Group #23764186 — subgroups

Subgroups — #23764186

Order 10112.

196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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	#19098605	C₂	1	2	yes	maximal
2	C₂×#14579095	C₂	1	1	yes	maximal, characteristic
3	#19098518	C₂	1	1	yes	maximal, characteristic
4	#19098331	C₂	1	2	yes	maximal
5	C₂×#108×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#11929608	C₂²	1	1	yes	characteristic
7	#14579120	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
9	#14579095	—	2	1	no	—
10	#14579095	—	2	1	no	—
11	#14579095	—	2	2	no	—
12	#14579093	—	2	2	no	—
13	#14579071	—	2	1	no	—
14	C₈×Dic₇₉	—	2	1	no	—
15	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
16	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	#108×C₇₉	C₄	1	4	yes	complemented
18	C₂²×Dic₇₉	—	2	2	no	—
19	#11929608	—	2	1	no	—
20	#11929608	Q₈	1	2	yes	—
21	C₂×C₇₉⋊C₈	—	2	1	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	—	2	2	no	—
24	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
26	C₂²⋊Dic₇₉	—	2	1	no	—
27	C₄×Dic₇₉	—	2	1	no	—
28	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
29	M₁₆×C₇₉	—	2	2	no	—
30	M₁₆×C₇₉	C₂×C₄	1	4	yes	—
31	C₂×C₈×C₇₉	—	2	2	no	—
32	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
34	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
35	C₂×C₈×C₇₉	Q₈	1	2	yes	—
36	C₂³×C₇₉	#41	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
43	C₂×Dic₇₉	—	2	1	no	—
44	C₂×Dic₇₉	—	2	1	no	—
45	C₂×Dic₇₉	—	4	2	no	—
46	C₂×Dic₇₉	—	8	2	no	—
47	C₈×C₇₉	—	2	4	no	—
48	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
49	C₈×C₇₉	C₄⋊C₄	1	2	yes	—
50	C₇₉⋊C₈	—	2	2	no	—
51	C₂²×C₇₉	—	2	1	no	—
52	C₂²×C₇₉	—	2	1	no	—
53	C₂²×C₇₉	C₄×Q₈	1	1	yes	characteristic
54	C₂²×C₇₉	#121	1	1	yes	characteristic
55	C₂²×C₇₉	#125	1	1	yes	characteristic
56	C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
58	C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
59	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
60	Dic₇₉	—	4	1	no	—
61	Dic₇₉	—	4	1	no	—
62	Dic₇₉	—	8	2	no	—
63	C₂×C₇₉	—	2	1	no	—
64	C₂×C₇₉	—	2	1	no	—
65	C₂×C₇₉	#389	1	1	yes	characteristic
66	C₂×C₇₉	#472	1	1	yes	characteristic
67	C₂×C₇₉	#473	1	1	yes	characteristic
68	#1952	—	79	1	no	maximal, Sylow
69	C₇₉	#1952	1	1	yes	characteristic, complemented, Sylow
70	C₂×#108	D₇₉	1	1	yes	characteristic
71	#428	—	79	2	no	—
72	C₂×#107	—	79	1	no	—
73	#405	—	79	1	no	—
74	#343	—	79	2	no	—
75	C₂×M₁₆	—	79	1	no	—
76	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
77	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
78	#117	—	79	1	no	—
79	C₂×C₄⋊C₄	—	79	2	no	—
80	#108	Dic₇₉	1	4	yes	complemented
81	#107	—	158	2	no	—
82	#107	—	158	1	no	—
83	#107	—	158	1	no	—
84	#106	—	158	2	no	—
85	#97	—	158	1	no	—
86	C₄×C₈	—	158	1	no	—
87	C₂²×C₄	—	158	2	no	—
88	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	M₁₆	—	79	2	no	—
91	M₁₆	—	158	1	no	—
92	M₁₆	C₂×Dic₇₉	1	4	yes	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	158	1	no	—
95	C₂×C₈	Dic₁₅₈	1	2	yes	—
96	C₂×C₈	D₃₁₆	1	1	yes	characteristic
97	C₂×C₈	D₃₁₆	1	1	yes	characteristic
98	C₂×C₈	C₂×Dic₇₉	1	2	yes	—
99	C₄⋊C₄	—	79	1	no	—
100	C₄⋊C₄	—	79	1	no	—
101	C₄⋊C₄	—	158	2	no	—
102	C₄⋊C₄	—	158	2	no	—
103	C₂²⋊C₄	—	158	1	no	—
104	C₄²	—	158	1	no	—
105	C₂³	#11929625	1	1	yes	characteristic
106	C₂×C₄	—	316	2	no	—
107	C₂×C₄	—	632	2	no	—
108	C₂×C₄	—	158	1	no	—
109	C₂×C₄	—	158	1	no	—
110	C₂×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
111	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
112	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
113	C₂×C₄	Q₈×D₇₉	1	1	yes	characteristic
114	C₂×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
115	C₂×C₄	#11929623	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₈	—	158	2	no	—
118	C₈	C₄⋊Dic₇₉	1	2	yes	—
119	C₈	C₄⋊Dic₇₉	1	2	yes	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	Q₈×Dic₇₉	1	1	yes	characteristic
123	C₂²	#14579136	1	1	yes	characteristic
124	C₂²	#14579152	1	1	yes	characteristic
125	C₄	—	316	1	no	—
126	C₄	—	316	1	no	—
127	C₄	—	632	2	no	—
128	C₄	C₂×C₄⋊Dic₇₉	1	1	yes	characteristic
129	C₄	D₄×Dic₇₉	1	1	yes	characteristic
130	C₄	#14579141	1	1	yes	characteristic
131	C₄	#14579160	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	#19098462	1	1	yes	characteristic
135	C₂	#19098834	1	1	yes	characteristic
136	C₂	#19098839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098605

C₂

yes

maximal

C₂×#14579095

C₂

yes

maximal, characteristic

#19098518

C₂

yes

maximal, characteristic

#19098331

C₂

yes

maximal

C₂×#108×C₇₉

C₂

yes

maximal, characteristic

C₂×#11929608

C₂²

yes

characteristic

#14579120

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

—

—

—

—

—

C₈×Dic₇₉

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

#108×C₇₉

C₄

yes

complemented

C₂²×Dic₇₉

—

#11929608

—

#11929608

Q₈

yes

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

characteristic

C₄⋊Dic₇₉

D₄

yes

characteristic

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

Q₈

yes

—

C₂³×C₇₉

#41

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

C₄⋊C₄

yes

—

C₈×C₇₉

C₄⋊C₄

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₄×Q₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×#108

D₇₉

yes

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#108

Dic₇₉

yes

complemented

#107

—

158

—

#107

—

158

—

#107

—

158

—

#106

—

158

—

#97

—

158

—

C₄×C₈

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

158

—

M₁₆

C₂×Dic₇₉

yes

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

Dic₁₅₈

yes

—

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

D₃₁₆

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

158

—

102

C₄⋊C₄

—

158

—

103

C₂²⋊C₄

—

158

—

104

C₄²

—

158

—

105

C₂³

#11929625

yes

characteristic

106

C₂×C₄

—

316

—

107

C₂×C₄

—

632

—

108

C₂×C₄

—

158

—

109

C₂×C₄

—

158

—

110

C₂×C₄

C₂²×Dic₇₉

yes

characteristic

111

C₂×C₄

D₄×D₇₉

yes

characteristic

112

C₂×C₄

C₂×D₃₁₆

yes

characteristic

113

C₂×C₄

Q₈×D₇₉

yes

characteristic

114

C₂×C₄

C₂×Dic₁₅₈

yes

characteristic

115

C₂×C₄

#11929623

yes

characteristic

116

C₈

—

117

C₈

—

158

—

118

C₈

C₄⋊Dic₇₉

yes

—

119

C₈

C₄⋊Dic₇₉

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

Q₈×Dic₇₉

yes

characteristic

123

C₂²

#14579136

yes

characteristic

124

C₂²

#14579152

yes

characteristic

125

C₄

—

316

—

126

C₄

—

316

—

127

C₄

—

632

—

128

C₄

C₂×C₄⋊Dic₇₉

yes

characteristic

129

C₄

D₄×Dic₇₉

yes

characteristic

130

C₄

#14579141

yes

characteristic

131

C₄

#14579160

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

#19098462

yes

characteristic

135

C₂

#19098834

yes

characteristic

136

C₂

#19098839

yes

characteristic

	subgroup	G/H
center	C₂²	#14579136
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#108×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂³×C₇₉	#41
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	C₂×#108	D₇₉
hypocenter	C₇₉	#1952
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#14579136

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#108×C₇₉

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
17. #108×C₇₉	C₄	semidirect
69. C₇₉	#1952	semidirect
80. #108	Dic₇₉	semidirect

H ≅ G/N

type

17. #108×C₇₉

C₄

semidirect

69. C₇₉

#1952

semidirect

80. #108

Dic₇₉

semidirect

Subgroups — #23764186

Conjugacy classes of subgroups

Complements