Group #22611991 — subgroups

Subgroups — #22611991

Order 9344.

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

normal subgroups only

This group has 158 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×#14556537	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988970	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988405	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988392	C₂	1	1	yes	maximal, characteristic, complemented
6	#17988388	C₂	1	1	yes	maximal, characteristic
7	C₂×SD₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	C₂×#11924016	—	2	1	no	—
10	#14556578	—	2	1	no	—
11	Q₈×Dic₇₃	—	2	1	no	—
12	#14556537	—	2	2	no	—
13	C₂×#11924003	C₂²	1	1	yes	characteristic
14	#14556525	C₂²	1	1	yes	characteristic
15	#14556515	—	2	1	no	—
16	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₇₃	C₂²	1	1	yes	characteristic
19	SD₃₂×C₇₃	—	2	2	no	—
20	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₄₆	—	2	1	no	—
22	Dic₂₉₂	—	2	1	no	—
23	Dic₂₉₂	—	2	1	no	—
24	#11924016	—	4	2	no	—
25	C₂×#10596831	D₄	1	1	yes	characteristic
26	C₄⋊Dic₇₃	—	2	1	no	—
27	C₄⋊Dic₇₃	—	4	1	no	—
28	C₂²⋊Dic₇₃	—	4	1	no	—
29	C₂²⋊Dic₇₃	—	4	1	no	—
30	C₄×Dic₇₃	—	4	1	no	—
31	C₄×Dic₇₃	D₄	1	1	yes	characteristic
32	#11924003	—	2	1	no	—
33	C₂×Q₈×C₇₃	—	2	1	no	—
34	C₂×D₄×C₇₃	—	2	1	no	—
35	Q₁₆×C₇₃	—	2	1	no	—
36	Q₁₆×C₇₃	D₄	1	2	yes	—
37	D₈×C₇₃	—	2	1	no	—
38	D₈×C₇₃	—	2	1	no	—
39	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
40	C₁₆×C₇₃	—	2	1	no	—
41	C₂³×C₇₃	—	4	1	no	—
42	Q₈×C₇₃	—	2	2	no	—
43	Q₈×C₇₃	—	4	1	no	—
44	D₄×C₇₃	—	4	1	no	—
45	D₄×C₇₃	—	4	1	no	—
46	C₂×C₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₇₃	—	4	1	no	—
49	C₂×Dic₇₃	—	4	1	no	—
50	C₂×Dic₇₃	D₈	1	1	yes	characteristic
51	C₂×Dic₇₃	D₈	1	1	yes	characteristic
52	Dic₁₄₆	—	4	1	no	—
53	Dic₁₄₆	—	4	1	no	—
54	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
55	C₈×C₇₃	#41	1	1	yes	characteristic
56	#10596831	—	2	1	no	—
57	C₂²×C₇₃	—	8	1	no	—
58	C₂²×C₇₃	—	8	1	no	—
59	C₂²×C₇₃	—	8	1	no	—
60	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
61	C₄×C₇₃	—	4	2	no	—
62	C₄×C₇₃	#121	1	1	yes	characteristic
63	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	Dic₇₃	—	2	1	no	—
65	Dic₇₃	—	2	1	no	—
66	Dic₇₃	—	8	1	no	—
67	Dic₇₃	—	8	1	no	—
68	C₂×C₇₃	—	16	1	no	—
69	C₂×C₇₃	#459	1	1	yes	characteristic
70	C₂×C₇₃	#508	1	1	yes	characteristic
71	C₂×C₇₃	#510	1	1	yes	characteristic
72	#2211	—	73	1	no	maximal, Sylow
73	C₇₃	#2211	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₃₂	—	73	1	no	—
75	C₂×SD₃₂	D₇₃	1	1	yes	characteristic
76	#495	—	73	1	no	—
77	C₄×Q₁₆	—	73	1	no	—
78	C₄⋊C₁₆	—	73	1	no	—
79	#358	—	73	1	no	—
80	#357	—	73	1	no	—
81	C₂×Q₁₆	—	73	1	no	—
82	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
83	C₂×SD₁₆	—	146	1	no	—
84	C₂×D₈	C₂×D₇₃	1	1	yes	characteristic
85	#124	—	146	1	no	—
86	C₄×Q₈	—	146	1	no	—
87	Q₃₂	—	146	2	no	—
88	SD₃₂	—	2	2	no	—
89	C₂×C₁₆	—	73	1	no	—
90	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
91	#107	—	73	1	no	—
92	#103	—	146	1	no	—
93	C₄×C₈	—	73	1	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	146	1	no	—
96	C₂×D₄	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	146	1	no	—
99	Q₁₆	—	146	1	no	—
100	Q₁₆	C₂²⋊D₇₃	1	2	yes	—
101	SD₁₆	—	292	2	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	C₂×C₈	—	73	1	no	—
105	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
106	C₄⋊C₄	—	292	1	no	—
107	C₄⋊C₄	—	146	1	no	—
108	C₂²⋊C₄	—	292	1	no	—
109	C₂²⋊C₄	—	292	1	no	—
110	C₄²	—	292	1	no	—
111	C₄²	—	73	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	—	146	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	2	2	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	292	1	no	—
118	Q₈	—	292	1	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	292	1	no	—
123	C₂×C₄	—	292	1	no	—
124	C₂×C₄	—	73	1	no	—
125	C₂×C₄	—	73	1	no	—
126	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
127	C₈	—	146	1	no	—
128	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
129	C₈	#11924027	1	1	yes	characteristic
130	C₂²	—	8	1	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	D₈×D₇₃	1	1	yes	characteristic
134	C₄	—	4	2	no	—
135	C₄	—	584	1	no	—
136	C₄	—	584	1	no	—
137	C₄	—	146	1	no	—
138	C₄	—	146	1	no	—
139	C₄	#14556563	1	1	yes	characteristic
140	C₄	#14556615	1	1	yes	characteristic
141	C₂	—	16	1	no	—
142	C₂	#17988780	1	1	yes	characteristic
143	C₂	#17989018	1	1	yes	characteristic
144	C₂	#17989026	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556537

C₂

yes

maximal, characteristic, complemented

#17988970

C₂

yes

maximal, characteristic

Q₁₆×Dic₇₃

C₂

yes

maximal, characteristic, complemented

#17988405

C₂

yes

maximal, characteristic, complemented

#17988392

C₂

yes

maximal, characteristic, complemented

#17988388

C₂

yes

maximal, characteristic

C₂×SD₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

characteristic

C₂×#11924016

—

#14556578

—

Q₈×Dic₇₃

—

#14556537

—

C₂×#11924003

C₂²

yes

characteristic

#14556525

C₂²

yes

characteristic

#14556515

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

C₂×D₈×C₇₃

C₂²

yes

characteristic

SD₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

—

#11924016

—

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

C₂×Q₈×C₇₃

—

C₂×D₄×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

D₄

yes

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

D₇₃

yes

characteristic

#495

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#357

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

C₂×SD₁₆

—

146

—

C₂×D₈

C₂×D₇₃

yes

characteristic

#124

—

146

—

C₄×Q₈

—

146

—

Q₃₂

—

146

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#107

—

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

146

—

Q₁₆

—

146

—

100

Q₁₆

C₂²⋊D₇₃

yes

—

101

SD₁₆

—

292

—

102

D₈

—

103

D₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂²×D₇₃

yes

characteristic

106

C₄⋊C₄

—

292

—

107

C₄⋊C₄

—

146

—

108

C₂²⋊C₄

—

292

—

109

C₂²⋊C₄

—

292

—

110

C₄²

—

292

—

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

146

—

114

C₂³

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

292

—

118

Q₈

—

292

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

292

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₇₃

yes

characteristic

127

C₈

—

146

—

128

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

129

C₈

#11924027

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

D₈×D₇₃

yes

characteristic

134

C₄

—

135

C₄

—

584

—

136

C₄

—

584

—

137

C₄

—

146

—

138

C₄

—

146

—

139

C₄

#14556563

yes

characteristic

140

C₄

#14556615

yes

characteristic

141

C₂

—

142

C₂

#17988780

yes

characteristic

143

C₂

#17989018

yes

characteristic

144

C₂

#17989026

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×SD₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₂×SD₃₂	D₇₃
hypocenter	C₇₃	#2211
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×SD₃₂×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₂×SD₃₂

D₇₃

hypocenter

C₇₃

#2211

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

N	H ≅ G/N	type
1. C₂×#14556537	C₂	semidirect
3. Q₁₆×Dic₇₃	C₂	semidirect
4. #17988405	C₂	semidirect
5. #17988392	C₂	semidirect
73. C₇₃	#2211	semidirect

H ≅ G/N

type

1. C₂×#14556537

C₂

semidirect

3. Q₁₆×Dic₇₃

C₂

semidirect

4. #17988405

C₂

semidirect

5. #17988392

C₂

semidirect

73. C₇₃

#2211

semidirect

Subgroups — #22611991

Conjugacy classes of subgroups

Complements