Group #14561744 — subgroups

Subgroups — #14561744

Order 2432.

136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₂×#10597276	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₉	—	2	1	no	—
6	C₂×#64520	—	2	1	no	—
7	C₁₉×M₃₂	—	2	1	no	—
8	C₁₉×M₃₂	C₄	1	2	yes	complemented
9	C₂×C₁₆×C₁₉	—	2	1	no	—
10	#10597276	—	2	1	no	—
11	#10597276	C₄	1	2	yes	complemented
12	#10597275	—	2	1	no	—
13	#10597275	C₄	1	2	yes	—
14	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×Dic₁₉	—	4	1	no	—
16	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
22	C₄⋊Dic₁₉	—	2	2	no	—
23	C₄⋊Dic₁₉	—	4	1	no	—
24	#64520	—	2	2	no	—
25	#64520	—	4	1	no	—
26	C₂×C₁₉⋊C₈	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₁₉	—	4	2	no	—
36	C₂×Dic₁₉	—	8	2	no	—
37	C₈×C₁₉	C₄²	1	1	yes	characteristic
38	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₁₉⋊C₈	—	4	2	no	—
42	#1387	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	#102	1	1	yes	characteristic
46	C₂²×C₁₉	#103	1	1	yes	characteristic
47	C₂²×C₁₉	#106	1	1	yes	characteristic
48	C₄×C₁₉	#95	1	1	yes	characteristic
49	C₄×C₁₉	#102	1	1	yes	characteristic
50	C₄×C₁₉	#103	1	1	yes	characteristic
51	C₄×C₁₉	#107	1	1	yes	characteristic
52	Dic₁₉	—	8	2	no	—
53	C₂×M₃₂	D₁₉	1	1	yes	characteristic
54	C₂×#108	—	19	1	no	—
55	C₂×#107	—	19	1	no	—
56	C₂×C₁₉	—	2	1	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	#340	1	1	yes	characteristic
59	C₂×C₁₉	#361	1	1	yes	characteristic
60	C₂×C₁₉	#362	1	1	yes	characteristic
61	C₂×M₁₆	—	38	1	no	—
62	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
63	C₂×C₄⋊C₄	—	38	1	no	—
64	M₃₂	—	2	1	no	—
65	M₃₂	Dic₁₉	1	2	yes	complemented
66	C₂×C₁₆	—	2	1	no	—
67	#108	—	19	2	no	—
68	#108	—	38	1	no	—
69	#107	—	19	2	no	—
70	#107	—	38	1	no	—
71	C₁₉	#1387	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	76	1	no	—
73	C₂²×C₄	D₇₆	1	1	yes	characteristic
74	M₁₆	—	38	2	no	—
75	M₁₆	—	76	1	no	—
76	C₂×C₈	—	76	1	no	—
77	C₂×C₈	Dic₃₈	1	1	yes	characteristic
78	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
79	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
81	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
83	C₄⋊C₄	—	38	2	no	—
84	C₄⋊C₄	—	76	1	no	—
85	C₁₆	—	2	2	no	—
86	C₂³	#64516	1	1	yes	characteristic
87	C₂×C₄	—	76	2	no	—
88	C₂×C₄	—	152	2	no	—
89	C₂×C₄	#64516	1	1	yes	characteristic
90	C₂×C₄	D₁₅₂	1	1	yes	characteristic
91	C₂×C₄	Dic₇₆	1	1	yes	characteristic
92	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
93	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
95	C₈	—	76	2	no	—
96	C₈	C₄×Dic₁₉	1	1	yes	characteristic
97	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
98	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
99	C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	#10597273	1	1	yes	characteristic
103	C₂²	#10597274	1	1	yes	characteristic
104	C₂²	#10597278	1	1	yes	characteristic
105	C₄	—	152	2	no	—
106	C₄	#10597273	1	1	yes	characteristic
107	C₄	#10597275	1	1	yes	characteristic
108	C₄	#10597278	1	1	yes	characteristic
109	C₄	C₁₉⋊#95	1	1	yes	characteristic
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#11926307	1	1	yes	characteristic
113	C₂	#11926358	1	1	yes	characteristic
114	C₂	#11926361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597276

C₂

yes

maximal, characteristic

C₂×#10597275

C₂

yes

maximal, characteristic

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×#64520

—

C₁₉×M₃₂

—

C₁₉×M₃₂

C₄

yes

complemented

C₂×C₁₆×C₁₉

—

#10597276

—

#10597276

C₄

yes

complemented

#10597275

—

#10597275

C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₂³×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

C₄²

yes

characteristic

C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

—

#1387

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×M₃₂

D₁₉

yes

characteristic

C₂×#108

—

C₂×#107

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

M₃₂

—

M₃₂

Dic₁₉

yes

complemented

C₂×C₁₆

—

—

—

—

—

C₁₉

#1387

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₁₆

—

C₂³

#64516

yes

characteristic

C₂×C₄

—

C₂×C₄

—

152

—

C₂×C₄

#64516

yes

characteristic

C₂×C₄

D₁₅₂

yes

characteristic

C₂×C₄

Dic₇₆

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₈

—

C₈

C₄×Dic₁₉

yes

characteristic

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₁₉

yes

characteristic

100

C₂²

—

101

C₂²

—

102

C₂²

#10597273

yes

characteristic

103

C₂²

#10597274

yes

characteristic

104

C₂²

#10597278

yes

characteristic

105

C₄

—

152

—

106

C₄

#10597273

yes

characteristic

107

C₄

#10597275

yes

characteristic

108

C₄

#10597278

yes

characteristic

109

C₄

C₁₉⋊#95

yes

characteristic

110

C₂

—

111

C₂

—

112

C₂

#11926307

yes

characteristic

113

C₂

#11926358

yes

characteristic

114

C₂

#11926361

yes

characteristic

	subgroup	G/H
center	C₂²	#10597278
commutator	C₈×C₁₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂²×C₁₉	#102
prime radical	C₂³×C₁₉	SD₁₆
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#1387
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

#10597278

commutator

C₈×C₁₉

C₄²

Frattini

C₂²×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×M₃₂

C₂

socle

C₂²×C₁₉

#102

prime radical

C₂³×C₁₉

SD₁₆

cosocle

C₂²×C₈×C₁₉

C₂²

hypercenter

C₂×M₃₂

D₁₉

hypocenter

C₁₉

#1387

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
8. C₁₉×M₃₂	C₄	semidirect
11. #10597276	C₄	semidirect
65. M₃₂	Dic₁₉	semidirect
71. C₁₉	#1387	semidirect

H ≅ G/N

type

8. C₁₉×M₃₂

C₄

semidirect

11. #10597276

C₄

semidirect

65. M₃₂

Dic₁₉

semidirect

71. C₁₉

#1387

semidirect

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

subgroup	index
C₂×#10597276	2
C₂×#10597275	2
C₂×C₁₉×M₃₂	2
#1387	19

subgroup

index

C₂×#10597276

C₂×#10597275

C₂×C₁₉×M₃₂

#1387

Subgroups — #14561744

Conjugacy classes of subgroups

Complements

Maximal subgroups