Group #14563752 — subgroups

Subgroups — #14563752

Order 2432.

260 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₄⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal
2	#11926299	C₂	1	4	yes	maximal
3	C₄³×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₉	C₄	1	2	yes	—
5	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₁₉⋊C₈	C₂²	1	4	yes	—
10	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
11	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
16	C₄²×C₁₉	—	2	4	no	—
17	C₄²×C₁₉	—	2	2	no	—
18	C₄²×C₁₉	—	2	4	no	—
19	C₄²×C₁₉	C₈	1	4	yes	complemented
20	C₄²×C₁₉	D₄	1	2	yes	—
21	C₄²×C₁₉	Q₈	1	2	yes	—
22	C₂×C₁₉⋊C₈	—	2	4	no	—
23	C₂×C₁₉⋊C₈	—	2	8	no	—
24	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉	—	2	2	no	—
26	C₂×C₄×C₁₉	—	2	2	no	—
27	C₂×C₄×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	—	2	2	no	—
29	C₂×C₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×C₈	1	4	yes	—
33	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₁₉	M₁₆	1	4	yes	—
35	C₂×C₄×C₁₉	M₁₆	1	2	yes	—
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#41	1	4	yes	—
39	C₁₉⋊C₈	—	4	4	no	—
40	#1831	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₁₉	#117	1	2	yes	—
43	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
44	C₂²×C₁₉	C₂×M₁₆	1	1	yes	characteristic
45	C₂²×C₁₉	C₂×M₁₆	1	2	yes	—
46	C₄×C₁₉	—	2	2	no	—
47	C₄×C₁₉	—	2	4	no	—
48	C₄×C₁₉	—	2	4	no	—
49	C₄×C₁₉	C₄⋊C₈	1	4	yes	—
50	C₄×C₁₉	#124	1	2	yes	—
51	C₄×C₁₉	#125	1	2	yes	—
52	C₂×C₄⋊C₈	—	19	2	no	—
53	C₄³	D₁₉	1	1	yes	characteristic
54	#336	—	19	4	no	—
55	C₂×C₁₉	#382	1	1	yes	characteristic
56	C₂×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₁₉	#423	1	1	yes	characteristic
58	C₂×C₁₉	#431	1	2	yes	—
59	C₂×C₁₉	#432	1	2	yes	—
60	C₂²×C₈	—	19	4	no	—
61	C₂×C₄²	Dic₁₉	1	2	yes	—
62	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
63	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₁₉	1	2	yes	—
65	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
66	C₄⋊C₈	—	38	4	no	—
67	C₁₉	#1831	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
69	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
70	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
73	C₂×C₈	—	38	4	no	—
74	C₂×C₈	—	38	8	no	—
75	C₄²	—	2	4	no	—
76	C₄²	—	2	2	no	—
77	C₄²	—	2	4	no	—
78	C₄²	C₁₉⋊C₈	1	4	yes	complemented
79	C₄²	Dic₃₈	1	2	yes	—
80	C₄²	D₇₆	1	2	yes	—
81	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	C₂×C₁₉⋊C₈	1	4	yes	—
88	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
89	C₂×C₄	#64520	1	4	yes	—
90	C₂×C₄	#64520	1	2	yes	—
91	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
92	C₂×C₄	C₄⋊Dic₁₉	1	2	yes	—
93	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
94	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
95	C₂×C₄	#64541	1	4	yes	—
96	C₈	—	76	4	no	—
97	C₂²	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
98	C₂²	C₂×#64520	1	1	yes	characteristic
99	C₂²	C₂×#64520	1	2	yes	—
100	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
101	C₂²	#10597372	1	2	yes	—
102	C₄	—	2	2	no	—
103	C₄	—	2	4	no	—
104	C₄	—	2	4	no	—
105	C₄	C₄⋊(C₁₉⋊C₈)	1	4	yes	—
106	C₄	#10597316	1	2	yes	—
107	C₄	#10597321	1	2	yes	—
108	C₂	#11926410	1	1	yes	characteristic
109	C₂	C₂×C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
110	C₂	#11926568	1	1	yes	characteristic
111	C₂	#11926597	1	2	yes	—
112	C₂	#11926601	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal

#11926299

C₂

yes

maximal

C₄³×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₄

yes

characteristic

C₂×C₄²×C₁₉

C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₈

yes

complemented

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#1831

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

—

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊C₈

yes

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

#125

yes

—

C₂×C₄⋊C₈

—

C₄³

D₁₉

yes

characteristic

#336

—

C₂×C₁₉

#382

yes

characteristic

C₂×C₁₉

C₂×C₄⋊C₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#432

yes

—

C₂²×C₈

—

C₂×C₄²

Dic₁₉

yes

—

C₂×C₄²

Dic₁₉

yes

characteristic

C₂×C₄²

Dic₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₁₉

#1831

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₁₉⋊C₈

yes

complemented

C₄²

Dic₃₈

yes

—

C₄²

D₇₆

yes

—

C₂³

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

#64520

yes

—

C₂×C₄

#64520

yes

—

C₂×C₄

C₄⋊Dic₁₉

yes

—

C₂×C₄

C₄⋊Dic₁₉

yes

—

C₂×C₄

C₂×Dic₃₈

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64541

yes

—

C₈

—

C₂²

C₂²×C₁₉⋊C₈

yes

C₂²

yes

C₂²

yes

—

100

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

101

C₂²

#10597372

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄⋊(C₁₉⋊C₈)

yes

—

106

C₄

#10597316

yes

—

107

C₄

#10597321

yes

—

108

C₂

#11926410

yes

characteristic

109

C₂

C₂×C₄⋊(C₁₉⋊C₈)

yes

characteristic

110

C₂

#11926568

yes

characteristic

111

C₂

#11926597

yes

—

112

C₂

#11926601

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂²×C₈
Fitting	C₄³×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄³	D₁₉
hypocenter	C₁₉	#1831
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂²×C₈

Fitting

C₄³×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₄³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
19. C₄²×C₁₉	C₈	semidirect
67. C₁₉	#1831	semidirect
78. C₄²	C₁₉⋊C₈	semidirect

H ≅ G/N

type

19. C₄²×C₁₉

C₈

semidirect

67. C₁₉

#1831

semidirect

78. C₄²

C₁₉⋊C₈

semidirect

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

subgroup	index
C₂×C₄⋊(C₁₉⋊C₈)	2
#11926299	2
C₄³×C₁₉	2
#1831	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

#11926299

C₄³×C₁₉

#1831

Subgroups — #14563752

Conjugacy classes of subgroups

Complements

Maximal subgroups