Group #18069950 — subgroups

Subgroups — #18069950

Order 4864.

136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561586	C₂	1	2	yes	maximal
2	C₁₉×#1837	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₁₉×#423	C₄	1	1	yes	characteristic
5	C₁₉×#423	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#341	—	2	2	no	—
8	C₂×M₁₆×C₁₉	—	2	1	no	—
9	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	—	4	1	no	—
13	C₁₉×C₄⋊C₈	—	4	1	no	—
14	C₄×C₈×C₁₉	—	2	1	no	—
15	C₄×C₈×C₁₉	C₈	1	2	yes	—
16	#10597269	—	4	2	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	M₁₆×C₁₉	—	4	2	no	—
20	M₁₆×C₁₉	—	4	2	no	—
21	C₂×C₈×C₁₉	—	2	2	no	—
22	C₂×C₈×C₁₉	—	2	2	no	—
23	C₂×C₈×C₁₉	—	4	1	no	—
24	C₂×C₈×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	—	4	1	no	—
26	C₄²×C₁₉	—	2	1	no	—
27	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
28	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
29	C₁₉⋊C₁₆	—	8	2	no	—
30	#7368	—	19	1	no	maximal, Sylow
31	C₂³×C₁₉	#101	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
39	C₈×C₁₉	—	4	2	no	—
40	C₈×C₁₉	—	4	2	no	—
41	C₈×C₁₉	—	8	1	no	—
42	#1837	D₁₉	1	1	yes	characteristic
43	#1327	—	19	2	no	—
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	—	4	1	no	—
46	C₂²×C₁₉	#324	1	1	yes	characteristic
47	C₄×C₁₉	—	2	2	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	4	1	no	—
50	C₄×C₁₉	#354	1	1	yes	characteristic
51	C₄×C₁₉	#355	1	1	yes	characteristic
52	#423	Dic₁₉	1	1	yes	characteristic
53	#423	C₂×D₁₉	1	1	yes	characteristic
54	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
55	#349	—	38	2	no	—
56	#341	—	2	2	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	4	1	no	—
59	C₂×C₁₉	#1324	1	1	yes	characteristic
60	C₂×M₁₆	—	2	1	no	—
61	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
62	C₂²×C₈	—	2	1	no	—
63	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
64	M₃₂	—	76	2	no	—
65	C₄⋊C₈	—	4	1	no	—
66	C₄⋊C₈	—	4	1	no	—
67	C₄×C₈	—	2	1	no	—
68	C₄×C₈	C₁₉⋊C₈	1	2	yes	—
69	C₁₉	#7368	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₄	—	2	1	no	—
71	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
72	M₁₆	—	4	2	no	—
73	M₁₆	—	4	2	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	—	4	1	no	—
78	C₂×C₈	—	4	1	no	—
79	C₄²	—	2	1	no	—
80	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
81	C₄²	#64520	1	1	yes	characteristic
82	C₁₆	—	152	2	no	—
83	C₂³	#10597293	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
90	C₂×C₄	#10597291	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	4	2	no	—
93	C₈	—	8	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	#11926270	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	2	1	no	—
99	C₄	—	4	1	no	—
100	C₄	#11926339	1	1	yes	characteristic
101	C₄	#11926341	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	4	1	no	—
104	C₂	#14561579	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561586

C₂

yes

maximal

C₁₉×#1837

C₂

yes

maximal, characteristic

#11926326

—

C₁₉×#423

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₁₉×#341

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₈

yes

—

#10597269

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#1837

D₁₉

yes

characteristic

#1327

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#324

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

yes

characteristic

#423

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

characteristic

#349

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1324

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²⋊D₁₉

yes

—

C₂²×C₈

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

—

C₁₉

#7368

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

C₄²

#64520

yes

characteristic

C₁₆

—

152

—

C₂³

#10597293

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

C₂×C₄

#10597291

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

#11926270

yes

characteristic

C₄

—

C₄

—

C₄

—

100

C₄

#11926339

yes

characteristic

101

C₄

#11926341

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

#14561579

yes

characteristic

	subgroup	G/H
center	C₄	#11926339
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1837	C₂
socle	C₂×C₁₉	#1324
prime radical	C₂³×C₁₉	#101
cosocle	C₁₉×#423	C₂²
hypercenter	#1837	D₁₉
hypocenter	C₁₉	#7368
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1837

subgroup

G/H

center

C₄

#11926339

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1837

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1837

N	H ≅ G/N	type
69. C₁₉	#7368	semidirect

H ≅ G/N

type

69. C₁₉

#7368

semidirect

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

subgroup	index
#14561586	2
C₁₉×#1837	2
#7368	19

subgroup

index

#14561586

C₁₉×#1837

#7368

Subgroups — #18069950

Conjugacy classes of subgroups

Complements

Maximal subgroups