Group #13114989 — subgroups

Subgroups — #13114989

Order 1664.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#88054	C₂	1	4	yes	maximal
3	#11718593	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
8	C₂²×#1055	C₂²	1	2	yes	—
9	C₁₃×C₄⋊C₈	—	2	2	no	—
10	#88071	C₄	1	2	yes	—
11	#88071	C₄	1	2	yes	—
12	#88054	—	2	8	no	—
13	C₄⋊#1055	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₃	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	—	2	4	no	—
20	C₄²×C₁₃	D₄	1	2	yes	—
21	C₄²×C₁₃	Q₈	1	2	yes	—
22	C₄×Dic₁₃	D₄	1	4	yes	—
23	C₄×Dic₁₃	Q₈	1	4	yes	—
24	C₂×#1055	—	2	2	no	—
25	C₂×#1055	—	2	4	no	—
26	#1843	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	—	2	2	no	—
29	C₂×C₄×C₁₃	—	2	2	no	—
30	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
33	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
36	C₂×Dic₁₃	—	2	4	no	—
37	C₂×Dic₁₃	—	2	4	no	—
38	C₂×Dic₁₃	C₄⋊C₄	1	8	yes	—
39	C₈×C₁₃	—	4	2	no	—
40	#1055	—	4	2	no	—
41	C₂×C₄⋊C₈	—	13	4	no	—
42	C₂×C₄⋊C₈	—	13	1	no	—
43	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic
44	#376	—	13	1	no	—
45	C₂²×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
46	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₁₃	#131	1	2	yes	—
48	C₂²×C₁₃	#131	1	2	yes	—
49	C₄×C₁₃	—	2	2	no	—
50	C₄×C₁₃	—	2	2	no	—
51	C₄×C₁₃	#127	1	1	yes	characteristic
52	C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
53	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₁₃	—	2	8	no	—
55	C₂²×C₈	—	13	2	no	—
56	C₂²×C₈	C₂×D₁₃	1	2	yes	—
57	C₂×C₄²	—	13	2	no	—
58	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
59	C₄⋊C₈	—	2	2	no	—
60	C₄⋊C₈	—	26	8	no	—
61	C₄⋊C₈	—	26	2	no	—
62	#95	—	13	2	no	—
63	#95	—	13	2	no	—
64	C₂×C₁₃	#384	1	1	yes	characteristic
65	C₂×C₁₃	#424	1	4	yes	—
66	C₂×C₁₃	#424	1	1	yes	characteristic
67	C₂×C₁₃	#424	1	1	yes	characteristic
68	C₂²×C₄	—	13	4	no	—
69	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
70	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
71	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
72	C₂×C₈	—	2	4	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	26	4	no	—
75	C₂×C₈	—	26	2	no	—
76	C₄²	—	13	4	no	—
77	C₄²	—	13	4	no	—
78	C₄²	Dic₂₆	1	2	yes	—
79	C₄²	C₂²⋊D₁₃	1	2	yes	—
80	C₁₃	#1843	1	1	yes	characteristic, complemented, Sylow
81	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	13	8	no	—
85	C₂×C₄	—	26	4	no	—
86	C₂×C₄	—	26	4	no	—
87	C₂×C₄	#6101	1	2	yes	—
88	C₂×C₄	#6101	1	2	yes	—
89	C₂×C₄	C₂×Dic₂₆	1	1	yes	characteristic
90	C₂×C₄	D₄×D₁₃	1	2	yes	—
91	C₂×C₄	Q₈×D₁₃	1	2	yes	—
92	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	52	2	no	—
95	C₂²	C₄⋊C₄×D₁₃	1	2	yes	—
96	C₂²	#88155	1	2	yes	—
97	C₂²	#88161	1	2	yes	—
98	C₂²	C₂×#6101	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	—	26	8	no	—
102	C₄	#88142	1	2	yes	—
103	C₄	#88194	1	1	yes	characteristic
104	C₄	#88198	1	1	yes	characteristic
105	C₂	#11718500	1	4	yes	—
106	C₂	#11718637	1	1	yes	characteristic
107	C₂	#11718763	1	1	yes	characteristic
108	C₂	#11718780	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#88054

C₂

yes

maximal

#11718593

C₂

yes

maximal, characteristic

C₂×C₄⋊#1055

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

—

C₂²×#1055

C₂²

yes

—

C₁₃×C₄⋊C₈

—

#88071

C₄

yes

—

#88071

C₄

yes

—

#88054

—

C₄⋊#1055

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

Q₈

yes

—

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

Q₈

yes

—

—

—

—

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

—

#1055

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₁₃

yes

characteristic

#376

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#131

yes

—

C₂²×C₁₃

#131

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#127

yes

characteristic

C₄×C₁₃

C₄⋊Q₈

yes

—

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₂×C₁₃

#384

yes

characteristic

C₂×C₁₃

#424

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂²×C₄

—

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₄×D₁₃

yes

characteristic

C₂²×C₄

C₂²×D₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

Dic₂₆

yes

—

C₄²

C₂²⋊D₁₃

yes

—

C₁₃

#1843

yes

characteristic, complemented, Sylow

C₂³

C₂×C₄×D₁₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#6101

yes

—

C₂×C₄

#6101

yes

—

C₂×C₄

C₂×Dic₂₆

yes

characteristic

C₂×C₄

D₄×D₁₃

yes

—

C₂×C₄

Q₈×D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

C₈

—

C₈

—

C₂²

C₄⋊C₄×D₁₃

yes

—

C₂²

#88155

yes

—

C₂²

#88161

yes

—

C₂²

C₂×#6101

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

#88142

yes

—

103

C₄

#88194

yes

characteristic

104

C₄

#88198

yes

characteristic

105

C₂

#11718500

yes

—

106

C₂

#11718637

yes

characteristic

107

C₂

#11718763

yes

characteristic

108

C₂

#11718780

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂²×C₄
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	#1843
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₃

commutator, socle, prime radical

C₂³×C₁₃

C₂²×C₄

Fitting

C₂×C₁₃×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₁₃

C₂³

hypercenter

C₂×C₄⋊C₈

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
80. C₁₃	#1843	semidirect

H ≅ G/N

type

80. C₁₃

#1843

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊C₈	2
C₂×#88054	2
#11718593	2
C₂×C₄⋊#1055	2
#1843	13

subgroup

index

C₂×C₁₃×C₄⋊C₈

C₂×#88054

#11718593

C₂×C₄⋊#1055

#1843

Subgroups — #13114989

Conjugacy classes of subgroups

Complements

Maximal subgroups