Group #15783098 — subgroups

Subgroups — #15783098

Order 3328.

238 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11718091	C₂	1	1	yes	maximal, characteristic
2	#13116432	C₂	1	1	yes	maximal, characteristic
3	#13112969	C₂	1	2	yes	maximal, complemented
4	C₃₂×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	#11718762	C₄	1	1	yes	characteristic
8	C₂×#88052	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₃₂	C₄	1	4	yes	complemented
10	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	#11718094	C₄	1	2	yes	—
13	C₁₆×Dic₁₃	C₂²	1	2	yes	—
14	#11718091	C₄	1	4	yes	complemented
15	C₂×#88034	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	#88180	C₈	1	1	yes	characteristic
18	C₂×#6099	C₈	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
23	#88055	C₈	1	2	yes	—
24	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
25	#88052	C₈	1	4	yes	—
26	C₂×#6090	C₂×C₄	1	2	yes	—
27	C₁₃×C₃₂	C₂×C₄	1	2	yes	—
28	C₁₃×C₃₂	C₂×C₄	1	2	yes	—
29	#88034	C₂×C₄	1	4	yes	—
30	#13549	—	13	1	no	maximal, Sylow
31	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₄²	1	2	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²⋊Dic₁₃	C₁₆	1	2	yes	—
37	C₄⋊Dic₁₃	C₁₆	1	2	yes	—
38	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
39	#6099	C₁₆	1	4	yes	—
40	C₂×#1055	C₂×C₈	1	2	yes	—
41	C₁₃×C₁₆	C₄²	1	2	yes	—
42	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
43	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
44	#6090	C₂×C₈	1	4	yes	—
45	C₂×M₆₄	—	13	1	no	—
46	C₂²×C₃₂	D₁₃	1	1	yes	characteristic
47	#2108	—	13	1	no	—
48	#1397	—	13	2	no	—
49	C₄×C₃₂	—	13	2	no	—
50	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
55	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	—
56	C₈×C₁₃	C₄×C₈	1	2	yes	—
57	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
58	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	#1055	C₂×C₁₆	1	4	yes	—
60	C₂×M₃₂	—	13	1	no	—
61	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
62	#405	—	13	1	no	—
63	M₆₄	—	13	4	no	—
64	C₂×C₃₂	—	13	2	no	—
65	C₂×C₃₂	Dic₁₃	1	4	yes	complemented
66	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
67	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
68	#346	—	13	2	no	—
69	C₄×C₁₆	—	13	2	no	—
70	C₂²×C₁₃	—	2	2	no	—
71	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
72	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
73	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
74	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
75	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
76	Dic₁₃	—	2	4	no	—
77	C₂×M₁₆	—	13	1	no	—
78	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
79	#117	—	13	1	no	—
80	M₃₂	—	13	4	no	—
81	C₂×C₁₆	—	13	2	no	—
82	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
83	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
84	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
85	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
86	#97	—	13	2	no	—
87	C₄×C₈	—	13	2	no	—
88	C₃₂	—	13	4	no	—
89	C₃₂	C₂×Dic₁₃	1	2	yes	—
90	C₃₂	C₂×Dic₁₃	1	2	yes	—
91	C₂×C₁₃	—	2	2	no	—
92	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
93	C₂×C₁₃	#2258	1	2	yes	—
94	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
95	M₁₆	—	13	4	no	—
96	C₂×C₈	—	13	2	no	—
97	C₂×C₈	C₈×D₁₃	1	2	yes	—
98	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
99	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
100	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
101	C₄⋊C₄	—	13	2	no	—
102	C₂²⋊C₄	—	13	2	no	—
103	C₄²	—	13	2	no	—
104	C₁₆	—	13	4	no	—
105	C₁₆	C₄×Dic₁₃	1	2	yes	—
106	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
107	C₁₆	C₂²×Dic₁₃	1	1	yes	characteristic
108	C₁₃	#13549	1	1	yes	characteristic, complemented, Sylow
109	C₂³	C₁₆×D₁₃	1	1	yes	characteristic
110	C₂×C₄	—	13	4	no	—
111	C₂×C₄	C₁₆×D₁₃	1	2	yes	—
112	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
113	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
114	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
115	C₈	—	13	4	no	—
116	C₈	C₈×Dic₁₃	1	2	yes	—
117	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
118	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
119	C₂²	—	2	2	no	—
120	C₂²	C₁₆×Dic₁₃	1	2	yes	—
121	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
122	C₄	—	26	4	no	—
123	C₄	C₁₆×Dic₁₃	1	2	yes	—
124	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
125	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
126	C₂	—	2	2	no	—
127	C₂	C₂×C₁₆×Dic₁₃	1	1	yes	characteristic
128	C₂	#13117129	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718091

C₂

yes

maximal, characteristic

#13116432

C₂

yes

maximal, characteristic

#13112969

C₂

yes

maximal, complemented

C₃₂×Dic₁₃

C₂

yes

maximal, complemented

C₂²×C₁₃×C₃₂

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

#11718762

C₄

yes

characteristic

C₂×#88052

C₄

yes

characteristic

C₂×C₁₃×C₃₂

C₄

yes

complemented

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

#11718094

C₄

yes

—

C₁₆×Dic₁₃

C₂²

yes

—

#11718091

C₄

yes

complemented

C₂×#88034

C₂²

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

#88180

C₈

yes

characteristic

C₂×#6099

C₈

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

#88055

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

#88052

C₈

yes

—

C₂×#6090

C₂×C₄

yes

—

C₁₃×C₃₂

C₂×C₄

yes

—

C₁₃×C₃₂

C₂×C₄

yes

—

#88034

C₂×C₄

yes

—

#13549

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂²⋊Dic₁₃

C₁₆

yes

—

C₄⋊Dic₁₃

C₁₆

yes

—

C₄×Dic₁₃

C₂×C₈

yes

—

#6099

C₁₆

yes

—

C₂×#1055

C₂×C₈

yes

—

C₁₃×C₁₆

C₄²

yes

—

C₁₃×C₁₆

C₂²×C₄

yes

characteristic

C₁₃×C₁₆

C₂²×C₄

yes

characteristic

#6090

C₂×C₈

yes

—

C₂×M₆₄

—

C₂²×C₃₂

D₁₃

yes

characteristic

#2108

—

#1397

—

C₄×C₃₂

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₄×C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₈×C₁₃

C₄×C₈

yes

—

C₈×C₁₃

C₂×C₄²

yes

characteristic

C₈×C₁₃

C₂²×C₈

yes

characteristic

#1055

C₂×C₁₆

yes

—

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

Dic₁₃

yes

complemented

C₂×C₃₂

C₂×D₁₃

yes

characteristic

C₂×C₃₂

C₂×D₁₃

yes

characteristic

#346

—

C₄×C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₄×C₁₆

yes

—

C₂²×C₁₃

C₂²×C₁₆

yes

characteristic

C₄×C₁₃

C₄×C₁₆

yes

—

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

C₂²×C₁₆

yes

characteristic

Dic₁₃

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₄×D₁₃

yes

—

C₂×C₁₆

C₂×Dic₁₃

yes

—

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

C₂×Dic₁₃

yes

—

C₃₂

C₂×Dic₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄×C₁₆

yes

characteristic

C₂×C₁₃

#2258

yes

—

C₂²×C₄

C₈×D₁₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₈×D₁₃

yes

—

C₂×C₈

C₈×D₁₃

yes

characteristic

C₂×C₈

C₄×Dic₁₃

yes

—

100

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

—

104

C₁₆

—

105

C₁₆

C₄×Dic₁₃

yes

—

106

C₁₆

C₂×C₄×D₁₃

yes

characteristic

107

C₁₆

C₂²×Dic₁₃

yes

characteristic

108

C₁₃

#13549

yes

characteristic, complemented, Sylow

109

C₂³

C₁₆×D₁₃

yes

characteristic

110

C₂×C₄

—

111

C₂×C₄

C₁₆×D₁₃

yes

—

112

C₂×C₄

C₁₆×D₁₃

yes

characteristic

113

C₂×C₄

C₈×Dic₁₃

yes

—

114

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

115

C₈

—

116

C₈

C₈×Dic₁₃

yes

—

117

C₈

C₂×C₈×D₁₃

yes

characteristic

118

C₈

C₂×C₄×Dic₁₃

yes

characteristic

119

C₂²

—

120

C₂²

C₁₆×Dic₁₃

yes

—

121

C₂²

C₂×C₁₆×D₁₃

yes

characteristic

122

C₄

—

123

C₄

C₁₆×Dic₁₃

yes

—

124

C₄

C₂×C₁₆×D₁₃

yes

characteristic

125

C₄

C₂×C₈×Dic₁₃

yes

characteristic

126

C₂

—

127

C₂

C₂×C₁₆×Dic₁₃

yes

characteristic

128

C₂

#13117129

yes

—

	subgroup	G/H
center	C₂×C₃₂	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₂²×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂²×C₃₂	D₁₃
hypocenter	C₁₃	#13549
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

subgroup

G/H

center

C₂×C₃₂

C₂×D₁₃

commutator

C₂×C₁₃

C₂×C₄×C₁₆

Frattini

C₂×C₁₆

C₂²×D₁₃

Fitting

C₂²×C₁₃×C₃₂

C₂

socle

C₂²×C₁₃

C₂²×C₁₆

prime radical

C₂³×C₁₃

C₂×C₁₆

cosocle

C₂×C₁₃×C₁₆

C₂³

hypercenter

C₂²×C₃₂

D₁₃

C₁₃

G ▷ C₂×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

N	H ≅ G/N	type
3. #13112969	C₂	semidirect
4. C₃₂×Dic₁₃	C₂	semidirect
9. C₂×C₁₃×C₃₂	C₄	semidirect
14. #11718091	C₄	semidirect
65. C₂×C₃₂	Dic₁₃	semidirect
108. C₁₃	#13549	semidirect

H ≅ G/N

type

3. #13112969

C₂

semidirect

4. C₃₂×Dic₁₃

C₂

semidirect

9. C₂×C₁₃×C₃₂

C₄

semidirect

14. #11718091

C₄

semidirect

65. C₂×C₃₂

Dic₁₃

semidirect

108. C₁₃

#13549

semidirect

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

subgroup	index
C₂×#11718091	2
#13116432	2
#13112969	2
C₃₂×Dic₁₃	2
C₂²×C₁₃×C₃₂	2
#13549	13

subgroup

index

C₂×#11718091

#13116432

#13112969

C₃₂×Dic₁₃

C₂²×C₁₃×C₃₂

#13549

Subgroups — #15783098

Conjugacy classes of subgroups

Complements

Maximal subgroups