Group #22625723 — subgroups

Subgroups — #22625723

Order 9344.

296 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 134 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×#14556658	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596833	C₂	1	2	yes	maximal
3	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
4	#17989453	C₂	1	2	yes	maximal
5	#17988438	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596833	C₂²	1	1	yes	characteristic
7	C₂²×#10596833	C₂²	1	2	yes	—
8	C₂²×#10596833	C₂²	1	1	yes	characteristic
9	#14556658	C₄	1	4	yes	complemented
10	C₄×#10596833	—	2	4	no	—
11	C₄×#10596833	C₄	1	4	yes	complemented
12	C₂×#11924007	C₄	1	2	yes	—
13	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
15	#14556498	C₄	1	1	yes	characteristic
16	#95×C₇₃	C₄	1	1	yes	characteristic
17	C₂×#10596833	—	2	2	no	—
18	C₂×#10596833	—	2	1	no	—
19	C₂×#10596833	—	2	1	no	—
20	C₂×#10596833	—	2	2	no	—
21	C₂×#10596833	C₂×C₄	1	2	yes	—
22	C₂×#10596833	C₂×C₄	1	4	yes	—
23	C₂×#10596833	C₂×C₄	1	2	yes	—
24	C₂×#10596833	D₄	1	2	yes	—
25	C₂×#10596833	Q₈	1	2	yes	—
26	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
27	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
29	#11924007	C₈	1	8	yes	complemented
30	C₄×Dic₇₃	—	2	2	no	—
31	C₄×Dic₇₃	—	2	2	no	—
32	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
33	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
34	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
36	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	—	2	2	no	—
40	C₂×C₄×C₇₃	C₄²	1	2	yes	—
41	C₂×C₄×C₇₃	C₂×C₈	1	4	yes	—
42	C₂×Dic₇₃	—	2	2	no	—
43	C₂×Dic₇₃	—	2	2	no	—
44	C₂×Dic₇₃	C₄²	1	2	yes	—
45	C₂×Dic₇₃	C₂×C₈	1	4	yes	—
46	C₂×Dic₇₃	C₂×C₈	1	4	yes	—
47	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×Dic₇₃	#41	1	1	yes	characteristic
52	C₂×Dic₇₃	#41	1	1	yes	characteristic
53	#10596833	—	2	2	no	—
54	#10596833	—	2	4	no	—
55	#10596833	C₄⋊C₄	1	4	yes	complemented
56	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
57	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
58	C₂²×C₇₃	C₄×Q₈	1	1	yes	characteristic
59	C₂²×C₇₃	C₂²×C₈	1	2	yes	—
60	C₂²×C₇₃	#131	1	2	yes	—
61	C₄×C₇₃	—	2	2	no	—
62	C₄×C₇₃	—	2	4	no	—
63	Dic₇₃	—	2	4	no	—
64	Dic₇₃	C₄×C₈	1	4	yes	complemented
65	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
66	Dic₇₃	#117	1	1	yes	characteristic
67	Dic₇₃	C₄×D₄	1	1	yes	characteristic
68	Dic₇₃	C₄×Q₈	1	1	yes	characteristic
69	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂×C₇₃	#405	1	1	yes	characteristic
72	C₂×C₇₃	C₈×D₄	1	2	yes	—
73	C₂×C₇₃	C₈×Q₈	1	2	yes	—
74	C₈×C₄⋊C₄	—	73	1	no	maximal, Sylow
75	C₇₃	C₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₄⋊C₈	—	73	1	no	—
77	C₂×C₄×C₈	—	73	1	no	—
78	C₂×C₄×C₈	—	73	2	no	—
79	C₄×C₄⋊C₄	—	73	1	no	—
80	#336	—	73	2	no	—
81	C₂²×C₈	—	73	1	no	—
82	C₂²×C₈	—	73	1	no	—
83	C₂²×C₈	—	73	2	no	—
84	C₂×C₄⋊C₄	—	73	2	no	—
85	C₂×C₄²	—	73	1	no	—
86	C₂×C₄²	—	73	2	no	—
87	C₄⋊C₈	—	73	4	no	—
88	C₄×C₈	—	73	4	no	—
89	C₄×C₈	—	146	4	no	—
90	#95	—	73	1	no	—
91	#95	#64408	1	1	yes	characteristic
92	C₂²×C₄	—	73	1	no	—
93	C₂²×C₄	—	73	1	no	—
94	C₂²×C₄	—	73	2	no	—
95	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
96	C₂²×C₄	C₂×#64408	1	2	yes	—
97	C₂×C₈	—	73	2	no	—
98	C₂×C₈	—	73	2	no	—
99	C₂×C₈	—	73	2	no	—
100	C₂×C₈	—	73	2	no	—
101	C₂×C₈	—	73	4	no	—
102	C₂×C₈	—	146	2	no	—
103	C₂×C₈	—	146	1	no	—
104	C₂×C₈	—	146	2	no	—
105	C₂×C₈	—	146	1	no	—
106	C₄⋊C₄	—	73	8	no	—
107	C₄²	—	73	2	no	—
108	C₄²	—	73	2	no	—
109	C₄²	—	146	2	no	—
110	C₄²	—	146	2	no	—
111	C₂³	C₂²×#64408	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	73	1	no	—
116	C₂×C₄	—	73	1	no	—
117	C₂×C₄	—	73	4	no	—
118	C₂×C₄	—	73	1	no	—
119	C₂×C₄	—	73	1	no	—
120	C₂×C₄	—	73	2	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	73	1	no	—
123	C₂×C₄	—	73	4	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	—	146	2	no	—
126	C₂×C₄	C₄×#64408	1	2	yes	—
127	C₂×C₄	#11924036	1	4	yes	—
128	C₈	—	73	4	no	—
129	C₈	—	146	4	no	—
130	C₈	—	146	2	no	—
131	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
132	C₂²	D₄×#64408	1	1	yes	characteristic
133	C₂²	Q₈×#64408	1	1	yes	characteristic
134	C₂²	C₂×#11924036	1	2	yes	—
135	C₂²	#14556678	1	2	yes	—
136	C₄	—	2	2	no	—
137	C₄	—	2	4	no	—
138	C₄	—	73	1	no	—
139	C₄	—	73	1	no	—
140	C₄	—	73	1	no	—
141	C₄	—	73	1	no	—
142	C₄	—	73	4	no	—
143	C₄	—	146	4	no	—
144	C₂	C₄⋊C₄×#64408	1	1	yes	characteristic
145	C₂	C₄×#11924036	1	1	yes	characteristic
146	C₂	#17989551	1	1	yes	characteristic
147	C₂	#17989614	1	2	yes	—
148	C₂	#17989636	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556658

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂

yes

maximal

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

#17989453

C₂

yes

maximal

#17988438

C₂

yes

maximal, characteristic

C₂²×#10596833

C₂²

yes

characteristic

C₂²×#10596833

C₂²

yes

—

C₂²×#10596833

C₂²

yes

characteristic

#14556658

C₄

yes

complemented

C₄×#10596833

—

C₄×#10596833

C₄

yes

complemented

C₂×#11924007

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

C₄

yes

characteristic

#95×C₇₃

C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂×#10596833

D₄

yes

—

C₂×#10596833

Q₈

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

#11924007

C₈

yes

complemented

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

—

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

C₂×Dic₇₃

yes

C₂×Dic₇₃

yes

—

—

C₄⋊C₄

yes

complemented

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₂²×C₇₃

C₄×Q₈

yes

characteristic

C₂²×C₇₃

C₂²×C₈

yes

—

C₂²×C₇₃

#131

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

C₄×C₈

yes

complemented

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

#117

yes

characteristic

Dic₇₃

C₄×D₄

yes

characteristic

Dic₇₃

C₄×Q₈

yes

characteristic

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#405

yes

characteristic

C₂×C₇₃

C₈×D₄

yes

—

C₂×C₇₃

C₈×Q₈

yes

—

C₈×C₄⋊C₄

—

maximal, Sylow

C₇₃

C₈×C₄⋊C₄

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

146

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂²×C₄

C₂×#64408

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

146

—

103

C₂×C₈

—

146

—

104

C₂×C₈

—

146

—

105

C₂×C₈

—

146

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

146

—

110

C₄²

—

146

—

111

C₂³

C₂²×#64408

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

C₄×#64408

yes

—

127

C₂×C₄

#11924036

yes

—

128

C₈

—

129

C₈

—

146

—

130

C₈

—

146

—

131

C₂²

C₂×C₄×#64408

yes

characteristic

132

C₂²

D₄×#64408

yes

characteristic

133

C₂²

Q₈×#64408

yes

characteristic

134

C₂²

C₂×#11924036

yes

—

135

C₂²

#14556678

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

146

—

144

C₂

C₄⋊C₄×#64408

yes

characteristic

145

C₂

C₄×#11924036

yes

characteristic

146

C₂

#17989551

yes

characteristic

147

C₂

#17989614

yes

—

148

C₂

#17989636

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Fitting	#95×C₇₃	C₄
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	#95	#64408
hypocenter	C₇₃	C₈×C₄⋊C₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#64408

commutator

C₂×C₇₃

C₂×C₄×C₈

Fitting

#95×C₇₃

C₄

socle

C₂³×C₇₃

C₂²×C₄

C₇₃

C₈×C₄⋊C₄

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
9. #14556658	C₄	semidirect
11. C₄×#10596833	C₄	semidirect
29. #11924007	C₈	semidirect
55. #10596833	C₄⋊C₄	semidirect
64. Dic₇₃	C₄×C₈	semidirect
75. C₇₃	C₈×C₄⋊C₄	semidirect

H ≅ G/N

type

9. #14556658

C₄

semidirect

11. C₄×#10596833

C₄

semidirect

29. #11924007

C₈

semidirect

55. #10596833

C₄⋊C₄

semidirect

64. Dic₇₃

C₄×C₈

semidirect

75. C₇₃

C₈×C₄⋊C₄

semidirect

Subgroups — #22625723

Conjugacy classes of subgroups

Complements