Group #14668477 — subgroups

Subgroups — #14668477

Order 2816.

290 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 83 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	#13070840	C₂	1	4	yes	maximal, complemented
2	#13068231	C₂	1	1	yes	maximal, characteristic
3	#13068226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1311	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622308	—	2	2	no	—
6	#10622308	C₂²	1	2	yes	—
7	#10622295	C₂²	1	2	yes	—
8	#10622294	—	2	2	no	—
9	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
10	C₈²×C₁₁	C₂²	1	1	yes	characteristic
11	#10622147	—	2	8	no	—
12	C₂×D₈₈	—	2	4	no	—
13	C₂×D₈₈	—	4	4	no	—
14	#66927	—	2	2	no	—
15	#66922	—	2	2	no	—
16	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
17	C₄×C₈×C₁₁	D₄	1	2	yes	—
18	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	#66882	—	2	4	no	—
20	#66880	—	4	4	no	—
21	#12513	—	11	1	no	maximal, Sylow
22	C₂×D₄₄	—	4	2	no	—
23	C₂×D₄₄	—	4	4	no	—
24	C₂×Dic₂₂	—	4	2	no	—
25	C₂×C₈×C₁₁	D₈	1	4	yes	—
26	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
27	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₄⋊Dic₁₁	—	4	2	no	—
29	C₄⋊Dic₁₁	—	4	2	no	—
30	D₈₈	—	4	8	no	—
31	D₈₈	—	8	8	no	—
32	C₁₁×C₁₆	—	2	4	no	—
33	#2240	—	11	4	no	—
34	#1712	—	11	1	no	—
35	#1710	—	11	1	no	—
36	#1311	D₁₁	1	1	yes	characteristic, complemented
37	C₂²×D₁₁	—	8	2	no	—
38	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
40	C₂×Dic₁₁	—	8	2	no	—
41	D₄₄	—	8	4	no	—
42	D₄₄	—	8	8	no	—
43	Dic₂₂	—	8	4	no	—
44	C₈×C₁₁	—	2	4	no	—
45	C₈×C₁₁	#135	1	4	yes	—
46	#500	—	11	2	no	—
47	#493	—	11	2	no	—
48	#493	—	22	2	no	—
49	#487	—	22	2	no	—
50	#357	—	22	8	no	—
51	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
52	C₈²	C₂×D₁₁	1	1	yes	characteristic
53	C₂²×C₁₁	#493	1	1	yes	characteristic
54	C₂×D₁₁	—	16	2	no	—
55	C₂×D₁₁	—	16	4	no	—
56	C₄×C₁₁	#495	1	2	yes	—
57	C₄×C₁₁	#509	1	4	yes	—
58	Dic₁₁	—	16	2	no	—
59	C₂×D₈	—	22	4	no	—
60	C₂×D₈	—	44	4	no	—
61	C₄⋊Q₈	—	22	2	no	—
62	#127	—	22	2	no	—
63	C₂×C₁₆	D₄₄	1	4	yes	—
64	#107	—	22	4	no	—
65	#103	—	44	4	no	—
66	C₄×C₈	D₄₄	1	2	yes	—
67	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
68	C₂×C₁₁	#1709	1	1	yes	characteristic
69	C₂×C₁₁	#2250	1	2	yes	—
70	D₁₁	—	32	2	no	—
71	C₂×Q₈	—	44	2	no	—
72	C₂×D₄	—	44	2	no	—
73	C₂×D₄	—	44	4	no	—
74	D₈	—	44	8	no	—
75	D₈	—	88	8	no	—
76	C₂×C₈	D₈₈	1	4	yes	—
77	C₂×C₈	C₂×D₄₄	1	2	yes	—
78	C₄⋊C₄	—	44	2	no	—
79	C₄⋊C₄	—	44	2	no	—
80	C₄²	C₂×D₄₄	1	1	yes	characteristic
81	C₁₆	—	2	4	no	—
82	C₁₁	#12513	1	1	yes	characteristic, complemented, Sylow
83	C₂³	—	88	2	no	—
84	Q₈	—	88	4	no	—
85	D₄	—	88	8	no	—
86	D₄	—	88	4	no	—
87	C₂×C₄	—	88	2	no	—
88	C₂×C₄	#66927	1	1	yes	characteristic
89	C₂×C₄	C₂×D₈₈	1	2	yes	—
90	C₈	—	2	4	no	—
91	C₈	#66957	1	4	yes	—
92	C₂²	—	176	4	no	—
93	C₂²	—	176	2	no	—
94	C₂²	#10622308	1	1	yes	characteristic
95	C₄	—	176	2	no	—
96	C₄	#10622309	1	2	yes	—
97	C₄	#10622521	1	4	yes	—
98	C₂	—	352	2	no	—
99	C₂	#13068222	1	1	yes	characteristic
100	C₂	#13070882	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13070840

C₂

yes

maximal, complemented

#13068231

C₂

yes

maximal, characteristic

#13068226

C₂

yes

maximal, characteristic, complemented

C₁₁×#1311

C₂

yes

maximal, characteristic, complemented

#10622308

—

#10622308

C₂²

yes

—

#10622295

C₂²

yes

—

#10622294

—

C₄×C₁₁×C₁₆

C₂²

yes

—

C₈²×C₁₁

C₂²

yes

characteristic

#10622147

—

C₂×D₈₈

—

C₂×D₈₈

—

#66927

—

#66922

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

C₂³

yes

—

—

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×Dic₂₂

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

D₈₈

—

D₈₈

—

C₁₁×C₁₆

—

—

—

—

D₁₁

yes

characteristic, complemented

C₂²×D₁₁

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×Dic₁₁

—

D₄₄

—

D₄₄

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

#135

yes

—

—

—

—

—

—

C₄×C₁₆

C₂×D₁₁

yes

—

C₈²

C₂×D₁₁

yes

characteristic

C₂²×C₁₁

#493

yes

characteristic

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

#495

yes

—

C₄×C₁₁

#509

yes

—

Dic₁₁

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

D₄₄

yes

—

#107

—

#103

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂²×D₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

D₁₁

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

C₂×C₈

D₈₈

yes

—

C₂×C₈

C₂×D₄₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×D₄₄

yes

characteristic

C₁₆

—

C₁₁

#12513

yes

characteristic, complemented, Sylow

C₂³

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

#66927

yes

characteristic

C₂×C₄

C₂×D₈₈

yes

—

C₈

—

C₈

#66957

yes

—

C₂²

—

176

—

C₂²

—

176

—

C₂²

#10622308

yes

characteristic

C₄

—

176

—

C₄

#10622309

yes

—

C₄

#10622521

yes

—

C₂

—

352

—

C₂

#13068222

yes

characteristic

100

C₂

#13070882

yes

—

	subgroup	G/H
center	C₂²	#10622308
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1311	C₂
socle	C₂²×C₁₁	#493
prime radical	#13068231	C₂
hypercenter	#1311	D₁₁
hypocenter	C₁₁	#12513
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

subgroup

G/H

center

C₂²

#10622308

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#1311

C₂

C₂²×C₁₁

C₂

D₁₁

C₁₁

G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

N	H ≅ G/N	type
1. #13070840	C₂	semidirect
3. #13068226	C₂	semidirect
4. C₁₁×#1311	C₂	semidirect
36. #1311	D₁₁	semidirect
82. C₁₁	#12513	semidirect

H ≅ G/N

type

1. #13070840

C₂

semidirect

3. #13068226

C₂

semidirect

4. C₁₁×#1311

C₂

semidirect

36. #1311

D₁₁

semidirect

82. C₁₁

#12513

semidirect

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

subgroup	index
#13070840	2
#13068231	2
#13068226	2
C₁₁×#1311	2
#12513	11

subgroup

index

C₁₁×#1311

Subgroups — #14668477

Conjugacy classes of subgroups

Complements

Maximal subgroups