Group #16829892 — subgroups

Subgroups — #16829892

Order 3712.

392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₂×#11745232	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271531	C₂	1	2	yes	maximal, complemented
3	#14271527	C₂	1	2	yes	maximal, complemented
4	#14271517	C₂	1	4	yes	maximal, complemented
5	#14271164	C₂	1	4	yes	maximal, complemented
6	C₄×#90777	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#532	C₂	1	1	yes	maximal, characteristic
8	C₂×#41×C₂₉	C₂²	1	2	yes	—
9	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂₉×#127	C₂²	1	1	yes	characteristic
11	C₂₉×#124	C₂²	1	2	yes	—
12	C₂₉×#121	—	2	2	no	—
13	C₄×D₄×C₂₉	—	2	2	no	—
14	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
16	C₂×#90779	—	2	2	no	—
17	C₂×#90777	C₂²	1	2	yes	—
18	#11745232	—	2	2	no	—
19	#11745232	C₂²	1	2	yes	—
20	#11745232	C₂²	1	2	yes	—
21	#11745183	C₂²	1	8	yes	—
22	#11745180	C₂²	1	8	yes	—
23	#11745151	C₂²	1	2	yes	—
24	C₄×#6597	C₂²	1	2	yes	—
25	#41×C₂₉	—	2	8	no	—
26	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
27	C₂×D₄×C₂₉	—	2	2	no	—
28	C₂×D₄×C₂₉	—	2	2	no	—
29	C₂×D₄×C₂₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₂₉	—	2	2	no	—
31	C₂²×C₄×C₂₉	D₄	1	2	yes	—
32	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₂₉	—	2	2	no	—
34	C₄⋊C₄×C₂₉	—	2	2	no	—
35	C₂²⋊C₄×C₂₉	—	2	4	no	—
36	C₄²×C₂₉	D₄	1	2	yes	—
37	C₄²×C₂₉	C₂³	1	1	yes	characteristic
38	C₄²×C₂₉	C₂³	1	1	yes	characteristic
39	C₄⋊Dic₂₉	—	2	2	no	—
40	C₄⋊Dic₂₉	C₂³	1	4	yes	—
41	#90779	—	2	4	no	—
42	#90779	—	2	4	no	—
43	#90777	—	2	4	no	—
44	C₂×#6597	C₂³	1	4	yes	—
45	C₂³×C₂₉	—	2	2	no	—
46	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
47	Q₈×C₂₉	—	2	4	no	—
48	D₄×C₂₉	—	2	4	no	—
49	D₄×C₂₉	—	4	4	no	—
50	D₄×C₂₉	—	4	4	no	—
51	C₂×C₄×C₂₉	—	2	2	no	—
52	C₂×C₄×C₂₉	—	4	2	no	—
53	C₂×C₄×C₂₉	—	4	4	no	—
54	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₂₉	#41	1	4	yes	—
58	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
59	C₂×Dic₂₉	—	2	4	no	—
60	C₂×Dic₂₉	—	4	4	no	—
61	#6597	—	2	4	no	—
62	#3142	—	29	1	no	maximal, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	—	4	2	no	—
65	C₂²×C₂₉	—	4	4	no	—
66	C₂²×C₂₉	#124	1	2	yes	—
67	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
68	C₄×C₂₉	—	2	2	no	—
69	C₄×C₂₉	—	2	2	no	—
70	C₄×C₂₉	—	4	2	no	—
71	C₄×C₂₉	#124	1	2	yes	—
72	C₄×C₂₉	C₂×#41	1	2	yes	—
73	Dic₂₉	—	4	4	no	—
74	#532	D₂₉	1	1	yes	characteristic
75	C₂×#125	—	29	1	no	—
76	#491	—	29	2	no	—
77	#490	—	29	2	no	—
78	#488	—	29	4	no	—
79	#417	—	29	4	no	—
80	C₄×M₁₆	—	29	1	no	—
81	C₂×C₂₉	—	2	2	no	—
82	C₂×C₂₉	—	8	2	no	—
83	C₂×C₂₉	C₂×#124	1	1	yes	characteristic
84	C₂×C₂₉	#575	1	2	yes	—
85	C₂×#41	C₂×D₂₉	1	2	yes	—
86	C₂×M₁₆	—	29	2	no	—
87	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
88	#127	C₂×D₂₉	1	1	yes	characteristic
89	#125	—	29	2	no	—
90	#125	—	29	2	no	—
91	#125	—	58	2	no	—
92	#124	C₂×D₂₉	1	2	yes	—
93	#121	—	2	2	no	—
94	C₄×D₄	—	2	2	no	—
95	C₂×C₄⋊C₄	—	29	2	no	—
96	C₂×C₄⋊C₄	—	58	2	no	—
97	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
98	#103	—	29	8	no	—
99	#102	—	29	8	no	—
100	#97	—	29	2	no	—
101	C₄×C₈	—	29	2	no	—
102	C₂₉	#3142	1	1	yes	characteristic, complemented, Sylow
103	#41	—	2	8	no	—
104	C₂×Q₈	C₂²×D₂₉	1	2	yes	—
105	C₂×D₄	—	2	2	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	C₂²×D₂₉	1	2	yes	—
108	C₂²×C₄	—	2	2	no	—
109	C₂²×C₄	—	58	2	no	—
110	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
111	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
112	M₁₆	—	58	4	no	—
113	C₂×C₈	—	29	4	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₄⋊C₄	—	29	4	no	—
116	C₄⋊C₄	—	58	2	no	—
117	C₄⋊C₄	—	58	4	no	—
118	C₄⋊C₄	—	58	4	no	—
119	C₂²⋊C₄	—	2	4	no	—
120	C₄²	C₂²⋊D₂₉	1	2	yes	—
121	C₄²	C₂²×D₂₉	1	1	yes	characteristic
122	C₄²	C₂²×D₂₉	1	1	yes	characteristic
123	C₂³	—	2	2	no	—
124	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
125	Q₈	—	2	4	no	—
126	D₄	—	2	4	no	—
127	D₄	—	4	4	no	—
128	D₄	—	4	4	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	58	4	no	—
133	C₂×C₄	—	116	4	no	—
134	C₂×C₄	#90807	1	4	yes	—
135	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
136	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
137	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
138	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
139	C₈	—	58	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	4	2	no	—
142	C₂²	—	4	4	no	—
143	C₂²	#11745298	1	2	yes	—
144	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	4	2	no	—
148	C₄	—	116	4	no	—
149	C₄	#11745298	1	2	yes	—
150	C₄	C₂×#90807	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	8	2	no	—
153	C₂	C₂×#11745298	1	1	yes	characteristic
154	C₂	#14271961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745232

C₂

yes

maximal, characteristic, complemented

#14271531

C₂

yes

maximal, complemented

#14271527

C₂

yes

maximal, complemented

#14271517

C₂

yes

maximal, complemented

#14271164

C₂

yes

maximal, complemented

C₄×#90777

C₂

yes

maximal, characteristic, complemented

C₂₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#124

C₂²

yes

—

C₂₉×#121

—

C₄×D₄×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

C₂×#90777

C₂²

yes

—

#11745232

—

#11745232

C₂²

yes

—

#11745232

C₂²

yes

—

#11745183

C₂²

yes

—

#11745180

C₂²

yes

—

#11745151

C₂²

yes

—

C₄×#6597

C₂²

yes

—

#41×C₂₉

—

C₂×Q₈×C₂₉

C₂³

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

—

—

—

C₂³

yes

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#3142

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#124

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

C₂×#41

yes

—

Dic₂₉

—

#532

D₂₉

yes

—

—

—

—

—

C₄×M₁₆

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#124

yes

characteristic

C₂×C₂₉

#575

yes

—

C₂×#41

C₂×D₂₉

yes

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₂₉

yes

characteristic

#127

C₂×D₂₉

yes

—

—

—

C₂×D₂₉

yes

—

#121

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#103

—

#102

—

100

#97

—

101

C₄×C₈

—

102

C₂₉

#3142

yes

characteristic, complemented, Sylow

103

#41

—

104

C₂×Q₈

C₂²×D₂₉

yes

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

C₂²×D₂₉

yes

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²⋊D₂₉

yes

—

111

C₂²×C₄

C₂²×D₂₉

yes

characteristic

112

M₁₆

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

C₂²⋊D₂₉

yes

—

121

C₄²

C₂²×D₂₉

yes

characteristic

122

C₄²

C₂²×D₂₉

yes

characteristic

123

C₂³

—

124

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

D₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

116

—

134

C₂×C₄

#90807

yes

—

135

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

136

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

137

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

138

C₂×C₄

C₂³×D₂₉

yes

characteristic

139

C₈

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#11745298

yes

—

144

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

116

—

149

C₄

#11745298

yes

—

150

C₄

C₂×#90807

yes

—

151

C₂

—

152

C₂

—

153

C₂

C₂×#11745298

yes

characteristic

154

C₂

#14271961

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting, prime radical	C₂₉×#532	C₂
socle	C₂²×C₂₉	C₂²×D₄
hypercenter	#532	D₂₉
hypocenter	C₂₉	#3142
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₂₉

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting, prime radical

C₂₉×#532

C₂

socle

C₂²×C₂₉

C₂²×D₄

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #532

N	H ≅ G/N	type
1. C₂×#11745232	C₂	semidirect
2. #14271531	C₂	semidirect
3. #14271527	C₂	semidirect
4. #14271517	C₂	semidirect
5. #14271164	C₂	semidirect
6. C₄×#90777	C₂	semidirect
102. C₂₉	#3142	semidirect

H ≅ G/N

type

1. C₂×#11745232

C₂

semidirect

2. #14271531

C₂

semidirect

3. #14271527

C₂

semidirect

4. #14271517

C₂

semidirect

5. #14271164

C₂

semidirect

6. C₄×#90777

C₂

semidirect

102. C₂₉

#3142

semidirect

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

subgroup	index
C₂×#11745232	2
#14271531	2
#14271527	2
#14271517	2
#14271164	2
C₄×#90777	2
C₂₉×#532	2
#3142	29

subgroup

index

C₂₉×#532

Subgroups — #16829892

Conjugacy classes of subgroups

Complements

Maximal subgroups