Group #13076885 — subgroups

Subgroups — #13076885

Order 1408.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₁₁×#384	C₂	1	1	yes	maximal, characteristic
2	#10622599	C₂	1	3	yes	maximal
3	#10622597	C₂	1	6	yes	maximal
4	#10622592	C₂	1	3	yes	maximal
5	#10622550	C₂	1	2	yes	maximal
6	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
8	C₂×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
9	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₁	C₂²	1	3	yes	—
11	C₂×Dic₁₁⋊C₄	C₂²	1	6	yes	—
12	C₁₁⋊#95	C₂²	1	6	yes	—
13	C₁₁⋊#95	C₂²	1	6	yes	—
14	C₁₁⋊#95	C₂²	1	3	yes	—
15	C₁₁⋊#95	C₂²	1	3	yes	—
16	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
18	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
19	C₂²×Dic₁₁	C₂³	1	6	yes	—
20	C₂²×Dic₁₁	C₂³	1	2	yes	—
21	C₂×Dic₂₂	—	4	3	no	—
22	C₁₁×C₄⋊C₄	—	4	3	no	—
23	C₁₁×C₄⋊C₄	—	4	3	no	—
24	C₄²×C₁₁	Q₈	1	4	yes	complemented
25	C₄⋊Dic₁₁	—	4	3	no	—
26	Dic₁₁⋊C₄	—	4	6	no	—
27	#2843	—	11	1	no	maximal, Sylow
28	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₁₁	—	2	3	no	—
30	C₂×C₄×C₁₁	—	2	3	no	—
31	C₂×C₄×C₁₁	—	2	6	no	—
32	C₂×C₄×C₁₁	—	2	3	no	—
33	C₂×C₄×C₁₁	—	2	3	no	—
34	C₂×C₄×C₁₁	C₂×Q₈	1	6	yes	—
35	C₂×Dic₁₁	—	2	6	no	—
36	C₂×Dic₁₁	—	2	6	no	—
37	C₂×Dic₁₁	—	2	12	no	—
38	Dic₂₂	—	4	4	no	—
39	#400	—	11	3	no	—
40	#398	—	11	6	no	—
41	#395	—	11	3	no	—
42	#384	D₁₁	1	1	yes	characteristic
43	#383	—	11	2	no	—
44	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
45	C₂²×C₁₁	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₁₁	2₋¹⁺⁴	1	3	yes	—
47	C₄×C₁₁	—	2	6	no	—
48	C₄×C₁₁	—	4	3	no	—
49	C₄×C₁₁	—	4	1	no	—
50	Dic₁₁	—	4	2	no	—
51	Dic₁₁	—	4	6	no	—
52	C₂²×Q₈	—	11	1	no	—
53	C₂×C₄⋊C₄	—	11	6	no	—
54	C₂×C₄⋊C₄	—	11	3	no	—
55	C₂×C₄⋊C₄	C₂×D₁₁	1	3	yes	—
56	C₂×C₄⋊C₄	C₂×D₁₁	1	3	yes	—
57	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
58	#95	—	11	6	no	—
59	#95	—	11	6	no	—
60	#95	—	11	3	no	—
61	#95	—	11	3	no	—
62	C₂×C₁₁	#544	1	3	yes	—
63	C₂×C₁₁	#560	1	1	yes	characteristic
64	C₂×C₁₁	#563	1	3	yes	—
65	C₂×Q₈	—	44	3	no	—
66	C₂²×C₄	—	11	6	no	—
67	C₂²×C₄	—	11	2	no	—
68	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
69	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
70	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
71	C₄⋊C₄	—	4	3	no	—
72	C₄⋊C₄	—	4	3	no	—
73	C₄⋊C₄	—	44	6	no	—
74	C₄⋊C₄	—	44	3	no	—
75	C₄²	Dic₂₂	1	4	yes	complemented
76	C₁₁	#2843	1	1	yes	characteristic, complemented, Sylow
77	C₂³	C₂³×D₁₁	1	1	yes	characteristic
78	Q₈	—	44	4	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	2	3	no	—
83	C₂×C₄	—	2	3	no	—
84	C₂×C₄	—	22	6	no	—
85	C₂×C₄	—	22	6	no	—
86	C₂×C₄	—	22	12	no	—
87	C₂×C₄	C₂×Dic₂₂	1	6	yes	—
88	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
89	C₂²	#67037	1	3	yes	—
90	C₂²	#67040	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	4	1	no	—
93	C₄	—	4	3	no	—
94	C₄	—	44	2	no	—
95	C₄	—	44	6	no	—
96	C₂	#10623031	1	3	yes	—
97	C₂	#10623251	1	1	yes	characteristic
98	C₂	#10623266	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#384

C₂

yes

maximal, characteristic

#10622599

C₂

yes

maximal

#10622597

C₂

yes

maximal

#10622592

C₂

yes

maximal

#10622550

C₂

yes

maximal

C₂²×Dic₂₂

C₂²

yes

characteristic

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂×Dic₂₂

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

Q₈

yes

complemented

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

#2843

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

—

—

—

D₁₁

yes

characteristic

#383

—

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

H(5,𝔽₂)

yes

—

C₂²×C₁₁

2₋¹⁺⁴

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

Dic₁₁

—

Dic₁₁

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄²

C₂×D₁₁

yes

—

—

—

—

C₂×C₁₁

#544

yes

—

C₂×C₁₁

#560

yes

characteristic

C₂×C₁₁

#563

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₁

yes

characteristic

C₂²×C₄

C₂²×D₁₁

yes

—

C₂²×C₄

C₂²×D₁₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₂₂

yes

complemented

C₁₁

#2843

yes

characteristic, complemented, Sylow

C₂³

C₂³×D₁₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₂₂

yes

—

C₂²

C₂²×Dic₂₂

yes

characteristic

C₂²

#67037

yes

—

C₂²

#67040

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₂

#10623031

yes

—

C₂

#10623251

yes

characteristic

C₂

#10623266

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#384	C₂
hypercenter	#384	D₁₁
hypocenter	C₁₁	#2843
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#384

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
24. C₄²×C₁₁	Q₈	semidirect
75. C₄²	Dic₂₂	semidirect
76. C₁₁	#2843	semidirect

H ≅ G/N

type

24. C₄²×C₁₁

Q₈

semidirect

75. C₄²

Dic₂₂

semidirect

76. C₁₁

#2843

semidirect

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

subgroup	index
C₁₁×#384	2
#10622599	2
#10622597	2
#10622592	2
#10622550	2
#2843	11

subgroup

index

C₁₁×#384

Subgroups — #13076885

Conjugacy classes of subgroups

Complements

Maximal subgroups