Group #19136403 — subgroups

Subgroups — #19136403

Order 5504.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#14582853	C₂	1	1	yes	maximal, characteristic
2	Dic₄₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₄₃)⋊C₁₆	C₂	1	2	yes	maximal
4	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	#13063282	C₄	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	#13063236	C₄	1	1	yes	characteristic
11	#13063235	C₄	1	1	yes	characteristic
12	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
19	(C₂×D₄₃)⋊C₄	C₈	1	2	yes	—
20	Dic₄₃⋊C₄	C₈	1	2	yes	—
21	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#10621872	—	2	2	no	—
25	C₈×D₄₃	—	2	2	no	—
26	C₁₆×C₄₃	—	2	2	no	—
27	C₄₃⋊C₁₆	—	2	2	no	—
28	C₂²×D₄₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₄₃	C₂×C₈	1	2	yes	—
32	C₂×Dic₄₃	C₂×C₈	1	1	yes	characteristic
33	C₄×D₄₃	—	2	1	no	—
34	C₄×D₄₃	—	2	1	no	—
35	C₈×C₄₃	M₁₆	1	2	yes	—
36	C₈×C₄₃	#41	1	2	yes	—
37	C₄₃⋊C₈	—	2	1	no	—
38	C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
40	C₂×D₄₃	—	2	1	no	—
41	C₂×D₄₃	—	2	2	no	—
42	C₄×C₄₃	—	2	2	no	—
43	C₄×C₄₃	#117	1	1	yes	characteristic
44	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
45	Dic₄₃	—	2	1	no	—
46	Dic₄₃	—	2	2	no	—
47	#2164	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	#431	1	1	yes	characteristic
49	C₂×C₄₃	#504	1	2	yes	—
50	D₄₃	—	4	1	no	—
51	#405	—	43	1	no	—
52	C₄⋊C₁₆	—	43	2	no	—
53	C₂²⋊C₁₆	—	43	2	no	—
54	#346	D₄₃	1	1	yes	characteristic, complemented
55	C₄×C₁₆	—	43	1	no	—
56	C₄₃	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	43	1	no	—
58	C₂²×C₈	—	43	1	no	—
59	#117	—	43	1	no	—
60	C₂×C₁₆	—	43	2	no	—
61	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
62	#97	—	43	1	no	—
63	#97	—	43	1	no	—
64	C₄×C₈	—	43	1	no	—
65	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
66	C₂²×C₄	—	43	1	no	—
67	M₁₆	—	86	2	no	—
68	C₂×C₈	—	43	1	no	—
69	C₂×C₈	—	43	1	no	—
70	C₂×C₈	—	86	2	no	—
71	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
73	C₄⋊C₄	—	43	2	no	—
74	C₂²⋊C₄	—	43	2	no	—
75	C₄²	—	43	1	no	—
76	C₄²	C₄×D₄₃	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	86	2	no	—
79	C₂³	—	43	1	no	—
80	C₂×C₄	—	43	2	no	—
81	C₂×C₄	—	43	1	no	—
82	C₂×C₄	—	86	1	no	—
83	C₂×C₄	—	86	1	no	—
84	C₂×C₄	C₈×D₄₃	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
86	C₈	—	86	1	no	—
87	C₈	—	86	1	no	—
88	C₈	#10621872	1	2	yes	—
89	C₈	#10621898	1	2	yes	—
90	C₂²	—	86	2	no	—
91	C₂²	—	86	1	no	—
92	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	86	2	no	—
95	C₄	—	86	1	no	—
96	C₄	#13063282	1	1	yes	characteristic
97	C₄	C₂×#10621872	1	1	yes	characteristic
98	C₂	—	172	1	no	—
99	C₂	#14582950	1	1	yes	characteristic
100	C₂	#14583317	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582853

C₂

yes

maximal, characteristic

Dic₄₃⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₄₃)⋊C₁₆

C₂

yes

maximal

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×#346

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₄

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063282

C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

—

#13063236

C₄

yes

characteristic

#13063235

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

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

(C₂×D₄₃)⋊C₄

C₈

yes

—

Dic₄₃⋊C₄

C₈

yes

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

—

C₂×Dic₄₃

C₂×C₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

M₁₆

yes

—

C₈×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

#10621872

yes

—

C₈

#10621898

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

172

—

C₂

#14582950

yes

characteristic

100

C₂

#14583317

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₈
Fitting	C₄₃×#346	C₂
hypercenter	#346	D₄₃
hypocenter	C₄₃	#2164
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂²×C₈

Fitting

C₄₃×#346

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
2. Dic₄₃⋊C₁₆	C₂	semidirect
4. C₄×C₄₃⋊C₁₆	C₂	semidirect
5. C₄₃×#346	C₂	semidirect
54. #346	D₄₃	semidirect
56. C₄₃	#2164	semidirect

H ≅ G/N

type

2. Dic₄₃⋊C₁₆

C₂

semidirect

4. C₄×C₄₃⋊C₁₆

C₂

semidirect

5. C₄₃×#346

C₂

semidirect

54. #346

D₄₃

semidirect

56. C₄₃

#2164

semidirect

Subgroups — #19136403

Conjugacy classes of subgroups

Complements