Group #22625379 — subgroups

Subgroups — C₂×#17989444 #22625379

Order 9344.

232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 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×#14556646	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556646	C₂	1	1	yes	maximal, characteristic
3	#17989444	C₂	1	4	yes	maximal, direct product factor
4	C₂×#14556582	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596833	—	2	1	no	—
6	C₂²×#10596833	—	2	1	no	—
7	#14556646	—	2	1	no	—
8	#14556646	—	2	1	no	—
9	#14556646	C₂²	1	2	yes	—
10	#14556646	C₂²	1	2	yes	—
11	#14556582	—	2	1	no	—
12	#14556582	—	2	1	no	—
13	#14556582	C₄	1	2	yes	—
14	#14556582	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₇₃	—	2	1	no	—
16	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
17	C₂×#11924007	—	2	1	no	—
18	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
20	C₂×#10596833	—	2	4	no	—
21	C₂×#10596833	—	2	4	no	—
22	C₂×#10596833	—	2	2	no	—
23	C₂×#10596833	—	2	2	no	—
24	C₂²×Dic₇₃	—	2	1	no	—
25	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
26	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
27	C₄⋊Dic₇₃	—	2	1	no	—
28	C₄⋊Dic₇₃	—	2	2	no	—
29	C₄⋊Dic₇₃	—	2	2	no	—
30	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
31	#11924007	—	2	2	no	—
32	#11924007	—	2	2	no	—
33	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
34	C₄×Dic₇₃	D₄	1	1	yes	characteristic
35	C₄×Dic₇₃	D₄	1	1	yes	characteristic
36	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₇₃	—	2	1	no	—
38	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₄⋊C₄×C₇₃	—	2	1	no	—
40	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
41	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₇₃	—	2	2	no	—
43	C₂×C₄×C₇₃	—	2	2	no	—
44	C₂×C₄×C₇₃	—	4	2	no	—
45	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₇₃	—	2	2	no	—
48	C₂×Dic₇₃	—	2	2	no	—
49	C₂×Dic₇₃	—	2	2	no	—
50	C₂×Dic₇₃	—	4	2	no	—
51	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
55	#10596833	—	2	4	no	—
56	#10596833	—	2	4	no	—
57	C₂²×C₇₃	#101	1	2	yes	—
58	C₂²×C₇₃	#104	1	2	yes	—
59	C₂²×C₇₃	#104	1	2	yes	—
60	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄×C₇₃	—	2	1	no	—
62	C₄×C₇₃	—	2	1	no	—
63	C₄×C₇₃	—	4	2	no	—
64	Dic₇₃	—	2	1	no	—
65	Dic₇₃	—	2	1	no	—
66	Dic₇₃	—	2	1	no	—
67	Dic₇₃	—	2	1	no	—
68	Dic₇₃	—	4	2	no	—
69	C₂×C₇₃	#330	1	4	yes	complemented
70	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
71	C₂×C₇₃	C₂×#104	1	1	yes	characteristic
72	C₂×C₇₃	C₂×#104	1	1	yes	characteristic
73	C₂×#330	—	73	1	no	maximal, Sylow
74	C₇₃	C₂×#330	1	1	yes	characteristic, complemented, Sylow
75	C₂×#125	—	73	1	no	—
76	C₂×#97	—	73	1	no	—
77	C₂×#97	—	73	1	no	—
78	#330	—	73	4	no	—
79	C₂²×C₈	—	146	1	no	—
80	C₂²×C₈	—	146	1	no	—
81	#125	—	73	2	no	—
82	#125	—	73	2	no	—
83	#125	—	146	1	no	—
84	#125	—	146	1	no	—
85	C₂×C₄⋊C₄	—	73	1	no	—
86	C₂×C₄⋊C₄	—	146	1	no	—
87	C₂×C₄⋊C₄	—	146	1	no	—
88	C₂×C₄⋊C₄	#64408	1	1	yes	characteristic
89	C₂×C₄²	—	73	1	no	—
90	#97	—	73	2	no	—
91	#97	—	73	2	no	—
92	#97	—	146	1	no	—
93	#97	—	146	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	73	1	no	—
96	C₂²×C₄	—	73	1	no	—
97	C₂²×C₄	—	146	1	no	—
98	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
99	C₂×C₈	—	146	2	no	—
100	C₂×C₈	—	146	2	no	—
101	C₂×C₈	—	146	4	no	—
102	C₂×C₈	—	146	4	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	73	2	no	—
105	C₄⋊C₄	—	146	2	no	—
106	C₄⋊C₄	—	146	2	no	—
107	C₄⋊C₄	—	146	2	no	—
108	C₄⋊C₄	—	146	2	no	—
109	C₄⋊C₄	—	146	1	no	—
110	C₄⋊C₄	C₂×#64408	1	2	yes	—
111	C₄²	—	73	1	no	—
112	C₄²	—	73	1	no	—
113	C₄²	—	73	1	no	—
114	C₄²	—	73	1	no	—
115	C₂³	C₂²⋊#64408	1	1	yes	characteristic
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	292	2	no	—
120	C₂×C₄	—	73	1	no	—
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	73	1	no	—
123	C₂×C₄	—	73	1	no	—
124	C₂×C₄	—	146	2	no	—
125	C₂×C₄	—	146	2	no	—
126	C₂×C₄	—	146	2	no	—
127	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
128	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
129	C₈	—	146	4	no	—
130	C₈	—	146	4	no	—
131	C₂²	#14556652	1	2	yes	—
132	C₂²	#14556655	1	2	yes	—
133	C₂²	#14556656	1	2	yes	—
134	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	2	1	no	—
137	C₄	—	4	2	no	—
138	C₄	—	292	2	no	—
139	C₄	—	146	1	no	—
140	C₄	—	146	1	no	—
141	C₄	—	146	1	no	—
142	C₄	—	146	1	no	—
143	C₂	#17989444	1	4	yes	direct product factor
144	C₂	C₂×#14556652	1	1	yes	characteristic
145	C₂	C₂×#14556655	1	1	yes	characteristic
146	C₂	C₂×#14556656	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556646

C₂

yes

maximal, characteristic

C₂×#14556646

C₂

yes

maximal, characteristic

#17989444

C₂

yes

maximal, direct product factor

C₂×#14556582

C₂

yes

maximal, characteristic

—

—

—

—

C₂²

yes

—

#14556646

C₂²

yes

—

#14556582

—

#14556582

—

#14556582

C₄

yes

—

#14556582

C₂²

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

C₂×#11924007

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₄

yes

—

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

#10596833

—

#10596833

—

C₂²×C₇₃

#101

yes

—

C₂²×C₇₃

#104

yes

—

C₂²×C₇₃

#104

yes

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×#97

—

C₂×#97

—

#330

—

C₂²×C₈

—

146

—

C₂²×C₈

—

146

—

#125

—

#125

—

#125

—

146

—

#125

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

#64408

yes

characteristic

C₂×C₄²

—

#97

—

#97

—

#97

—

146

—

#97

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

146

—

100

C₂×C₈

—

146

—

101

C₂×C₈

—

146

—

102

C₂×C₈

—

146

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

146

—

106

C₄⋊C₄

—

146

—

107

C₄⋊C₄

—

146

—

108

C₄⋊C₄

—

146

—

109

C₄⋊C₄

—

146

—

110

C₄⋊C₄

C₂×#64408

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₂³

C₂²⋊#64408

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

292

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

146

—

125

C₂×C₄

—

146

—

126

C₂×C₄

—

146

—

127

C₂×C₄

C₂²⋊#64408

yes

characteristic

128

C₂×C₄

C₂²×#64408

yes

characteristic

129

C₈

—

146

—

130

C₈

—

146

—

131

C₂²

#14556652

yes

—

132

C₂²

#14556655

yes

—

133

C₂²

#14556656

yes

—

134

C₂²

C₂×C₂²⋊#64408

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

292

—

139

C₄

—

146

—

140

C₄

—

146

—

141

C₄

—

146

—

142

C₄

—

146

—

143

C₂

#17989444

yes

direct product factor

144

C₂

C₂×#14556652

yes

characteristic

145

C₂

C₂×#14556655

yes

characteristic

146

C₂

C₂×#14556656

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×C₄⋊C₄×C₇₃	C₄
socle	C₂³×C₇₃	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#64408
hypocenter	C₇₃	C₂×#330
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂×C₄⋊C₄×C₇₃

C₄

socle

C₂³×C₇₃

C₂²⋊C₄

C₂×C₄⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
3. #17989444	C₂	direct (N × H)
69. C₂×C₇₃	#330	semidirect
74. C₇₃	C₂×#330	semidirect
143. C₂	#17989444	direct (N × H)

H ≅ G/N

type

3. #17989444

C₂

direct (N × H)

69. C₂×C₇₃

#330

semidirect

74. C₇₃

C₂×#330

semidirect

143. C₂

#17989444

direct (N × H)

Subgroups — C₂×#17989444 #22625379

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989444 #22625379

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989444 #22625379