Group #19136405 — subgroups

Subgroups — #19136405

Order 5504.

128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14582851	C₂	1	1	yes	maximal, characteristic
2	#14582719	C₂	1	2	yes	maximal, complemented
3	#14582680	C₂	1	2	yes	maximal
4	#14582677	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	C₄	1	1	yes	characteristic
7	C₂×#10621872	C₂²	1	1	yes	characteristic
8	C₄²×D₄₃	C₄	1	1	yes	characteristic
9	#13063265	C₂²	1	2	yes	—
10	#13063236	C₄	1	1	yes	characteristic
11	C₈×Dic₄₃	C₄	1	1	yes	characteristic
12	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
13	M₃₂×C₄₃	C₂²	1	2	yes	—
14	#97×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₃	—	2	1	no	—
16	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₄₃	—	2	1	no	—
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	#10621872	—	2	2	no	—
26	C₁₆×C₄₃	—	2	2	no	—
27	C₄₃⋊C₁₆	—	2	2	no	—
28	C₂²×D₄₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₄₃	—	2	1	no	—
32	C₂×Dic₄₃	M₁₆	1	1	yes	characteristic
33	C₄×D₄₃	—	2	1	no	—
34	C₄×D₄₃	—	2	1	no	—
35	C₄×D₄₃	—	4	2	no	—
36	C₈×C₄₃	—	2	1	no	—
37	C₈×C₄₃	#41	1	2	yes	—
38	C₄₃⋊C₈	—	2	1	no	—
39	C₄₃⋊C₈	M₁₆	1	2	yes	—
40	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₄₃	—	2	1	no	—
42	C₂×D₄₃	—	4	1	no	—
43	C₄×C₄₃	—	4	1	no	—
44	C₄×C₄₃	#117	1	1	yes	characteristic
45	C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
46	Dic₄₃	—	2	2	no	—
47	Dic₄₃	—	2	1	no	—
48	#2165	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	#432	1	1	yes	characteristic
51	D₄₃	—	4	1	no	—
52	C₄×M₁₆	—	43	1	no	—
53	#364	—	43	2	no	—
54	#349	—	43	2	no	—
55	#347	—	43	1	no	—
56	#347	D₄₃	1	1	yes	characteristic, complemented
57	C₄₃	#2165	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	43	1	no	—
59	C₂×M₁₆	—	43	1	no	—
60	C₂×C₄²	—	43	1	no	—
61	M₃₂	—	43	2	no	—
62	M₃₂	C₂×D₄₃	1	2	yes	—
63	#97	—	43	1	no	—
64	#97	C₂×D₄₃	1	1	yes	characteristic
65	C₄×C₈	—	43	1	no	—
66	C₄×C₈	—	43	1	no	—
67	C₂²×C₄	—	43	1	no	—
68	C₂²×C₄	—	86	1	no	—
69	M₁₆	—	86	2	no	—
70	M₁₆	—	86	2	no	—
71	C₂×C₈	—	43	1	no	—
72	C₂×C₈	—	43	1	no	—
73	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
75	C₄²	—	43	1	no	—
76	C₄²	—	86	1	no	—
77	C₄²	C₄×D₄₃	1	1	yes	characteristic
78	C₁₆	—	2	2	no	—
79	C₁₆	—	86	2	no	—
80	C₂³	—	43	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	43	1	no	—
83	C₂×C₄	—	86	1	no	—
84	C₂×C₄	—	86	1	no	—
85	C₂×C₄	—	86	1	no	—
86	C₂×C₄	—	172	2	no	—
87	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	43	2	no	—
90	C₈	—	86	1	no	—
91	C₈	#10621898	1	2	yes	—
92	C₂²	—	86	1	no	—
93	C₂²	—	172	1	no	—
94	C₂²	M₁₆×D₄₃	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	86	2	no	—
97	C₄	—	86	1	no	—
98	C₄	#13063282	1	1	yes	characteristic
99	C₄	M₁₆×D₄₃	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	172	1	no	—
102	C₂	#14582954	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582851

C₂

yes

maximal, characteristic

#14582719

C₂

yes

maximal, complemented

#14582680

C₂

yes

maximal

#14582677

C₂

yes

maximal, characteristic, complemented

C₄₃×#347

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₄

yes

characteristic

C₂×#10621872

C₂²

yes

characteristic

C₄²×D₄₃

C₄

yes

characteristic

#13063265

C₂²

yes

—

#13063236

C₄

yes

characteristic

C₈×Dic₄₃

C₄

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

—

#97×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

—

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

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

characteristic

#10621872

—

#10621872

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

M₁₆

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

M₁₆

yes

—

C₂²×C₄₃

C₂×M₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₂×M₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2165

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#432

yes

characteristic

D₄₃

—

C₄×M₁₆

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2165

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×C₄²

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

—

#97

—

#97

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

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

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#10621898

yes

—

C₂²

—

C₂²

—

172

—

C₂²

M₁₆×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#13063282

yes

characteristic

C₄

M₁₆×D₄₃

yes

characteristic

100

C₂

—

101

C₂

—

172

—

102

C₂

#14582954

yes

characteristic

	subgroup	G/H
center	C₄	#13063282
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#347	C₂
socle	C₂×C₄₃	#432
hypercenter	#347	D₄₃
hypocenter	C₄₃	#2165
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#13063282

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#347

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #14582719	C₂	semidirect
4. #14582677	C₂	semidirect
5. C₄₃×#347	C₂	semidirect
56. #347	D₄₃	semidirect
57. C₄₃	#2165	semidirect

H ≅ G/N

type

2. #14582719

C₂

semidirect

4. #14582677

C₂

semidirect

5. C₄₃×#347

C₂

semidirect

56. #347

D₄₃

semidirect

57. C₄₃

#2165

semidirect

Subgroups — #19136405

Conjugacy classes of subgroups

Complements