Group #16821541 — subgroups

Subgroups — #16821541

Order 3712.

154 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic₂₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745177	C₂	1	1	yes	maximal, characteristic
3	#14271541	C₂	1	1	yes	maximal, characteristic
4	#14271257	C₂	1	1	yes	maximal, characteristic
5	#14270981	C₂	1	1	yes	maximal, characteristic
6	#14270966	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	#11745306	—	2	1	no	—
10	C₂×#90785	—	2	1	no	—
11	C₂×Dic₁₁₆	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₁₆	C₂²	1	1	yes	characteristic
13	#11745249	—	2	1	no	—
14	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#107	C₂²	1	1	yes	characteristic
16	#11745177	—	2	2	no	—
17	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
18	C₂×#90768	C₂²	1	1	yes	characteristic
19	#11745158	—	2	1	no	—
20	Dic₂₃₂	—	2	2	no	—
21	C₂×Q₈×C₂₉	—	2	1	no	—
22	C₂×Dic₅₈	—	2	1	no	—
23	C₂×Dic₅₈	—	2	1	no	—
24	Q₁₆×C₂₉	—	2	1	no	—
25	Q₁₆×C₂₉	—	2	1	no	—
26	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₂₉	—	2	1	no	—
28	#90785	—	4	2	no	—
29	#90779	—	4	1	no	—
30	#90779	—	4	1	no	—
31	#90779	—	4	1	no	—
32	C₄×Dic₂₉	—	4	1	no	—
33	C₄×Dic₂₉	D₄	1	1	yes	characteristic
34	C₂×#6597	D₄	1	1	yes	characteristic
35	Dic₁₁₆	—	2	1	no	—
36	Dic₁₁₆	—	2	1	no	—
37	Dic₁₁₆	—	2	1	no	—
38	Dic₁₁₆	D₄	1	2	yes	—
39	C₁₆×C₂₉	—	2	1	no	—
40	#90768	—	2	1	no	—
41	Q₈×C₂₉	—	4	1	no	—
42	Q₈×C₂₉	—	4	1	no	—
43	C₂×C₄×C₂₉	—	4	1	no	—
44	C₂×C₄×C₂₉	—	4	1	no	—
45	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₂₉	—	4	1	no	—
47	C₂×Dic₂₉	—	4	1	no	—
48	C₂×Dic₂₉	D₈	1	1	yes	characteristic
49	C₂×Dic₂₉	D₈	1	1	yes	characteristic
50	Dic₅₈	—	2	2	no	—
51	Dic₅₈	—	4	1	no	—
52	Dic₅₈	—	4	1	no	—
53	Dic₅₈	—	4	1	no	—
54	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₂₉	#41	1	1	yes	characteristic
56	#6597	—	2	1	no	—
57	#2209	—	29	1	no	maximal, Sylow
58	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
59	C₄×C₂₉	—	8	1	no	—
60	C₄×C₂₉	—	8	1	no	—
61	C₄×C₂₉	#121	1	1	yes	characteristic
62	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
63	Dic₂₉	—	2	1	no	—
64	Dic₂₉	—	4	2	no	—
65	Dic₂₉	—	8	1	no	—
66	Dic₂₉	Q₃₂	1	2	yes	complemented
67	C₂×Q₃₂	—	29	1	no	—
68	C₂×Q₃₂	—	29	1	no	—
69	#494	—	29	1	no	—
70	C₄×Q₁₆	—	29	1	no	—
71	C₄⋊C₁₆	—	29	1	no	—
72	#358	—	29	1	no	—
73	#358	D₂₉	1	1	yes	characteristic
74	C₂×C₂₉	#459	1	1	yes	characteristic
75	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
76	C₂×C₂₉	#510	1	1	yes	characteristic
77	C₂×Q₁₆	—	29	1	no	—
78	C₂×Q₁₆	—	29	1	no	—
79	C₂×Q₁₆	—	58	1	no	—
80	C₂×Q₁₆	C₂×D₂₉	1	1	yes	characteristic
81	C₄⋊Q₈	—	58	1	no	—
82	C₄×Q₈	—	58	1	no	—
83	Q₃₂	—	58	2	no	—
84	Q₃₂	—	58	2	no	—
85	C₂×C₁₆	—	29	1	no	—
86	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
87	#107	C₂×D₂₉	1	1	yes	characteristic
88	#103	—	58	1	no	—
89	C₄×C₈	—	29	1	no	—
90	C₂₉	#2209	1	1	yes	characteristic, complemented, Sylow
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	58	1	no	—
93	C₂×Q₈	—	58	1	no	—
94	Q₁₆	—	2	1	no	—
95	Q₁₆	—	2	1	no	—
96	Q₁₆	—	29	2	no	—
97	Q₁₆	—	58	1	no	—
98	Q₁₆	—	58	1	no	—
99	Q₁₆	—	58	1	no	—
100	Q₁₆	—	116	2	no	—
101	C₂×C₈	—	29	1	no	—
102	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	116	1	no	—
105	C₄⋊C₄	—	116	1	no	—
106	C₄⋊C₄	—	116	1	no	—
107	C₄²	—	29	1	no	—
108	C₄²	—	116	1	no	—
109	C₁₆	—	2	1	no	—
110	C₁₆	—	58	1	no	—
111	Q₈	—	4	1	no	—
112	Q₈	—	4	1	no	—
113	Q₈	—	58	2	no	—
114	Q₈	—	116	1	no	—
115	Q₈	—	116	1	no	—
116	Q₈	—	116	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	29	1	no	—
120	C₂×C₄	—	29	1	no	—
121	C₂×C₄	—	116	1	no	—
122	C₂×C₄	—	116	1	no	—
123	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
124	C₈	—	58	1	no	—
125	C₈	#90805	1	1	yes	characteristic
126	C₈	D₄×D₂₉	1	1	yes	characteristic
127	C₂²	D₈×D₂₉	1	1	yes	characteristic
128	C₄	—	8	1	no	—
129	C₄	—	8	1	no	—
130	C₄	—	29	2	no	—
131	C₄	—	58	1	no	—
132	C₄	—	116	2	no	—
133	C₄	—	232	1	no	—
134	C₄	#11745246	1	1	yes	characteristic
135	C₄	#11745276	1	1	yes	characteristic
136	C₂	#14271357	1	1	yes	characteristic
137	C₂	Q₃₂×D₂₉	1	1	yes	characteristic
138	C₂	#14271602	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₂₃₂

C₂

yes

maximal, characteristic

C₂×#11745177

C₂

yes

maximal, characteristic

#14271541

C₂

yes

maximal, characteristic

#14271257

C₂

yes

maximal, characteristic

#14270981

C₂

yes

maximal, characteristic

#14270966

C₂

yes

maximal, characteristic

C₂₉×#358

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₂₉

C₂²

yes

characteristic

#11745306

—

C₂×#90785

—

C₂×Dic₁₁₆

C₂²

yes

characteristic

C₂×Dic₁₁₆

C₂²

yes

characteristic

#11745249

—

C₂×C₁₆×C₂₉

C₂²

yes

characteristic

C₂₉×#107

C₂²

yes

characteristic

#11745177

—

C₈×Dic₂₉

C₂²

yes

characteristic

C₂×#90768

C₂²

yes

characteristic

#11745158

—

Dic₂₃₂

—

C₂×Q₈×C₂₉

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

Q₁₆×C₂₉

—

Q₁₆×C₂₉

—

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₄⋊C₄×C₂₉

—

—

—

—

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

characteristic

C₂×#6597

D₄

yes

characteristic

Dic₁₁₆

—

Dic₁₁₆

—

Dic₁₁₆

—

Dic₁₁₆

D₄

yes

—

C₁₆×C₂₉

—

#90768

—

Q₈×C₂₉

—

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

D₈

yes

characteristic

C₂×Dic₂₉

D₈

yes

characteristic

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

Dic₅₈

—

C₈×C₂₉

C₂×D₄

yes

C₈×C₂₉

yes

—

—

C₂²×C₂₉

C₂×D₈

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

Q₃₂

yes

complemented

C₂×Q₃₂

—

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#358

D₂₉

yes

characteristic

C₂×C₂₉

#459

yes

characteristic

C₂×C₂₉

C₂×Q₃₂

yes

characteristic

C₂×C₂₉

#510

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₂₉

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₂₉

yes

characteristic

#107

C₂×D₂₉

yes

characteristic

#103

—

C₄×C₈

—

C₂₉

#2209

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

Q₁₆

—

116

—

101

C₂×C₈

—

102

C₂×C₈

C₂²×D₂₉

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

116

—

105

C₄⋊C₄

—

116

—

106

C₄⋊C₄

—

116

—

107

C₄²

—

108

C₄²

—

116

—

109

C₁₆

—

110

C₁₆

—

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

116

—

115

Q₈

—

116

—

116

Q₈

—

116

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

116

—

122

C₂×C₄

—

116

—

123

C₂×C₄

D₄×D₂₉

yes

characteristic

124

C₈

—

125

C₈

#90805

yes

characteristic

126

C₈

D₄×D₂₉

yes

characteristic

127

C₂²

D₈×D₂₉

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

116

—

133

C₄

—

232

—

134

C₄

#11745246

yes

characteristic

135

C₄

#11745276

yes

characteristic

136

C₂

#14271357

yes

characteristic

137

C₂

Q₃₂×D₂₉

yes

characteristic

138

C₂

#14271602

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₂₉
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#358	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	#358	D₂₉
hypocenter	C₂₉	#2209
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₂₉

commutator, cosocle

C₂×C₈×C₂₉

C₂³

Frattini

C₂×C₈

C₂²×D₂₉

Fitting

C₂₉×#358

C₂

socle, prime radical

C₂²×C₂₉

C₂×D₈

D₂₉

C₂₉

G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
66. Dic₂₉	Q₃₂	semidirect
90. C₂₉	#2209	semidirect

H ≅ G/N

type

66. Dic₂₉

Q₃₂

semidirect

90. C₂₉

#2209

semidirect

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

subgroup	index
C₂×Dic₂₃₂	2
C₂×#11745177	2
#14271541	2
#14271257	2
#14270981	2
#14270966	2
C₂₉×#358	2
#2209	29

subgroup

index

C₂×Dic₂₃₂

C₂₉×#358

Subgroups — #16821541

Conjugacy classes of subgroups

Complements

Maximal subgroups