Group #14565772 — subgroups

Subgroups — #14565772

Order 2432.

142 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926949	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926369	C₂	1	2	yes	maximal, complemented
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926345	C₂	1	2	yes	maximal
5	C₄×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₁₉	—	2	1	no	—
8	#10597315	—	2	1	no	—
9	C₁₉×#107	C₂²	1	1	yes	characteristic
10	C₁₉×#102	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597275	—	2	1	no	—
13	#10597275	C₂²	1	2	yes	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×D₄×C₁₉	—	2	1	no	—
16	C₂²×C₄×C₁₉	—	4	1	no	—
17	C₂×Dic₃₈	—	4	1	no	—
18	D₈×C₁₉	—	2	1	no	—
19	D₈×C₁₉	Q₈	1	2	yes	complemented
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²⋊C₄×C₁₉	—	4	1	no	—
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	4	1	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	D₄×C₁₉	—	2	2	no	—
30	D₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	—	8	2	no	—
33	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₁₉	—	4	2	no	—
37	Dic₃₈	—	8	2	no	—
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₁₉	#41	1	1	yes	characteristic
41	#2224	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	4	2	no	—
43	C₂²×C₁₉	—	8	1	no	—
44	C₂²×C₁₉	—	8	1	no	—
45	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	1	no	—
48	C₄×C₁₉	D₁₆	1	2	yes	—
49	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
50	C₄×C₁₉	#137	1	1	yes	characteristic
51	Dic₁₉	—	8	2	no	—
52	#500	—	19	1	no	—
53	C₄×D₈	D₁₉	1	1	yes	characteristic
54	#366	—	19	2	no	—
55	C₄⋊C₁₆	—	19	1	no	—
56	#357	—	19	2	no	—
57	C₂×C₁₉	—	8	2	no	—
58	C₂×C₁₉	#474	1	1	yes	characteristic
59	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
60	C₂×C₁₉	#510	1	1	yes	characteristic
61	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
62	C₄⋊Q₈	—	38	1	no	—
63	C₄×D₄	—	2	1	no	—
64	C₂×C₁₆	—	19	2	no	—
65	#107	—	19	2	no	—
66	#107	—	38	1	no	—
67	#107	C₂×D₁₉	1	1	yes	characteristic
68	#102	—	2	1	no	—
69	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
70	C₁₉	#2224	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₈	—	76	1	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂²×C₄	—	4	1	no	—
74	D₈	—	2	1	no	—
75	D₈	Dic₃₈	1	2	yes	complemented
76	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	38	2	no	—
80	C₄⋊C₄	—	76	1	no	—
81	C₂²⋊C₄	—	4	1	no	—
82	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
83	C₁₆	—	38	2	no	—
84	C₂³	—	4	1	no	—
85	Q₈	—	152	2	no	—
86	D₄	—	2	2	no	—
87	D₄	—	4	1	no	—
88	C₂×C₄	—	4	1	no	—
89	C₂×C₄	—	8	2	no	—
90	C₂×C₄	—	76	2	no	—
91	C₂×C₄	#64525	1	1	yes	characteristic
92	C₂×C₄	#64525	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	C₂×Dic₃₈	1	1	yes	characteristic
96	C₈	#64541	1	1	yes	characteristic
97	C₂²	—	4	2	no	—
98	C₂²	—	8	1	no	—
99	C₂²	—	8	1	no	—
100	C₂²	C₂×#64525	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	8	1	no	—
103	C₄	—	152	2	no	—
104	C₄	#10597283	1	2	yes	—
105	C₄	#10597370	1	1	yes	characteristic
106	C₄	#10597397	1	1	yes	characteristic
107	C₂	—	8	2	no	—
108	C₂	#11926824	1	1	yes	characteristic
109	C₂	C₂×#10597283	1	1	yes	characteristic
110	C₂	#11926984	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic, complemented

#11926369

C₂

yes

maximal, complemented

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#11926345

C₂

yes

maximal

C₄×D₈×C₁₉

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₄×D₄×C₁₉

—

#10597315

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

—

#10597275

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₁₆

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

#500

—

C₄×D₈

D₁₉

yes

characteristic

#366

—

C₄⋊C₁₆

—

#357

—

C₂×C₁₉

—

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×D₁₆

yes

characteristic

C₂×C₁₉

#510

yes

characteristic

C₂×D₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×D₄

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₁₉

yes

characteristic

#102

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2224

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

Dic₃₈

yes

complemented

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

152

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

C₂×Dic₃₈

yes

characteristic

C₈

#64541

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#64525

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

152

—

104

C₄

#10597283

yes

—

105

C₄

#10597370

yes

characteristic

106

C₄

#10597397

yes

characteristic

107

C₂

—

108

C₂

#11926824

yes

characteristic

109

C₂

C₂×#10597283

yes

characteristic

110

C₂

#11926984

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×D₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	C₄×D₈	D₁₉
hypocenter	C₁₉	#2224
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×D₈×C₁₉

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

hypercenter

C₄×D₈

D₁₉

hypocenter

C₁₉

#2224

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. #11926949	C₂	semidirect
2. #11926369	C₂	semidirect
3. C₄⋊(C₁₉⋊C₁₆)	C₂	semidirect
19. D₈×C₁₉	Q₈	semidirect
70. C₁₉	#2224	semidirect
75. D₈	Dic₃₈	semidirect

H ≅ G/N

type

1. #11926949

C₂

semidirect

2. #11926369

C₂

semidirect

3. C₄⋊(C₁₉⋊C₁₆)

C₂

semidirect

19. D₈×C₁₉

Q₈

semidirect

70. C₁₉

#2224

semidirect

75. D₈

Dic₃₈

semidirect

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

subgroup	index
#11926949	2
#11926369	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926345	2
C₄×D₈×C₁₉	2
#2224	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₄×D₈×C₁₉

Subgroups — #14565772

Conjugacy classes of subgroups

Complements

Maximal subgroups