Group #22625193 — subgroups

Subgroups — #22625193

Order 9344.

236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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	#17989608	C₂	1	2	yes	maximal
2	#17989433	C₂	1	2	yes	maximal
3	#17989432	C₂	1	2	yes	maximal
4	C₂×C₄×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#10596833	—	2	2	no	—
6	C₂²⋊#10596833	C₂²	1	4	yes	—
7	#14556646	—	2	2	no	—
8	C₂²×Dic₁₄₆	C₄	1	1	yes	characteristic
9	C₄×Dic₁₄₆	—	2	2	no	—
10	C₄×Dic₁₄₆	—	2	2	no	—
11	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
12	C₂×#11924007	C₄	1	1	yes	characteristic
13	C₂×#11924007	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
17	C₂×#10596833	—	2	4	no	—
18	C₂×Dic₁₄₆	—	2	2	no	—
19	C₂×Dic₁₄₆	—	2	2	no	—
20	C₂×Dic₁₄₆	—	2	2	no	—
21	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₄⋊Dic₇₃	—	2	2	no	—
26	#11924007	—	2	2	no	—
27	#11924007	—	2	2	no	—
28	C₄×Dic₇₃	—	2	1	no	—
29	C₄×Dic₇₃	—	2	1	no	—
30	C₄×Dic₇₃	D₄	1	2	yes	—
31	C₄×Dic₇₃	D₄	1	2	yes	—
32	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₇₃	—	2	1	no	—
36	C₄²×C₇₃	—	2	1	no	—
37	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	—	2	1	no	—
39	C₂×C₄×C₇₃	—	2	1	no	—
40	C₂×C₄×C₇₃	—	2	2	no	—
41	C₂×C₄×C₇₃	—	2	1	no	—
42	C₂×C₄×C₇₃	—	4	1	no	—
43	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
46	C₂×Dic₇₃	—	2	1	no	—
47	C₂×Dic₇₃	—	2	1	no	—
48	C₂×Dic₇₃	—	2	1	no	—
49	C₂×Dic₇₃	—	2	1	no	—
50	C₂×Dic₇₃	—	2	1	no	—
51	C₂×Dic₇₃	—	4	1	no	—
52	C₂×Dic₇₃	—	4	1	no	—
53	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
54	C₂×Dic₇₃	M₁₆	1	2	yes	—
55	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
56	Dic₁₄₆	—	2	8	no	—
57	#10596833	—	4	4	no	—
58	C₂²×C₇₃	—	2	1	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
62	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
63	C₄×C₇₃	—	2	2	no	—
64	C₄×C₇₃	—	2	1	no	—
65	C₄×C₇₃	—	4	1	no	—
66	C₄×C₇₃	#101	1	2	yes	—
67	Dic₇₃	—	2	2	no	—
68	Dic₇₃	—	2	2	no	—
69	Dic₇₃	—	2	2	no	—
70	Dic₇₃	—	4	1	no	—
71	C₂×C₇₃	—	2	1	no	—
72	C₂×C₇₃	—	2	1	no	—
73	C₂×C₇₃	#407	1	1	yes	characteristic
74	C₂×C₇₃	#410	1	1	yes	characteristic
75	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
76	#1467	—	73	1	no	maximal, Sylow
77	C₇₃	#1467	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₄×Q₈	—	73	1	no	—
79	#432	—	73	2	no	—
80	#324	—	73	2	no	—
81	#324	—	73	2	no	—
82	C₂²×Q₈	—	73	1	no	—
83	C₄×Q₈	—	146	2	no	—
84	C₄×Q₈	—	146	2	no	—
85	C₂×C₄⋊C₄	—	73	1	no	—
86	C₂×C₄⋊C₄	—	73	1	no	—
87	C₂×C₄⋊C₄	—	73	1	no	—
88	C₂×C₄²	—	73	1	no	—
89	C₂×C₄²	—	73	1	no	—
90	C₂×C₄²	#64408	1	1	yes	characteristic
91	C₄⋊C₈	—	146	2	no	—
92	C₂²⋊C₈	—	73	4	no	—
93	#97	—	146	2	no	—
94	C₂×Q₈	—	146	2	no	—
95	C₂×Q₈	—	146	2	no	—
96	C₂×Q₈	—	146	2	no	—
97	C₂²×C₄	—	73	1	no	—
98	C₂²×C₄	—	73	1	no	—
99	C₂²×C₄	—	73	1	no	—
100	C₂²×C₄	—	73	1	no	—
101	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
102	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
103	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
104	C₂×C₈	—	146	4	no	—
105	C₄⋊C₄	—	146	2	no	—
106	C₄⋊C₄	—	146	2	no	—
107	C₄⋊C₄	—	146	2	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	73	2	no	—
111	C₄²	—	73	2	no	—
112	C₄²	—	146	1	no	—
113	C₄²	—	146	1	no	—
114	C₂³	C₂²×#64408	1	1	yes	characteristic
115	Q₈	—	146	8	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	292	1	no	—
122	C₂×C₄	—	292	1	no	—
123	C₂×C₄	—	73	2	no	—
124	C₂×C₄	—	73	2	no	—
125	C₂×C₄	—	73	2	no	—
126	C₂×C₄	—	146	1	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	—	146	1	no	—
129	C₂×C₄	—	146	1	no	—
130	C₂×C₄	—	146	1	no	—
131	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
132	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
133	C₂×C₄	#11924038	1	2	yes	—
134	C₈	—	292	4	no	—
135	C₂²	—	2	1	no	—
136	C₂²	—	2	1	no	—
137	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
138	C₂²	D₇₃⋊M₁₆	1	1	yes	characteristic
139	C₂²	C₂×#11924038	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	2	1	no	—
142	C₄	—	4	1	no	—
143	C₄	—	292	1	no	—
144	C₄	—	146	2	no	—
145	C₄	—	146	2	no	—
146	C₄	—	146	2	no	—
147	C₄	#14556652	1	2	yes	—
148	C₂	—	2	1	no	—
149	C₂	—	2	1	no	—
150	C₂	#17989558	1	1	yes	characteristic
151	C₂	#17989566	1	1	yes	characteristic
152	C₂	C₂×#14556652	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989608

C₂

yes

maximal

#17989433

C₂

yes

maximal

#17989432

C₂

yes

maximal

C₂×C₄×Dic₁₄₆

C₂

yes

maximal, characteristic

C₄⋊#10596833

—

C₂²⋊#10596833

C₂²

yes

—

#14556646

—

C₂²×Dic₁₄₆

C₄

yes

characteristic

C₄×Dic₁₄₆

—

C₄×Dic₁₄₆

—

C₂×C₄⋊Dic₇₃

C₂²

yes

characteristic

C₂×#11924007

C₄

yes

characteristic

C₂×#11924007

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

M₁₆

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

characteristic

C₂²×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#101

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

—

#432

—

#324

—

#324

—

C₂²×Q₈

—

C₄×Q₈

—

146

—

C₄×Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#64408

yes

characteristic

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

#97

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂×#64408

yes

characteristic

102

C₂²×C₄

C₂×#64408

yes

characteristic

103

C₂²×C₄

C₂×#64408

yes

characteristic

104

C₂×C₈

—

146

—

105

C₄⋊C₄

—

146

—

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

146

—

113

C₄²

—

146

—

114

C₂³

C₂²×#64408

yes

characteristic

115

Q₈

—

146

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

292

—

122

C₂×C₄

—

292

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

146

—

127

C₂×C₄

—

146

—

128

C₂×C₄

—

146

—

129

C₂×C₄

—

146

—

130

C₂×C₄

—

146

—

131

C₂×C₄

C₂²⋊#64408

yes

characteristic

132

C₂×C₄

C₂²⋊#64408

yes

characteristic

133

C₂×C₄

#11924038

yes

—

134

C₈

—

292

—

135

C₂²

—

136

C₂²

—

137

C₂²

C₂×C₂²⋊#64408

yes

characteristic

138

C₂²

D₇₃⋊M₁₆

yes

characteristic

139

C₂²

C₂×#11924038

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

292

—

144

C₄

—

146

—

145

C₄

—

146

—

146

C₄

—

146

—

147

C₄

#14556652

yes

—

148

C₂

—

149

C₂

—

150

C₂

#17989558

yes

characteristic

151

C₂

#17989566

yes

characteristic

152

C₂

C₂×#14556652

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂³	C₂²×#64408
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	#1467
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂³

C₂²×#64408

Fitting

C₂×C₄²×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₂×C₄²

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
77. C₇₃	#1467	semidirect

H ≅ G/N

type

77. C₇₃

#1467

semidirect

Subgroups — #22625193

Conjugacy classes of subgroups

Complements