Group #14563676 — subgroups

Subgroups — #14563676

Order 2432.

272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#64515	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	2	yes	maximal, complemented
3	#11926507	C₂	1	2	yes	maximal
4	#11926309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#64515	—	2	4	no	—
12	C₂×#64515	C₄	1	4	yes	—
13	#10597279	—	2	4	no	—
14	(C₂×D₁₉)⋊C₈	—	2	4	no	—
15	C₂³×D₁₉	Q₈	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₉	Q₈	1	1	yes	characteristic
18	C₂×C₄×D₁₉	—	2	2	no	—
19	C₂×C₄×D₁₉	—	2	2	no	—
20	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₁₉	D₄	1	2	yes	—
22	M₁₆×C₁₉	—	2	2	no	—
23	M₁₆×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	#64520	—	2	2	no	—
28	#64520	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
32	#64515	—	2	8	no	—
33	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₂²×D₁₉	—	2	2	no	—
35	C₂²×D₁₉	—	4	2	no	—
36	C₂²×D₁₉	C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#41	1	2	yes	—
41	C₂×Dic₁₉	—	2	2	no	—
42	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
43	C₄×D₁₉	—	2	2	no	—
44	C₄×D₁₉	—	2	2	no	—
45	C₄×D₁₉	—	2	4	no	—
46	C₈×C₁₉	—	2	2	no	—
47	C₈×C₁₉	—	4	2	no	—
48	C₁₉⋊C₈	—	4	2	no	—
49	C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
50	#1811	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
54	C₂×D₁₉	—	2	2	no	—
55	C₂×D₁₉	—	2	4	no	—
56	C₂×D₁₉	—	4	4	no	—
57	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₄×C₁₉	#117	1	1	yes	characteristic
59	C₄×C₁₉	#121	1	2	yes	—
60	Dic₁₉	—	2	2	no	—
61	C₂²×M₁₆	—	19	1	no	—
62	C₂×#108	—	19	2	no	—
63	#407	—	19	2	no	—
64	#341	—	19	1	no	—
65	#341	D₁₉	1	1	yes	characteristic, complemented
66	C₂×C₁₉	—	2	2	no	—
67	C₂×C₁₉	#380	1	1	yes	characteristic
68	C₂×C₁₉	#430	1	2	yes	—
69	D₁₉	—	4	2	no	—
70	C₂³×C₄	—	19	1	no	—
71	C₂×M₁₆	—	19	4	no	—
72	C₂×M₁₆	—	19	2	no	—
73	C₂×M₁₆	—	38	4	no	—
74	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
75	C₂²×C₈	—	19	1	no	—
76	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
77	#108	—	38	4	no	—
78	C₂²⋊C₈	—	38	4	no	—
79	C₁₉	#1811	1	1	yes	characteristic, complemented, Sylow
80	C₂⁴	—	19	1	no	—
81	C₂²×C₄	—	19	1	no	—
82	C₂²×C₄	—	19	2	no	—
83	C₂²×C₄	—	19	2	no	—
84	C₂²×C₄	—	38	2	no	—
85	C₂²×C₄	—	38	2	no	—
86	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	2	2	no	—
89	M₁₆	—	38	8	no	—
90	M₁₆	—	38	2	no	—
91	M₁₆	—	38	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	19	2	no	—
95	C₂×C₈	—	19	4	no	—
96	C₂×C₈	—	38	2	no	—
97	C₂×C₈	C₄×D₁₉	1	2	yes	—
98	C₂³	—	19	2	no	—
99	C₂³	—	38	2	no	—
100	C₂³	—	76	2	no	—
101	C₂³	Q₈×D₁₉	1	1	yes	characteristic
102	C₂×C₄	—	19	2	no	—
103	C₂×C₄	—	38	2	no	—
104	C₂×C₄	—	38	2	no	—
105	C₂×C₄	—	38	2	no	—
106	C₂×C₄	—	38	4	no	—
107	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
108	C₂×C₄	#64541	1	2	yes	—
109	C₂×C₄	D₄×D₁₉	1	2	yes	—
110	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	2	no	—
113	C₈	—	19	4	no	—
114	C₈	—	76	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	38	4	no	—
117	C₂²	—	38	2	no	—
118	C₂²	—	76	4	no	—
119	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
120	C₂²	#10597342	1	2	yes	—
121	C₄	—	38	2	no	—
122	C₄	#10597318	1	1	yes	characteristic
123	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
124	C₄	#10597330	1	2	yes	—
125	C₂	—	2	2	no	—
126	C₂	—	76	2	no	—
127	C₂	#11926403	1	1	yes	characteristic
128	C₂	#11926591	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64515

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, complemented

#11926507

C₂

yes

maximal

#11926309

C₂

yes

maximal, characteristic, complemented

C₁₉×#341

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×#64515

—

C₂×#64515

C₄

yes

—

#10597279

—

(C₂×D₁₉)⋊C₈

—

C₂³×D₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

Q₈

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₄×D₁₉

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

#64515

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1811

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

C₂²×M₁₆

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#380

yes

characteristic

C₂×C₁₉

#430

yes

—

D₁₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#108

—

C₂²⋊C₈

—

C₁₉

#1811

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

Q₈×D₁₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

108

C₂×C₄

#64541

yes

—

109

C₂×C₄

D₄×D₁₉

yes

—

110

C₂×C₄

D₄×D₁₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

120

C₂²

#10597342

yes

—

121

C₄

—

122

C₄

#10597318

yes

characteristic

123

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

124

C₄

#10597330

yes

—

125

C₂

—

126

C₂

—

127

C₂

#11926403

yes

characteristic

128

C₂

#11926591

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#341	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#341	D₁₉
hypocenter	C₁₉	#1811
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#341

C₂

socle

C₂²×C₁₉

C₂×C₄⋊C₄

prime radical

C₂³×D₁₉

Q₈

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
4. #11926309	C₂	semidirect
5. C₁₉×#341	C₂	semidirect
65. #341	D₁₉	semidirect
79. C₁₉	#1811	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

4. #11926309

C₂

semidirect

5. C₁₉×#341

C₂

semidirect

65. #341

D₁₉

semidirect

79. C₁₉

#1811

semidirect

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

subgroup	index
C₂²×#64515	2
C₂×#10597279	2
#11926507	2
#11926309	2
C₁₉×#341	2
#1811	19

subgroup

index

C₂²×#64515

C₁₉×#341

Subgroups — #14563676

Conjugacy classes of subgroups

Complements

Maximal subgroups