Group #19136188 — subgroups

Subgroups — #19136188

Order 5504.

196 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13063264	C₂	1	2	yes	maximal
2	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582675	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×Dic₄₃	C₂	1	2	yes	maximal, complemented
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	C₄²×D₄₃	C₄	1	1	yes	characteristic
9	#13063264	C₄	1	8	yes	complemented
10	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
11	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
12	C₈×Dic₄₃	C₄	1	1	yes	characteristic
13	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄₃	C₈	1	2	yes	—
17	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₄₃	C₈	1	2	yes	—
22	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₈×D₄₃	C₈	1	4	yes	—
26	C₈×D₄₃	C₂×C₄	1	4	yes	—
27	C₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
28	C₄₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
29	C₂²×D₄₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₄₃	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₄₃	C₂×C₈	1	2	yes	—
34	C₄×D₄₃	—	2	4	no	—
35	C₄×D₄₃	C₄²	1	2	yes	—
36	C₄×D₄₃	C₂×C₈	1	2	yes	—
37	C₈×C₄₃	C₂×C₈	1	2	yes	—
38	C₈×C₄₃	C₂²×C₄	1	2	yes	—
39	C₄₃⋊C₈	C₄²	1	2	yes	—
40	C₄₃⋊C₈	C₂×C₈	1	2	yes	—
41	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
42	C₂×D₄₃	—	2	2	no	—
43	C₂×D₄₃	C₄×C₈	1	2	yes	—
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
46	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
47	Dic₄₃	C₄×C₈	1	2	yes	—
48	Dic₄₃	M₃₂	1	4	yes	complemented
49	C₄×M₃₂	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₄₃	C₂×M₃₂	1	2	yes	—
52	D₄₃	—	2	2	no	—
53	C₂×M₃₂	—	43	2	no	—
54	C₂×C₄×C₈	—	43	1	no	—
55	#346	—	43	1	no	—
56	#346	D₄₃	1	1	yes	characteristic, complemented
57	C₄×C₁₆	—	43	2	no	—
58	C₄₃	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	43	1	no	—
60	C₂²×C₈	—	43	1	no	—
61	C₂×C₄²	—	43	1	no	—
62	M₃₂	—	43	8	no	—
63	C₂×C₁₆	—	43	2	no	—
64	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
65	C₄×C₈	—	43	1	no	—
66	C₄×C₈	—	43	1	no	—
67	C₄×C₈	—	43	1	no	—
68	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂²×C₄	—	43	1	no	—
70	C₂²×C₄	—	43	2	no	—
71	C₂×C₈	—	43	1	no	—
72	C₂×C₈	—	43	1	no	—
73	C₂×C₈	—	43	4	no	—
74	C₂×C₈	—	43	4	no	—
75	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
77	C₄²	—	43	2	no	—
78	C₄²	—	43	1	no	—
79	C₄²	C₄×D₄₃	1	1	yes	characteristic
80	C₁₆	—	43	4	no	—
81	C₁₆	C₄×D₄₃	1	4	yes	complemented
82	C₂³	—	43	1	no	—
83	C₂×C₄	—	43	2	no	—
84	C₂×C₄	—	43	1	no	—
85	C₂×C₄	—	43	2	no	—
86	C₂×C₄	—	43	2	no	—
87	C₂×C₄	—	86	4	no	—
88	C₂×C₄	C₈×D₄₃	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₈	—	43	2	no	—
91	C₈	—	43	2	no	—
92	C₈	C₈×D₄₃	1	2	yes	—
93	C₈	C₂×C₄×D₄₃	1	2	yes	—
94	C₂²	—	43	2	no	—
95	C₂²	—	86	2	no	—
96	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	43	4	no	—
99	C₄	—	43	2	no	—
100	C₄	C₄²×D₄₃	1	1	yes	characteristic
101	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
102	C₂	—	86	2	no	—
103	C₂	C₄×C₈×D₄₃	1	1	yes	characteristic
104	C₂	M₃₂×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063264

C₂

yes

maximal

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

#14582675

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₄₃

C₂

yes

maximal, complemented

C₄₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₄

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

characteristic

C₄²×D₄₃

C₄

yes

characteristic

#13063264

C₄

yes

complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₄×C₄₃⋊C₈

C₄

yes

characteristic

C₈×Dic₄₃

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₈

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

C₈

yes

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₈×D₄₃

C₈

yes

—

C₈×D₄₃

C₂×C₄

yes

—

C₁₆×C₄₃

C₂×C₄

yes

complemented

C₄₃⋊C₁₆

C₂×C₄

yes

complemented

C₂²×D₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

—

C₄×D₄₃

—

C₄×D₄₃

C₄²

yes

—

C₄×D₄₃

C₂×C₈

yes

—

C₈×C₄₃

C₂×C₈

yes

—

C₈×C₄₃

C₂²×C₄

yes

—

C₄₃⋊C₈

C₄²

yes

—

C₄₃⋊C₈

C₂×C₈

yes

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

C₄×C₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

C₂²×C₈

yes

characteristic

Dic₄₃

C₄×C₈

yes

—

Dic₄₃

M₃₂

yes

complemented

C₄×M₃₂

—

maximal, Sylow

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

C₂×M₃₂

yes

—

D₄₃

—

C₂×M₃₂

—

C₂×C₄×C₈

—

#346

—

#346

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

C₄×M₃₂

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

—

C₄²

—

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

C₄×D₄₃

yes

complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₄₃

yes

—

C₈

C₂×C₄×D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

100

C₄

C₄²×D₄₃

yes

characteristic

101

C₄

C₂×C₈×D₄₃

yes

characteristic

102

C₂

—

103

C₂

C₄×C₈×D₄₃

yes

characteristic

104

C₂

M₃₂×D₄₃

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂²×C₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	C₄×M₃₂
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#346

C₂

socle

C₂²×C₄₃

C₂²×C₈

hypercenter

#346

D₄₃

hypocenter

C₄₃

C₄×M₃₂

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
3. #14582675	C₂	semidirect
4. C₁₆×Dic₄₃	C₂	semidirect
5. C₄₃×#346	C₂	semidirect
9. #13063264	C₄	semidirect
27. C₁₆×C₄₃	C₂×C₄	semidirect
28. C₄₃⋊C₁₆	C₂×C₄	semidirect
48. Dic₄₃	M₃₂	semidirect
56. #346	D₄₃	semidirect
58. C₄₃	C₄×M₃₂	semidirect
81. C₁₆	C₄×D₄₃	semidirect

H ≅ G/N

type

3. #14582675

C₂

semidirect

4. C₁₆×Dic₄₃

C₂

semidirect

5. C₄₃×#346

C₂

semidirect

9. #13063264

C₄

semidirect

27. C₁₆×C₄₃

C₂×C₄

semidirect

28. C₄₃⋊C₁₆

C₂×C₄

semidirect

48. Dic₄₃

M₃₂

semidirect

56. #346

D₄₃

semidirect

58. C₄₃

C₄×M₃₂

semidirect

81. C₁₆

C₄×D₄₃

semidirect

Subgroups — #19136188

Conjugacy classes of subgroups

Complements