Group #14572245 — subgroups

Subgroups — #14572245

Order 2432.

440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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	#11927310	C₂	1	2	yes	maximal
2	C₂×#10597353	C₂	1	1	yes	maximal, characteristic
3	#11926593	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926591	C₂	1	4	yes	maximal, complemented
5	C₂×#10597279	C₂	1	2	yes	maximal, complemented
6	#108×D₁₉	C₂	1	4	yes	maximal, complemented
7	C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64541	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#10597353	—	2	4	no	—
14	#10597353	C₄	1	8	yes	—
15	M₁₆×D₁₉	C₂²	1	8	yes	—
16	#10597347	—	2	4	no	—
17	C₂×#64515	C₂²	1	2	yes	—
18	C₂×C₈×D₁₉	C₂²	1	2	yes	—
19	C₁₉×#108	C₂²	1	4	yes	—
20	#10597279	C₂²	1	4	yes	—
21	#10597279	C₂²	1	4	yes	—
22	#10597276	C₂²	1	4	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₂²⋊D₁₉	Q₈	1	2	yes	—
25	#64541	C₂×C₄	1	4	yes	—
26	#64541	D₄	1	4	yes	—
27	C₂×D₇₆	Q₈	1	1	yes	characteristic
28	C₂×C₄×D₁₉	C₂³	1	2	yes	—
29	C₂×Dic₃₈	Q₈	1	1	yes	characteristic
30	M₁₆×C₁₉	—	2	2	no	—
31	M₁₆×C₁₉	C₂×C₄	1	4	yes	—
32	M₁₆×C₁₉	C₂³	1	4	yes	—
33	C₂×C₈×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	C₂³	1	2	yes	—
35	#64520	—	2	2	no	—
36	#64520	C₂³	1	4	yes	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
39	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
41	#64515	—	2	8	no	—
42	#64515	C₂×C₄	1	8	yes	—
43	C₈×D₁₉	—	2	8	no	—
44	C₈×D₁₉	C₂×C₄	1	8	yes	—
45	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂²×D₁₉	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
51	C₂²⋊D₁₉	C₄⋊C₄	1	8	yes	—
52	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
53	D₇₆	C₄⋊C₄	1	4	yes	—
54	C₄×D₁₉	C₂²×C₄	1	4	yes	—
55	C₄×D₁₉	C₂×D₄	1	4	yes	—
56	Dic₃₈	C₄⋊C₄	1	4	yes	—
57	C₈×C₁₉	—	2	4	no	—
58	C₈×C₁₉	C₂²×C₄	1	4	yes	—
59	C₁₉⋊C₈	—	2	4	no	—
60	C₁₉⋊C₈	C₂²×C₄	1	2	yes	—
61	C₁₉⋊C₈	C₂²×C₄	1	2	yes	—
62	#2916	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	4	1	no	—
64	C₂²×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
65	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
66	C₂×D₁₉	—	4	2	no	—
67	C₂×D₁₉	C₂×C₄⋊C₄	1	4	yes	—
68	C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
69	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
70	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	Dic₁₉	C₂×C₄⋊C₄	1	4	yes	—
72	#568	—	19	2	no	—
73	C₂×#131	—	19	1	no	—
74	#430	—	19	1	no	—
75	#430	—	19	4	no	—
76	#430	D₁₉	1	1	yes	characteristic, complemented
77	C₂×#108	—	19	2	no	—
78	C₂×#108	—	19	4	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	2	2	no	—
81	C₂×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
82	D₁₉	—	2	4	no	—
83	C₂×#41	—	19	1	no	—
84	#131	—	19	8	no	—
85	#131	—	38	4	no	—
86	#131	—	38	4	no	—
87	C₂×M₁₆	—	19	2	no	—
88	C₂×M₁₆	—	19	2	no	—
89	C₂×M₁₆	—	19	8	no	—
90	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
91	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×C₈	—	19	1	no	—
93	C₂²×C₈	—	19	2	no	—
94	#108	—	19	4	no	—
95	#108	—	19	4	no	—
96	#108	—	19	4	no	—
97	#108	C₂×D₁₉	1	4	yes	—
98	C₁₉	#2916	1	1	yes	characteristic, complemented, Sylow
99	#41	—	19	4	no	—
100	#41	—	19	4	no	—
101	C₂×Q₈	—	19	1	no	—
102	C₂×D₄	—	19	2	no	—
103	C₂×D₄	—	19	1	no	—
104	C₂²×C₄	—	19	2	no	—
105	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
106	M₁₆	—	2	2	no	—
107	M₁₆	—	19	8	no	—
108	M₁₆	—	19	4	no	—
109	M₁₆	—	38	8	no	—
110	M₁₆	—	38	2	no	—
111	M₁₆	C₄×D₁₉	1	4	yes	—
112	M₁₆	C₂²×D₁₉	1	4	yes	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	19	4	no	—
115	C₂×C₈	—	19	1	no	—
116	C₂×C₈	—	19	1	no	—
117	C₂×C₈	—	19	8	no	—
118	C₂×C₈	—	38	8	no	—
119	C₂×C₈	—	38	2	no	—
120	C₂×C₈	C₂²×D₁₉	1	2	yes	—
121	C₂³	—	19	2	no	—
122	C₂³	Q₈×D₁₉	1	1	yes	characteristic
123	Q₈	—	19	4	no	—
124	D₄	—	19	8	no	—
125	D₄	—	19	4	no	—
126	C₂×C₄	—	19	2	no	—
127	C₂×C₄	—	19	4	no	—
128	C₂×C₄	—	19	4	no	—
129	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
130	C₂×C₄	D₄×D₁₉	1	2	yes	—
131	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
132	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
133	C₈	—	2	4	no	—
134	C₈	—	19	2	no	—
135	C₈	—	19	2	no	—
136	C₈	—	38	4	no	—
137	C₈	C₂×C₄×D₁₉	1	4	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	—	19	4	no	—
140	C₂²	—	76	2	no	—
141	C₂²	C₄⋊C₄×D₁₉	1	2	yes	—
142	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
143	C₄	—	19	4	no	—
144	C₄	C₄⋊C₄×D₁₉	1	2	yes	—
145	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
146	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	2	no	—
149	C₂	—	38	4	no	—
150	C₂	C₂×C₄⋊C₄×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927310

C₂

yes

maximal

C₂×#10597353

C₂

yes

maximal, characteristic

#11926593

C₂

yes

maximal, characteristic, complemented

#11926591

C₂

yes

maximal, complemented

C₂×#10597279

C₂

yes

maximal, complemented

#108×D₁₉

C₂

yes

maximal, complemented

C₁₉×#430

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597353

—

#10597353

C₄

yes

—

M₁₆×D₁₉

C₂²

yes

—

#10597347

—

C₂×#64515

C₂²

yes

—

C₂×C₈×D₁₉

C₂²

yes

—

C₁₉×#108

C₂²

yes

—

#10597279

C₂²

yes

—

#10597279

C₂²

yes

—

#10597276

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

Q₈

yes

—

#64541

C₂×C₄

yes

—

#64541

D₄

yes

—

C₂×D₇₆

Q₈

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

—

C₂×Dic₃₈

Q₈

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

M₁₆×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

#64520

—

#64520

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

characteristic

#64515

—

#64515

C₂×C₄

yes

—

C₈×D₁₉

—

C₈×D₁₉

C₂×C₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂²×D₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

D₇₆

C₄⋊C₄

yes

—

C₄×D₁₉

C₂²×C₄

yes

—

C₄×D₁₉

C₂×D₄

yes

—

Dic₃₈

C₄⋊C₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

C₂²×C₄

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²×C₄

yes

—

C₁₉⋊C₈

C₂²×C₄

yes

—

#2916

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

C₂×C₄⋊C₄

yes

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₄×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

C₂×C₄⋊C₄

yes

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×#108

—

C₂×#108

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂²×C₄⋊C₄

yes

characteristic

D₁₉

—

C₂×#41

—

#131

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2916

yes

characteristic, complemented, Sylow

#41

—

100

#41

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂²×D₁₉

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

C₄×D₁₉

yes

—

112

M₁₆

C₂²×D₁₉

yes

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

C₂²×D₁₉

yes

—

121

C₂³

—

122

C₂³

Q₈×D₁₉

yes

characteristic

123

Q₈

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₁₉

yes

—

130

C₂×C₄

D₄×D₁₉

yes

—

131

C₂×C₄

Q₈×D₁₉

yes

characteristic

132

C₂×C₄

C₂³×D₁₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

C₂×C₄×D₁₉

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₄⋊C₄×D₁₉

yes

—

142

C₂²

C₂×Q₈×D₁₉

yes

characteristic

143

C₄

—

144

C₄

C₄⋊C₄×D₁₉

yes

—

145

C₄

C₂²×C₄×D₁₉

yes

characteristic

146

C₄

C₂×D₄×D₁₉

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

—

150

C₂

C₂×C₄⋊C₄×D₁₉

yes

characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₁₉
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#430	C₂
socle	C₂×C₁₉	C₂²×C₄⋊C₄
prime radical	C₂×#64541	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#430	D₁₉
hypocenter	C₁₉	#2916
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

C₂×D₄×D₁₉

commutator

C₄×C₁₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#430

C₂

socle

C₂×C₁₉

C₂²×C₄⋊C₄

prime radical

C₂×#64541

C₂²

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
3. #11926593	C₂	semidirect
4. #11926591	C₂	semidirect
5. C₂×#10597279	C₂	semidirect
6. #108×D₁₉	C₂	semidirect
7. C₁₉×#430	C₂	semidirect
76. #430	D₁₉	semidirect
98. C₁₉	#2916	semidirect

H ≅ G/N

type

3. #11926593

C₂

semidirect

4. #11926591

C₂

semidirect

5. C₂×#10597279

C₂

semidirect

6. #108×D₁₉

C₂

semidirect

7. C₁₉×#430

C₂

semidirect

76. #430

D₁₉

semidirect

98. C₁₉

#2916

semidirect

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

subgroup	index
#11927310	2
C₂×#10597353	2
#11926593	2
#11926591	2
C₂×#10597279	2
#108×D₁₉	2
C₁₉×#430	2
#2916	19

subgroup

index

#108×D₁₉

C₁₉×#430

#2916

Subgroups — #14572245

Conjugacy classes of subgroups

Complements

Maximal subgroups