Group #14647458 — subgroups

Subgroups — #14647458

Order 2816.

262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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	#13068754	C₂	1	1	yes	maximal, characteristic
2	#13068747	C₂	1	1	yes	maximal, characteristic
3	#13066475	C₂	1	4	yes	maximal
4	C₁₁×#1450	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#431	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	#10622549	C₂²	1	2	yes	—
8	#10622537	C₂²	1	2	yes	—
9	C₁₁×#322	C₄	1	2	yes	complemented
10	C₈²×C₁₁	C₄	1	2	yes	complemented
11	#10622190	—	2	2	no	—
12	#10622189	—	2	2	no	—
13	C₂²×C₈×C₁₁	D₄	1	2	yes	—
14	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄⋊Dic₁₁	—	2	2	no	—
16	C₂×#4318	—	2	2	no	—
17	C₁₁×C₄⋊C₈	—	2	2	no	—
18	C₁₁×C₂²⋊C₈	—	2	2	no	—
19	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	Q₈	1	2	yes	—
23	C₁₁⋊#95	—	2	4	no	—
24	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
25	#8791	—	11	1	no	maximal, Sylow
26	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₁	#41	1	2	yes	—
28	C₂²×Dic₁₁	—	4	2	no	—
29	C₂×C₈×C₁₁	—	2	4	no	—
30	C₂×C₈×C₁₁	—	2	4	no	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
35	C₄²×C₁₁	#41	1	2	yes	—
36	C₄⋊Dic₁₁	—	4	4	no	—
37	#4318	—	4	4	no	—
38	C₂×C₁₁⋊C₈	—	4	2	no	—
39	#1837	—	11	1	no	—
40	#1835	—	11	1	no	—
41	#1450	D₁₁	1	1	yes	characteristic
42	#1286	—	11	4	no	—
43	C₂³×C₁₁	#124	1	1	yes	characteristic
44	C₂×C₄×C₁₁	—	4	2	no	—
45	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₁	#117	1	2	yes	—
47	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
48	C₂×C₄×C₁₁	#125	1	2	yes	—
49	C₂×C₄×C₁₁	#135	1	4	yes	—
50	C₂×Dic₁₁	—	8	4	no	—
51	C₂×Dic₁₁	—	8	2	no	—
52	C₈×C₁₁	—	2	2	no	—
53	C₈×C₁₁	—	2	2	no	—
54	C₈×C₁₁	—	4	4	no	—
55	C₁₁⋊C₈	—	8	2	no	—
56	#431	C₂×D₁₁	1	2	yes	—
57	#423	—	11	2	no	—
58	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
59	#382	—	11	2	no	—
60	#341	—	22	2	no	—
61	#340	—	22	2	no	—
62	#322	Dic₁₁	1	2	yes	complemented
63	C₈²	Dic₁₁	1	2	yes	complemented
64	C₂²×C₁₁	—	2	2	no	—
65	C₂²×C₁₁	#382	1	1	yes	characteristic
66	C₂²×C₁₁	#488	1	2	yes	—
67	C₄×C₁₁	—	2	2	no	—
68	C₄×C₁₁	—	2	2	no	—
69	C₄×C₁₁	#427	1	2	yes	—
70	C₄×C₁₁	#488	1	2	yes	—
71	Dic₁₁	—	16	2	no	—
72	C₂×M₁₆	—	22	2	no	—
73	C₂²×C₈	D₄₄	1	2	yes	—
74	C₂×C₄⋊C₄	—	22	2	no	—
75	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
76	C₄⋊C₈	—	2	2	no	—
77	C₄⋊C₈	—	22	4	no	—
78	C₂²⋊C₈	—	2	2	no	—
79	C₄×C₈	Dic₂₂	1	2	yes	—
80	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
81	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
82	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
83	#95	—	22	4	no	—
84	C₂×C₁₁	—	2	2	no	—
85	C₂×C₁₁	#1833	1	2	yes	—
86	C₂×C₁₁	#1835	1	1	yes	characteristic
87	C₂²×C₄	—	44	2	no	—
88	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
89	C₂²×C₄	#4339	1	2	yes	—
90	M₁₆	—	44	4	no	—
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	2	4	no	—
93	C₂×C₈	—	44	2	no	—
94	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
95	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
96	C₄⋊C₄	—	44	4	no	—
97	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
98	C₄²	#4339	1	2	yes	—
99	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
100	C₁₁	#8791	1	1	yes	characteristic, complemented, Sylow
101	C₂³	#66928	1	1	yes	characteristic
102	C₂×C₄	—	4	2	no	—
103	C₂×C₄	—	88	4	no	—
104	C₂×C₄	—	88	2	no	—
105	C₂×C₄	#66923	1	2	yes	—
106	C₂×C₄	#66928	1	1	yes	characteristic
107	C₂×C₄	#66957	1	4	yes	—
108	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
109	C₂×C₄	#66979	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	2	2	no	—
112	C₈	—	4	4	no	—
113	C₈	—	88	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#10622310	1	2	yes	—
116	C₂²	#10622549	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	2	2	no	—
119	C₄	—	176	2	no	—
120	C₄	#10622310	1	2	yes	—
121	C₄	#10622719	1	2	yes	—
122	C₂	—	2	2	no	—
123	C₂	#13068740	1	2	yes	—
124	C₂	#13068747	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068754

C₂

yes

maximal, characteristic

#13068747

C₂

yes

maximal, characteristic

#13066475

C₂

yes

maximal

C₁₁×#1450

C₂

yes

maximal, characteristic

C₁₁×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622549

C₂²

yes

—

#10622537

C₂²

yes

—

C₁₁×#322

C₄

yes

complemented

C₈²×C₁₁

C₄

yes

complemented

#10622190

—

#10622189

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×#4318

—

C₁₁×C₄⋊C₈

—

C₁₁×C₂²⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

Q₈

yes

—

C₁₁⋊#95

—

C₄⋊(C₁₁⋊C₈)

—

#8791

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₄⋊Dic₁₁

—

#4318

—

C₂×C₁₁⋊C₈

—

#1837

—

#1835

—

#1450

D₁₁

yes

characteristic

#1286

—

C₂³×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

#125

yes

—

C₂×C₄×C₁₁

#135

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

#431

C₂×D₁₁

yes

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

Dic₁₁

yes

complemented

C₈²

Dic₁₁

yes

complemented

C₂²×C₁₁

—

C₂²×C₁₁

#382

yes

characteristic

C₂²×C₁₁

#488

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#427

yes

—

C₄×C₁₁

#488

yes

—

Dic₁₁

—

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

characteristic

#95

—

C₂×C₁₁

—

C₂×C₁₁

#1833

yes

—

C₂×C₁₁

#1835

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

C₂²×C₄

#4339

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄⋊C₄

—

C₄²

C₂×Dic₂₂

yes

characteristic

C₄²

#4339

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

100

C₁₁

#8791

yes

characteristic, complemented, Sylow

101

C₂³

#66928

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

#66923

yes

—

106

C₂×C₄

#66928

yes

characteristic

107

C₂×C₄

#66957

yes

—

108

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

109

C₂×C₄

#66979

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

#10622310

yes

—

116

C₂²

#10622549

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

176

—

120

C₄

#10622310

yes

—

121

C₄

#10622719

yes

—

122

C₂

—

123

C₂

#13068740

yes

—

124

C₂

#13068747

yes

characteristic

	subgroup	G/H
center	C₂²	#10622549
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1450	C₂
socle	C₂²×C₁₁	#382
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1450	D₁₁
hypocenter	C₁₁	#8791
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

subgroup

G/H

center

C₂²

#10622549

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1450

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1450

N	H ≅ G/N	type
9. C₁₁×#322	C₄	semidirect
10. C₈²×C₁₁	C₄	semidirect
62. #322	Dic₁₁	semidirect
63. C₈²	Dic₁₁	semidirect
100. C₁₁	#8791	semidirect

H ≅ G/N

type

9. C₁₁×#322

C₄

semidirect

10. C₈²×C₁₁

C₄

semidirect

62. #322

Dic₁₁

semidirect

63. C₈²

Dic₁₁

semidirect

100. C₁₁

#8791

semidirect

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

subgroup	index
#13068754	2
#13068747	2
#13066475	2
C₁₁×#1450	2
#8791	11

subgroup

index

C₁₁×#1450

Subgroups — #14647458

Conjugacy classes of subgroups

Complements

Maximal subgroups