Group #19136433 — subgroups

Subgroups — #19136433

Order 5504.

146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14583315	C₂	1	2	yes	maximal, complemented
2	#14583017	C₂	1	1	yes	maximal, characteristic
3	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582682	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₄	1	1	yes	characteristic
7	#13063331	C₂²	1	2	yes	—
8	#13063265	C₂²	1	2	yes	—
9	#13063264	—	2	2	no	—
10	C₁₆×D₄₃	—	2	2	no	—
11	#13063261	C₄	1	1	yes	characteristic
12	#13063253	C₄	1	2	yes	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	#10621898	C₂×C₄	1	2	yes	—
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	#10621877	C₂×C₄	1	2	yes	—
21	Dic₁₇₂	C₈	1	1	yes	characteristic
22	D₃₄₄	C₈	1	1	yes	characteristic
23	#10621873	C₈	1	2	yes	—
24	#10621872	—	2	2	no	—
25	C₈×D₄₃	—	2	2	no	—
26	C₁₆×C₄₃	—	2	1	no	—
27	C₁₆×C₄₃	D₄	1	1	yes	characteristic
28	C₁₆×C₄₃	D₄	1	1	yes	characteristic
29	C₄₃⋊C₁₆	—	2	2	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²⋊D₄₃	—	2	2	no	—
33	D₁₇₂	C₂×C₈	1	2	yes	—
34	C₄×D₄₃	—	2	2	no	—
35	Dic₈₆	C₂×C₈	1	2	yes	—
36	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
37	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
38	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₃	#41	1	1	yes	characteristic
40	C₄₃⋊C₈	—	2	2	no	—
41	C₂²×C₄₃	#131	1	1	yes	characteristic
42	C₂×D₄₃	—	2	2	no	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
45	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
46	Dic₄₃	—	2	2	no	—
47	#2170	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	2	1	no	—
49	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
50	D₄₃	—	4	2	no	—
51	#504	—	43	2	no	—
52	#443	—	43	1	no	—
53	#364	—	43	1	no	—
54	#350	—	43	2	no	—
55	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
56	C₄₃	#2170	1	1	yes	characteristic, complemented, Sylow
57	#135	—	43	1	no	—
58	#131	—	43	2	no	—
59	M₃₂	—	43	2	no	—
60	M₃₂	—	86	2	no	—
61	C₂×C₁₆	—	86	2	no	—
62	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
63	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
64	#108	—	43	1	no	—
65	#104	—	43	2	no	—
66	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
67	#41	—	43	2	no	—
68	Q₁₆	—	43	1	no	—
69	SD₁₆	—	43	2	no	—
70	D₈	—	43	1	no	—
71	M₁₆	—	43	2	no	—
72	M₁₆	—	86	2	no	—
73	C₂×C₈	—	86	2	no	—
74	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
76	C₄²	C₄×D₄₃	1	1	yes	characteristic
77	C₁₆	—	2	1	no	—
78	C₁₆	—	86	2	no	—
79	C₁₆	D₁₇₂	1	1	yes	characteristic
80	C₁₆	D₁₇₂	1	1	yes	characteristic
81	Q₈	—	43	2	no	—
82	D₄	—	43	2	no	—
83	D₄	—	86	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	86	2	no	—
86	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
87	C₈	—	86	2	no	—
88	C₈	C₈×D₄₃	1	1	yes	characteristic
89	C₈	C₈×D₄₃	1	1	yes	characteristic
90	C₈	C₂×D₁₇₂	1	1	yes	characteristic
91	C₈	#10621898	1	1	yes	characteristic
92	C₂²	—	86	2	no	—
93	C₂²	#13063331	1	1	yes	characteristic
94	C₄	—	2	2	no	—
95	C₄	—	86	2	no	—
96	C₄	C₄×D₁₇₂	1	1	yes	characteristic
97	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	172	2	no	—
100	C₂	C₈×D₁₇₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583315

C₂

yes

maximal, complemented

#14583017

C₂

yes

maximal, characteristic

#14582720

C₂

yes

maximal, characteristic, complemented

#14582682

C₂

yes

maximal, complemented

C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

#13063347

C₄

yes

characteristic

#13063331

C₂²

yes

—

#13063265

C₂²

yes

—

#13063264

—

C₁₆×D₄₃

—

#13063261

C₄

yes

characteristic

#13063253

C₄

yes

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

#10621898

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

#10621877

C₂×C₄

yes

—

Dic₁₇₂

C₈

yes

characteristic

D₃₄₄

C₈

yes

characteristic

#10621873

C₈

yes

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

C₂×C₈

yes

—

C₄×D₄₃

—

Dic₈₆

C₂×C₈

yes

—

C₈×C₄₃

C₂×C₈

yes

characteristic

C₈×C₄₃

C₂×C₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

#131

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

C₂²×C₈

yes

characteristic

Dic₄₃

—

#2170

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₈×D₄

yes

characteristic

D₄₃

—

—

—

—

—

C₄×C₁₆

D₄₃

yes

characteristic, complemented

C₄₃

#2170

yes

characteristic, complemented, Sylow

#135

—

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

D₁₇₂

yes

characteristic

C₁₆

D₁₇₂

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

C₈×D₄₃

yes

characteristic

C₈

C₈×D₄₃

yes

characteristic

C₈

C₂×D₁₇₂

yes

characteristic

C₈

#10621898

yes

characteristic

C₂²

—

C₂²

#13063331

yes

characteristic

C₄

—

C₄

—

C₄

C₄×D₁₇₂

yes

characteristic

C₄

C₂×C₈×D₄₃

yes

characteristic

C₂

—

C₂

—

172

—

100

C₂

C₈×D₁₇₂

yes

characteristic

	subgroup	G/H
center	C₁₆	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₈×D₄
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#2170
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

subgroup

G/H

center

C₁₆

D₁₇₂

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×C₁₆×C₄₃

C₂

socle

C₂×C₄₃

C₈×D₄

hypercenter

C₄×C₁₆

D₄₃

hypocenter

C₄₃

#2170

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. #14583315	C₂	semidirect
3. #14582720	C₂	semidirect
4. #14582682	C₂	semidirect
5. C₄×C₁₆×C₄₃	C₂	semidirect
55. C₄×C₁₆	D₄₃	semidirect
56. C₄₃	#2170	semidirect

H ≅ G/N

type

1. #14583315

C₂

semidirect

3. #14582720

C₂

semidirect

4. #14582682

C₂

semidirect

5. C₄×C₁₆×C₄₃

C₂

semidirect

55. C₄×C₁₆

D₄₃

semidirect

56. C₄₃

#2170

semidirect

Subgroups — #19136433

Conjugacy classes of subgroups

Complements