Group #14566355 — subgroups

Subgroups — #14566355

Order 2432.

516 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q₈×Dic₁₉	C₂	1	2	yes	maximal
2	#11926451	C₂	1	2	yes	maximal
3	#11926430	C₂	1	8	yes	maximal
4	#11926410	C₂	1	1	yes	maximal, characteristic
5	#11926390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₁₉×C₄⋊Q₈	C₄	1	8	yes	complemented
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	Q₈×Dic₁₉	—	2	8	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₁₉⋊#95	C₂²	1	4	yes	—
18	C₁₉⋊#95	C₂²	1	4	yes	—
19	C₁₉⋊#95	C₂²	1	8	yes	—
20	C₂×Q₈×C₁₉	—	2	4	no	—
21	C₂×Q₈×C₁₉	—	2	4	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	8	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂³	1	2	yes	—
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂²×Dic₁₉	C₂³	1	2	yes	—
29	C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
30	C₄²×C₁₉	C₂×C₄	1	4	yes	—
31	C₄⋊Dic₁₉	—	2	4	no	—
32	C₄⋊Dic₁₉	—	2	8	no	—
33	C₄×Dic₁₉	—	2	2	no	—
34	C₄×Dic₁₉	—	2	8	no	—
35	C₄×Dic₁₉	D₄	1	4	yes	—
36	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
37	Q₈×C₁₉	—	2	16	no	—
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	2	4	no	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	4	yes	—
42	C₂×C₄×C₁₉	C₂²×C₄	1	8	yes	—
43	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	#41	1	2	yes	—
46	C₂×Dic₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	2	no	—
49	C₂×Dic₁₉	—	2	8	no	—
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
52	#2327	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
54	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
56	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
57	C₄×C₁₉	—	2	8	no	—
58	C₄×C₁₉	—	2	4	no	—
59	C₄×C₁₉	C₄×D₄	1	4	yes	—
60	Dic₁₉	—	2	4	no	—
61	Dic₁₉	—	4	4	no	—
62	Dic₁₉	—	4	2	no	—
63	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
64	C₂×C₄×Q₈	—	19	2	no	—
65	#391	—	19	2	no	—
66	#387	—	19	8	no	—
67	#382	—	19	1	no	—
68	#376	—	19	1	no	—
69	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
70	C₂×C₁₉	#519	1	2	yes	—
71	C₂×C₁₉	#536	1	2	yes	—
72	C₂×C₁₉	#541	1	2	yes	—
73	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
74	C₄⋊Q₈	Dic₁₉	1	8	yes	complemented
75	C₄×Q₈	—	38	8	no	—
76	C₂×C₄⋊C₄	—	19	2	no	—
77	C₂×C₄⋊C₄	—	19	4	no	—
78	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
79	C₂×C₄²	—	19	1	no	—
80	C₂×C₄²	—	19	4	no	—
81	C₂×C₄²	—	19	1	no	—
82	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
83	#95	—	19	4	no	—
84	#95	—	19	4	no	—
85	#95	—	19	8	no	—
86	C₁₉	#2327	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	2	4	no	—
88	C₂×Q₈	—	2	4	no	—
89	C₂×Q₈	C₂×Dic₁₉	1	8	yes	—
90	C₂²×C₄	—	19	2	no	—
91	C₂²×C₄	—	19	2	no	—
92	C₂²×C₄	—	19	4	no	—
93	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
94	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	C₄⋊C₄	—	38	8	no	—
97	C₄⋊C₄	—	38	4	no	—
98	C₄⋊C₄	C₂×Dic₁₉	1	16	yes	—
99	C₄²	—	19	4	no	—
100	C₄²	—	38	8	no	—
101	C₄²	—	38	2	no	—
102	C₄²	C₂×Dic₁₉	1	4	yes	—
103	C₂³	C₂³×D₁₉	1	1	yes	characteristic
104	Q₈	—	2	16	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	19	4	no	—
109	C₂×C₄	—	38	4	no	—
110	C₂×C₄	—	38	4	no	—
111	C₂×C₄	—	38	2	no	—
112	C₂×C₄	—	38	8	no	—
113	C₂×C₄	—	38	4	no	—
114	C₂×C₄	D₄×D₁₉	1	2	yes	—
115	C₂×C₄	#64543	1	2	yes	—
116	C₂×C₄	C₂²×Dic₁₉	1	4	yes	—
117	C₂×C₄	C₂²×Dic₁₉	1	8	yes	—
118	C₂×C₄	C₂²×Dic₁₉	1	2	yes	—
119	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
120	C₂²	C₂×#64543	1	1	yes	characteristic
121	C₂²	#10597433	1	4	yes	—
122	C₂²	C₂³×Dic₁₉	1	1	yes	characteristic
123	C₄	—	2	8	no	—
124	C₄	—	2	4	no	—
125	C₄	—	38	4	no	—
126	C₄	—	76	4	no	—
127	C₄	—	76	2	no	—
128	C₄	D₄×Dic₁₉	1	4	yes	—
129	C₂	C₂×D₄×Dic₁₉	1	1	yes	characteristic
130	C₂	#11927022	1	2	yes	—
131	C₂	#11927119	1	2	yes	—
132	C₂	#11927155	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₁₉

C₂

yes

maximal

#11926451

C₂

yes

maximal

#11926430

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic

#11926390

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

Q₈×Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

#2327

—

maximal, Sylow

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic

C₂×C₄×Q₈

—

—

—

—

—

C₂×C₁₉

C₂×C₄×D₄

yes

characteristic

C₂×C₁₉

#519

yes

—

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#541

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₄⋊Q₈

Dic₁₉

yes

complemented

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2327

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂×Dic₁₉

yes

—

103

C₂³

C₂³×D₁₉

yes

characteristic

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

D₄×D₁₉

yes

—

115

C₂×C₄

#64543

yes

—

116

C₂×C₄

C₂²×Dic₁₉

yes

—

117

C₂×C₄

C₂²×Dic₁₉

yes

—

118

C₂×C₄

C₂²×Dic₁₉

yes

—

119

C₂²

C₂×D₄×D₁₉

yes

characteristic

120

C₂²

C₂×#64543

yes

characteristic

121

C₂²

#10597433

yes

—

122

C₂²

C₂³×Dic₁₉

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

D₄×Dic₁₉

yes

—

129

C₂

C₂×D₄×Dic₁₉

yes

characteristic

130

C₂

#11927022

yes

—

131

C₂

#11927119

yes

—

132

C₂

#11927155

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2327
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator

C₂²×C₁₉

C₂³×C₄

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
8. C₁₉×C₄⋊Q₈	C₄	semidirect
74. C₄⋊Q₈	Dic₁₉	semidirect
86. C₁₉	#2327	semidirect

H ≅ G/N

type

8. C₁₉×C₄⋊Q₈

C₄

semidirect

74. C₄⋊Q₈

Dic₁₉

semidirect

86. C₁₉

#2327

semidirect

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

subgroup	index
C₂×Q₈×Dic₁₉	2
#11926451	2
#11926430	2
#11926410	2
#11926390	2
C₂×C₁₉×C₄⋊Q₈	2
#2327	19

subgroup

index

C₂×Q₈×Dic₁₉

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14566355

Conjugacy classes of subgroups

Complements

Maximal subgroups