Group #14563923 — subgroups

Subgroups — #14563923

Order 2432.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11927311	C₂	1	1	yes	maximal, characteristic
2	#11926571	C₂	1	2	yes	maximal, complemented
3	#11926511	C₂	1	1	yes	maximal, characteristic
4	#11926314	C₂	1	2	yes	maximal, complemented
5	C₁₉×#410	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#117	C₂²	1	2	yes	—
8	#10597394	—	2	4	no	—
9	C₂×#64520	—	2	2	no	—
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×#99	C₄	1	4	yes	—
14	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
15	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
16	#41×C₁₉	—	2	2	no	—
17	#41×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×D₄×C₁₉	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₄²×C₁₉	—	2	2	no	—
26	#64520	—	2	4	no	—
27	#64520	—	2	2	no	—
28	#64520	—	2	2	no	—
29	#64520	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	4	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂×C₁₉⋊C₈	—	2	1	no	—
33	C₂×C₁₉⋊C₈	—	2	1	no	—
34	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
35	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
36	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₁₉	—	2	2	no	—
38	D₄×C₁₉	—	2	4	no	—
39	D₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₁₉⋊C₈	—	2	4	no	—
49	C₁₉⋊C₈	—	4	1	no	—
50	C₁₉⋊C₈	—	4	1	no	—
51	#1868	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	—	2	2	no	—
53	C₂²×C₁₉	—	4	1	no	—
54	C₂²×C₁₉	—	4	2	no	—
55	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₉	C₄×D₄	1	2	yes	—
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	—	4	4	no	—
59	C₄×C₁₉	#120	1	1	yes	characteristic
60	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
61	C₄×C₁₉	#123	1	1	yes	characteristic
62	#568	—	19	1	no	—
63	#424	—	19	2	no	—
64	#410	D₁₉	1	1	yes	characteristic
65	#408	—	19	1	no	—
66	#344	—	19	2	no	—
67	C₂×C₁₉	—	2	2	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	4	2	no	—
70	C₂×C₁₉	#385	1	1	yes	characteristic
71	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
72	#131	—	38	4	no	—
73	C₂×M₁₆	—	19	2	no	—
74	C₂×M₁₆	—	19	1	no	—
75	C₂×M₁₆	—	38	2	no	—
76	C₂²×C₈	—	19	1	no	—
77	#117	C₂×D₁₉	1	2	yes	—
78	C₄⋊C₈	—	38	4	no	—
79	#99	Dic₁₉	1	4	yes	—
80	C₂²⋊C₈	—	38	2	no	—
81	C₁₉	#1868	1	1	yes	characteristic, complemented, Sylow
82	#41	—	2	2	no	—
83	#41	—	2	2	no	—
84	C₂×Q₈	Dic₃₈	1	1	yes	characteristic
85	C₂×D₄	Dic₃₈	1	1	yes	characteristic
86	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
87	C₂²×C₄	D₇₆	1	2	yes	—
88	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	M₁₆	—	38	4	no	—
90	M₁₆	—	38	2	no	—
91	M₁₆	—	38	2	no	—
92	M₁₆	—	38	2	no	—
93	C₂×C₈	—	19	4	no	—
94	C₂×C₈	—	38	4	no	—
95	C₂×C₈	—	38	1	no	—
96	C₂×C₈	—	38	1	no	—
97	C₂×C₈	—	38	2	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
100	C₄²	—	2	2	no	—
101	C₂³	C₄⋊Dic₁₉	1	2	yes	—
102	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
103	Q₈	—	2	2	no	—
104	D₄	—	2	4	no	—
105	D₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
110	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
111	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
112	C₂×C₄	D₄×D₁₉	1	2	yes	—
113	C₂×C₄	#64543	1	2	yes	—
114	C₈	—	38	4	no	—
115	C₈	—	76	1	no	—
116	C₈	—	76	1	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	2	no	—
120	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
121	C₂²	D₄×Dic₁₉	1	2	yes	—
122	C₄	—	2	2	no	—
123	C₄	—	4	4	no	—
124	C₄	#10597324	1	2	yes	—
125	C₄	#10597328	1	1	yes	characteristic
126	C₄	#10597332	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#11926419	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic

#11926571

C₂

yes

maximal, complemented

#11926511

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, complemented

C₁₉×#410

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

#10597394

—

C₂×#64520

—

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#99

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1868

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

yes

—

—

D₁₉

yes

characteristic

#408

—

#344

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#385

yes

characteristic

C₂×#41

C₂×D₁₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

C₂×D₁₉

yes

—

C₄⋊C₈

—

#99

Dic₁₉

yes

—

C₂²⋊C₈

—

C₁₉

#1868

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

Dic₃₈

yes

characteristic

C₂×D₄

Dic₃₈

yes

characteristic

C₂×D₄

C₂×Dic₁₉

yes

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

C₂×Dic₁₉

yes

—

100

C₄²

—

101

C₂³

C₄⋊Dic₁₉

yes

—

102

C₂³

C₂²×Dic₁₉

yes

characteristic

103

Q₈

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊Dic₁₉

yes

—

110

C₂×C₄

C₂×Dic₃₈

yes

characteristic

111

C₂×C₄

C₂×D₇₆

yes

characteristic

112

C₂×C₄

D₄×D₁₉

yes

—

113

C₂×C₄

#64543

yes

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

121

C₂²

D₄×Dic₁₉

yes

—

122

C₄

—

123

C₄

—

124

C₄

#10597324

yes

—

125

C₄

#10597328

yes

characteristic

126

C₄

#10597332

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#11926419

yes

characteristic

	subgroup	G/H
center	C₄	#10597328
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#410	C₂
socle	C₂×C₁₉	#385
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#410	D₁₉
hypocenter	C₁₉	#1868
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

subgroup

G/H

center

C₄

#10597328

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#410

C₂

socle

C₂×C₁₉

#385

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

N	H ≅ G/N	type
2. #11926571	C₂	semidirect
4. #11926314	C₂	semidirect
81. C₁₉	#1868	semidirect

H ≅ G/N

type

2. #11926571

C₂

semidirect

4. #11926314

C₂

semidirect

81. C₁₉

#1868

semidirect

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

subgroup	index
#11927311	2
#11926571	2
#11926511	2
#11926314	2
C₁₉×#410	2
#1868	19

subgroup

index

C₁₉×#410

Subgroups — #14563923

Conjugacy classes of subgroups

Complements

Maximal subgroups