Group #15783412 — subgroups

Subgroups — #15783412

Order 3328.

198 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 143 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	2	yes	maximal
2	#13113034	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₃×#405	C₄	1	1	yes	characteristic
7	C₁₃×#346	C₄	1	2	yes	—
8	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
9	#11718091	—	2	2	no	—
10	#11718091	C₂²	1	4	yes	—
11	C₂×#88034	—	2	2	no	—
12	C₂×C₁₃×M₁₆	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₁₃×#117	C₈	1	1	yes	characteristic
15	C₁₃×M₃₂	—	2	2	no	—
16	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
21	C₁₃×#97	C₈	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	#88034	—	2	4	no	—
24	#13630	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₁₃×M₁₆	C₁₆	1	4	yes	—
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
31	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₁₃×C₂²⋊C₄	—	2	1	no	—
34	C₄²×C₁₃	C₂×C₈	1	2	yes	—
35	C₁₃×C₁₆	—	2	2	no	—
36	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
37	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
38	C₁₃×C₁₆	C₂×Q₈	1	1	yes	characteristic
39	C₂×M₆₄	—	13	2	no	—
40	#2108	D₁₃	1	1	yes	characteristic
41	#1422	—	13	4	no	—
42	C₂³×C₁₃	M₃₂	1	1	yes	characteristic
43	C₂×C₄×C₁₃	—	2	2	no	—
44	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
45	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
46	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
48	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
49	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
50	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
52	C₂×M₃₂	Dic₁₃	1	1	yes	characteristic
53	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
54	#405	Dic₁₃	1	1	yes	characteristic
55	M₆₄	—	13	4	no	—
56	M₆₄	—	26	2	no	—
57	C₂×C₃₂	—	26	2	no	—
58	#346	Dic₁₃	1	2	yes	—
59	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
60	C₂²×C₁₃	—	4	1	no	—
61	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
62	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
63	C₄×C₁₃	—	4	2	no	—
64	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
65	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
67	C₂×M₁₆	#1055	1	1	yes	characteristic
68	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
69	#117	#1055	1	1	yes	characteristic
70	M₃₂	—	2	2	no	—
71	C₂×C₁₆	Dic₂₆	1	2	yes	—
72	C₂×C₁₆	D₅₂	1	2	yes	—
73	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
74	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
75	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
76	#97	#1055	1	2	yes	—
77	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
78	C₃₂	—	26	4	no	—
79	C₂×C₁₃	—	2	1	no	—
80	C₂×C₁₃	—	2	2	no	—
81	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
82	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
83	M₁₆	#6090	1	4	yes	—
84	C₂×C₈	C₂×#1055	1	1	yes	characteristic
85	C₂×C₈	C₂×#1055	1	2	yes	—
86	C₂×C₈	#6099	1	2	yes	—
87	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
88	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
89	C₄⋊C₄	—	2	1	no	—
90	C₂²⋊C₄	—	2	1	no	—
91	C₄²	C₂×#1055	1	2	yes	—
92	C₁₆	—	2	2	no	—
93	C₁₆	C₄⋊Dic₁₃	1	2	yes	—
94	C₁₆	C₂×Dic₂₆	1	1	yes	characteristic
95	C₁₆	C₂×D₅₂	1	1	yes	characteristic
96	C₁₃	#13630	1	1	yes	characteristic, complemented, Sylow
97	C₂³	#88052	1	1	yes	characteristic
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	C₄⋊#1055	1	2	yes	—
100	C₂×C₄	C₂×#6090	1	2	yes	—
101	C₂×C₄	#88052	1	1	yes	characteristic
102	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
103	C₈	C₄⋊#1055	1	2	yes	—
104	C₈	C₂×#6090	1	4	yes	—
105	C₈	C₂×#6099	1	1	yes	characteristic
106	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
107	C₂²	—	4	1	no	—
108	C₂²	C₄⋊#6090	1	2	yes	—
109	C₂²	C₂×#88052	1	1	yes	characteristic
110	C₄	—	4	2	no	—
111	C₄	C₄⋊#6090	1	2	yes	—
112	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
113	C₄	C₂²×#6090	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	2	2	no	—
116	C₂	C₂×C₄⋊#6090	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718091

C₂

yes

maximal

#13113034

C₂

yes

maximal, complemented

C₁₃×#2108

C₂

yes

maximal, characteristic

C₂×C₁₃×M₃₂

C₄

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₁₃×#405

C₄

yes

characteristic

C₁₃×#346

C₄

yes

—

C₄×C₁₃×C₁₆

C₂²

yes

—

#11718091

—

#11718091

C₂²

yes

—

C₂×#88034

—

C₂×C₁₃×M₁₆

C₈

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₁₃×#117

C₈

yes

characteristic

C₁₃×M₃₂

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

D₄

yes

—

C₂×C₁₃×C₁₆

Q₈

yes

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₁₃×#97

C₈

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

#88034

—

#13630

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₁₃×M₁₆

C₁₆

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

C₂×C₈

yes

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₄⋊C₄

yes

—

C₁₃×C₁₆

C₂×D₄

yes

characteristic

C₁₃×C₁₆

C₂×Q₈

yes

characteristic

C₂×M₆₄

—

#2108

D₁₃

yes

characteristic

#1422

—

C₂³×C₁₃

M₃₂

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

M₃₂

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₈×C₁₃

C₄⋊C₈

yes

—

C₈×C₁₃

C₂×C₁₆

yes

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

C₂×M₃₂

Dic₁₃

yes

characteristic

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

#405

Dic₁₃

yes

characteristic

M₆₄

—

M₆₄

—

C₂×C₃₂

—

#346

Dic₁₃

yes

—

C₄×C₁₆

C₂×D₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

C₄⋊C₁₆

yes

—

C₂²×C₁₃

C₂×M₃₂

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₄⋊C₁₆

yes

—

C₄×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₃

C₂²×C₁₆

yes

characteristic

C₂×M₁₆

#1055

yes

characteristic

C₂²×C₈

C₂×Dic₁₃

yes

yes

M₃₂

—

C₂×C₁₆

Dic₂₆

yes

—

C₂×C₁₆

D₅₂

yes

—

C₂×C₁₆

C₂×Dic₁₃

yes

—

C₂×C₁₆

C₂×Dic₁₃

yes

characteristic

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

#97

#1055

yes

—

C₄×C₈

C₂×Dic₁₃

yes

—

C₃₂

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄⋊C₁₆

yes

C₂²×C₄

yes

M₁₆

yes

—

C₂×C₈

C₂×#1055

yes

characteristic

C₂×C₈

C₂×#1055

yes

—

C₂×C₈

#6099

yes

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₂×C₈

C₂²×Dic₁₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×#1055

yes

—

C₁₆

—

C₁₆

C₄⋊Dic₁₃

yes

—

C₁₆

C₂×Dic₂₆

yes

characteristic

C₁₆

C₂×D₅₂

yes

characteristic

C₁₃

#13630

yes

characteristic, complemented, Sylow

C₂³

#88052

yes

characteristic

C₂×C₄

—

C₂×C₄

C₄⋊#1055

yes

—

100

C₂×C₄

C₂×#6090

yes

—

101

C₂×C₄

#88052

yes

characteristic

102

C₂×C₄

C₂²×#1055

yes

characteristic

103

C₈

C₄⋊#1055

yes

—

104

C₈

C₂×#6090

yes

—

105

C₈

C₂×#6099

yes

characteristic

106

C₈

C₂×C₄⋊Dic₁₃

yes

characteristic

107

C₂²

—

108

C₂²

C₄⋊#6090

yes

—

109

C₂²

C₂×#88052

yes

characteristic

110

C₄

—

111

C₄

C₄⋊#6090

yes

—

112

C₄

C₂×C₄⋊#1055

yes

characteristic

113

C₄

C₂²×#6090

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

C₂×C₄⋊#6090

yes

characteristic

	subgroup	G/H
center	C₁₆	C₂×D₅₂
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₁₃×#2108	C₂
socle	C₂×C₁₃	C₂×C₄⋊C₁₆
prime radical	C₂³×C₁₃	M₃₂
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	#2108	D₁₃
hypocenter	C₁₃	#13630
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂²×C₁₆ ◁ #2108

subgroup

G/H

center

C₁₆

C₂×D₅₂

commutator

C₄×C₁₃

C₂²×C₁₆

Frattini

C₂×C₁₆

C₂²×D₁₃

Fitting

C₁₃×#2108

C₂

socle

C₂×C₁₃

C₂×C₄⋊C₁₆

prime radical

C₂³×C₁₃

M₃₂

cosocle

C₂×C₁₃×C₁₆

C₂³

D₁₃

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₁₆ ◁ C₂²×C₁₆ ◁ #2108

N	H ≅ G/N	type
2. #13113034	C₂	semidirect
96. C₁₃	#13630	semidirect

H ≅ G/N

type

2. #13113034

C₂

semidirect

96. C₁₃

#13630

semidirect

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

subgroup	index
C₂×#11718091	2
#13113034	2
C₁₃×#2108	2
#13630	13

subgroup

index

C₂×#11718091

#13113034

C₁₃×#2108

#13630

Subgroups — #15783412

Conjugacy classes of subgroups

Complements

Maximal subgroups