Group #15750484 — subgroups

Subgroups — #15750484

Order 3328.

140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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	#13116927	C₂	1	1	yes	maximal, characteristic
2	#13112930	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₂²⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	#11718777	—	2	1	no	—
6	C₂×#88059	—	2	1	no	—
7	C₂×Dic₁₀₄	C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₃₂	—	2	1	no	—
9	#11718096	C₄	1	1	yes	characteristic
10	#11718095	—	2	1	no	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	#88178	—	4	1	no	—
13	C₂×#6099	—	4	1	no	—
14	C₂×Dic₅₂	—	2	1	no	—
15	C₂×C₁₃×C₁₆	—	4	1	no	—
16	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	#88059	—	2	2	no	—
19	#88059	—	4	1	no	—
20	#88058	—	2	1	no	—
21	#88056	—	4	1	no	—
22	Dic₁₀₄	—	4	1	no	—
23	C₁₃×C₃₂	—	4	1	no	—
24	#7421	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
26	C₂×Dic₂₆	—	4	1	no	—
27	C₂×C₈×C₁₃	—	2	1	no	—
28	C₂×C₈×C₁₃	—	2	1	no	—
29	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
31	C₂²⋊Dic₁₃	—	8	1	no	—
32	C₄⋊Dic₁₃	—	4	1	no	—
33	#6101	—	8	1	no	—
34	#6099	—	4	2	no	—
35	#6099	—	8	1	no	—
36	C₂×#1055	—	8	1	no	—
37	Dic₅₂	—	4	1	no	—
38	Dic₅₂	—	4	1	no	—
39	C₁₃×C₁₆	—	2	1	no	—
40	C₁₃×C₁₆	—	2	1	no	—
41	#2216	—	13	1	no	—
42	C₂²⋊C₃₂	D₁₃	1	1	yes	characteristic
43	#1381	—	13	1	no	—
44	C₂³×C₁₃	SD₃₂	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	2	1	no	—
46	C₂×C₄×C₁₃	—	2	1	no	—
47	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
48	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
49	C₂×Dic₁₃	—	8	1	no	—
50	C₂×Dic₁₃	—	8	1	no	—
51	Dic₂₆	—	8	1	no	—
52	Dic₂₆	—	8	1	no	—
53	C₈×C₁₃	—	2	1	no	—
54	C₈×C₁₃	#99	1	1	yes	characteristic
55	C₈×C₁₃	#104	1	1	yes	characteristic
56	#1055	—	8	2	no	—
57	C₂×Q₃₂	—	13	1	no	—
58	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
59	#467	—	26	1	no	—
60	C₂×#108	—	26	1	no	—
61	C₂×C₃₂	—	2	1	no	—
62	#366	—	13	1	no	—
63	#358	—	26	1	no	—
64	C₂²×C₁₃	—	2	1	no	—
65	C₂²×C₁₃	—	2	1	no	—
66	C₂²×C₁₃	—	2	1	no	—
67	C₂²×C₁₃	#357	1	1	yes	characteristic
68	C₄×C₁₃	—	2	1	no	—
69	C₄×C₁₃	#327	1	1	yes	characteristic
70	C₄×C₁₃	#360	1	1	yes	characteristic
71	Dic₁₃	—	16	1	no	—
72	Dic₁₃	—	16	1	no	—
73	C₂×Q₁₆	—	26	1	no	—
74	C₂×M₁₆	—	52	1	no	—
75	C₂²×C₈	D₅₂	1	1	yes	characteristic
76	C₂²⋊Q₈	—	52	1	no	—
77	Q₃₂	—	52	1	no	—
78	C₂×C₁₆	—	4	1	no	—
79	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
80	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
81	#108	—	26	2	no	—
82	#108	—	52	1	no	—
83	#107	—	26	1	no	—
84	#103	—	52	1	no	—
85	C₃₂	—	4	1	no	—
86	C₂×C₁₃	—	4	1	no	—
87	C₂×C₁₃	#1347	1	1	yes	characteristic
88	C₂×C₁₃	#1417	1	1	yes	characteristic
89	C₂×C₁₃	#1420	1	1	yes	characteristic
90	C₂×Q₈	—	52	1	no	—
91	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
92	Q₁₆	—	52	1	no	—
93	Q₁₆	—	52	1	no	—
94	M₁₆	—	52	2	no	—
95	M₁₆	—	104	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	104	1	no	—
99	C₂×C₈	#6095	1	1	yes	characteristic
100	C₂×C₈	#6103	1	1	yes	characteristic
101	C₄⋊C₄	—	52	1	no	—
102	C₄⋊C₄	—	104	1	no	—
103	C₂²⋊C₄	—	104	1	no	—
104	C₁₆	—	2	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₃	#7421	1	1	yes	characteristic, complemented, Sylow
107	C₂³	#88040	1	1	yes	characteristic
108	Q₈	—	104	1	no	—
109	Q₈	—	104	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	104	1	no	—
113	C₂×C₄	—	104	1	no	—
114	C₂×C₄	D₂₀₈	1	1	yes	characteristic
115	C₂×C₄	#88061	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	104	2	no	—
118	C₈	#88046	1	1	yes	characteristic
119	C₈	#88065	1	1	yes	characteristic
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	#11718101	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	208	1	no	—
126	C₄	—	208	1	no	—
127	C₄	#11718062	1	1	yes	characteristic
128	C₄	#11718110	1	1	yes	characteristic
129	C₂	—	4	1	no	—
130	C₂	#13112846	1	1	yes	characteristic
131	C₂	#13113021	1	1	yes	characteristic
132	C₂	#13113030	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13116927

C₂

yes

maximal, characteristic

#13112930

C₂

yes

maximal, characteristic

C₁₃×C₂²⋊C₃₂

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

#11718777

—

C₂×#88059

—

C₂×Dic₁₀₄

C₄

yes

characteristic

C₂×C₁₃×C₃₂

—

#11718096

C₄

yes

characteristic

#11718095

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

#88178

—

C₂×#6099

—

C₂×Dic₅₂

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

D₄

yes

—

—

—

—

Dic₁₀₄

—

C₁₃×C₃₂

—

#7421

—

maximal, Sylow

C₂²×C₄×C₁₃

D₈

yes

characteristic

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

SD₁₆

yes

characteristic

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

—

—

—

—

Dic₅₂

—

Dic₅₂

—

C₁₃×C₁₆

—

C₁₃×C₁₆

—

#2216

—

C₂²⋊C₃₂

D₁₃

yes

characteristic

#1381

—

C₂³×C₁₃

SD₃₂

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#102

yes

characteristic

C₂×C₄×C₁₃

D₁₆

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

—

C₂×Q₃₂

—

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

#467

—

C₂×#108

—

C₂×C₃₂

—

#366

—

#358

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#357

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

D₅₂

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₃

yes

—

—

—

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂²×C₄

D₁₀₄

yes

characteristic

Q₁₆

—

Q₁₆

—

M₁₆

—

M₁₆

—

104

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

104

—

C₂×C₈

#6095

yes

characteristic

100

C₂×C₈

#6103

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

104

—

103

C₂²⋊C₄

—

104

—

104

C₁₆

—

105

C₁₆

—

106

C₁₃

#7421

yes

characteristic, complemented, Sylow

107

C₂³

#88040

yes

characteristic

108

Q₈

—

104

—

109

Q₈

—

104

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

104

—

113

C₂×C₄

—

104

—

114

C₂×C₄

D₂₀₈

yes

characteristic

115

C₂×C₄

#88061

yes

characteristic

116

C₈

—

117

C₈

—

104

—

118

C₈

#88046

yes

characteristic

119

C₈

#88065

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#11718101

yes

characteristic

124

C₄

—

125

C₄

—

208

—

126

C₄

—

208

—

127

C₄

#11718062

yes

characteristic

128

C₄

#11718110

yes

characteristic

129

C₂

—

130

C₂

#13112846

yes

characteristic

131

C₂

#13113021

yes

characteristic

132

C₂

#13113030

yes

characteristic

	subgroup	G/H
center	C₂²	#11718101
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₁₃
Fitting	C₁₃×C₂²⋊C₃₂	C₂
socle	C₂²×C₁₃	#357
prime radical	C₂³×C₁₃	SD₃₂
cosocle	C₂²×C₁₃×C₁₆	C₂²
hypercenter	C₂²⋊C₃₂	D₁₃
hypocenter	C₁₃	#7421
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

subgroup

G/H

center

C₂²

#11718101

commutator

C₂×C₁₃×C₁₆

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₁₃

Fitting

C₁₃×C₂²⋊C₃₂

C₂

socle

C₂²×C₁₃

#357

prime radical

C₂³×C₁₃

SD₃₂

cosocle

C₂²×C₁₃×C₁₆

C₂²

hypercenter

C₂²⋊C₃₂

D₁₃

hypocenter

C₁₃

#7421

LCS

G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²⋊C₃₂

N	H ≅ G/N	type
106. C₁₃	#7421	semidirect

H ≅ G/N

type

106. C₁₃

#7421

semidirect

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

subgroup	index
#13116927	2
#13112930	2
C₁₃×C₂²⋊C₃₂	2
#7421	13

subgroup

index

#13116927

#13112930

C₁₃×C₂²⋊C₃₂

#7421

Subgroups — #15750484

Conjugacy classes of subgroups

Complements

Maximal subgroups