Group #14571672 — subgroups

Subgroups — #14571672

Order 2432.

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

normal subgroups only

This group has 444 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	C₂×#10597370	C₂	1	2	yes	maximal
2	#11926484	C₂	1	4	yes	maximal, complemented
3	#11926469	C₂	1	4	yes	maximal
4	#11926465	C₂	1	4	yes	maximal, complemented
5	C₁₉×#381	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	#10597370	—	2	8	no	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
14	C₁₉×#95	C₂²	1	4	yes	—
15	C₁₉⋊#95	C₂²	1	8	yes	—
16	C₁₉⋊#95	C₂²	1	4	yes	—
17	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	—	4	2	no	—
19	C₂²×C₄×C₁₉	D₄	1	4	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂²×Dic₁₉	C₂³	1	4	yes	—
23	C₂²×Dic₁₉	C₂³	1	4	yes	—
24	C₂×Dic₃₈	—	2	4	no	—
25	C₂×Dic₃₈	—	4	4	no	—
26	C₂²⋊C₄×C₁₉	—	4	2	no	—
27	C₂²⋊Dic₁₉	—	2	8	no	—
28	C₄⋊Dic₁₉	—	2	4	no	—
29	C₄⋊Dic₁₉	—	4	4	no	—
30	Dic₁₉⋊C₄	—	2	8	no	—
31	C₂³×C₁₉	—	2	2	no	—
32	C₂³×C₁₉	—	2	4	no	—
33	C₂³×C₁₉	C₂×D₄	1	2	yes	—
34	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	2	8	no	—
38	C₂×C₄×C₁₉	—	4	4	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
40	C₂×Dic₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	—	2	8	no	—
43	C₂×Dic₁₉	—	2	8	no	—
44	Dic₃₈	—	4	8	no	—
45	#2817	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	—	2	2	no	—
47	C₂²×C₁₉	—	2	4	no	—
48	C₂²×C₁₉	—	4	4	no	—
49	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
50	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
51	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
52	C₄×C₁₉	—	2	4	no	—
53	C₄×C₁₉	—	4	4	no	—
54	Dic₁₉	—	4	4	no	—
55	Dic₁₉	—	4	4	no	—
56	C₂×C₂²⋊Q₈	—	19	2	no	—
57	#400	—	19	4	no	—
58	#397	—	19	4	no	—
59	#395	—	19	4	no	—
60	#381	D₁₉	1	1	yes	characteristic
61	C₂×C₁₉	—	4	2	no	—
62	C₂×C₁₉	#534	1	1	yes	characteristic
63	C₂×C₁₉	#536	1	2	yes	—
64	C₂×C₁₉	#563	1	4	yes	—
65	C₂²×Q₈	—	19	2	no	—
66	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
67	C₂²⋊Q₈	—	38	8	no	—
68	C₂×C₄⋊C₄	—	19	4	no	—
69	C₂×C₄⋊C₄	—	19	2	no	—
70	C₂×C₄⋊C₄	—	19	4	no	—
71	C₂×C₂²⋊C₄	—	19	4	no	—
72	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
73	#95	—	19	8	no	—
74	#95	—	19	4	no	—
75	#95	C₂×D₁₉	1	4	yes	—
76	C₁₉	#2817	1	1	yes	characteristic, complemented, Sylow
77	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
78	C₂×Q₈	—	38	4	no	—
79	C₂×Q₈	—	76	4	no	—
80	C₂²×C₄	—	4	2	no	—
81	C₂²×C₄	—	19	4	no	—
82	C₂²×C₄	—	19	4	no	—
83	C₂²×C₄	D₇₆	1	4	yes	—
84	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
85	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
86	C₄⋊C₄	—	38	8	no	—
87	C₄⋊C₄	—	38	4	no	—
88	C₄⋊C₄	—	76	4	no	—
89	C₂²⋊C₄	—	4	2	no	—
90	C₂²⋊C₄	—	38	8	no	—
91	C₂³	—	2	2	no	—
92	C₂³	—	2	4	no	—
93	C₂³	C₂×D₇₆	1	2	yes	—
94	C₂³	C₂³×D₁₉	1	1	yes	characteristic
95	Q₈	—	76	8	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	2	8	no	—
99	C₂×C₄	—	4	4	no	—
100	C₂×C₄	—	38	4	no	—
101	C₂×C₄	—	38	4	no	—
102	C₂×C₄	—	38	8	no	—
103	C₂×C₄	—	38	8	no	—
104	C₂×C₄	C₂×D₇₆	1	4	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	4	no	—
107	C₂²	—	4	4	no	—
108	C₂²	C₂²×D₇₆	1	1	yes	characteristic
109	C₂²	#10597430	1	2	yes	—
110	C₂²	#10597436	1	4	yes	—
111	C₄	—	2	4	no	—
112	C₄	—	4	4	no	—
113	C₄	—	76	4	no	—
114	C₄	—	76	4	no	—
115	C₂	—	4	2	no	—
116	C₂	#11927106	1	1	yes	characteristic
117	C₂	#11927120	1	2	yes	—
118	C₂	#11927297	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597370

C₂

yes

maximal

#11926484

C₂

yes

maximal, complemented

#11926469

C₂

yes

maximal

#11926465

C₂

yes

maximal, complemented

C₁₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

#2817

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₂²⋊Q₈

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#563

yes

—

C₂²×Q₈

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

#95

—

#95

C₂×D₁₉

yes

—

C₁₉

#2817

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

C₂×D₇₆

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₇₆

yes

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂²×D₇₆

yes

characteristic

109

C₂²

#10597430

yes

—

110

C₂²

#10597436

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₂

—

116

C₂

#11927106

yes

characteristic

117

C₂

#11927120

yes

—

118

C₂

#11927297

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#381	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	#381	D₁₉
hypocenter	C₁₉	#2817
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#381

C₂

prime radical

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
2. #11926484	C₂	semidirect
4. #11926465	C₂	semidirect
76. C₁₉	#2817	semidirect

H ≅ G/N

type

2. #11926484

C₂

semidirect

4. #11926465

C₂

semidirect

76. C₁₉

#2817

semidirect

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

subgroup	index
C₂×#10597370	2
#11926484	2
#11926469	2
#11926465	2
C₁₉×#381	2
#2817	19

subgroup

index

C₁₉×#381

Subgroups — #14571672

Conjugacy classes of subgroups

Complements

Maximal subgroups