Group #14574136 — subgroups

Subgroups — C₂×#11926943 #14574136

Order 2432.

360 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597316	C₂	1	1	yes	maximal, characteristic
2	#11926943	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597264	C₂	1	2	yes	maximal
4	C₂×#10597265	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#125	—	2	2	no	—
8	C₁₉×#125	C₂²	1	4	yes	—
9	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×Dic₁₉⋊C₄	—	2	2	no	—
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#10597316	—	2	2	no	—
17	#10597316	C₂²	1	4	yes	—
18	#10597265	C₂²	1	8	yes	—
19	#10597264	C₂²	1	8	yes	—
20	C₄×C₁₉⋊C₈	C₂²	1	4	yes	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	D₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	8	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
28	C₄²×C₁₉	D₄	1	2	yes	—
29	C₄²×C₁₉	C₂³	1	2	yes	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	C₂³	1	4	yes	—
32	Dic₁₉⋊C₄	—	2	8	no	—
33	C₂×C₁₉⋊C₈	Q₈	1	4	yes	—
34	C₂×C₁₉⋊C₈	Q₈	1	4	yes	—
35	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
36	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	4	4	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	4	4	no	—
48	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
49	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
50	C₂×#499	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
52	C₂²×C₁₉	#135	1	4	yes	—
53	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
54	C₄×C₁₉	—	2	4	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
57	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
58	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
59	Dic₁₉	—	4	4	no	—
60	C₂×#125	—	19	1	no	—
61	C₂×#125	D₁₉	1	1	yes	characteristic
62	#499	—	19	8	no	—
63	C₂×#107	—	19	2	no	—
64	C₂×#106	—	19	2	no	—
65	C₂×C₄×C₈	—	19	1	no	—
66	C₂×C₁₉	#499	1	4	yes	complemented
67	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₁₉	C₂×#135	1	2	yes	—
69	C₂²×C₈	—	19	1	no	—
70	C₂²×C₈	—	19	1	no	—
71	#125	—	2	2	no	—
72	#125	—	19	4	no	—
73	#125	—	38	2	no	—
74	#125	C₂×D₁₉	1	4	yes	—
75	C₂×C₄⋊C₄	—	2	2	no	—
76	C₂×C₄⋊C₄	—	19	2	no	—
77	C₂×C₄⋊C₄	—	38	2	no	—
78	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
79	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
80	#107	—	19	8	no	—
81	#106	—	19	8	no	—
82	C₄×C₈	—	19	4	no	—
83	C₁₉	C₂×#499	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	38	2	no	—
86	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
87	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
88	C₂×C₈	—	19	4	no	—
89	C₂×C₈	—	19	4	no	—
90	C₂×C₈	—	19	2	no	—
91	C₂×C₈	—	19	2	no	—
92	C₄⋊C₄	—	2	8	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄⋊C₄	—	19	4	no	—
95	C₄⋊C₄	—	38	8	no	—
96	C₄⋊C₄	—	38	2	no	—
97	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
98	C₄²	C₂²⋊D₁₉	1	2	yes	—
99	C₄²	C₂²×D₁₉	1	2	yes	—
100	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	—	4	4	no	—
104	C₂×C₄	—	38	4	no	—
105	C₂×C₄	—	76	4	no	—
106	C₂×C₄	Q₈×D₁₉	1	2	yes	—
107	C₂×C₄	Q₈×D₁₉	1	2	yes	—
108	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
111	C₈	—	19	4	no	—
112	C₈	—	19	4	no	—
113	C₂²	#10597390	1	2	yes	—
114	C₂²	#10597396	1	4	yes	—
115	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
116	C₄	—	2	4	no	—
117	C₄	—	4	4	no	—
118	C₄	—	76	4	no	—
119	C₄	#10597390	1	2	yes	—
120	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
121	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
122	C₂	#11926943	1	4	yes	direct product factor
123	C₂	C₂×#10597390	1	1	yes	characteristic
124	C₂	C₂×#10597396	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926943

C₂

yes

maximal, direct product factor

C₂×#10597264

C₂

yes

maximal

C₂×#10597265

C₂

yes

maximal

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597316

—

#10597316

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

C₂×Q₈

yes

—

C₁₉⋊C₈

C₂×Q₈

yes

—

C₂×#499

—

maximal, Sylow

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂²×Q₈

yes

characteristic

Dic₁₉

—

C₂×#125

—

C₂×#125

D₁₉

yes

—

—

—

C₂×C₄×C₈

—

C₂×C₁₉

#499

yes

complemented

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

C₂×#135

yes

—

C₂²×C₈

—

C₂²×C₈

—

—

—

—

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#107

—

#106

—

C₄×C₈

—

C₁₉

C₂×#499

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₄²

C₂²⋊D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

—

100

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

Q₈×D₁₉

yes

—

107

C₂×C₄

Q₈×D₁₉

yes

—

108

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

110

C₂×C₄

C₂³×D₁₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₂²

#10597390

yes

—

114

C₂²

#10597396

yes

—

115

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

#10597390

yes

—

120

C₄

C₂×Q₈×D₁₉

yes

characteristic

121

C₄

C₂×Q₈×D₁₉

yes

characteristic

122

C₂

#11926943

yes

direct product factor

123

C₂

C₂×#10597390

yes

characteristic

124

C₂

C₂×#10597396

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	C₂×#499
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #11926943	C₂	direct (N × H)
66. C₂×C₁₉	#499	semidirect
83. C₁₉	C₂×#499	semidirect
122. C₂	#11926943	direct (N × H)

H ≅ G/N

type

2. #11926943

C₂

direct (N × H)

66. C₂×C₁₉

#499

semidirect

83. C₁₉

C₂×#499

semidirect

122. C₂

#11926943

direct (N × H)

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

subgroup	index
C₂×#10597316	2
#11926943	2
C₂×#10597264	2
C₂×#10597265	2
C₂×C₄×C₁₉⋊C₈	2
C₂×C₁₉×#125	2
C₂×#499	19

subgroup

index

C₂×C₄×C₁₉⋊C₈

C₂×C₁₉×#125

C₂×#499

Subgroups — C₂×#11926943 #14574136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926943 #14574136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926943 #14574136