Group #18070013 — subgroups

Subgroups — #18070013

Order 4864.

116 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561771	C₂	1	1	yes	maximal, characteristic
2	#14561703	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic
4	#11926378	—	2	1	no	—
5	#11926365	—	2	1	no	—
6	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic
7	C₄×Q₁₆×C₁₉	—	2	1	no	—
8	C₁₉×#367	C₄	1	1	yes	characteristic
9	C₁₉×#358	—	2	1	no	—
10	C₁₉×#346	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₁₉	—	2	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₁₉×Q₃₂	—	2	1	no	—
14	C₁₉×Q₃₂	C₈	1	2	yes	—
15	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×#107	—	2	1	no	—
18	C₁₉×#103	—	4	1	no	—
19	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
20	#10597269	—	4	1	no	—
21	C₁₉⋊C₃₂	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	4	1	no	—
23	Q₁₆×C₁₉	—	2	2	no	—
24	Q₁₆×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	—	4	1	no	—
28	C₄⋊C₄×C₁₉	—	8	1	no	—
29	C₄²×C₁₉	—	8	1	no	—
30	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
31	C₁₆×C₁₉	—	2	1	no	—
32	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
34	C₁₉⋊C₁₆	—	8	1	no	—
35	#7391	—	19	1	no	maximal, Sylow
36	Q₈×C₁₉	—	4	2	no	—
37	Q₈×C₁₉	—	8	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	8	1	no	—
40	C₂×C₄×C₁₉	—	8	1	no	—
41	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
42	C₈×C₁₉	—	2	1	no	—
43	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
44	C₈×C₁₉	#104	1	1	yes	characteristic
45	#2176	D₁₉	1	1	yes	characteristic
46	#1398	—	19	1	no	—
47	#1369	—	19	1	no	—
48	C₂²×C₁₉	#361	1	1	yes	characteristic
49	C₄×C₁₉	—	4	1	no	—
50	C₄×C₁₉	—	8	2	no	—
51	C₄×C₁₉	—	16	1	no	—
52	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
53	C₄×C₁₉	#360	1	1	yes	characteristic
54	C₂×Q₃₂	Dic₁₉	1	1	yes	characteristic
55	C₄×Q₁₆	—	2	1	no	—
56	M₆₄	—	38	1	no	—
57	#367	Dic₁₉	1	1	yes	characteristic
58	#364	—	38	1	no	—
59	#358	—	2	1	no	—
60	#346	C₂×D₁₉	1	1	yes	characteristic
61	C₂×C₁₉	—	2	1	no	—
62	C₂×C₁₉	#1333	1	1	yes	characteristic
63	C₂×Q₁₆	—	2	1	no	—
64	C₄×Q₈	—	4	1	no	—
65	Q₃₂	—	2	1	no	—
66	Q₃₂	C₁₉⋊C₈	1	2	yes	—
67	M₃₂	—	76	1	no	—
68	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
69	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
70	#107	—	2	1	no	—
71	#103	—	4	1	no	—
72	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
73	C₃₂	—	38	2	no	—
74	C₁₉	#7391	1	1	yes	characteristic, complemented, Sylow
75	C₂×Q₈	—	4	1	no	—
76	Q₁₆	—	2	2	no	—
77	Q₁₆	—	4	1	no	—
78	C₂×C₈	#64525	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
80	C₄⋊C₄	—	4	1	no	—
81	C₄⋊C₄	—	8	1	no	—
82	C₄²	—	8	1	no	—
83	C₄²	#64526	1	1	yes	characteristic
84	C₁₆	—	2	1	no	—
85	C₁₆	—	152	1	no	—
86	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
87	C₁₆	#64520	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	8	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	8	1	no	—
92	C₂×C₄	—	8	1	no	—
93	C₂×C₄	#10597289	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
96	C₈	#10597294	1	1	yes	characteristic
97	C₂²	#11926357	1	1	yes	characteristic
98	C₄	—	4	1	no	—
99	C₄	—	8	2	no	—
100	C₄	—	16	1	no	—
101	C₄	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
102	C₄	#11926354	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	#14561602	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561771

C₂

yes

maximal, characteristic

#14561703

C₂

yes

maximal, characteristic

C₁₉×#2176

C₂

yes

maximal, characteristic

#11926378

—

#11926365

—

C₂×C₁₉×Q₃₂

C₄

yes

characteristic

C₄×Q₁₆×C₁₉

—

C₁₉×#367

C₄

yes

characteristic

C₁₉×#358

—

C₁₉×#346

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

C₈

yes

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597269

—

C₁₉⋊C₃₂

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7391

—

maximal, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

C₈×C₁₉

yes

D₁₉

yes

characteristic

#1398

—

#1369

—

C₂²×C₁₉

#361

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#360

yes

characteristic

C₂×Q₃₂

Dic₁₉

yes

characteristic

C₄×Q₁₆

—

M₆₄

—

#367

Dic₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1333

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

C₁₉⋊C₈

yes

—

M₃₂

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

#107

—

#103

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7391

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#64525

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

#64526

yes

characteristic

C₁₆

—

C₁₆

—

152

—

C₁₆

C₂×C₁₉⋊C₈

yes

characteristic

C₁₆

#64520

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10597289

yes

characteristic

C₈

—

C₈

C₂²⋊(C₁₉⋊C₈)

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

100

C₄

—

101

C₄

D₄⋊(C₁₉⋊C₈)

yes

characteristic

102

C₄

#11926354

yes

characteristic

103

C₂

—

104

C₂

#14561602

yes

characteristic

	subgroup	G/H
center	C₂	#14561602
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	#346	C₂×D₁₉
Fitting	C₁₉×#2176	C₂
socle	C₂×C₁₉	#1333
prime radical	C₂²×C₁₉	#361
cosocle	C₁₉×#346	C₂²
hypercenter	#2176	D₁₉
hypocenter	C₁₉	#7391
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #2176

subgroup

G/H

center

C₂

#14561602

commutator

C₁₆×C₁₉

C₂×C₈

Frattini

#346

C₂×D₁₉

Fitting

C₁₉×#2176

C₂

C₂×C₁₉

C₂²×C₁₉

C₁₉×#346

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #2176

N	H ≅ G/N	type
74. C₁₉	#7391	semidirect

H ≅ G/N

type

74. C₁₉

#7391

semidirect

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

subgroup	index
#14561771	2
#14561703	2
C₁₉×#2176	2
#7391	19

subgroup

index

#14561771

#14561703

C₁₉×#2176

#7391

Subgroups — #18070013

Conjugacy classes of subgroups

Complements

Maximal subgroups