Group #14565218 — subgroups

Subgroups — #14565218

Order 2432.

148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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	#11926592	C₂	1	1	yes	maximal, characteristic
2	#11926571	C₂	1	1	yes	maximal, characteristic
3	#11926314	C₂	1	1	yes	maximal, characteristic
4	#11926308	C₂	1	1	yes	maximal, characteristic
5	#11926308	C₂	1	1	yes	maximal, characteristic
6	C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#10597279	—	2	2	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₁₉	—	2	1	no	—
19	M₁₆×C₁₉	—	2	1	no	—
20	M₁₆×C₁₉	—	2	1	no	—
21	M₁₆×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	—	2	1	no	—
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
26	C₄²×C₁₉	—	2	1	no	—
27	#64520	—	2	1	no	—
28	#64520	—	2	1	no	—
29	#64520	—	2	1	no	—
30	#64520	—	2	1	no	—
31	#64520	—	2	1	no	—
32	#64520	—	2	1	no	—
33	C₂×C₁₉⋊C₈	—	2	1	no	—
34	C₂×C₁₉⋊C₈	—	2	1	no	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₈×C₁₉	—	4	1	no	—
48	C₈×C₁₉	—	4	1	no	—
49	C₁₉⋊C₈	—	2	2	no	—
50	C₁₉⋊C₈	—	4	1	no	—
51	C₁₉⋊C₈	—	4	1	no	—
52	C₁₉⋊C₈	—	4	1	no	—
53	#2103	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
56	C₂²×C₁₉	#125	1	1	yes	characteristic
57	C₂²×C₁₉	#125	1	1	yes	characteristic
58	C₄×C₁₉	—	4	2	no	—
59	C₄×C₁₉	#123	1	1	yes	characteristic
60	C₄×C₁₉	#124	1	1	yes	characteristic
61	C₄×C₁₉	#126	1	1	yes	characteristic
62	C₄×C₁₉	#126	1	1	yes	characteristic
63	#430	—	19	1	no	—
64	#424	—	19	1	no	—
65	#344	—	19	1	no	—
66	#344	D₁₉	1	1	yes	characteristic
67	#341	—	19	1	no	—
68	#341	—	19	1	no	—
69	#338	—	19	1	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	#400	1	1	yes	characteristic
74	C₂×M₁₆	—	19	1	no	—
75	C₂×M₁₆	—	19	1	no	—
76	C₂×M₁₆	—	19	1	no	—
77	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
78	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
79	C₂²×C₈	—	19	1	no	—
80	#117	C₂×D₁₉	1	1	yes	characteristic
81	#108	—	38	2	no	—
82	C₄⋊C₈	—	38	2	no	—
83	C₁₉	#2103	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	2	1	no	—
87	M₁₆	—	2	1	no	—
88	M₁₆	—	2	1	no	—
89	M₁₆	—	38	1	no	—
90	M₁₆	—	38	1	no	—
91	M₁₆	—	38	1	no	—
92	M₁₆	—	38	1	no	—
93	M₁₆	—	38	1	no	—
94	M₁₆	—	38	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	19	2	no	—
98	C₂×C₈	—	38	1	no	—
99	C₂×C₈	—	38	1	no	—
100	C₂×C₈	—	38	1	no	—
101	C₂×C₈	—	38	1	no	—
102	C₂×C₈	—	38	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₂²⋊C₄	Dic₃₈	1	2	yes	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	#64541	1	1	yes	characteristic
109	C₂×C₄	#64541	1	1	yes	characteristic
110	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
111	C₂×C₄	#64543	1	1	yes	characteristic
112	C₂×C₄	#64543	1	1	yes	characteristic
113	C₂×C₄	#64545	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	38	2	no	—
117	C₈	—	76	1	no	—
118	C₈	—	76	1	no	—
119	C₈	—	76	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#10597316	1	1	yes	characteristic
122	C₂²	#10597324	1	1	yes	characteristic
123	C₂²	#10597336	1	1	yes	characteristic
124	C₄	—	4	2	no	—
125	C₄	#10597325	1	1	yes	characteristic
126	C₄	#10597331	1	1	yes	characteristic
127	C₄	#10597340	1	1	yes	characteristic
128	C₄	#10597344	1	1	yes	characteristic
129	C₂	—	2	1	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	#11926486	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926592

C₂

yes

maximal, characteristic

#11926571

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal, characteristic

C₁₉⋊#338

C₂

yes

maximal, characteristic

C₁₉×#344

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

Q₈

yes

—

C₄²×C₁₉

—

—

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2103

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#400

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#117

C₂×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₁₉

#2103

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

Dic₃₈

yes

—

105

C₄²

—

106

C₂³

C₂×Dic₃₈

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

#64541

yes

characteristic

109

C₂×C₄

#64541

yes

characteristic

110

C₂×C₄

D₄×D₁₉

yes

characteristic

111

C₂×C₄

#64543

yes

characteristic

112

C₂×C₄

#64543

yes

characteristic

113

C₂×C₄

#64545

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₈

—

120

C₂²

—

121

C₂²

#10597316

yes

characteristic

122

C₂²

#10597324

yes

characteristic

123

C₂²

#10597336

yes

characteristic

124

C₄

—

125

C₄

#10597325

yes

characteristic

126

C₄

#10597331

yes

characteristic

127

C₄

#10597340

yes

characteristic

128

C₄

#10597344

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

—

132

C₂

#11926486

yes

characteristic

	subgroup	G/H
center	C₄	#10597331
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#344	C₂
socle	C₂×C₁₉	#400
prime radical	C₂³×C₁₉	C₂×Q₈
hypercenter	#344	D₁₉
hypocenter	C₁₉	#2103
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₄

#10597331

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#344

C₂

socle

C₂×C₁₉

#400

prime radical

C₂³×C₁₉

C₂×Q₈

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
83. C₁₉	#2103	semidirect

H ≅ G/N

type

83. C₁₉

#2103

semidirect

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

subgroup	index
#11926592	2
#11926571	2
#11926314	2
#11926308	2
C₁₉⋊#338	2
C₁₉×#344	2
#2103	19

subgroup

index

C₁₉⋊#338

C₁₉×#344

#2103

Subgroups — #14565218

Conjugacy classes of subgroups

Complements

Maximal subgroups