Group #14565211 — subgroups

Subgroups — #14565211

Order 2432.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#11926593	C₂	1	1	yes	maximal, characteristic
2	#11926567	C₂	1	1	yes	maximal, characteristic
3	#11926314	C₂	1	2	yes	maximal
4	#11926303	C₂	1	2	yes	maximal
5	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#117	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	#10597276	—	2	2	no	—
12	Dic₁₉⋊C₈	—	2	2	no	—
13	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₉	—	2	1	no	—
15	M₁₆×C₁₉	—	2	2	no	—
16	C₂×C₈×C₁₉	D₄	1	2	yes	—
17	C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₄²×C₁₉	—	2	2	no	—
20	C₄×Dic₁₉	—	2	1	no	—
21	C₄×Dic₁₉	Q₈	1	1	yes	characteristic
22	C₄×Dic₁₉	Q₈	1	1	yes	characteristic
23	#64520	—	2	2	no	—
24	#64520	—	2	2	no	—
25	#64520	—	2	2	no	—
26	C₂×C₁₉⋊C₈	—	2	1	no	—
27	C₂×C₁₉⋊C₈	—	2	2	no	—
28	C₂³×C₁₉	#41	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	4	2	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	#41	1	2	yes	—
33	C₂×C₄×C₁₉	#41	1	2	yes	—
34	C₂×Dic₁₉	—	2	1	no	—
35	C₂×Dic₁₉	—	2	1	no	—
36	C₂×Dic₁₉	—	4	2	no	—
37	C₈×C₁₉	—	2	2	no	—
38	C₁₉⋊C₈	—	4	1	no	—
39	C₁₉⋊C₈	—	4	2	no	—
40	#2102	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	—	4	1	no	—
42	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂²×C₁₉	#126	1	2	yes	—
44	C₄×C₁₉	—	8	2	no	—
45	C₄×C₁₉	#123	1	1	yes	characteristic
46	C₄×C₁₉	#124	1	1	yes	characteristic
47	C₄×C₁₉	#125	1	2	yes	—
48	Dic₁₉	—	2	2	no	—
49	Dic₁₉	—	4	1	no	—
50	#430	—	19	1	no	—
51	#423	—	19	1	no	—
52	#344	—	19	2	no	—
53	#339	—	19	2	no	—
54	H(3,ℤ/4)	D₁₉	1	1	yes	characteristic
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	2	2	no	—
57	C₂×C₁₉	#400	1	1	yes	characteristic
58	C₂×M₁₆	—	19	2	no	—
59	C₂×M₁₆	—	19	1	no	—
60	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
61	#117	C₂×D₁₉	1	2	yes	—
62	C₂×C₄²	—	19	1	no	—
63	#108	—	38	2	no	—
64	C₄⋊C₈	—	38	2	no	—
65	C₁₉	#2102	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	38	1	no	—
67	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	38	2	no	—
70	M₁₆	—	38	2	no	—
71	M₁₆	—	38	2	no	—
72	C₂×C₈	—	38	1	no	—
73	C₂×C₈	—	38	2	no	—
74	C₂×C₈	D₇₆	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	19	1	no	—
79	C₄²	—	19	1	no	—
80	C₄²	—	38	1	no	—
81	C₂³	#64543	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	38	1	no	—
84	C₂×C₄	—	38	1	no	—
85	C₂×C₄	—	76	2	no	—
86	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
87	C₂×C₄	#64541	1	2	yes	—
88	C₂×C₄	#64543	1	2	yes	—
89	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	76	2	no	—
92	C₈	—	76	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#10597325	1	2	yes	—
95	C₂²	#10597343	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	—	38	2	no	—
98	C₄	—	76	1	no	—
99	C₄	#10597321	1	1	yes	characteristic
100	C₄	#10597332	1	1	yes	characteristic
101	C₄	#10597335	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#11926484	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic

#11926567

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal

#11926303

C₂

yes

maximal

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

#10597276

—

Dic₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

Q₈

yes

characteristic

C₄×Dic₁₉

Q₈

yes

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2102

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#126

yes

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#400

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₁₉

#2102

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#64543

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64541

yes

—

C₂×C₄

#64543

yes

—

C₂×C₄

Q₈×D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#10597325

yes

—

C₂²

#10597343

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#10597321

yes

characteristic

100

C₄

#10597332

yes

characteristic

101

C₄

#10597335

yes

—

102

C₂

—

103

C₂

—

104

C₂

#11926484

yes

characteristic

	subgroup	G/H
center	C₄	#10597321
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×H(3,ℤ/4)	C₂
socle	C₂×C₁₉	#400
prime radical	C₂³×C₁₉	#41
hypercenter	H(3,ℤ/4)	D₁₉
hypocenter	C₁₉	#2102
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#10597321

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×H(3,ℤ/4)

C₂

C₂×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
65. C₁₉	#2102	semidirect

H ≅ G/N

type

65. C₁₉

#2102

semidirect

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

subgroup	index
#11926593	2
#11926567	2
#11926314	2
#11926303	2
C₁₉×H(3,ℤ/4)	2
#2102	19

subgroup

index

C₁₉×H(3,ℤ/4)

Subgroups — #14565211

Conjugacy classes of subgroups

Complements

Maximal subgroups