Group #22626322 — subgroups

Subgroups — #22626322

Order 9344.

144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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	#17989646	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989645	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989510	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989486	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989485	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989475	C₂	1	1	yes	maximal, characteristic, complemented
7	#17988701	C₂	1	1	yes	maximal, characteristic
8	#14556666	—	2	1	no	—
9	#14556665	—	2	1	no	—
10	#14556665	C₂²	1	1	yes	characteristic
11	#14556665	C₂²	1	1	yes	characteristic
12	#14556664	—	2	1	no	—
13	C₂×#11924031	—	2	1	no	—
14	C₂×#11924031	C₂²	1	1	yes	characteristic
15	C₂×#11924031	C₂²	1	1	yes	characteristic
16	#14556611	C₄	1	1	yes	characteristic
17	#14556599	C₂²	1	1	yes	characteristic
18	#14556598	C₂²	1	1	yes	characteristic
19	#14556526	C₄	1	1	yes	characteristic
20	#14556519	C₄	1	1	yes	characteristic
21	C₄×#10596831	C₂²	1	1	yes	characteristic
22	#104×C₇₃	C₄	1	1	yes	characteristic
23	#11924031	—	2	1	no	—
24	#11924031	—	2	1	no	—
25	#11924031	—	2	1	no	—
26	#11924031	D₄	1	1	yes	characteristic
27	#11924031	D₄	1	1	yes	characteristic
28	#11924028	C₂×C₄	1	1	yes	characteristic
29	#11924018	C₈	1	1	yes	characteristic
30	#11924016	C₈	1	1	yes	characteristic
31	#11924015	C₈	1	1	yes	characteristic
32	#11924013	C₈	1	1	yes	characteristic
33	#11924012	—	2	1	no	—
34	#11924012	C₂×C₄	1	1	yes	characteristic
35	#11924011	—	2	1	no	—
36	C₂×#10596831	—	2	1	no	—
37	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
38	C₂×#10596831	C₂³	1	1	yes	characteristic
39	C₈×D₇₃	—	2	1	no	—
40	#41×C₇₃	C₂×C₄	1	1	yes	characteristic
41	M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
42	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
43	Q₈×C₇₃	C₂×C₈	1	1	yes	characteristic
44	D₄×C₇₃	—	2	1	no	—
45	D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₇₃	—	2	1	no	—
47	C₂×C₄×C₇₃	—	2	1	no	—
48	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²⋊D₇₃	—	2	1	no	—
50	D₂₉₂	C₂×C₈	1	1	yes	characteristic
51	C₄×D₇₃	—	2	1	no	—
52	Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
53	C₈×C₇₃	—	2	1	no	—
54	#10596831	—	2	1	no	—
55	#10596831	C₂×C₈	1	1	yes	characteristic
56	#10596831	C₂×C₈	1	1	yes	characteristic
57	#10596831	C₂×D₄	1	1	yes	characteristic
58	#10596831	#41	1	1	yes	characteristic
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	#131	1	1	yes	characteristic
61	C₂×D₇₃	—	2	1	no	—
62	C₄×C₇₃	—	2	1	no	—
63	C₄×C₇₃	—	4	1	no	—
64	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
65	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
66	Dic₇₃	—	2	1	no	—
67	C₂×C₇₃	—	2	1	no	—
68	C₂×C₇₃	—	4	1	no	—
69	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
70	D₇₃	—	4	1	no	—
71	#2171	—	73	1	no	maximal, Sylow
72	C₇₃	#2171	1	1	yes	characteristic, complemented, Sylow
73	#504	—	73	1	no	—
74	#504	—	73	1	no	—
75	#443	—	73	1	no	—
76	#364	—	73	1	no	—
77	#350	—	73	1	no	—
78	#350	—	73	1	no	—
79	#346	—	73	1	no	—
80	#135	—	73	1	no	—
81	#131	—	73	1	no	—
82	#131	—	73	1	no	—
83	M₃₂	—	73	1	no	—
84	M₃₂	—	73	1	no	—
85	M₃₂	—	146	1	no	—
86	M₃₂	—	146	1	no	—
87	C₂×C₁₆	—	73	1	no	—
88	C₂×C₁₆	—	73	1	no	—
89	C₂×C₁₆	—	146	1	no	—
90	C₂×C₁₆	—	146	1	no	—
91	#108	—	73	1	no	—
92	#104	—	73	1	no	—
93	#104	#64408	1	1	yes	characteristic
94	C₄×C₈	—	73	1	no	—
95	#41	—	73	1	no	—
96	#41	C₂×#64408	1	1	yes	characteristic
97	Q₁₆	—	73	1	no	—
98	SD₁₆	—	73	1	no	—
99	SD₁₆	—	73	1	no	—
100	D₈	—	73	1	no	—
101	M₁₆	—	73	1	no	—
102	M₁₆	—	146	1	no	—
103	M₁₆	—	146	1	no	—
104	M₁₆	C₂×#64408	1	1	yes	characteristic
105	C₂×C₈	—	73	1	no	—
106	C₂×C₈	—	73	1	no	—
107	C₂×C₈	—	146	1	no	—
108	C₂×C₈	—	146	1	no	—
109	C₄²	C₂×#64408	1	1	yes	characteristic
110	C₁₆	—	73	1	no	—
111	C₁₆	—	73	1	no	—
112	C₁₆	—	146	1	no	—
113	C₁₆	—	146	1	no	—
114	C₁₆	—	146	1	no	—
115	Q₈	—	73	1	no	—
116	Q₈	#11924036	1	1	yes	characteristic
117	D₄	—	2	1	no	—
118	D₄	—	73	1	no	—
119	D₄	—	146	1	no	—
120	D₄	#11924036	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	146	1	no	—
124	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	73	1	no	—
127	C₈	—	73	1	no	—
128	C₈	—	73	1	no	—
129	C₈	—	73	1	no	—
130	C₈	—	146	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	146	1	no	—
133	C₂²	#14556678	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	4	1	no	—
136	C₄	—	146	1	no	—
137	C₄	D₄×#64408	1	1	yes	characteristic
138	C₄	C₂×#11924036	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	292	1	no	—
142	C₂	#17989614	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989646

C₂

yes

maximal, characteristic, complemented

#17989645

C₂

yes

maximal, characteristic, complemented

#17989510

C₂

yes

maximal, characteristic, complemented

#17989486

C₂

yes

maximal, characteristic, complemented

#17989485

C₂

yes

maximal, characteristic, complemented

#17989475

C₂

yes

maximal, characteristic, complemented

#17988701

C₂

yes

maximal, characteristic

#14556666

—

#14556665

—

#14556665

C₂²

yes

characteristic

#14556665

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

#14556611

C₄

yes

characteristic

#14556599

C₂²

yes

characteristic

#14556598

C₂²

yes

characteristic

#14556526

C₄

yes

characteristic

#14556519

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

#104×C₇₃

C₄

yes

—

—

—

D₄

yes

characteristic

#11924031

D₄

yes

characteristic

#11924028

C₂×C₄

yes

characteristic

#11924018

C₈

yes

characteristic

#11924016

C₈

yes

characteristic

#11924015

C₈

yes

characteristic

#11924013

C₈

yes

characteristic

#11924012

—

#11924012

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

—

#41×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

Q₈×C₇₃

C₂×C₈

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²⋊D₇₃

—

D₂₉₂

C₂×C₈

yes

characteristic

C₄×D₇₃

—

Dic₁₄₆

C₂×C₈

yes

characteristic

C₈×C₇₃

—

#10596831

—

#10596831

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

#10596831

C₂×D₄

yes

yes

C₂²×C₇₃

—

C₂²×C₇₃

#131

yes

characteristic

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

—

#2171

—

maximal, Sylow

C₇₃

#2171

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

—

—

—

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

—

—

yes

C₄×C₈

—

—

yes

Q₁₆

—

SD₁₆

—

SD₁₆

—

100

D₈

—

101

M₁₆

—

102

M₁₆

—

146

—

103

M₁₆

—

146

—

104

M₁₆

C₂×#64408

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

146

—

108

C₂×C₈

—

146

—

109

C₄²

C₂×#64408

yes

characteristic

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

146

—

113

C₁₆

—

146

—

114

C₁₆

—

146

—

115

Q₈

—

116

Q₈

#11924036

yes

characteristic

117

D₄

—

118

D₄

—

119

D₄

—

146

—

120

D₄

#11924036

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

146

—

124

C₂×C₄

C₂²×#64408

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

146

—

131

C₂²

—

132

C₂²

—

146

—

133

C₂²

#14556678

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

146

—

137

C₄

D₄×#64408

yes

characteristic

138

C₄

C₂×#11924036

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

292

—

142

C₂

#17989614

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#64408
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	#104×C₇₃	C₄
socle	C₂×C₇₃	C₈×D₄
hypercenter	#104	#64408
hypocenter	C₇₃	#2171
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #104

subgroup

G/H

center

C₄

D₄×#64408

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×#64408

Fitting

#104×C₇₃

C₄

socle

C₂×C₇₃

C₈×D₄

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #104

N	H ≅ G/N	type
1. #17989646	C₂	semidirect
2. #17989645	C₂	semidirect
3. #17989510	C₂	semidirect
4. #17989486	C₂	semidirect
5. #17989485	C₂	semidirect
6. #17989475	C₂	semidirect
72. C₇₃	#2171	semidirect

H ≅ G/N

type

1. #17989646

C₂

semidirect

2. #17989645

C₂

semidirect

3. #17989510

C₂

semidirect

4. #17989486

C₂

semidirect

5. #17989485

C₂

semidirect

6. #17989475

C₂

semidirect

72. C₇₃

#2171

semidirect

Subgroups — #22626322

Conjugacy classes of subgroups

Complements