Group #13070192 — subgroups

Subgroups — #13070192

Order 1408.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#10622738	C₂	1	1	yes	maximal, characteristic
2	#10622731	C₂	1	1	yes	maximal, characteristic
3	C₁₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
4	#10622171	C₂	1	2	yes	maximal
5	#10622170	C₂	1	2	yes	maximal
6	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₁₁×#117	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
9	C₂×#4318	C₂²	1	1	yes	characteristic
10	C₂×#4318	C₂²	1	2	yes	—
11	#66883	—	2	2	no	—
12	Dic₁₁⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₁	—	2	1	no	—
15	C₁₁×M₁₆	—	2	2	no	—
16	C₂×C₈×C₁₁	D₄	1	2	yes	—
17	C₁₁×C₄⋊C₄	—	2	2	no	—
18	C₁₁×C₂²⋊C₄	—	2	2	no	—
19	C₄²×C₁₁	—	2	2	no	—
20	C₄×Dic₁₁	—	2	1	no	—
21	C₄×Dic₁₁	Q₈	1	1	yes	characteristic
22	C₄×Dic₁₁	Q₈	1	1	yes	characteristic
23	#4318	—	2	2	no	—
24	#4318	—	2	2	no	—
25	#4318	—	2	2	no	—
26	C₂×C₁₁⋊C₈	—	2	1	no	—
27	C₂×C₁₁⋊C₈	—	2	2	no	—
28	#2102	—	11	1	no	maximal, Sylow
29	C₂³×C₁₁	#41	1	1	yes	characteristic
30	C₂×C₄×C₁₁	—	4	2	no	—
31	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₁₁	#41	1	2	yes	—
34	C₂×C₄×C₁₁	#41	1	2	yes	—
35	C₂×Dic₁₁	—	2	1	no	—
36	C₂×Dic₁₁	—	2	1	no	—
37	C₂×Dic₁₁	—	4	2	no	—
38	C₈×C₁₁	—	2	2	no	—
39	C₁₁⋊C₈	—	4	1	no	—
40	C₁₁⋊C₈	—	4	2	no	—
41	#430	—	11	1	no	—
42	#423	—	11	1	no	—
43	#344	—	11	2	no	—
44	#339	—	11	2	no	—
45	H(3,ℤ/4)	D₁₁	1	1	yes	characteristic
46	C₂²×C₁₁	—	4	1	no	—
47	C₂²×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
48	C₂²×C₁₁	#126	1	2	yes	—
49	C₄×C₁₁	—	8	2	no	—
50	C₄×C₁₁	#123	1	1	yes	characteristic
51	C₄×C₁₁	#124	1	1	yes	characteristic
52	C₄×C₁₁	#125	1	2	yes	—
53	Dic₁₁	—	2	2	no	—
54	Dic₁₁	—	4	1	no	—
55	C₂×M₁₆	—	11	2	no	—
56	C₂×M₁₆	—	11	1	no	—
57	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
58	#117	C₂×D₁₁	1	2	yes	—
59	C₂×C₄²	—	11	1	no	—
60	#108	—	22	2	no	—
61	C₄⋊C₈	—	22	2	no	—
62	C₂×C₁₁	—	2	1	no	—
63	C₂×C₁₁	—	2	2	no	—
64	C₂×C₁₁	#400	1	1	yes	characteristic
65	C₂²×C₄	—	22	1	no	—
66	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	M₁₆	—	22	2	no	—
69	M₁₆	—	22	2	no	—
70	M₁₆	—	22	2	no	—
71	C₂×C₈	—	22	1	no	—
72	C₂×C₈	—	22	2	no	—
73	C₂×C₈	D₄₄	1	2	yes	—
74	C₄⋊C₄	—	2	2	no	—
75	C₂²⋊C₄	—	2	2	no	—
76	C₄²	—	2	2	no	—
77	C₄²	—	11	1	no	—
78	C₄²	—	11	1	no	—
79	C₄²	—	22	1	no	—
80	C₁₁	#2102	1	1	yes	characteristic, complemented, Sylow
81	C₂³	#4341	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	22	1	no	—
84	C₂×C₄	—	22	1	no	—
85	C₂×C₄	—	44	2	no	—
86	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
87	C₂×C₄	#4339	1	2	yes	—
88	C₂×C₄	#4341	1	2	yes	—
89	C₂×C₄	Q₈×D₁₁	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	44	2	no	—
92	C₈	—	44	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#66932	1	2	yes	—
95	C₂²	#66950	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	—	22	2	no	—
98	C₄	—	44	1	no	—
99	C₄	#66928	1	1	yes	characteristic
100	C₄	#66939	1	1	yes	characteristic
101	C₄	#66942	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#10622272	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10622738

C₂

yes

maximal, characteristic

#10622731

C₂

yes

maximal, characteristic

C₁₁×H(3,ℤ/4)

C₂

yes

maximal, characteristic

#10622171

C₂

yes

maximal

#10622170

C₂

yes

maximal

C₂×C₁₁×M₁₆

C₂²

yes

characteristic

C₁₁×#117

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂×#4318

C₂²

yes

characteristic

C₂×#4318

C₂²

yes

—

#66883

—

Dic₁₁⋊C₈

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

Q₈

yes

characteristic

C₄×Dic₁₁

Q₈

yes

—

—

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

—

C₂³×C₁₁

yes

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

—

—

—

—

D₁₁

yes

characteristic

C₂²×C₁₁

—

C₂²×C₁₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₁

#126

yes

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₁

yes

characteristic

#117

C₂×D₁₁

yes

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#400

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄₄

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₁

#2102

yes

characteristic, complemented, Sylow

C₂³

#4341

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄₄

yes

characteristic

C₂×C₄

#4339

yes

—

C₂×C₄

#4341

yes

—

C₂×C₄

Q₈×D₁₁

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#66932

yes

—

C₂²

#66950

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#66928

yes

characteristic

100

C₄

#66939

yes

characteristic

101

C₄

#66942

yes

—

102

C₂

—

103

C₂

—

104

C₂

#10622272

yes

characteristic

	subgroup	G/H
center	C₄	#66928
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×H(3,ℤ/4)	C₂
socle	C₂×C₁₁	#400
prime radical	C₂³×C₁₁	#41
hypercenter	H(3,ℤ/4)	D₁₁
hypocenter	C₁₁	#2102
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#66928

commutator, cosocle

C₂²×C₄×C₁₁

C₂³

Frattini

C₂²×C₄

C₂²×D₁₁

Fitting

C₁₁×H(3,ℤ/4)

C₂

C₂×C₁₁

C₂³×C₁₁

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
80. C₁₁	#2102	semidirect

H ≅ G/N

type

80. C₁₁

#2102

semidirect

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

subgroup	index
#10622738	2
#10622731	2
C₁₁×H(3,ℤ/4)	2
#10622171	2
#10622170	2
#2102	11

subgroup

index

C₁₁×H(3,ℤ/4)

Subgroups — #13070192

Conjugacy classes of subgroups

Complements

Maximal subgroups