Group #22627149 — subgroups

Subgroups — #22627149

Order 9344.

146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17989709	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989708	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989691	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989688	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989687	C₂	1	1	yes	maximal, characteristic, complemented
6	#64408⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989630	C₂	1	1	yes	maximal, characteristic
8	#14556688	—	2	1	no	—
9	#14556688	C₂²	1	1	yes	characteristic
10	#14556688	C₂²	1	1	yes	characteristic
11	#14556687	—	2	1	no	—
12	#14556686	—	2	1	no	—
13	#14556686	C₂²	1	1	yes	characteristic
14	#14556686	C₂²	1	1	yes	characteristic
15	C₂×#11924040	—	2	1	no	—
16	#14556679	C₂²	1	1	yes	characteristic
17	#14556678	C₂²	1	1	yes	characteristic
18	#14556661	C₄	1	1	yes	characteristic
19	#14556656	C₄	1	1	yes	characteristic
20	#14556655	C₄	1	1	yes	characteristic
21	C₈×#64408	C₂²	1	1	yes	characteristic
22	#14556612	C₄	1	1	yes	characteristic
23	#11924040	—	2	1	no	—
24	#11924040	—	2	1	no	—
25	#11924040	—	2	1	no	—
26	#11924040	D₄	1	1	yes	characteristic
27	#11924040	D₄	1	1	yes	characteristic
28	#11924038	—	2	1	no	—
29	#11924038	C₂×C₄	1	1	yes	characteristic
30	#11924038	C₂×C₄	1	1	yes	characteristic
31	#11924037	—	2	1	no	—
32	#11924036	—	2	1	no	—
33	#11924036	C₂³	1	1	yes	characteristic
34	C₂×#10596833	—	2	1	no	—
35	C₄×#64408	C₂×C₄	1	1	yes	characteristic
36	#11924029	C₂×C₄	1	1	yes	characteristic
37	#11924027	C₂×C₄	1	1	yes	characteristic
38	#11924018	C₈	1	1	yes	characteristic
39	#11924017	C₈	1	1	yes	characteristic
40	#11924013	C₈	1	1	yes	characteristic
41	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
42	SD₁₆×C₇₃	C₈	1	1	yes	characteristic
43	C₂×#64408	—	2	1	no	—
44	Q₈×C₇₃	C₂×C₈	1	1	yes	characteristic
45	D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
46	C₂²⋊D₇₃	—	2	1	no	—
47	C₂×Dic₇₃	—	2	1	no	—
48	D₂₉₂	—	2	1	no	—
49	D₂₉₂	C₂×C₈	1	1	yes	characteristic
50	C₄×D₇₃	—	2	1	no	—
51	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
52	Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
53	#10596833	—	2	1	no	—
54	#10596833	—	2	1	no	—
55	#10596833	C₂×D₄	1	1	yes	characteristic
56	#10596833	#41	1	1	yes	characteristic
57	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
58	#10596831	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₇₃	—	2	1	no	—
60	C₂×D₇₃	—	2	1	no	—
61	C₂×D₇₃	#131	1	1	yes	characteristic
62	#64408	—	2	2	no	—
63	C₄×C₇₃	—	2	1	no	—
64	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
65	Dic₇₃	—	2	1	no	—
66	Dic₇₃	C₄×D₄	1	1	yes	characteristic
67	C₂×C₇₃	—	4	1	no	—
68	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
69	D₇₃	—	2	1	no	—
70	D₇₃	—	4	1	no	—
71	#2170	—	73	1	no	maximal, Sylow
72	C₇₃	#2170	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	C₄×C₁₆	—	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	—	73	1	no	—
94	C₄×C₈	—	73	1	no	—
95	#41	—	73	1	no	—
96	#41	—	73	1	no	—
97	Q₁₆	—	73	1	no	—
98	SD₁₆	—	73	1	no	—
99	SD₁₆	#10596842	1	1	yes	characteristic
100	D₈	—	73	1	no	—
101	M₁₆	—	73	1	no	—
102	M₁₆	—	73	1	no	—
103	M₁₆	—	146	1	no	—
104	M₁₆	—	146	1	no	—
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	—	73	1	no	—
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	C₂×#10596842	1	1	yes	characteristic
117	D₄	—	73	1	no	—
118	D₄	—	146	1	no	—
119	D₄	—	146	1	no	—
120	D₄	C₂×#10596842	1	1	yes	characteristic
121	C₂×C₄	—	73	1	no	—
122	C₂×C₄	—	146	1	no	—
123	C₂×C₄	—	146	1	no	—
124	C₂×C₄	—	146	1	no	—
125	C₈	—	73	1	no	—
126	C₈	—	73	1	no	—
127	C₈	—	73	1	no	—
128	C₈	—	146	1	no	—
129	C₈	—	146	1	no	—
130	C₈	C₂×#10596842	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	73	1	no	—
133	C₂²	—	146	1	no	—
134	C₄	—	2	1	no	—
135	C₄	—	73	1	no	—
136	C₄	—	146	2	no	—
137	C₄	—	146	1	no	—
138	C₄	C₂²×#10596842	1	1	yes	characteristic
139	C₂	—	4	1	no	—
140	C₂	—	292	1	no	—
141	C₂	—	146	1	no	—
142	C₂	D₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989709

C₂

yes

maximal, characteristic, complemented

#17989708

C₂

yes

maximal, characteristic, complemented

#17989691

C₂

yes

maximal, characteristic, complemented

#17989688

C₂

yes

maximal, characteristic, complemented

#17989687

C₂

yes

maximal, characteristic, complemented

#64408⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#17989630

C₂

yes

maximal, characteristic

#14556688

—

#14556688

C₂²

yes

characteristic

#14556688

C₂²

yes

—

—

C₂²

yes

characteristic

#14556686

C₂²

yes

characteristic

C₂×#11924040

—

#14556679

C₂²

yes

characteristic

#14556678

C₂²

yes

characteristic

#14556661

C₄

yes

characteristic

#14556656

C₄

yes

characteristic

#14556655

C₄

yes

characteristic

C₈×#64408

C₂²

yes

characteristic

#14556612

C₄

yes

—

—

—

D₄

yes

characteristic

#11924040

D₄

yes

characteristic

#11924038

—

#11924038

C₂×C₄

yes

characteristic

#11924038

C₂×C₄

yes

—

—

C₂³

yes

characteristic

C₂×#10596833

—

C₄×#64408

C₂×C₄

yes

characteristic

#11924029

C₂×C₄

yes

characteristic

#11924027

C₂×C₄

yes

characteristic

#11924018

C₈

yes

characteristic

#11924017

C₈

yes

characteristic

#11924013

C₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

SD₁₆×C₇₃

C₈

yes

characteristic

C₂×#64408

—

Q₈×C₇₃

C₂×C₈

yes

characteristic

D₄×C₇₃

C₂×C₈

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

C₂×C₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

Dic₁₄₆

C₂×C₈

yes

—

—

C₂×D₄

yes

yes

C₈×C₇₃

C₂×C₈

yes

characteristic

#10596831

C₂×C₈

yes

characteristic

C₂²×C₇₃

—

C₂×D₇₃

—

C₂×D₇₃

#131

yes

characteristic

#64408

—

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄×D₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₈×D₄

yes

characteristic

D₇₃

—

D₇₃

—

#2170

—

maximal, Sylow

C₇₃

#2170

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

C₄×C₁₆

—

#135

—

#131

—

#131

—

M₃₂

—

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

#108

—

#104

—

#104

—

C₄×C₈

—

#41

—

#41

—

Q₁₆

—

SD₁₆

—

SD₁₆

#10596842

yes

characteristic

100

D₈

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

146

—

104

M₁₆

—

146

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

146

—

108

C₂×C₈

—

146

—

109

C₄²

—

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

146

—

113

C₁₆

—

146

—

114

C₁₆

—

146

—

115

Q₈

—

116

Q₈

C₂×#10596842

yes

characteristic

117

D₄

—

118

D₄

—

146

—

119

D₄

—

146

—

120

D₄

C₂×#10596842

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

146

—

123

C₂×C₄

—

146

—

124

C₂×C₄

—

146

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

146

—

129

C₈

—

146

—

130

C₈

C₂×#10596842

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

—

146

—

134

C₄

—

135

C₄

—

136

C₄

—

146

—

137

C₄

—

146

—

138

C₄

C₂²×#10596842

yes

characteristic

139

C₂

—

140

C₂

—

292

—

141

C₂

—

146

—

142

C₂

D₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#10596842
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄	C₂²×#10596842
Fitting	SD₁₆×C₇₃	C₈
socle	C₂×C₇₃	C₈×D₄
hypercenter	SD₁₆	#10596842
hypocenter	C₇₃	#2170
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

subgroup

G/H

center

C₂

D₄×#10596842

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄

C₂²×#10596842

Fitting

SD₁₆×C₇₃

C₈

socle

C₂×C₇₃

C₈×D₄

SD₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

N	H ≅ G/N	type
1. #17989709	C₂	semidirect
2. #17989708	C₂	semidirect
3. #17989691	C₂	semidirect
4. #17989688	C₂	semidirect
5. #17989687	C₂	semidirect
6. #64408⋊C₁₆	C₂	semidirect
72. C₇₃	#2170	semidirect

H ≅ G/N

type

1. #17989709

C₂

semidirect

2. #17989708

C₂

semidirect

3. #17989691

C₂

semidirect

4. #17989688

C₂

semidirect

5. #17989687

C₂

semidirect

6. #64408⋊C₁₆

C₂

semidirect

72. C₇₃

#2170

semidirect

Subgroups — #22627149

Conjugacy classes of subgroups

Complements