Group #14565740 — subgroups

Subgroups — #14565740

Order 2432.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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×#10597255	C₂	1	1	yes	maximal, characteristic
2	#11926782	C₂	1	2	yes	maximal
3	#11926372	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926348	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
7	#10597392	—	2	2	no	—
8	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×Q₃₂	—	2	2	no	—
10	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	#10597292	—	2	2	no	—
12	#10597275	C₂²	1	2	yes	—
13	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
14	#10597255	—	2	2	no	—
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₉	—	2	2	no	—
18	Q₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
20	(C₂×D₁₉)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₁₉	—	2	2	no	—
22	Dic₁₉⋊C₄	—	4	2	no	—
23	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
24	C₈×D₁₉	—	2	1	no	—
25	C₈×D₁₉	—	2	1	no	—
26	C₁₆×C₁₉	D₄	1	2	yes	—
27	C₁₉⋊C₁₆	—	2	1	no	—
28	C₂²×D₁₉	D₈	1	1	yes	characteristic
29	Q₈×C₁₉	—	4	2	no	—
30	Q₈×C₁₉	—	4	2	no	—
31	C₂×C₄×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₁₉	—	4	2	no	—
34	C₂×Dic₁₉	D₈	1	1	yes	characteristic
35	C₄×D₁₉	—	2	1	no	—
36	C₄×D₁₉	—	2	1	no	—
37	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	#41	1	1	yes	characteristic
39	C₁₉⋊C₈	—	2	1	no	—
40	#2219	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₂×D₁₉	—	2	1	no	—
43	C₂×D₁₉	—	2	2	no	—
44	C₄×C₁₉	—	8	2	no	—
45	C₄×C₁₉	#121	1	1	yes	characteristic
46	C₄×C₁₉	#135	1	1	yes	characteristic
47	Dic₁₉	—	2	1	no	—
48	Dic₁₉	—	8	2	no	—
49	C₂×Q₃₂	D₁₉	1	1	yes	characteristic, complemented
50	C₂×M₃₂	—	19	1	no	—
51	#467	—	19	2	no	—
52	#367	—	19	1	no	—
53	#358	—	19	2	no	—
54	C₂×C₁₉	#466	1	1	yes	characteristic
55	C₂×C₁₉	#510	1	2	yes	—
56	D₁₉	—	4	1	no	—
57	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
58	C₂²×C₈	—	19	1	no	—
59	C₂²⋊Q₈	—	38	2	no	—
60	Q₃₂	—	2	2	no	—
61	M₃₂	—	38	2	no	—
62	C₂×C₁₆	—	19	1	no	—
63	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
64	#107	—	19	2	no	—
65	#103	—	38	2	no	—
66	C₁₉	#2219	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	2	2	no	—
68	C₂²×C₄	—	19	1	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	19	1	no	—
72	C₂×C₈	—	38	1	no	—
73	C₂×C₈	—	38	1	no	—
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄⋊C₄	—	38	2	no	—
76	C₄⋊C₄	—	76	2	no	—
77	C₂²⋊C₄	—	76	2	no	—
78	C₁₆	—	38	1	no	—
79	C₁₆	C₂²⋊D₁₉	1	2	yes	—
80	C₂³	—	19	1	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	19	1	no	—
85	C₂×C₄	—	38	1	no	—
86	C₂×C₄	—	38	1	no	—
87	C₂×C₄	—	76	2	no	—
88	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
89	C₈	—	38	1	no	—
90	C₈	#64543	1	1	yes	characteristic
91	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
92	C₂²	—	38	2	no	—
93	C₂²	—	38	1	no	—
94	C₂²	D₈×D₁₉	1	1	yes	characteristic
95	C₄	—	8	2	no	—
96	C₄	—	38	1	no	—
97	C₄	—	152	2	no	—
98	C₄	#10597358	1	1	yes	characteristic
99	C₄	#10597384	1	1	yes	characteristic
100	C₂	—	76	1	no	—
101	C₂	#11926777	1	1	yes	characteristic
102	C₂	#11926986	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597255

C₂

yes

maximal, characteristic

#11926782

C₂

yes

maximal

#11926372

C₂

yes

maximal, characteristic, complemented

#11926348

C₂

yes

maximal, complemented

C₂×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

—

#10597392

—

C₂×C₈×D₁₉

C₂²

yes

characteristic

C₁₉×Q₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597292

—

#10597275

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597255

—

C₂×Q₈×C₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₈×D₁₉

—

C₈×D₁₉

—

C₁₆×C₁₉

D₄

yes

—

C₁₉⋊C₁₆

—

C₂²×D₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2219

—

maximal, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

D₁₉

yes

characteristic, complemented

C₂×M₃₂

—

#467

—

#367

—

#358

—

C₂×C₁₉

#466

yes

characteristic

C₂×C₁₉

#510

yes

—

D₁₉

—

C₂×Q₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

—

#103

—

C₁₉

#2219

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

C₂²⋊D₁₉

yes

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₈

—

C₈

#64543

yes

characteristic

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

D₈×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#11926777

yes

characteristic

102

C₂

#11926986

yes

—

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₃₂	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂²×D₁₉	D₈
hypercenter	C₂×Q₃₂	D₁₉
hypocenter	C₁₉	#2219
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₁₉×Q₃₂

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂²×D₁₉

D₈

hypercenter

C₂×Q₃₂

D₁₉

hypocenter

C₁₉

#2219

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #11926372	C₂	semidirect
4. #11926348	C₂	semidirect
5. C₂×C₁₉×Q₃₂	C₂	semidirect
49. C₂×Q₃₂	D₁₉	semidirect
66. C₁₉	#2219	semidirect

H ≅ G/N

type

3. #11926372

C₂

semidirect

4. #11926348

C₂

semidirect

5. C₂×C₁₉×Q₃₂

C₂

semidirect

49. C₂×Q₃₂

D₁₉

semidirect

66. C₁₉

#2219

semidirect

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

subgroup	index
C₂×#10597255	2
#11926782	2
#11926372	2
#11926348	2
C₂×C₁₉×Q₃₂	2
#2219	19

subgroup

index

C₂×C₁₉×Q₃₂

Subgroups — #14565740

Conjugacy classes of subgroups

Complements

Maximal subgroups