Group #14564628 — subgroups

Subgroups — #14564628

Order 2432.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11926568	C₂	1	1	yes	maximal, characteristic
3	#11926312	C₂	1	4	yes	maximal
4	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂×Dic₁₉⋊C₄	C₄	1	4	yes	—
9	C₂×#64520	C₂²	1	2	yes	—
10	#10597316	—	2	2	no	—
11	#10597316	—	2	1	no	—
12	#10597316	—	2	1	no	—
13	C₁₉×#97	—	2	1	no	—
14	C₄×C₈×C₁₉	—	2	1	no	—
15	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
19	M₁₆×C₁₉	—	2	2	no	—
20	M₁₆×C₁₉	Q₈	1	4	yes	—
21	C₂×C₈×C₁₉	—	2	2	no	—
22	C₄²×C₁₉	D₄	1	2	yes	—
23	C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	Dic₁₉⋊C₄	—	2	4	no	—
28	Dic₁₉⋊C₄	—	2	4	no	—
29	#64520	—	2	4	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	4	2	no	—
33	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₂×Dic₁₉	—	2	4	no	—
40	C₂×Dic₁₉	—	4	4	no	—
41	C₈×C₁₉	—	2	4	no	—
42	C₁₉⋊C₈	—	4	2	no	—
43	#1998	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	2	no	—
45	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₁₉	C₄×Q₈	1	2	yes	—
47	C₄×C₁₉	—	2	2	no	—
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
50	C₄×C₁₉	#124	1	1	yes	characteristic
51	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
52	Dic₁₉	—	4	4	no	—
53	C₂×#125	—	19	1	no	—
54	#423	—	19	1	no	—
55	C₄×M₁₆	D₁₉	1	1	yes	characteristic
56	#343	—	19	4	no	—
57	C₂×C₁₉	—	2	2	no	—
58	C₂×C₁₉	#391	1	1	yes	characteristic
59	C₂×C₁₉	#413	1	2	yes	—
60	C₂×M₁₆	—	19	2	no	—
61	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
62	#125	—	38	2	no	—
63	#125	—	38	1	no	—
64	#125	—	38	1	no	—
65	C₂×C₄⋊C₄	—	19	4	no	—
66	C₂×C₄⋊C₄	—	19	2	no	—
67	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
68	C₄⋊C₈	—	38	2	no	—
69	#97	—	2	1	no	—
70	C₄×C₈	—	2	1	no	—
71	C₁₉	#1998	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	19	4	no	—
73	C₂²×C₄	C₄×D₁₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
75	M₁₆	—	2	2	no	—
76	M₁₆	—	38	4	no	—
77	M₁₆	Dic₃₈	1	4	yes	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	38	2	no	—
80	C₄⋊C₄	—	38	4	no	—
81	C₄⋊C₄	—	38	4	no	—
82	C₄⋊C₄	—	38	2	no	—
83	C₄⋊C₄	—	38	2	no	—
84	C₄²	D₇₆	1	2	yes	—
85	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
86	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
87	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	38	4	no	—
90	C₂×C₄	—	76	4	no	—
91	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
92	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
93	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
94	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
95	C₂×C₄	#64541	1	2	yes	—
96	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
97	C₈	—	2	4	no	—
98	C₈	—	76	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₄×Dic₃₈	1	2	yes	—
101	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	76	4	no	—
105	C₄	#10597315	1	1	yes	characteristic
106	C₄	#10597321	1	1	yes	characteristic
107	C₄	#10597370	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	#11926450	1	1	yes	characteristic
110	C₂	#11926526	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal

C₄×M₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×#64520

C₂²

yes

—

#10597316

—

#10597316

—

#10597316

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1998

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

C₂×#125

—

#423

—

C₄×M₁₆

D₁₉

yes

characteristic

#343

—

C₂×C₁₉

—

C₂×C₁₉

#391

yes

characteristic

C₂×C₁₉

#413

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1998

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Dic₃₈

yes

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₇₆

yes

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₂³

C₂×C₄×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64541

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₂²

—

100

C₂²

C₄×Dic₃₈

yes

—

101

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#10597315

yes

characteristic

106

C₄

#10597321

yes

characteristic

107

C₄

#10597370

yes

—

108

C₂

—

109

C₂

#11926450

yes

characteristic

110

C₂

#11926526

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₄×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄×M₁₆	D₁₉
hypocenter	C₁₉	#1998
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₄×M₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₄×M₁₆

D₁₉

hypocenter

C₁₉

#1998

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
71. C₁₉	#1998	semidirect

H ≅ G/N

type

71. C₁₉

#1998

semidirect

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

subgroup	index
C₂×#10597316	2
#11926568	2
#11926312	2
C₄×M₁₆×C₁₉	2
#1998	19

subgroup

index

C₄×M₁₆×C₁₉

Subgroups — #14564628

Conjugacy classes of subgroups

Complements

Maximal subgroups