Group #19134723 — subgroups

Subgroups — #19134723

Order 5504.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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	#14582769	C₂	1	2	yes	maximal
2	#14582662	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₄₃	—	2	2	no	—
5	C₂×C₄⋊Dic₄₃	—	2	2	no	—
6	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₃	C₄	1	4	yes	complemented
10	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
13	C₂²×Dic₄₃	—	2	4	no	—
14	C₂×C₈×C₄₃	—	2	4	no	—
15	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
16	C₄²×C₄₃	C₂×C₄	1	2	yes	—
17	C₄²×C₄₃	Q₈	1	2	yes	—
18	C₄⋊Dic₄₃	—	2	8	no	—
19	C₄⋊Dic₄₃	—	4	4	no	—
20	C₄⋊Dic₄₃	—	4	4	no	—
21	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₃	D₈	1	2	yes	—
25	C₂×C₄×C₄₃	SD₁₆	1	4	yes	—
26	C₂×C₄×C₄₃	Q₁₆	1	2	yes	—
27	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	#41	1	4	yes	—
30	C₂×Dic₄₃	—	4	4	no	—
31	C₂×Dic₄₃	—	4	4	no	—
32	C₂×Dic₄₃	—	4	4	no	—
33	C₈×C₄₃	—	2	4	no	—
34	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄₃	#124	1	2	yes	—
36	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
37	C₂²×C₄₃	C₂×SD₁₆	1	2	yes	—
38	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
39	C₄×C₄₃	#106	1	4	yes	—
40	C₄×C₄₃	#107	1	4	yes	—
41	C₄×C₄₃	#117	1	2	yes	—
42	C₄×C₄₃	#125	1	2	yes	—
43	Dic₄₃	—	8	4	no	—
44	#1834	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	#382	1	1	yes	characteristic
46	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
47	C₂×C₄₃	C₂×#107	1	1	yes	characteristic
48	C₂×C₄₃	#486	1	2	yes	—
49	C₂×C₄₃	#487	1	2	yes	—
50	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
51	#384	—	43	2	no	—
52	#340	—	43	4	no	—
53	C₄₃	#1834	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	C₂×D₄₃	1	2	yes	—
55	C₂×C₄⋊C₄	—	43	4	no	—
56	C₂×C₄⋊C₄	—	86	2	no	—
57	C₂×C₄⋊C₄	—	86	2	no	—
58	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
59	C₄×C₈	Dic₄₃	1	4	yes	complemented
60	C₂²×C₄	—	86	4	no	—
61	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
62	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
63	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
64	C₂×C₈	—	2	4	no	—
65	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
66	C₄⋊C₄	—	86	8	no	—
67	C₄⋊C₄	—	172	4	no	—
68	C₄⋊C₄	—	172	4	no	—
69	C₄²	Dic₈₆	1	2	yes	—
70	C₄²	C₂×Dic₄₃	1	2	yes	—
71	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
72	C₂×C₄	—	172	4	no	—
73	C₂×C₄	—	172	4	no	—
74	C₂×C₄	—	172	4	no	—
75	C₂×C₄	#10621873	1	4	yes	—
76	C₂×C₄	D₃₄₄	1	2	yes	—
77	C₂×C₄	Dic₁₇₂	1	2	yes	—
78	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
79	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
80	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
81	C₂×C₄	#10621898	1	4	yes	—
82	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
83	C₈	—	2	4	no	—
84	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
85	C₂²	#13063313	1	2	yes	—
86	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
87	C₂²	C₂×#10621873	1	2	yes	—
88	C₂²	C₂×Dic₁₇₂	1	1	yes	characteristic
89	C₄	—	344	4	no	—
90	C₄	#13063257	1	4	yes	—
91	C₄	#13063259	1	4	yes	—
92	C₄	#13063284	1	2	yes	—
93	C₄	#13063317	1	2	yes	—
94	C₂	#14582765	1	1	yes	characteristic
95	C₂	C₂×#13063257	1	1	yes	characteristic
96	C₂	C₂×#13063259	1	1	yes	characteristic
97	C₂	#14583246	1	2	yes	—
98	C₂	#14583250	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582769

C₂

yes

maximal

#14582662

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₂²×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

#106

yes

—

C₄×C₄₃

#107

yes

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

#125

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#487

yes

—

C₂×C₄×C₈

D₄₃

yes

characteristic

#384

—

#340

—

C₄₃

#1834

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄×C₈

Dic₄₃

yes

complemented

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

Dic₈₆

yes

—

C₄²

C₂×Dic₄₃

yes

—

C₂³

C₂×D₁₇₂

yes

characteristic

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

—

C₂×C₄

D₃₄₄

yes

—

C₂×C₄

Dic₁₇₂

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

#10621898

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

C₂²

#13063313

yes

—

C₂²

C₂×D₃₄₄

yes

characteristic

C₂²

C₂×#10621873

yes

—

C₂²

C₂×Dic₁₇₂

yes

characteristic

C₄

—

344

—

C₄

#13063257

yes

—

C₄

#13063259

yes

—

C₄

#13063284

yes

—

C₄

#13063317

yes

—

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

C₂

#14583250

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1834
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

#1834

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₈×C₄₃	C₄	semidirect
53. C₄₃	#1834	semidirect
59. C₄×C₈	Dic₄₃	semidirect

H ≅ G/N

type

9. C₄×C₈×C₄₃

C₄

semidirect

53. C₄₃

#1834

semidirect

59. C₄×C₈

Dic₄₃

semidirect

Subgroups — #19134723

Conjugacy classes of subgroups

Complements