Group #23762876 — subgroups

Subgroups — #23762876

Order 10112.

198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 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	#19098755	C₂	1	2	yes	maximal, complemented
2	#19098642	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098314	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098307	C₂	1	2	yes	maximal, complemented
5	#493×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929609	—	2	2	no	—
7	C₂×#11929607	—	2	1	no	—
8	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
9	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
11	#14579082	—	2	2	no	—
12	(C₂×D₇₉)⋊C₈	—	2	1	no	—
13	C₂×D₈×C₇₉	—	2	1	no	—
14	C₂×D₈×C₇₉	—	2	1	no	—
15	#127×C₇₉	C₂²	1	2	yes	—
16	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×D₃₁₆	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₉	—	2	1	no	—
19	#11929609	—	4	4	no	—
20	#11929607	—	4	2	no	—
21	C₂×C₇₉⋊C₈	—	2	1	no	—
22	C₂×C₇₉⋊C₈	—	2	2	no	—
23	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
24	(C₂×D₇₉)⋊C₄	—	2	1	no	—
25	C₂×D₄×C₇₉	—	2	2	no	—
26	C₂×D₄×C₇₉	—	2	2	no	—
27	C₂×D₄×C₇₉	—	2	2	no	—
28	D₈×C₇₉	—	4	2	no	—
29	D₈×C₇₉	—	4	2	no	—
30	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
31	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
32	C₄²×C₇₉	C₂³	1	1	yes	characteristic
33	C₂³×C₇₉	—	4	2	no	—
34	C₂²×D₇₉	—	2	1	no	—
35	D₄×C₇₉	—	4	2	no	—
36	D₄×C₇₉	—	4	2	no	—
37	D₄×C₇₉	—	4	2	no	—
38	D₄×C₇₉	—	4	2	no	—
39	D₄×C₇₉	—	8	2	no	—
40	C₂×C₄×C₇₉	C₂×D₄	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	D₃₁₆	—	2	2	no	—
45	C₄×D₇₉	—	4	1	no	—
46	C₄×D₇₉	—	4	1	no	—
47	C₈×C₇₉	—	2	1	no	—
48	C₈×C₇₉	D₈	1	2	yes	complemented
49	C₇₉⋊C₈	—	4	1	no	—
50	C₇₉⋊C₈	—	4	2	no	—
51	C₂²×C₇₉	—	8	2	no	—
52	C₂²×C₇₉	—	8	2	no	—
53	C₂²×C₇₉	—	8	2	no	—
54	C₂²×C₇₉	#121	1	1	yes	characteristic
55	C₂×D₇₉	—	4	1	no	—
56	C₂×D₇₉	—	4	1	no	—
57	C₂×D₇₉	—	4	1	no	—
58	C₄×C₇₉	—	2	1	no	—
59	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
60	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
61	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
62	Dic₇₉	—	4	1	no	—
63	C₂×C₇₉	—	16	2	no	—
64	C₂×C₇₉	#459	1	1	yes	characteristic
65	C₂×C₇₉	#469	1	1	yes	characteristic
66	C₂×C₇₉	#472	1	1	yes	characteristic
67	D₇₉	—	8	1	no	—
68	#1687	—	79	1	no	maximal, Sylow
69	C₇₉	#1687	1	1	yes	characteristic, complemented, Sylow
70	#493	D₇₉	1	1	yes	characteristic, complemented
71	#459	—	79	2	no	—
72	#436	—	79	1	no	—
73	#334	—	79	1	no	—
74	#331	—	79	2	no	—
75	C₂×D₈	—	2	1	no	—
76	C₂×D₈	—	2	1	no	—
77	C₂×D₈	—	158	2	no	—
78	C₂×M₁₆	—	158	1	no	—
79	#127	C₂×D₇₉	1	2	yes	—
80	C₄×D₄	—	79	1	no	—
81	C₄⋊C₈	—	79	1	no	—
82	C₄⋊C₈	—	79	2	no	—
83	#102	—	158	2	no	—
84	C₂²⋊C₈	—	158	1	no	—
85	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
86	C₂×D₄	—	2	2	no	—
87	C₂×D₄	—	2	2	no	—
88	C₂×D₄	—	2	2	no	—
89	C₂×D₄	—	79	1	no	—
90	C₂²×C₄	—	158	1	no	—
91	D₈	—	4	2	no	—
92	D₈	—	4	2	no	—
93	D₈	—	316	4	no	—
94	M₁₆	—	316	2	no	—
95	C₂×C₈	—	158	2	no	—
96	C₂×C₈	—	158	1	no	—
97	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
98	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
99	C₄⋊C₄	—	79	1	no	—
100	C₂²⋊C₄	—	158	1	no	—
101	C₄²	C₂²×D₇₉	1	1	yes	characteristic
102	C₂³	—	4	2	no	—
103	C₂³	—	158	1	no	—
104	D₄	—	4	2	no	—
105	D₄	—	4	2	no	—
106	D₄	—	4	2	no	—
107	D₄	—	4	2	no	—
108	D₄	—	8	2	no	—
109	D₄	—	158	2	no	—
110	C₂×C₄	—	316	1	no	—
111	C₂×C₄	—	316	1	no	—
112	C₂×C₄	—	158	1	no	—
113	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
114	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
115	C₂×C₄	#11929623	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	316	1	no	—
118	C₈	—	316	2	no	—
119	C₈	#11929609	1	2	yes	complemented
120	C₂²	—	8	2	no	—
121	C₂²	—	8	2	no	—
122	C₂²	—	8	2	no	—
123	C₂²	—	316	1	no	—
124	C₂²	—	316	1	no	—
125	C₂²	—	316	1	no	—
126	C₂²	#14579132	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	316	1	no	—
129	C₄	C₂×#11929609	1	1	yes	characteristic
130	C₄	#14579185	1	2	yes	—
131	C₄	#14579187	1	1	yes	characteristic
132	C₂	—	16	2	no	—
133	C₂	—	632	1	no	—
134	C₂	#19098755	1	1	yes	characteristic
135	C₂	#19098813	1	1	yes	characteristic
136	C₂	#19098830	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098755

C₂

yes

maximal, complemented

#19098642

C₂

yes

maximal, characteristic, complemented

#19098314

C₂

yes

maximal, characteristic, complemented

#19098307

C₂

yes

maximal, complemented

#493×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929609

—

C₂×#11929607

—

C₄×D₃₁₆

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

#14579082

—

(C₂×D₇₉)⋊C₈

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

#127×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

D₄

yes

characteristic

C₂×C₄×D₇₉

—

#11929609

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

D₄

yes

characteristic

(C₂×D₇₉)⋊C₄

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

—

C₈×C₇₉

D₈

yes

complemented

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1687

—

maximal, Sylow

C₇₉

#1687

yes

characteristic, complemented, Sylow

#493

D₇₉

yes

characteristic, complemented

—

—

—

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

158

—

C₂×M₁₆

—

158

—

#127

C₂×D₇₉

yes

—

C₄×D₄

—

C₄⋊C₈

—

C₄⋊C₈

—

#102

—

158

—

C₂²⋊C₈

—

158

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

158

—

D₈

—

D₈

—

D₈

—

316

—

M₁₆

—

316

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₄⋊C₄

—

100

C₂²⋊C₄

—

158

—

101

C₄²

C₂²×D₇₉

yes

characteristic

102

C₂³

—

103

C₂³

—

158

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

108

D₄

—

109

D₄

—

158

—

110

C₂×C₄

—

316

—

111

C₂×C₄

—

316

—

112

C₂×C₄

—

158

—

113

C₂×C₄

D₄×D₇₉

yes

characteristic

114

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

115

C₂×C₄

#11929623

yes

characteristic

116

C₈

—

117

C₈

—

316

—

118

C₈

—

316

—

119

C₈

#11929609

yes

complemented

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

316

—

124

C₂²

—

316

—

125

C₂²

—

316

—

126

C₂²

#14579132

yes

characteristic

127

C₄

—

128

C₄

—

316

—

129

C₄

C₂×#11929609

yes

characteristic

130

C₄

#14579185

yes

—

131

C₄

#14579187

yes

characteristic

132

C₂

—

133

C₂

—

632

—

134

C₂

#19098755

yes

characteristic

135

C₂

#19098813

yes

characteristic

136

C₂

#19098830

yes

characteristic

	subgroup	G/H
center	C₂²	#14579132
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#493×C₇₉	C₂
socle	C₂²×C₇₉	#121
hypercenter	#493	D₇₉
hypocenter	C₇₉	#1687
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#14579132

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#493×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #19098755	C₂	semidirect
2. #19098642	C₂	semidirect
3. #19098314	C₂	semidirect
4. #19098307	C₂	semidirect
5. #493×C₇₉	C₂	semidirect
48. C₈×C₇₉	D₈	semidirect
69. C₇₉	#1687	semidirect
70. #493	D₇₉	semidirect
119. C₈	#11929609	semidirect

H ≅ G/N

type

1. #19098755

C₂

semidirect

2. #19098642

C₂

semidirect

3. #19098314

C₂

semidirect

4. #19098307

C₂

semidirect

5. #493×C₇₉

C₂

semidirect

48. C₈×C₇₉

D₈

semidirect

69. C₇₉

#1687

semidirect

70. #493

D₇₉

semidirect

119. C₈

#11929609

semidirect

Subgroups — #23762876

Conjugacy classes of subgroups

Complements