Group #14572011 — subgroups

Subgroups — #14572011

Order 2432.

504 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10597334	C₂	1	2	yes	maximal
2	#11926448	C₂	1	8	yes	maximal
3	#11926410	C₂	1	1	yes	maximal, characteristic
4	#11926409	C₂	1	2	yes	maximal
5	C₄²×Dic₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#382	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₃₈	C₂²	1	4	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	#10597334	—	2	8	no	—
16	C₁₉×#95	C₂²	1	4	yes	—
17	C₁₉⋊#95	C₂²	1	8	yes	—
18	C₁₉⋊#95	C₂²	1	4	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	C₂³	1	4	yes	—
23	C₂²×Dic₁₉	C₂³	1	2	yes	—
24	C₂²×Dic₁₉	C₂³	1	2	yes	—
25	C₂×Dic₃₈	—	2	8	no	—
26	C₂×Dic₃₈	—	2	16	no	—
27	C₄⋊C₄×C₁₉	—	2	4	no	—
28	C₄²×C₁₉	Q₈	1	4	yes	complemented
29	C₄⋊Dic₁₉	—	2	4	no	—
30	Dic₁₉⋊C₄	—	2	8	no	—
31	C₄×Dic₁₉	—	2	8	no	—
32	C₄×Dic₁₉	D₄	1	4	yes	—
33	C₄×Dic₁₉	Q₈	1	4	yes	complemented
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	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
40	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
42	C₂×Dic₁₉	—	2	4	no	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	—	2	8	no	—
45	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
46	C₂×Dic₁₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₁₉	#41	1	8	yes	—
48	Dic₃₈	—	4	16	no	—
49	#2862	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
51	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₁₉	C₂×#41	1	4	yes	—
54	C₄×C₁₉	—	2	4	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	C₄⋊Q₈	1	4	yes	—
57	Dic₁₉	—	2	4	no	—
58	Dic₁₉	—	4	4	no	—
59	Dic₁₉	#124	1	8	yes	—
60	C₂×C₄⋊Q₈	—	19	2	no	—
61	#391	—	19	8	no	—
62	#382	—	19	2	no	—
63	#382	—	19	1	no	—
64	#382	D₁₉	1	1	yes	characteristic
65	C₄³	—	19	1	no	—
66	C₂×C₁₉	C₂×#124	1	2	yes	—
67	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₁₉	#533	1	2	yes	—
69	C₂×C₁₉	#533	1	2	yes	—
70	C₂²×Q₈	—	19	4	no	—
71	C₄⋊Q₈	—	38	8	no	—
72	C₂×C₄⋊C₄	—	19	2	no	—
73	C₂×C₄⋊C₄	—	19	4	no	—
74	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
75	C₂×C₄²	—	19	1	no	—
76	C₂×C₄²	—	19	1	no	—
77	C₂×C₄²	—	19	4	no	—
78	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
79	#95	—	19	8	no	—
80	#95	—	19	4	no	—
81	#95	C₂×D₁₉	1	4	yes	—
82	C₁₉	#2862	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	—	38	8	no	—
84	C₂×Q₈	—	38	16	no	—
85	C₂²×C₄	—	19	2	no	—
86	C₂²×C₄	—	19	2	no	—
87	C₂²×C₄	—	19	4	no	—
88	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
89	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	38	8	no	—
93	C₄⋊C₄	—	38	4	no	—
94	C₄²	—	19	4	no	—
95	C₄²	—	19	4	no	—
96	C₄²	—	38	8	no	—
97	C₄²	Dic₃₈	1	4	yes	complemented
98	C₂³	C₂³×D₁₉	1	1	yes	characteristic
99	Q₈	—	76	16	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	19	4	no	—
104	C₂×C₄	—	19	8	no	—
105	C₂×C₄	—	19	4	no	—
106	C₂×C₄	—	38	4	no	—
107	C₂×C₄	—	38	4	no	—
108	C₂×C₄	—	38	8	no	—
109	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
110	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
111	C₂×C₄	D₄×D₁₉	1	2	yes	—
112	C₂×C₄	Q₈×D₁₉	1	2	yes	—
113	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
114	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
115	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
116	C₂²	#41×D₁₉	1	4	yes	—
117	C₄	—	2	4	no	—
118	C₄	—	4	4	no	—
119	C₄	—	19	8	no	—
120	C₄	—	38	4	no	—
121	C₄	—	76	4	no	—
122	C₄	#10597334	1	4	yes	—
123	C₂	#124×D₁₉	1	2	yes	—
124	C₂	C₂×#10597334	1	1	yes	characteristic
125	C₂	#11927097	1	2	yes	—
126	C₂	#11927100	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597334

C₂

yes

maximal

#11926448

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic

#11926409

C₂

yes

maximal

C₄²×Dic₁₉

C₂

yes

maximal, characteristic

C₁₉×#382

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

#10597334

—

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×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

Q₈

yes

complemented

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

Q₈

yes

complemented

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

#41

yes

—

Dic₃₈

—

#2862

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#124

yes

—

C₂×C₄⋊Q₈

—

—

—

—

D₁₉

yes

characteristic

C₄³

—

C₂×C₁₉

C₂×#124

yes

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#533

yes

—

C₂×C₁₉

#533

yes

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

—

C₁₉

#2862

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₃₈

yes

complemented

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

100

C₂×C₄

—

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

C₂×Dic₃₈

yes

—

110

C₂×C₄

C₂×Dic₃₈

yes

—

111

C₂×C₄

D₄×D₁₉

yes

—

112

C₂×C₄

Q₈×D₁₉

yes

—

113

C₂²

C₂²×Dic₃₈

yes

characteristic

114

C₂²

C₂×D₄×D₁₉

yes

characteristic

115

C₂²

C₂×Q₈×D₁₉

yes

characteristic

116

C₂²

#41×D₁₉

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#10597334

yes

—

123

C₂

#124×D₁₉

yes

—

124

C₂

C₂×#10597334

yes

characteristic

125

C₂

#11927097

yes

—

126

C₂

#11927100

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	#2862
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
28. C₄²×C₁₉	Q₈	semidirect
33. C₄×Dic₁₉	Q₈	semidirect
82. C₁₉	#2862	semidirect
97. C₄²	Dic₃₈	semidirect

H ≅ G/N

type

28. C₄²×C₁₉

Q₈

semidirect

33. C₄×Dic₁₉

Q₈

semidirect

82. C₁₉

#2862

semidirect

97. C₄²

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597334	2
#11926448	2
#11926410	2
#11926409	2
C₄²×Dic₁₉	2
C₁₉×#382	2
#2862	19

subgroup

index

C₄²×Dic₁₉

C₁₉×#382

#2862

Subgroups — #14572011

Conjugacy classes of subgroups

Complements

Maximal subgroups