Group #14565682 — subgroups

Subgroups — #14565682

Order 2432.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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×#10597286	C₂	1	2	yes	maximal
2	C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#11926348	C₂	1	2	yes	maximal
5	C₁₉×#494	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	—	2	1	no	—
7	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
8	C₁₉×C₄⋊Q₈	—	2	1	no	—
9	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
10	C₄×Dic₃₈	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597286	—	2	4	no	—
13	#10597275	C₂²	1	1	yes	characteristic
14	#10597273	—	2	1	no	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Dic₃₈	—	2	1	no	—
18	Q₁₆×C₁₉	—	2	2	no	—
19	Q₁₆×C₁₉	—	2	2	no	—
20	Q₁₆×C₁₉	—	4	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	4	1	no	—
24	C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	2	1	no	—
27	Dic₁₉⋊C₄	—	4	1	no	—
28	C₄×Dic₁₉	—	4	1	no	—
29	Dic₇₆	—	2	1	no	—
30	Dic₇₆	D₄	1	2	yes	—
31	C₁₉⋊C₁₆	—	2	2	no	—
32	Q₈×C₁₉	—	4	2	no	—
33	Q₈×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₁₉	—	4	1	no	—
39	C₂×Dic₁₉	—	4	1	no	—
40	Dic₃₈	—	2	2	no	—
41	Dic₃₈	—	4	1	no	—
42	C₈×C₁₉	—	2	1	no	—
43	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₈×C₁₉	#41	1	1	yes	characteristic
45	#2209	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	8	2	no	—
49	C₄×C₁₉	Q₃₂	1	2	yes	complemented
50	C₄×C₁₉	#121	1	1	yes	characteristic
51	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
52	Dic₁₉	—	4	2	no	—
53	Dic₁₉	—	8	1	no	—
54	C₂×Q₃₂	—	19	2	no	—
55	#494	D₁₉	1	1	yes	characteristic
56	C₄×Q₁₆	—	19	1	no	—
57	C₄⋊C₁₆	—	19	1	no	—
58	#358	—	19	2	no	—
59	C₂×C₁₉	#459	1	1	yes	characteristic
60	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
61	C₂×C₁₉	#510	1	1	yes	characteristic
62	C₂×Q₁₆	—	2	1	no	—
63	C₂×Q₁₆	—	19	1	no	—
64	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
65	C₄⋊Q₈	—	2	1	no	—
66	C₄×Q₈	—	38	1	no	—
67	Q₃₂	—	38	4	no	—
68	C₂×C₁₆	—	19	2	no	—
69	#107	—	19	1	no	—
70	#103	—	38	1	no	—
71	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
72	C₁₉	#2209	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	38	1	no	—
75	Q₁₆	—	2	2	no	—
76	Q₁₆	—	2	2	no	—
77	Q₁₆	—	4	2	no	—
78	Q₁₆	—	19	2	no	—
79	Q₁₆	—	38	1	no	—
80	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
82	C₄⋊C₄	—	4	1	no	—
83	C₄⋊C₄	—	4	1	no	—
84	C₄⋊C₄	—	38	1	no	—
85	C₄⋊C₄	—	76	1	no	—
86	C₄²	—	76	1	no	—
87	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₁₆	—	38	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	38	2	no	—
92	Q₈	—	76	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	—	76	1	no	—
95	C₂×C₄	—	76	1	no	—
96	C₂×C₄	#64525	1	1	yes	characteristic
97	C₂×C₄	#64525	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	D₄×D₁₉	1	1	yes	characteristic
101	C₈	#64543	1	1	yes	characteristic
102	C₂²	C₂×#64525	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	2	no	—
105	C₄	—	76	2	no	—
106	C₄	—	152	1	no	—
107	C₄	#10597286	1	2	yes	complemented
108	C₄	#10597378	1	1	yes	characteristic
109	C₄	#10597384	1	1	yes	characteristic
110	C₂	#11926736	1	1	yes	characteristic
111	C₂	C₂×#10597286	1	1	yes	characteristic
112	C₂	#11926985	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597286

C₂

yes

maximal

C₄×Dic₇₆

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal

C₁₉×#494

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597286

—

#10597275

C₂²

yes

characteristic

#10597273

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

D₄

yes

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₃₂

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

#494

D₁₉

yes

characteristic

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

C₂×C₁₉

#459

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#510

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

#107

—

#103

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2209

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

100

C₈

D₄×D₁₉

yes

characteristic

101

C₈

#64543

yes

characteristic

102

C₂²

C₂×#64525

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

152

—

107

C₄

#10597286

yes

complemented

108

C₄

#10597378

yes

characteristic

109

C₄

#10597384

yes

characteristic

110

C₂

#11926736

yes

characteristic

111

C₂

C₂×#10597286

yes

characteristic

112

C₂

#11926985

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#494	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	#494	D₁₉
hypocenter	C₁₉	#2209
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#494

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
49. C₄×C₁₉	Q₃₂	semidirect
72. C₁₉	#2209	semidirect
107. C₄	#10597286	semidirect

H ≅ G/N

type

49. C₄×C₁₉

Q₃₂

semidirect

72. C₁₉

#2209

semidirect

107. C₄

#10597286

semidirect

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

subgroup	index
C₂×#10597286	2
C₄×Dic₇₆	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926348	2
C₁₉×#494	2
#2209	19

subgroup

index

C₂×#10597286

C₄×Dic₇₆

C₄⋊(C₁₉⋊C₁₆)

#11926348

C₁₉×#494

#2209

Subgroups — #14565682

Conjugacy classes of subgroups

Complements

Maximal subgroups