Group #23765475 — subgroups

Subgroups — #23765475

Order 10112.

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

normal subgroups only

This group has 170 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	#19099001	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098999	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098938	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098679	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098383	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098375	C₂	1	1	yes	maximal, characteristic, complemented
7	#361×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#14579183	C₂²	1	1	yes	characteristic
9	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
10	C₂×#11929609	—	2	1	no	—
11	#14579169	—	2	1	no	—
12	#14579157	—	2	1	no	—
13	#14579106	—	2	1	no	—
14	#14579105	—	2	1	no	—
15	D₁₂₆₄	—	2	1	no	—
16	#14579102	—	2	1	no	—
17	#14579101	C₂²	1	1	yes	characteristic
18	#14579087	—	2	1	no	—
19	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
24	C₂×D₃₁₆	—	2	1	no	—
25	C₂×C₂²⋊D₇₉	—	4	2	no	—
26	Dic₃₁₆	D₄	1	1	yes	characteristic, complemented
27	#11929613	—	2	1	no	—
28	D₆₃₂	—	2	1	no	—
29	D₆₃₂	—	2	1	no	—
30	D₆₃₂	D₄	1	1	yes	characteristic, complemented
31	#11929609	—	4	1	no	—
32	#11929609	—	4	1	no	—
33	#11929607	—	4	1	no	—
34	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
35	C₈×D₇₉	—	4	1	no	—
36	C₄×Dic₇₉	D₄	1	1	yes	characteristic
37	C₇₉⋊C₁₆	—	2	1	no	—
38	C₂×D₄×C₇₉	—	2	1	no	—
39	D₈×C₇₉	—	2	1	no	—
40	D₈×C₇₉	—	2	1	no	—
41	M₁₆×C₇₉	—	2	1	no	—
42	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
43	C₁₆×C₇₉	—	2	1	no	—
44	C₂³×C₇₉	—	4	1	no	—
45	C₂²×D₇₉	—	4	1	no	—
46	D₄×C₇₉	—	4	1	no	—
47	D₄×C₇₉	—	4	1	no	—
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂²⋊D₇₉	—	4	1	no	—
50	C₂²⋊D₇₉	—	8	4	no	—
51	C₂×Dic₇₉	—	2	1	no	—
52	D₃₁₆	—	2	1	no	—
53	D₃₁₆	—	4	1	no	—
54	D₃₁₆	—	4	1	no	—
55	C₄×D₇₉	—	4	1	no	—
56	Dic₁₅₈	—	2	1	no	—
57	C₈×C₇₉	—	4	1	no	—
58	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
59	C₈×C₇₉	#41	1	1	yes	characteristic
60	C₇₉⋊C₈	D₈	1	1	yes	characteristic
61	C₇₉⋊C₈	D₈	1	1	yes	characteristic
62	C₂²×C₇₉	—	8	2	no	—
63	C₂²×C₇₉	—	8	1	no	—
64	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×D₇₉	—	4	1	no	—
66	C₂×D₇₉	—	8	2	no	—
67	C₂×D₇₉	—	8	1	no	—
68	C₄×C₇₉	#121	1	1	yes	characteristic
69	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
70	Dic₇₉	—	2	2	no	—
71	Dic₇₉	—	4	1	no	—
72	C₂×C₇₉	—	2	1	no	—
73	C₂×C₇₉	—	16	1	no	—
74	C₂×C₇₉	#459	1	1	yes	characteristic
75	D₇₉	—	8	1	no	—
76	D₇₉	—	16	1	no	—
77	#2213	—	79	1	no	maximal, Sylow
78	C₇₉	#2213	1	1	yes	characteristic, complemented, Sylow
79	#509	—	79	1	no	—
80	#509	—	79	1	no	—
81	#493	—	79	1	no	—
82	#443	—	79	1	no	—
83	#364	—	79	1	no	—
84	#361	—	79	1	no	—
85	#361	D₇₉	1	1	yes	characteristic, complemented
86	#135	—	79	1	no	—
87	C₂×D₈	—	79	1	no	—
88	C₂×D₈	—	158	1	no	—
89	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
90	#131	—	158	1	no	—
91	#127	—	158	1	no	—
92	SD₃₂	—	158	1	no	—
93	SD₃₂	—	158	1	no	—
94	D₁₆	—	158	1	no	—
95	D₁₆	—	158	1	no	—
96	M₃₂	—	79	1	no	—
97	M₃₂	C₂×D₇₉	1	1	yes	characteristic
98	#108	C₂×D₇₉	1	1	yes	characteristic
99	#104	—	158	1	no	—
100	C₄×C₈	—	79	1	no	—
101	#41	—	158	1	no	—
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	—	316	2	no	—
104	C₂×D₄	—	158	1	no	—
105	Q₁₆	—	79	1	no	—
106	SD₁₆	—	158	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	2	1	no	—
109	D₈	—	316	1	no	—
110	D₈	—	316	1	no	—
111	D₈	—	79	1	no	—
112	D₈	—	158	1	no	—
113	D₈	—	158	1	no	—
114	M₁₆	—	2	1	no	—
115	M₁₆	—	316	1	no	—
116	C₂×C₈	—	316	1	no	—
117	C₂×C₈	—	79	1	no	—
118	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
119	C₄²	—	79	1	no	—
120	C₁₆	—	2	1	no	—
121	C₁₆	—	158	1	no	—
122	C₂³	—	4	1	no	—
123	C₂³	—	316	1	no	—
124	Q₈	—	158	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	316	1	no	—
128	D₄	—	316	1	no	—
129	D₄	—	316	1	no	—
130	D₄	—	632	4	no	—
131	D₄	—	158	1	no	—
132	C₂×C₄	—	316	1	no	—
133	C₂×C₄	—	158	1	no	—
134	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
135	C₈	—	4	1	no	—
136	C₈	—	79	1	no	—
137	C₈	—	79	1	no	—
138	C₈	D₄×D₇₉	1	1	yes	characteristic
139	C₈	#11929624	1	1	yes	characteristic
140	C₂²	—	8	2	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	316	1	no	—
143	C₂²	—	632	2	no	—
144	C₂²	—	632	1	no	—
145	C₂²	#14579188	1	1	yes	characteristic
146	C₄	—	316	1	no	—
147	C₄	—	158	2	no	—
148	C₄	#14579134	1	1	yes	characteristic
149	C₄	D₈×D₇₉	1	1	yes	characteristic
150	C₂	—	2	1	no	—
151	C₂	—	16	1	no	—
152	C₂	—	632	1	no	—
153	C₂	—	1264	1	no	—
154	C₂	#19098757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19099001

C₂

yes

maximal, characteristic, complemented

#19098999

C₂

yes

maximal, characteristic, complemented

#19098938

C₂

yes

maximal, characteristic, complemented

#19098679

C₂

yes

maximal, characteristic, complemented

#19098383

C₂

yes

maximal, characteristic, complemented

#19098375

C₂

yes

maximal, characteristic, complemented

#361×C₇₉

C₂

yes

maximal, characteristic, complemented

#14579183

C₂²

yes

characteristic

C₂×D₆₃₂

C₂²

yes

—

—

—

—

—

D₁₂₆₄

—

#14579102

—

#14579101

C₂²

yes

characteristic

#14579087

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

characteristic

#108×C₇₉

C₂²

yes

characteristic

#11929624

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

Dic₃₁₆

D₄

yes

characteristic, complemented

#11929613

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

D₄

yes

characteristic, complemented

#11929609

—

#11929609

—

#11929607

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₈×D₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

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

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

D₈

yes

characteristic

C₇₉⋊C₈

D₈

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

#121

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#459

yes

characteristic

D₇₉

—

D₇₉

—

#2213

—

maximal, Sylow

C₇₉

#2213

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#135

—

C₂×D₈

—

C₂×D₈

—

158

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#131

—

158

—

#127

—

158

—

SD₃₂

—

158

—

SD₃₂

—

158

—

D₁₆

—

158

—

D₁₆

—

158

—

M₃₂

—

M₃₂

C₂×D₇₉

yes

characteristic

#108

C₂×D₇₉

yes

characteristic

#104

—

158

—

100

C₄×C₈

—

101

#41

—

158

—

102

C₂×D₄

—

103

C₂×D₄

—

316

—

104

C₂×D₄

—

158

—

105

Q₁₆

—

106

SD₁₆

—

158

—

107

D₈

—

108

D₈

—

109

D₈

—

316

—

110

D₈

—

316

—

111

D₈

—

112

D₈

—

158

—

113

D₈

—

158

—

114

M₁₆

—

115

M₁₆

—

316

—

116

C₂×C₈

—

316

—

117

C₂×C₈

—

118

C₂×C₈

C₂²×D₇₉

yes

characteristic

119

C₄²

—

120

C₁₆

—

121

C₁₆

—

158

—

122

C₂³

—

123

C₂³

—

316

—

124

Q₈

—

158

—

125

D₄

—

126

D₄

—

127

D₄

—

316

—

128

D₄

—

316

—

129

D₄

—

316

—

130

D₄

—

632

—

131

D₄

—

158

—

132

C₂×C₄

—

316

—

133

C₂×C₄

—

158

—

134

C₂×C₄

D₄×D₇₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

D₄×D₇₉

yes

characteristic

139

C₈

#11929624

yes

characteristic

140

C₂²

—

141

C₂²

—

142

C₂²

—

316

—

143

C₂²

—

632

—

144

C₂²

—

632

—

145

C₂²

#14579188

yes

characteristic

146

C₄

—

316

—

147

C₄

—

158

—

148

C₄

#14579134

yes

characteristic

149

C₄

D₈×D₇₉

yes

characteristic

150

C₂

—

151

C₂

—

152

C₂

—

632

—

153

C₂

—

1264

—

154

C₂

#19098757

yes

characteristic

	subgroup	G/H
center	C₂	#19098757
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#361×C₇₉	C₂
socle	C₂×C₇₉	#459
hypercenter	#361	D₇₉
hypocenter	C₇₉	#2213
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

subgroup

G/H

center

C₂

#19098757

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. #19099001	C₂	semidirect
2. #19098999	C₂	semidirect
3. #19098938	C₂	semidirect
4. #19098679	C₂	semidirect
5. #19098383	C₂	semidirect
6. #19098375	C₂	semidirect
7. #361×C₇₉	C₂	semidirect
26. Dic₃₁₆	D₄	semidirect
30. D₆₃₂	D₄	semidirect
78. C₇₉	#2213	semidirect
85. #361	D₇₉	semidirect

H ≅ G/N

type

1. #19099001

C₂

semidirect

2. #19098999

C₂

semidirect

3. #19098938

C₂

semidirect

4. #19098679

C₂

semidirect

5. #19098383

C₂

semidirect

6. #19098375

C₂

semidirect

7. #361×C₇₉

C₂

semidirect

26. Dic₃₁₆

D₄

semidirect

30. D₆₃₂

D₄

semidirect

78. C₇₉

#2213

semidirect

85. #361

D₇₉

semidirect

Subgroups — #23765475

Conjugacy classes of subgroups

Complements