Group #18069944 — subgroups

Subgroups — #18069944

Order 4864.

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14561775	C₂	1	2	yes	maximal
2	C₁₉×#2151	C₂	1	1	yes	maximal, characteristic
3	#11926378	—	2	2	no	—
4	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
5	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×#405	C₄	1	1	yes	characteristic
7	C₁₉×C₄⋊C₁₆	—	2	2	no	—
8	C₂×M₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₁₉×#117	C₈	1	1	yes	characteristic
11	C₁₉×M₃₂	—	4	1	no	—
12	C₂×C₁₆×C₁₉	—	2	1	no	—
13	C₂×C₁₆×C₁₉	—	4	1	no	—
14	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
15	C₁₉×#97	—	2	1	no	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	C₁₉⋊C₃₂	—	4	2	no	—
18	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
19	M₁₆×C₁₉	—	4	1	no	—
20	C₂×C₈×C₁₉	—	2	1	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂²⋊C₄×C₁₉	C₁₆	1	2	yes	—
27	C₄²×C₁₉	—	2	1	no	—
28	C₁₆×C₁₉	—	2	2	no	—
29	C₁₆×C₁₉	—	4	1	no	—
30	#7365	—	19	1	no	maximal, Sylow
31	C₂³×C₁₉	C₂×C₁₆	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	2	no	—
35	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	—	4	1	no	—
39	C₈×C₁₉	#99	1	1	yes	characteristic
40	C₈×C₁₉	#101	1	1	yes	characteristic
41	#2151	D₁₉	1	1	yes	characteristic
42	#1400	—	19	2	no	—
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	—	4	1	no	—
45	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	4	2	no	—
48	C₄×C₁₉	#324	1	1	yes	characteristic
49	C₄×C₁₉	#349	1	1	yes	characteristic
50	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
51	C₂²×C₁₆	Dic₁₉	1	1	yes	characteristic
52	#405	Dic₁₉	1	1	yes	characteristic
53	M₆₄	—	38	2	no	—
54	C₄⋊C₁₆	—	2	2	no	—
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	4	1	no	—
57	C₂×C₁₉	#1322	1	1	yes	characteristic
58	C₂×M₁₆	C₁₉⋊C₈	1	1	yes	characteristic
59	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
60	#117	C₁₉⋊C₈	1	1	yes	characteristic
61	M₃₂	—	4	1	no	—
62	C₂×C₁₆	—	2	1	no	—
63	C₂×C₁₆	—	4	1	no	—
64	C₂×C₁₆	C₂²⋊D₁₉	1	2	yes	—
65	#97	—	2	1	no	—
66	C₄×C₈	—	2	1	no	—
67	C₃₂	—	76	2	no	—
68	C₁₉	#7365	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
70	M₁₆	—	4	1	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	#64520	1	1	yes	characteristic
75	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
76	C₄⋊C₄	—	2	1	no	—
77	C₂²⋊C₄	C₁₉⋊C₁₆	1	2	yes	—
78	C₄²	—	2	1	no	—
79	C₁₆	—	2	2	no	—
80	C₁₆	—	4	1	no	—
81	C₂³	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	#10597269	1	1	yes	characteristic
86	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
87	C₈	—	2	1	no	—
88	C₈	—	4	1	no	—
89	C₈	#10597291	1	1	yes	characteristic
90	C₈	#10597293	1	1	yes	characteristic
91	C₂²	—	2	1	no	—
92	C₂²	—	4	1	no	—
93	C₂²	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	4	2	no	—
96	C₄	#11926270	1	1	yes	characteristic
97	C₄	#11926326	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	4	1	no	—
100	C₂	#14561575	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561775

C₂

yes

maximal

C₁₉×#2151

C₂

yes

maximal, characteristic

#11926378

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₁₉×#405

C₄

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₂×M₁₆×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

C₈

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₁₆

yes

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7365

—

maximal, Sylow

C₂³×C₁₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

M₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

D₁₉

yes

characteristic

#1400

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

C₂×D₁₉

yes

characteristic

C₂²×C₁₆

Dic₁₉

yes

characteristic

#405

Dic₁₉

yes

characteristic

M₆₄

—

C₄⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1322

yes

characteristic

C₂×M₁₆

C₁₉⋊C₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

#117

C₁₉⋊C₈

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₉

yes

—

#97

—

C₄×C₈

—

C₃₂

—

C₁₉

#7365

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64520

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

C₁₉⋊C₁₆

yes

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

C₂×C₁₉⋊C₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597269

yes

characteristic

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

C₂²⋊(C₁₉⋊C₁₆)

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

—

100

C₂

#14561575

yes

characteristic

	subgroup	G/H
center	C₈	#10597291
commutator, prime radical	C₂³×C₁₉	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#2151	C₂
socle	C₂×C₁₉	#1322
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#2151	D₁₉
hypocenter	C₁₉	#7365
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #2151

subgroup

G/H

center

C₈

#10597291

commutator, prime radical

C₂³×C₁₉

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#2151

C₂

socle

C₂×C₁₉

#1322

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #2151

N	H ≅ G/N	type
68. C₁₉	#7365	semidirect

H ≅ G/N

type

68. C₁₉

#7365

semidirect

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

subgroup	index
#14561775	2
C₁₉×#2151	2
#7365	19

subgroup

index

#14561775

C₁₉×#2151

#7365

Subgroups — #18069944

Conjugacy classes of subgroups

Complements

Maximal subgroups