Group #23762709 — subgroups

Subgroups — #23762709

Order 10112.

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

normal subgroups only

This group has 196 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
2	#19098969	C₂	1	2	yes	maximal, complemented
3	#19098304	C₂	1	2	yes	maximal, complemented
4	#19098303	C₂	1	1	yes	maximal, characteristic
5	#497×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	#14579094	—	2	2	no	—
12	#14579092	—	2	2	no	—
13	#14579072	C₂²	1	2	yes	—
14	C₂×Q₁₆×C₇₉	—	2	1	no	—
15	C₂×SD₁₆×C₇₉	—	2	1	no	—
16	C₄⋊Q₈×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	—	2	1	no	—
31	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
32	C₂×D₄×C₇₉	D₄	1	1	yes	characteristic
33	Q₁₆×C₇₉	—	4	2	no	—
34	SD₁₆×C₇₉	—	4	2	no	—
35	C₂×C₈×C₇₉	—	2	1	no	—
36	C₄⋊C₄×C₇₉	—	2	2	no	—
37	C₂²⋊C₄×C₇₉	—	2	2	no	—
38	C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₂³×C₇₉	—	2	1	no	—
40	Q₈×C₇₉	—	4	1	no	—
41	Q₈×C₇₉	—	4	1	no	—
42	Q₈×C₇₉	—	4	1	no	—
43	D₄×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	—	2	1	no	—
45	C₂×C₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×Dic₇₉	—	2	2	no	—
49	C₂×Dic₇₉	—	2	2	no	—
50	C₂×Dic₇₉	—	8	1	no	—
51	Dic₁₅₈	—	8	1	no	—
52	C₈×C₇₉	—	2	2	no	—
53	C₇₉⋊C₈	—	2	4	no	—
54	C₂²×C₇₉	—	4	1	no	—
55	C₂²×C₇₉	—	4	2	no	—
56	C₂²×C₇₉	#120	1	1	yes	characteristic
57	C₄×C₇₉	—	2	1	no	—
58	C₄×C₇₉	—	2	2	no	—
59	C₄×C₇₉	—	4	1	no	—
60	C₄×C₇₉	—	8	1	no	—
61	Dic₇₉	—	4	2	no	—
62	Dic₇₉	—	4	2	no	—
63	C₂×C₇₉	—	8	1	no	—
64	C₂×C₇₉	#453	1	1	yes	characteristic
65	C₂×C₇₉	#456	1	2	yes	—
66	#1660	—	79	1	no	maximal, Sylow
67	C₇₉	#1660	1	1	yes	characteristic, complemented, Sylow
68	#563	—	79	1	no	—
69	#501	—	79	2	no	—
70	#497	D₇₉	1	1	yes	characteristic
71	#330	—	79	2	no	—
72	#329	—	79	1	no	—
73	C₂×Q₁₆	—	2	1	no	—
74	C₂×SD₁₆	—	2	1	no	—
75	C₄⋊Q₈	—	158	1	no	—
76	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
77	#126	—	158	2	no	—
78	#125	—	79	2	no	—
79	#124	C₂×D₇₉	1	1	yes	characteristic
80	#123	—	158	1	no	—
81	C₂²⋊Q₈	—	158	2	no	—
82	#107	—	158	2	no	—
83	#106	—	158	2	no	—
84	#97	—	79	2	no	—
85	#97	C₂×D₇₉	1	1	yes	characteristic
86	C₂×Q₈	—	2	1	no	—
87	C₂×Q₈	—	158	1	no	—
88	C₂×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
89	C₂×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
90	C₂²×C₄	—	158	1	no	—
91	Q₁₆	—	4	2	no	—
92	SD₁₆	—	4	2	no	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	158	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	79	2	no	—
97	C₄⋊C₄	—	79	2	no	—
98	C₄⋊C₄	—	158	2	no	—
99	C₄⋊C₄	—	158	2	no	—
100	C₄⋊C₄	—	158	2	no	—
101	C₂²⋊C₄	—	2	2	no	—
102	C₂²⋊C₄	—	158	2	no	—
103	C₂²⋊C₄	—	158	1	no	—
104	C₄²	—	158	1	no	—
105	C₄²	C₂²×D₇₉	1	1	yes	characteristic
106	C₂³	—	2	1	no	—
107	Q₈	—	4	1	no	—
108	Q₈	—	4	1	no	—
109	Q₈	—	4	1	no	—
110	Q₈	—	632	1	no	—
111	D₄	—	4	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	632	1	no	—
115	C₂×C₄	—	158	2	no	—
116	C₂×C₄	—	158	2	no	—
117	C₂×C₄	D₄×D₇₉	1	2	yes	—
118	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	—	158	4	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	2	no	—
123	C₂²	#14579129	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	2	2	no	—
126	C₄	—	4	1	no	—
127	C₄	—	8	1	no	—
128	C₄	—	316	2	no	—
129	C₄	—	316	2	no	—
130	C₂	—	8	1	no	—
131	C₂	#19098730	1	1	yes	characteristic
132	C₂	#19098744	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099313

C₂

yes

maximal, characteristic

#19098969

C₂

yes

maximal, complemented

#19098304

C₂

yes

maximal, complemented

#19098303

C₂

yes

maximal, characteristic

#497×C₇₉

C₂

yes

maximal, characteristic

#14579159

—

#14579154

—

#14579153

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×Q₁₆×C₇₉

—

C₂×SD₁₆×C₇₉

—

C₄⋊Q₈×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

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×D₄×C₇₉

D₄

yes

characteristic

Q₁₆×C₇₉

—

SD₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

C₂×C₄×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

#120

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#453

yes

characteristic

C₂×C₇₉

#456

yes

—

#1660

—

maximal, Sylow

C₇₉

#1660

yes

characteristic, complemented, Sylow

#563

—

#501

—

#497

D₇₉

yes

characteristic

#330

—

#329

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

#126

—

158

—

#125

—

#124

C₂×D₇₉

yes

characteristic

#123

—

158

—

C₂²⋊Q₈

—

158

—

#107

—

158

—

#106

—

158

—

#97

—

#97

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

C₂²⋊D₇₉

yes

characteristic

C₂×D₄

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

—

158

—

Q₁₆

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

—

158

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

100

C₄⋊C₄

—

158

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

158

—

103

C₂²⋊C₄

—

158

—

104

C₄²

—

158

—

105

C₄²

C₂²×D₇₉

yes

characteristic

106

C₂³

—

107

Q₈

—

108

Q₈

—

109

Q₈

—

110

Q₈

—

632

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

632

—

115

C₂×C₄

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

D₄×D₇₉

yes

—

118

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

119

C₈

—

120

C₈

—

158

—

121

C₂²

—

122

C₂²

—

123

C₂²

#14579129

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

316

—

129

C₄

—

316

—

130

C₂

—

131

C₂

#19098730

yes

characteristic

132

C₂

#19098744

yes

—

	subgroup	G/H
center	C₂²	#14579129
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#497×C₇₉	C₂
socle	C₂²×C₇₉	#120
prime radical	C₂×D₄×C₇₉	D₄
hypercenter	#497	D₇₉
hypocenter	C₇₉	#1660
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #497

subgroup

G/H

center

C₂²

#14579129

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#497×C₇₉

C₂

socle

C₂²×C₇₉

#120

prime radical

C₂×D₄×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #497

N	H ≅ G/N	type
2. #19098969	C₂	semidirect
3. #19098304	C₂	semidirect
67. C₇₉	#1660	semidirect

H ≅ G/N

type

2. #19098969

C₂

semidirect

3. #19098304

C₂

semidirect

67. C₇₉

#1660

semidirect

Subgroups — #23762709

Conjugacy classes of subgroups

Complements