Group #19135560 — subgroups

Subgroups — #19135560

Order 5504.

252 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂×#13063317	C₂	1	1	yes	maximal, characteristic
2	#14582765	C₂	1	1	yes	maximal, characteristic
3	#14582662	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	#13063317	—	2	2	no	—
6	#13063317	C₄	1	4	yes	complemented
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×Dic₄₃⋊C₄	—	2	2	no	—
10	C₄₃⋊#95	—	2	2	no	—
11	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	—	2	2	no	—
14	C₂²×C₄×C₄₃	D₄	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	—	2	2	no	—
17	C₂²×Dic₄₃	—	2	2	no	—
18	C₂×C₈×C₄₃	—	2	2	no	—
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	Q₈	1	4	yes	—
21	C₄²×C₄₃	C₂×C₄	1	2	yes	—
22	C₄²×C₄₃	D₄	1	2	yes	—
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	4	no	—
25	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
26	Dic₄₃⋊C₄	—	2	8	no	—
27	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	—	2	4	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₄₃	#41	1	2	yes	—
34	C₂×Dic₄₃	—	2	4	no	—
35	C₂×Dic₄₃	—	4	4	no	—
36	C₂×Dic₄₃	—	4	2	no	—
37	C₂×Dic₄₃	—	4	4	no	—
38	C₈×C₄₃	—	2	4	no	—
39	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄₃	#124	1	1	yes	characteristic
41	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₄₃	#135	1	4	yes	—
43	C₄×C₄₃	—	2	4	no	—
44	C₄×C₄₃	C₄×Q₈	1	2	yes	—
45	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
46	Dic₄₃	—	4	4	no	—
47	Dic₄₃	—	8	2	no	—
48	#1991	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	#391	1	1	yes	characteristic
50	C₂×C₄₃	#416	1	2	yes	—
51	C₂×C₄₃	#488	1	2	yes	—
52	C₂×C₄₃	#499	1	2	yes	—
53	C₂×#125	—	43	1	no	—
54	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
55	#382	—	43	1	no	—
56	#340	—	43	4	no	—
57	C₄₃	#1991	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	C₂×D₄₃	1	2	yes	—
59	#125	—	43	4	no	—
60	#125	—	86	2	no	—
61	C₂×C₄⋊C₄	—	43	2	no	—
62	C₂×C₄⋊C₄	—	43	2	no	—
63	C₂×C₄⋊C₄	—	86	2	no	—
64	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
65	C₄×C₈	—	2	2	no	—
66	#95	—	86	2	no	—
67	C₂²×C₄	—	86	2	no	—
68	C₂²×C₄	—	86	2	no	—
69	C₂²×C₄	D₁₇₂	1	2	yes	—
70	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₈₆	1	4	yes	—
74	C₄⋊C₄	—	43	4	no	—
75	C₄⋊C₄	—	86	8	no	—
76	C₄⋊C₄	—	86	2	no	—
77	C₄⋊C₄	—	86	4	no	—
78	C₄²	C₄×D₄₃	1	2	yes	—
79	C₄²	C₂²⋊D₄₃	1	2	yes	—
80	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	86	4	no	—
83	C₂×C₄	—	172	2	no	—
84	C₂×C₄	—	172	4	no	—
85	C₂×C₄	—	172	4	no	—
86	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
87	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
88	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
89	C₂×C₄	#10621898	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
91	C₈	—	2	4	no	—
92	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
93	C₂²	#13063313	1	1	yes	characteristic
94	C₂²	#13063325	1	1	yes	characteristic
95	C₂²	#13063347	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	344	2	no	—
98	C₄	—	172	4	no	—
99	C₄	C₄×Dic₈₆	1	2	yes	—
100	C₄	#13063304	1	2	yes	—
101	C₂	#14582805	1	1	yes	characteristic
102	C₂	#14582896	1	2	yes	—
103	C₂	#14583254	1	2	yes	—
104	C₂	#14583301	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal, characteristic

#14582765

C₂

yes

maximal, characteristic

#14582662

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

#13063317

—

#13063317

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

D₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#124

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

#135

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₄×Q₈

yes

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#488

yes

—

C₂×C₄₃

#499

yes

—

C₂×#125

—

C₂×C₄×C₈

D₄₃

yes

characteristic

#382

—

#340

—

C₄₃

#1991

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₄₃

yes

—

C₄²

C₂²⋊D₄₃

yes

—

C₂³

C₂×D₁₇₂

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

#10621898

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

344

—

C₄

—

172

—

C₄

C₄×Dic₈₆

yes

—

100

C₄

#13063304

yes

—

101

C₂

#14582805

yes

characteristic

102

C₂

#14582896

yes

—

103

C₂

#14583254

yes

—

104

C₂

#14583301

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1991
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

#1991

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
6. #13063317	C₄	semidirect
57. C₄₃	#1991	semidirect

H ≅ G/N

type

6. #13063317

C₄

semidirect

57. C₄₃

#1991

semidirect

Subgroups — #19135560

Conjugacy classes of subgroups

Complements