Group #16798192 — subgroups

Subgroups — #16798192

Order 3328.

830 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 232 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	#13130765	C₂	1	8	yes	maximal, complemented
2	#13130500	C₂	1	6	yes	maximal
3	D₁₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6118	C₂²	1	4	yes	—
5	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
6	C₁₃×#376	C₄	1	1	yes	characteristic
7	#11718593	C₄	1	3	yes	—
8	D₁₃×#95	C₄	1	4	yes	—
9	#11718309	C₂²	1	4	yes	—
10	#11718290	C₂²	1	24	yes	—
11	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
12	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
13	C₂²×#1057	C₂³	1	8	yes	—
14	C₂×#6118	—	2	24	no	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
16	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
17	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
18	C₄²×D₁₃	—	2	12	no	—
19	C₁₃×#95	C₂×C₄	1	4	yes	—
20	#88071	C₂×C₄	1	12	yes	—
21	#20773	—	13	1	no	maximal, Sylow
22	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
24	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
26	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
27	C₂×C₄×D₁₃	—	2	12	no	—
28	C₂×C₄×D₁₃	—	4	12	no	—
29	C₂×C₄×D₁₃	#41	1	12	yes	—
30	C₂×#1057	—	2	24	no	—
31	#6118	—	4	16	no	—
32	C₄²×C₁₃	—	2	6	no	—
33	C₄×Dic₁₃	—	2	6	no	—
34	C₄×Dic₁₃	—	2	12	no	—
35	C₂×#376	—	13	1	no	—
36	#1840	—	13	8	no	—
37	#1728	—	13	6	no	—
38	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
39	C₂²×D₁₃	—	2	4	no	—
40	C₂²×D₁₃	#117	1	6	yes	—
41	C₂×C₄×C₁₃	—	2	6	no	—
42	C₂×C₄×C₁₃	—	2	12	no	—
43	C₂×C₄×C₁₃	#117	1	6	yes	—
44	C₂×Dic₁₃	—	2	6	no	—
45	C₂×Dic₁₃	—	2	12	no	—
46	C₂×Dic₁₃	C₂×#41	1	6	yes	—
47	C₄×D₁₃	—	4	24	no	—
48	C₄×D₁₃	#126	1	16	yes	—
49	#1057	—	4	8	no	—
50	C₂²×M₁₆	—	13	4	no	—
51	C₂²×C₄²	—	13	3	no	—
52	#376	—	13	3	no	—
53	#376	—	13	4	no	—
54	#376	#261	1	1	yes	characteristic
55	C₂×#95	—	13	4	no	—
56	#336	—	13	24	no	—
57	C₂²×C₁₃	C₂×#117	1	3	yes	—
58	C₂²×C₁₃	#568	1	4	yes	—
59	C₂×D₁₃	—	2	12	no	—
60	C₂×D₁₃	#383	1	4	yes	—
61	C₄×C₁₃	—	4	6	no	—
62	C₄×C₁₃	#383	1	4	yes	—
63	Dic₁₃	—	4	6	no	—
64	Dic₁₃	C₂×#126	1	4	yes	—
65	C₂³×C₄	—	13	1	no	—
66	C₂³×C₄	—	13	6	no	—
67	C₂×M₁₆	—	26	24	no	—
68	C₂²×C₈	—	13	8	no	—
69	C₂×C₄²	—	13	6	no	—
70	C₂×C₄²	—	13	3	no	—
71	C₂×C₄²	—	26	12	no	—
72	C₂×C₄²	C₂×#261	1	3	yes	—
73	#95	—	13	12	no	—
74	#95	C₂×#261	1	4	yes	—
75	C₂×C₁₃	C₂×#383	1	1	yes	characteristic
76	C₂×C₁₃	#2921	1	6	yes	—
77	D₁₃	—	2	4	no	—
78	C₂⁴	—	13	1	no	—
79	C₂²×C₄	—	13	1	no	—
80	C₂²×C₄	—	13	12	no	—
81	C₂²×C₄	—	13	6	no	—
82	C₂²×C₄	—	26	12	no	—
83	C₂²×C₄	—	52	12	no	—
84	C₂²×C₄	C₂²×#261	1	6	yes	—
85	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
86	M₁₆	—	52	16	no	—
87	C₂×C₈	—	26	24	no	—
88	C₄²	—	2	6	no	—
89	C₄²	—	26	12	no	—
90	C₄²	—	26	6	no	—
91	C₁₃	#20773	1	1	yes	characteristic, complemented, Sylow
92	C₂³	—	13	6	no	—
93	C₂³	—	26	4	no	—
94	C₂³	C₂³×#261	1	1	yes	characteristic
95	C₂×C₄	—	2	6	no	—
96	C₂×C₄	—	2	12	no	—
97	C₂×C₄	—	13	6	no	—
98	C₂×C₄	—	13	16	no	—
99	C₂×C₄	—	26	6	no	—
100	C₂×C₄	—	26	12	no	—
101	C₂×C₄	—	52	24	no	—
102	C₂×C₄	#88237	1	6	yes	—
103	C₈	—	52	8	no	—
104	C₂²	—	13	4	no	—
105	C₂²	—	26	12	no	—
106	C₂²	C₂×#88237	1	3	yes	—
107	C₂²	#11719629	1	4	yes	—
108	C₄	—	4	6	no	—
109	C₄	—	13	4	no	—
110	C₄	—	52	6	no	—
111	C₄	#11719061	1	4	yes	—
112	C₂	—	26	4	no	—
113	C₂	C₂×#11719061	1	1	yes	characteristic
114	C₂	#13131517	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130765

C₂

yes

maximal, complemented

#13130500

C₂

yes

maximal

D₁₃×#376

C₂

yes

maximal, characteristic

C₂²×#6118

C₂²

yes

—

C₂×C₄²×D₁₃

C₂²

yes

—

C₁₃×#376

C₄

yes

characteristic

#11718593

C₄

yes

—

D₁₃×#95

C₄

yes

—

#11718309

C₂²

yes

—

#11718290

C₂²

yes

—

C₂²×C₄×D₁₃

C₂×C₄

yes

—

C₂²×C₄×D₁₃

C₂³

yes

characteristic

C₂²×#1057

C₂³

yes

—

C₂×#6118

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂³

yes

—

C₄²×D₁₃

—

C₁₃×#95

C₂×C₄

yes

—

#88071

C₂×C₄

yes

—

#20773

—

maximal, Sylow

C₂³×D₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₂⁴

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

#41

yes

—

C₂×#1057

—

#6118

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#376

—

#1840

—

#1728

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

#117

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#117

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×#41

yes

—

C₄×D₁₃

—

C₄×D₁₃

#126

yes

—

#1057

—

C₂²×M₁₆

—

C₂²×C₄²

—

—

—

yes

C₂×#95

—

#336

—

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

#568

yes

—

C₂×D₁₃

—

C₂×D₁₃

#383

yes

—

C₄×C₁₃

—

C₄×C₁₃

#383

yes

—

Dic₁₃

—

Dic₁₃

C₂×#126

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

—

#95

—

#95

C₂×#261

yes

—

C₂×C₁₃

C₂×#383

yes

characteristic

C₂×C₁₃

#2921

yes

—

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×#261

yes

—

C₂²×C₄

C₂²×#261

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#20773

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

C₂³×#261

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

#88237

yes

—

103

C₈

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×#88237

yes

—

107

C₂²

#11719629

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#11719061

yes

—

112

C₂

—

113

C₂

C₂×#11719061

yes

characteristic

114

C₂

#13131517

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×#261
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#376	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×Dic₁₃	C₂⁴
hypercenter	#376	#261
hypocenter	C₁₃	#20773
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×#261

commutator, socle

C₂³×C₁₃

C₂³×C₄

Fitting

C₁₃×#376

C₄

prime radical

C₂³×D₁₃

C₂²×C₄

cosocle

C₂²×Dic₁₃

C₂⁴

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #13130765	C₂	semidirect
91. C₁₃	#20773	semidirect

H ≅ G/N

type

1. #13130765

C₂

semidirect

91. C₁₃

#20773

semidirect

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

subgroup	index
#13130765	2
#13130500	2
D₁₃×#376	2
#20773	13

subgroup

index

#13130765

#13130500

D₁₃×#376

#20773

Subgroups — #16798192

Conjugacy classes of subgroups

Complements

Maximal subgroups