Group #16821102 — subgroups

Subgroups — #16821102

Order 3712.

260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂²×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745160	C₂	1	1	yes	maximal, characteristic, complemented
3	#14270942	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×D₂₉	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×#6597	C₄	1	1	yes	characteristic
8	C₂×C₈×D₂₉	—	2	2	no	—
9	C₂×C₈×D₂₉	—	2	2	no	—
10	C₂×C₈×D₂₉	C₄	1	2	yes	—
11	C₂×C₈×D₂₉	C₂²	1	2	yes	—
12	C₂₉×M₃₂	—	2	2	no	—
13	C₂×C₁₆×C₂₉	C₂²	1	2	yes	complemented
14	#11745160	—	2	2	no	—
15	C₂×#90768	C₂²	1	2	yes	complemented
16	C₂³×D₂₉	C₈	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₈	1	1	yes	characteristic
19	C₂×C₄×D₂₉	—	2	2	no	—
20	C₂×C₄×D₂₉	—	2	2	no	—
21	C₂×C₄×D₂₉	C₈	1	2	yes	—
22	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	D₄	1	2	yes	—
25	C₂×C₈×C₂₉	D₄	1	2	yes	—
26	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
27	C₂×#6597	—	2	2	no	—
28	C₂×#6597	C₂×C₄	1	2	yes	—
29	C₈×D₂₉	—	2	4	no	—
30	C₈×D₂₉	—	2	2	no	—
31	C₈×D₂₉	—	2	2	no	—
32	C₁₆×C₂₉	—	2	2	no	—
33	#90768	—	2	2	no	—
34	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₂₉	—	2	2	no	—
36	C₂²×D₂₉	—	2	4	no	—
37	C₂²×D₂₉	C₂×C₈	1	2	yes	—
38	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
41	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
44	C₄×D₂₉	—	2	4	no	—
45	C₄×D₂₉	—	2	2	no	—
46	C₄×D₂₉	—	2	2	no	—
47	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
48	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
49	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
50	#6597	—	2	2	no	—
51	#2112	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	—	2	2	no	—
53	C₂²×C₂₉	C₂²⋊C₈	1	2	yes	—
54	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
55	C₂×D₂₉	—	2	8	no	—
56	C₂×D₂₉	—	2	2	no	—
57	C₂×D₂₉	—	2	2	no	—
58	C₂×D₂₉	M₃₂	1	4	yes	complemented
59	C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
60	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
62	Dic₂₉	—	2	2	no	—
63	C₂³×C₈	—	29	1	no	—
64	C₂×M₃₂	—	29	1	no	—
65	C₂×M₃₂	D₂₉	1	1	yes	characteristic, complemented
66	C₂²⋊C₁₆	—	29	4	no	—
67	C₂×C₂₉	—	2	2	no	—
68	C₂×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
69	C₂×C₂₉	C₂×M₃₂	1	2	yes	—
70	D₂₉	—	2	4	no	—
71	C₂³×C₄	—	29	1	no	—
72	C₂²×C₈	—	29	1	no	—
73	C₂²×C₈	—	29	2	no	—
74	C₂²×C₈	—	29	2	no	—
75	C₂²×C₈	—	58	2	no	—
76	C₂²×C₈	—	58	2	no	—
77	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
78	M₃₂	—	2	2	no	—
79	M₃₂	—	58	2	no	—
80	C₂×C₁₆	—	29	2	no	—
81	C₂×C₁₆	C₂×D₂₉	1	2	yes	complemented
82	C₂₉	#2112	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	—	29	1	no	—
84	C₂²×C₄	—	29	1	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂²×C₄	—	29	2	no	—
87	C₂²×C₄	—	58	2	no	—
88	C₂²×C₄	—	58	2	no	—
89	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	58	2	no	—
92	C₂×C₈	—	58	4	no	—
93	C₂×C₈	—	58	2	no	—
94	C₂×C₈	—	58	2	no	—
95	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
96	C₂×C₈	D₁₁₆	1	2	yes	—
97	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
98	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
99	C₁₆	—	2	2	no	—
100	C₁₆	—	58	2	no	—
101	C₂³	—	29	2	no	—
102	C₂³	—	58	4	no	—
103	C₂³	—	58	2	no	—
104	C₂³	C₈×D₂₉	1	1	yes	characteristic
105	C₂×C₄	—	29	2	no	—
106	C₂×C₄	—	58	2	no	—
107	C₂×C₄	—	58	2	no	—
108	C₂×C₄	—	58	4	no	—
109	C₂×C₄	—	58	2	no	—
110	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
111	C₂×C₄	#90772	1	2	yes	—
112	C₂×C₄	#90781	1	2	yes	—
113	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
114	C₈	—	58	2	no	—
115	C₈	#90781	1	2	yes	—
116	C₈	C₂×D₁₁₆	1	1	yes	characteristic
117	C₈	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
118	C₂²	—	2	2	no	—
119	C₂²	—	29	4	no	—
120	C₂²	—	58	8	no	—
121	C₂²	—	58	2	no	—
122	C₂²	—	58	2	no	—
123	C₂²	#11745168	1	2	yes	—
124	C₂²	C₂×C₈×D₂₉	1	1	yes	characteristic
125	C₄	—	58	2	no	—
126	C₄	#11745168	1	2	yes	—
127	C₄	C₂×#90772	1	1	yes	characteristic
128	C₄	C₂×#90781	1	1	yes	characteristic
129	C₂	—	2	2	no	—
130	C₂	—	58	4	no	—
131	C₂	C₂×#11745168	1	1	yes	characteristic
132	C₂	M₃₂×D₂₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₂₉

C₂

yes

maximal, characteristic

C₂×#11745160

C₂

yes

maximal, characteristic, complemented

#14270942

C₂

yes

maximal, complemented

C₂×C₂₉×M₃₂

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₂₉

C₄

yes

characteristic

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂²×#6597

C₄

yes

characteristic

C₂×C₈×D₂₉

—

C₂×C₈×D₂₉

—

C₂×C₈×D₂₉

C₄

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

C₂₉×M₃₂

—

C₂×C₁₆×C₂₉

C₂²

yes

complemented

#11745160

—

C₂×#90768

C₂²

yes

complemented

C₂³×D₂₉

C₈

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₈

yes

characteristic

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

C₈

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

D₄

yes

—

C₂×C₈×C₂₉

C₂³

yes

characteristic

C₂×#6597

—

C₂×#6597

C₂×C₄

yes

—

C₈×D₂₉

—

C₈×D₂₉

—

C₈×D₂₉

—

C₁₆×C₂₉

—

#90768

—

C₂³×C₂₉

C₂×C₈

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂²×D₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×C₈

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₈×C₂₉

C₂²⋊C₄

yes

—

C₈×C₂₉

C₂×D₄

yes

characteristic

C₈×C₂₉

C₂×D₄

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂²⋊C₈

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

M₃₂

yes

complemented

C₄×C₂₉

C₂²⋊C₈

yes

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₂×M₁₆

yes

characteristic

Dic₂₉

—

C₂³×C₈

—

C₂×M₃₂

—

C₂×M₃₂

D₂₉

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₂₉

C₂×M₃₂

yes

—

D₂₉

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₂₉

yes

complemented

C₂₉

#2112

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₂₉

yes

characteristic

C₂×C₈

D₁₁₆

yes

—

C₂×C₈

C₂²⋊D₂₉

yes

—

C₂×C₈

C₂²×D₂₉

yes

characteristic

C₁₆

—

100

C₁₆

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₈×D₂₉

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₈×D₂₉

yes

characteristic

111

C₂×C₄

#90772

yes

—

112

C₂×C₄

#90781

yes

—

113

C₂×C₄

C₂×C₄×D₂₉

yes

characteristic

114

C₈

—

115

C₈

#90781

yes

—

116

C₈

C₂×D₁₁₆

yes

characteristic

117

C₈

C₂×C₂²⋊D₂₉

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#11745168

yes

—

124

C₂²

C₂×C₈×D₂₉

yes

characteristic

125

C₄

—

126

C₄

#11745168

yes

—

127

C₄

C₂×#90772

yes

characteristic

128

C₄

C₂×#90781

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

C₂×#11745168

yes

characteristic

132

C₂

M₃₂×D₂₉

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₂₉×M₃₂	C₂
prime radical	C₂³×D₂₉	C₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₂×M₃₂	D₂₉
hypocenter	C₂₉	#2112
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₂₉

commutator, socle

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×C₂₉×M₃₂

C₂

prime radical

C₂³×D₂₉

C₈

cosocle

C₂×C₈×C₂₉

C₂³

hypercenter

C₂×M₃₂

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. C₂×#11745160	C₂	semidirect
3. #14270942	C₂	semidirect
4. C₂×C₂₉×M₃₂	C₂	semidirect
13. C₂×C₁₆×C₂₉	C₂²	semidirect
15. C₂×#90768	C₂²	semidirect
58. C₂×D₂₉	M₃₂	semidirect
65. C₂×M₃₂	D₂₉	semidirect
81. C₂×C₁₆	C₂×D₂₉	semidirect
82. C₂₉	#2112	semidirect

H ≅ G/N

type

2. C₂×#11745160

C₂

semidirect

3. #14270942

C₂

semidirect

4. C₂×C₂₉×M₃₂

C₂

semidirect

13. C₂×C₁₆×C₂₉

C₂²

semidirect

15. C₂×#90768

C₂²

semidirect

58. C₂×D₂₉

M₃₂

semidirect

65. C₂×M₃₂

D₂₉

semidirect

81. C₂×C₁₆

C₂×D₂₉

semidirect

82. C₂₉

#2112

semidirect

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

subgroup	index
C₂²×C₈×D₂₉	2
C₂×#11745160	2
#14270942	2
C₂×C₂₉×M₃₂	2
#2112	29

subgroup

index

C₂²×C₈×D₂₉

C₂×#11745160

#14270942

C₂×C₂₉×M₃₂

#2112

Subgroups — #16821102

Conjugacy classes of subgroups

Complements

Maximal subgroups