Group #16820745 — subgroups

Subgroups — #16820745

Order 3712.

296 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14271189	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271168	C₂	1	2	yes	maximal, complemented
3	C₂×#11745181	C₂	1	2	yes	maximal, complemented
4	#14270928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
7	C₂×D₈×C₂₉	—	2	4	no	—
8	C₂×D₈×C₂₉	—	2	2	no	—
9	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#11745288	C₂²	1	1	yes	characteristic
11	C₂×#90777	C₂²	1	1	yes	characteristic
12	C₂×#90777	C₂²	1	2	yes	—
13	#11745181	—	2	4	no	—
14	#11745180	—	2	4	no	—
15	#11745162	—	2	2	no	—
16	C₂⁴×C₂₉	—	2	2	no	—
17	C₂×D₄×C₂₉	—	2	2	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	2	no	—
20	C₂×D₄×C₂₉	—	2	2	no	—
21	C₂×D₄×C₂₉	—	2	2	no	—
22	C₂×D₄×C₂₉	D₄	1	4	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	D₈×C₂₉	—	2	8	no	—
25	C₂×C₈×C₂₉	—	2	2	no	—
26	C₂×C₈×C₂₉	D₄	1	2	yes	—
27	C₂²⋊Dic₂₉	—	2	1	no	—
28	C₄⋊Dic₂₉	D₄	1	2	yes	—
29	C₄×Dic₂₉	—	2	1	no	—
30	#90777	—	2	2	no	—
31	#90777	—	2	2	no	—
32	#90777	—	2	2	no	—
33	C₂×#6597	—	2	1	no	—
34	C₂×#6597	—	2	2	no	—
35	C₂³×C₂₉	—	2	4	no	—
36	C₂³×C₂₉	—	4	2	no	—
37	C₂³×C₂₉	—	4	2	no	—
38	C₂³×C₂₉	—	8	4	no	—
39	C₂³×C₂₉	#41	1	1	yes	characteristic
40	D₄×C₂₉	—	2	4	no	—
41	D₄×C₂₉	—	2	4	no	—
42	D₄×C₂₉	—	4	2	no	—
43	D₄×C₂₉	—	4	2	no	—
44	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	#41	1	2	yes	—
48	C₂×Dic₂₉	—	2	2	no	—
49	C₈×C₂₉	—	2	2	no	—
50	#6597	—	4	1	no	—
51	#6597	—	4	2	no	—
52	#2045	—	29	1	no	maximal, Sylow
53	C₂²×C₂₉	—	2	2	no	—
54	C₂²×C₂₉	—	4	4	no	—
55	C₂²×C₂₉	—	8	4	no	—
56	C₂²×C₂₉	—	8	4	no	—
57	C₂²×C₂₉	—	8	4	no	—
58	C₂²×C₂₉	#121	1	1	yes	characteristic
59	C₂²×C₂₉	#123	1	2	yes	—
60	C₄×C₂₉	#120	1	1	yes	characteristic
61	C₄×C₂₉	#121	1	2	yes	—
62	C₄×C₂₉	#124	1	1	yes	characteristic
63	Dic₂₉	—	4	2	no	—
64	C₂²×D₈	D₂₉	1	1	yes	characteristic
65	#424	—	29	1	no	—
66	#418	—	29	2	no	—
67	C₂×#100	—	29	2	no	—
68	#341	—	29	1	no	—
69	C₂×C₂₉	—	2	2	no	—
70	C₂×C₂₉	—	8	4	no	—
71	C₂×C₂₉	#394	1	1	yes	characteristic
72	C₂×C₂₉	#472	1	2	yes	—
73	C₂²×D₄	C₂×D₂₉	1	2	yes	—
74	C₂×D₈	—	2	4	no	—
75	C₂×D₈	—	2	2	no	—
76	C₂×M₁₆	—	29	2	no	—
77	C₂×M₁₆	—	29	1	no	—
78	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
79	#117	—	29	1	no	—
80	C₄⋊C₈	—	58	2	no	—
81	#102	—	58	4	no	—
82	#100	—	58	4	no	—
83	C₂₉	#2045	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	—	2	2	no	—
85	C₂×D₄	—	2	2	no	—
86	C₂×D₄	—	2	2	no	—
87	C₂×D₄	—	2	2	no	—
88	C₂×D₄	—	2	2	no	—
89	C₂×D₄	—	2	2	no	—
90	C₂×D₄	C₂²⋊D₂₉	1	4	yes	—
91	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
92	D₈	—	2	8	no	—
93	M₁₆	—	58	2	no	—
94	M₁₆	—	58	2	no	—
95	M₁₆	—	58	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	58	2	no	—
98	C₂×C₈	—	58	1	no	—
99	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
100	C₄⋊C₄	—	29	2	no	—
101	C₂²⋊C₄	—	58	1	no	—
102	C₄²	—	58	1	no	—
103	C₂³	—	2	4	no	—
104	C₂³	—	4	2	no	—
105	C₂³	—	4	2	no	—
106	C₂³	—	8	4	no	—
107	C₂³	#90807	1	1	yes	characteristic
108	D₄	—	2	4	no	—
109	D₄	—	2	4	no	—
110	D₄	—	4	2	no	—
111	D₄	—	4	2	no	—
112	C₂×C₄	—	58	2	no	—
113	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
114	C₂×C₄	#90807	1	2	yes	—
115	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
116	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
117	C₈	—	2	2	no	—
118	C₈	—	116	2	no	—
119	C₈	—	116	1	no	—
120	C₂²	—	2	2	no	—
121	C₂²	—	4	4	no	—
122	C₂²	—	8	4	no	—
123	C₂²	—	8	4	no	—
124	C₂²	—	8	4	no	—
125	C₂²	#11745297	1	2	yes	—
126	C₂²	#11745300	1	1	yes	characteristic
127	C₄	—	116	2	no	—
128	C₄	#11745298	1	1	yes	characteristic
129	C₄	#11745301	1	2	yes	—
130	C₄	#11745315	1	1	yes	characteristic
131	C₂	—	2	2	no	—
132	C₂	—	8	4	no	—
133	C₂	#14271077	1	1	yes	characteristic
134	C₂	#14271430	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271189

C₂

yes

maximal, characteristic, complemented

#14271168

C₂

yes

maximal, complemented

C₂×#11745181

C₂

yes

maximal, complemented

#14270928

C₂

yes

maximal, characteristic, complemented

C₂²×D₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

C₂²

yes

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

#11745181

—

#11745180

—

#11745162

—

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

D₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

—

—

—

—

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

#41

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₈×C₂₉

—

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#121

yes

characteristic

C₂²×C₂₉

#123

yes

—

C₄×C₂₉

#120

yes

characteristic

C₄×C₂₉

#121

yes

—

C₄×C₂₉

#124

yes

characteristic

Dic₂₉

—

C₂²×D₈

D₂₉

yes

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#394

yes

characteristic

C₂×C₂₉

#472

yes

—

C₂²×D₄

C₂×D₂₉

yes

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

—

C₄⋊C₈

—

#102

—

#100

—

C₂₉

#2045

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

#90807

yes

characteristic

108

D₄

—

109

D₄

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

D₄×D₂₉

yes

characteristic

114

C₂×C₄

#90807

yes

—

115

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

116

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

117

C₈

—

118

C₈

—

116

—

119

C₈

—

116

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

#11745297

yes

—

126

C₂²

#11745300

yes

characteristic

127

C₄

—

116

—

128

C₄

#11745298

yes

characteristic

129

C₄

#11745301

yes

—

130

C₄

#11745315

yes

characteristic

131

C₂

—

132

C₂

—

133

C₂

#14271077

yes

characteristic

134

C₂

#14271430

yes

—

	subgroup	G/H
center	C₂²	#11745300
commutator, cosocle	C₂²×C₄×C₂₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting, prime radical	C₂²×D₈×C₂₉	C₂
socle	C₂²×C₂₉	#121
hypercenter	C₂²×D₈	D₂₉
hypocenter	C₂₉	#2045
LCS	G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

subgroup

G/H

center

C₂²

#11745300

commutator, cosocle

C₂²×C₄×C₂₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting, prime radical

C₂²×D₈×C₂₉

C₂

socle

C₂²×C₂₉

#121

hypercenter

C₂²×D₈

D₂₉

hypocenter

C₂₉

#2045

LCS

G ▷ C₂²×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

N	H ≅ G/N	type
1. #14271189	C₂	semidirect
2. #14271168	C₂	semidirect
3. C₂×#11745181	C₂	semidirect
4. #14270928	C₂	semidirect
83. C₂₉	#2045	semidirect

H ≅ G/N

type

1. #14271189

C₂

semidirect

2. #14271168

C₂

semidirect

3. C₂×#11745181

C₂

semidirect

4. #14270928

C₂

semidirect

83. C₂₉

#2045

semidirect

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

subgroup	index
#14271189	2
#14271168	2
C₂×#11745181	2
#14270928	2
C₂²×D₈×C₂₉	2
#2045	29

subgroup

index

C₂²×D₈×C₂₉

Subgroups — #16820745

Conjugacy classes of subgroups

Complements

Maximal subgroups