Group #15783406 — subgroups

Subgroups — #15783406

Order 3328.

206 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 123 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	C₂²×#88034	C₂	1	1	yes	maximal, characteristic
2	#13116432	C₂	1	1	yes	maximal, characteristic
3	#13113031	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	#11718762	C₄	1	1	yes	characteristic
7	C₂×#88052	C₄	1	1	yes	characteristic
8	C₁₃×M₆₄	—	2	2	no	—
9	C₂×C₁₃×C₃₂	C₂²	1	2	yes	—
10	#11718094	C₄	1	2	yes	—
11	C₁₆×Dic₁₃	C₂²	1	2	yes	—
12	C₂×#88034	—	2	2	no	—
13	C₂×#88034	C₂²	1	2	yes	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	#88180	C₈	1	1	yes	characteristic
16	C₂×#6099	C₈	1	1	yes	characteristic
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	#88055	C₈	1	2	yes	—
22	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
23	#88052	—	2	2	no	—
24	C₂×#6090	C₂×C₄	1	2	yes	—
25	C₁₃×C₃₂	—	2	2	no	—
26	#88034	—	2	2	no	—
27	#13628	—	13	1	no	maximal, Sylow
28	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²⋊Dic₁₃	C₁₆	1	2	yes	—
34	C₄⋊Dic₁₃	C₁₆	1	2	yes	—
35	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
36	#6099	—	2	2	no	—
37	C₂×#1055	C₂×C₈	1	2	yes	—
38	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
39	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
40	C₁₃×C₁₆	C₂×Q₈	1	1	yes	characteristic
41	#6090	—	2	2	no	—
42	C₂×M₆₄	D₁₃	1	1	yes	characteristic
43	C₂²×C₃₂	—	13	1	no	—
44	#2108	—	13	1	no	—
45	C₄⋊C₃₂	—	13	4	no	—
46	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
48	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
50	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
51	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	—
52	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
53	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
55	#1055	—	2	2	no	—
56	C₂×M₃₂	—	13	1	no	—
57	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
58	#405	—	13	1	no	—
59	M₆₄	—	2	2	no	—
60	C₂×C₃₂	—	13	2	no	—
61	C₂×C₃₂	—	26	2	no	—
62	C₂×C₃₂	C₂×D₁₃	1	2	yes	—
63	#346	—	13	2	no	—
64	C₄×C₁₆	—	13	2	no	—
65	C₂²×C₁₃	—	2	2	no	—
66	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
67	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
68	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
69	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
70	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
71	Dic₁₃	—	2	4	no	—
72	C₂×M₁₆	—	13	1	no	—
73	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
74	#117	—	13	1	no	—
75	M₃₂	—	26	2	no	—
76	C₂×C₁₆	—	13	2	no	—
77	C₂×C₁₆	Dic₂₆	1	2	yes	—
78	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
79	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
80	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
81	#97	—	13	2	no	—
82	C₄×C₈	—	13	2	no	—
83	C₃₂	—	2	2	no	—
84	C₃₂	—	26	2	no	—
85	C₂×C₁₃	—	2	2	no	—
86	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
87	C₂×C₁₃	#2258	1	2	yes	—
88	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
89	M₁₆	—	26	2	no	—
90	C₂×C₈	—	13	2	no	—
91	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
92	C₂×C₈	#6094	1	2	yes	—
93	C₂×C₈	#6101	1	2	yes	—
94	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
95	C₄⋊C₄	—	13	2	no	—
96	C₂²⋊C₄	—	13	2	no	—
97	C₄²	—	13	2	no	—
98	C₁₆	—	26	2	no	—
99	C₁₆	#6101	1	2	yes	—
100	C₁₆	C₂×Dic₂₆	1	1	yes	characteristic
101	C₁₆	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
102	C₁₃	#13628	1	1	yes	characteristic, complemented, Sylow
103	C₂³	C₁₆×D₁₃	1	1	yes	characteristic
104	C₂×C₄	—	13	4	no	—
105	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
106	C₂×C₄	#88038	1	2	yes	—
107	C₂×C₄	#88054	1	2	yes	—
108	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
109	C₈	—	26	2	no	—
110	C₈	#88054	1	2	yes	—
111	C₈	C₂×#6094	1	1	yes	characteristic
112	C₈	C₂×#6101	1	1	yes	characteristic
113	C₂²	—	2	2	no	—
114	C₂²	#11718093	1	2	yes	—
115	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
116	C₄	—	26	4	no	—
117	C₄	#11718093	1	2	yes	—
118	C₄	C₂×#88038	1	1	yes	characteristic
119	C₄	C₂×#88054	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×#11718093	1	1	yes	characteristic
122	C₂	#13117131	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#88034

C₂

yes

maximal, characteristic

#13116432

C₂

yes

maximal, characteristic

#13113031

C₂

yes

maximal, complemented

C₂×C₁₃×M₆₄

C₂

yes

maximal, characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

#11718762

C₄

yes

characteristic

C₂×#88052

C₄

yes

characteristic

C₁₃×M₆₄

—

C₂×C₁₃×C₃₂

C₂²

yes

—

#11718094

C₄

yes

—

C₁₆×Dic₁₃

C₂²

yes

—

C₂×#88034

—

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

D₄

yes

—

C₂×C₁₃×C₁₆

Q₈

yes

—

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

#88055

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

#88052

—

C₂×#6090

C₂×C₄

yes

—

C₁₃×C₃₂

—

#88034

—

#13628

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂²⋊Dic₁₃

C₁₆

yes

—

C₄⋊Dic₁₃

C₁₆

yes

—

C₄×Dic₁₃

C₂×C₈

yes

—

#6099

—

C₂×#1055

C₂×C₈

yes

—

C₁₃×C₁₆

C₄⋊C₄

yes

—

C₁₃×C₁₆

C₂×D₄

yes

characteristic

C₁₃×C₁₆

C₂×Q₈

yes

characteristic

#6090

—

C₂×M₆₄

D₁₃

yes

characteristic

C₂²×C₃₂

—

#2108

—

C₄⋊C₃₂

—

C₂³×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×Dic₁₃

C₂×C₁₆

yes

—

C₈×C₁₃

C₄⋊C₈

yes

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₃

C₂×M₁₆

yes

characteristic

#1055

—

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₁₃

yes

characteristic

#405

—

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₁₃

yes

—

#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

C₂×M₃₂

yes

characteristic

Dic₁₃

—

C₂×M₁₆

—

C₂²×C₈

C₄×D₁₃

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

Dic₂₆

yes

—

C₂×C₁₆

C₄×D₁₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₃

yes

—

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

#97

—

C₄×C₈

—

C₃₂

—

C₃₂

—

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

characteristic

C₂×C₈

#6094

yes

—

C₂×C₈

#6101

yes

—

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

#6101

yes

—

100

C₁₆

C₂×Dic₂₆

yes

characteristic

101

C₁₆

C₂×C₂²⋊D₁₃

yes

characteristic

102

C₁₃

#13628

yes

characteristic, complemented, Sylow

103

C₂³

C₁₆×D₁₃

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

C₁₆×D₁₃

yes

characteristic

106

C₂×C₄

#88038

yes

—

107

C₂×C₄

#88054

yes

—

108

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

109

C₈

—

110

C₈

#88054

yes

—

111

C₈

C₂×#6094

yes

characteristic

112

C₈

C₂×#6101

yes

characteristic

113

C₂²

—

114

C₂²

#11718093

yes

—

115

C₂²

C₂×C₁₆×D₁₃

yes

characteristic

116

C₄

—

117

C₄

#11718093

yes

—

118

C₄

C₂×#88038

yes

characteristic

119

C₄

C₂×#88054

yes

characteristic

120

C₂

—

121

C₂

C₂×#11718093

yes

characteristic

122

C₂

#13117131

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂×C₁₃×M₆₄	C₂
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	#13628
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₁₆

Fitting

C₂×C₁₃×M₆₄

C₂

prime radical

C₂³×C₁₃

C₂×C₁₆

cosocle

C₂×C₁₃×C₁₆

C₂³

hypercenter

C₂×M₆₄

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₁₆ ◁ C₂×M₆₄

N	H ≅ G/N	type
3. #13113031	C₂	semidirect
102. C₁₃	#13628	semidirect

H ≅ G/N

type

3. #13113031

C₂

semidirect

102. C₁₃

#13628

semidirect

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

subgroup	index
C₂²×#88034	2
#13116432	2
#13113031	2
C₂×C₁₃×M₆₄	2
#13628	13

subgroup

index

C₂²×#88034

#13116432

#13113031

C₂×C₁₃×M₆₄

#13628

Subgroups — #15783406

Conjugacy classes of subgroups

Complements

Maximal subgroups