Group #14563271 — subgroups

Subgroups — #14563271

Order 2432.

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

normal subgroups only

This group has 208 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	#11926920	C₂	1	1	yes	maximal, characteristic
2	#11926916	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926894	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926892	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926891	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926265	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#64526	—	2	2	no	—
11	C₂×#64525	—	2	2	no	—
12	#10597320	C₂²	1	1	yes	characteristic
13	#10597315	C₂²	1	1	yes	characteristic
14	C₁₉×#102	—	2	2	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#10597292	—	2	2	no	—
17	#10597278	—	2	2	no	—
18	#10597266	—	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×D₇₆	—	2	1	no	—
26	C₂×D₇₆	—	2	1	no	—
27	C₂×D₇₆	—	2	1	no	—
28	C₂×Dic₃₈	—	2	1	no	—
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#64526	—	4	4	no	—
34	#64525	—	4	4	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
38	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
39	C₂³×C₁₉	—	4	1	no	—
40	C₂²×D₁₉	—	4	1	no	—
41	Q₈×C₁₉	—	4	2	no	—
42	D₄×C₁₉	—	4	2	no	—
43	D₄×C₁₉	—	4	2	no	—
44	D₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₁₉	—	4	1	no	—
50	D₇₆	—	4	2	no	—
51	D₇₆	—	4	2	no	—
52	D₇₆	—	4	2	no	—
53	Dic₃₈	—	4	2	no	—
54	C₈×C₁₉	—	2	2	no	—
55	C₁₉⋊C₈	—	2	2	no	—
56	C₁₉⋊C₈	—	2	2	no	—
57	#1717	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	8	1	no	—
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	#127	1	1	yes	characteristic
62	C₂×D₁₉	—	8	1	no	—
63	C₂×D₁₉	—	8	1	no	—
64	C₂×D₁₉	—	8	1	no	—
65	C₄×C₁₉	—	8	1	no	—
66	C₄×C₁₉	#135	1	2	yes	—
67	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
68	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
69	Dic₁₉	—	8	1	no	—
70	#493	—	19	1	no	—
71	#492	—	19	1	no	—
72	#487	—	19	1	no	—
73	#486	—	19	1	no	—
74	#486	—	19	1	no	—
75	#486	D₁₉	1	1	yes	characteristic, complemented
76	#322	—	19	1	no	—
77	C₂×C₁₉	—	16	1	no	—
78	C₂×C₁₉	#495	1	1	yes	characteristic
79	C₂×C₁₉	#496	1	1	yes	characteristic
80	C₂×C₁₉	#496	1	1	yes	characteristic
81	D₁₉	—	16	1	no	—
82	C₂×SD₁₆	—	38	2	no	—
83	C₂×D₈	—	38	2	no	—
84	C₄⋊Q₈	—	19	1	no	—
85	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
86	#127	—	19	1	no	—
87	#127	C₂×D₁₉	1	1	yes	characteristic
88	#103	—	38	2	no	—
89	#102	—	2	2	no	—
90	#102	—	38	2	no	—
91	#102	—	38	2	no	—
92	C₄×C₈	—	19	1	no	—
93	C₄×C₈	—	19	1	no	—
94	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
95	C₁₉	#1717	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	38	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	38	1	no	—
102	C₂×D₄	—	38	1	no	—
103	C₂×D₄	—	38	1	no	—
104	SD₁₆	—	76	4	no	—
105	D₈	—	76	4	no	—
106	C₂×C₈	—	19	2	no	—
107	C₂×C₈	—	19	2	no	—
108	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	38	1	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	C₂³	—	4	1	no	—
115	C₂³	—	76	1	no	—
116	Q₈	—	4	2	no	—
117	Q₈	—	76	2	no	—
118	D₄	—	4	2	no	—
119	D₄	—	4	2	no	—
120	D₄	—	4	2	no	—
121	D₄	—	76	2	no	—
122	D₄	—	76	2	no	—
123	D₄	—	76	2	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	76	1	no	—
126	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
127	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
128	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
129	C₈	—	2	2	no	—
130	C₈	—	38	2	no	—
131	C₈	—	38	2	no	—
132	C₂²	—	8	1	no	—
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	152	1	no	—
136	C₂²	—	152	1	no	—
137	C₂²	—	152	1	no	—
138	C₂²	#10597386	1	1	yes	characteristic
139	C₄	—	8	1	no	—
140	C₄	—	152	1	no	—
141	C₄	#10597357	1	2	yes	—
142	C₄	#10597360	1	2	yes	—
143	C₄	#10597396	1	2	yes	—
144	C₂	—	16	1	no	—
145	C₂	—	304	1	no	—
146	C₂	#11926926	1	1	yes	characteristic
147	C₂	#11926930	1	1	yes	characteristic
148	C₂	#11926932	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926920

C₂

yes

maximal, characteristic

#11926916

C₂

yes

maximal, characteristic, complemented

#11926894

C₂

yes

maximal, characteristic, complemented

#11926892

C₂

yes

maximal, characteristic, complemented

#11926891

C₂

yes

maximal, characteristic, complemented

#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#486

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

—

—

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×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64526

—

#64525

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂²×D₁₉

—

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

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1717

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#135

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic, complemented

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

—

#127

C₂×D₁₉

yes

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1717

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

SD₁₆

—

105

D₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²⋊D₁₉

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

C₂²×D₁₉

yes

characteristic

114

C₂³

—

115

C₂³

—

116

Q₈

—

117

Q₈

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

—

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₁₉

yes

characteristic

127

C₂×C₄

D₄×D₁₉

yes

characteristic

128

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

152

—

136

C₂²

—

152

—

137

C₂²

—

152

—

138

C₂²

#10597386

yes

characteristic

139

C₄

—

140

C₄

—

152

—

141

C₄

#10597357

yes

—

142

C₄

#10597360

yes

—

143

C₄

#10597396

yes

—

144

C₂

—

145

C₂

—

304

—

146

C₂

#11926926

yes

characteristic

147

C₂

#11926930

yes

characteristic

148

C₂

#11926932

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	#11926920	C₂
hypercenter	#486	D₁₉
hypocenter	C₁₉	#1717
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

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
2. #11926916	C₂	semidirect
3. #11926894	C₂	semidirect
4. #11926892	C₂	semidirect
5. #11926891	C₂	semidirect
6. #11926265	C₂	semidirect
7. C₁₉×#486	C₂	semidirect
75. #486	D₁₉	semidirect
95. C₁₉	#1717	semidirect

H ≅ G/N

type

2. #11926916

C₂

semidirect

3. #11926894

C₂

semidirect

4. #11926892

C₂

semidirect

5. #11926891

C₂

semidirect

6. #11926265

C₂

semidirect

7. C₁₉×#486

C₂

semidirect

75. #486

D₁₉

semidirect

95. C₁₉

#1717

semidirect

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

subgroup	index
#11926920	2
#11926916	2
#11926894	2
#11926892	2
#11926891	2
#11926265	2
C₁₉×#486	2
#1717	19

subgroup

index

C₁₉×#486

Subgroups — #14563271

Conjugacy classes of subgroups

Complements

Maximal subgroups