Group #23761276 — subgroups

Subgroups — #23761276

Order 10112.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098527	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#407×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929608	—	2	1	no	—
5	C₂²×C₇₉⋊C₈	C₄	1	2	yes	—
6	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
7	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
8	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
9	C₂²⋊(C₇₉⋊C₈)	C₄	1	2	yes	—
10	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×C₇₉	—	2	1	no	—
12	C₂²⋊C₈×C₇₉	—	2	1	no	—
13	C₂²⋊C₈×C₇₉	C₄	1	2	yes	—
14	#11929608	—	4	2	no	—
15	C₂×C₇₉⋊C₈	—	2	2	no	—
16	C₂×C₇₉⋊C₈	—	2	2	no	—
17	C₂×C₇₉⋊C₈	—	4	2	no	—
18	C₂⁴×C₇₉	Q₈	1	1	yes	characteristic
19	C₂²×C₄×C₇₉	—	4	2	no	—
20	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
26	M₁₆×C₇₉	—	4	2	no	—
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₂³×C₇₉	—	2	2	no	—
29	C₂³×C₇₉	—	4	1	no	—
30	C₂³×C₇₉	—	4	1	no	—
31	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂³×C₇₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	—	2	2	no	—
35	C₂×C₄×C₇₉	—	2	2	no	—
36	C₂×C₄×C₇₉	—	2	2	no	—
37	C₂×C₄×C₇₉	—	4	1	no	—
38	C₂×C₄×C₇₉	—	4	1	no	—
39	C₂×C₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₈×C₇₉	—	4	2	no	—
45	C₇₉⋊C₈	—	4	2	no	—
46	C₇₉⋊C₈	—	4	2	no	—
47	C₂²×C₇₉	—	2	1	no	—
48	C₂²×C₇₉	—	2	1	no	—
49	C₂²×C₇₉	—	2	1	no	—
50	C₂²×C₇₉	—	2	1	no	—
51	C₂²×C₇₉	—	2	1	no	—
52	C₂²×C₇₉	—	2	1	no	—
53	C₂²×C₇₉	—	2	1	no	—
54	C₂²×C₇₉	—	2	1	no	—
55	C₂²×C₇₉	—	4	4	no	—
56	C₂²×C₇₉	#95	1	1	yes	characteristic
57	C₂²×C₇₉	#108	1	2	yes	—
58	C₄×C₇₉	—	2	1	no	—
59	C₄×C₇₉	—	2	1	no	—
60	C₄×C₇₉	—	2	1	no	—
61	C₄×C₇₉	#99	1	2	yes	—
62	C₂×C₇₉	—	2	2	no	—
63	C₂×C₇₉	—	4	1	no	—
64	C₂×C₇₉	—	4	1	no	—
65	C₂×C₇₉	#338	1	1	yes	characteristic
66	C₂×C₇₉	#341	1	1	yes	characteristic
67	C₂×C₇₉	#342	1	1	yes	characteristic
68	#1293	—	79	1	no	maximal, Sylow
69	C₇₉	#1293	1	1	yes	characteristic, complemented, Sylow
70	#407	—	79	1	no	—
71	#407	D₇₉	1	1	yes	characteristic
72	C₂×C₂²⋊C₈	—	79	1	no	—
73	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
74	C₂×M₁₆	—	2	1	no	—
75	C₂×M₁₆	—	158	1	no	—
76	C₂²×C₈	—	79	2	no	—
77	C₂²⋊C₈	—	2	1	no	—
78	C₂²⋊C₈	—	79	2	no	—
79	C₂²⋊C₈	—	158	1	no	—
80	C₂²⋊C₈	—	158	1	no	—
81	C₂²⋊C₈	—	158	1	no	—
82	C₂²⋊C₈	Dic₇₉	1	2	yes	—
83	C₂⁴	Dic₁₅₈	1	1	yes	characteristic
84	C₂²×C₄	—	4	2	no	—
85	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
86	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
87	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
88	C₂²×C₄	C₂×Dic₇₉	1	1	yes	characteristic
89	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
91	M₁₆	—	4	2	no	—
92	M₁₆	—	316	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	316	2	no	—
95	C₂×C₈	—	158	2	no	—
96	C₂×C₈	—	158	2	no	—
97	C₂³	—	2	2	no	—
98	C₂³	—	4	1	no	—
99	C₂³	—	4	1	no	—
100	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
101	C₂³	Dic₇₉⋊C₄	1	1	yes	characteristic
102	C₂³	C₄⋊Dic₇₉	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	1	no	—
109	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
110	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
111	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
112	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
113	C₈	—	4	2	no	—
114	C₈	—	316	2	no	—
115	C₈	—	316	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	—	4	4	no	—
125	C₂²	C₇₉⋊#95	1	1	yes	characteristic
126	C₂²	#14579096	1	2	yes	—
127	C₄	—	2	1	no	—
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	#14579075	1	2	yes	—
131	C₂	—	2	2	no	—
132	C₂	—	4	1	no	—
133	C₂	—	4	1	no	—
134	C₂	C₇₉⋊#338	1	1	yes	characteristic
135	C₂	#19098327	1	1	yes	characteristic
136	C₂	#19098329	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098527

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₇₉⋊C₈)

C₂

yes

maximal, characteristic

#407×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

—

C₂²×C₇₉⋊C₈

C₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

C₄

yes

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×M₁₆×C₇₉

—

C₂²⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

C₄

yes

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂⁴×C₇₉

Q₈

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂³×C₇₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₄

yes

characteristic

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#95

yes

characteristic

C₂²×C₇₉

#108

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#99

yes

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

#407

—

#407

D₇₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

158

—

C₂²×C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

158

—

C₂²⋊C₈

—

158

—

C₂²⋊C₈

—

158

—

C₂²⋊C₈

Dic₇₉

yes

—

C₂⁴

Dic₁₅₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂×Dic₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

C₂²×C₄

C₂²⋊D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

316

—

C₂×C₈

—

C₂×C₈

—

316

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

Dic₇₉⋊C₄

yes

characteristic

101

C₂³

Dic₇₉⋊C₄

yes

characteristic

102

C₂³

C₄⋊Dic₇₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄×Dic₇₉

yes

characteristic

110

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

111

C₂×C₄

(C₂×D₇₉)⋊C₄

yes

characteristic

112

C₂×C₄

C₂²⋊Dic₇₉

yes

characteristic

113

C₈

—

114

C₈

—

316

—

115

C₈

—

316

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₇₉⋊#95

yes

characteristic

126

C₂²

#14579096

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#14579075

yes

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

C₇₉⋊#338

yes

characteristic

135

C₂

#19098327

yes

characteristic

136

C₂

#19098329

yes

characteristic

	subgroup	G/H
center	C₂²	C₇₉⋊#95
commutator	C₂×C₄×C₇₉	C₄²
Frattini	C₂³×C₄	C₂×D₇₉
Fitting	#407×C₇₉	C₂
socle	C₂²×C₇₉	#95
prime radical	C₂⁴×C₇₉	Q₈
cosocle	C₂³×C₄×C₇₉	C₂²
hypercenter	#407	D₇₉
hypocenter	C₇₉	#1293
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₇₉⋊#95

commutator

C₂×C₄×C₇₉

C₄²

Frattini

C₂³×C₄

C₂×D₇₉

Fitting

#407×C₇₉

C₂

socle

C₂²×C₇₉

#95

prime radical

C₂⁴×C₇₉

Q₈

cosocle

C₂³×C₄×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
69. C₇₉	#1293	semidirect

H ≅ G/N

type

69. C₇₉

#1293

semidirect

Subgroups — #23761276

Conjugacy classes of subgroups

Complements