Group #18076213 — subgroups

Subgroups — #18076213

Order 4864.

322 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 147 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	#14563752	C₂	1	2	yes	maximal
2	#14561470	C₂	1	4	yes	maximal
3	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
5	#11926299	—	2	4	no	—
6	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
7	C₄³×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#336	C₄	1	4	yes	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	D₄	1	2	yes	—
12	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	—	2	4	no	—
15	C₄×C₈×C₁₉	—	2	4	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
17	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₈×C₁₉	—	2	4	no	—
22	C₂×C₈×C₁₉	—	2	8	no	—
23	C₄²×C₁₉	—	2	4	no	—
24	C₄²×C₁₉	—	2	4	no	—
25	C₄²×C₁₉	—	4	2	no	—
26	C₄²×C₁₉	#41	1	4	yes	—
27	C₂×C₁₉⋊C₈	—	4	4	no	—
28	C₂×C₁₉⋊C₈	—	4	8	no	—
29	#8788	—	19	1	no	maximal, Sylow
30	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	2	no	—
32	C₂×C₄×C₁₉	—	2	4	no	—
33	C₂×C₄×C₁₉	—	2	4	no	—
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	#117	1	2	yes	—
36	C₂×C₄×C₁₉	#124	1	2	yes	—
37	C₂×C₄×C₁₉	#125	1	2	yes	—
38	C₂×C₄×C₁₉	#131	1	4	yes	—
39	C₂×C₄×C₁₉	#135	1	4	yes	—
40	C₈×C₁₉	—	4	4	no	—
41	C₁₉⋊C₈	—	8	4	no	—
42	#1831	—	19	2	no	—
43	#1744	D₁₉	1	1	yes	characteristic
44	#1277	—	19	4	no	—
45	C₂²×C₁₉	#382	1	1	yes	characteristic
46	C₂²×C₁₉	#424	1	2	yes	—
47	C₂²×C₁₉	#427	1	2	yes	—
48	C₂²×C₁₉	#430	1	2	yes	—
49	C₄×C₁₉	—	2	2	no	—
50	C₄×C₁₉	—	4	4	no	—
51	C₄×C₁₉	#433	1	4	yes	—
52	C₄×C₁₉	#488	1	4	yes	—
53	C₂×C₄⋊C₈	—	19	4	no	—
54	C₂×C₄×C₈	C₂×D₁₉	1	2	yes	—
55	C₄³	C₂×D₁₉	1	1	yes	characteristic
56	#336	—	38	4	no	—
57	#336	Dic₁₉	1	4	yes	—
58	C₂×C₁₉	#1572	1	4	yes	—
59	C₂×C₁₉	#1832	1	1	yes	characteristic
60	C₂×C₁₉	#1835	1	1	yes	characteristic
61	C₂×C₁₉	#1838	1	1	yes	characteristic
62	C₂²×C₈	—	38	4	no	—
63	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
64	C₂×C₄²	Dic₃₈	1	2	yes	—
65	C₂×C₄²	D₇₆	1	2	yes	—
66	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
67	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
68	C₄⋊C₈	—	38	8	no	—
69	C₄×C₈	—	2	4	no	—
70	C₁₉	#8788	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
72	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
73	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
74	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
75	C₂×C₈	—	2	8	no	—
76	C₂×C₈	—	2	4	no	—
77	C₂×C₈	—	76	4	no	—
78	C₂×C₈	—	76	8	no	—
79	C₄²	—	2	4	no	—
80	C₄²	—	2	4	no	—
81	C₄²	—	4	2	no	—
82	C₄²	#64541	1	4	yes	—
83	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	#10597316	1	2	yes	—
89	C₂×C₄	#10597321	1	2	yes	—
90	C₂×C₄	#10597350	1	4	yes	—
91	C₂×C₄	#10597372	1	2	yes	—
92	C₂×C₄	#10597394	1	4	yes	—
93	C₈	—	4	4	no	—
94	C₈	—	152	4	no	—
95	C₂²	#11926410	1	1	yes	characteristic
96	C₂²	#11926571	1	2	yes	—
97	C₂²	#11926582	1	2	yes	—
98	C₂²	#11926593	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	4	4	no	—
101	C₄	#11926605	1	4	yes	—
102	C₄	#11926899	1	4	yes	—
103	C₂	#14562415	1	4	yes	—
104	C₂	#14563755	1	1	yes	characteristic
105	C₂	#14563766	1	1	yes	characteristic
106	C₂	#14563776	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal

#14561470

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#11926299

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

Q₈

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8788

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

#131

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1831

—

#1744

D₁₉

yes

characteristic

#1277

—

C₂²×C₁₉

#382

yes

characteristic

C₂²×C₁₉

#424

yes

—

C₂²×C₁₉

#427

yes

—

C₂²×C₁₉

#430

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#433

yes

—

C₄×C₁₉

#488

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

—

C₄³

C₂×D₁₉

yes

characteristic

#336

—

#336

Dic₁₉

yes

—

C₂×C₁₉

#1572

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂×Dic₁₉

yes

—

C₂×C₄²

Dic₃₈

yes

—

C₂×C₄²

D₇₆

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₁₉

#8788

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄⋊Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₃₈

yes

characteristic

C₂²×C₄

C₂×D₇₆

yes

characteristic

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#64541

yes

—

C₂³

C₂×C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597316

yes

—

C₂×C₄

#10597321

yes

—

C₂×C₄

#10597350

yes

—

C₂×C₄

#10597372

yes

—

C₂×C₄

#10597394

yes

—

C₈

—

C₈

—

152

—

C₂²

#11926410

yes

characteristic

C₂²

#11926571

yes

—

C₂²

#11926582

yes

—

C₂²

#11926593

yes

—

C₄

—

100

C₄

—

101

C₄

#11926605

yes

—

102

C₄

#11926899

yes

—

103

C₂

#14562415

yes

—

104

C₂

#14563755

yes

characteristic

105

C₂

#14563766

yes

characteristic

106

C₂

#14563776

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#8788
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₂×D₇₆

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

N	H ≅ G/N	type
70. C₁₉	#8788	semidirect

H ≅ G/N

type

70. C₁₉

#8788

semidirect

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

subgroup	index
#14563752	2
#14561470	2
C₁₉×#1744	2
#8788	19

subgroup

index

#14563752

#14561470

C₁₉×#1744

#8788

Subgroups — #18076213

Conjugacy classes of subgroups

Complements

Maximal subgroups