Group #14563492 — subgroups

Subgroups — #14563492

Order 2432.

260 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₂×#10597260	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11926299	C₂	1	2	yes	maximal
5	C₁₉×#376	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
10	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
11	C₁₉×#95	C₄	1	4	yes	—
12	C₄⋊(C₁₉⋊C₈)	C₄	1	8	yes	complemented
13	#10597260	—	2	2	no	—
14	C₄×C₁₉⋊C₈	—	2	2	no	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₄²×C₁₉	—	2	2	no	—
20	C₄²×C₁₉	C₂×C₄	1	4	yes	—
21	C₄²×C₁₉	D₄	1	2	yes	—
22	C₄²×C₁₉	Q₈	1	2	yes	—
23	C₂×C₁₉⋊C₈	—	2	2	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂×C₁₉⋊C₈	—	2	2	no	—
26	C₂×C₁₉⋊C₈	—	2	2	no	—
27	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	4	no	—
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	—	2	2	no	—
33	C₂×C₄×C₁₉	—	2	4	no	—
34	C₂×C₄×C₁₉	C₄²	1	4	yes	—
35	C₂×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
36	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#41	1	2	yes	—
40	C₁₉⋊C₈	—	2	4	no	—
41	C₁₉⋊C₈	—	2	4	no	—
42	#1768	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₉	#117	1	1	yes	characteristic
46	C₂²×C₁₉	#131	1	4	yes	—
47	C₄×C₁₉	—	2	4	no	—
48	C₄×C₁₉	—	2	4	no	—
49	C₄×C₁₉	—	4	2	no	—
50	C₄×C₁₉	C₄×D₄	1	2	yes	—
51	C₄×C₁₉	C₄×Q₈	1	2	yes	—
52	C₂×C₄⋊C₈	—	19	2	no	—
53	C₂×#97	—	19	1	no	—
54	C₂×C₄×C₈	—	19	1	no	—
55	#376	D₁₉	1	1	yes	characteristic
56	#336	—	19	2	no	—
57	C₂×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₁₉	#405	1	2	yes	—
59	C₂×C₁₉	#424	1	2	yes	—
60	C₂×C₁₉	#433	1	2	yes	—
61	C₂²×C₈	—	19	2	no	—
62	C₂²×C₈	—	19	2	no	—
63	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
66	C₄⋊C₈	—	19	8	no	—
67	#97	—	38	2	no	—
68	C₄×C₈	—	38	2	no	—
69	#95	Dic₁₉	1	4	yes	—
70	C₁₉	#1768	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
72	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
73	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
75	C₂×C₈	—	19	4	no	—
76	C₂×C₈	—	19	4	no	—
77	C₂×C₈	—	38	2	no	—
78	C₂×C₈	—	38	2	no	—
79	C₂×C₈	—	38	2	no	—
80	C₂×C₈	—	38	2	no	—
81	C₄²	—	2	2	no	—
82	C₄²	Dic₃₈	1	2	yes	—
83	C₄²	C₄×D₁₉	1	4	yes	—
84	C₄²	D₇₆	1	2	yes	—
85	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	C₄×Dic₁₉	1	4	yes	—
91	C₂×C₄	C₄⋊Dic₁₉	1	4	yes	—
92	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
94	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
95	C₂×C₄	#64541	1	2	yes	—
96	C₈	—	38	4	no	—
97	C₈	—	38	4	no	—
98	C₂²	C₂×C₄×Dic₁₉	1	1	yes	characteristic
99	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
100	C₂²	#10597372	1	1	yes	characteristic
101	C₂²	#10597394	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	2	4	no	—
104	C₄	—	4	2	no	—
105	C₄	C₄×Dic₃₈	1	2	yes	—
106	C₄	C₄×D₇₆	1	2	yes	—
107	C₂	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
108	C₂	#11926500	1	2	yes	—
109	C₂	#11926571	1	2	yes	—
110	C₂	#11926605	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal

C₁₉×#376

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

complemented

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1768

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

C₄×Q₈

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

—

#376

D₁₉

yes

characteristic

#336

—

C₂×C₁₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₉

#405

yes

—

C₂×C₁₉

#424

yes

—

C₂×C₁₉

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

#95

Dic₁₉

yes

—

C₁₉

#1768

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

Dic₃₈

yes

—

C₄²

C₄×D₁₉

yes

—

C₄²

D₇₆

yes

—

C₂³

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₁₉

yes

—

C₂×C₄

C₄⋊Dic₁₉

yes

—

C₂×C₄

C₂×Dic₃₈

yes

characteristic

C₂×C₄

C₂×C₄×D₁₉

yes

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64541

yes

—

C₈

—

C₈

—

C₂²

C₂×C₄×Dic₁₉

yes

characteristic

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

100

C₂²

#10597372

yes

characteristic

101

C₂²

#10597394

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄×Dic₃₈

yes

—

106

C₄

C₄×D₇₆

yes

—

107

C₂

C₄×C₄⋊Dic₁₉

yes

characteristic

108

C₂

#11926500

yes

—

109

C₂

#11926571

yes

—

110

C₂

#11926605

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄²
Fitting	C₁₉×#376	C₂
socle, prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#376	D₁₉
hypocenter	C₁₉	#1768
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂×C₄²

Fitting

C₁₉×#376

C₂

socle, prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
12. C₄⋊(C₁₉⋊C₈)	C₄	semidirect
70. C₁₉	#1768	semidirect

H ≅ G/N

type

12. C₄⋊(C₁₉⋊C₈)

C₄

semidirect

70. C₁₉

#1768

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
C₂×#10597260	2
C₂×C₄×C₁₉⋊C₈	2
#11926299	2
C₁₉×#376	2
#1768	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₂×#10597260

C₂×C₄×C₁₉⋊C₈

#11926299

C₁₉×#376

#1768

Subgroups — #14563492

Conjugacy classes of subgroups

Complements

Maximal subgroups