Group #19134500 — subgroups

Subgroups — #19134500

Order 5504.

220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₂×#13063260	C₂	1	2	yes	maximal
2	M₁₆×Dic₄₃	C₂	1	2	yes	maximal
3	C₂×#13063235	C₂	1	1	yes	maximal, characteristic
4	#14582664	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
9	#13063260	C₄	1	8	yes	complemented
10	#13063235	—	2	2	no	—
11	#13063235	C₄	1	4	yes	—
12	C₈×Dic₄₃	—	2	2	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	Q₈	1	2	yes	—
17	M₁₆×C₄₃	—	2	2	no	—
18	M₁₆×C₄₃	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
23	C₄×Dic₄₃	D₄	1	2	yes	—
24	#10621877	—	2	2	no	—
25	#10621877	C₂×C₄	1	4	yes	—
26	C₂×C₄₃⋊C₈	—	2	2	no	—
27	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
29	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	#41	1	2	yes	—
34	C₂×Dic₄₃	—	4	2	no	—
35	C₂×Dic₄₃	C₄⋊C₄	1	4	yes	—
36	C₈×C₄₃	—	2	2	no	—
37	C₈×C₄₃	—	2	4	no	—
38	C₄₃⋊C₈	—	2	4	no	—
39	C₄₃⋊C₈	C₄²	1	4	yes	—
40	C₂²×C₄₃	—	2	2	no	—
41	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
43	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
44	C₄×C₄₃	#117	1	1	yes	characteristic
45	C₄×C₄₃	C₄×D₄	1	2	yes	—
46	Dic₄₃	—	2	4	no	—
47	#1778	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	2	2	no	—
49	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄₃	#430	1	2	yes	—
51	C₂×#108	—	43	2	no	—
52	C₄×M₁₆	—	43	2	no	—
53	C₂×#97	—	43	1	no	—
54	#341	—	43	1	no	—
55	#341	D₄₃	1	1	yes	characteristic
56	C₄₃	#1778	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	43	2	no	—
58	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
59	C₂²×C₈	—	43	1	no	—
60	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₂×C₄²	—	43	1	no	—
62	#108	—	43	8	no	—
63	#97	—	43	4	no	—
64	#97	—	86	2	no	—
65	C₄×C₈	—	86	2	no	—
66	C₂²×C₄	—	43	2	no	—
67	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	43	4	no	—
70	M₁₆	—	86	2	no	—
71	M₁₆	C₄×D₄₃	1	4	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	43	2	no	—
75	C₂×C₈	—	43	4	no	—
76	C₂×C₈	—	86	2	no	—
77	C₂×C₈	C₄×D₄₃	1	2	yes	—
78	C₄²	—	43	2	no	—
79	C₄²	—	43	2	no	—
80	C₂³	Q₈×D₄₃	1	1	yes	characteristic
81	C₂×C₄	—	43	4	no	—
82	C₂×C₄	—	172	2	no	—
83	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
84	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
85	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
86	C₂×C₄	#10621900	1	2	yes	—
87	C₈	—	2	2	no	—
88	C₈	—	2	4	no	—
89	C₈	—	43	4	no	—
90	C₈	—	86	4	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₄⋊C₄×D₄₃	1	1	yes	characteristic
93	C₂²	#13063290	1	2	yes	—
94	C₄	—	86	4	no	—
95	C₄	C₄²×D₄₃	1	1	yes	characteristic
96	C₄	#13063281	1	1	yes	characteristic
97	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
98	C₂	—	2	2	no	—
99	C₂	#14582750	1	1	yes	characteristic
100	C₂	#14582946	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063260

C₂

yes

maximal

M₁₆×Dic₄₃

C₂

yes

maximal

C₂×#13063235

C₂

yes

maximal, characteristic

#14582664

C₂

yes

maximal, characteristic

C₄₃×#341

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063260

C₄

yes

complemented

#13063235

—

#13063235

C₄

yes

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

Q₈

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

D₄

yes

—

#10621877

—

#10621877

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄⋊C₄

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄²

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

—

Dic₄₃

—

#1778

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₄₃

#430

yes

—

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

#341

D₄₃

yes

characteristic

C₄₃

#1778

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

#108

—

#97

—

#97

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₄×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621900

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₄⋊C₄×D₄₃

yes

characteristic

C₂²

#13063290

yes

—

C₄

—

C₄

C₄²×D₄₃

yes

characteristic

C₄

#13063281

yes

characteristic

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

C₂

—

C₂

#14582750

yes

characteristic

100

C₂

#14582946

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#341	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	#341	D₄₃
hypocenter	C₄₃	#1778
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₄×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#341

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
9. #13063260	C₄	semidirect
56. C₄₃	#1778	semidirect

H ≅ G/N

type

9. #13063260

C₄

semidirect

56. C₄₃

#1778

semidirect

Subgroups — #19134500

Conjugacy classes of subgroups

Complements