Group #23764657 — subgroups

Subgroups — #23764657

Order 10112.

296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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	C₂²×D₆₃₂	C₂	1	1	yes	maximal, characteristic
2	#19098589	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098569	C₂	1	2	yes	maximal, complemented
4	C₂×#14579077	C₂	1	2	yes	maximal, complemented
5	#341×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₁₆	C₂²	1	2	yes	—
7	C₂×D₆₃₂	—	2	2	no	—
8	C₂×D₆₃₂	—	2	4	no	—
9	C₂×#11929608	C₂²	1	1	yes	characteristic
10	#14579120	C₂²	1	1	yes	characteristic
11	Dic₇₉⋊C₈	—	2	2	no	—
12	#14579083	—	2	4	no	—
13	#14579077	—	2	4	no	—
14	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂³×D₇₉	—	2	2	no	—
17	C₂×D₃₁₆	—	2	2	no	—
18	C₂×D₃₁₆	—	2	2	no	—
19	C₂×D₃₁₆	—	2	2	no	—
20	C₂×D₃₁₆	—	2	2	no	—
21	C₂×D₃₁₆	—	2	2	no	—
22	C₂×D₃₁₆	D₄	1	4	yes	—
23	D₆₃₂	—	2	8	no	—
24	#11929608	—	2	2	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₄⋊Dic₇₉	D₄	1	2	yes	—
27	C₂²⋊Dic₇₉	—	2	1	no	—
28	C₄×Dic₇₉	—	2	1	no	—
29	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
30	M₁₆×C₇₉	—	2	2	no	—
31	M₁₆×C₇₉	—	2	2	no	—
32	C₂×C₈×C₇₉	—	2	2	no	—
33	C₂×C₈×C₇₉	—	2	2	no	—
34	C₂×C₈×C₇₉	D₄	1	2	yes	—
35	C₂³×C₇₉	#41	1	1	yes	characteristic
36	C₂²×D₇₉	—	2	4	no	—
37	C₂²×D₇₉	—	4	2	no	—
38	C₂²×D₇₉	—	4	2	no	—
39	C₂²×D₇₉	—	8	4	no	—
40	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	#41	1	2	yes	—
44	C₂×Dic₇₉	—	2	2	no	—
45	D₃₁₆	—	2	4	no	—
46	D₃₁₆	—	2	4	no	—
47	D₃₁₆	—	4	2	no	—
48	D₃₁₆	—	4	2	no	—
49	C₈×C₇₉	—	2	2	no	—
50	C₈×C₇₉	—	4	2	no	—
51	C₇₉⋊C₈	—	4	1	no	—
52	C₂²×C₇₉	—	2	2	no	—
53	C₂²×C₇₉	#121	1	1	yes	characteristic
54	C₂²×C₇₉	#123	1	2	yes	—
55	C₂×D₇₉	—	4	4	no	—
56	C₂×D₇₉	—	8	4	no	—
57	C₂×D₇₉	—	8	4	no	—
58	C₂×D₇₉	—	8	4	no	—
59	C₄×C₇₉	#120	1	1	yes	characteristic
60	C₄×C₇₉	#121	1	2	yes	—
61	C₄×C₇₉	#124	1	1	yes	characteristic
62	Dic₇₉	—	4	2	no	—
63	C₂×C₇₉	—	2	2	no	—
64	C₂×C₇₉	#394	1	1	yes	characteristic
65	C₂×C₇₉	#472	1	2	yes	—
66	D₇₉	—	8	4	no	—
67	#2045	—	79	1	no	maximal, Sylow
68	C₇₉	#2045	1	1	yes	characteristic, complemented, Sylow
69	C₂²×D₈	—	79	1	no	—
70	#424	—	79	1	no	—
71	#418	—	79	2	no	—
72	C₂×#100	—	79	2	no	—
73	#341	D₇₉	1	1	yes	characteristic, complemented
74	C₂²×D₄	—	79	2	no	—
75	C₂×D₈	—	158	4	no	—
76	C₂×D₈	—	158	2	no	—
77	C₂×M₁₆	—	79	1	no	—
78	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
79	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
80	#117	—	79	1	no	—
81	C₄⋊C₈	—	158	2	no	—
82	#102	—	158	4	no	—
83	#100	—	158	4	no	—
84	C₂⁴	—	158	2	no	—
85	C₂×D₄	—	79	4	no	—
86	C₂×D₄	—	158	2	no	—
87	C₂×D₄	—	158	2	no	—
88	C₂×D₄	—	158	2	no	—
89	C₂×D₄	—	158	2	no	—
90	C₂×D₄	—	158	2	no	—
91	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
92	D₈	—	158	8	no	—
93	M₁₆	—	2	2	no	—
94	M₁₆	—	2	2	no	—
95	M₁₆	—	158	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	158	1	no	—
99	C₂×C₈	D₃₁₆	1	2	yes	—
100	C₄⋊C₄	—	79	2	no	—
101	C₂²⋊C₄	—	158	1	no	—
102	C₄²	—	158	1	no	—
103	C₂³	—	316	2	no	—
104	C₂³	—	316	2	no	—
105	C₂³	—	632	4	no	—
106	C₂³	—	158	4	no	—
107	C₂³	#11929625	1	1	yes	characteristic
108	D₄	—	316	2	no	—
109	D₄	—	316	2	no	—
110	D₄	—	158	4	no	—
111	D₄	—	158	4	no	—
112	C₂×C₄	—	158	2	no	—
113	C₂×C₄	D₄×D₇₉	1	2	yes	—
114	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
115	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
116	C₂×C₄	#11929624	1	2	yes	—
117	C₈	—	2	2	no	—
118	C₈	—	4	2	no	—
119	C₈	—	316	1	no	—
120	C₂²	—	2	2	no	—
121	C₂²	—	316	4	no	—
122	C₂²	—	632	4	no	—
123	C₂²	—	632	4	no	—
124	C₂²	—	632	4	no	—
125	C₂²	#14579136	1	1	yes	characteristic
126	C₂²	#14579146	1	2	yes	—
127	C₄	—	316	2	no	—
128	C₄	#14579131	1	1	yes	characteristic
129	C₄	#14579134	1	2	yes	—
130	C₄	#14579149	1	1	yes	characteristic
131	C₂	—	2	2	no	—
132	C₂	—	632	4	no	—
133	C₂	#19098481	1	1	yes	characteristic
134	C₂	#19098834	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₆₃₂

C₂

yes

maximal, characteristic

#19098589

C₂

yes

maximal, characteristic, complemented

#19098569

C₂

yes

maximal, complemented

C₂×#14579077

C₂

yes

maximal, complemented

#341×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₁₆

C₂²

yes

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×#11929608

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

Dic₇₉⋊C₈

—

#14579083

—

#14579077

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

D₄

yes

—

D₆₃₂

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₂³×C₇₉

#41

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

#123

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

#120

yes

characteristic

C₄×C₇₉

#121

yes

—

C₄×C₇₉

#124

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#394

yes

characteristic

C₂×C₇₉

#472

yes

—

D₇₉

—

#2045

—

maximal, Sylow

C₇₉

#2045

yes

characteristic, complemented, Sylow

C₂²×D₈

—

—

—

—

D₇₉

yes

characteristic, complemented

C₂²×D₄

—

C₂×D₈

—

158

—

C₂×D₈

—

158

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

C₄⋊C₈

—

158

—

#102

—

158

—

#100

—

158

—

C₂⁴

—

158

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂×D₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

D₈

—

158

—

M₁₆

—

M₁₆

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

D₃₁₆

yes

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

158

—

102

C₄²

—

158

—

103

C₂³

—

316

—

104

C₂³

—

316

—

105

C₂³

—

632

—

106

C₂³

—

158

—

107

C₂³

#11929625

yes

characteristic

108

D₄

—

316

—

109

D₄

—

316

—

110

D₄

—

158

—

111

D₄

—

158

—

112

C₂×C₄

—

158

—

113

C₂×C₄

D₄×D₇₉

yes

—

114

C₂×C₄

D₄×D₇₉

yes

characteristic

115

C₂×C₄

C₂×D₃₁₆

yes

characteristic

116

C₂×C₄

#11929624

yes

—

117

C₈

—

118

C₈

—

119

C₈

—

316

—

120

C₂²

—

121

C₂²

—

316

—

122

C₂²

—

632

—

123

C₂²

—

632

—

124

C₂²

—

632

—

125

C₂²

#14579136

yes

characteristic

126

C₂²

#14579146

yes

—

127

C₄

—

316

—

128

C₄

#14579131

yes

characteristic

129

C₄

#14579134

yes

—

130

C₄

#14579149

yes

characteristic

131

C₂

—

132

C₂

—

632

—

133

C₂

#19098481

yes

characteristic

134

C₂

#19098834

yes

—

	subgroup	G/H
center	C₂²	#14579136
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#341×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂²×D₆₃₂	C₂
hypercenter	#341	D₇₉
hypocenter	C₇₉	#2045
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#14579136

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#341×C₇₉

C₂

socle

C₂²×C₇₉

#121

prime radical

C₂²×D₆₃₂

C₂

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
2. #19098589	C₂	semidirect
3. #19098569	C₂	semidirect
4. C₂×#14579077	C₂	semidirect
5. #341×C₇₉	C₂	semidirect
68. C₇₉	#2045	semidirect
73. #341	D₇₉	semidirect

H ≅ G/N

type

2. #19098589

C₂

semidirect

3. #19098569

C₂

semidirect

4. C₂×#14579077

C₂

semidirect

5. #341×C₇₉

C₂

semidirect

68. C₇₉

#2045

semidirect

73. #341

D₇₉

semidirect

Subgroups — #23764657

Conjugacy classes of subgroups

Complements