Group #14565775 — subgroups

Subgroups — #14565775

Order 2432.

130 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11926948	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926372	C₂	1	1	yes	maximal, characteristic
4	#11926371	C₂	1	1	yes	maximal, characteristic
5	Dic₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	#11926348	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#358	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	Q₈×Dic₁₉	—	2	1	no	—
10	#10597334	—	2	1	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#107	C₂²	1	1	yes	characteristic
13	#10597292	—	2	1	no	—
14	#10597275	C₂²	1	1	yes	characteristic
15	#10597275	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
18	#10597264	—	2	1	no	—
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×Dic₃₈	—	4	1	no	—
21	Q₁₆×C₁₉	—	2	1	no	—
22	Q₁₆×C₁₉	Q₈	1	2	yes	complemented
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊Dic₁₉	—	2	1	no	—
26	C₄⋊Dic₁₉	—	2	1	no	—
27	C₄⋊Dic₁₉	—	4	1	no	—
28	Dic₁₉⋊C₄	—	4	1	no	—
29	C₄×Dic₁₉	—	4	1	no	—
30	C₄×Dic₁₉	D₄	1	1	yes	characteristic
31	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
32	C₁₆×C₁₉	—	2	1	no	—
33	C₁₉⋊C₁₆	—	2	1	no	—
34	Q₈×C₁₉	—	2	2	no	—
35	Q₈×C₁₉	—	4	1	no	—
36	C₂×C₄×C₁₉	—	4	1	no	—
37	C₂×C₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₁₉	—	4	1	no	—
40	C₂×Dic₁₉	—	4	1	no	—
41	C₂×Dic₁₉	D₈	1	1	yes	characteristic
42	C₂×Dic₁₉	D₈	1	1	yes	characteristic
43	Dic₃₈	—	8	2	no	—
44	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₁₉	#41	1	1	yes	characteristic
46	C₁₉⋊C₈	—	2	1	no	—
47	#2225	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
49	C₄×C₁₉	—	4	2	no	—
50	C₄×C₁₉	—	8	1	no	—
51	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₄×C₁₉	#137	1	1	yes	characteristic
53	Dic₁₉	—	2	1	no	—
54	Dic₁₉	—	8	1	no	—
55	Dic₁₉	—	8	1	no	—
56	Dic₁₉	SD₃₂	1	2	yes	—
57	#500	—	19	1	no	—
58	C₄×Q₁₆	—	19	1	no	—
59	#367	—	19	1	no	—
60	#367	—	19	1	no	—
61	C₄⋊C₁₆	—	19	1	no	—
62	#358	—	19	1	no	—
63	#358	D₁₉	1	1	yes	characteristic
64	C₂×C₁₉	#474	1	1	yes	characteristic
65	C₂×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
66	C₂×C₁₉	#510	1	1	yes	characteristic
67	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
68	C₄⋊Q₈	—	38	1	no	—
69	C₄×Q₈	—	38	1	no	—
70	C₂×C₁₆	—	19	1	no	—
71	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
72	#107	—	19	1	no	—
73	#107	—	19	1	no	—
74	#107	—	38	1	no	—
75	#107	C₂×D₁₉	1	1	yes	characteristic
76	#103	—	38	1	no	—
77	C₄×C₈	—	19	1	no	—
78	C₁₉	#2225	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	76	1	no	—
81	Q₁₆	—	2	1	no	—
82	Q₁₆	Dic₃₈	1	2	yes	complemented
83	C₂×C₈	—	19	1	no	—
84	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
85	C₄⋊C₄	—	2	1	no	—
86	C₄⋊C₄	—	38	1	no	—
87	C₄⋊C₄	—	38	1	no	—
88	C₄⋊C₄	—	76	1	no	—
89	C₄⋊C₄	—	76	1	no	—
90	C₄²	—	19	1	no	—
91	C₄²	—	76	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	38	1	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	4	1	no	—
96	Q₈	—	152	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	19	1	no	—
100	C₂×C₄	—	19	1	no	—
101	C₂×C₄	—	76	1	no	—
102	C₂×C₄	—	76	1	no	—
103	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
104	C₈	—	38	1	no	—
105	C₈	C₂×Dic₃₈	1	1	yes	characteristic
106	C₈	#64543	1	1	yes	characteristic
107	C₂²	D₈×D₁₉	1	1	yes	characteristic
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	19	2	no	—
111	C₄	—	38	1	no	—
112	C₄	—	152	1	no	—
113	C₄	—	152	1	no	—
114	C₄	#10597324	1	1	yes	characteristic
115	C₄	#10597361	1	1	yes	characteristic
116	C₂	#11926822	1	1	yes	characteristic
117	C₂	SD₃₂×D₁₉	1	1	yes	characteristic
118	C₂	#11926986	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926948

C₂

yes

maximal, characteristic

Q₁₆×Dic₁₉

C₂

yes

maximal, characteristic

#11926372

C₂

yes

maximal, characteristic

#11926371

C₂

yes

maximal, characteristic

Dic₁₉⋊C₁₆

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal, characteristic

C₁₉×#358

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

—

#10597334

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597292

—

#10597275

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

Dic₃₈

—

C₈×C₁₉

C₂×Q₈

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2225

—

maximal, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

SD₃₂

yes

—

#500

—

C₄×Q₁₆

—

#367

—

#367

—

C₄⋊C₁₆

—

#358

—

#358

D₁₉

yes

characteristic

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×C₁₉

#510

yes

characteristic

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

—

—

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

—

C₁₉

#2225

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

Dic₃₈

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

152

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

D₄×D₁₉

yes

characteristic

104

C₈

—

105

C₈

C₂×Dic₃₈

yes

characteristic

106

C₈

#64543

yes

characteristic

107

C₂²

D₈×D₁₉

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

152

—

113

C₄

—

152

—

114

C₄

#10597324

yes

characteristic

115

C₄

#10597361

yes

characteristic

116

C₂

#11926822

yes

characteristic

117

C₂

SD₃₂×D₁₉

yes

characteristic

118

C₂

#11926986

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#358	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	#358	D₁₉
hypocenter	C₁₉	#2225
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#358

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
22. Q₁₆×C₁₉	Q₈	semidirect
78. C₁₉	#2225	semidirect
82. Q₁₆	Dic₃₈	semidirect

H ≅ G/N

type

22. Q₁₆×C₁₉

Q₈

semidirect

78. C₁₉

#2225

semidirect

82. Q₁₆

Dic₃₈

semidirect

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

subgroup	index
#11926948	2
Q₁₆×Dic₁₉	2
#11926372	2
#11926371	2
Dic₁₉⋊C₁₆	2
#11926348	2
C₁₉×#358	2
#2225	19

subgroup

index

Q₁₆×Dic₁₉

Dic₁₉⋊C₁₆

C₁₉×#358

Subgroups — #14565775

Conjugacy classes of subgroups

Complements

Maximal subgroups