Group #14658823 — subgroups

Subgroups — #14658823

Order 2816.

526 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 165 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	#13069422	C₂	1	3	yes	maximal
2	#13068776	C₂	1	3	yes	maximal, complemented
3	C₁₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66927	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
6	C₂×#66885	—	2	6	no	—
7	C₂×#66882	—	2	6	no	—
8	#10622548	C₂²	1	3	yes	—
9	C₂²×D₄₄	—	2	3	no	—
10	C₂²×C₈×C₁₁	D₄	1	6	yes	—
11	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₁	—	2	3	no	—
13	C₂×C₄⋊Dic₁₁	—	2	6	no	—
14	#66927	—	2	3	no	—
15	#66927	Q₈	1	2	yes	—
16	C₄×C₈×C₁₁	—	2	6	no	—
17	#66885	—	4	12	no	—
18	#66882	—	4	12	no	—
19	#10673	—	11	1	no	maximal, Sylow
20	C₂³×D₁₁	—	4	1	no	—
21	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
22	C₂²×Dic₁₁	—	4	3	no	—
23	C₂×D₄₄	—	2	6	no	—
24	C₂×D₄₄	—	4	3	no	—
25	C₂×D₄₄	—	4	6	no	—
26	C₂×D₄₄	—	4	6	no	—
27	C₂×C₈×C₁₁	—	2	6	no	—
28	C₂×C₈×C₁₁	—	2	6	no	—
29	C₂×C₈×C₁₁	D₈	1	12	yes	—
30	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
31	C₄²×C₁₁	#41	1	3	yes	—
32	C₄⋊Dic₁₁	—	4	12	no	—
33	C₄⋊Dic₁₁	—	4	6	no	—
34	#1957	—	11	3	no	—
35	#1845	—	11	3	no	—
36	#1273	D₁₁	1	1	yes	characteristic, complemented
37	C₂³×C₁₁	#127	1	1	yes	characteristic
38	C₂²×D₁₁	—	4	2	no	—
39	C₂²×D₁₁	—	8	3	no	—
40	C₂²×D₁₁	—	8	3	no	—
41	C₂×C₄×C₁₁	C₂²⋊Q₈	1	3	yes	—
42	C₂×C₄×C₁₁	#123	1	3	yes	—
43	C₂×C₄×C₁₁	C₂×D₈	1	6	yes	—
44	C₂×C₄×C₁₁	#137	1	6	yes	—
45	C₂×Dic₁₁	—	8	6	no	—
46	C₂×Dic₁₁	—	8	3	no	—
47	D₄₄	—	4	12	no	—
48	D₄₄	—	8	6	no	—
49	C₈×C₁₁	—	2	12	no	—
50	C₂×#127	—	11	1	no	—
51	C₂×#107	—	22	6	no	—
52	C₂×#102	—	22	6	no	—
53	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
54	#384	—	11	3	no	—
55	C₂²×C₁₁	#399	1	1	yes	characteristic
56	C₂²×C₁₁	#493	1	3	yes	—
57	C₂²×C₁₁	#497	1	3	yes	—
58	C₂×D₁₁	—	8	6	no	—
59	C₂×D₁₁	—	16	1	no	—
60	C₂×D₁₁	—	16	3	no	—
61	C₄×C₁₁	#474	1	6	yes	—
62	C₄×C₁₁	#480	1	6	yes	—
63	Dic₁₁	—	16	3	no	—
64	C₂²×D₄	—	22	3	no	—
65	C₂²×C₈	D₄₄	1	6	yes	—
66	#127	—	11	2	no	—
67	#127	—	22	3	no	—
68	C₂×C₄⋊C₄	—	22	3	no	—
69	C₂×C₄⋊C₄	—	22	6	no	—
70	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
71	#107	—	44	12	no	—
72	#102	—	44	12	no	—
73	C₄×C₈	—	2	6	no	—
74	C₂×C₁₁	#1712	1	1	yes	characteristic
75	C₂×C₁₁	#1722	1	3	yes	—
76	C₂×C₁₁	#2093	1	3	yes	—
77	D₁₁	—	16	2	no	—
78	C₂⁴	—	44	1	no	—
79	C₂×D₄	—	22	6	no	—
80	C₂×D₄	—	44	3	no	—
81	C₂×D₄	—	44	6	no	—
82	C₂×D₄	—	44	6	no	—
83	C₂²×C₄	—	44	3	no	—
84	C₂²×C₄	C₂×D₄₄	1	3	yes	—
85	C₂×C₈	—	2	6	no	—
86	C₂×C₈	—	2	6	no	—
87	C₂×C₈	D₈₈	1	12	yes	—
88	C₄⋊C₄	—	44	6	no	—
89	C₄⋊C₄	—	44	12	no	—
90	C₄²	#4341	1	3	yes	—
91	C₄²	Q₈×D₁₁	1	1	yes	characteristic
92	C₁₁	#10673	1	1	yes	characteristic, complemented, Sylow
93	C₂³	—	44	2	no	—
94	C₂³	—	88	3	no	—
95	C₂³	—	88	3	no	—
96	C₂³	#66927	1	1	yes	characteristic
97	D₄	—	44	12	no	—
98	D₄	—	88	6	no	—
99	C₂×C₄	—	88	3	no	—
100	C₂×C₄	—	88	6	no	—
101	C₂×C₄	#66939	1	3	yes	—
102	C₂×C₄	#66950	1	3	yes	—
103	C₂×C₄	C₂×D₈₈	1	6	yes	—
104	C₂×C₄	#66962	1	6	yes	—
105	C₈	—	2	12	no	—
106	C₂²	—	88	6	no	—
107	C₂²	—	176	1	no	—
108	C₂²	—	176	3	no	—
109	C₂²	#10622290	1	1	yes	characteristic
110	C₂²	#10622308	1	3	yes	—
111	C₂²	#10622328	1	3	yes	—
112	C₄	—	176	3	no	—
113	C₄	#10622349	1	6	yes	—
114	C₄	#10622459	1	6	yes	—
115	C₂	—	176	2	no	—
116	C₂	#13068231	1	1	yes	characteristic
117	C₂	#13068287	1	3	yes	—
118	C₂	#13070143	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13069422

C₂

yes

maximal

#13068776

C₂

yes

maximal, complemented

C₁₁×#1273

C₂

yes

maximal, characteristic, complemented

C₂×#66927

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×#66885

—

C₂×#66882

—

#10622548

C₂²

yes

—

C₂²×D₄₄

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₂×C₄⋊Dic₁₁

—

#66927

—

#66927

Q₈

yes

—

C₄×C₈×C₁₁

—

—

—

—

C₂³×D₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×Dic₁₁

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

D₈

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

#1957

—

#1845

—

#1273

D₁₁

yes

characteristic, complemented

C₂³×C₁₁

#127

yes

characteristic

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂×C₄×C₁₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₁

#123

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

D₄₄

—

D₄₄

—

C₈×C₁₁

—

C₂×#127

—

C₂×#107

—

C₂×#102

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

#384

—

C₂²×C₁₁

#399

yes

characteristic

C₂²×C₁₁

#493

yes

—

C₂²×C₁₁

#497

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

#474

yes

—

C₄×C₁₁

#480

yes

—

Dic₁₁

—

C₂²×D₄

—

C₂²×C₈

D₄₄

yes

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#107

—

#102

—

C₄×C₈

—

C₂×C₁₁

#1712

yes

characteristic

C₂×C₁₁

#1722

yes

—

C₂×C₁₁

#2093

yes

—

D₁₁

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₈₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#4341

yes

—

C₄²

Q₈×D₁₁

yes

characteristic

C₁₁

#10673

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

#66927

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

#66939

yes

—

102

C₂×C₄

#66950

yes

—

103

C₂×C₄

C₂×D₈₈

yes

—

104

C₂×C₄

#66962

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

—

176

—

108

C₂²

—

176

—

109

C₂²

#10622290

yes

characteristic

110

C₂²

#10622308

yes

—

111

C₂²

#10622328

yes

—

112

C₄

—

176

—

113

C₄

#10622349

yes

—

114

C₄

#10622459

yes

—

115

C₂

—

176

—

116

C₂

#13068231

yes

characteristic

117

C₂

#13068287

yes

—

118

C₂

#13070143

yes

—

	subgroup	G/H
center	C₂³	#66927
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1273	C₂
socle	C₂³×C₁₁	#127
prime radical	C₂×#66927	C₂²
hypercenter	#1273	D₁₁
hypocenter	C₁₁	#10673
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#66927

commutator, cosocle

C₂×C₄²×C₁₁

C₂³

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1273

C₂

C₂³×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. #13068776	C₂	semidirect
3. C₁₁×#1273	C₂	semidirect
36. #1273	D₁₁	semidirect
92. C₁₁	#10673	semidirect

H ≅ G/N

type

2. #13068776

C₂

semidirect

3. C₁₁×#1273

C₂

semidirect

36. #1273

D₁₁

semidirect

92. C₁₁

#10673

semidirect

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

subgroup	index
#13069422	2
#13068776	2
C₁₁×#1273	2
#10673	11

subgroup

index

#13069422

#13068776

C₁₁×#1273

#10673

Subgroups — #14658823

Conjugacy classes of subgroups

Complements

Maximal subgroups