Group #14562947 — subgroups

Subgroups — #14562947

Order 2432.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11927294	C₂	1	1	yes	maximal, characteristic
2	#11926953	C₂	1	2	yes	maximal, complemented
3	#11926939	C₂	1	1	yes	maximal, characteristic
4	#11926285	C₂	1	2	yes	maximal, complemented
5	C₁₉×#329	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#124	C₂²	1	1	yes	characteristic
7	#10597390	—	2	1	no	—
8	C₂×#64528	—	2	1	no	—
9	#10597381	—	2	1	no	—
10	C₂×#64526	—	2	1	no	—
11	#10597325	—	2	2	no	—
12	#10597324	—	2	2	no	—
13	#10597316	C₂²	1	2	yes	—
14	#10597315	C₂²	1	1	yes	characteristic
15	C₁₉×#97	C₂²	1	2	yes	—
16	#10597275	—	2	2	no	—
17	#10597274	—	2	2	no	—
18	#10597260	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×Dic₁₉	—	2	1	no	—
22	C₂×Dic₃₈	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂²⋊C₄×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²⋊Dic₁₉	—	2	2	no	—
28	C₂²⋊Dic₁₉	—	2	1	no	—
29	#64528	—	4	2	no	—
30	#64526	—	4	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	D₄	1	2	yes	—
33	C₄⋊Dic₁₉	D₄	1	2	yes	—
34	Dic₁₉⋊C₄	—	2	2	no	—
35	Dic₁₉⋊C₄	—	2	2	no	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	C₄×Dic₁₉	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂³×C₁₉	—	2	1	no	—
40	Q₈×C₁₉	—	4	1	no	—
41	D₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	—	8	1	no	—
49	Dic₃₈	—	4	1	no	—
50	Dic₃₈	—	4	1	no	—
51	Dic₃₈	—	8	1	no	—
52	C₈×C₁₉	—	2	4	no	—
53	C₁₉⋊C₈	—	2	2	no	—
54	#1660	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	4	1	no	—
56	C₂²×C₁₉	—	4	2	no	—
57	C₂²×C₁₉	#120	1	1	yes	characteristic
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	4	1	no	—
61	Dic₁₉	—	4	2	no	—
62	Dic₁₉	—	4	2	no	—
63	Dic₁₉	—	8	1	no	—
64	#563	—	19	1	no	—
65	#501	—	19	2	no	—
66	#497	—	19	1	no	—
67	#330	—	19	2	no	—
68	#329	D₁₉	1	1	yes	characteristic
69	C₂×C₁₉	—	8	1	no	—
70	C₂×C₁₉	#453	1	1	yes	characteristic
71	C₂×C₁₉	#456	1	2	yes	—
72	C₂×Q₁₆	—	38	1	no	—
73	C₂×SD₁₆	—	38	1	no	—
74	C₄⋊Q₈	—	19	1	no	—
75	C₄⋊Q₈	—	38	1	no	—
76	#126	—	38	2	no	—
77	#125	—	19	2	no	—
78	#124	C₂×D₁₉	1	1	yes	characteristic
79	#123	—	38	1	no	—
80	C₂²⋊Q₈	—	38	2	no	—
81	#107	—	38	2	no	—
82	#106	—	38	2	no	—
83	#97	—	19	1	no	—
84	#97	C₂×D₁₉	1	2	yes	—
85	C₁₉	#1660	1	1	yes	characteristic, complemented, Sylow
86	C₂×Q₈	—	38	1	no	—
87	C₂×Q₈	—	38	1	no	—
88	C₂×Q₈	D₇₆	1	1	yes	characteristic
89	C₂×D₄	D₇₆	1	1	yes	characteristic
90	C₂²×C₄	—	38	1	no	—
91	Q₁₆	—	76	2	no	—
92	SD₁₆	—	76	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	38	1	no	—
95	C₄⋊C₄	—	19	2	no	—
96	C₄⋊C₄	—	19	2	no	—
97	C₄⋊C₄	—	38	2	no	—
98	C₄⋊C₄	—	38	2	no	—
99	C₄⋊C₄	—	38	2	no	—
100	C₄⋊C₄	—	38	2	no	—
101	C₂²⋊C₄	—	2	2	no	—
102	C₂²⋊C₄	—	38	2	no	—
103	C₂²⋊C₄	—	38	1	no	—
104	C₄²	—	38	1	no	—
105	C₄²	C₂²×D₁₉	1	1	yes	characteristic
106	C₂³	—	2	1	no	—
107	Q₈	—	4	1	no	—
108	Q₈	—	76	1	no	—
109	Q₈	—	76	1	no	—
110	Q₈	—	152	1	no	—
111	D₄	—	4	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	38	2	no	—
114	C₂×C₄	—	38	2	no	—
115	C₂×C₄	—	76	1	no	—
116	C₂×C₄	—	152	1	no	—
117	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
118	C₂×C₄	D₄×D₁₉	1	2	yes	—
119	C₈	—	2	4	no	—
120	C₈	—	38	2	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	2	no	—
123	C₂²	#10597328	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	2	2	no	—
126	C₄	—	4	1	no	—
127	C₄	—	76	2	no	—
128	C₄	—	76	2	no	—
129	C₄	—	152	1	no	—
130	C₂	—	8	1	no	—
131	C₂	#11926714	1	1	yes	characteristic
132	C₂	#11926728	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927294

C₂

yes

maximal, characteristic

#11926953

C₂

yes

maximal, complemented

#11926939

C₂

yes

maximal, characteristic

#11926285

C₂

yes

maximal, complemented

C₁₉×#329

C₂

yes

maximal, characteristic

C₁₉×#124

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

#10597315

C₂²

yes

characteristic

C₁₉×#97

C₂²

yes

—

#10597275

—

#10597274

—

#10597260

C₂²

yes

characteristic

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1660

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#453

yes

characteristic

C₂×C₁₉

#456

yes

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#126

—

#125

—

#124

C₂×D₁₉

yes

characteristic

#123

—

C₂²⋊Q₈

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#1660

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₇₆

yes

characteristic

C₂×D₄

D₇₆

yes

characteristic

C₂²×C₄

—

Q₁₆

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

C₂²×D₁₉

yes

characteristic

106

C₂³

—

107

Q₈

—

108

Q₈

—

109

Q₈

—

110

Q₈

—

152

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

152

—

117

C₂×C₄

C₂×D₇₆

yes

characteristic

118

C₂×C₄

D₄×D₁₉

yes

—

119

C₈

—

120

C₈

—

121

C₂²

—

122

C₂²

—

123

C₂²

#10597328

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

152

—

130

C₂

—

131

C₂

#11926714

yes

characteristic

132

C₂

#11926728

yes

—

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#329	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂×D₄×C₁₉	D₄
hypercenter	#329	D₁₉
hypocenter	C₁₉	#1660
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #329

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#329

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂×D₄×C₁₉

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #329

N	H ≅ G/N	type
2. #11926953	C₂	semidirect
4. #11926285	C₂	semidirect
85. C₁₉	#1660	semidirect

H ≅ G/N

type

2. #11926953

C₂

semidirect

4. #11926285

C₂

semidirect

85. C₁₉

#1660

semidirect

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

subgroup	index
#11927294	2
#11926953	2
#11926939	2
#11926285	2
C₁₉×#329	2
#1660	19

subgroup

index

C₁₉×#329

Subgroups — #14562947

Conjugacy classes of subgroups

Complements

Maximal subgroups