Group #15783891 — subgroups

Subgroups — #15783891

Order 3328.

182 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 75 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	#13117111	C₂	1	1	yes	maximal, characteristic
2	#13113017	C₂	1	4	yes	maximal
3	C₄×#88034	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2247	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×Q₃₂	—	2	1	no	—
6	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
7	C₁₃×#494	—	2	1	no	—
8	#11718343	—	2	1	no	—
9	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	#11718096	—	2	1	no	—
11	#11718096	C₂²	1	2	yes	—
12	C₂×#88034	C₂²	1	2	yes	—
13	C₂×C₁₃×Q₁₆	—	2	2	no	—
14	C₂×C₁₃×Q₁₆	—	4	1	no	—
15	C₁₃×C₄⋊Q₈	—	4	1	no	—
16	#88123	—	4	1	no	—
17	C₁₃×Q₃₂	—	2	4	no	—
18	C₁₃×Q₃₂	—	4	2	no	—
19	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
22	#88058	—	2	2	no	—
23	#88058	—	4	1	no	—
24	#88034	—	2	2	no	—
25	#13720	—	13	1	no	maximal, Sylow
26	C₂×Q₈×C₁₃	—	4	2	no	—
27	C₂×Dic₂₆	—	8	1	no	—
28	C₁₃×Q₁₆	—	4	2	no	—
29	C₁₃×Q₁₆	—	4	2	no	—
30	C₁₃×Q₁₆	—	8	2	no	—
31	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₁₃×C₄⋊C₄	—	8	1	no	—
34	C₁₃×C₄⋊C₄	—	8	1	no	—
35	C₄²×C₁₃	D₈	1	1	yes	characteristic
36	C₄⋊Dic₁₃	—	4	2	no	—
37	C₄⋊Dic₁₃	—	8	1	no	—
38	C₁₃×C₁₆	SD₁₆	1	2	yes	—
39	C₁₃×C₁₆	#41	1	2	yes	—
40	#2252	—	13	1	no	—
41	#2247	D₁₃	1	1	yes	characteristic
42	#1416	—	13	4	no	—
43	C₄×C₃₂	—	13	1	no	—
44	Q₈×C₁₃	—	8	2	no	—
45	Q₈×C₁₃	—	8	2	no	—
46	C₂×C₄×C₁₃	—	8	2	no	—
47	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
50	C₂×Dic₁₃	—	8	2	no	—
51	Dic₂₆	—	16	2	no	—
52	C₈×C₁₃	SD₃₂	1	2	yes	—
53	C₈×C₁₃	#124	1	1	yes	characteristic
54	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
55	C₂×Q₃₂	—	2	1	no	—
56	C₂×Q₃₂	C₂×D₁₃	1	2	yes	—
57	#500	—	26	1	no	—
58	#494	—	2	1	no	—
59	C₂×C₃₂	—	13	2	no	—
60	#366	—	13	2	no	—
61	#366	—	26	1	no	—
62	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
63	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
64	C₄×C₁₃	—	16	2	no	—
65	C₄×C₁₃	SD₆₄	1	2	yes	—
66	C₄×C₁₃	Q₆₄	1	2	yes	—
67	C₄×C₁₃	#486	1	1	yes	characteristic
68	C₄×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
69	Dic₁₃	—	16	2	no	—
70	C₂×Q₁₆	—	2	2	no	—
71	C₂×Q₁₆	—	4	1	no	—
72	C₄⋊Q₈	—	4	1	no	—
73	C₄⋊Q₈	—	52	1	no	—
74	Q₃₂	—	2	4	no	—
75	Q₃₂	—	4	2	no	—
76	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
77	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
78	#107	—	26	2	no	—
79	#107	—	52	1	no	—
80	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
81	C₃₂	—	26	2	no	—
82	C₂×C₁₃	#2240	1	1	yes	characteristic
83	C₂×C₁₃	C₂×SD₆₄	1	1	yes	characteristic
84	C₂×C₁₃	C₂×Q₆₄	1	1	yes	characteristic
85	C₂×Q₈	—	4	2	no	—
86	C₂×Q₈	—	104	1	no	—
87	Q₁₆	—	4	2	no	—
88	Q₁₆	—	4	2	no	—
89	Q₁₆	—	8	2	no	—
90	C₂×C₈	#6104	1	1	yes	characteristic
91	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
92	C₄⋊C₄	—	8	1	no	—
93	C₄⋊C₄	—	8	1	no	—
94	C₄⋊C₄	—	52	2	no	—
95	C₄⋊C₄	—	104	1	no	—
96	C₄²	#6104	1	1	yes	characteristic
97	C₁₆	#6105	1	2	yes	—
98	C₁₆	#6129	1	2	yes	—
99	C₁₃	#13720	1	1	yes	characteristic, complemented, Sylow
100	Q₈	—	8	2	no	—
101	Q₈	—	8	2	no	—
102	Q₈	—	208	2	no	—
103	C₂×C₄	—	8	2	no	—
104	C₂×C₄	—	104	2	no	—
105	C₂×C₄	#88066	1	1	yes	characteristic
106	C₂×C₄	#88066	1	1	yes	characteristic
107	C₂×C₄	C₂×#6104	1	1	yes	characteristic
108	C₈	#88067	1	2	yes	—
109	C₈	C₂×#6105	1	1	yes	characteristic
110	C₈	#88190	1	1	yes	characteristic
111	C₂²	C₂×#88066	1	1	yes	characteristic
112	C₄	—	16	2	no	—
113	C₄	—	208	2	no	—
114	C₄	#11718113	1	2	yes	—
115	C₄	#11718114	1	2	yes	—
116	C₄	#11718731	1	1	yes	characteristic
117	C₄	C₂×#88067	1	1	yes	characteristic
118	C₂	#13117059	1	1	yes	characteristic
119	C₂	C₂×#11718113	1	1	yes	characteristic
120	C₂	C₂×#11718114	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13117111

C₂

yes

maximal, characteristic

#13113017

C₂

yes

maximal

C₄×#88034

C₂

yes

maximal, characteristic

C₁₃×#2247

C₂

yes

maximal, characteristic

C₂×C₁₃×Q₃₂

—

C₂×C₁₃×Q₃₂

C₂²

yes

—

C₁₃×#494

—

#11718343

—

C₄×C₁₃×C₁₆

C₂²

yes

characteristic

#11718096

—

#11718096

C₂²

yes

—

C₂×#88034

C₂²

yes

—

C₂×C₁₃×Q₁₆

—

C₂×C₁₃×Q₁₆

—

C₁₃×C₄⋊Q₈

—

#88123

—

C₁₃×Q₃₂

—

C₁₃×Q₃₂

—

C₂×C₁₃×C₁₆

D₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

—

—

—

—

C₂×Q₈×C₁₃

—

C₂×Dic₂₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₁₃×Q₁₆

—

C₂×C₈×C₁₃

D₈

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

D₈

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₁₃×C₁₆

SD₁₆

yes

—

C₁₃×C₁₆

#41

yes

—

#2252

—

#2247

D₁₃

yes

characteristic

#1416

—

C₄×C₃₂

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

D₁₆

yes

characteristic

C₂×C₄×C₁₃

D₁₆

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×Dic₁₃

—

Dic₂₆

—

C₈×C₁₃

SD₃₂

yes

—

C₈×C₁₃

#124

yes

characteristic

C₈×C₁₃

C₂×SD₁₆

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

C₂×D₁₃

yes

—

#500

—

#494

—

C₂×C₃₂

—

#366

—

#366

—

C₄×C₁₆

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

C₂×D₁₆

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

SD₆₄

yes

—

C₄×C₁₃

Q₆₄

yes

—

C₄×C₁₃

#486

yes

characteristic

C₄×C₁₃

C₂×SD₃₂

yes

characteristic

Dic₁₃

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₂²⋊D₁₃

yes

characteristic

C₂×C₁₆

C₂²×D₁₃

yes

characteristic

#107

—

#107

—

C₄×C₈

C₂²⋊D₁₃

yes

characteristic

C₃₂

—

C₂×C₁₃

#2240

yes

characteristic

C₂×C₁₃

C₂×SD₆₄

yes

characteristic

C₂×C₁₃

C₂×Q₆₄

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

104

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#6104

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

104

—

C₄²

#6104

yes

characteristic

C₁₆

#6105

yes

—

C₁₆

#6129

yes

—

C₁₃

#13720

yes

characteristic, complemented, Sylow

100

Q₈

—

101

Q₈

—

102

Q₈

—

208

—

103

C₂×C₄

—

104

C₂×C₄

—

104

—

105

C₂×C₄

#88066

yes

characteristic

106

C₂×C₄

#88066

yes

characteristic

107

C₂×C₄

C₂×#6104

yes

characteristic

108

C₈

#88067

yes

—

109

C₈

C₂×#6105

yes

characteristic

110

C₈

#88190

yes

characteristic

111

C₂²

C₂×#88066

yes

characteristic

112

C₄

—

113

C₄

—

208

—

114

C₄

#11718113

yes

—

115

C₄

#11718114

yes

—

116

C₄

#11718731

yes

characteristic

117

C₄

C₂×#88067

yes

characteristic

118

C₂

#13117059

yes

characteristic

119

C₂

C₂×#11718113

yes

characteristic

120

C₂

C₂×#11718114

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#88066
commutator, cosocle	C₂×C₁₃×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₁₃×#2247	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₁₆
hypercenter	#2247	D₁₃
hypocenter	C₁₃	#13720
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂²

C₂×#88066

commutator, cosocle

C₂×C₁₃×C₁₆

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₃

Fitting

C₁₃×#2247

C₂

socle, prime radical

C₂²×C₁₃

C₂×D₁₆

D₁₃

C₁₃

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
99. C₁₃	#13720	semidirect

H ≅ G/N

type

99. C₁₃

#13720

semidirect

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

subgroup	index
#13117111	2
#13113017	2
C₄×#88034	2
C₁₃×#2247	2
#13720	13

subgroup

index

C₁₃×#2247

Subgroups — #15783891

Conjugacy classes of subgroups

Complements

Maximal subgroups