Group #16819487 — subgroups

Subgroups — #16819487

Order 3712.

272 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11745249	C₂	1	1	yes	maximal, characteristic
2	#14271186	C₂	1	2	yes	maximal
3	C₂×#11745172	C₂	1	2	yes	maximal
4	#14270932	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#343	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90779	C₄	1	2	yes	—
10	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
11	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×#90777	C₂²	1	2	yes	—
13	#11745249	—	2	2	no	—
14	#11745249	—	2	2	no	—
15	#11745172	—	2	4	no	—
16	#11745162	—	2	2	no	—
17	#11745162	—	2	2	no	—
18	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
22	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₅₈	—	2	2	no	—
24	C₂×Dic₅₈	—	2	2	no	—
25	C₂×Dic₅₈	D₄	1	2	yes	—
26	C₂×Dic₅₈	Q₈	1	2	yes	—
27	M₁₆×C₂₉	—	2	2	no	—
28	M₁₆×C₂₉	—	2	2	no	—
29	C₂×C₈×C₂₉	—	2	2	no	—
30	C₄⋊C₄×C₂₉	—	2	2	no	—
31	#90779	—	2	4	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₄×Dic₂₉	—	2	2	no	—
34	C₄×Dic₂₉	D₄	1	2	yes	—
35	C₄×Dic₂₉	D₄	1	2	yes	—
36	#90777	—	2	2	no	—
37	#90777	—	2	2	no	—
38	C₂×#6597	—	2	2	no	—
39	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	—	2	2	no	—
41	C₂×C₄×C₂₉	—	4	2	no	—
42	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₂₉	#41	1	2	yes	—
46	C₂×Dic₂₉	—	2	2	no	—
47	C₂×Dic₂₉	—	2	2	no	—
48	C₂×Dic₂₉	—	2	2	no	—
49	C₂×Dic₂₉	—	4	1	no	—
50	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
52	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×Dic₂₉	C₄⋊C₄	1	4	yes	—
54	Dic₅₈	—	2	4	no	—
55	Dic₅₈	—	2	4	no	—
56	C₈×C₂₉	—	4	2	no	—
57	#6597	—	4	2	no	—
58	#1801	—	29	1	no	maximal, Sylow
59	C₂²×C₂₉	—	2	1	no	—
60	C₂²×C₂₉	—	2	1	no	—
61	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₂₉	#117	1	1	yes	characteristic
64	C₄×C₂₉	—	4	2	no	—
65	C₄×C₂₉	#121	1	2	yes	—
66	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
67	Dic₂₉	—	2	4	no	—
68	Dic₂₉	—	2	1	no	—
69	Dic₂₉	—	2	2	no	—
70	Dic₂₉	#101	1	2	yes	complemented
71	C₂×C₄×Q₈	—	29	1	no	—
72	#423	—	29	2	no	—
73	C₂×#101	—	29	2	no	—
74	#343	—	29	1	no	—
75	#343	D₂₉	1	1	yes	characteristic
76	C₂×C₂₉	—	2	1	no	—
77	C₂×C₂₉	—	2	1	no	—
78	C₂×C₂₉	#380	1	1	yes	characteristic
79	C₂×C₂₉	C₂×#101	1	1	yes	characteristic
80	C₂×C₂₉	#413	1	1	yes	characteristic
81	C₂²×Q₈	—	29	1	no	—
82	C₂×M₁₆	—	29	2	no	—
83	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
84	C₄×Q₈	—	58	2	no	—
85	C₄×Q₈	—	58	2	no	—
86	C₂×C₄⋊C₄	—	29	2	no	—
87	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
88	C₂×C₄²	—	29	1	no	—
89	C₂×C₄²	—	29	2	no	—
90	C₄⋊C₈	—	58	2	no	—
91	C₄⋊C₈	—	58	2	no	—
92	#101	—	58	4	no	—
93	C₂₉	#1801	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	29	2	no	—
95	C₂×Q₈	—	29	2	no	—
96	C₂×Q₈	—	58	2	no	—
97	C₂×Q₈	—	58	2	no	—
98	C₂²×C₄	—	29	1	no	—
99	C₂²×C₄	—	29	2	no	—
100	C₂²×C₄	—	29	1	no	—
101	C₂²×C₄	C₄×D₂₉	1	2	yes	—
102	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
103	M₁₆	—	2	2	no	—
104	M₁₆	—	2	2	no	—
105	M₁₆	—	58	2	no	—
106	M₁₆	—	58	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	58	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	58	4	no	—
111	C₄²	—	29	2	no	—
112	C₄²	—	29	2	no	—
113	C₄²	—	58	2	no	—
114	C₄²	—	58	2	no	—
115	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
116	Q₈	—	58	4	no	—
117	Q₈	—	58	4	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	29	1	no	—
121	C₂×C₄	—	29	1	no	—
122	C₂×C₄	—	29	2	no	—
123	C₂×C₄	—	29	4	no	—
124	C₂×C₄	—	58	2	no	—
125	C₂×C₄	—	58	2	no	—
126	C₂×C₄	—	58	2	no	—
127	C₂×C₄	—	116	1	no	—
128	C₂×C₄	#90805	1	2	yes	—
129	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
130	C₂×C₄	D₄×D₂₉	1	2	yes	—
131	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
132	C₈	—	4	2	no	—
133	C₈	—	116	2	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	#11745234	1	1	yes	characteristic
137	C₂²	C₂²⋊C₄×D₂₉	1	1	yes	characteristic
138	C₂²	C₄⋊C₄×D₂₉	1	1	yes	characteristic
139	C₄	—	4	2	no	—
140	C₄	—	29	2	no	—
141	C₄	—	58	4	no	—
142	C₄	—	58	1	no	—
143	C₄	—	58	2	no	—
144	C₄	#11745246	1	2	yes	—
145	C₄	#11745258	1	2	yes	—
146	C₂	—	2	1	no	—
147	C₂	—	2	1	no	—
148	C₂	#14271022	1	1	yes	characteristic
149	C₂	#101×D₂₉	1	1	yes	characteristic
150	C₂	#14271144	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745249

C₂

yes

maximal, characteristic

#14271186

C₂

yes

maximal

C₂×#11745172

C₂

yes

maximal

#14270932

C₂

yes

maximal, characteristic

C₂₉×#343

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

characteristic

C₂×#90779

C₄

yes

—

C₂×C₄×Dic₂₉

C₄

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

—

—

—

—

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₂×Dic₅₈

D₄

yes

—

C₂×Dic₅₈

Q₈

yes

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

D₄

yes

—

#90777

—

#90777

—

C₂×#6597

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

—

#6597

—

#1801

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

#121

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#101

yes

complemented

C₂×C₄×Q₈

—

—

—

—

D₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

#101

—

C₂₉

#1801

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₄×D₂₉

yes

—

102

C₂²×C₄

C₂²×D₂₉

yes

characteristic

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₂³

C₂×C₄×D₂₉

yes

characteristic

116

Q₈

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

116

—

128

C₂×C₄

#90805

yes

—

129

C₂×C₄

D₄×D₂₉

yes

characteristic

130

C₂×C₄

D₄×D₂₉

yes

—

131

C₂×C₄

Q₈×D₂₉

yes

characteristic

132

C₈

—

133

C₈

—

116

—

134

C₂²

—

135

C₂²

—

136

C₂²

#11745234

yes

characteristic

137

C₂²

C₂²⋊C₄×D₂₉

yes

characteristic

138

C₂²

C₄⋊C₄×D₂₉

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

#11745246

yes

—

145

C₄

#11745258

yes

—

146

C₂

—

147

C₂

—

148

C₂

#14271022

yes

characteristic

149

C₂

#101×D₂₉

yes

characteristic

150

C₂

#14271144

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₉
commutator, prime radical	C₂³×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#343	C₂
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#343	D₂₉
hypocenter	C₂₉	#1801
LCS	G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₉

commutator, prime radical

C₂³×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#343

C₂

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
70. Dic₂₉	#101	semidirect
93. C₂₉	#1801	semidirect

H ≅ G/N

type

70. Dic₂₉

#101

semidirect

93. C₂₉

#1801

semidirect

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

subgroup	index
C₂×#11745249	2
#14271186	2
C₂×#11745172	2
#14270932	2
C₂₉×#343	2
#1801	29

subgroup

index

C₂₉×#343

Subgroups — #16819487

Conjugacy classes of subgroups

Complements

Maximal subgroups