Group #19134349 — subgroups

Subgroups — #19134349

Order 5504.

200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14582857	C₂	1	1	yes	maximal, characteristic
2	#14582855	C₂	1	2	yes	maximal
3	C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic
4	#14582655	C₂	1	2	yes	maximal
5	C₄₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	#13063284	C₂²	1	1	yes	characteristic
9	#13063236	C₄	1	4	yes	complemented
10	#13063235	C₄	1	2	yes	complemented
11	C₄×C₄₃⋊C₈	C₄	1	4	yes	complemented
12	C₈×Dic₄₃	C₄	1	2	yes	complemented
13	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	#117×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	M₁₆×C₄₃	—	2	2	no	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄⋊C₄×C₄₃	—	2	2	no	—
19	C₂²⋊C₄×C₄₃	—	2	2	no	—
20	C₄²×C₄₃	C₂×C₄	1	4	yes	—
21	C₂²⋊Dic₄₃	—	2	1	no	—
22	C₄⋊Dic₄₃	—	2	1	no	—
23	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
24	#10621877	—	2	2	no	—
25	#10621877	—	2	2	no	—
26	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
31	C₂³×C₄₃	#41	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	4	no	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	#41	1	2	yes	—
36	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
37	C₂×Dic₄₃	—	2	2	no	—
38	C₈×C₄₃	—	2	2	no	—
39	C₄₃⋊C₈	—	2	4	no	—
40	C₄₃⋊C₈	C₄²	1	1	yes	characteristic
41	C₄₃⋊C₈	C₄²	1	1	yes	characteristic
42	C₄₃⋊C₈	C₄²	1	2	yes	—
43	C₂²×C₄₃	—	4	1	no	—
44	C₂²×C₄₃	#117	1	2	yes	—
45	C₂²×C₄₃	#117	1	1	yes	characteristic
46	C₄×C₄₃	—	4	4	no	—
47	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₄₃	#117	1	1	yes	characteristic
49	C₄×C₄₃	#117	1	2	yes	—
50	Dic₄₃	—	4	2	no	—
51	#1747	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	2	1	no	—
53	C₂×C₄₃	—	2	2	no	—
54	C₂×C₄₃	#376	1	1	yes	characteristic
55	#405	—	43	1	no	—
56	#405	—	43	2	no	—
57	#338	—	43	1	no	—
58	H(3,ℤ/4)	—	43	2	no	—
59	H(3,ℤ/4)	D₄₃	1	1	yes	characteristic
60	C₄₃	#1747	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	43	2	no	—
62	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
63	C₂²×C₈	—	43	1	no	—
64	#117	—	43	1	no	—
65	#117	C₂×D₄₃	1	2	yes	—
66	#97	—	43	2	no	—
67	#97	—	43	4	no	—
68	C₄×C₈	—	43	2	no	—
69	C₄×C₈	—	43	4	no	—
70	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	86	2	no	—
73	M₁₆	—	86	2	no	—
74	C₂×C₈	—	43	1	no	—
75	C₂×C₈	—	43	2	no	—
76	C₂×C₈	—	43	1	no	—
77	C₂×C₈	—	43	2	no	—
78	C₂×C₈	—	43	4	no	—
79	C₂×C₈	C₄×D₄₃	1	2	yes	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	86	1	no	—
82	C₂²⋊C₄	—	2	2	no	—
83	C₂²⋊C₄	—	86	1	no	—
84	C₄²	—	43	2	no	—
85	C₄²	C₄×D₄₃	1	4	yes	—
86	C₂³	#10621900	1	1	yes	characteristic
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	86	2	no	—
89	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
91	C₂×C₄	#10621900	1	2	yes	—
92	C₂×C₄	#10621902	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	43	1	no	—
95	C₈	—	43	1	no	—
96	C₈	—	43	2	no	—
97	C₈	—	86	4	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#13063281	1	2	yes	—
100	C₂²	#13063283	1	1	yes	characteristic
101	C₄	—	4	4	no	—
102	C₄	—	172	2	no	—
103	C₄	C₄²×D₄₃	1	1	yes	characteristic
104	C₄	#13063281	1	1	yes	characteristic
105	C₄	#13063283	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	—	2	1	no	—
108	C₂	#14582744	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582857

C₂

yes

maximal, characteristic

#14582855

C₂

yes

maximal

C₄₃⋊#338

C₂

yes

maximal, characteristic

#14582655

C₂

yes

maximal

C₄₃×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063284

C₂²

yes

characteristic

#13063236

C₄

yes

complemented

#13063235

C₄

yes

complemented

C₄×C₄₃⋊C₈

C₄

yes

complemented

C₈×Dic₄₃

C₄

yes

complemented

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄²

yes

characteristic

C₄₃⋊C₈

C₄²

yes

characteristic

C₄₃⋊C₈

C₄²

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#117

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

#1747

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#1747

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×D₄₃

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₃

yes

—

C₂³

#10621900

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

#10621900

yes

—

C₂×C₄

#10621902

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#13063281

yes

—

100

C₂²

#13063283

yes

characteristic

101

C₄

—

102

C₄

—

172

—

103

C₄

C₄²×D₄₃

yes

characteristic

104

C₄

#13063281

yes

characteristic

105

C₄

#13063283

yes

—

106

C₂

—

107

C₂

—

108

C₂

#14582744

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₄₃
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×H(3,ℤ/4)	C₂
socle	C₂×C₄₃	#376
hypercenter	H(3,ℤ/4)	D₄₃
hypocenter	C₄₃	#1747
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

C₄²×D₄₃

commutator

C₄×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×H(3,ℤ/4)

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₄×C₄₃ ▷ C₄₃

C₁ ◁ C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
9. #13063236	C₄	semidirect
10. #13063235	C₄	semidirect
11. C₄×C₄₃⋊C₈	C₄	semidirect
12. C₈×Dic₄₃	C₄	semidirect
60. C₄₃	#1747	semidirect

H ≅ G/N

type

9. #13063236

C₄

semidirect

10. #13063235

C₄

semidirect

11. C₄×C₄₃⋊C₈

C₄

semidirect

12. C₈×Dic₄₃

C₄

semidirect

60. C₄₃

#1747

semidirect

Subgroups — #19134349

Conjugacy classes of subgroups

Complements