Group #14565787 — subgroups

Subgroups — #14565787

Order 2432.

130 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926949	C₂	1	1	yes	maximal, characteristic
2	#11926369	C₂	1	2	yes	maximal
3	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#11926348	C₂	1	2	yes	maximal
5	C₄×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₄×Q₈×C₁₉	—	2	1	no	—
8	#10597315	—	2	1	no	—
9	C₁₉×#107	C₂²	1	1	yes	characteristic
10	C₁₉×#103	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597275	—	2	1	no	—
13	#10597275	C₂²	1	2	yes	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×Dic₃₈	—	4	1	no	—
17	Q₁₆×C₁₉	—	2	1	no	—
18	Q₁₆×C₁₉	Q₈	1	2	yes	complemented
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	4	1	no	—
23	C₄²×C₁₉	—	4	1	no	—
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	4	1	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	Q₈×C₁₉	—	2	2	no	—
29	Q₈×C₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₉	—	4	2	no	—
36	Dic₃₈	—	8	2	no	—
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2227	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	—	4	2	no	—
44	C₄×C₁₉	—	8	1	no	—
45	C₄×C₁₉	Q₃₂	1	2	yes	—
46	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
47	C₄×C₁₉	#137	1	1	yes	characteristic
48	Dic₁₉	—	8	2	no	—
49	#500	—	19	1	no	—
50	C₄×Q₁₆	D₁₉	1	1	yes	characteristic
51	#366	—	19	2	no	—
52	C₄⋊C₁₆	—	19	1	no	—
53	#358	—	19	2	no	—
54	C₂×C₁₉	#474	1	1	yes	characteristic
55	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₁₉	#509	1	1	yes	characteristic
57	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
58	C₄⋊Q₈	—	38	1	no	—
59	C₄×Q₈	—	2	1	no	—
60	C₂×C₁₆	—	19	2	no	—
61	#107	—	19	2	no	—
62	#107	—	38	1	no	—
63	#107	C₂×D₁₉	1	1	yes	characteristic
64	#103	—	2	1	no	—
65	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	C₁₉	#2227	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	2	1	no	—
68	C₂×Q₈	—	76	1	no	—
69	Q₁₆	—	2	1	no	—
70	Q₁₆	Dic₃₈	1	2	yes	complemented
71	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	—	2	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄⋊C₄	—	38	2	no	—
76	C₄⋊C₄	—	76	1	no	—
77	C₄²	—	4	1	no	—
78	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₁₆	—	38	2	no	—
80	Q₈	—	2	2	no	—
81	Q₈	—	4	1	no	—
82	Q₈	—	152	2	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	—	76	2	no	—
86	C₂×C₄	#64525	1	1	yes	characteristic
87	C₂×C₄	#64525	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	C₂×Dic₃₈	1	1	yes	characteristic
91	C₈	#64541	1	1	yes	characteristic
92	C₂²	C₂×#64525	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	4	2	no	—
95	C₄	—	8	1	no	—
96	C₄	—	152	2	no	—
97	C₄	#10597286	1	2	yes	—
98	C₄	#10597370	1	1	yes	characteristic
99	C₄	#10597397	1	1	yes	characteristic
100	C₂	#11926824	1	1	yes	characteristic
101	C₂	C₂×#10597286	1	1	yes	characteristic
102	C₂	#11926979	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic

#11926369

C₂

yes

maximal

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

#11926348

C₂

yes

maximal

C₄×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

#10597315

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

—

#10597275

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂×Q₈

yes

C₈×C₁₉

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₃₂

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

#500

—

C₄×Q₁₆

D₁₉

yes

characteristic

#366

—

C₄⋊C₁₆

—

#358

—

C₂×C₁₉

#474

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2227

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

Dic₃₈

yes

complemented

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

—

152

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

C₂×Dic₃₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

152

—

C₄

#10597286

yes

—

C₄

yes

C₄

yes

100

C₂

#11926824

yes

characteristic

101

C₂

C₂×#10597286

yes

characteristic

102

C₂

#11926979

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×Q₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×Q₁₆	D₁₉
hypocenter	C₁₉	#2227
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×Q₁₆×C₁₉

C₂

socle, prime radical

C₂²×C₁₉

C₂×D₈

hypercenter

C₄×Q₁₆

D₁₉

hypocenter

C₁₉

#2227

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
18. Q₁₆×C₁₉	Q₈	semidirect
66. C₁₉	#2227	semidirect
70. Q₁₆	Dic₃₈	semidirect

H ≅ G/N

type

18. Q₁₆×C₁₉

Q₈

semidirect

66. C₁₉

#2227

semidirect

70. Q₁₆

Dic₃₈

semidirect

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

subgroup	index
#11926949	2
#11926369	2
C₄⋊(C₁₉⋊C₁₆)	2
#11926348	2
C₄×Q₁₆×C₁₉	2
#2227	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₄×Q₁₆×C₁₉

Subgroups — #14565787

Conjugacy classes of subgroups

Complements

Maximal subgroups