Group #14658458 — subgroups

Subgroups — #14658458

Order 2816.

328 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 79 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	#13067407	C₂	1	3	yes	maximal, complemented
2	#13067285	C₂	1	3	yes	maximal
3	C₁₁×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66927	C₂²	1	1	yes	characteristic
5	C₁₁×#423	C₂²	1	3	yes	—
6	#10622538	C₂²	1	3	yes	—
7	#10622123	—	2	3	no	—
8	#10622123	—	2	3	no	—
9	#10622118	—	2	3	no	—
10	#10622117	—	2	3	no	—
11	C₂²×D₄₄	—	2	3	no	—
12	C₂×C₁₁×M₁₆	—	2	3	no	—
13	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
14	#66927	—	2	3	no	—
15	#66927	Q₈	1	2	yes	—
16	C₁₁×C₄⋊C₈	—	2	3	no	—
17	C₁₁×C₄⋊C₈	—	2	3	no	—
18	C₂²⋊(C₁₁⋊C₈)	—	2	3	no	—
19	C₄⋊(C₁₁⋊C₈)	D₄	1	3	yes	—
20	C₄⋊(C₁₁⋊C₈)	D₄	1	3	yes	—
21	C₄×C₁₁⋊C₈	—	2	3	no	—
22	#10612	—	11	1	no	maximal, Sylow
23	C₂³×D₁₁	—	4	1	no	—
24	C₂²×C₄×C₁₁	#41	1	3	yes	—
25	C₂×D₄₄	—	2	6	no	—
26	C₂×D₄₄	—	4	3	no	—
27	C₂×D₄₄	—	8	3	no	—
28	C₂×D₄₄	—	8	3	no	—
29	C₁₁×M₁₆	—	8	3	no	—
30	C₂×C₈×C₁₁	—	4	3	no	—
31	C₄²×C₁₁	C₂×D₄	1	3	yes	—
32	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₁₁⋊C₈	—	2	3	no	—
34	C₂×C₁₁⋊C₈	—	2	3	no	—
35	#1574	—	11	3	no	—
36	#1545	—	11	3	no	—
37	#1309	D₁₁	1	1	yes	characteristic, complemented
38	C₂³×C₁₁	#126	1	1	yes	characteristic
39	C₂²×D₁₁	—	4	2	no	—
40	C₂²×D₁₁	—	8	6	no	—
41	C₂×C₄×C₁₁	—	2	3	no	—
42	C₂×C₄×C₁₁	—	2	3	no	—
43	C₂×C₄×C₁₁	#121	1	3	yes	—
44	C₂×C₄×C₁₁	C₂²⋊Q₈	1	3	yes	—
45	D₄₄	—	8	6	no	—
46	D₄₄	—	8	3	no	—
47	D₄₄	—	8	3	no	—
48	C₈×C₁₁	—	8	3	no	—
49	C₁₁⋊C₈	—	4	3	no	—
50	C₁₁⋊C₈	—	4	3	no	—
51	C₂×#127	—	11	1	no	—
52	#431	—	11	3	no	—
53	#423	C₂×D₁₁	1	3	yes	—
54	#335	—	22	3	no	—
55	#334	—	22	3	no	—
56	#331	—	22	3	no	—
57	#331	—	22	3	no	—
58	C₂²×C₁₁	—	2	3	no	—
59	C₂²×C₁₁	#396	1	1	yes	characteristic
60	C₂×D₁₁	—	8	6	no	—
61	C₂×D₁₁	—	16	4	no	—
62	C₄×C₁₁	—	2	3	no	—
63	C₄×C₁₁	#471	1	3	yes	—
64	C₄×C₁₁	#472	1	3	yes	—
65	C₂²×D₄	—	22	3	no	—
66	C₂×M₁₆	—	2	3	no	—
67	#127	—	11	2	no	—
68	#127	—	22	3	no	—
69	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
70	C₄⋊C₈	—	2	3	no	—
71	C₄⋊C₈	—	2	3	no	—
72	C₄⋊C₈	—	11	3	no	—
73	C₄⋊C₈	—	11	3	no	—
74	C₂²⋊C₈	—	22	3	no	—
75	C₄×C₈	—	22	3	no	—
76	C₂×C₁₁	—	4	1	no	—
77	C₂×C₁₁	#2063	1	3	yes	—
78	D₁₁	—	16	2	no	—
79	C₂⁴	—	44	1	no	—
80	C₂×D₄	—	22	6	no	—
81	C₂×D₄	—	44	3	no	—
82	C₂×D₄	—	88	3	no	—
83	C₂×D₄	—	88	3	no	—
84	C₂²×C₄	#4339	1	3	yes	—
85	M₁₆	—	8	3	no	—
86	C₂×C₈	—	4	3	no	—
87	C₂×C₈	—	22	3	no	—
88	C₂×C₈	—	22	3	no	—
89	C₄²	D₄×D₁₁	1	3	yes	—
90	C₄²	Q₈×D₁₁	1	1	yes	characteristic
91	C₁₁	#10612	1	1	yes	characteristic, complemented, Sylow
92	C₂³	—	44	2	no	—
93	C₂³	—	88	6	no	—
94	C₂³	#66929	1	1	yes	characteristic
95	D₄	—	88	6	no	—
96	D₄	—	88	3	no	—
97	D₄	—	88	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	#66937	1	3	yes	—
101	C₂×C₄	#66949	1	3	yes	—
102	C₈	—	8	3	no	—
103	C₈	—	44	3	no	—
104	C₈	—	44	3	no	—
105	C₂²	—	2	3	no	—
106	C₂²	—	88	6	no	—
107	C₂²	—	176	4	no	—
108	C₂²	#10622289	1	1	yes	characteristic
109	C₄	—	2	3	no	—
110	C₄	#10622362	1	3	yes	—
111	C₄	#10622367	1	3	yes	—
112	C₂	—	4	1	no	—
113	C₂	—	176	2	no	—
114	C₂	#13069977	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13067407

C₂

yes

maximal, complemented

#13067285

C₂

yes

maximal

C₁₁×#1309

C₂

yes

maximal, characteristic, complemented

C₂×#66927

C₂²

yes

characteristic

C₁₁×#423

C₂²

yes

—

#10622538

C₂²

yes

—

—

—

—

—

C₂²×D₄₄

—

C₂×C₁₁×M₁₆

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

#66927

—

#66927

Q₈

yes

—

C₁₁×C₄⋊C₈

—

C₁₁×C₄⋊C₈

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#10612

—

maximal, Sylow

C₂³×D₁₁

—

C₂²×C₄×C₁₁

#41

yes

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1574

—

#1545

—

#1309

D₁₁

yes

characteristic, complemented

C₂³×C₁₁

#126

yes

characteristic

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

D₄₄

—

D₄₄

—

D₄₄

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂×#127

—

#431

—

#423

C₂×D₁₁

yes

—

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#396

yes

characteristic

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#471

yes

—

C₄×C₁₁

#472

yes

—

C₂²×D₄

—

C₂×M₁₆

—

#127

—

#127

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×C₁₁

—

C₂×C₁₁

#2063

yes

—

D₁₁

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

#4339

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

D₄×D₁₁

yes

—

C₄²

Q₈×D₁₁

yes

characteristic

C₁₁

#10612

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

#66929

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#66937

yes

—

101

C₂×C₄

#66949

yes

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

176

—

108

C₂²

#10622289

yes

characteristic

109

C₄

—

110

C₄

#10622362

yes

—

111

C₄

#10622367

yes

—

112

C₂

—

113

C₂

—

176

—

114

C₂

#13069977

yes

—

	subgroup	G/H
center	C₂²	#10622289
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1309	C₂
socle	C₂²×C₁₁	#396
prime radical	C₂×#66927	C₂²
hypercenter	#1309	D₁₁
hypocenter	C₁₁	#10612
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#10622289

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1309

C₂

C₂²×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
1. #13067407	C₂	semidirect
3. C₁₁×#1309	C₂	semidirect
37. #1309	D₁₁	semidirect
91. C₁₁	#10612	semidirect

H ≅ G/N

type

1. #13067407

C₂

semidirect

3. C₁₁×#1309

C₂

semidirect

37. #1309

D₁₁

semidirect

91. C₁₁

#10612

semidirect

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

subgroup	index
#13067407	2
#13067285	2
C₁₁×#1309	2
#10612	11

subgroup

index

#13067407

#13067285

C₁₁×#1309

#10612

Subgroups — #14658458

Conjugacy classes of subgroups

Complements

Maximal subgroups