Group #14571907 — subgroups

Subgroups — #14571907

Order 2432.

356 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 133 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	#11926486	C₂	1	4	yes	maximal
2	#11926483	C₂	1	2	yes	maximal
3	#11926465	C₂	1	4	yes	maximal
4	#11926464	C₂	1	2	yes	maximal
5	#11926410	C₂	1	2	yes	maximal
6	C₁₉×#382	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
15	C₁₉×#95	C₂²	1	4	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	4	yes	—
18	C₁₉⋊#95	C₂²	1	2	yes	—
19	C₁₉⋊#95	C₂²	1	4	yes	—
20	C₁₉⋊#95	C₂²	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
25	C₂²×Dic₁₉	C₂³	1	4	yes	—
26	C₂²×Dic₁₉	C₂³	1	4	yes	—
27	C₂×Dic₃₈	—	4	4	no	—
28	C₂×Dic₃₈	—	4	2	no	—
29	C₄⋊C₄×C₁₉	—	4	1	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄²×C₁₉	Q₈	1	4	yes	complemented
32	C₄⋊Dic₁₉	—	4	2	no	—
33	C₄⋊Dic₁₉	—	4	2	no	—
34	C₄⋊Dic₁₉	—	4	2	no	—
35	Dic₁₉⋊C₄	—	4	4	no	—
36	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	4	no	—
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	—	2	4	no	—
53	Dic₃₈	—	4	8	no	—
54	#2844	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
56	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
57	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
58	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
59	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
60	C₄×C₁₉	—	2	4	no	—
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	4	2	no	—
63	C₄×C₁₉	—	4	2	no	—
64	Dic₁₉	—	4	4	no	—
65	Dic₁₉	—	4	4	no	—
66	#400	—	19	2	no	—
67	#400	—	19	4	no	—
68	#395	—	19	2	no	—
69	#395	—	19	4	no	—
70	#382	—	19	2	no	—
71	#382	D₁₉	1	1	yes	characteristic
72	C₂×C₁₉	#544	1	2	yes	—
73	C₂×C₁₉	#544	1	1	yes	characteristic
74	C₂×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
75	C₂×C₁₉	#563	1	2	yes	—
76	C₂×C₁₉	#563	1	1	yes	characteristic
77	C₂²×Q₈	—	19	2	no	—
78	C₂×C₄⋊C₄	—	19	2	no	—
79	C₂×C₄⋊C₄	—	19	2	no	—
80	C₂×C₄⋊C₄	—	19	4	no	—
81	C₂×C₄⋊C₄	—	19	2	no	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
83	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
84	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
85	#95	—	19	4	no	—
86	#95	—	19	4	no	—
87	#95	—	19	2	no	—
88	#95	—	19	4	no	—
89	#95	—	19	2	no	—
90	#95	C₂×D₁₉	1	4	yes	—
91	C₁₉	#2844	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	76	2	no	—
93	C₂×Q₈	—	76	4	no	—
94	C₂²×C₄	—	19	4	no	—
95	C₂²×C₄	—	19	4	no	—
96	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
97	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	4	1	no	—
102	C₄⋊C₄	—	76	4	no	—
103	C₄⋊C₄	—	76	2	no	—
104	C₄⋊C₄	—	76	2	no	—
105	C₄⋊C₄	—	76	2	no	—
106	C₄²	Dic₃₈	1	4	yes	complemented
107	C₂³	C₂³×D₁₉	1	1	yes	characteristic
108	Q₈	—	76	8	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	38	4	no	—
118	C₂×C₄	—	38	4	no	—
119	C₂×C₄	—	38	4	no	—
120	C₂×C₄	—	38	4	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	38	4	no	—
123	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
124	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
125	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
126	C₂²	#10597430	1	1	yes	characteristic
127	C₂²	#10597433	1	1	yes	characteristic
128	C₂²	#10597435	1	2	yes	—
129	C₂²	#10597436	1	2	yes	—
130	C₄	—	2	4	no	—
131	C₄	—	2	2	no	—
132	C₄	—	4	2	no	—
133	C₄	—	4	2	no	—
134	C₄	—	76	4	no	—
135	C₄	—	76	4	no	—
136	C₂	#11927172	1	2	yes	—
137	C₂	#11927175	1	1	yes	characteristic
138	C₂	#11927286	1	1	yes	characteristic
139	C₂	#11927294	1	1	yes	characteristic
140	C₂	#11927298	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926486

C₂

yes

maximal

#11926483

C₂

yes

maximal

#11926465

C₂

yes

maximal

#11926464

C₂

yes

maximal

#11926410

C₂

yes

maximal

C₁₉×#382

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

Q₈

yes

complemented

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2844

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

#544

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#563

yes

characteristic

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

—

C₂×D₁₉

yes

—

C₁₉

#2844

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

Dic₃₈

yes

complemented

107

C₂³

C₂³×D₁₉

yes

characteristic

108

Q₈

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₂×Dic₃₈

yes

—

124

C₂×C₄

C₂×Dic₃₈

yes

—

125

C₂²

C₂²×Dic₃₈

yes

characteristic

126

C₂²

#10597430

yes

characteristic

127

C₂²

#10597433

yes

characteristic

128

C₂²

#10597435

yes

—

129

C₂²

#10597436

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₂

#11927172

yes

—

137

C₂

#11927175

yes

characteristic

138

C₂

#11927286

yes

characteristic

139

C₂

#11927294

yes

characteristic

140

C₂

#11927298

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#382	C₂
hypercenter	#382	D₁₉
hypocenter	C₁₉	#2844
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#382

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
31. C₄²×C₁₉	Q₈	semidirect
91. C₁₉	#2844	semidirect
106. C₄²	Dic₃₈	semidirect

H ≅ G/N

type

31. C₄²×C₁₉

Q₈

semidirect

91. C₁₉

#2844

semidirect

106. C₄²

Dic₃₈

semidirect

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

subgroup	index
#11926486	2
#11926483	2
#11926465	2
#11926464	2
#11926410	2
C₁₉×#382	2
#2844	19

subgroup

index

C₁₉×#382

Subgroups — #14571907

Conjugacy classes of subgroups

Complements

Maximal subgroups