Group #16821208 — subgroups

Subgroups — #16821208

Order 3712.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11745160	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271201	C₂	1	1	yes	maximal, characteristic, complemented
3	#14270964	C₂	1	4	yes	maximal, complemented
4	C₂²×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₄×C₂₉	—	2	1	no	—
6	C₂×D₈×C₂₉	—	2	1	no	—
7	C₂×D₈×C₂₉	—	2	2	no	—
8	C₂×D₈×C₂₉	C₄	1	4	yes	complemented
9	C₂×D₈×C₂₉	C₂²	1	2	yes	—
10	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745288	—	2	1	no	—
12	#11745166	C₂²	1	2	yes	complemented
13	#11745165	—	2	1	no	—
14	#11745160	—	2	2	no	—
15	C₂×#90768	C₂²	1	2	yes	complemented
16	C₂⁴×C₂₉	—	4	1	no	—
17	C₂×D₄×C₂₉	—	2	4	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	4	1	no	—
20	C₂×D₄×C₂₉	—	4	2	no	—
21	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
22	D₈×C₂₉	—	2	4	no	—
23	D₈×C₂₉	—	2	2	no	—
24	D₈×C₂₉	C₂×C₄	1	4	yes	—
25	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₂₉	D₄	1	2	yes	—
28	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
29	C₂²⋊Dic₂₉	—	4	1	no	—
30	C₄⋊Dic₂₉	—	2	2	no	—
31	C₄×Dic₂₉	—	4	1	no	—
32	#90768	—	2	2	no	—
33	C₂³×C₂₉	—	4	4	no	—
34	C₂³×C₂₉	—	4	2	no	—
35	C₂³×C₂₉	—	8	4	no	—
36	C₂³×C₂₉	D₈	1	1	yes	characteristic
37	D₄×C₂₉	—	2	4	no	—
38	D₄×C₂₉	—	4	4	no	—
39	D₄×C₂₉	—	4	2	no	—
40	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
42	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
43	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
44	C₂×Dic₂₉	—	4	2	no	—
45	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
46	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
47	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
48	#2140	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	—	2	2	no	—
50	C₂²×C₂₉	—	4	4	no	—
51	C₂²×C₂₉	—	8	8	no	—
52	C₂²×C₂₉	—	8	4	no	—
53	C₂²×C₂₉	#102	1	2	yes	—
54	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
55	C₄×C₂₉	#102	1	2	yes	—
56	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₂₉	—	8	2	no	—
59	C₂²×D₈	D₂₉	1	1	yes	characteristic
60	C₂×M₃₂	—	29	1	no	—
61	#427	—	29	1	no	—
62	#357	—	29	4	no	—
63	C₂×C₂₉	—	2	2	no	—
64	C₂×C₂₉	—	8	4	no	—
65	C₂×C₂₉	C₂×#102	1	1	yes	characteristic
66	C₂×C₂₉	#509	1	2	yes	—
67	C₂²×D₄	—	2	1	no	—
68	C₂×D₈	—	2	1	no	—
69	C₂×D₈	—	2	2	no	—
70	C₂×D₈	Dic₂₉	1	4	yes	complemented
71	C₂×D₈	C₂×D₂₉	1	2	yes	—
72	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
73	#117	—	58	1	no	—
74	M₃₂	—	58	2	no	—
75	C₂×C₁₆	—	29	2	no	—
76	#107	—	29	2	no	—
77	#106	—	58	1	no	—
78	C₂₉	#2140	1	1	yes	characteristic, complemented, Sylow
79	C₂⁴	—	4	1	no	—
80	C₂×D₄	—	2	4	no	—
81	C₂×D₄	—	2	2	no	—
82	C₂×D₄	—	4	1	no	—
83	C₂×D₄	—	4	2	no	—
84	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
85	D₈	—	2	4	no	—
86	D₈	—	2	2	no	—
87	D₈	C₂×Dic₂₉	1	4	yes	—
88	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
89	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
90	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
91	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
92	C₄⋊C₄	—	58	2	no	—
93	C₂²⋊C₄	—	116	1	no	—
94	C₄²	—	116	1	no	—
95	C₁₆	—	58	2	no	—
96	C₂³	—	4	2	no	—
97	C₂³	—	4	4	no	—
98	C₂³	—	8	4	no	—
99	C₂³	#90782	1	1	yes	characteristic
100	D₄	—	2	4	no	—
101	D₄	—	4	2	no	—
102	D₄	—	4	4	no	—
103	C₂×C₄	—	116	2	no	—
104	C₂×C₄	#90782	1	1	yes	characteristic
105	C₂×C₄	#90783	1	2	yes	—
106	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
107	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
108	C₈	C₂²⋊Dic₂₉	1	2	yes	—
109	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
110	C₈	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
111	C₂²	—	2	2	no	—
112	C₂²	—	4	4	no	—
113	C₂²	—	8	8	no	—
114	C₂²	—	8	4	no	—
115	C₂²	#11745180	1	2	yes	—
116	C₂²	C₂×#90782	1	1	yes	characteristic
117	C₄	—	232	2	no	—
118	C₄	#11745180	1	2	yes	—
119	C₄	C₂×#90783	1	1	yes	characteristic
120	C₄	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	8	4	no	—
123	C₂	C₂×#11745180	1	1	yes	characteristic
124	C₂	#14271599	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745160

C₂

yes

maximal, characteristic, complemented

#14271201

C₂

yes

maximal, characteristic, complemented

#14270964

C₂

yes

maximal, complemented

C₂²×D₈×C₂₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₂₉

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

C₄

yes

complemented

C₂×D₈×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

—

#11745166

C₂²

yes

—

—

C₂²

yes

complemented

C₂⁴×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

D₈×C₂₉

—

D₈×C₂₉

—

D₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

#90768

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

D₈

yes

characteristic

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

D₈

yes

characteristic

C₂×C₄×C₂₉

SD₁₆

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

—

C₈×C₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

C₂²×C₄

yes

characteristic

C₈×C₂₉

C₂×D₄

yes

characteristic

#2140

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#102

yes

—

C₂²×C₂₉

C₂×D₈

yes

characteristic

C₄×C₂₉

#102

yes

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₂×SD₁₆

yes

characteristic

Dic₂₉

—

C₂²×D₈

D₂₉

yes

characteristic

C₂×M₃₂

—

#427

—

#357

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#102

yes

characteristic

C₂×C₂₉

#509

yes

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

Dic₂₉

yes

complemented

C₂×D₈

C₂×D₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

#107

—

#106

—

C₂₉

#2140

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

D₈

—

D₈

—

D₈

C₂×Dic₂₉

yes

—

C₂×C₈

C₂×Dic₂₉

yes

—

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

—

C₂×C₈

C₂²×D₂₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

116

—

C₄²

—

116

—

C₁₆

—

C₂³

—

C₂³

—

C₂³

—

C₂³

#90782

yes

characteristic

100

D₄

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

116

—

104

C₂×C₄

#90782

yes

characteristic

105

C₂×C₄

#90783

yes

—

106

C₂×C₄

C₂²⋊Dic₂₉

yes

—

107

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

108

C₈

C₂²⋊Dic₂₉

yes

—

109

C₈

C₂²×Dic₂₉

yes

characteristic

110

C₈

C₂×C₂²⋊D₂₉

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

#11745180

yes

—

116

C₂²

C₂×#90782

yes

characteristic

117

C₄

—

232

—

118

C₄

#11745180

yes

—

119

C₄

C₂×#90783

yes

characteristic

120

C₄

C₂×C₂²⋊Dic₂₉

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

C₂×#11745180

yes

characteristic

124

C₂

#14271599

yes

—

	subgroup	G/H
center	C₂²	C₂×#90782
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting, prime radical	C₂²×D₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂²×D₈	D₂₉
hypocenter	C₂₉	#2140
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

subgroup

G/H

center

C₂²

C₂×#90782

commutator

C₈×C₂₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₂₉

Fitting, prime radical

C₂²×D₈×C₂₉

C₂

socle

C₂²×C₂₉

C₂×D₈

cosocle

C₂×C₈×C₂₉

C₂³

hypercenter

C₂²×D₈

D₂₉

hypocenter

C₂₉

#2140

LCS

G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₈

N	H ≅ G/N	type
1. C₂×#11745160	C₂	semidirect
2. #14271201	C₂	semidirect
3. #14270964	C₂	semidirect
8. C₂×D₈×C₂₉	C₄	semidirect
12. #11745166	C₂²	semidirect
15. C₂×#90768	C₂²	semidirect
70. C₂×D₈	Dic₂₉	semidirect
78. C₂₉	#2140	semidirect

H ≅ G/N

type

1. C₂×#11745160

C₂

semidirect

2. #14271201

C₂

semidirect

3. #14270964

C₂

semidirect

8. C₂×D₈×C₂₉

C₄

semidirect

12. #11745166

C₂²

semidirect

15. C₂×#90768

C₂²

semidirect

70. C₂×D₈

Dic₂₉

semidirect

78. C₂₉

#2140

semidirect

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

subgroup	index
C₂×#11745160	2
#14271201	2
#14270964	2
C₂²×D₈×C₂₉	2
#2140	29

subgroup

index

C₂²×D₈×C₂₉

Subgroups — #16821208

Conjugacy classes of subgroups

Complements

Maximal subgroups