Group #22609447 — subgroups

Subgroups — #22609447

Order 9344.

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

normal subgroups only

This group has 152 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	#17988990	C₂	1	1	yes	maximal, characteristic
2	#17988797	C₂	1	1	yes	maximal, characteristic
3	#17988718	C₂	1	1	yes	maximal, characteristic
4	#17988337	C₂	1	1	yes	maximal, characteristic
5	#17988334	C₂	1	1	yes	maximal, characteristic
6	#17988333	C₂	1	1	yes	maximal, characteristic
7	#462×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924018	—	2	1	no	—
9	#14556591	C₂²	1	1	yes	characteristic
10	#14556524	—	2	1	no	—
11	#14556524	—	2	1	no	—
12	C₄⋊#10596831	—	2	1	no	—
13	C₄⋊#10596831	C₂²	1	1	yes	characteristic
14	C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	#14556514	—	2	1	no	—
16	#14556502	—	2	1	no	—
17	C₄×#10596831	C₂²	1	1	yes	characteristic
18	C₂×Q₁₆×C₇₃	—	2	1	no	—
19	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
22	#103×C₇₃	—	2	1	no	—
23	C₂×Dic₁₄₆	—	2	1	no	—
24	#11924018	—	4	2	no	—
25	C₂×#10596831	—	2	1	no	—
26	C₂×#10596831	—	2	1	no	—
27	C₂×#10596831	D₄	1	1	yes	characteristic
28	C₂×#10596831	D₄	1	1	yes	characteristic
29	C₄⋊Dic₇₃	—	2	1	no	—
30	C₄⋊Dic₇₃	—	2	1	no	—
31	C₂×Q₈×C₇₃	—	2	1	no	—
32	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
33	Q₁₆×C₇₃	—	4	2	no	—
34	C₂×C₈×C₇₃	—	2	1	no	—
35	C₄⋊C₄×C₇₃	—	2	1	no	—
36	C₄⋊C₄×C₇₃	—	2	1	no	—
37	C₄⋊C₄×C₇₃	—	2	1	no	—
38	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
39	C₄²×C₇₃	—	2	1	no	—
40	C₄²×C₇₃	C₂³	1	1	yes	characteristic
41	Q₈×C₇₃	—	2	1	no	—
42	Q₈×C₇₃	—	2	1	no	—
43	Q₈×C₇₃	—	4	1	no	—
44	Q₈×C₇₃	—	4	1	no	—
45	C₂×C₄×C₇₃	—	2	1	no	—
46	C₂×C₄×C₇₃	—	2	1	no	—
47	C₂×C₄×C₇₃	—	4	1	no	—
48	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
51	C₂×Dic₇₃	—	4	1	no	—
52	Dic₁₄₆	—	4	1	no	—
53	Dic₁₄₆	—	4	1	no	—
54	C₈×C₇₃	—	4	1	no	—
55	#10596831	—	2	1	no	—
56	#10596831	—	4	1	no	—
57	#10596831	—	4	1	no	—
58	#10596831	Q₁₆	1	2	yes	complemented
59	C₂²×C₇₃	#121	1	1	yes	characteristic
60	C₄×C₇₃	—	2	1	no	—
61	C₄×C₇₃	—	4	1	no	—
62	C₄×C₇₃	—	4	1	no	—
63	C₄×C₇₃	—	8	1	no	—
64	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
65	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
67	C₄×C₇₃	#137	1	1	yes	characteristic
68	Dic₇₃	—	8	1	no	—
69	C₂×C₇₃	#462	1	1	yes	characteristic
70	C₂×C₇₃	#469	1	1	yes	characteristic
71	C₂×C₇₃	#473	1	1	yes	characteristic
72	#1694	—	73	1	no	maximal, Sylow
73	C₇₃	#1694	1	1	yes	characteristic, complemented, Sylow
74	#500	—	73	1	no	—
75	#462	—	73	1	no	—
76	#462	D₇₃	1	1	yes	characteristic
77	#446	—	73	1	no	—
78	#334	—	73	1	no	—
79	#332	—	73	1	no	—
80	#332	—	73	1	no	—
81	C₂×Q₁₆	—	2	1	no	—
82	C₂×Q₁₆	—	146	1	no	—
83	C₄⋊Q₈	—	73	1	no	—
84	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
85	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
86	#107	—	146	1	no	—
87	#107	—	146	1	no	—
88	C₄⋊C₈	—	73	1	no	—
89	C₄⋊C₈	—	73	1	no	—
90	C₄⋊C₈	—	146	1	no	—
91	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
92	#103	—	2	1	no	—
93	#103	—	146	1	no	—
94	#97	—	146	1	no	—
95	C₄×C₈	—	73	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	146	1	no	—
98	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
99	Q₁₆	—	4	2	no	—
100	Q₁₆	—	292	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	73	1	no	—
103	C₂×C₈	—	73	1	no	—
104	C₂×C₈	—	146	1	no	—
105	C₂×C₈	—	146	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	146	1	no	—
110	C₄⋊C₄	—	146	1	no	—
111	C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
112	C₄²	—	2	1	no	—
113	C₄²	C₂²×D₇₃	1	1	yes	characteristic
114	Q₈	—	2	1	no	—
115	Q₈	—	2	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	4	1	no	—
118	Q₈	—	292	1	no	—
119	Q₈	—	292	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	292	1	no	—
124	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
125	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
126	C₂×C₄	#11924027	1	1	yes	characteristic
127	C₈	—	4	1	no	—
128	C₈	—	292	1	no	—
129	C₈	—	292	1	no	—
130	C₈	—	73	2	no	—
131	C₈	—	146	1	no	—
132	C₂²	#14556563	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	4	1	no	—
135	C₄	—	4	1	no	—
136	C₄	—	8	1	no	—
137	C₄	—	584	1	no	—
138	C₄	Q₁₆×D₇₃	1	1	yes	characteristic
139	C₄	#14556616	1	1	yes	characteristic
140	C₄	#14556617	1	1	yes	characteristic
141	C₄	#14556623	1	1	yes	characteristic
142	C₂	#17988795	1	1	yes	characteristic
143	C₂	#17988838	1	1	yes	characteristic
144	C₂	#17988860	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988990

C₂

yes

maximal, characteristic

#17988797

C₂

yes

maximal, characteristic

#17988718

C₂

yes

maximal, characteristic

#17988337

C₂

yes

maximal, characteristic

#17988334

C₂

yes

maximal, characteristic

#17988333

C₂

yes

maximal, characteristic

#462×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924018

—

#14556591

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

—

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#103×C₇₃

—

C₂×Dic₁₄₆

—

—

—

—

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

—

—

—

Q₁₆

yes

complemented

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#500

—

#462

—

#462

D₇₃

yes

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

C₂×D₇₃

yes

characteristic

#107

—

146

—

#107

—

146

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#103

—

#103

—

146

—

#97

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²⋊D₇₃

yes

characteristic

Q₁₆

—

100

Q₁₆

—

292

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

146

—

110

C₄⋊C₄

—

146

—

111

C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

112

C₄²

—

113

C₄²

C₂²×D₇₃

yes

characteristic

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

292

—

119

Q₈

—

292

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

292

—

124

C₂×C₄

D₄×D₇₃

yes

characteristic

125

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

126

C₂×C₄

#11924027

yes

characteristic

127

C₈

—

128

C₈

—

292

—

129

C₈

—

292

—

130

C₈

—

131

C₈

—

146

—

132

C₂²

#14556563

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

584

—

138

C₄

Q₁₆×D₇₃

yes

characteristic

139

C₄

#14556616

yes

characteristic

140

C₄

#14556617

yes

characteristic

141

C₄

#14556623

yes

characteristic

142

C₂

#17988795

yes

characteristic

143

C₂

#17988838

yes

characteristic

144

C₂

#17988860

yes

characteristic

	subgroup	G/H
center	C₂²	#14556563
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#462×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#462	D₇₃
hypocenter	C₇₃	#1694
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

subgroup

G/H

center

C₂²

#14556563

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#462×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #462

N	H ≅ G/N	type
58. #10596831	Q₁₆	semidirect
73. C₇₃	#1694	semidirect

H ≅ G/N

type

58. #10596831

Q₁₆

semidirect

73. C₇₃

#1694

semidirect

Subgroups — #22609447

Conjugacy classes of subgroups

Complements