Group #14562775 — subgroups

Subgroups — #14562775

Order 2432.

206 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 65 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	#11926923	C₂	1	1	yes	maximal, characteristic
2	#11926839	C₂	1	2	yes	maximal
3	#11926293	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
5	Q₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	—	2	2	no	—
7	C₁₉×C₄⋊Q₈	—	2	2	no	—
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	—	2	2	no	—
10	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₂×#64528	—	2	2	no	—
12	#10597315	C₂²	1	1	yes	characteristic
13	#10597292	—	2	2	no	—
14	#10597264	—	2	2	no	—
15	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
16	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	D₄	1	2	yes	—
19	C₂×Q₈×C₁₉	D₄	1	2	yes	—
20	C₂×Dic₃₈	—	2	1	no	—
21	C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₄²×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	—	2	2	no	—
27	C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#64528	—	4	4	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	1	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	Q₈×C₁₉	—	2	2	no	—
33	Q₈×C₁₉	—	4	2	no	—
34	Q₈×C₁₉	—	8	2	no	—
35	Q₈×C₁₉	Q₁₆	1	4	yes	complemented
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₂×Dic₁₉	—	4	1	no	—
42	Dic₃₈	—	4	2	no	—
43	C₁₉⋊C₈	—	2	2	no	—
44	C₁₉⋊C₈	—	4	2	no	—
45	#1633	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	#120	1	1	yes	characteristic
47	C₄×C₁₉	—	2	4	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	4	2	no	—
50	C₄×C₁₉	—	4	2	no	—
51	C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
52	C₄×C₁₉	#137	1	2	yes	—
53	Dic₁₉	—	8	1	no	—
54	Q₈²	D₁₉	1	1	yes	characteristic
55	#494	—	19	1	no	—
56	#477	—	19	2	no	—
57	#333	—	19	1	no	—
58	Q₈⋊C₈	—	19	2	no	—
59	C₂×C₁₉	#451	1	2	yes	—
60	C₂×C₁₉	#453	1	1	yes	characteristic
61	C₂×Q₁₆	—	38	2	no	—
62	C₄⋊Q₈	—	2	2	no	—
63	C₄⋊Q₈	—	2	2	no	—
64	C₄⋊Q₈	—	19	1	no	—
65	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
66	C₄×Q₈	—	2	2	no	—
67	C₄×Q₈	C₂×D₁₉	1	2	yes	—
68	#107	—	38	2	no	—
69	C₄⋊C₈	—	19	2	no	—
70	#103	—	38	2	no	—
71	C₄×C₈	—	19	1	no	—
72	C₁₉	#1633	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	2	2	no	—
74	C₂×Q₈	—	38	1	no	—
75	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
76	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
77	Q₁₆	—	76	4	no	—
78	C₂×C₈	—	38	1	no	—
79	C₂×C₈	—	38	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	38	2	no	—
84	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
85	C₄²	—	2	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	C₂²×D₁₉	1	1	yes	characteristic
88	Q₈	—	2	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	8	2	no	—
91	Q₈	—	76	2	no	—
92	Q₈	#64528	1	4	yes	complemented
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	76	1	no	—
97	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
99	C₈	—	38	2	no	—
100	C₈	—	76	2	no	—
101	C₂²	#10597399	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	4	2	no	—
106	C₄	—	152	1	no	—
107	C₄	#10597388	1	2	yes	—
108	C₄	C₂×#64528	1	2	yes	—
109	C₂	#11926700	1	2	yes	—
110	C₂	#11926712	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926923

C₂

yes

maximal, characteristic

#11926839

C₂

yes

maximal

#11926293

C₂

yes

maximal, characteristic

Q₈⋊(C₁₉⋊C₈)

C₂

yes

maximal

Q₈²×C₁₉

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₂×#64528

—

#10597315

C₂²

yes

characteristic

#10597292

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

Q₁₆

yes

complemented

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

#137

yes

—

Dic₁₉

—

Q₈²

D₁₉

yes

—

—

—

Q₈⋊C₈

—

C₂×C₁₉

#451

yes

—

C₂×C₁₉

#453

yes

characteristic

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

C₂×D₁₉

yes

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₁₉

#1633

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

#64528

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

C₈

—

100

C₈

—

101

C₂²

#10597399

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

152

—

107

C₄

#10597388

yes

—

108

C₄

C₂×#64528

yes

—

109

C₂

#11926700

yes

—

110

C₂

#11926712

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	Q₈²×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	#120
hypercenter	Q₈²	D₁₉
hypocenter	C₁₉	#1633
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

subgroup

G/H

center

C₂²

#10597399

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

Q₈²×C₁₉

C₂

socle, prime radical

C₂²×C₁₉

#120

hypercenter

Q₈²

D₁₉

hypocenter

C₁₉

#1633

LCS

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ Q₈²

N	H ≅ G/N	type
35. Q₈×C₁₉	Q₁₆	semidirect
72. C₁₉	#1633	semidirect
92. Q₈	#64528	semidirect

H ≅ G/N

type

35. Q₈×C₁₉

Q₁₆

semidirect

72. C₁₉

#1633

semidirect

92. Q₈

#64528

semidirect

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

subgroup	index
#11926923	2
#11926839	2
#11926293	2
Q₈⋊(C₁₉⋊C₈)	2
Q₈²×C₁₉	2
#1633	19

subgroup

index

#11926923

#11926839

#11926293

Q₈⋊(C₁₉⋊C₈)

Q₈²×C₁₉

#1633

Subgroups — #14562775

Conjugacy classes of subgroups

Complements

Maximal subgroups