Group #16829895 — subgroups

Subgroups — #16829895

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	#14271713	C₂	1	1	yes	maximal, characteristic
2	#14271533	C₂	1	2	yes	maximal, complemented
3	#14271529	C₂	1	2	yes	maximal, complemented
4	#14271520	C₂	1	4	yes	maximal, complemented
5	#14271162	C₂	1	4	yes	maximal, complemented
6	C₄×#90777	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90805	C₂²	1	2	yes	—
9	C₂₉×#125	—	2	2	no	—
10	C₂₉×#125	C₂²	1	2	yes	—
11	C₂₉×#125	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
13	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
15	#11745292	—	2	2	no	—
16	C₂×#90777	C₂²	1	2	yes	—
17	#11745237	C₂²	1	2	yes	—
18	#11745236	C₂²	1	1	yes	characteristic
19	C₄×D₁₁₆	—	2	2	no	—
20	#11745231	C₂²	1	1	yes	characteristic
21	#11745158	C₂²	1	8	yes	—
22	#11745157	C₂²	1	8	yes	—
23	#11745151	C₂²	1	2	yes	—
24	C₄×#6597	C₂²	1	2	yes	—
25	C₂²×C₄×C₂₉	—	2	2	no	—
26	C₂²×C₄×C₂₉	D₄	1	2	yes	—
27	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊D₂₉	—	2	2	no	—
29	#90805	—	2	8	no	—
30	C₂×D₁₁₆	—	2	2	no	—
31	C₂×D₁₁₆	C₂³	1	2	yes	—
32	C₂×C₄×D₂₉	—	2	2	no	—
33	C₂×Dic₅₈	C₂³	1	2	yes	—
34	C₄⋊C₄×C₂₉	—	2	4	no	—
35	C₄⋊C₄×C₂₉	—	2	4	no	—
36	C₄⋊C₄×C₂₉	—	2	2	no	—
37	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
38	C₄²×C₂₉	D₄	1	2	yes	—
39	C₄²×C₂₉	C₂³	1	1	yes	characteristic
40	C₄²×C₂₉	C₂³	1	1	yes	characteristic
41	#90781	—	2	4	no	—
42	C₄⋊Dic₂₉	—	2	2	no	—
43	#90777	—	2	4	no	—
44	C₂×#6597	C₂³	1	4	yes	—
45	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×D₂₉	—	2	2	no	—
47	C₂×C₄×C₂₉	—	2	4	no	—
48	C₂×C₄×C₂₉	—	4	2	no	—
49	C₂×C₄×C₂₉	—	4	4	no	—
50	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₂₉	#41	1	4	yes	—
54	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
55	C₂²⋊D₂₉	—	4	4	no	—
56	C₂×Dic₂₉	—	2	2	no	—
57	D₁₁₆	—	2	4	no	—
58	D₁₁₆	—	4	4	no	—
59	C₄×D₂₉	—	4	4	no	—
60	Dic₅₈	—	2	4	no	—
61	#6597	—	2	4	no	—
62	#3142	—	29	1	no	maximal, Sylow
63	C₂²×C₂₉	—	2	2	no	—
64	C₂²×C₂₉	#124	1	2	yes	—
65	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
66	C₂×D₂₉	—	4	2	no	—
67	C₂×D₂₉	—	4	4	no	—
68	C₄×C₂₉	—	2	2	no	—
69	C₄×C₂₉	—	2	2	no	—
70	C₄×C₂₉	—	4	4	no	—
71	C₄×C₂₉	#124	1	2	yes	—
72	C₄×C₂₉	C₂×#41	1	2	yes	—
73	Dic₂₉	—	4	2	no	—
74	#532	—	29	1	no	—
75	C₂×#125	D₂₉	1	1	yes	characteristic, complemented
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	C₂×#124	1	1	yes	characteristic
83	C₂×C₂₉	#575	1	2	yes	—
84	D₂₉	—	8	2	no	—
85	C₂×#41	—	29	2	no	—
86	C₂×M₁₆	—	29	2	no	—
87	C₄⋊Q₈	—	29	1	no	—
88	#127	—	29	1	no	—
89	#125	—	2	2	no	—
90	#125	C₂×D₂₉	1	2	yes	—
91	#125	C₂×D₂₉	1	2	yes	—
92	#124	—	29	2	no	—
93	#121	—	58	2	no	—
94	C₄×D₄	—	58	2	no	—
95	C₂×C₄⋊C₄	—	2	2	no	—
96	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
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	—	58	8	no	—
104	C₂×Q₈	—	29	2	no	—
105	C₂×D₄	—	29	2	no	—
106	C₂×D₄	—	58	2	no	—
107	C₂×D₄	—	58	2	no	—
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	4	no	—
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	58	2	no	—
118	C₄⋊C₄	C₂²×D₂₉	1	4	yes	—
119	C₂²⋊C₄	—	58	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	—	58	2	no	—
124	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
125	Q₈	—	58	4	no	—
126	D₄	—	58	4	no	—
127	D₄	—	116	4	no	—
128	D₄	—	116	4	no	—
129	C₂×C₄	—	2	4	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	58	2	no	—
133	C₂×C₄	—	116	4	no	—
134	C₂×C₄	#90809	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	—	116	2	no	—
142	C₂²	—	116	4	no	—
143	C₂²	#11745309	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	4	no	—
148	C₄	—	116	2	no	—
149	C₄	#11745309	1	2	yes	—
150	C₄	C₂×#90809	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	232	2	no	—
153	C₂	C₂×#11745309	1	1	yes	characteristic
154	C₂	#14271961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271713

C₂

yes

maximal, characteristic

#14271533

C₂

yes

maximal, complemented

#14271529

C₂

yes

maximal, complemented

#14271520

C₂

yes

maximal, complemented

#14271162

C₂

yes

maximal, complemented

C₄×#90777

C₂

yes

maximal, characteristic, complemented

C₂×C₂₉×#125

C₂

yes

maximal, characteristic, complemented

C₂×#90805

C₂²

yes

—

C₂₉×#125

—

C₂₉×#125

C₂²

yes

—

C₂₉×#125

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

#11745292

—

C₂×#90777

C₂²

yes

—

#11745237

C₂²

yes

—

#11745236

C₂²

yes

characteristic

C₄×D₁₁₆

—

#11745231

C₂²

yes

characteristic

#11745158

C₂²

yes

—

#11745157

C₂²

yes

—

#11745151

C₂²

yes

—

C₄×#6597

C₂²

yes

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×C₂²⋊D₂₉

—

#90805

—

C₂×D₁₁₆

—

C₂×D₁₁₆

C₂³

yes

—

C₂×C₄×D₂₉

—

C₂×Dic₅₈

C₂³

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

#90781

—

C₄⋊Dic₂₉

—

#90777

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂²×D₂₉

—

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

C₂²⋊D₂₉

—

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

C₄×D₂₉

—

Dic₅₈

—

#6597

—

#3142

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

#124

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

C₂×#41

yes

—

Dic₂₉

—

#532

—

C₂×#125

D₂₉

yes

characteristic, complemented

—

—

—

—

C₄×M₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#124

yes

characteristic

C₂×C₂₉

#575

yes

—

D₂₉

—

C₂×#41

—

C₂×M₁₆

—

C₄⋊Q₈

—

#127

—

#125

—

#125

C₂×D₂₉

yes

—

#125

C₂×D₂₉

yes

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

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

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

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

C₂²×D₂₉

yes

—

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

—

116

—

128

D₄

—

116

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

116

—

134

C₂×C₄

#90809

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

—

116

—

142

C₂²

—

116

—

143

C₂²

#11745309

yes

—

144

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

116

—

149

C₄

#11745309

yes

—

150

C₄

C₂×#90809

yes

—

151

C₂

—

152

C₂

—

232

—

153

C₂

C₂×#11745309

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	C₂×C₂₉×#125	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	#14271713	C₂
hypercenter	C₂×#125	D₂₉
hypocenter	C₂₉	#3142
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₂₉

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂×C₂₉×#125

C₂

socle

C₂²×C₂₉

C₂²×D₄

C₂

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #14271533	C₂	semidirect
3. #14271529	C₂	semidirect
4. #14271520	C₂	semidirect
5. #14271162	C₂	semidirect
6. C₄×#90777	C₂	semidirect
7. C₂×C₂₉×#125	C₂	semidirect
75. C₂×#125	D₂₉	semidirect
102. C₂₉	#3142	semidirect

H ≅ G/N

type

2. #14271533

C₂

semidirect

3. #14271529

C₂

semidirect

4. #14271520

C₂

semidirect

5. #14271162

C₂

semidirect

6. C₄×#90777

C₂

semidirect

7. C₂×C₂₉×#125

C₂

semidirect

75. C₂×#125

D₂₉

semidirect

102. C₂₉

#3142

semidirect

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

subgroup	index
#14271713	2
#14271533	2
#14271529	2
#14271520	2
#14271162	2
C₄×#90777	2
C₂×C₂₉×#125	2
#3142	29

subgroup

index

C₂×C₂₉×#125

Subgroups — #16829895

Conjugacy classes of subgroups

Complements

Maximal subgroups