Group #23762982 — subgroups

Subgroups — #23762982

Order 10112.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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	#19098914	C₂	1	1	yes	maximal, characteristic
2	#19098858	C₂	1	1	yes	maximal, characteristic
3	#19098848	C₂	1	1	yes	maximal, characteristic
4	#19098314	C₂	1	1	yes	maximal, characteristic
5	#19098311	C₂	1	1	yes	maximal, characteristic
6	#19098310	C₂	1	1	yes	maximal, characteristic
7	#446×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579161	C₂²	1	1	yes	characteristic
9	#14579161	C₂²	1	1	yes	characteristic
10	#14579094	—	2	1	no	—
11	#14579092	—	2	1	no	—
12	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	#14579086	—	2	1	no	—
15	#14579086	—	2	1	no	—
16	#14579085	—	2	1	no	—
17	#14579085	—	2	1	no	—
18	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₇₉	—	2	1	no	—
20	C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
21	#97×C₇₉	—	2	1	no	—
22	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₅₈	—	2	1	no	—
24	C₂×Dic₁₅₈	—	2	1	no	—
25	C₂×C₇₉⋊C₈	—	2	1	no	—
26	C₂×C₇₉⋊C₈	—	2	1	no	—
27	C₄⋊Dic₇₉	—	2	1	no	—
28	C₄⋊Dic₇₉	—	2	1	no	—
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×Q₈×C₇₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₇₉	—	2	1	no	—
33	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
37	C₄²×C₇₉	—	2	1	no	—
38	C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	Q₈×C₇₉	—	2	1	no	—
40	Q₈×C₇₉	—	2	1	no	—
41	C₂×C₄×C₇₉	—	2	1	no	—
42	C₂×C₄×C₇₉	—	2	1	no	—
43	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
46	C₂×Dic₇₉	—	4	1	no	—
47	C₂×Dic₇₉	—	4	1	no	—
48	Dic₁₅₈	—	4	1	no	—
49	Dic₁₅₈	—	4	1	no	—
50	Dic₁₅₈	—	8	1	no	—
51	C₈×C₇₉	—	2	1	no	—
52	C₈×C₇₉	—	2	1	no	—
53	C₈×C₇₉	—	4	1	no	—
54	C₇₉⋊C₈	—	4	1	no	—
55	C₇₉⋊C₈	—	4	1	no	—
56	C₂²×C₇₉	#121	1	1	yes	characteristic
57	C₄×C₇₉	—	2	1	no	—
58	C₄×C₇₉	—	4	1	no	—
59	C₄×C₇₉	—	4	1	no	—
60	C₄×C₇₉	#135	1	1	yes	characteristic
61	C₄×C₇₉	#137	1	1	yes	characteristic
62	C₄×C₇₉	#137	1	1	yes	characteristic
63	C₄×C₇₉	#137	1	1	yes	characteristic
64	Dic₇₉	—	8	1	no	—
65	Dic₇₉	—	8	1	no	—
66	C₂×C₇₉	#464	1	1	yes	characteristic
67	C₂×C₇₉	#470	1	1	yes	characteristic
68	C₂×C₇₉	#471	1	1	yes	characteristic
69	#1704	—	79	1	no	maximal, Sylow
70	C₇₉	#1704	1	1	yes	characteristic, complemented, Sylow
71	#487	—	79	1	no	—
72	#477	—	79	1	no	—
73	#475	—	79	1	no	—
74	#446	D₇₉	1	1	yes	characteristic
75	#334	—	79	1	no	—
76	#333	—	79	1	no	—
77	#332	—	79	1	no	—
78	C₄⋊Q₈	—	79	1	no	—
79	C₄⋊Q₈	—	79	1	no	—
80	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
81	#107	—	158	1	no	—
82	#106	—	158	1	no	—
83	C₄⋊C₈	—	2	1	no	—
84	C₄⋊C₈	—	79	1	no	—
85	C₄⋊C₈	—	79	1	no	—
86	C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
87	#103	—	158	1	no	—
88	#103	—	158	1	no	—
89	#103	—	158	1	no	—
90	#103	—	158	1	no	—
91	#97	—	2	1	no	—
92	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
93	C₂×Q₈	—	158	1	no	—
94	C₂×Q₈	—	158	1	no	—
95	C₂×Q₈	D₃₁₆	1	1	yes	characteristic
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	158	1	no	—
98	C₂×C₈	—	158	1	no	—
99	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
100	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	158	1	no	—
103	C₄⋊C₄	—	158	1	no	—
104	C₄⋊C₄	—	158	1	no	—
105	C₄⋊C₄	—	158	1	no	—
106	C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
107	C₄²	—	2	1	no	—
108	C₄²	C₂²×D₇₉	1	1	yes	characteristic
109	Q₈	—	2	1	no	—
110	Q₈	—	2	1	no	—
111	Q₈	—	316	1	no	—
112	Q₈	—	316	1	no	—
113	Q₈	—	632	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	316	1	no	—
117	C₂×C₄	—	316	1	no	—
118	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
119	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
120	C₂×C₄	#11929624	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	2	1	no	—
123	C₈	—	4	1	no	—
124	C₈	—	316	1	no	—
125	C₈	—	316	1	no	—
126	C₂²	#14579135	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	4	1	no	—
129	C₄	—	4	1	no	—
130	C₄	—	632	1	no	—
131	C₄	—	632	1	no	—
132	C₄	#14579181	1	1	yes	characteristic
133	C₄	#14579192	1	1	yes	characteristic
134	C₄	#14579194	1	1	yes	characteristic
135	C₄	#14579194	1	1	yes	characteristic
136	C₂	#19098785	1	1	yes	characteristic
137	C₂	#19098821	1	1	yes	characteristic
138	C₂	#19098826	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098914

C₂

yes

maximal, characteristic

#19098858

C₂

yes

maximal, characteristic

#19098848

C₂

yes

maximal, characteristic

#19098314

C₂

yes

maximal, characteristic

#19098311

C₂

yes

maximal, characteristic

#19098310

C₂

yes

maximal, characteristic

#446×C₇₉

C₂

yes

maximal, characteristic

#14579161

C₂²

yes

characteristic

#14579161

C₂²

yes

characteristic

#14579094

—

#14579092

—

C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₇₉⋊C₈)

C₂²

yes

—

—

—

—

C₄×Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

C₂²

yes

characteristic

#97×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

#121

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

D₇₉

yes

—

—

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₇₉

yes

characteristic

#107

—

158

—

#106

—

158

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₉

yes

characteristic

#103

—

158

—

#103

—

158

—

#103

—

158

—

#103

—

158

—

#97

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂×Q₈

D₃₁₆

yes

characteristic

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

100

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

158

—

103

C₄⋊C₄

—

158

—

104

C₄⋊C₄

—

158

—

105

C₄⋊C₄

—

158

—

106

C₄⋊C₄

D₃₁₆

yes

characteristic

107

C₄²

—

108

C₄²

C₂²×D₇₉

yes

characteristic

109

Q₈

—

110

Q₈

—

111

Q₈

—

316

—

112

Q₈

—

316

—

113

Q₈

—

632

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

316

—

117

C₂×C₄

—

316

—

118

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

119

C₂×C₄

C₂×D₃₁₆

yes

characteristic

120

C₂×C₄

#11929624

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

316

—

125

C₈

—

316

—

126

C₂²

#14579135

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

632

—

131

C₄

—

632

—

132

C₄

#14579181

yes

characteristic

133

C₄

#14579192

yes

characteristic

134

C₄

#14579194

yes

characteristic

135

C₄

#14579194

yes

characteristic

136

C₂

#19098785

yes

characteristic

137

C₂

#19098821

yes

characteristic

138

C₂

#19098826

yes

characteristic

	subgroup	G/H
center	C₂²	#14579135
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#446×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#121
hypercenter	#446	D₇₉
hypocenter	C₇₉	#1704
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#14579135

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#446×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
70. C₇₉	#1704	semidirect

H ≅ G/N

type

70. C₇₉

#1704

semidirect

Subgroups — #23762982

Conjugacy classes of subgroups

Complements