Group #16821293 — subgroups

Subgroups — #16821293

Order 3712.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#14270981	C₂	1	2	yes	maximal, complemented
3	#14270942	C₂	1	2	yes	maximal
4	#14270939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₂₉	C₄	1	1	yes	characteristic
7	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
8	C₄²×D₂₉	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₈×Dic₂₉	C₄	1	1	yes	characteristic
12	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×#90768	C₂²	1	2	yes	—
14	C₄×#6597	C₄	1	1	yes	characteristic
15	C₂×C₄×D₂₉	C₈	1	1	yes	characteristic
16	C₂×C₄×D₂₉	C₈	1	1	yes	characteristic
17	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
20	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₂₉	C₈	1	1	yes	characteristic
22	C₄×Dic₂₉	C₈	1	1	yes	characteristic
23	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×#6597	C₂×C₄	1	1	yes	characteristic
25	C₂×#6597	C₂×C₄	1	1	yes	characteristic
26	C₈×D₂₉	—	2	2	no	—
27	C₈×D₂₉	—	2	2	no	—
28	C₁₆×C₂₉	—	2	2	no	—
29	#90768	—	2	2	no	—
30	C₂²×D₂₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
37	C₄×D₂₉	—	2	2	no	—
38	C₄×D₂₉	—	2	1	no	—
39	C₄×D₂₉	—	2	1	no	—
40	C₄×D₂₉	—	2	2	no	—
41	C₈×C₂₉	M₁₆	1	2	yes	—
42	C₈×C₂₉	#41	1	2	yes	—
43	#6597	—	2	1	no	—
44	#6597	—	2	1	no	—
45	#2163	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×D₂₉	—	2	1	no	—
48	C₂×D₂₉	—	2	1	no	—
49	C₂×D₂₉	M₃₂	1	2	yes	—
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	#117	1	1	yes	characteristic
53	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
54	Dic₂₉	—	2	1	no	—
55	Dic₂₉	—	2	1	no	—
56	Dic₂₉	M₃₂	1	2	yes	—
57	C₂×C₄×C₈	—	29	1	no	—
58	C₄⋊C₁₆	—	29	2	no	—
59	C₂²⋊C₁₆	—	29	2	no	—
60	#346	—	29	1	no	—
61	#346	D₂₉	1	1	yes	characteristic, complemented
62	C₂×C₂₉	#431	1	1	yes	characteristic
63	C₂×C₂₉	C₂×M₃₂	1	1	yes	characteristic
64	C₂×C₂₉	C₂×M₃₂	1	1	yes	characteristic
65	D₂₉	—	2	2	no	—
66	C₂²×C₈	—	29	1	no	—
67	C₂²×C₈	—	29	1	no	—
68	C₂×C₄²	—	29	1	no	—
69	C₂×C₁₆	—	29	2	no	—
70	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
71	C₄×C₈	—	29	1	no	—
72	C₄×C₈	—	29	1	no	—
73	C₄×C₈	—	29	1	no	—
74	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
75	C₂₉	#2163	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₄	—	29	1	no	—
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	—	29	1	no	—
79	C₂×C₈	—	29	1	no	—
80	C₂×C₈	—	29	1	no	—
81	C₂×C₈	—	58	2	no	—
82	C₂×C₈	—	58	2	no	—
83	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
85	C₄²	—	29	1	no	—
86	C₄²	—	29	1	no	—
87	C₄²	—	29	1	no	—
88	C₄²	C₄×D₂₉	1	1	yes	characteristic
89	C₁₆	—	2	2	no	—
90	C₁₆	—	58	2	no	—
91	C₂³	—	29	1	no	—
92	C₂×C₄	—	29	1	no	—
93	C₂×C₄	—	29	1	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	58	2	no	—
96	C₂×C₄	—	58	2	no	—
97	C₂×C₄	—	58	1	no	—
98	C₂×C₄	—	58	1	no	—
99	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
100	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
102	C₈	—	58	1	no	—
103	C₈	—	58	1	no	—
104	C₈	#90772	1	2	yes	—
105	C₈	#90805	1	2	yes	—
106	C₂²	—	29	2	no	—
107	C₂²	—	58	1	no	—
108	C₂²	—	58	1	no	—
109	C₂²	C₂×C₈×D₂₉	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	29	2	no	—
113	C₄	—	58	1	no	—
114	C₄	—	58	1	no	—
115	C₄	#11745234	1	1	yes	characteristic
116	C₄	C₂×#90772	1	1	yes	characteristic
117	C₂	—	58	2	no	—
118	C₂	#14271214	1	1	yes	characteristic
119	C₂	M₃₂×D₂₉	1	1	yes	characteristic
120	C₂	M₃₂×D₂₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₂₉

C₂

yes

maximal, characteristic

#14270981

C₂

yes

maximal, complemented

#14270942

C₂

yes

maximal

#14270939

C₂

yes

maximal, characteristic, complemented

C₂₉×#346

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₂₉

C₄

yes

characteristic

C₂×C₈×D₂₉

C₂²

yes

characteristic

C₄²×D₂₉

C₄

yes

characteristic

C₂×C₁₆×C₂₉

C₂²

yes

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₈×Dic₂₉

C₄

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

C₂×#90768

C₂²

yes

—

C₄×#6597

C₄

yes

characteristic

C₂×C₄×D₂₉

C₈

yes

characteristic

C₂×C₄×D₂₉

C₈

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₈

yes

characteristic

C₄×Dic₂₉

C₈

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₈×D₂₉

—

C₈×D₂₉

—

C₁₆×C₂₉

—

#90768

—

C₂²×D₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₈×C₂₉

M₁₆

yes

—

C₈×C₂₉

#41

yes

—

—

—

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

M₃₂

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

characteristic

C₄×C₂₉

C₂×M₁₆

yes

characteristic

Dic₂₉

—

Dic₂₉

—

Dic₂₉

M₃₂

yes

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#346

D₂₉

yes

characteristic, complemented

C₂×C₂₉

#431

yes

characteristic

C₂×C₂₉

C₂×M₃₂

yes

characteristic

C₂×C₂₉

C₂×M₃₂

yes

characteristic

D₂₉

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₂₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#2163

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

C₂²×D₂₉

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₂₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₂₉

yes

characteristic

100

C₂×C₄

C₈×D₂₉

yes

characteristic

101

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

#90772

yes

—

105

C₈

#90805

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₈×D₂₉

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

#11745234

yes

characteristic

116

C₄

C₂×#90772

yes

characteristic

117

C₂

—

118

C₂

#14271214

yes

characteristic

119

C₂

M₃₂×D₂₉

yes

characteristic

120

C₂

M₃₂×D₂₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂₉×#346	C₂
prime radical	C₂²×D₂₉	C₂×C₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	#346	D₂₉
hypocenter	C₂₉	#2163
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₂₉

commutator, socle

C₂²×C₂₉

C₂²×C₈

Fitting

C₂₉×#346

C₂

prime radical

C₂²×D₂₉

C₂×C₈

cosocle

C₂×C₈×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
2. #14270981	C₂	semidirect
4. #14270939	C₂	semidirect
5. C₂₉×#346	C₂	semidirect
61. #346	D₂₉	semidirect
75. C₂₉	#2163	semidirect

H ≅ G/N

type

2. #14270981

C₂

semidirect

4. #14270939

C₂

semidirect

5. C₂₉×#346

C₂

semidirect

61. #346

D₂₉

semidirect

75. C₂₉

#2163

semidirect

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

subgroup	index
C₄×C₈×D₂₉	2
#14270981	2
#14270942	2
#14270939	2
C₂₉×#346	2
#2163	29

subgroup

index

C₄×C₈×D₂₉

C₂₉×#346

Subgroups — #16821293

Conjugacy classes of subgroups

Complements

Maximal subgroups