Group #14563296 — subgroups

Subgroups — #14563296

Order 2432.

186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926940	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926923	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926895	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926890	C₂	1	1	yes	maximal, characteristic
5	#11926890	C₂	1	1	yes	maximal, characteristic
6	#11926265	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#486	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	2	no	—
11	#10597315	C₂²	1	1	yes	characteristic
12	#10597315	C₂²	1	1	yes	characteristic
13	C₁₉×#102	—	2	2	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597289	—	2	2	no	—
16	#10597289	—	2	2	no	—
17	#10597273	—	2	2	no	—
18	#10597265	—	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×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×C₈×C₁₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	#64528	—	4	4	no	—
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	C₂³×C₁₉	—	4	1	no	—
39	Q₈×C₁₉	—	4	2	no	—
40	D₄×C₁₉	—	4	2	no	—
41	D₄×C₁₉	—	4	2	no	—
42	D₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	—	4	1	no	—
49	Dic₃₈	—	4	2	no	—
50	Dic₃₈	—	4	2	no	—
51	C₈×C₁₉	—	2	2	no	—
52	C₁₉⋊C₈	—	2	2	no	—
53	C₁₉⋊C₈	—	2	2	no	—
54	#1720	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	8	1	no	—
56	C₂²×C₁₉	—	8	1	no	—
57	C₂²×C₁₉	—	8	1	no	—
58	C₂²×C₁₉	#127	1	1	yes	characteristic
59	C₄×C₁₉	—	8	1	no	—
60	C₄×C₁₉	#135	1	2	yes	—
61	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
62	C₄×C₁₉	#137	1	2	yes	—
63	Dic₁₉	—	8	1	no	—
64	Dic₁₉	—	8	1	no	—
65	#498	—	19	1	no	—
66	#494	—	19	1	no	—
67	#487	—	19	1	no	—
68	#486	—	19	1	no	—
69	#486	—	19	1	no	—
70	#486	D₁₉	1	1	yes	characteristic
71	#322	—	19	1	no	—
72	C₂×C₁₉	—	16	1	no	—
73	C₂×C₁₉	#495	1	1	yes	characteristic
74	C₂×C₁₉	#496	1	1	yes	characteristic
75	C₂×C₁₉	#497	1	1	yes	characteristic
76	C₂×Q₁₆	—	38	2	no	—
77	C₄⋊Q₈	—	19	1	no	—
78	C₄⋊Q₈	—	19	1	no	—
79	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
80	#127	C₂×D₁₉	1	1	yes	characteristic
81	#106	—	38	2	no	—
82	#103	—	38	2	no	—
83	#102	—	2	2	no	—
84	#102	—	38	2	no	—
85	#102	—	38	2	no	—
86	C₄×C₈	—	19	1	no	—
87	C₄×C₈	—	19	1	no	—
88	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
89	C₁₉	#1720	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	2	1	no	—
91	C₂×Q₈	—	38	1	no	—
92	C₂×Q₈	—	38	1	no	—
93	C₂×D₄	—	2	1	no	—
94	C₂×D₄	—	2	1	no	—
95	C₂×D₄	—	2	1	no	—
96	Q₁₆	—	76	4	no	—
97	C₂×C₈	—	19	2	no	—
98	C₂×C₈	—	19	2	no	—
99	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	38	1	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₄²	C₂²×D₁₉	1	1	yes	characteristic
107	C₂³	—	4	1	no	—
108	Q₈	—	4	2	no	—
109	Q₈	—	76	2	no	—
110	Q₈	—	76	2	no	—
111	D₄	—	4	2	no	—
112	D₄	—	4	2	no	—
113	D₄	—	4	2	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	76	1	no	—
116	C₂×C₄	—	76	1	no	—
117	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
120	C₈	—	2	2	no	—
121	C₈	—	38	2	no	—
122	C₈	—	38	2	no	—
123	C₂²	—	8	1	no	—
124	C₂²	—	8	1	no	—
125	C₂²	—	8	1	no	—
126	C₂²	#10597386	1	1	yes	characteristic
127	C₄	—	8	1	no	—
128	C₄	—	152	1	no	—
129	C₄	—	152	1	no	—
130	C₄	#10597357	1	2	yes	—
131	C₄	#10597361	1	2	yes	—
132	C₄	#10597396	1	2	yes	—
133	C₂	—	16	1	no	—
134	C₂	#11926926	1	1	yes	characteristic
135	C₂	#11926932	1	1	yes	characteristic
136	C₂	#11926935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926940

C₂

yes

maximal, characteristic, complemented

#11926923

C₂

yes

maximal, characteristic, complemented

#11926895

C₂

yes

maximal, characteristic, complemented

#11926890

C₂

yes

maximal, characteristic

#11926890

C₂

yes

maximal, characteristic

#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#486

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₂×#64528

—

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#102

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

#1720

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1720

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

C₂²×D₁₉

yes

characteristic

107

C₂³

—

108

Q₈

—

109

Q₈

—

110

Q₈

—

111

D₄

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

D₄×D₁₉

yes

characteristic

118

C₂×C₄

D₄×D₁₉

yes

characteristic

119

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

120

C₈

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

#10597386

yes

characteristic

127

C₄

—

128

C₄

—

152

—

129

C₄

—

152

—

130

C₄

#10597357

yes

—

131

C₄

#10597361

yes

—

132

C₄

#10597396

yes

—

133

C₂

—

134

C₂

#11926926

yes

characteristic

135

C₂

#11926932

yes

characteristic

136

C₂

#11926935

yes

characteristic

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#486	C₂
socle	C₂²×C₁₉	#127
prime radical	C₁₉×#127	C₂²
hypercenter	#486	D₁₉
hypocenter	C₁₉	#1720
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#486

C₂

socle

C₂²×C₁₉

#127

prime radical

C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #11926940	C₂	semidirect
2. #11926923	C₂	semidirect
3. #11926895	C₂	semidirect
6. #11926265	C₂	semidirect
89. C₁₉	#1720	semidirect

H ≅ G/N

type

1. #11926940

C₂

semidirect

2. #11926923

C₂

semidirect

3. #11926895

C₂

semidirect

6. #11926265

C₂

semidirect

89. C₁₉

#1720

semidirect

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

subgroup	index
#11926940	2
#11926923	2
#11926895	2
#11926890	2
#11926265	2
C₁₉×#486	2
#1720	19

subgroup

index

C₁₉×#486

Subgroups — #14563296

Conjugacy classes of subgroups

Complements

Maximal subgroups