Group #14571902 — subgroups

Subgroups — #14571902

Order 2432.

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

normal subgroups only

This group has 348 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	3	yes	maximal
2	#11926478	C₂	1	3	yes	maximal
3	#11926476	C₂	1	3	yes	maximal
4	#11926465	C₂	1	3	yes	maximal
5	#11926414	C₂	1	1	yes	maximal, characteristic
6	#11926412	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#383	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
15	C₁₉×#95	C₂²	1	3	yes	—
16	C₁₉×#95	C₂²	1	3	yes	—
17	C₁₉⋊#95	C₂²	1	3	yes	—
18	C₁₉⋊#95	C₂²	1	3	yes	—
19	C₁₉⋊#95	C₂²	1	3	yes	—
20	C₁₉⋊#95	C₂²	1	3	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂³	1	3	yes	—
27	C₂²×Dic₁₉	C₂³	1	3	yes	—
28	C₂×Dic₃₈	—	4	3	no	—
29	C₄²×C₁₉	Q₈	1	4	yes	complemented
30	C₄⋊Dic₁₉	—	4	3	no	—
31	C₄⋊Dic₁₉	—	4	3	no	—
32	C₄⋊Dic₁₉	—	4	3	no	—
33	Dic₁₉⋊C₄	—	4	3	no	—
34	Dic₁₉⋊C₄	—	4	3	no	—
35	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₁₉	—	2	3	no	—
37	C₂×C₄×C₁₉	—	2	3	no	—
38	C₂×C₄×C₁₉	—	2	3	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×C₄×C₁₉	—	2	6	no	—
41	C₂×C₄×C₁₉	C₂×Q₈	1	6	yes	—
42	C₂×Dic₁₉	—	2	3	no	—
43	C₂×Dic₁₉	—	2	3	no	—
44	C₂×Dic₁₉	—	2	3	no	—
45	C₂×Dic₁₉	—	2	3	no	—
46	C₂×Dic₁₉	—	2	3	no	—
47	C₂×Dic₁₉	—	2	3	no	—
48	C₂×Dic₁₉	—	2	6	no	—
49	Dic₃₈	—	4	4	no	—
50	#2843	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
53	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
54	C₄×C₁₉	—	2	6	no	—
55	C₄×C₁₉	—	4	1	no	—
56	C₄×C₁₉	—	4	3	no	—
57	Dic₁₉	—	4	1	no	—
58	Dic₁₉	—	4	1	no	—
59	Dic₁₉	—	4	3	no	—
60	Dic₁₉	—	4	3	no	—
61	#400	—	19	3	no	—
62	#398	—	19	3	no	—
63	#398	—	19	3	no	—
64	#395	—	19	3	no	—
65	#384	—	19	1	no	—
66	#383	—	19	1	no	—
67	#383	D₁₉	1	1	yes	characteristic
68	C₂×C₁₉	#544	1	3	yes	—
69	C₂×C₁₉	#560	1	1	yes	characteristic
70	C₂×C₁₉	#563	1	3	yes	—
71	C₂²×Q₈	—	19	1	no	—
72	C₂×C₄⋊C₄	—	19	3	no	—
73	C₂×C₄⋊C₄	—	19	3	no	—
74	C₂×C₄⋊C₄	—	19	3	no	—
75	C₂×C₄⋊C₄	—	19	3	no	—
76	C₂×C₄⋊C₄	—	19	3	no	—
77	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	#95	—	19	3	no	—
79	#95	—	19	3	no	—
80	#95	—	19	3	no	—
81	#95	—	19	3	no	—
82	#95	C₂×D₁₉	1	3	yes	—
83	#95	C₂×D₁₉	1	3	yes	—
84	C₁₉	#2843	1	1	yes	characteristic, complemented, Sylow
85	C₂×Q₈	—	76	3	no	—
86	C₂²×C₄	—	19	3	no	—
87	C₂²×C₄	—	19	1	no	—
88	C₂²×C₄	—	19	1	no	—
89	C₂²×C₄	—	19	3	no	—
90	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
93	C₄⋊C₄	—	76	3	no	—
94	C₄⋊C₄	—	76	3	no	—
95	C₄⋊C₄	—	76	3	no	—
96	C₄⋊C₄	—	76	3	no	—
97	C₄⋊C₄	—	76	3	no	—
98	C₄²	Dic₃₈	1	4	yes	complemented
99	C₂³	C₂³×D₁₉	1	1	yes	characteristic
100	Q₈	—	76	4	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	6	no	—
106	C₂×C₄	—	38	3	no	—
107	C₂×C₄	—	38	3	no	—
108	C₂×C₄	—	38	3	no	—
109	C₂×C₄	—	38	3	no	—
110	C₂×C₄	—	38	3	no	—
111	C₂×C₄	—	38	3	no	—
112	C₂×C₄	—	38	6	no	—
113	C₂×C₄	C₂×Dic₃₈	1	6	yes	—
114	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
115	C₂²	#10597435	1	3	yes	—
116	C₂²	#10597436	1	3	yes	—
117	C₄	—	2	6	no	—
118	C₄	—	4	3	no	—
119	C₄	—	4	1	no	—
120	C₄	—	76	3	no	—
121	C₄	—	76	1	no	—
122	C₄	—	76	1	no	—
123	C₄	—	76	3	no	—
124	C₂	#11927172	1	3	yes	—
125	C₂	#11927285	1	1	yes	characteristic
126	C₂	#11927296	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926486

C₂

yes

maximal

#11926478

C₂

yes

maximal

#11926476

C₂

yes

maximal

#11926465

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic

#11926412

C₂

yes

maximal, characteristic

C₁₉×#383

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

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

—

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

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₄²×C₁₉

Q₈

yes

complemented

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

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×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2843

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

#544

yes

—

C₂×C₁₉

#560

yes

characteristic

C₂×C₁₉

#563

yes

—

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₂×D₁₉

yes

—

#95

C₂×D₁₉

yes

—

C₁₉

#2843

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Dic₃₈

yes

complemented

C₂³

C₂³×D₁₉

yes

characteristic

100

Q₈

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×Dic₃₈

yes

—

114

C₂²

C₂²×Dic₃₈

yes

characteristic

115

C₂²

#10597435

yes

—

116

C₂²

#10597436

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₂

#11927172

yes

—

125

C₂

#11927285

yes

characteristic

126

C₂

#11927296

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#383	C₂
hypercenter	#383	D₁₉
hypocenter	C₁₉	#2843
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#383

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
29. C₄²×C₁₉	Q₈	semidirect
84. C₁₉	#2843	semidirect
98. C₄²	Dic₃₈	semidirect

H ≅ G/N

type

29. C₄²×C₁₉

Q₈

semidirect

84. C₁₉

#2843

semidirect

98. C₄²

Dic₃₈

semidirect

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

subgroup	index
#11926486	2
#11926478	2
#11926476	2
#11926465	2
#11926414	2
#11926412	2
C₁₉×#383	2
#2843	19

subgroup

index

C₁₉×#383

Subgroups — #14571902

Conjugacy classes of subgroups

Complements

Maximal subgroups