Group #22611340 — subgroups

Subgroups — #22611340

Order 9344.

238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556514	C₂	1	2	yes	maximal
2	#17988493	C₂	1	1	yes	maximal, characteristic
3	#17988349	C₂	1	2	yes	maximal
4	#17988342	C₂	1	1	yes	maximal, characteristic
5	#384×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
9	#14556514	—	2	4	no	—
10	#14556498	—	2	1	no	—
11	#14556498	—	2	1	no	—
12	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
13	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
14	C₂×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₆	—	2	2	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	—	2	1	no	—
19	C₂×Dic₁₄₆	D₄	1	2	yes	—
20	C₂²×Dic₇₃	—	2	1	no	—
21	C₂²×Dic₇₃	—	2	1	no	—
22	C₂×#10596831	—	2	2	no	—
23	C₂×#10596831	—	2	2	no	—
24	C₂×#10596831	—	2	2	no	—
25	C₄⋊Dic₇₃	—	2	2	no	—
26	C₂²×C₄×C₇₃	—	2	2	no	—
27	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄⋊C₄×C₇₃	—	4	2	no	—
33	C₄⋊C₄×C₇₃	—	4	2	no	—
34	C₄²×C₇₃	—	2	2	no	—
35	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	—	2	1	no	—
37	C₂×C₄×C₇₃	—	2	1	no	—
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	—	4	2	no	—
41	C₂×C₄×C₇₃	—	4	2	no	—
42	C₂×C₄×C₇₃	—	4	2	no	—
43	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
44	C₂×C₄×C₇₃	Q₁₆	1	2	yes	—
45	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
47	C₂×C₄×C₇₃	#41	1	2	yes	—
48	C₂×C₄×C₇₃	#41	1	2	yes	—
49	C₂×Dic₇₃	—	2	2	no	—
50	C₂×Dic₇₃	—	4	1	no	—
51	C₂×Dic₇₃	—	4	1	no	—
52	C₂×Dic₇₃	—	4	1	no	—
53	C₂×Dic₇₃	—	4	1	no	—
54	C₂×Dic₇₃	—	4	1	no	—
55	Dic₁₄₆	—	2	4	no	—
56	Dic₁₄₆	—	4	2	no	—
57	#10596831	—	4	2	no	—
58	C₂²×C₇₃	#121	1	1	yes	characteristic
59	C₂²×C₇₃	#123	1	1	yes	characteristic
60	C₂²×C₇₃	#124	1	1	yes	characteristic
61	C₂²×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
62	C₂²×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
64	C₂²×C₇₃	#137	1	1	yes	characteristic
65	C₄×C₇₃	—	2	2	no	—
66	C₄×C₇₃	—	2	2	no	—
67	C₄×C₇₃	—	8	2	no	—
68	C₄×C₇₃	#123	1	2	yes	—
69	C₄×C₇₃	#126	1	2	yes	—
70	Dic₇₃	—	4	2	no	—
71	Dic₇₃	—	8	1	no	—
72	C₂×C₇₃	#397	1	1	yes	characteristic
73	C₂×C₇₃	#460	1	1	yes	characteristic
74	C₂×C₇₃	#462	1	1	yes	characteristic
75	C₂×C₇₃	#483	1	1	yes	characteristic
76	C₂×C₇₃	#484	1	1	yes	characteristic
77	C₂×C₇₃	#487	1	1	yes	characteristic
78	C₂×C₇₃	#489	1	1	yes	characteristic
79	#2072	—	73	1	no	maximal, Sylow
80	C₇₃	#2072	1	1	yes	characteristic, complemented, Sylow
81	C₂×#103	—	73	2	no	—
82	#391	—	73	1	no	—
83	#384	D₇₃	1	1	yes	characteristic
84	#340	—	73	2	no	—
85	#336	—	73	1	no	—
86	C₂²×Q₈	—	73	1	no	—
87	C₂²×C₈	—	73	2	no	—
88	C₂×C₄⋊C₄	—	2	1	no	—
89	C₂×C₄⋊C₄	—	2	1	no	—
90	C₂×C₄⋊C₄	—	73	1	no	—
91	C₂×C₄⋊C₄	C₂×D₇₃	1	2	yes	—
92	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
93	#103	—	146	4	no	—
94	#95	—	146	1	no	—
95	#95	—	146	1	no	—
96	C₂×Q₈	—	73	2	no	—
97	C₂×Q₈	—	146	2	no	—
98	C₂×Q₈	—	146	2	no	—
99	C₂×Q₈	—	146	1	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	146	1	no	—
102	C₂²×C₄	—	146	1	no	—
103	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
104	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
106	C₂×C₈	—	146	2	no	—
107	C₂×C₈	—	146	2	no	—
108	C₂×C₈	—	146	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	—	4	2	no	—
112	C₄⋊C₄	—	4	2	no	—
113	C₄⋊C₄	—	146	2	no	—
114	C₄²	—	2	2	no	—
115	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
116	Q₈	—	292	2	no	—
117	Q₈	—	146	4	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	292	1	no	—
126	C₂×C₄	—	292	1	no	—
127	C₂×C₄	—	292	1	no	—
128	C₂×C₄	—	292	1	no	—
129	C₂×C₄	—	292	1	no	—
130	C₂×C₄	—	146	2	no	—
131	C₂×C₄	#11924016	1	2	yes	—
132	C₂×C₄	#11924018	1	2	yes	—
133	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
134	C₂×C₄	#11924027	1	1	yes	characteristic
135	C₂×C₄	#11924028	1	2	yes	—
136	C₂×C₄	#11924029	1	2	yes	—
137	C₈	—	292	2	no	—
138	C₂²	#14556562	1	1	yes	characteristic
139	C₂²	#14556574	1	1	yes	characteristic
140	C₂²	#14556580	1	1	yes	characteristic
141	C₂²	C₂×#11924016	1	1	yes	characteristic
142	C₂²	C₂×#11924018	1	1	yes	characteristic
143	C₂²	#14556617	1	1	yes	characteristic
144	C₂²	#14556622	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	8	2	no	—
148	C₄	—	292	2	no	—
149	C₄	—	584	1	no	—
150	C₄	#14556576	1	2	yes	—
151	C₄	#14556586	1	2	yes	—
152	C₂	#17988513	1	1	yes	characteristic
153	C₂	#17988784	1	1	yes	characteristic
154	C₂	#17988794	1	1	yes	characteristic
155	C₂	#17988917	1	1	yes	characteristic
156	C₂	#17988922	1	1	yes	characteristic
157	C₂	#17988939	1	1	yes	characteristic
158	C₂	#17988949	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556514

C₂

yes

maximal

#17988493

C₂

yes

maximal, characteristic

#17988349

C₂

yes

maximal

#17988342

C₂

yes

maximal, characteristic

#384×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂²×#10596831

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

—

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

Q₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

C₂×SD₁₆

yes

characteristic

C₂²×C₇₃

C₂×Q₁₆

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#126

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#103

—

#391

—

#384

D₇₃

yes

characteristic

#340

—

#336

—

C₂²×Q₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#103

—

146

—

#95

—

146

—

#95

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

100

C₂²×C₄

—

101

C₂²×C₄

—

146

—

102

C₂²×C₄

—

146

—

103

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

104

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

105

C₂²×C₄

C₂²×D₇₃

yes

characteristic

106

C₂×C₈

—

146

—

107

C₂×C₈

—

146

—

108

C₂×C₈

—

146

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

146

—

114

C₄²

—

115

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

116

Q₈

—

292

—

117

Q₈

—

146

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

292

—

126

C₂×C₄

—

292

—

127

C₂×C₄

—

292

—

128

C₂×C₄

—

292

—

129

C₂×C₄

—

292

—

130

C₂×C₄

—

146

—

131

C₂×C₄

#11924016

yes

—

132

C₂×C₄

#11924018

yes

—

133

C₂×C₄

D₄×D₇₃

yes

characteristic

134

C₂×C₄

#11924027

yes

characteristic

135

C₂×C₄

#11924028

yes

—

136

C₂×C₄

#11924029

yes

—

137

C₈

—

292

—

138

C₂²

#14556562

yes

characteristic

139

C₂²

#14556574

yes

characteristic

140

C₂²

#14556580

yes

characteristic

141

C₂²

C₂×#11924016

yes

characteristic

142

C₂²

C₂×#11924018

yes

characteristic

143

C₂²

#14556617

yes

characteristic

144

C₂²

#14556622

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

292

—

149

C₄

—

584

—

150

C₄

#14556576

yes

—

151

C₄

#14556586

yes

—

152

C₂

#17988513

yes

characteristic

153

C₂

#17988784

yes

characteristic

154

C₂

#17988794

yes

characteristic

155

C₂

#17988917

yes

characteristic

156

C₂

#17988922

yes

characteristic

157

C₂

#17988939

yes

characteristic

158

C₂

#17988949

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₇₃
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#384×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	#384	D₇₃
hypocenter	C₇₃	#2072
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₇₃

commutator

C₂²×C₄×C₇₃

C₂³

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#384×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

D₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
80. C₇₃	#2072	semidirect

H ≅ G/N

type

80. C₇₃

#2072

semidirect

Subgroups — #22611340

Conjugacy classes of subgroups

Complements