Group #16835724 — subgroups

Subgroups — #16835724

Order 3712.

228 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 82 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×#11745214	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#90770	C₂	1	1	yes	maximal, characteristic, complemented
3	#14272058	C₂	1	4	yes	maximal, complemented
4	C₂×#11745269	C₂	1	1	yes	maximal, characteristic
5	C₂×#90805	C₄	1	1	yes	characteristic
6	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
7	C₂²×#6597	C₂²	1	1	yes	characteristic
8	#11745269	—	2	2	no	—
9	#11745269	—	2	2	no	—
10	C₂×#90772	C₄	1	2	yes	—
11	C₂×C₈×D₂₉	C₂²	1	2	yes	—
12	#11745214	—	2	2	no	—
13	C₂×#90770	—	2	2	no	—
14	C₂×#90770	C₂²	1	2	yes	—
15	C₂×#90770	C₂²	1	2	yes	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₂₉	C₈	1	2	yes	—
18	#90805	—	2	2	no	—
19	#90805	—	2	2	no	—
20	C₂×D₁₁₆	C₈	1	1	yes	characteristic
21	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
22	C₂×Dic₅₈	C₈	1	1	yes	characteristic
23	M₁₆×C₂₉	—	2	2	no	—
24	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
25	C₂×#6597	C₂×C₄	1	1	yes	characteristic
26	C₂×#6597	D₄	1	2	yes	—
27	C₂×#6597	D₄	1	2	yes	—
28	C₂×#6597	C₂³	1	1	yes	characteristic
29	#90772	—	2	4	no	—
30	C₈×D₂₉	—	2	2	no	—
31	C₈×D₂₉	—	2	2	no	—
32	#90770	—	2	2	no	—
33	#90770	—	2	2	no	—
34	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₂₉	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
39	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₂₉	—	2	4	no	—
41	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
42	D₁₁₆	—	2	2	no	—
43	C₄×D₂₉	—	2	2	no	—
44	C₄×D₂₉	—	2	2	no	—
45	Dic₅₈	—	2	2	no	—
46	C₈×C₂₉	—	2	2	no	—
47	#6597	C₂²⋊C₄	1	2	yes	—
48	#6597	C₂×D₄	1	1	yes	characteristic
49	#6597	C₂×D₄	1	1	yes	characteristic
50	#2113	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	2	2	no	—
52	C₂²×C₂₉	C₂²⋊C₈	1	2	yes	—
53	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
54	C₂×D₂₉	—	2	2	no	—
55	C₂×D₂₉	—	2	4	no	—
56	C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
57	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
59	Dic₂₉	—	2	2	no	—
60	C₂×#131	—	29	1	no	—
61	C₂×M₃₂	—	29	1	no	—
62	C₂²×C₁₆	—	29	1	no	—
63	C₂²⋊C₁₆	—	29	4	no	—
64	C₂×C₂₉	—	2	2	no	—
65	C₂×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
66	C₂×C₂₉	#504	1	2	yes	—
67	D₂₉	—	4	2	no	—
68	C₂×#41	—	29	1	no	—
69	#131	—	58	2	no	—
70	#131	—	58	2	no	—
71	C₂×M₁₆	—	29	2	no	—
72	C₂×M₁₆	#1181	1	1	yes	characteristic
73	C₂²×C₈	—	29	1	no	—
74	C₂²×C₈	—	29	2	no	—
75	M₃₂	—	58	2	no	—
76	C₂×C₁₆	—	29	2	no	—
77	C₂×C₁₆	—	29	2	no	—
78	C₂×C₁₆	—	58	2	no	—
79	C₂₉	#2113	1	1	yes	characteristic, complemented, Sylow
80	#41	—	58	2	no	—
81	#41	—	58	2	no	—
82	C₂×Q₈	—	29	1	no	—
83	C₂×D₄	—	29	2	no	—
84	C₂×D₄	—	29	1	no	—
85	C₂²×C₄	—	29	2	no	—
86	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	58	4	no	—
89	C₂×C₈	—	29	2	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	1	no	—
92	C₂×C₈	—	29	1	no	—
93	C₂×C₈	—	58	2	no	—
94	C₂×C₈	—	58	2	no	—
95	C₂×C₈	C₂×#1181	1	2	yes	—
96	C₁₆	—	58	2	no	—
97	C₁₆	—	58	2	no	—
98	C₂³	—	29	2	no	—
99	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
100	Q₈	—	58	2	no	—
101	D₄	—	58	4	no	—
102	D₄	—	58	2	no	—
103	C₂×C₄	—	29	2	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	—	58	2	no	—
106	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
107	C₂×C₄	#90796	1	2	yes	—
108	C₂×C₄	C₂²⋊#1181	1	2	yes	—
109	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	29	1	no	—
112	C₈	—	29	1	no	—
113	C₈	—	29	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	58	2	no	—
116	C₂²	—	58	4	no	—
117	C₂²	#11745219	1	2	yes	—
118	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
119	C₄	—	58	2	no	—
120	C₄	#11745219	1	2	yes	—
121	C₄	C₂×#90796	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊#1181	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	116	2	no	—
125	C₂	C₂×#11745219	1	1	yes	characteristic
126	C₂	#14272222	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745214

C₂

yes

maximal, characteristic, complemented

C₂²×#90770

C₂

yes

maximal, characteristic, complemented

#14272058

C₂

yes

maximal, complemented

C₂×#11745269

C₂

yes

maximal, characteristic

C₂×#90805

C₄

yes

characteristic

C₂×M₁₆×C₂₉

C₄

yes

characteristic

C₂²×#6597

C₂²

yes

—

—

C₄

yes

—

C₂×C₈×D₂₉

C₂²

yes

—

#11745214

—

C₂×#90770

—

C₂×#90770

C₂²

yes

—

C₂×#90770

C₂²

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₂₉

C₈

yes

—

#90805

—

#90805

—

C₂×D₁₁₆

C₈

yes

characteristic

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×Dic₅₈

C₈

yes

characteristic

M₁₆×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂×#6597

C₂³

yes

characteristic

#90772

—

C₈×D₂₉

—

C₈×D₂₉

—

#90770

—

#90770

—

C₂³×C₂₉

C₂×C₈

yes

characteristic

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

C₂²⋊D₂₉

—

C₂×Dic₂₉

C₂×C₈

yes

—

D₁₁₆

—

C₄×D₂₉

—

C₄×D₂₉

—

Dic₅₈

—

C₈×C₂₉

—

#6597

C₂²⋊C₄

yes

—

#6597

C₂×D₄

yes

characteristic

#6597

C₂×D₄

yes

characteristic

#2113

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂²⋊C₈

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

C₂²⋊C₈

yes

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₂×M₁₆

yes

characteristic

Dic₂₉

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₂₉

#504

yes

—

D₂₉

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

#1181

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂₉

#2113

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1181

yes

—

C₁₆

—

C₁₆

—

C₂³

—

C₂³

D₂₉⋊C₈

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

D₂₉⋊C₈

yes

characteristic

107

C₂×C₄

#90796

yes

—

108

C₂×C₄

C₂²⋊#1181

yes

—

109

C₂×C₄

C₂²×#1181

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

#11745219

yes

—

118

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

119

C₄

—

120

C₄

#11745219

yes

—

121

C₄

C₂×#90796

yes

characteristic

122

C₄

C₂×C₂²⋊#1181

yes

characteristic

123

C₂

—

124

C₂

—

116

—

125

C₂

C₂×#11745219

yes

characteristic

126

C₂

#14272222

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×M₁₆×C₂₉	C₄
prime radical	C₂×#90805	C₄
cosocle	C₂×#6597	C₂³
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#2113
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator, socle

C₂²×C₂₉

C₂²×C₈

Fitting

C₂×M₁₆×C₂₉

C₄

C₄

C₂³

C₂×M₁₆

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#11745214	C₂	semidirect
2. C₂²×#90770	C₂	semidirect
3. #14272058	C₂	semidirect
79. C₂₉	#2113	semidirect

H ≅ G/N

type

1. C₂×#11745214

C₂

semidirect

2. C₂²×#90770

C₂

semidirect

3. #14272058

C₂

semidirect

79. C₂₉

#2113

semidirect

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

subgroup	index
C₂×#11745214	2
C₂²×#90770	2
#14272058	2
C₂×#11745269	2
#2113	29

subgroup

index

C₂²×#90770

Subgroups — #16835724

Conjugacy classes of subgroups

Complements

Maximal subgroups