Group #23762696 — subgroups

Subgroups — #23762696

Order 10112.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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	#19099313	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098927	C₂	1	2	yes	maximal, complemented
3	#19098304	C₂	1	2	yes	maximal, complemented
4	#19098303	C₂	1	1	yes	maximal, characteristic, complemented
5	#496×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579159	—	2	1	no	—
7	#14579154	—	2	2	no	—
8	#14579153	C₂²	1	2	yes	—
9	#14579142	—	2	1	no	—
10	#14579138	—	2	2	no	—
11	#14579082	—	2	2	no	—
12	#14579082	—	2	2	no	—
13	#14579072	C₂²	1	2	yes	—
14	C₂×SD₁₆×C₇₉	—	2	1	no	—
15	C₂×D₈×C₇₉	—	2	1	no	—
16	#127×C₇₉	C₂²	1	1	yes	characteristic
17	#124×C₇₉	C₂²	1	1	yes	characteristic
18	#97×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₅₈	—	2	1	no	—
20	C₂²×Dic₇₉	—	2	1	no	—
21	C₂×C₇₉⋊C₈	—	2	2	no	—
22	C₄⋊Dic₇₉	D₄	1	2	yes	—
23	C₄⋊Dic₇₉	D₄	1	2	yes	—
24	Dic₇₉⋊C₄	—	2	2	no	—
25	Dic₇₉⋊C₄	—	2	2	no	—
26	Dic₇₉⋊C₄	—	2	2	no	—
27	C₂²⋊Dic₇₉	—	2	2	no	—
28	C₂²⋊Dic₇₉	—	2	1	no	—
29	C₄×Dic₇₉	—	2	1	no	—
30	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
31	C₂×D₄×C₇₉	—	2	1	no	—
32	C₂×D₄×C₇₉	—	2	2	no	—
33	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
34	SD₁₆×C₇₉	—	4	2	no	—
35	D₈×C₇₉	—	4	2	no	—
36	C₂×C₈×C₇₉	—	2	1	no	—
37	C₂²⋊C₄×C₇₉	—	2	2	no	—
38	C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₂³×C₇₉	—	2	1	no	—
40	C₂³×C₇₉	—	4	1	no	—
41	Q₈×C₇₉	—	4	1	no	—
42	D₄×C₇₉	—	4	1	no	—
43	D₄×C₇₉	—	4	1	no	—
44	D₄×C₇₉	—	4	1	no	—
45	D₄×C₇₉	—	4	4	no	—
46	C₂×C₄×C₇₉	—	2	1	no	—
47	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₇₉	—	2	2	no	—
50	C₂×Dic₇₉	—	2	2	no	—
51	C₂×Dic₇₉	—	8	1	no	—
52	Dic₁₅₈	—	8	1	no	—
53	C₈×C₇₉	—	2	2	no	—
54	C₇₉⋊C₈	—	4	2	no	—
55	C₂²×C₇₉	—	4	1	no	—
56	C₂²×C₇₉	—	4	2	no	—
57	C₂²×C₇₉	—	8	1	no	—
58	C₂²×C₇₉	—	8	2	no	—
59	C₂²×C₇₉	#120	1	1	yes	characteristic
60	C₄×C₇₉	—	2	1	no	—
61	C₄×C₇₉	—	2	2	no	—
62	C₄×C₇₉	—	4	1	no	—
63	Dic₇₉	—	4	2	no	—
64	Dic₇₉	—	4	2	no	—
65	C₂×C₇₉	—	8	1	no	—
66	C₂×C₇₉	—	16	1	no	—
67	C₂×C₇₉	#453	1	1	yes	characteristic
68	C₂×C₇₉	#454	1	2	yes	—
69	#1657	—	79	1	no	maximal, Sylow
70	C₇₉	#1657	1	1	yes	characteristic, complemented, Sylow
71	#563	—	79	1	no	—
72	#496	D₇₉	1	1	yes	characteristic
73	#490	—	79	2	no	—
74	#330	—	79	2	no	—
75	#329	—	79	1	no	—
76	C₂×SD₁₆	—	2	1	no	—
77	C₂×D₈	—	2	1	no	—
78	C₄⋊Q₈	—	158	1	no	—
79	#127	C₂×D₇₉	1	1	yes	characteristic
80	#126	—	158	2	no	—
81	#125	—	79	2	no	—
82	#124	C₂×D₇₉	1	1	yes	characteristic
83	#123	—	158	1	no	—
84	C₂²⋊Q₈	—	158	2	no	—
85	#102	—	158	2	no	—
86	#102	—	158	2	no	—
87	#97	—	79	2	no	—
88	#97	C₂×D₇₉	1	1	yes	characteristic
89	C₂×Q₈	—	158	1	no	—
90	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	—	2	1	no	—
93	C₂×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
94	C₂²×C₄	—	158	1	no	—
95	SD₁₆	—	4	2	no	—
96	D₈	—	4	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	158	2	no	—
99	C₄⋊C₄	—	79	2	no	—
100	C₄⋊C₄	—	79	2	no	—
101	C₄⋊C₄	—	158	2	no	—
102	C₄⋊C₄	—	158	2	no	—
103	C₄⋊C₄	—	158	2	no	—
104	C₂²⋊C₄	—	2	2	no	—
105	C₂²⋊C₄	—	158	2	no	—
106	C₂²⋊C₄	—	158	1	no	—
107	C₄²	—	158	1	no	—
108	C₄²	C₂²×D₇₉	1	1	yes	characteristic
109	C₂³	—	2	1	no	—
110	C₂³	—	4	1	no	—
111	Q₈	—	4	1	no	—
112	Q₈	—	632	1	no	—
113	D₄	—	4	1	no	—
114	D₄	—	4	1	no	—
115	D₄	—	4	1	no	—
116	D₄	—	4	4	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	632	1	no	—
119	C₂×C₄	—	158	2	no	—
120	C₂×C₄	—	158	2	no	—
121	C₂×C₄	D₄×D₇₉	1	2	yes	—
122	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	316	2	no	—
125	C₂²	—	4	1	no	—
126	C₂²	—	4	2	no	—
127	C₂²	—	8	1	no	—
128	C₂²	—	8	2	no	—
129	C₂²	#14579129	1	1	yes	characteristic
130	C₄	—	2	1	no	—
131	C₄	—	2	2	no	—
132	C₄	—	4	1	no	—
133	C₄	—	316	2	no	—
134	C₄	—	316	2	no	—
135	C₂	—	8	1	no	—
136	C₂	—	16	1	no	—
137	C₂	#19098730	1	1	yes	characteristic
138	C₂	#19098734	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099313

C₂

yes

maximal, characteristic, complemented

#19098927

C₂

yes

maximal, complemented

#19098304

C₂

yes

maximal, complemented

#19098303

C₂

yes

maximal, characteristic, complemented

#496×C₇₉

C₂

yes

maximal, characteristic

#14579159

—

#14579154

—

#14579153

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×SD₁₆×C₇₉

—

C₂×D₈×C₇₉

—

#127×C₇₉

C₂²

yes

characteristic

#124×C₇₉

C₂²

yes

characteristic

#97×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₄

yes

characteristic

SD₁₆×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂³×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#120

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#453

yes

characteristic

C₂×C₇₉

#454

yes

—

#1657

—

maximal, Sylow

C₇₉

#1657

yes

characteristic, complemented, Sylow

#563

—

#496

D₇₉

yes

—

—

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

158

—

#127

C₂×D₇₉

yes

characteristic

#126

—

158

—

#125

—

#124

C₂×D₇₉

yes

characteristic

#123

—

158

—

C₂²⋊Q₈

—

158

—

#102

—

158

—

#102

—

158

—

#97

—

#97

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

—

158

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

158

—

102

C₄⋊C₄

—

158

—

103

C₄⋊C₄

—

158

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

158

—

106

C₂²⋊C₄

—

158

—

107

C₄²

—

158

—

108

C₄²

C₂²×D₇₉

yes

characteristic

109

C₂³

—

110

C₂³

—

111

Q₈

—

112

Q₈

—

632

—

113

D₄

—

114

D₄

—

115

D₄

—

116

D₄

—

117

C₂×C₄

—

118

C₂×C₄

—

632

—

119

C₂×C₄

—

158

—

120

C₂×C₄

—

158

—

121

C₂×C₄

D₄×D₇₉

yes

—

122

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

123

C₈

—

124

C₈

—

316

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#14579129

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

316

—

134

C₄

—

316

—

135

C₂

—

136

C₂

—

137

C₂

#19098730

yes

characteristic

138

C₂

#19098734

yes

—

	subgroup	G/H
center	C₂²	#14579129
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting, prime radical	#496×C₇₉	C₂
socle	C₂²×C₇₉	#120
hypercenter	#496	D₇₉
hypocenter	C₇₉	#1657
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

subgroup

G/H

center

C₂²

#14579129

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting, prime radical

#496×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #496

N	H ≅ G/N	type
1. #19099313	C₂	semidirect
2. #19098927	C₂	semidirect
3. #19098304	C₂	semidirect
4. #19098303	C₂	semidirect
70. C₇₉	#1657	semidirect

H ≅ G/N

type

1. #19099313

C₂

semidirect

2. #19098927

C₂

semidirect

3. #19098304

C₂

semidirect

4. #19098303

C₂

semidirect

70. C₇₉

#1657

semidirect

Subgroups — #23762696

Conjugacy classes of subgroups

Complements