Group #18070196 — subgroups

Subgroups — #18070196

Order 4864.

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

normal subgroups only

This group has 102 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	C₄⋊(C₁₉⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
2	#14561709	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2253	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉⋊C₃₂	—	2	1	no	—
5	#11926297	—	2	1	no	—
6	C₁₉×#499	—	2	1	no	—
7	C₁₉×#367	—	2	1	no	—
8	C₁₉×#366	C₄	1	1	yes	characteristic
9	C₁₉×#366	C₄	1	1	yes	characteristic
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#125	—	4	1	no	—
12	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₁₉×#107	—	2	1	no	—
15	C₁₉×#107	—	2	1	no	—
16	C₁₉×#106	—	4	1	no	—
17	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
19	C₁₉⋊C₃₂	—	4	1	no	—
20	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	4	1	no	—
23	C₄⋊C₄×C₁₉	—	4	1	no	—
24	C₄⋊C₄×C₁₉	—	8	1	no	—
25	C₄⋊C₄×C₁₉	—	8	1	no	—
26	C₄²×C₁₉	D₈	1	1	yes	characteristic
27	C₂×C₁₉⋊C₈	—	8	1	no	—
28	C₁₆×C₁₉	—	2	1	no	—
29	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
31	#7452	—	19	1	no	maximal, Sylow
32	C₂×C₄×C₁₉	—	8	1	no	—
33	C₂×C₄×C₁₉	—	8	1	no	—
34	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
35	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	#101	1	1	yes	characteristic
39	C₈×C₁₉	#103	1	1	yes	characteristic
40	C₁₉⋊C₈	—	16	1	no	—
41	#2253	D₁₉	1	1	yes	characteristic
42	C₄⋊C₃₂	—	19	1	no	—
43	#1372	—	19	1	no	—
44	C₂²×C₁₉	#357	1	1	yes	characteristic
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	16	1	no	—
48	C₄×C₁₉	—	16	1	no	—
49	C₄×C₁₉	#332	1	1	yes	characteristic
50	C₄×C₁₉	#362	1	1	yes	characteristic
51	#499	—	2	1	no	—
52	C₂×C₃₂	—	38	1	no	—
53	#367	—	2	1	no	—
54	#366	Dic₁₉	1	1	yes	characteristic
55	#366	Dic₁₉	1	1	yes	characteristic
56	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
57	#335	—	38	1	no	—
58	C₂×C₁₉	#1364	1	1	yes	characteristic
59	C₂×C₁₉	#1417	1	1	yes	characteristic
60	C₂×C₁₉	#1418	1	1	yes	characteristic
61	#125	—	4	1	no	—
62	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
63	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
64	#107	—	2	1	no	—
65	#107	—	2	1	no	—
66	#106	—	4	1	no	—
67	C₄⋊C₈	—	76	1	no	—
68	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
69	C₃₂	—	76	1	no	—
70	C₁₉	#7452	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₈	—	152	1	no	—
72	C₂×C₈	#64526	1	1	yes	characteristic
73	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
74	C₄⋊C₄	—	4	1	no	—
75	C₄⋊C₄	—	4	1	no	—
76	C₄⋊C₄	—	8	1	no	—
77	C₄⋊C₄	—	8	1	no	—
78	C₄²	#64525	1	1	yes	characteristic
79	C₁₆	—	2	1	no	—
80	C₁₆	#64527	1	1	yes	characteristic
81	C₁₆	#64528	1	1	yes	characteristic
82	C₂×C₄	—	8	1	no	—
83	C₂×C₄	—	8	1	no	—
84	C₂×C₄	#10597283	1	1	yes	characteristic
85	C₂×C₄	#10597284	1	1	yes	characteristic
86	C₂×C₄	#10597289	1	1	yes	characteristic
87	C₈	—	2	1	no	—
88	C₈	—	304	1	no	—
89	C₈	#10597292	1	1	yes	characteristic
90	C₈	#10597293	1	1	yes	characteristic
91	C₂²	#11926345	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	16	1	no	—
95	C₄	—	16	1	no	—
96	C₄	#11926290	1	1	yes	characteristic
97	C₄	#11926360	1	1	yes	characteristic
98	C₂	#14561690	1	1	yes	characteristic
99	C₂	#14561819	1	1	yes	characteristic
100	C₂	#14561822	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₁₉⋊C₃₂)

C₂

yes

maximal, characteristic

#14561709

C₂

yes

maximal, characteristic

C₁₉×#2253

C₂

yes

maximal, characteristic

C₂×C₁₉⋊C₃₂

—

#11926297

—

C₁₉×#499

—

C₁₉×#367

—

C₁₉×#366

C₄

yes

characteristic

C₁₉×#366

C₄

yes

characteristic

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄⋊(C₁₉⋊C₈)

—

C₁₉⋊C₃₂

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

SD₁₆

yes

characteristic

C₁₆×C₁₉

Q₁₆

yes

characteristic

#7452

—

maximal, Sylow

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2253

D₁₉

yes

characteristic

C₄⋊C₃₂

—

#1372

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₃₂

—

#367

—

#366

Dic₁₉

yes

characteristic

#366

Dic₁₉

yes

characteristic

C₄×C₁₆

C₂×D₁₉

yes

characteristic

#335

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

C₄⋊C₈

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7452

yes

characteristic, complemented, Sylow

C₂×C₈

—

152

—

C₂×C₈

#64526

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

#64525

yes

characteristic

C₁₆

—

C₁₆

yes

C₁₆

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

304

—

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

yes

C₂

yes

100

C₂

#14561822

yes

characteristic

	subgroup	G/H
center	C₂²	#11926345
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#2253	C₂
socle, prime radical	C₂²×C₁₉	#357
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2253	D₁₉
hypocenter	C₁₉	#7452
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2253

subgroup

G/H

center

C₂²

#11926345

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#2253

C₂

socle, prime radical

C₂²×C₁₉

#357

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2253

N	H ≅ G/N	type
70. C₁₉	#7452	semidirect

H ≅ G/N

type

70. C₁₉

#7452

semidirect

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

subgroup	index
C₄⋊(C₁₉⋊C₃₂)	2
#14561709	2
C₁₉×#2253	2
#7452	19

subgroup

index

C₄⋊(C₁₉⋊C₃₂)

#14561709

C₁₉×#2253

#7452

Subgroups — #18070196

Conjugacy classes of subgroups

Complements

Maximal subgroups