Group #19143204 — subgroups

Subgroups — #19143204

Order 5504.

440 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 249 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	#14583666	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063332	C₂	1	1	yes	maximal, characteristic
3	#14582947	C₂	1	6	yes	maximal, complemented
4	C₂×#13063260	C₂	1	6	yes	maximal, complemented
5	C₄₃×#568	C₂	1	1	yes	maximal, characteristic
6	#13063332	—	2	4	no	—
7	#13063332	C₄	1	8	yes	—
8	C₂×#10621877	C₂²	1	6	yes	—
9	C₂×#10621877	C₂²	1	3	yes	—
10	C₂²×C₄₃⋊C₈	C₂²	1	3	yes	—
11	#13063260	C₂²	1	4	yes	—
12	#13063260	C₂²	1	12	yes	—
13	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
14	#131×C₄₃	—	2	4	no	—
15	C₂×M₁₆×C₄₃	C₂²	1	6	yes	—
16	#41×C₄₃	C₂×C₄	1	4	yes	—
17	#41×C₄₃	D₄	1	4	yes	—
18	C₂×Q₈×C₄₃	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₄₃	Q₈	1	3	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
21	M₁₆×C₄₃	—	2	6	no	—
22	M₁₆×C₄₃	C₂³	1	4	yes	—
23	C₂×C₈×C₄₃	—	2	6	no	—
24	#10621877	—	2	6	no	—
25	#10621877	C₂×C₄	1	12	yes	—
26	#10621877	C₂³	1	4	yes	—
27	C₂×C₄₃⋊C₈	—	2	6	no	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	12	yes	—
29	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
30	C₂×C₄₃⋊C₈	C₂³	1	3	yes	—
31	C₂³×C₄₃	C₂×Q₈	1	3	yes	—
32	Q₈×C₄₃	C₄⋊C₄	1	4	yes	—
33	D₄×C₄₃	C₄⋊C₄	1	12	yes	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
36	C₂×C₄×C₄₃	C₂×Q₈	1	3	yes	—
37	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₈×C₄₃	—	2	4	no	—
39	C₄₃⋊C₈	—	2	4	no	—
40	C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
41	C₄₃⋊C₈	C₂²×C₄	1	6	yes	—
42	C₂²×C₄₃	—	4	3	no	—
43	C₂²×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
44	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
45	C₄×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
46	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
47	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
48	#2916	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	—	2	6	no	—
51	C₂×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
52	#568	—	43	1	no	—
53	#568	D₄₃	1	1	yes	characteristic
54	C₂×#131	—	43	1	no	—
55	#430	—	43	6	no	—
56	C₂×#108	—	43	6	no	—
57	C₄₃	#2916	1	1	yes	characteristic, complemented, Sylow
58	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
59	#131	—	2	4	no	—
60	#131	—	43	8	no	—
61	#131	—	86	4	no	—
62	C₂×M₁₆	—	43	3	no	—
63	C₂×M₁₆	—	43	6	no	—
64	C₂×M₁₆	C₂×D₄₃	1	6	yes	—
65	C₂²×C₈	—	43	3	no	—
66	#108	—	43	4	no	—
67	#108	—	43	12	no	—
68	#41	C₄×D₄₃	1	4	yes	—
69	#41	C₂²⋊D₄₃	1	4	yes	—
70	C₂×Q₈	Dic₈₆	1	1	yes	characteristic
71	C₂×D₄	Dic₈₆	1	3	yes	—
72	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
73	M₁₆	—	2	6	no	—
74	M₁₆	—	43	12	no	—
75	M₁₆	—	43	4	no	—
76	M₁₆	—	86	6	no	—
77	M₁₆	C₂²×D₄₃	1	4	yes	—
78	C₂×C₈	—	2	6	no	—
79	C₂×C₈	—	43	12	no	—
80	C₂×C₈	—	43	1	no	—
81	C₂×C₈	—	43	3	no	—
82	C₂×C₈	—	86	6	no	—
83	C₂³	C₂×Dic₈₆	1	3	yes	—
84	Q₈	Dic₄₃⋊C₄	1	4	yes	—
85	D₄	Dic₄₃⋊C₄	1	12	yes	—
86	C₂×C₄	C₂×Dic₈₆	1	3	yes	—
87	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
88	C₂×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
89	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	43	2	no	—
92	C₈	—	43	6	no	—
93	C₈	—	86	4	no	—
94	C₂²	—	4	3	no	—
95	C₂²	C₂×Dic₄₃⋊C₄	1	6	yes	—
96	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
97	C₄	C₂×Dic₄₃⋊C₄	1	6	yes	—
98	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
99	C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	2	6	no	—
102	C₂	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583666

C₂

yes

maximal, characteristic

C₂×#13063332

C₂

yes

maximal, characteristic

#14582947

C₂

yes

maximal, complemented

C₂×#13063260

C₂

yes

maximal, complemented

C₄₃×#568

C₂

yes

maximal, characteristic

#13063332

—

#13063332

C₄

yes

—

C₂×#10621877

C₂²

yes

—

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063260

C₂²

yes

—

#13063260

C₂²

yes

—

C₂×#41×C₄₃

C₂²

yes

characteristic

#131×C₄₃

—

C₂×M₁₆×C₄₃

C₂²

yes

—

#41×C₄₃

C₂×C₄

yes

—

#41×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

Q₈

yes

characteristic

C₂×D₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

—

#10621877

—

#10621877

C₂×C₄

yes

—

#10621877

C₂³

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

Q₈×C₄₃

C₄⋊C₄

yes

—

D₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂²×C₄

yes

—

C₄₃⋊C₈

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂²×D₄

yes

characteristic

#2916

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂²×C₄⋊C₄

yes

characteristic

#568

—

#568

D₄₃

yes

—

—

—

C₄₃

#2916

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₃

yes

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₂²×C₈

—

#108

—

#108

—

#41

C₄×D₄₃

yes

—

#41

C₂²⋊D₄₃

yes

—

C₂×Q₈

Dic₈₆

yes

characteristic

C₂×D₄

Dic₈₆

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂²×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂³

C₂×Dic₈₆

yes

—

Q₈

Dic₄₃⋊C₄

yes

—

D₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₂×Dic₄₃⋊C₄

yes

—

C₂²

C₂²×Dic₈₆

yes

characteristic

C₄

C₂×Dic₄₃⋊C₄

yes

—

C₄

C₂²×C₄×D₄₃

yes

characteristic

C₄

C₂²×C₂²⋊D₄₃

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

C₂²×Dic₄₃⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₂²×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#568	C₂
socle	C₂×C₄₃	C₂²×C₄⋊C₄
hypercenter	#568	D₄₃
hypocenter	C₄₃	#2916
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

subgroup

G/H

center

C₄

C₂²×C₂²⋊D₄₃

commutator

C₄×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#568

C₂

socle

C₂×C₄₃

C₂²×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

N	H ≅ G/N	type
3. #14582947	C₂	semidirect
4. C₂×#13063260	C₂	semidirect
57. C₄₃	#2916	semidirect

H ≅ G/N

type

3. #14582947

C₂

semidirect

4. C₂×#13063260

C₂

semidirect

57. C₄₃

#2916

semidirect

Subgroups — #19143204

Conjugacy classes of subgroups

Complements