Group #14571887 — subgroups

Subgroups — #14571887

Order 2432.

580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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	#11926457	C₂	1	6	yes	maximal, complemented
2	#11926456	C₂	1	3	yes	maximal, complemented
3	#11926455	C₂	1	2	yes	maximal, complemented
4	#11926399	C₂	1	3	yes	maximal
5	C₁₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
8	C₂²×Dic₃₈	C₂²	1	3	yes	complemented
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
12	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	6	yes	—
13	C₁₉×#95	C₂²	1	3	yes	complemented
14	C₁₉⋊#95	C₂²	1	6	yes	complemented
15	C₁₉⋊#95	C₂²	1	3	yes	complemented
16	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
17	C₂³×D₁₉	—	4	3	no	—
18	C₂³×D₁₉	—	4	3	no	—
19	C₂³×D₁₉	Q₈	1	4	yes	complemented
20	C₂³×D₁₉	C₂³	1	2	yes	—
21	C₂×Q₈×C₁₉	—	4	3	no	—
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂²×Dic₁₉	C₂³	1	6	yes	—
25	C₂×Dic₃₈	—	4	3	no	—
26	C₂×Dic₃₈	—	4	6	no	—
27	C₂²⋊C₄×C₁₉	—	4	3	no	—
28	C₂²⋊Dic₁₉	—	4	3	no	—
29	(C₂×D₁₉)⋊C₄	—	4	6	no	—
30	(C₂×D₁₉)⋊C₄	—	4	6	no	—
31	C₂³×C₁₉	—	2	3	no	—
32	C₂³×C₁₉	—	2	3	no	—
33	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
34	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
35	C₂²×D₁₉	—	2	6	no	—
36	C₂²×D₁₉	—	2	6	no	—
37	C₂²×D₁₉	—	4	12	no	—
38	C₂²×D₁₉	—	4	12	no	—
39	C₂²×D₁₉	—	4	4	no	—
40	C₂²×D₁₉	C₂×Q₈	1	4	yes	—
41	Q₈×C₁₉	—	4	4	no	—
42	C₂×C₄×C₁₉	—	2	6	no	—
43	C₂×C₄×C₁₉	—	2	6	no	—
44	C₂×C₄×C₁₉	—	2	3	no	—
45	C₂×C₄×C₁₉	—	2	3	no	—
46	C₂×Dic₁₉	—	2	6	no	—
47	C₂×Dic₁₉	—	2	6	no	—
48	C₂×Dic₁₉	—	2	6	no	—
49	Dic₃₈	—	4	12	no	—
50	#2840	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	6	no	—
52	C₂²×C₁₉	—	4	3	no	—
53	C₂²×C₁₉	—	4	1	no	—
54	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
55	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
56	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
57	C₂×D₁₉	—	2	12	no	—
58	C₂×D₁₉	—	4	16	no	—
59	C₂×D₁₉	—	4	6	no	—
60	C₂×D₁₉	—	4	2	no	—
61	C₄×C₁₉	—	4	3	no	—
62	C₄×C₁₉	—	4	3	no	—
63	Dic₁₉	—	4	6	no	—
64	#393	—	19	2	no	—
65	#393	—	19	3	no	—
66	#393	—	19	6	no	—
67	#393	D₁₉	1	1	yes	characteristic, complemented
68	#379	—	19	3	no	—
69	C₂×C₁₉	—	4	2	no	—
70	C₂×C₁₉	#543	1	3	yes	—
71	C₂×C₁₉	H(3,𝔽₄)	1	3	yes	—
72	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
73	D₁₉	—	4	4	no	—
74	C₂⁵	—	19	1	no	—
75	C₂²×Q₈	—	19	3	no	—
76	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
77	C₂×C₂²⋊C₄	—	19	3	no	—
78	C₂×C₂²⋊C₄	—	19	6	no	—
79	C₂×C₂²⋊C₄	—	19	6	no	—
80	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
81	#95	—	19	6	no	—
82	#95	—	19	3	no	—
83	#95	C₂×D₁₉	1	3	yes	complemented
84	C₁₉	#2840	1	1	yes	characteristic, complemented, Sylow
85	C₂⁴	—	19	2	no	—
86	C₂⁴	—	19	4	no	—
87	C₂⁴	—	76	3	no	—
88	C₂⁴	—	76	3	no	—
89	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
90	C₂×Q₈	—	4	3	no	—
91	C₂×Q₈	—	76	3	no	—
92	C₂×Q₈	—	76	6	no	—
93	C₂²×C₄	—	19	6	no	—
94	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
96	C₂²⋊C₄	—	4	3	no	—
97	C₂²⋊C₄	—	76	6	no	—
98	C₂²⋊C₄	—	76	6	no	—
99	C₂²⋊C₄	—	76	3	no	—
100	C₂³	—	2	3	no	—
101	C₂³	—	2	3	no	—
102	C₂³	—	19	4	no	—
103	C₂³	—	38	6	no	—
104	C₂³	—	38	6	no	—
105	C₂³	—	76	12	no	—
106	C₂³	—	76	12	no	—
107	C₂³	—	76	4	no	—
108	C₂³	Q₈×D₁₉	1	2	yes	—
109	C₂³	C₂³×D₁₉	1	1	yes	characteristic
110	Q₈	—	4	4	no	—
111	Q₈	—	76	12	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	6	no	—
115	C₂×C₄	—	2	6	no	—
116	C₂×C₄	—	38	6	no	—
117	C₂×C₄	—	38	6	no	—
118	C₂×C₄	—	38	6	no	—
119	C₂²	—	2	6	no	—
120	C₂²	—	4	3	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	38	12	no	—
123	C₂²	—	76	16	no	—
124	C₂²	—	76	6	no	—
125	C₂²	—	76	2	no	—
126	C₂²	#10597430	1	3	yes	—
127	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
128	C₂²	#10597435	1	3	yes	—
129	C₄	—	4	3	no	—
130	C₄	—	4	3	no	—
131	C₄	—	76	6	no	—
132	C₂	—	4	2	no	—
133	C₂	—	76	4	no	—
134	C₂	#11927169	1	3	yes	—
135	C₂	#11927286	1	3	yes	—
136	C₂	#11927287	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926457

C₂

yes

maximal, complemented

#11926456

C₂

yes

maximal, complemented

#11926455

C₂

yes

maximal, complemented

#11926399

C₂

yes

maximal

C₁₉×#393

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic, complemented

C₂²×Dic₃₈

C₂²

yes

complemented

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

—

C₂³×D₁₉

—

C₂³×D₁₉

Q₈

yes

complemented

C₂³×D₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×Q₈

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2840

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#379

—

C₂×C₁₉

—

C₂×C₁₉

#543

yes

—

C₂×C₁₉

H(3,𝔽₄)

yes

—

C₂×C₁₉

H(3,𝔽₄)

yes

characteristic

D₁₉

—

C₂⁵

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

#95

—

#95

C₂×D₁₉

yes

complemented

C₁₉

#2840

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

Q₈×D₁₉

yes

—

109

C₂³

C₂³×D₁₉

yes

characteristic

110

Q₈

—

111

Q₈

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

#10597430

yes

—

127

C₂²

C₂×Q₈×D₁₉

yes

characteristic

128

C₂²

#10597435

yes

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₂

—

133

C₂

—

134

C₂

#11927169

yes

—

135

C₂

#11927286

yes

—

136

C₂

#11927287

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#393	C₂
prime radical	C₂⁴×D₁₉	C₂²
hypercenter	#393	D₁₉
hypocenter	C₁₉	#2840
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #393

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#393

C₂

prime radical

C₂⁴×D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #393

N	H ≅ G/N	type
1. #11926457	C₂	semidirect
2. #11926456	C₂	semidirect
3. #11926455	C₂	semidirect
5. C₁₉×#393	C₂	semidirect
7. C₂²×Q₈×C₁₉	C₂²	semidirect
8. C₂²×Dic₃₈	C₂²	semidirect
13. C₁₉×#95	C₂²	semidirect
14. C₁₉⋊#95	C₂²	semidirect
15. C₁₉⋊#95	C₂²	semidirect
19. C₂³×D₁₉	Q₈	semidirect
67. #393	D₁₉	semidirect
76. C₂²×Q₈	C₂×D₁₉	semidirect
83. #95	C₂×D₁₉	semidirect
84. C₁₉	#2840	semidirect

H ≅ G/N

type

1. #11926457

C₂

semidirect

2. #11926456

C₂

semidirect

3. #11926455

C₂

semidirect

5. C₁₉×#393

C₂

semidirect

7. C₂²×Q₈×C₁₉

C₂²

semidirect

8. C₂²×Dic₃₈

C₂²

semidirect

13. C₁₉×#95

C₂²

semidirect

14. C₁₉⋊#95

C₂²

semidirect

15. C₁₉⋊#95

C₂²

semidirect

19. C₂³×D₁₉

Q₈

semidirect

67. #393

D₁₉

semidirect

76. C₂²×Q₈

C₂×D₁₉

semidirect

83. #95

C₂×D₁₉

semidirect

84. C₁₉

#2840

semidirect

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

subgroup	index
#11926457	2
#11926456	2
#11926455	2
#11926399	2
C₁₉×#393	2
#2840	19

subgroup

index

C₁₉×#393

Subgroups — #14571887

Conjugacy classes of subgroups

Complements

Maximal subgroups