Group #18070187 — subgroups

Subgroups — #18070187

Order 4864.

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

normal subgroups only

This group has 126 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	#14561833	C₂	1	1	yes	maximal, characteristic
2	#14561711	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2247	C₂	1	1	yes	maximal, characteristic
4	#11926378	—	2	1	no	—
5	#11926365	—	2	1	no	—
6	C₂×C₁₉×Q₃₂	—	2	1	no	—
7	C₂×C₁₉×Q₃₂	C₄	1	2	yes	—
8	C₁₉×#494	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₉	—	2	2	no	—
11	C₂×Q₁₆×C₁₉	—	4	1	no	—
12	C₁₉×C₄⋊Q₈	—	4	1	no	—
13	C₁₉×Q₃₂	—	4	2	no	—
14	C₁₉×Q₃₂	—	4	1	no	—
15	C₁₉×Q₃₂	—	4	1	no	—
16	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
19	#10597269	—	4	1	no	—
20	C₁₉⋊C₃₂	—	4	1	no	—
21	C₂×Q₈×C₁₉	—	4	2	no	—
22	Q₁₆×C₁₉	—	4	2	no	—
23	Q₁₆×C₁₉	—	4	2	no	—
24	Q₁₆×C₁₉	—	8	1	no	—
25	Q₁₆×C₁₉	—	8	1	no	—
26	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	8	2	no	—
29	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₁₆×C₁₉	—	2	1	no	—
31	C₁₆×C₁₉	D₈	1	1	yes	characteristic
32	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₁₉⋊C₁₆	—	8	1	no	—
34	#7449	—	19	1	no	maximal, Sylow
35	Q₈×C₁₉	—	8	2	no	—
36	Q₈×C₁₉	—	8	2	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	8	2	no	—
39	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
40	C₈×C₁₉	#100	1	1	yes	characteristic
41	C₈×C₁₉	#102	1	1	yes	characteristic
42	C₈×C₁₉	D₁₆	1	1	yes	characteristic
43	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
44	#2247	D₁₉	1	1	yes	characteristic
45	#1422	—	19	1	no	—
46	#1373	—	19	1	no	—
47	C₂²×C₁₉	#361	1	1	yes	characteristic
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	—	16	2	no	—
50	C₄×C₁₉	#331	1	1	yes	characteristic
51	C₄×C₁₉	#357	1	1	yes	characteristic
52	C₂×Q₃₂	—	2	1	no	—
53	C₂×Q₃₂	Dic₁₉	1	2	yes	—
54	#494	—	2	1	no	—
55	M₆₄	—	38	1	no	—
56	#364	—	38	1	no	—
57	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	#1361	1	1	yes	characteristic
60	C₂×Q₁₆	—	2	2	no	—
61	C₂×Q₁₆	—	4	1	no	—
62	C₄⋊Q₈	—	4	1	no	—
63	Q₃₂	—	4	2	no	—
64	Q₃₂	—	4	1	no	—
65	Q₃₂	—	4	1	no	—
66	M₃₂	—	76	1	no	—
67	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
69	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₃₂	—	76	1	no	—
71	C₁₉	#7449	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	4	2	no	—
73	Q₁₆	—	4	2	no	—
74	Q₁₆	—	4	2	no	—
75	Q₁₆	—	8	1	no	—
76	Q₁₆	—	8	1	no	—
77	C₂×C₈	#64525	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
79	C₄⋊C₄	—	8	2	no	—
80	C₄²	#64526	1	1	yes	characteristic
81	C₁₆	—	2	1	no	—
82	C₁₆	—	152	1	no	—
83	C₁₆	#64525	1	1	yes	characteristic
84	C₁₆	#64526	1	1	yes	characteristic
85	Q₈	—	8	2	no	—
86	Q₈	—	8	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	8	2	no	—
89	C₂×C₄	#10597289	1	1	yes	characteristic
90	C₈	#10597283	1	1	yes	characteristic
91	C₈	#10597284	1	1	yes	characteristic
92	C₈	#10597289	1	1	yes	characteristic
93	C₈	#10597290	1	1	yes	characteristic
94	C₂²	#11926357	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	16	2	no	—
97	C₄	#11926288	1	1	yes	characteristic
98	C₄	#11926345	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	#14561681	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561833

C₂

yes

maximal, characteristic

#14561711

C₂

yes

maximal, characteristic

C₁₉×#2247

C₂

yes

maximal, characteristic

#11926378

—

#11926365

—

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

C₄

yes

—

C₁₉×#494

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597269

—

C₁₉⋊C₃₂

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7449

—

maximal, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

#2247

D₁₉

yes

characteristic

#1422

—

#1373

—

C₂²×C₁₉

#361

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

—

C₂×Q₃₂

Dic₁₉

yes

—

#494

—

M₆₄

—

#364

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1361

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7449

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

#64525

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄⋊C₄

—

C₄²

#64526

yes

characteristic

C₁₆

—

C₁₆

—

152

—

C₁₆

yes

C₁₆

yes

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

#14561681

yes

characteristic

	subgroup	G/H
center	C₂	#14561681
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#2247	C₂
socle	C₂×C₁₉	#1361
prime radical	C₂²×C₁₉	#361
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2247	D₁₉
hypocenter	C₁₉	#7449
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂

#14561681

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#2247

C₂

C₂×C₁₉

C₂²×C₁₉

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
71. C₁₉	#7449	semidirect

H ≅ G/N

type

71. C₁₉

#7449

semidirect

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

subgroup	index
#14561833	2
#14561711	2
C₁₉×#2247	2
#7449	19

subgroup

index

#14561833

#14561711

C₁₉×#2247

#7449

Subgroups — #18070187

Conjugacy classes of subgroups

Complements

Maximal subgroups