Group #19147748 — subgroups

Subgroups — #19147748

Order 5504.

350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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	#14583716	C₂	1	2	yes	maximal, complemented
2	#14583342	C₂	1	6	yes	maximal, complemented
3	#14583331	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₃₄₄	C₂	1	3	yes	maximal, complemented
5	C₄₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063372	—	2	2	no	—
7	#13063358	—	2	6	no	—
8	#13063347	C₂²	1	6	yes	—
9	C₂×Dic₁₇₂	C₂²	1	6	yes	—
10	Dic₃₄₄	C₂²	1	3	yes	—
11	Dic₃₄₄	C₂²	1	6	yes	—
12	#13063270	C₂²	1	6	yes	—
13	D₆₈₈	C₂²	1	1	yes	characteristic
14	#131×C₄₃	C₂²	1	1	yes	characteristic
15	M₃₂×C₄₃	C₂²	1	3	yes	—
16	C₂×C₁₆×C₄₃	C₂²	1	3	yes	—
17	#41×C₄₃	D₄	1	1	yes	characteristic
18	Q₈×D₄₃	—	4	2	no	—
19	#10621900	—	4	6	no	—
20	#10621898	—	2	6	no	—
21	C₂×Dic₈₆	—	2	6	no	—
22	M₁₆×C₄₃	D₄	1	3	yes	—
23	C₂×C₈×C₄₃	C₂³	1	3	yes	—
24	Dic₁₇₂	—	2	6	no	—
25	Dic₁₇₂	C₂³	1	6	yes	—
26	D₃₄₄	C₂³	1	2	yes	—
27	#10621873	—	2	6	no	—
28	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
29	C₁₆×C₄₃	C₂³	1	3	yes	—
30	Q₈×C₄₃	D₈	1	1	yes	characteristic
31	D₄×C₄₃	D₈	1	3	yes	—
32	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
33	C₂²⋊D₄₃	—	4	6	no	—
34	C₂×Dic₄₃	—	4	6	no	—
35	D₁₇₂	—	2	2	no	—
36	C₄×D₄₃	—	4	6	no	—
37	Dic₈₆	—	2	6	no	—
38	Dic₈₆	—	4	6	no	—
39	C₈×C₄₃	C₂×D₄	1	3	yes	—
40	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₂²×C₄₃	C₂×D₈	1	3	yes	—
42	C₂×D₄₃	—	4	2	no	—
43	C₄×C₄₃	C₂×D₈	1	3	yes	—
44	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
45	Dic₄₃	—	4	6	no	—
46	#3417	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	2	3	no	—
48	C₂×C₄₃	C₂²×D₈	1	1	yes	characteristic
49	D₄₃	—	8	2	no	—
50	#578	—	43	2	no	—
51	#510	—	43	6	no	—
52	#508	—	43	3	no	—
53	C₂×Q₃₂	—	43	3	no	—
54	#504	D₄₃	1	1	yes	characteristic, complemented
55	C₄₃	#3417	1	1	yes	characteristic, complemented, Sylow
56	2₋¹⁺⁴	—	86	2	no	—
57	#137	—	86	6	no	—
58	#135	—	43	6	no	—
59	C₂×Q₁₆	—	43	6	no	—
60	#131	C₂×D₄₃	1	1	yes	characteristic
61	Q₃₂	—	43	3	no	—
62	Q₃₂	—	43	6	no	—
63	SD₃₂	—	43	6	no	—
64	D₁₆	—	43	1	no	—
65	M₃₂	C₂×D₄₃	1	3	yes	—
66	C₂×C₁₆	C₂×D₄₃	1	3	yes	—
67	#41	—	86	6	no	—
68	#41	—	172	6	no	—
69	#41	D₁₇₂	1	1	yes	characteristic
70	C₂×Q₈	—	86	6	no	—
71	C₂×Q₈	—	172	2	no	—
72	Q₁₆	—	43	6	no	—
73	Q₁₆	—	86	6	no	—
74	SD₁₆	—	86	6	no	—
75	D₈	—	43	2	no	—
76	M₁₆	D₁₇₂	1	3	yes	—
77	C₂×C₈	C₂²×D₄₃	1	3	yes	—
78	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
79	C₁₆	C₂²×D₄₃	1	3	yes	—
80	Q₈	—	86	6	no	—
81	Q₈	—	172	6	no	—
82	Q₈	D₃₄₄	1	1	yes	characteristic
83	D₄	—	86	2	no	—
84	D₄	—	172	6	no	—
85	D₄	D₃₄₄	1	3	yes	—
86	C₂×C₄	—	172	6	no	—
87	C₂×C₄	—	172	6	no	—
88	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
89	C₈	C₂×D₁₇₂	1	3	yes	—
90	C₈	C₂³×D₄₃	1	1	yes	characteristic
91	C₂²	—	172	2	no	—
92	C₂²	C₂×D₃₄₄	1	3	yes	—
93	C₄	—	172	6	no	—
94	C₄	C₂×D₃₄₄	1	3	yes	—
95	C₄	C₂²×D₁₇₂	1	1	yes	characteristic
96	C₂	—	2	3	no	—
97	C₂	—	344	2	no	—
98	C₂	C₂²×D₃₄₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583716

C₂

yes

maximal, complemented

#14583342

C₂

yes

maximal, complemented

#14583331

C₂

yes

maximal, complemented

C₂×Dic₃₄₄

C₂

yes

maximal, complemented

C₄₃×#504

C₂

yes

maximal, characteristic, complemented

#13063372

—

#13063358

—

#13063347

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

—

Dic₃₄₄

C₂²

yes

—

Dic₃₄₄

C₂²

yes

—

#13063270

C₂²

yes

—

D₆₈₈

C₂²

yes

characteristic

#131×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

—

C₂×C₁₆×C₄₃

C₂²

yes

—

#41×C₄₃

D₄

yes

characteristic

Q₈×D₄₃

—

#10621900

—

#10621898

—

C₂×Dic₈₆

—

M₁₆×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

Dic₁₇₂

—

Dic₁₇₂

C₂³

yes

—

D₃₄₄

C₂³

yes

—

#10621873

—

C₁₆×C₄₃

C₂³

yes

characteristic

C₁₆×C₄₃

C₂³

yes

—

Q₈×C₄₃

D₈

yes

characteristic

D₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

—

C₈×C₄₃

C₂⁴

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

—

C₂×D₄₃

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂²×D₄

yes

characteristic

Dic₄₃

—

#3417

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂²×D₈

yes

characteristic

D₄₃

—

#578

—

#510

—

#508

—

C₂×Q₃₂

—

#504

D₄₃

yes

characteristic, complemented

C₄₃

#3417

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

#137

—

#135

—

C₂×Q₁₆

—

#131

C₂×D₄₃

yes

characteristic

Q₃₂

—

Q₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

C₂×D₄₃

yes

—

C₂×C₁₆

C₂×D₄₃

yes

—

#41

—

#41

—

172

—

#41

D₁₇₂

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

172

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

D₁₇₂

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₁₆

C₂²×D₄₃

yes

characteristic

C₁₆

C₂²×D₄₃

yes

—

Q₈

—

Q₈

—

172

—

Q₈

D₃₄₄

yes

characteristic

D₄

—

D₄

—

172

—

D₄

D₃₄₄

yes

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₈

C₂×D₁₇₂

yes

—

C₈

C₂³×D₄₃

yes

characteristic

C₂²

—

172

—

C₂²

C₂×D₃₄₄

yes

—

C₄

—

172

—

C₄

C₂×D₃₄₄

yes

—

C₄

C₂²×D₁₇₂

yes

characteristic

C₂

—

C₂

—

344

—

C₂

C₂²×D₃₄₄

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×D₃₄₄
commutator	C₈×C₄₃	C₂⁴
Frattini	C₈	C₂³×D₄₃
Fitting	C₄₃×#504	C₂
socle	C₂×C₄₃	C₂²×D₈
hypercenter	#504	D₄₃
hypocenter	C₄₃	#3417
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #504

subgroup

G/H

center

C₂

C₂²×D₃₄₄

commutator

C₈×C₄₃

C₂⁴

Frattini

C₈

C₂³×D₄₃

Fitting

C₄₃×#504

C₂

socle

C₂×C₄₃

C₂²×D₈

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #504

N	H ≅ G/N	type
1. #14583716	C₂	semidirect
2. #14583342	C₂	semidirect
3. #14583331	C₂	semidirect
4. C₂×Dic₃₄₄	C₂	semidirect
5. C₄₃×#504	C₂	semidirect
54. #504	D₄₃	semidirect
55. C₄₃	#3417	semidirect

H ≅ G/N

type

1. #14583716

C₂

semidirect

2. #14583342

C₂

semidirect

3. #14583331

C₂

semidirect

4. C₂×Dic₃₄₄

C₂

semidirect

5. C₄₃×#504

C₂

semidirect

54. #504

D₄₃

semidirect

55. C₄₃

#3417

semidirect

Subgroups — #19147748

Conjugacy classes of subgroups

Complements