Group #23765519 — subgroups

Subgroups — #23765519

Order 10112.

148 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579102	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098981	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098834	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098830	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098392	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098377	C₂	1	1	yes	maximal, characteristic, complemented
7	#361×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#14579189	—	2	1	no	—
9	#14579187	—	2	1	no	—
10	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
11	#14579167	C₂²	1	1	yes	characteristic
12	#14579102	—	2	1	no	—
13	#14579102	—	2	1	no	—
14	#14579100	—	2	1	no	—
15	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₁₆×D₇₉	—	2	1	no	—
17	#14579097	C₂²	1	1	yes	characteristic
18	#14579078	—	2	1	no	—
19	#14579077	—	2	1	no	—
20	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
21	M₃₂×C₇₉	C₂²	1	1	yes	characteristic
22	#108×C₇₉	C₂²	1	1	yes	characteristic
23	#11929624	D₄	1	1	yes	characteristic
24	C₂×D₃₁₆	—	2	1	no	—
25	#11929613	—	4	1	no	—
26	#11929612	—	4	1	no	—
27	D₆₃₂	—	2	1	no	—
28	D₆₃₂	—	2	1	no	—
29	D₆₃₂	—	4	1	no	—
30	#11929609	—	4	1	no	—
31	#11929608	—	2	1	no	—
32	#11929608	D₄	1	1	yes	characteristic
33	#11929607	—	2	1	no	—
34	C₈×D₇₉	—	2	1	no	—
35	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
36	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
37	C₂×D₄×C₇₉	—	2	1	no	—
38	D₈×C₇₉	—	2	1	no	—
39	D₈×C₇₉	—	2	1	no	—
40	M₁₆×C₇₉	—	2	1	no	—
41	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
42	C₁₆×C₇₉	—	2	1	no	—
43	C₂³×C₇₉	—	4	1	no	—
44	C₂²×D₇₉	—	4	1	no	—
45	D₄×C₇₉	—	4	1	no	—
46	D₄×C₇₉	—	4	1	no	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂²⋊D₇₉	—	2	1	no	—
49	D₃₁₆	—	4	1	no	—
50	D₃₁₆	—	4	1	no	—
51	D₃₁₆	D₈	1	1	yes	characteristic
52	C₄×D₇₉	—	2	1	no	—
53	Dic₁₅₈	D₈	1	1	yes	characteristic
54	C₈×C₇₉	—	4	1	no	—
55	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
56	C₈×C₇₉	#41	1	1	yes	characteristic
57	C₇₉⋊C₈	—	2	1	no	—
58	C₇₉⋊C₈	—	4	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	—	16	1	no	—
61	C₂²×C₇₉	#135	1	1	yes	characteristic
62	C₂×D₇₉	—	2	1	no	—
63	C₂×D₇₉	—	8	1	no	—
64	C₂×D₇₉	—	16	1	no	—
65	C₄×C₇₉	#121	1	1	yes	characteristic
66	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
67	Dic₇₉	—	2	1	no	—
68	C₂×C₇₉	—	2	1	no	—
69	C₂×C₇₉	—	16	1	no	—
70	C₂×C₇₉	#466	1	1	yes	characteristic
71	D₇₉	—	4	1	no	—
72	D₇₉	—	16	1	no	—
73	#2221	—	79	1	no	maximal, Sylow
74	C₇₉	#2221	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₁₆	—	79	1	no	—
76	#504	—	79	1	no	—
77	#472	—	79	1	no	—
78	#472	—	79	1	no	—
79	#368	—	79	1	no	—
80	#361	—	79	1	no	—
81	#361	D₇₉	1	1	yes	characteristic, complemented
82	AGL(1,ℤ/8)	—	158	1	no	—
83	AGL(1,ℤ/8)	—	158	1	no	—
84	C₂×D₈	—	79	1	no	—
85	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
86	#131	—	79	1	no	—
87	D₁₆	—	158	1	no	—
88	D₁₆	—	158	1	no	—
89	M₃₂	—	158	1	no	—
90	M₃₂	C₂×D₇₉	1	1	yes	characteristic
91	C₂×C₁₆	—	79	1	no	—
92	C₂×C₁₆	—	158	1	no	—
93	#108	—	79	1	no	—
94	#108	C₂×D₇₉	1	1	yes	characteristic
95	#100	—	158	1	no	—
96	#100	—	158	1	no	—
97	#41	—	79	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	158	1	no	—
100	SD₁₆	—	316	1	no	—
101	SD₁₆	—	316	1	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	316	1	no	—
105	D₈	—	316	1	no	—
106	D₈	—	158	1	no	—
107	D₈	—	158	1	no	—
108	M₁₆	—	2	1	no	—
109	M₁₆	—	79	1	no	—
110	M₁₆	—	158	1	no	—
111	M₁₆	—	158	1	no	—
112	C₂×C₈	—	158	1	no	—
113	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
114	C₁₆	—	2	1	no	—
115	C₁₆	—	79	1	no	—
116	C₁₆	—	79	1	no	—
117	C₂³	—	4	1	no	—
118	C₂³	—	316	1	no	—
119	Q₈	—	79	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	316	1	no	—
123	D₄	—	316	1	no	—
124	D₄	—	79	1	no	—
125	D₄	—	158	1	no	—
126	C₂×C₄	—	158	1	no	—
127	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
128	C₈	—	4	1	no	—
129	C₈	—	316	1	no	—
130	C₈	—	158	1	no	—
131	C₈	D₄×D₇₉	1	1	yes	characteristic
132	C₈	#11929624	1	1	yes	characteristic
133	C₂²	—	8	1	no	—
134	C₂²	—	16	1	no	—
135	C₂²	—	632	1	no	—
136	C₂²	—	158	1	no	—
137	C₂²	—	1264	1	no	—
138	C₂²	#14579182	1	1	yes	characteristic
139	C₄	—	158	1	no	—
140	C₄	#14579134	1	1	yes	characteristic
141	C₄	D₈×D₇₉	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	16	1	no	—
144	C₂	—	316	1	no	—
145	C₂	—	1264	1	no	—
146	C₂	#19098798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579102

C₂

yes

maximal, characteristic, complemented

#19098981

C₂

yes

maximal, characteristic, complemented

#19098834

C₂

yes

maximal, characteristic, complemented

#19098830

C₂

yes

maximal, characteristic, complemented

#19098392

C₂

yes

maximal, characteristic, complemented

#19098377

C₂

yes

maximal, characteristic, complemented

#361×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579189

—

#14579187

—

C₂×D₆₃₂

C₂²

yes

characteristic

#14579167

C₂²

yes

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₇₉

—

#14579097

C₂²

yes

characteristic

#14579078

—

#14579077

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

characteristic

#108×C₇₉

C₂²

yes

characteristic

#11929624

D₄

yes

characteristic

C₂×D₃₁₆

—

#11929613

—

#11929612

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

—

#11929609

—

#11929608

—

#11929608

D₄

yes

characteristic

#11929607

—

C₈×D₇₉

—

C₇₉⋊C₁₆

D₄

yes

characteristic

C₇₉⋊C₁₆

D₄

yes

characteristic

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²⋊D₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

D₈

yes

characteristic

C₄×D₇₉

—

Dic₁₅₈

D₈

yes

characteristic

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#135

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

#121

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#466

yes

characteristic

D₇₉

—

D₇₉

—

#2221

—

maximal, Sylow

C₇₉

#2221

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

—

—

—

—

—

D₇₉

yes

characteristic, complemented

AGL(1,ℤ/8)

—

158

—

AGL(1,ℤ/8)

—

158

—

C₂×D₈

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#131

—

D₁₆

—

158

—

D₁₆

—

158

—

M₃₂

—

158

—

M₃₂

C₂×D₇₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

158

—

#108

—

#108

C₂×D₇₉

yes

characteristic

#100

—

158

—

#100

—

158

—

#41

—

C₂×D₄

—

C₂×D₄

—

158

—

100

SD₁₆

—

316

—

101

SD₁₆

—

316

—

102

D₈

—

103

D₈

—

104

D₈

—

316

—

105

D₈

—

316

—

106

D₈

—

158

—

107

D₈

—

158

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

158

—

111

M₁₆

—

158

—

112

C₂×C₈

—

158

—

113

C₂×C₈

C₂²×D₇₉

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₁₆

—

117

C₂³

—

118

C₂³

—

316

—

119

Q₈

—

120

D₄

—

121

D₄

—

122

D₄

—

316

—

123

D₄

—

316

—

124

D₄

—

125

D₄

—

158

—

126

C₂×C₄

—

158

—

127

C₂×C₄

D₄×D₇₉

yes

characteristic

128

C₈

—

129

C₈

—

316

—

130

C₈

—

158

—

131

C₈

D₄×D₇₉

yes

characteristic

132

C₈

#11929624

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

632

—

136

C₂²

—

158

—

137

C₂²

—

1264

—

138

C₂²

#14579182

yes

characteristic

139

C₄

—

158

—

140

C₄

#14579134

yes

characteristic

141

C₄

D₈×D₇₉

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

—

316

—

145

C₂

—

1264

—

146

C₂

#19098798

yes

characteristic

	subgroup	G/H
center	C₂	#19098798
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#361×C₇₉	C₂
socle	C₂×C₇₉	#466
hypercenter	#361	D₇₉
hypocenter	C₇₉	#2221
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

subgroup

G/H

center

C₂

#19098798

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#361×C₇₉

C₂

C₂×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

N	H ≅ G/N	type
1. C₂×#14579102	C₂	semidirect
2. #19098981	C₂	semidirect
3. #19098834	C₂	semidirect
4. #19098830	C₂	semidirect
5. #19098392	C₂	semidirect
6. #19098377	C₂	semidirect
7. #361×C₇₉	C₂	semidirect
74. C₇₉	#2221	semidirect
81. #361	D₇₉	semidirect

H ≅ G/N

type

1. C₂×#14579102

C₂

semidirect

2. #19098981

C₂

semidirect

3. #19098834

C₂

semidirect

4. #19098830

C₂

semidirect

5. #19098392

C₂

semidirect

6. #19098377

C₂

semidirect

7. #361×C₇₉

C₂

semidirect

74. C₇₉

#2221

semidirect

81. #361

D₇₉

semidirect

Subgroups — #23765519

Conjugacy classes of subgroups

Complements