Group #16836282 — subgroups

Subgroups — #16836282

Order 3712.

364 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 166 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	#14272215	C₂	1	4	yes	maximal, complemented
2	#14272212	C₂	1	4	yes	maximal, complemented
3	#14272170	C₂	1	2	yes	maximal
4	#14272168	C₂	1	1	yes	maximal, characteristic
5	#14272128	C₂	1	2	yes	maximal
6	C₄×D₂₉⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#14271719	C₂	1	1	yes	maximal, characteristic
8	C₂×#90796	C₂²	1	2	yes	—
9	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂₉×#125	C₄	1	1	yes	characteristic
12	#11745258	C₄	1	4	yes	—
13	#11745254	C₂²	1	2	yes	—
14	#11745250	C₄	1	2	yes	—
15	#11745249	C₂²	1	4	yes	—
16	C₄²×D₂₉	C₂²	1	1	yes	characteristic
17	#11745232	C₄	1	1	yes	characteristic
18	#11745220	C₂²	1	4	yes	—
19	#11745220	C₂²	1	4	yes	—
20	#11745218	C₂²	1	4	yes	—
21	C₄⋊#6599	C₂²	1	4	yes	—
22	C₄×#6599	C₂²	1	2	yes	—
23	C₄×#6599	C₂²	1	2	yes	—
24	C₄×#6599	C₂²	1	4	yes	—
25	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₅₈	C₂×C₄	1	4	yes	—
28	C₂×#6599	C₂³	1	2	yes	—
29	C₂×#6599	C₂³	1	4	yes	—
30	C₂×#6599	C₂³	1	1	yes	characteristic
31	C₂×#6599	C₂³	1	1	yes	characteristic
32	#90796	—	2	4	no	—
33	D₂₉⋊C₈	—	2	2	no	—
34	D₂₉⋊C₈	Q₈	1	4	yes	complemented
35	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
36	C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
37	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
38	#90781	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₂₉	C₂×C₄	1	2	yes	—
40	#90779	C₂×C₄	1	4	yes	—
41	#90779	C₂×C₄	1	4	yes	—
42	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
43	C₄×Dic₂₉	C₂³	1	2	yes	—
44	C₄×Dic₂₉	C₂³	1	4	yes	—
45	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
50	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
51	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
52	C₄×D₂₉	—	2	4	no	—
53	C₄×D₂₉	C₂×Q₈	1	2	yes	—
54	C₄×D₂₉	#41	1	2	yes	—
55	Dic₅₈	—	2	8	no	—
56	#6599	—	2	2	no	—
57	#6599	—	2	4	no	—
58	#6599	C₂×Q₈	1	2	yes	—
59	#6599	C₂×Q₈	1	2	yes	—
60	#2960	—	29	1	no	maximal, Sylow
61	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
62	C₂×D₂₉	—	2	2	no	—
63	C₂×D₂₉	C₄×Q₈	1	2	yes	—
64	C₄×C₂₉	—	2	4	no	—
65	C₄×C₂₉	—	2	2	no	—
66	C₄×C₂₉	C₄×Q₈	1	2	yes	—
67	Dic₂₉	—	2	4	no	—
68	Dic₂₉	#131	1	4	yes	—
69	Dic₂₉	C₂²×Q₈	1	1	yes	characteristic
70	Dic₂₉	C₂×#41	1	1	yes	characteristic
71	#533	—	29	1	no	—
72	#446	—	29	4	no	—
73	C₈×Q₈	—	29	4	no	—
74	#424	—	29	2	no	—
75	#423	—	29	1	no	—
76	#405	—	29	2	no	—
77	C₂×C₄×C₈	—	29	1	no	—
78	C₂×C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic
79	C₂×C₂₉	C₂×#131	1	2	yes	—
80	D₂₉	—	2	2	no	—
81	C₂×M₁₆	—	29	2	no	—
82	C₂²×C₈	—	29	1	no	—
83	C₂²×C₈	—	29	1	no	—
84	C₄⋊Q₈	—	29	2	no	—
85	#125	—	29	1	no	—
86	#125	#1181	1	1	yes	characteristic
87	C₂²⋊Q₈	—	29	4	no	—
88	C₄×Q₈	—	29	4	no	—
89	#117	—	29	2	no	—
90	C₂×C₄²	—	29	1	no	—
91	C₄⋊C₈	—	29	4	no	—
92	C₄⋊C₈	—	29	4	no	—
93	C₄⋊C₈	—	29	4	no	—
94	#97	—	29	4	no	—
95	C₄×C₈	—	29	2	no	—
96	C₄×C₈	—	29	2	no	—
97	C₄×C₈	—	29	4	no	—
98	C₂₉	#2960	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	29	4	no	—
100	C₂²×C₄	—	29	1	no	—
101	C₂²×C₄	—	29	2	no	—
102	M₁₆	—	58	4	no	—
103	C₂×C₈	—	29	1	no	—
104	C₂×C₈	—	29	1	no	—
105	C₂×C₈	—	29	4	no	—
106	C₂×C₈	—	29	2	no	—
107	C₂×C₈	—	29	4	no	—
108	C₂×C₈	—	58	2	no	—
109	C₄⋊C₄	—	29	2	no	—
110	C₄⋊C₄	—	29	4	no	—
111	C₄⋊C₄	—	29	4	no	—
112	C₄⋊C₄	C₂×#1181	1	2	yes	—
113	C₄⋊C₄	C₂×#1181	1	4	yes	—
114	C₂²⋊C₄	—	29	4	no	—
115	C₄²	—	29	2	no	—
116	C₄²	—	29	4	no	—
117	C₄²	—	29	1	no	—
118	C₄²	C₂×#1181	1	1	yes	characteristic
119	C₂³	—	29	1	no	—
120	Q₈	—	58	8	no	—
121	C₂×C₄	—	29	1	no	—
122	C₂×C₄	—	29	2	no	—
123	C₂×C₄	—	29	2	no	—
124	C₂×C₄	—	29	2	no	—
125	C₂×C₄	—	29	4	no	—
126	C₂×C₄	—	58	4	no	—
127	C₂×C₄	C₂²×#1181	1	2	yes	—
128	C₂×C₄	C₂²×#1181	1	4	yes	—
129	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
130	C₈	—	29	2	no	—
131	C₈	—	29	2	no	—
132	C₈	—	58	2	no	—
133	C₈	—	58	4	no	—
134	C₂²	—	29	2	no	—
135	C₂²	—	58	2	no	—
136	C₂²	C₂³×#1181	1	1	yes	characteristic
137	C₄	—	2	2	no	—
138	C₄	—	2	4	no	—
139	C₄	—	29	1	no	—
140	C₄	—	29	1	no	—
141	C₄	—	29	4	no	—
142	C₄	—	58	4	no	—
143	C₄	Q₈×#1181	1	2	yes	—
144	C₂	—	58	2	no	—
145	C₂	C₂×Q₈×#1181	1	1	yes	characteristic
146	C₂	D₂₉⋊#131	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14272215

C₂

yes

maximal, complemented

#14272212

C₂

yes

maximal, complemented

#14272170

C₂

yes

maximal

#14272168

C₂

yes

maximal, characteristic

#14272128

C₂

yes

maximal

C₄×D₂₉⋊C₈

C₂

yes

maximal, characteristic

#14271719

C₂

yes

maximal, characteristic

C₂×#90796

C₂²

yes

—

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

C₂×D₂₉⋊C₈

C₂²

yes

characteristic

C₂₉×#125

C₄

yes

characteristic

#11745258

C₄

yes

—

#11745254

C₂²

yes

—

#11745250

C₄

yes

—

#11745249

C₂²

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745232

C₄

yes

characteristic

#11745220

C₂²

yes

—

#11745220

C₂²

yes

—

#11745218

C₂²

yes

—

C₄⋊#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

—

C₄×#6599

C₂²

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

C₂³

yes

—

C₂×#6599

C₂³

yes

—

C₂×#6599

C₂³

yes

characteristic

C₂×#6599

C₂³

yes

characteristic

#90796

—

D₂₉⋊C₈

—

D₂₉⋊C₈

Q₈

yes

complemented

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

#90781

C₂×C₄

yes

—

C₄⋊Dic₂₉

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

#90779

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂³

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂²×D₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂⁴

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

C₂×Q₈

yes

—

C₄×D₂₉

#41

yes

—

Dic₅₈

—

#6599

—

#6599

—

#6599

C₂×Q₈

yes

—

#6599

C₂×Q₈

yes

—

#2960

—

maximal, Sylow

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

C₄×Q₈

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

Dic₂₉

—

Dic₂₉

#131

yes

—

Dic₂₉

C₂²×Q₈

yes

characteristic

Dic₂₉

C₂×#41

yes

characteristic

#533

—

#446

—

C₈×Q₈

—

#424

—

#423

—

#405

—

C₂×C₄×C₈

—

C₂×C₂₉

C₂×C₄×Q₈

yes

characteristic

C₂×C₂₉

C₂×#131

yes

—

D₂₉

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#2960

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

C₂×#1181

yes

—

113

C₄⋊C₄

C₂×#1181

yes

—

114

C₂²⋊C₄

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

C₂×#1181

yes

characteristic

119

C₂³

—

120

Q₈

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

C₂²×#1181

yes

—

128

C₂×C₄

C₂²×#1181

yes

—

129

C₂×C₄

C₂²×#1181

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₂³×#1181

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

Q₈×#1181

yes

—

144

C₂

—

145

C₂

C₂×Q₈×#1181

yes

characteristic

146

C₂

D₂₉⋊#131

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#125	C₄
prime radical	C₂²×D₂₉	C₂²×C₄
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	#125	#1181
hypocenter	C₂₉	#2960
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#1181

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂₉×#125

C₄

prime radical

C₂²×D₂₉

C₂²×C₄

cosocle

C₂×Dic₂₉

C₂⁴

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #14272215	C₂	semidirect
2. #14272212	C₂	semidirect
34. D₂₉⋊C₈	Q₈	semidirect
98. C₂₉	#2960	semidirect

H ≅ G/N

type

1. #14272215

C₂

semidirect

2. #14272212

C₂

semidirect

34. D₂₉⋊C₈

Q₈

semidirect

98. C₂₉

#2960

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14272215	2
#14272212	2
#14272170	2
#14272168	2
#14272128	2
C₄×D₂₉⋊C₈	2
#14271719	2
#2960	29

subgroup

index

C₄×D₂₉⋊C₈

Subgroups — #16836282

Conjugacy classes of subgroups

Complements

Maximal subgroups