Group #15783883 — subgroups

Subgroups — #15783883

Order 3328.

160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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	#13116944	C₂	1	1	yes	maximal, characteristic
2	#13113043	C₂	1	2	yes	maximal, complemented
3	#13113028	C₂	1	2	yes	maximal, complemented
4	#13112976	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2161	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	—	2	1	no	—
8	#11718777	—	2	1	no	—
9	C₂×Dic₁₀₄	C₂²	1	1	yes	characteristic
10	C₁₃×#368	—	2	1	no	—
11	C₁₃×#368	C₂²	1	2	yes	—
12	#11718097	C₂²	1	1	yes	characteristic
13	#11718095	—	2	1	no	—
14	#11718091	C₂²	1	2	yes	—
15	C₂×C₁₃×M₁₆	—	4	1	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	#88178	—	4	1	no	—
18	C₂×Dic₅₂	—	2	1	no	—
19	C₁₃×M₃₂	—	2	2	no	—
20	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₁₃×#108	—	2	2	no	—
23	C₁₃×#108	—	4	1	no	—
24	#88058	—	2	1	no	—
25	#88056	—	4	1	no	—
26	Dic₁₀₄	—	2	2	no	—
27	#88034	—	2	2	no	—
28	#13718	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
30	C₂×Dic₂₆	—	4	1	no	—
31	C₁₃×M₁₆	—	4	2	no	—
32	C₁₃×M₁₆	—	8	1	no	—
33	C₂×C₈×C₁₃	—	2	1	no	—
34	C₂×C₈×C₁₃	—	2	1	no	—
35	C₂×C₈×C₁₃	—	8	1	no	—
36	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂²⋊Dic₁₃	—	8	1	no	—
39	C₄⋊Dic₁₃	—	4	1	no	—
40	#6101	—	8	1	no	—
41	Dic₅₂	—	4	1	no	—
42	Dic₅₂	—	4	1	no	—
43	C₁₃×C₁₆	—	2	1	no	—
44	C₁₃×C₁₆	#41	1	2	yes	—
45	#2219	—	13	1	no	—
46	#2161	D₁₃	1	1	yes	characteristic
47	#1426	—	13	2	no	—
48	#1420	—	13	2	no	—
49	#1400	—	13	1	no	—
50	C₂³×C₁₃	SD₃₂	1	1	yes	characteristic
51	C₂×C₄×C₁₃	—	2	1	no	—
52	C₂×C₄×C₁₃	—	2	1	no	—
53	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
55	C₂×Dic₁₃	—	8	1	no	—
56	C₂×Dic₁₃	—	8	1	no	—
57	Dic₂₆	—	8	1	no	—
58	Dic₂₆	—	8	1	no	—
59	C₈×C₁₃	—	2	1	no	—
60	C₈×C₁₃	—	8	2	no	—
61	C₈×C₁₃	#123	1	1	yes	characteristic
62	C₈×C₁₃	#137	1	1	yes	characteristic
63	C₂×Q₃₂	—	13	1	no	—
64	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
65	#467	—	26	1	no	—
66	C₂×#108	—	2	1	no	—
67	M₆₄	—	13	2	no	—
68	#368	—	2	1	no	—
69	#368	C₂×D₁₃	1	2	yes	—
70	#367	—	13	1	no	—
71	#358	—	26	1	no	—
72	C₂²×C₁₃	—	2	1	no	—
73	C₂²×C₁₃	—	4	1	no	—
74	C₂²×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
75	C₄×C₁₃	—	2	1	no	—
76	C₄×C₁₃	#480	1	1	yes	characteristic
77	C₄×C₁₃	#509	1	1	yes	characteristic
78	Dic₁₃	—	16	1	no	—
79	Dic₁₃	—	16	1	no	—
80	C₂×Q₁₆	—	26	1	no	—
81	C₂×M₁₆	—	4	1	no	—
82	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
83	C₂²⋊Q₈	—	52	1	no	—
84	Q₃₂	—	26	2	no	—
85	M₃₂	—	2	2	no	—
86	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
87	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
88	#108	—	2	2	no	—
89	#108	—	4	1	no	—
90	#107	—	26	1	no	—
91	#103	—	52	1	no	—
92	C₃₂	—	26	2	no	—
93	C₂×C₁₃	—	2	1	no	—
94	C₂×C₁₃	—	4	1	no	—
95	C₂×C₁₃	#2233	1	1	yes	characteristic
96	C₂×Q₈	—	52	1	no	—
97	C₂²×C₄	#6104	1	1	yes	characteristic
98	Q₁₆	—	52	1	no	—
99	Q₁₆	—	52	1	no	—
100	M₁₆	—	4	2	no	—
101	M₁₆	—	8	1	no	—
102	C₂×C₈	—	2	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	8	1	no	—
105	C₂×C₈	#6104	1	1	yes	characteristic
106	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
107	C₄⋊C₄	—	52	1	no	—
108	C₄⋊C₄	—	104	1	no	—
109	C₂²⋊C₄	—	104	1	no	—
110	C₁₆	—	2	1	no	—
111	C₁₆	#6127	1	2	yes	—
112	C₁₃	#13718	1	1	yes	characteristic, complemented, Sylow
113	C₂³	#88068	1	1	yes	characteristic
114	Q₈	—	104	1	no	—
115	Q₈	—	104	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	104	1	no	—
119	C₂×C₄	—	104	1	no	—
120	C₂×C₄	#88068	1	1	yes	characteristic
121	C₂×C₄	C₂×#6104	1	1	yes	characteristic
122	C₈	—	2	1	no	—
123	C₈	—	8	2	no	—
124	C₈	#88183	1	1	yes	characteristic
125	C₈	#88196	1	1	yes	characteristic
126	C₂²	—	2	1	no	—
127	C₂²	—	4	1	no	—
128	C₂²	C₂×#88068	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	208	1	no	—
131	C₄	—	208	1	no	—
132	C₄	#11718628	1	1	yes	characteristic
133	C₄	#11718808	1	1	yes	characteristic
134	C₂	—	2	1	no	—
135	C₂	—	4	1	no	—
136	C₂	#13117021	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13116944

C₂

yes

maximal, characteristic

#13113043

C₂

yes

maximal, complemented

#13113028

C₂

yes

maximal, complemented

#13112976

C₂

yes

maximal, characteristic

C₁₃×#2161

C₂

yes

maximal, characteristic

C₂×C₁₃×M₃₂

C₂²

yes

characteristic

C₂×C₁₃×#108

—

#11718777

—

C₂×Dic₁₀₄

C₂²

yes

characteristic

C₁₃×#368

—

C₁₃×#368

C₂²

yes

—

#11718097

C₂²

yes

characteristic

#11718095

—

#11718091

C₂²

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

#88178

—

C₂×Dic₅₂

—

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

D₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₁₃×#108

—

C₁₃×#108

—

#88058

—

#88056

—

Dic₁₀₄

—

#88034

—

#13718

—

maximal, Sylow

C₂²×C₄×C₁₃

D₈

yes

characteristic

C₂×Dic₂₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

Dic₅₂

—

Dic₅₂

—

C₁₃×C₁₆

—

C₁₃×C₁₆

#41

yes

—

#2219

—

#2161

D₁₃

yes

—

—

—

C₂³×C₁₃

SD₃₂

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

SD₃₂

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

yes

C₈×C₁₃

yes

C₂×Q₃₂

—

C₂×M₃₂

C₂×D₁₃

yes

characteristic

#467

—

C₂×#108

—

M₆₄

—

#368

—

#368

C₂×D₁₃

yes

—

#367

—

#358

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×SD₃₂

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂²⋊D₁₃

yes

characteristic

C₂×C₁₆

C₂²×D₁₃

yes

—

—

—

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#2233

yes

characteristic

C₂×Q₈

—

C₂²×C₄

#6104

yes

characteristic

Q₁₆

—

Q₁₆

—

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

#6104

yes

characteristic

106

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

107

C₄⋊C₄

—

108

C₄⋊C₄

—

104

—

109

C₂²⋊C₄

—

104

—

110

C₁₆

—

111

C₁₆

#6127

yes

—

112

C₁₃

#13718

yes

characteristic, complemented, Sylow

113

C₂³

#88068

yes

characteristic

114

Q₈

—

104

—

115

Q₈

—

104

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

104

—

119

C₂×C₄

—

104

—

120

C₂×C₄

#88068

yes

characteristic

121

C₂×C₄

C₂×#6104

yes

characteristic

122

C₈

—

123

C₈

—

124

C₈

#88183

yes

characteristic

125

C₈

#88196

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

C₂×#88068

yes

characteristic

129

C₄

—

130

C₄

—

208

—

131

C₄

—

208

—

132

C₄

#11718628

yes

characteristic

133

C₄

#11718808

yes

characteristic

134

C₂

—

135

C₂

—

136

C₂

#13117021

yes

characteristic

	subgroup	G/H
center	C₂	#13117021
commutator, cosocle	C₂×C₁₃×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₁₃×#2161	C₂
socle	C₂×C₁₃	#2233
prime radical	C₂³×C₁₃	SD₃₂
hypercenter	#2161	D₁₃
hypocenter	C₁₃	#13718
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2161

subgroup

G/H

center

C₂

#13117021

commutator, cosocle

C₂×C₁₃×C₁₆

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₃

Fitting

C₁₃×#2161

C₂

socle

C₂×C₁₃

#2233

prime radical

C₂³×C₁₃

SD₃₂

D₁₃

C₁₃

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2161

N	H ≅ G/N	type
2. #13113043	C₂	semidirect
3. #13113028	C₂	semidirect
112. C₁₃	#13718	semidirect

H ≅ G/N

type

2. #13113043

C₂

semidirect

3. #13113028

C₂

semidirect

112. C₁₃

#13718

semidirect

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

subgroup	index
#13116944	2
#13113043	2
#13113028	2
#13112976	2
C₁₃×#2161	2
#13718	13

subgroup

index

C₁₃×#2161

Subgroups — #15783883

Conjugacy classes of subgroups

Complements

Maximal subgroups