Group #19134340 — subgroups

Subgroups — #19134340

Order 5504.

296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582653	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
7	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
9	C₄×C₄₃⋊C₈	C₄	1	4	yes	complemented
10	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₄	1	4	yes	complemented
13	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₄₃	—	2	4	no	—
18	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
19	C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₄²×C₄₃	C₂×C₄	1	2	yes	—
21	C₄×Dic₄₃	—	2	4	no	—
22	C₄×Dic₄₃	—	2	4	no	—
23	C₄×Dic₄₃	C₈	1	8	yes	complemented
24	C₂×C₄₃⋊C₈	—	2	4	no	—
25	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
26	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₃	C₄²	1	2	yes	—
28	C₂×C₄×C₄₃	C₄²	1	2	yes	—
29	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₄₃	M₁₆	1	4	yes	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	#41	1	4	yes	—
34	C₂×Dic₄₃	—	2	4	no	—
35	C₂×Dic₄₃	—	2	4	no	—
36	C₂×Dic₄₃	C₂×C₈	1	8	yes	—
37	C₈×C₄₃	—	2	4	no	—
38	C₄₃⋊C₈	—	2	4	no	—
39	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
40	C₂²×C₄₃	#117	1	2	yes	—
41	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
42	C₂²×C₄₃	C₂×M₁₆	1	2	yes	—
43	C₄×C₄₃	C₄×C₈	1	4	yes	—
44	C₄×C₄₃	#97	1	4	yes	—
45	C₄×C₄₃	#117	1	2	yes	—
46	C₄×C₄₃	#117	1	2	yes	—
47	Dic₄₃	—	2	8	no	—
48	#1744	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	#376	1	1	yes	characteristic
50	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₄₃	C₂×#97	1	1	yes	characteristic
52	C₂×C₄₃	#431	1	4	yes	—
53	C₂×C₄×C₈	—	43	1	no	—
54	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
55	C₄³	—	43	1	no	—
56	#336	—	43	4	no	—
57	C₄₃	#1744	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	—	43	2	no	—
59	C₂²×C₈	C₂×D₄₃	1	2	yes	—
60	C₂×C₄²	—	43	2	no	—
61	C₂×C₄²	—	43	2	no	—
62	C₂×C₄²	—	43	2	no	—
63	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
64	C₄×C₈	—	43	4	no	—
65	C₄×C₈	Dic₄₃	1	4	yes	complemented
66	C₂²×C₄	—	43	4	no	—
67	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
69	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	43	4	no	—
72	C₂×C₈	—	86	4	no	—
73	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
74	C₄²	—	43	8	no	—
75	C₄²	—	86	4	no	—
76	C₄²	—	86	4	no	—
77	C₄²	C₄×D₄₃	1	2	yes	—
78	C₄²	C₂×Dic₄₃	1	2	yes	—
79	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
80	C₂×C₄	—	43	8	no	—
81	C₂×C₄	—	86	4	no	—
82	C₂×C₄	—	86	4	no	—
83	C₂×C₄	C₈×D₄₃	1	4	yes	—
84	C₂×C₄	#10621872	1	4	yes	—
85	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
86	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
87	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
88	C₂×C₄	#10621898	1	4	yes	—
89	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	86	4	no	—
92	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
93	C₂²	#13063282	1	2	yes	—
94	C₂²	C₂×C₈×D₄₃	1	2	yes	—
95	C₂²	C₂×#10621872	1	2	yes	—
96	C₄	—	86	8	no	—
97	C₄	C₈×Dic₄₃	1	4	yes	—
98	C₄	#13063235	1	4	yes	—
99	C₄	#13063282	1	2	yes	—
100	C₄	#13063284	1	2	yes	—
101	C₂	#14582745	1	1	yes	characteristic
102	C₂	C₂×C₈×Dic₄₃	1	1	yes	characteristic
103	C₂	C₂×#13063235	1	1	yes	characteristic
104	C₂	#14582950	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄²×Dic₄₃

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄×C₄₃⋊C₈

C₄

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₈

yes

complemented

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

M₁₆

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×C₈

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

C₄×C₈

yes

—

C₄×C₄₃

#97

yes

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

#117

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

C₂×#97

yes

characteristic

C₂×C₄₃

#431

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄³

—

#336

—

C₄₃

#1744

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₄×C₈

Dic₄₃

yes

complemented

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₃

yes

—

C₄²

C₂×Dic₄₃

yes

—

C₂³

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

#10621872

yes

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

#10621898

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

C₂²

#13063282

yes

—

C₂²

C₂×C₈×D₄₃

yes

—

C₂²

C₂×#10621872

yes

—

C₄

—

C₄

C₈×Dic₄₃

yes

—

C₄

#13063235

yes

—

C₄

#13063282

yes

—

100

C₄

#13063284

yes

—

101

C₂

#14582745

yes

characteristic

102

C₂

C₂×C₈×Dic₄₃

yes

characteristic

103

C₂

C₂×#13063235

yes

characteristic

104

C₂

#14582950

yes

—

	subgroup	G/H
center	C₂×C₄²	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1744
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄²

C₂×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂²×C₄

hypercenter

C₂×C₄×C₈

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₄₃⋊C₈	C₄	semidirect
12. C₄×C₈×C₄₃	C₄	semidirect
23. C₄×Dic₄₃	C₈	semidirect
57. C₄₃	#1744	semidirect
65. C₄×C₈	Dic₄₃	semidirect

H ≅ G/N

type

9. C₄×C₄₃⋊C₈

C₄

semidirect

12. C₄×C₈×C₄₃

C₄

semidirect

23. C₄×Dic₄₃

C₈

semidirect

57. C₄₃

#1744

semidirect

65. C₄×C₈

Dic₄₃

semidirect

Subgroups — #19134340

Conjugacy classes of subgroups

Complements