Group #14563310 — subgroups

Subgroups — #14563310

Order 2432.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926947	C₂	1	1	yes	maximal, characteristic
2	#11926947	C₂	1	1	yes	maximal, characteristic
3	#11926940	C₂	1	1	yes	maximal, characteristic
4	#11926896	C₂	1	1	yes	maximal, characteristic
5	#11926895	C₂	1	1	yes	maximal, characteristic
6	#11926266	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#494	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₁₉	—	2	2	no	—
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	#10597315	C₂²	1	1	yes	characteristic
12	#10597315	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597273	—	2	2	no	—
15	#10597267	—	2	2	no	—
16	#10597265	—	2	2	no	—
17	#10597264	—	2	2	no	—
18	#10597264	—	2	2	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	Q₁₆×C₁₉	—	4	4	no	—
26	C₂×C₈×C₁₉	D₄	1	2	yes	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
37	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
38	Q₈×C₁₉	—	4	2	no	—
39	Q₈×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₁₉	—	4	1	no	—
46	C₂×Dic₁₉	—	4	1	no	—
47	Dic₃₈	—	4	2	no	—
48	Dic₃₈	—	4	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₁₉⋊C₈	—	2	2	no	—
51	C₁₉⋊C₈	Q₁₆	1	4	yes	complemented
52	#1723	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	#127	1	1	yes	characteristic
54	C₄×C₁₉	—	8	1	no	—
55	C₄×C₁₉	—	8	1	no	—
56	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
57	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
58	C₄×C₁₉	#137	1	2	yes	—
59	Dic₁₉	—	8	1	no	—
60	Dic₁₉	—	8	1	no	—
61	#500	—	19	1	no	—
62	#500	—	19	1	no	—
63	#498	—	19	1	no	—
64	#494	D₁₉	1	1	yes	characteristic
65	#487	—	19	1	no	—
66	#487	—	19	1	no	—
67	#322	—	19	1	no	—
68	C₂×C₁₉	#494	1	1	yes	characteristic
69	C₂×C₁₉	#496	1	1	yes	characteristic
70	C₂×C₁₉	#497	1	1	yes	characteristic
71	C₂×Q₁₆	—	2	2	no	—
72	C₄⋊Q₈	—	19	1	no	—
73	C₄⋊Q₈	—	19	1	no	—
74	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
75	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
76	#107	—	38	2	no	—
77	#107	—	38	2	no	—
78	#106	—	38	2	no	—
79	#103	—	38	2	no	—
80	#103	—	38	2	no	—
81	C₄×C₈	—	19	1	no	—
82	C₄×C₈	—	19	1	no	—
83	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
84	C₁₉	#1723	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	—	2	1	no	—
86	C₂×Q₈	—	2	1	no	—
87	C₂×Q₈	—	38	1	no	—
88	C₂×Q₈	—	38	1	no	—
89	Q₁₆	—	4	4	no	—
90	C₂×C₈	—	19	2	no	—
91	C₂×C₈	—	19	2	no	—
92	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	2	1	no	—
97	C₄⋊C₄	—	38	1	no	—
98	C₄⋊C₄	—	38	1	no	—
99	C₄⋊C₄	—	38	1	no	—
100	C₄⋊C₄	—	38	1	no	—
101	C₄²	C₂²×D₁₉	1	1	yes	characteristic
102	Q₈	—	4	2	no	—
103	Q₈	—	4	2	no	—
104	Q₈	—	76	2	no	—
105	Q₈	—	76	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	76	1	no	—
109	C₂×C₄	—	76	1	no	—
110	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
111	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	19	4	no	—
115	C₈	—	38	2	no	—
116	C₂²	#10597386	1	1	yes	characteristic
117	C₄	—	8	1	no	—
118	C₄	—	8	1	no	—
119	C₄	—	152	1	no	—
120	C₄	—	152	1	no	—
121	C₄	Q₁₆×D₁₉	1	2	yes	—
122	C₄	#10597364	1	2	yes	—
123	C₄	#10597378	1	2	yes	—
124	C₂	#11926922	1	1	yes	characteristic
125	C₂	#11926931	1	1	yes	characteristic
126	C₂	#11926937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926947

C₂

yes

maximal, characteristic

#11926947

C₂

yes

maximal, characteristic

#11926940

C₂

yes

maximal, characteristic

#11926896

C₂

yes

maximal, characteristic

#11926895

C₂

yes

maximal, characteristic

#11926266

C₂

yes

maximal, characteristic

C₁₉×#494

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

Q₁₆

yes

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1723

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂²×D₁₉

yes

characteristic

102

Q₈

—

103

Q₈

—

104

Q₈

—

105

Q₈

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

D₄×D₁₉

yes

characteristic

111

C₂×C₄

D₄×D₁₉

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₂²

#10597386

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

152

—

120

C₄

—

152

—

121

C₄

Q₁₆×D₁₉

yes

—

122

C₄

#10597364

yes

—

123

C₄

#10597378

yes

—

124

C₂

#11926922

yes

characteristic

125

C₂

#11926931

yes

characteristic

126

C₂

#11926937

yes

characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#494	C₂
socle, prime radical	C₂²×C₁₉	#127
hypercenter	#494	D₁₉
hypocenter	C₁₉	#1723
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#494

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
51. C₁₉⋊C₈	Q₁₆	semidirect
84. C₁₉	#1723	semidirect

H ≅ G/N

type

51. C₁₉⋊C₈

Q₁₆

semidirect

84. C₁₉

#1723

semidirect

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

subgroup	index
#11926947	2
#11926940	2
#11926896	2
#11926895	2
#11926266	2
C₁₉×#494	2
#1723	19

subgroup

index

C₁₉×#494

Subgroups — #14563310

Conjugacy classes of subgroups

Complements

Maximal subgroups