Group #23762273 — subgroups

Subgroups — #23762273

Order 10112.

152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19098693	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
4	#19098314	C₂	1	1	yes	maximal, characteristic
5	#19098295	C₂	1	1	yes	maximal, characteristic
6	#19098295	C₂	1	1	yes	maximal, characteristic
7	#322×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₄	1	1	yes	characteristic
9	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
10	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
11	#14579095	C₄	1	1	yes	characteristic
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	Dic₇₉⋊C₈	—	2	1	no	—
15	Dic₇₉⋊C₈	—	2	1	no	—
16	#14579086	C₄	1	1	yes	characteristic
17	#14579086	C₄	1	1	yes	characteristic
18	#14579071	—	2	1	no	—
19	C₈×Dic₇₉	—	2	1	no	—
20	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
25	Dic₃₁₆	—	2	2	no	—
26	C₂×C₇₉⋊C₈	—	2	1	no	—
27	C₂×C₇₉⋊C₈	—	2	1	no	—
28	C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
29	C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
30	Dic₇₉⋊C₄	—	2	1	no	—
31	Dic₇₉⋊C₄	—	2	1	no	—
32	C₄×Dic₇₉	—	2	1	no	—
33	C₄×Dic₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	—	2	1	no	—
35	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
38	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
39	C₄²×C₇₉	C₂³	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
43	C₂×Dic₇₉	—	2	1	no	—
44	C₂×Dic₇₉	—	2	1	no	—
45	C₂×Dic₇₉	—	2	1	no	—
46	C₂×Dic₇₉	—	2	1	no	—
47	Dic₁₅₈	—	2	1	no	—
48	Dic₁₅₈	—	2	1	no	—
49	Dic₁₅₈	—	2	1	no	—
50	Dic₁₅₈	M₁₆	1	2	yes	—
51	C₈×C₇₉	—	2	2	no	—
52	C₈×C₇₉	—	2	1	no	—
53	C₈×C₇₉	—	2	1	no	—
54	C₈×C₇₉	—	2	1	no	—
55	C₈×C₇₉	—	2	1	no	—
56	C₇₉⋊C₈	—	4	1	no	—
57	C₇₉⋊C₈	—	4	1	no	—
58	C₂²×C₇₉	C₄×D₄	1	1	yes	characteristic
59	C₄×C₇₉	—	2	1	no	—
60	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
61	C₄×C₇₉	#131	1	1	yes	characteristic
62	C₄×C₇₉	#137	1	1	yes	characteristic
63	C₄×C₇₉	#137	1	1	yes	characteristic
64	Dic₇₉	—	2	2	no	—
65	Dic₇₉	—	4	1	no	—
66	Dic₇₉	—	4	1	no	—
67	Dic₇₉	—	4	1	no	—
68	C₂×C₇₉	#435	1	1	yes	characteristic
69	C₂×C₇₉	#441	1	1	yes	characteristic
70	C₂×C₇₉	#443	1	1	yes	characteristic
71	#1587	—	79	1	no	maximal, Sylow
72	C₇₉	#1587	1	1	yes	characteristic, complemented, Sylow
73	#446	—	79	1	no	—
74	C₈×Q₈	—	79	1	no	—
75	C₄×Q₁₆	—	79	1	no	—
76	#334	—	79	1	no	—
77	Q₈⋊C₈	—	79	1	no	—
78	Q₈⋊C₈	—	79	1	no	—
79	#322	D₇₉	1	1	yes	characteristic
80	C₂×Q₁₆	—	79	1	no	—
81	C₄×Q₈	—	79	1	no	—
82	C₄×Q₈	—	79	1	no	—
83	#107	—	79	1	no	—
84	C₄⋊C₈	—	79	1	no	—
85	C₄⋊C₈	—	79	1	no	—
86	C₄⋊C₈	—	158	1	no	—
87	C₄⋊C₈	—	158	1	no	—
88	#103	—	79	1	no	—
89	#103	—	79	1	no	—
90	#97	—	158	1	no	—
91	C₄×C₈	—	158	1	no	—
92	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
93	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
94	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
95	C₂×Q₈	—	79	1	no	—
96	C₂×Q₈	—	79	1	no	—
97	Q₁₆	—	158	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	158	1	no	—
100	C₂×C₈	—	158	1	no	—
101	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
102	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
103	C₂×C₈	D₃₁₆	1	1	yes	characteristic
104	C₂×C₈	D₃₁₆	1	1	yes	characteristic
105	C₄⋊C₄	—	79	1	no	—
106	C₄⋊C₄	—	79	1	no	—
107	C₄⋊C₄	—	158	1	no	—
108	C₄⋊C₄	—	158	1	no	—
109	C₄²	—	158	1	no	—
110	C₄²	—	158	1	no	—
111	C₄²	C₂²×D₇₉	1	1	yes	characteristic
112	Q₈	—	79	2	no	—
113	Q₈	—	158	1	no	—
114	Q₈	—	158	1	no	—
115	Q₈	—	158	1	no	—
116	C₂×C₄	—	158	1	no	—
117	C₂×C₄	—	158	1	no	—
118	C₂×C₄	—	158	1	no	—
119	C₂×C₄	—	158	1	no	—
120	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
121	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
122	C₂×C₄	#11929624	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	2	1	no	—
125	C₈	—	2	1	no	—
126	C₈	—	2	1	no	—
127	C₈	—	2	1	no	—
128	C₈	—	316	1	no	—
129	C₈	—	316	1	no	—
130	C₂²	C₄×D₃₁₆	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	316	1	no	—
133	C₄	—	316	1	no	—
134	C₄	—	316	1	no	—
135	C₄	—	158	2	no	—
136	C₄	M₁₆×D₇₉	1	1	yes	characteristic
137	C₄	#14579169	1	1	yes	characteristic
138	C₄	#14579194	1	1	yes	characteristic
139	C₄	#14579194	1	1	yes	characteristic
140	C₂	#19098636	1	1	yes	characteristic
141	C₂	#19098671	1	1	yes	characteristic
142	C₂	#19098681	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098693

C₂

yes

maximal, characteristic

C₈×Dic₁₅₈

C₂

yes

maximal, characteristic

C₄×Dic₃₁₆

C₂

yes

maximal, characteristic

#19098314

C₂

yes

maximal, characteristic

#19098295

C₂

yes

maximal, characteristic

#19098295

C₂

yes

maximal, characteristic

#322×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₄

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₂²

yes

characteristic

#14579095

C₄

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

#14579086

C₄

yes

characteristic

#14579086

C₄

yes

characteristic

#14579071

—

C₈×Dic₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

C₂×C₄

yes

characteristic

C₂×Dic₁₅₈

C₂×C₄

yes

characteristic

Dic₃₁₆

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

C₂×C₄

yes

characteristic

C₄⋊Dic₇₉

C₂×C₄

yes

characteristic

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

M₁₆

yes

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₂×M₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#446

—

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

Q₈⋊C₈

—

#322

D₇₉

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

158

—

C₄⋊C₈

—

158

—

#103

—

#103

—

#97

—

158

—

C₄×C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

100

C₂×C₈

—

158

—

101

C₂×C₈

C₄×D₇₉

yes

characteristic

102

C₂×C₈

C₄×D₇₉

yes

characteristic

103

C₂×C₈

D₃₁₆

yes

characteristic

104

C₂×C₈

D₃₁₆

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

—

158

—

109

C₄²

—

158

—

110

C₄²

—

158

—

111

C₄²

C₂²×D₇₉

yes

characteristic

112

Q₈

—

113

Q₈

—

158

—

114

Q₈

—

158

—

115

Q₈

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

—

158

—

120

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

121

C₂×C₄

C₂×D₃₁₆

yes

characteristic

122

C₂×C₄

#11929624

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

316

—

129

C₈

—

316

—

130

C₂²

C₄×D₃₁₆

yes

characteristic

131

C₄

—

132

C₄

—

316

—

133

C₄

—

316

—

134

C₄

—

316

—

135

C₄

—

158

—

136

C₄

M₁₆×D₇₉

yes

characteristic

137

C₄

#14579169

yes

characteristic

138

C₄

#14579194

yes

characteristic

139

C₄

#14579194

yes

characteristic

140

C₂

#19098636

yes

characteristic

141

C₂

#19098671

yes

characteristic

142

C₂

#19098681

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₄²	C₂²×D₇₉
Fitting	#322×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₄×D₄
cosocle	C₄²×C₇₉	C₂³
hypercenter	#322	D₇₉
hypocenter	C₇₉	#1587
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₃₁₆

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₄²

C₂²×D₇₉

Fitting

#322×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₄×D₄

cosocle

C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
72. C₇₉	#1587	semidirect

H ≅ G/N

type

72. C₇₉

#1587

semidirect

Subgroups — #23762273

Conjugacy classes of subgroups

Complements