Group #16835730 — subgroups

Subgroups — #16835730

Order 3712.

220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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	2	yes	maximal, complemented
2	#14272060	C₂	1	4	yes	maximal, complemented
3	C₂×#11745269	C₂	1	1	yes	maximal, characteristic
4	C₂×#90805	C₄	1	1	yes	characteristic
5	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₂²×#6597	C₂²	1	1	yes	characteristic
7	#11745269	—	2	2	no	—
8	#11745269	—	2	2	no	—
9	C₂×#90772	C₂²	1	2	yes	—
10	C₂×C₈×D₂₉	C₄	1	2	yes	—
11	#11745214	—	2	2	no	—
12	#11745214	C₂²	1	4	yes	—
13	C₂×#90770	—	2	2	no	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₂²⋊D₂₉	C₈	1	2	yes	—
16	#90805	—	2	2	no	—
17	#90805	—	2	2	no	—
18	C₂×D₁₁₆	C₈	1	1	yes	characteristic
19	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
20	C₂×Dic₅₈	C₈	1	1	yes	characteristic
21	M₁₆×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
23	C₂×#6597	C₂×C₄	1	1	yes	characteristic
24	C₂×#6597	D₄	1	2	yes	—
25	C₂×#6597	D₄	1	2	yes	—
26	C₂×#6597	C₂³	1	1	yes	characteristic
27	#90772	—	2	4	no	—
28	C₈×D₂₉	—	2	2	no	—
29	C₈×D₂₉	—	2	2	no	—
30	#90770	—	2	4	no	—
31	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
32	C₂²×D₂₉	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²⋊D₂₉	—	2	4	no	—
38	C₂×Dic₂₉	C₂×C₈	1	2	yes	—
39	D₁₁₆	—	2	2	no	—
40	C₄×D₂₉	—	2	2	no	—
41	C₄×D₂₉	—	2	2	no	—
42	Dic₅₈	—	2	2	no	—
43	C₈×C₂₉	—	2	2	no	—
44	#6597	C₂²⋊C₄	1	1	yes	characteristic
45	#6597	C₂²⋊C₄	1	1	yes	characteristic
46	#6597	C₂×D₄	1	2	yes	—
47	#2115	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	—	4	1	no	—
49	C₂²×C₂₉	C₂²⋊C₈	1	2	yes	—
50	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
51	C₂×D₂₉	—	2	2	no	—
52	C₂×D₂₉	—	4	2	no	—
53	C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
54	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
56	Dic₂₉	—	2	2	no	—
57	C₂×#131	—	29	1	no	—
58	C₂×M₃₂	—	29	2	no	—
59	#349	—	29	4	no	—
60	C₂×C₂₉	—	2	1	no	—
61	C₂×C₂₉	—	2	2	no	—
62	C₂×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
63	D₂₉	—	4	2	no	—
64	C₂×#41	—	29	1	no	—
65	#131	—	58	2	no	—
66	#131	—	58	2	no	—
67	C₂×M₁₆	—	29	2	no	—
68	C₂×M₁₆	#1181	1	1	yes	characteristic
69	C₂²×C₈	—	29	1	no	—
70	C₂²×C₈	—	29	2	no	—
71	M₃₂	—	29	4	no	—
72	M₃₂	—	58	2	no	—
73	C₂×C₁₆	—	58	2	no	—
74	C₂₉	#2115	1	1	yes	characteristic, complemented, Sylow
75	#41	—	58	2	no	—
76	#41	—	58	2	no	—
77	C₂×Q₈	—	29	1	no	—
78	C₂×D₄	—	29	2	no	—
79	C₂×D₄	—	29	1	no	—
80	C₂²×C₄	—	29	2	no	—
81	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
82	M₁₆	—	2	2	no	—
83	M₁₆	—	58	4	no	—
84	C₂×C₈	—	29	2	no	—
85	C₂×C₈	—	29	2	no	—
86	C₂×C₈	—	29	1	no	—
87	C₂×C₈	—	29	1	no	—
88	C₂×C₈	—	58	2	no	—
89	C₂×C₈	—	58	2	no	—
90	C₂×C₈	C₂×#1181	1	2	yes	—
91	C₁₆	—	58	4	no	—
92	C₂³	—	29	2	no	—
93	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
94	Q₈	—	58	2	no	—
95	D₄	—	58	4	no	—
96	D₄	—	58	2	no	—
97	C₂×C₄	—	29	2	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	—	58	2	no	—
100	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
101	C₂×C₄	#90796	1	2	yes	—
102	C₂×C₄	C₂²⋊#1181	1	2	yes	—
103	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
104	C₈	—	2	2	no	—
105	C₈	—	29	2	no	—
106	C₈	—	29	1	no	—
107	C₈	—	29	1	no	—
108	C₂²	—	4	1	no	—
109	C₂²	—	58	2	no	—
110	C₂²	—	116	2	no	—
111	C₂²	#11745219	1	2	yes	—
112	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
113	C₄	—	58	2	no	—
114	C₄	#11745219	1	2	yes	—
115	C₄	C₂×#90796	1	1	yes	characteristic
116	C₄	C₂×C₂²⋊#1181	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	2	no	—
119	C₂	—	116	2	no	—
120	C₂	C₂×#11745219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745214

C₂

yes

maximal, complemented

#14272060

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

—

—

C₂²

yes

—

C₂×C₈×D₂₉

C₄

yes

—

#11745214

—

#11745214

C₂²

yes

—

C₂×#90770

—

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

—

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

characteristic

#6597

C₂²⋊C₄

yes

characteristic

#6597

C₂×D₄

yes

—

#2115

—

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

—

#349

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₂²⋊C₈

yes

characteristic

D₂₉

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

#1181

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂₉

#2115

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

—

C₂³

—

C₂³

D₂₉⋊C₈

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

D₂₉⋊C₈

yes

characteristic

101

C₂×C₄

#90796

yes

—

102

C₂×C₄

C₂²⋊#1181

yes

—

103

C₂×C₄

C₂²×#1181

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

116

—

111

C₂²

#11745219

yes

—

112

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

113

C₄

—

114

C₄

#11745219

yes

—

115

C₄

C₂×#90796

yes

characteristic

116

C₄

C₂×C₂²⋊#1181

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

116

—

120

C₂

C₂×#11745219

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊#1181
commutator	C₂²×C₂₉	C₂²×C₈
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂×M₁₆×C₂₉	C₄
socle	C₂×C₂₉	C₂×C₂²⋊C₈
prime radical	C₂×#90805	C₄
cosocle	C₂×#6597	C₂³
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#2115
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

C₂×C₂²⋊#1181

commutator

C₂²×C₂₉

C₂²×C₈

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂×M₁₆×C₂₉

C₄

socle

C₂×C₂₉

C₂×C₂²⋊C₈

C₄

C₂³

C₂×M₁₆

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
1. C₂×#11745214	C₂	semidirect
2. #14272060	C₂	semidirect
74. C₂₉	#2115	semidirect

H ≅ G/N

type

1. C₂×#11745214

C₂

semidirect

2. #14272060

C₂

semidirect

74. C₂₉

#2115

semidirect

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

subgroup	index
C₂×#11745214	2
#14272060	2
C₂×#11745269	2
#2115	29

subgroup

index

Subgroups — #16835730

Conjugacy classes of subgroups

Complements

Maximal subgroups