Group #16821069 — subgroups

Subgroups — #16821069

Order 3712.

158 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271211	C₂	1	1	yes	maximal, characteristic
2	#14271186	C₂	1	1	yes	maximal, characteristic
3	#14270935	C₂	1	1	yes	maximal, characteristic
4	#14270924	C₂	1	1	yes	maximal, characteristic
5	#14270922	C₂	1	1	yes	maximal, characteristic
6	#14270919	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₂₉×#117	C₂²	1	1	yes	characteristic
11	#11745288	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×#90777	C₂²	1	1	yes	characteristic
14	C₂×#90777	C₂²	1	1	yes	characteristic
15	#11745170	—	2	2	no	—
16	#11745162	—	2	2	no	—
17	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₂₉	—	2	1	no	—
19	M₁₆×C₂₉	—	2	1	no	—
20	M₁₆×C₂₉	—	2	1	no	—
21	M₁₆×C₂₉	—	2	1	no	—
22	M₁₆×C₂₉	—	2	1	no	—
23	C₂×C₈×C₂₉	—	2	1	no	—
24	C₂×C₈×C₂₉	—	2	1	no	—
25	C₄⋊C₄×C₂₉	—	2	1	no	—
26	C₂²⋊C₄×C₂₉	—	2	1	no	—
27	C₄²×C₂₉	—	2	1	no	—
28	C₂²⋊Dic₂₉	—	2	1	no	—
29	C₄⋊Dic₂₉	—	2	1	no	—
30	C₄×Dic₂₉	—	2	1	no	—
31	C₄×Dic₂₉	—	2	1	no	—
32	C₄×Dic₂₉	Q₈	1	1	yes	characteristic
33	C₄×Dic₂₉	Q₈	1	1	yes	characteristic
34	#90777	—	2	1	no	—
35	#90777	—	2	1	no	—
36	#90777	—	2	1	no	—
37	#90777	—	2	1	no	—
38	C₂×#6597	—	2	1	no	—
39	C₂×#6597	D₄	1	2	yes	—
40	C₂³×C₂₉	#41	1	1	yes	characteristic
41	C₂×C₄×C₂₉	—	4	1	no	—
42	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
47	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
48	C₂×Dic₂₉	—	2	1	no	—
49	C₂×Dic₂₉	—	2	1	no	—
50	C₂×Dic₂₉	—	4	2	no	—
51	C₂×Dic₂₉	—	4	1	no	—
52	C₈×C₂₉	—	4	1	no	—
53	C₈×C₂₉	—	4	1	no	—
54	#6597	—	2	2	no	—
55	#6597	—	4	1	no	—
56	#2102	—	29	1	no	maximal, Sylow
57	C₂²×C₂₉	—	4	1	no	—
58	C₂²×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂²×C₂₉	#126	1	1	yes	characteristic
60	C₂²×C₂₉	#126	1	1	yes	characteristic
61	C₄×C₂₉	—	8	1	no	—
62	C₄×C₂₉	#123	1	1	yes	characteristic
63	C₄×C₂₉	#124	1	1	yes	characteristic
64	C₄×C₂₉	#125	1	1	yes	characteristic
65	C₄×C₂₉	#125	1	1	yes	characteristic
66	Dic₂₉	—	2	2	no	—
67	Dic₂₉	—	4	1	no	—
68	Dic₂₉	—	8	1	no	—
69	#430	—	29	1	no	—
70	#423	—	29	1	no	—
71	#344	—	29	1	no	—
72	#344	D₂₉	1	1	yes	characteristic
73	#339	—	29	1	no	—
74	#339	—	29	1	no	—
75	H(3,ℤ/4)	—	29	1	no	—
76	C₂×C₂₉	—	2	1	no	—
77	C₂×C₂₉	—	2	1	no	—
78	C₂×C₂₉	—	2	1	no	—
79	C₂×C₂₉	#400	1	1	yes	characteristic
80	C₂×M₁₆	—	29	1	no	—
81	C₂×M₁₆	—	29	1	no	—
82	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
83	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
84	#117	—	29	1	no	—
85	#117	C₂×D₂₉	1	1	yes	characteristic
86	C₂×C₄²	—	29	1	no	—
87	#108	—	58	2	no	—
88	C₄⋊C₈	—	58	2	no	—
89	C₂₉	#2102	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	58	1	no	—
91	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
92	M₁₆	—	2	1	no	—
93	M₁₆	—	2	1	no	—
94	M₁₆	—	2	1	no	—
95	M₁₆	—	2	1	no	—
96	M₁₆	—	58	1	no	—
97	M₁₆	—	58	1	no	—
98	M₁₆	—	58	1	no	—
99	M₁₆	—	58	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	29	2	no	—
103	C₂×C₈	—	58	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	58	1	no	—
106	C₂²⋊C₄	—	2	1	no	—
107	C₂²⋊C₄	—	58	1	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	29	1	no	—
110	C₄²	—	29	1	no	—
111	C₄²	—	58	1	no	—
112	C₄²	—	58	1	no	—
113	C₂³	#90805	1	1	yes	characteristic
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	58	1	no	—
116	C₂×C₄	—	58	1	no	—
117	C₂×C₄	—	116	2	no	—
118	C₂×C₄	—	116	1	no	—
119	C₂×C₄	#90805	1	1	yes	characteristic
120	C₂×C₄	#90805	1	1	yes	characteristic
121	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
122	C₂×C₄	#90807	1	1	yes	characteristic
123	C₂×C₄	#90807	1	1	yes	characteristic
124	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	4	1	no	—
127	C₈	—	58	2	no	—
128	C₈	—	116	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	#11745238	1	1	yes	characteristic
131	C₂²	#11745241	1	1	yes	characteristic
132	C₂²	#11745258	1	1	yes	characteristic
133	C₄	—	8	1	no	—
134	C₄	—	58	2	no	—
135	C₄	—	116	1	no	—
136	C₄	—	232	1	no	—
137	C₄	#11745245	1	1	yes	characteristic
138	C₄	#11745247	1	1	yes	characteristic
139	C₄	#11745251	1	1	yes	characteristic
140	C₄	#11745251	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#14271104	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271211

C₂

yes

maximal, characteristic

#14271186

C₂

yes

maximal, characteristic

#14270935

C₂

yes

maximal, characteristic

#14270924

C₂

yes

maximal, characteristic

#14270922

C₂

yes

maximal, characteristic

#14270919

C₂

yes

maximal, characteristic

C₂₉×#344

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

characteristic

#11745170

—

#11745162

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

Q₈

yes

characteristic

C₄×Dic₂₉

Q₈

yes

—

—

—

—

—

D₄

yes

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂²⋊Q₈

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

—

—

—

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#400

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

characteristic

C₂×M₁₆

C₂×D₂₉

yes

characteristic

#117

—

#117

C₂×D₂₉

yes

characteristic

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₂₉

#2102

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₂³

#90805

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

116

—

118

C₂×C₄

—

116

—

119

C₂×C₄

#90805

yes

characteristic

120

C₂×C₄

#90805

yes

characteristic

121

C₂×C₄

D₄×D₂₉

yes

characteristic

122

C₂×C₄

#90807

yes

characteristic

123

C₂×C₄

#90807

yes

characteristic

124

C₂×C₄

Q₈×D₂₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

116

—

129

C₂²

—

130

C₂²

#11745238

yes

characteristic

131

C₂²

#11745241

yes

characteristic

132

C₂²

#11745258

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

116

—

136

C₄

—

232

—

137

C₄

#11745245

yes

characteristic

138

C₄

#11745247

yes

characteristic

139

C₄

#11745251

yes

characteristic

140

C₄

#11745251

yes

characteristic

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

#14271104

yes

characteristic

	subgroup	G/H
center	C₄	#11745247
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂₉×#344	C₂
socle	C₂×C₂₉	#400
prime radical	C₂³×C₂₉	#41
hypercenter	#344	D₂₉
hypocenter	C₂₉	#2102
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₄

#11745247

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂₉×#344

C₂

C₂×C₂₉

C₂³×C₂₉

D₂₉

C₂₉

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
89. C₂₉	#2102	semidirect

H ≅ G/N

type

89. C₂₉

#2102

semidirect

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

subgroup	index
#14271211	2
#14271186	2
#14270935	2
#14270924	2
#14270922	2
#14270919	2
C₂₉×#344	2
#2102	29

subgroup

index

C₂₉×#344

Subgroups — #16821069

Conjugacy classes of subgroups

Complements

Maximal subgroups