yes	characteristic
68	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
69	Dic₇₃	—	2	1	no	—
70	Dic₇₃	—	4	2	no	—
71	Dic₇₃	SD₃₂	1	2	yes	complemented
72	C₂×C₇₃	—	16	1	no	—
73	C₂×C₇₃	#459	1	1	yes	characteristic
74	C₂×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
75	C₂×C₇₃	#509	1	1	yes	characteristic
76	D₇₃	—	16	1	no	—
77	#2207	—	73	1	no	maximal, Sylow
78	C₇₃	#2207	1	1	yes	characteristic, complemented, Sylow
79	C₂×SD₃₂	—	73	1	no	—
80	C₂×SD₃₂	—	73	1	no	—
81	#493	—	73	1	no	—
82	C₄×Q₁₆	—	73	1	no	—
83	C₄⋊C₁₆	—	73	1	no	—
84	#357	—	73	1	no	—
85	#357	D₇₃	1	1	yes	characteristic, complemented
86	C₂×Q₁₆	—	73	1	no	—
87	C₂×D₈	—	73	1	no	—
88	C₂×D₈	—	146	1	no	—
89	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
90	#127	—	146	1	no	—
91	C₄×Q₈	—	146	1	no	—
92	SD₃₂	—	146	2	no	—
93	SD₃₂	—	146	2	no	—
94	C₂×C₁₆	—	73	1	no	—
95	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
96	#107	C₂×D₇₃	1	1	yes	characteristic
97	#103	—	146	1	no	—
98	C₄×C₈	—	73	1	no	—
99	C₂×Q₈	—	146	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	292	1	no	—
102	C₂×D₄	—	292	1	no	—
103	C₂×D₄	—	146	1	no	—
104	Q₁₆	—	73	2	no	—
105	Q₁₆	—	146	1	no	—
106	D₈	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	292	2	no	—
109	D₈	—	146	1	no	—
110	D₈	—	146	1	no	—
111	C₂×C₈	—	73	1	no	—
112	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
113	C₄⋊C₄	—	2	1	no	—
114	C₄⋊C₄	—	292	1	no	—
115	C₄²	—	292	1	no	—
116	C₄²	—	73	1	no	—
117	C₁₆	—	2	1	no	—
118	C₁₆	—	146	1	no	—
119	C₂³	—	4	1	no	—
120	C₂³	—	292	1	no	—
121	Q₈	—	292	1	no	—
122	Q₈	—	146	2	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	292	1	no	—
126	D₄	—	292	1	no	—
127	D₄	—	584	2	no	—
128	D₄	—	584	2	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	292	1	no	—
131	C₂×C₄	—	73	1	no	—
132	C₂×C₄	—	73	1	no	—
133	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
134	C₈	—	146	1	no	—
135	C₈	D₄×D₇₃	1	1	yes	characteristic
136	C₈	#11924028	1	1	yes	characteristic
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	—	584	1	no	—
141	C₂²	—	584	1	no	—
142	C₂²	—	584	1	no	—
143	C₂²	D₈×D₇₃	1	1	yes	characteristic
144	C₄	—	8	1	no	—
145	C₄	—	292	2	no	—
146	C₄	—	73	2	no	—
147	C₄	—	146	1	no	—
148	C₄	#14556564	1	1	yes	characteristic
149	C₄	#14556618	1	1	yes	characteristic
150	C₂	—	16	1	no	—
151	C₂	—	1168	1	no	—
152	C₂	#17988781	1	1	yes	characteristic
153	C₂	SD₃₂×D₇₃	1	1	yes	characteristic
154	C₂	#17989021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556536

C₂

yes

maximal, characteristic, complemented

C₂×#14556535

C₂

yes

maximal, characteristic, complemented

#17988962

C₂

yes

maximal, characteristic

#17988681

C₂

yes

maximal, characteristic, complemented

#17988405

C₂

yes

maximal, characteristic, complemented

#17988387

C₂

yes

maximal, characteristic, complemented

#357×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×D₅₈₄

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

#14556514

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂×C₂²⋊D₇₃

—

Dic₂₉₂

—

Dic₂₉₂

D₄

yes

complemented

D₅₈₄

—

D₅₈₄

—

#11924013

—

C₂×#10596831

D₄

yes

characteristic

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

C₂×D₄×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂²×D₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

SD₃₂

yes

complemented

C₂×C₇₃

—

C₂×C₇₃

#459

yes

characteristic

C₂×C₇₃

C₂×SD₃₂

yes

characteristic

C₂×C₇₃

#509

yes

characteristic

D₇₃

—

#2207

—

maximal, Sylow

C₇₃

#2207

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₂×SD₃₂

—

#493

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#357

—

#357

D₇₃

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

146

—

C₂×D₈

C₂×D₇₃

yes

characteristic

#127

—

146

—

C₄×Q₈

—

146

—

SD₃₂

—

146

—

SD₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#107

C₂×D₇₃

yes

characteristic

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

146

—

100

C₂×D₄

—

101

C₂×D₄

—

292

—

102

C₂×D₄

—

292

—

103

C₂×D₄

—

146

—

104

Q₁₆

—

105

Q₁₆

—

146

—

106

D₈

—

107

D₈

—

108

D₈

—

292

—

109

D₈

—

146

—

110

D₈

—

146

—

111

C₂×C₈

—

112

C₂×C₈

C₂²×D₇₃

yes

characteristic

113

C₄⋊C₄

—

114

C₄⋊C₄

—

292

—

115

C₄²

—

292

—

116

C₄²

—

117

C₁₆

—

118

C₁₆

—

146

—

119

C₂³

—

120

C₂³

—

292

—

121

Q₈

—

292

—

122

Q₈

—

146

—

123

D₄

—

124

D₄

—

125

D₄

—

292

—

126

D₄

—

292

—

127

D₄

—

584

—

128

D₄

—

584

—

129

C₂×C₄

—

130

C₂×C₄

—

292

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

D₄×D₇₃

yes

characteristic

134

C₈

—

146

—

135

C₈

D₄×D₇₃

yes

characteristic

136

C₈

#11924028

yes

characteristic

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

584

—

141

C₂²

—

584

—

142

C₂²

—

584

—

143

C₂²

D₈×D₇₃

yes

characteristic

144

C₄

—

145

C₄

—

292

—

146

C₄

—

147

C₄

—

146

—

148

C₄

#14556564

yes

characteristic

149

C₄

#14556618

yes

characteristic

150

C₂

—

151

C₂

—

1168

—

152

C₂

#17988781

yes

characteristic

153

C₂

SD₃₂×D₇₃

yes

characteristic

154

C₂

#17989021

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#357×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#357	D₇₃
hypocenter	C₇₃	#2207
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#357×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×#14556536	C₂	semidirect
2. C₂×#14556535	C₂	semidirect
4. #17988681	C₂	semidirect
5. #17988405	C₂	semidirect
6. #17988387	C₂	semidirect
7. #357×C₇₃	C₂	semidirect
26. Dic₂₉₂	D₄	semidirect
71. Dic₇₃	SD₃₂	semidirect
78. C₇₃	#2207	semidirect
85. #357	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556536

C₂

semidirect

2. C₂×#14556535

C₂

semidirect

4. #17988681

C₂

semidirect

5. #17988405

C₂

semidirect

6. #17988387

C₂

semidirect

7. #357×C₇₃

C₂

semidirect

26. Dic₂₉₂

D₄

semidirect

71. Dic₇₃

SD₃₂

semidirect

78. C₇₃

#2207

semidirect

85. #357

D₇₃

semidirect

Subgroups — #22611970

Conjugacy classes of subgroups

Complements