Group #14647577 — subgroups

Subgroups — #14647577

Order 2816.

354 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 203 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	#13068788	C₂	1	2	yes	maximal
2	#13067375	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	—	2	4	no	—
7	#10622537	C₂²	1	4	yes	—
8	C₈²×C₁₁	C₄	1	1	yes	characteristic
9	C₈²×C₁₁	C₄	1	2	yes	—
10	C₈²×C₁₁	C₄	1	1	yes	characteristic
11	#10622096	—	2	8	no	—
12	C₂²×C₈×C₁₁	D₄	1	2	yes	—
13	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
14	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×#4318	—	2	4	no	—
16	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₁	D₄	1	4	yes	—
21	C₄×C₈×C₁₁	Q₈	1	2	yes	—
22	#66883	—	4	8	no	—
23	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
24	#8823	—	11	1	no	maximal, Sylow
25	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
27	C₂×C₈×C₁₁	—	2	8	no	—
28	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
29	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₁	D₈	1	4	yes	—
33	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
34	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₄²×C₁₁	C₂×D₄	1	2	yes	—
36	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
37	#4318	—	4	8	no	—
38	C₂×C₁₁⋊C₈	—	4	4	no	—
39	#1848	—	11	2	no	—
40	#1567	—	11	4	no	—
41	C₂×C₈²	D₁₁	1	1	yes	characteristic
42	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₁	—	2	4	no	—
44	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
47	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
48	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
49	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
50	C₈×C₁₁	—	2	4	no	—
51	C₈×C₁₁	#107	1	4	yes	—
52	C₈×C₁₁	#107	1	4	yes	—
53	C₈×C₁₁	#108	1	8	yes	complemented
54	C₁₁⋊C₈	—	8	4	no	—
55	C₂×#108	—	22	4	no	—
56	#423	—	11	4	no	—
57	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
59	#335	—	22	8	no	—
60	C₈²	Dic₁₁	1	1	yes	characteristic
61	C₈²	Dic₁₁	1	2	yes	—
62	C₈²	Dic₁₁	1	1	yes	characteristic
63	C₂²×C₁₁	—	2	2	no	—
64	C₂²×C₁₁	#384	1	1	yes	characteristic
65	C₂²×C₁₁	#500	1	2	yes	—
66	C₄×C₁₁	—	2	2	no	—
67	C₄×C₁₁	C₂×#107	1	2	yes	—
68	C₄×C₁₁	C₂×#108	1	4	yes	—
69	C₄×C₁₁	#493	1	1	yes	characteristic
70	C₄×C₁₁	#494	1	1	yes	characteristic
71	C₂×M₁₆	—	22	4	no	—
72	C₂²×C₈	Dic₂₂	1	4	yes	—
73	C₂²×C₈	D₄₄	1	2	yes	—
74	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
75	#108	—	44	8	no	—
76	C₄⋊C₈	—	22	8	no	—
77	C₄×C₈	Dic₂₂	1	2	yes	—
78	C₄×C₈	D₄₄	1	4	yes	—
79	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
80	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
81	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
82	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
83	C₂×C₁₁	—	2	2	no	—
84	C₂×C₁₁	#1845	1	1	yes	characteristic
85	C₂×C₁₁	#1848	1	2	yes	—
86	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
87	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
88	M₁₆	—	44	8	no	—
89	C₂×C₈	—	2	8	no	—
90	C₂×C₈	—	44	4	no	—
91	C₂×C₈	D₈₈	1	4	yes	—
92	C₂×C₈	Dic₄₄	1	4	yes	—
93	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
94	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
95	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
96	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
97	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
98	C₄²	C₂×D₄₄	1	2	yes	—
99	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
100	C₁₁	#8823	1	1	yes	characteristic, complemented, Sylow
101	C₂³	#66922	1	1	yes	characteristic
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	#66922	1	2	yes	—
104	C₂×C₄	#66927	1	1	yes	characteristic
105	C₂×C₄	C₂×D₈₈	1	2	yes	—
106	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
107	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
108	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
109	C₈	—	2	4	no	—
110	C₈	—	88	4	no	—
111	C₈	#66882	1	4	yes	—
112	C₈	#66882	1	4	yes	—
113	C₈	#66883	1	8	yes	complemented
114	C₂²	—	2	2	no	—
115	C₂²	#10622295	1	2	yes	—
116	C₂²	#10622548	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	#10622308	1	1	yes	characteristic
119	C₄	#10622312	1	1	yes	characteristic
120	C₄	C₂×#66882	1	2	yes	—
121	C₄	C₂×#66883	1	4	yes	—
122	C₂	—	2	2	no	—
123	C₂	#13068776	1	1	yes	characteristic
124	C₂	#13068788	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal

#13067375

C₂

yes

maximal

C₂×C₈²×C₁₁

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622537

C₂²

yes

—

C₈²×C₁₁

C₄

yes

characteristic

C₈²×C₁₁

C₄

yes

—

C₈²×C₁₁

C₄

yes

characteristic

#10622096

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#8823

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

#1848

—

#1567

—

C₂×C₈²

D₁₁

yes

characteristic

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

#107

yes

—

C₈×C₁₁

#107

yes

—

C₈×C₁₁

#108

yes

complemented

C₁₁⋊C₈

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

#335

—

C₈²

Dic₁₁

yes

characteristic

C₈²

Dic₁₁

yes

—

C₈²

Dic₁₁

yes

characteristic

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#500

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#107

yes

—

C₄×C₁₁

C₂×#108

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂²×C₈

Dic₂₂

yes

—

C₂²×C₈

D₄₄

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1845

yes

characteristic

C₂×C₁₁

#1848

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₈₈

yes

—

C₂×C₈

Dic₄₄

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄²

C₂×Dic₂₂

yes

characteristic

C₄²

C₂×D₄₄

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

100

C₁₁

#8823

yes

characteristic, complemented, Sylow

101

C₂³

#66922

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

#66922

yes

—

104

C₂×C₄

#66927

yes

characteristic

105

C₂×C₄

C₂×D₈₈

yes

—

106

C₂×C₄

C₂×Dic₄₄

yes

—

107

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

108

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

#66882

yes

—

112

C₈

#66882

yes

—

113

C₈

#66883

yes

complemented

114

C₂²

—

115

C₂²

#10622295

yes

—

116

C₂²

#10622548

yes

characteristic

117

C₄

—

118

C₄

#10622308

yes

characteristic

119

C₄

#10622312

yes

characteristic

120

C₄

C₂×#66882

yes

—

121

C₄

C₂×#66883

yes

—

122

C₂

—

123

C₂

#13068776

yes

characteristic

124

C₂

#13068788

yes

—

	subgroup	G/H
center	C₂×C₄	#66927
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₈²×C₁₁	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈²	D₁₁
hypocenter	C₁₁	#8823
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂×C₄

#66927

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₂×C₈²×C₁₁

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

hypercenter

C₂×C₈²

D₁₁

hypocenter

C₁₁

#8823

LCS

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
53. C₈×C₁₁	#108	semidirect
100. C₁₁	#8823	semidirect
113. C₈	#66883	semidirect

H ≅ G/N

type

53. C₈×C₁₁

#108

semidirect

100. C₁₁

#8823

semidirect

113. C₈

#66883

semidirect

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

subgroup	index
#13068788	2
#13067375	2
C₂×C₈²×C₁₁	2
#8823	11

subgroup

index

#13068788

#13067375

C₂×C₈²×C₁₁

#8823

Subgroups — #14647577

Conjugacy classes of subgroups

Complements

Maximal subgroups