Group #23765460 — subgroups

Subgroups — #23765460

Order 10112.

158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14579107	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098946	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098368	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098364	C₂	1	1	yes	maximal, characteristic
7	C₂×SD₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#11929612	—	2	1	no	—
10	#14579148	—	2	1	no	—
11	Q₈×Dic₇₉	—	2	1	no	—
12	#14579107	—	2	2	no	—
13	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	#14579095	C₂²	1	1	yes	characteristic
15	#14579085	—	2	1	no	—
16	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
19	SD₃₂×C₇₉	—	2	2	no	—
20	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	Dic₃₁₆	—	2	1	no	—
23	Dic₃₁₆	—	2	1	no	—
24	#11929612	—	4	2	no	—
25	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
26	C₄⋊Dic₇₉	—	2	1	no	—
27	C₄⋊Dic₇₉	—	4	1	no	—
28	C₂²⋊Dic₇₉	—	4	1	no	—
29	C₂²⋊Dic₇₉	—	4	1	no	—
30	C₄×Dic₇₉	—	4	1	no	—
31	C₄×Dic₇₉	D₄	1	1	yes	characteristic
32	C₇₉⋊C₁₆	—	2	1	no	—
33	C₂×Q₈×C₇₉	—	2	1	no	—
34	C₂×D₄×C₇₉	—	2	1	no	—
35	Q₁₆×C₇₉	—	2	1	no	—
36	Q₁₆×C₇₉	D₄	1	2	yes	—
37	D₈×C₇₉	—	2	1	no	—
38	D₈×C₇₉	—	2	1	no	—
39	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
40	C₁₆×C₇₉	—	2	1	no	—
41	C₂³×C₇₉	—	4	1	no	—
42	Q₈×C₇₉	—	2	2	no	—
43	Q₈×C₇₉	—	4	1	no	—
44	D₄×C₇₉	—	4	1	no	—
45	D₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	—	4	1	no	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₇₉	—	4	1	no	—
49	C₂×Dic₇₉	—	4	1	no	—
50	C₂×Dic₇₉	D₈	1	1	yes	characteristic
51	C₂×Dic₇₉	D₈	1	1	yes	characteristic
52	Dic₁₅₈	—	4	1	no	—
53	Dic₁₅₈	—	4	1	no	—
54	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₇₉	#41	1	1	yes	characteristic
56	C₇₉⋊C₈	—	2	1	no	—
57	C₂²×C₇₉	—	8	1	no	—
58	C₂²×C₇₉	—	8	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
61	C₄×C₇₉	—	4	2	no	—
62	C₄×C₇₉	#121	1	1	yes	characteristic
63	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
64	Dic₇₉	—	2	1	no	—
65	Dic₇₉	—	2	1	no	—
66	Dic₇₉	—	8	1	no	—
67	Dic₇₉	—	8	1	no	—
68	C₂×C₇₉	—	16	1	no	—
69	C₂×C₇₉	#459	1	1	yes	characteristic
70	C₂×C₇₉	#508	1	1	yes	characteristic
71	C₂×C₇₉	#510	1	1	yes	characteristic
72	#2211	—	79	1	no	maximal, Sylow
73	C₇₉	#2211	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₃₂	—	79	1	no	—
75	C₂×SD₃₂	D₇₉	1	1	yes	characteristic
76	#495	—	79	1	no	—
77	C₄×Q₁₆	—	79	1	no	—
78	C₄⋊C₁₆	—	79	1	no	—
79	#358	—	79	1	no	—
80	#357	—	79	1	no	—
81	C₂×Q₁₆	—	79	1	no	—
82	C₂×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
83	C₂×SD₁₆	—	158	1	no	—
84	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
85	#124	—	158	1	no	—
86	C₄×Q₈	—	158	1	no	—
87	Q₃₂	—	158	2	no	—
88	SD₃₂	—	2	2	no	—
89	C₂×C₁₆	—	79	1	no	—
90	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
91	#107	—	79	1	no	—
92	#103	—	158	1	no	—
93	C₄×C₈	—	79	1	no	—
94	C₂×Q₈	—	2	1	no	—
95	C₂×Q₈	—	158	1	no	—
96	C₂×D₄	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	158	1	no	—
99	Q₁₆	—	158	1	no	—
100	Q₁₆	C₂²⋊D₇₉	1	2	yes	—
101	SD₁₆	—	316	2	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	C₂×C₈	—	79	1	no	—
105	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
106	C₄⋊C₄	—	316	1	no	—
107	C₄⋊C₄	—	158	1	no	—
108	C₂²⋊C₄	—	316	1	no	—
109	C₂²⋊C₄	—	316	1	no	—
110	C₄²	—	316	1	no	—
111	C₄²	—	79	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	—	158	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	2	2	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	316	1	no	—
118	Q₈	—	316	1	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	316	1	no	—
123	C₂×C₄	—	316	1	no	—
124	C₂×C₄	—	79	1	no	—
125	C₂×C₄	—	79	1	no	—
126	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
127	C₈	—	158	1	no	—
128	C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
129	C₈	#11929623	1	1	yes	characteristic
130	C₂²	—	8	1	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	D₈×D₇₉	1	1	yes	characteristic
134	C₄	—	4	2	no	—
135	C₄	—	632	1	no	—
136	C₄	—	632	1	no	—
137	C₄	—	158	1	no	—
138	C₄	—	158	1	no	—
139	C₄	#14579133	1	1	yes	characteristic
140	C₄	#14579185	1	1	yes	characteristic
141	C₂	—	16	1	no	—
142	C₂	#19098756	1	1	yes	characteristic
143	C₂	#19098994	1	1	yes	characteristic
144	C₂	#19099002	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579107

C₂

yes

maximal, characteristic, complemented

#19098946

C₂

yes

maximal, characteristic

Q₁₆×Dic₇₉

C₂

yes

maximal, characteristic, complemented

Dic₇₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19098368

C₂

yes

maximal, characteristic, complemented

#19098364

C₂

yes

maximal, characteristic

C₂×SD₃₂×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₂×#11929612

—

#14579148

—

Q₈×Dic₇₉

—

#14579107

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579085

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×D₈×C₇₉

C₂²

yes

characteristic

SD₃₂×C₇₉

—

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929612

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

D₄

yes

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×SD₃₂

D₇₉

yes

characteristic

#495

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#357

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₇₉

yes

characteristic

C₂×SD₁₆

—

158

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#124

—

158

—

C₄×Q₈

—

158

—

Q₃₂

—

158

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#103

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

158

—

Q₁₆

—

158

—

100

Q₁₆

C₂²⋊D₇₉

yes

—

101

SD₁₆

—

316

—

102

D₈

—

103

D₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂²×D₇₉

yes

characteristic

106

C₄⋊C₄

—

316

—

107

C₄⋊C₄

—

158

—

108

C₂²⋊C₄

—

316

—

109

C₂²⋊C₄

—

316

—

110

C₄²

—

316

—

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

158

—

114

C₂³

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

316

—

118

Q₈

—

316

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

316

—

123

C₂×C₄

—

316

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₇₉

yes

characteristic

127

C₈

—

158

—

128

C₈

C₂×C₂²⋊D₇₉

yes

characteristic

129

C₈

#11929623

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

D₈×D₇₉

yes

characteristic

134

C₄

—

135

C₄

—

632

—

136

C₄

—

632

—

137

C₄

—

158

—

138

C₄

—

158

—

139

C₄

#14579133

yes

characteristic

140

C₄

#14579185

yes

characteristic

141

C₂

—

142

C₂

#19098756

yes

characteristic

143

C₂

#19098994

yes

characteristic

144

C₂

#19099002

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×SD₃₂×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₈×C₇₉	C₂²
hypercenter	C₂×SD₃₂	D₇₉
hypocenter	C₇₉	#2211
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×SD₃₂×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₈×C₇₉

C₂²

hypercenter

C₂×SD₃₂

D₇₉

hypocenter

C₇₉

#2211

LCS

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×SD₃₂

N	H ≅ G/N	type
1. C₂×#14579107	C₂	semidirect
3. Q₁₆×Dic₇₉	C₂	semidirect
4. Dic₇₉⋊C₁₆	C₂	semidirect
5. #19098368	C₂	semidirect
73. C₇₉	#2211	semidirect

H ≅ G/N

type

1. C₂×#14579107

C₂

semidirect

3. Q₁₆×Dic₇₉

C₂

semidirect

4. Dic₇₉⋊C₁₆

C₂

semidirect

5. #19098368

C₂

semidirect

73. C₇₉

#2211

semidirect

Subgroups — #23765460

Conjugacy classes of subgroups

Complements