Group #14561665 — subgroups

Subgroups — #14561665

Order 2432.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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	#11926313	C₂	1	1	yes	maximal, characteristic
2	#11926270	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#395	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
6	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64520	—	2	1	no	—
8	C₁₉×#95	—	2	1	no	—
9	C₁₉×#95	C₄	1	1	yes	characteristic
10	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂×Q₈×C₁₉	—	4	2	no	—
12	C₂×Q₈×C₁₉	—	4	1	no	—
13	C₂²×C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄×C₁₉	—	2	1	no	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₄⋊C₄×C₁₉	—	4	2	no	—
20	#64520	—	2	2	no	—
21	#64520	—	4	1	no	—
22	C₂×C₁₉⋊C₈	—	4	1	no	—
23	C₂×C₁₉⋊C₈	—	4	1	no	—
24	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	Q₈×C₁₉	—	4	2	no	—
26	Q₈×C₁₉	—	4	2	no	—
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	—	2	1	no	—
29	C₂×C₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
41	C₁₉⋊C₈	—	4	2	no	—
42	C₁₉⋊C₈	—	8	1	no	—
43	#1354	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	2	1	no	—
46	C₂²×C₁₉	#99	1	1	yes	characteristic
47	C₂²×C₁₉	#103	1	1	yes	characteristic
48	C₂²×C₁₉	#104	1	1	yes	characteristic
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	2	1	no	—
51	C₄×C₁₉	—	4	2	no	—
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	4	2	no	—
54	C₄×C₁₉	—	4	1	no	—
55	#395	D₁₉	1	1	yes	characteristic
56	#343	—	19	1	no	—
57	#324	—	19	1	no	—
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	—	2	1	no	—
60	C₂×C₁₉	#328	1	1	yes	characteristic
61	C₂×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
62	C₂×C₁₉	#356	1	1	yes	characteristic
63	C₂²×Q₈	Dic₁₉	1	1	yes	characteristic
64	C₂×M₁₆	—	38	1	no	—
65	C₂×C₄⋊C₄	—	2	1	no	—
66	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
67	C₂²⋊C₈	—	38	1	no	—
68	#95	—	2	1	no	—
69	#95	Dic₁₉	1	1	yes	characteristic
70	C₁₉	#1354	1	1	yes	characteristic, complemented, Sylow
71	C₂×Q₈	—	4	2	no	—
72	C₂×Q₈	—	4	1	no	—
73	C₂²×C₄	—	2	1	no	—
74	C₂²×C₄	—	2	1	no	—
75	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
76	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
77	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
78	M₁₆	—	38	2	no	—
79	M₁₆	—	76	1	no	—
80	C₂×C₈	—	76	1	no	—
81	C₂×C₈	—	76	1	no	—
82	C₄⋊C₄	—	4	1	no	—
83	C₄⋊C₄	—	4	2	no	—
84	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
85	Q₈	—	4	2	no	—
86	Q₈	—	4	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	#64527	1	1	yes	characteristic
100	C₂×C₄	#64528	1	1	yes	characteristic
101	C₈	—	76	2	no	—
102	C₈	—	152	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	#10597291	1	1	yes	characteristic
106	C₂²	#10597292	1	1	yes	characteristic
107	C₂²	#10597294	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	4	2	no	—
111	C₄	—	4	1	no	—
112	C₄	—	4	2	no	—
113	C₄	—	4	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	2	1	no	—
116	C₂	#11926281	1	1	yes	characteristic
117	C₂	#11926331	1	1	yes	characteristic
118	C₂	#11926343	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926313

C₂

yes

maximal, characteristic

#11926270

C₂

yes

maximal, characteristic

C₁₉×#395

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₁₉×#95

—

C₁₉×#95

C₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

Q₁₆

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1354

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

#395

D₁₉

yes

characteristic

#343

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#328

yes

characteristic

C₂×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₂×C₁₉

#356

yes

characteristic

C₂²×Q₈

Dic₁₉

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂²⋊C₈

—

#95

—

#95

Dic₁₉

yes

characteristic

C₁₉

#1354

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

C₂²⋊Dic₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64527

yes

characteristic

100

C₂×C₄

#64528

yes

characteristic

101

C₈

—

102

C₈

—

152

—

103

C₂²

—

104

C₂²

—

105

C₂²

#10597291

yes

characteristic

106

C₂²

#10597292

yes

characteristic

107

C₂²

#10597294

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₂

—

115

C₂

—

116

C₂

#11926281

yes

characteristic

117

C₂

#11926331

yes

characteristic

118

C₂

#11926343

yes

characteristic

	subgroup	G/H
center	C₂²	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₄
Frattini	C₂×C₄⋊C₄	C₂×D₁₉
Fitting	C₁₉×#395	C₂
socle	C₂²×C₁₉	#99
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄⋊C₄×C₁₉	C₂²
hypercenter	#395	D₁₉
hypocenter	C₁₉	#1354
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #395

subgroup

G/H

center

C₂²

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₄

Frattini

C₂×C₄⋊C₄

C₂×D₁₉

Fitting

C₁₉×#395

C₂

socle

C₂²×C₁₉

#99

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄⋊C₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #395

N	H ≅ G/N	type
70. C₁₉	#1354	semidirect

H ≅ G/N

type

70. C₁₉

#1354

semidirect

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

subgroup	index
#11926313	2
#11926270	2
C₁₉×#395	2
#1354	19

subgroup

index

#11926313

#11926270

C₁₉×#395

#1354

Subgroups — #14561665

Conjugacy classes of subgroups

Complements

Maximal subgroups