Group #19133733 — subgroups

Subgroups — #19133733

Order 5504.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583629	C₂	1	1	yes	maximal, characteristic
2	#14583191	C₂	1	2	yes	maximal
3	#14582648	C₂	1	1	yes	maximal, characteristic
4	#14582631	C₂	1	2	yes	maximal
5	C₄₃×#494	C₂	1	1	yes	maximal, characteristic
6	#13063324	—	2	2	no	—
7	#13063323	—	2	2	no	—
8	C₄×Dic₈₆	C₂²	1	2	yes	—
9	#13063290	—	2	2	no	—
10	#13063258	—	2	2	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
12	#13063248	—	2	2	no	—
13	C₂×Q₁₆×C₄₃	—	2	2	no	—
14	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	—	2	1	no	—
18	C₂×Q₈×C₄₃	D₄	1	2	yes	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×Dic₈₆	D₄	1	2	yes	—
21	Q₁₆×C₄₃	—	4	4	no	—
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₄²×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₄₃	D₄	1	2	yes	—
27	Dic₄₃⋊C₄	—	2	4	no	—
28	Dic₄₃⋊C₄	—	2	2	no	—
29	C₄×Dic₄₃	—	2	2	no	—
30	C₄×Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	Q₈×C₄₃	—	4	2	no	—
33	Q₈×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₃	—	2	2	no	—
39	C₂×Dic₄₃	—	2	2	no	—
40	Dic₈₆	—	2	2	no	—
41	Dic₈₆	—	8	2	no	—
42	Dic₈₆	Q₁₆	1	4	yes	complemented
43	C₈×C₄₃	—	2	2	no	—
44	C₄₃⋊C₈	—	4	2	no	—
45	C₂²×C₄₃	#120	1	1	yes	characteristic
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	4	2	no	—
48	C₄×C₄₃	—	8	1	no	—
49	C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
50	C₄×C₄₃	#137	1	2	yes	—
51	Dic₄₃	—	2	4	no	—
52	Dic₄₃	—	4	2	no	—
53	#1633	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	#451	1	2	yes	—
55	C₂×C₄₃	#453	1	1	yes	characteristic
56	Q₈²	—	43	1	no	—
57	#494	D₄₃	1	1	yes	characteristic
58	#477	—	43	2	no	—
59	#333	—	43	1	no	—
60	Q₈⋊C₈	—	43	2	no	—
61	C₄₃	#1633	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	2	2	no	—
63	C₄⋊Q₈	—	86	2	no	—
64	C₄⋊Q₈	—	86	2	no	—
65	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
66	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
67	C₄×Q₈	—	43	2	no	—
68	C₄×Q₈	—	86	2	no	—
69	#107	—	86	2	no	—
70	C₄⋊C₈	—	43	2	no	—
71	#103	—	86	2	no	—
72	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	43	2	no	—
75	C₂×Q₈	—	86	2	no	—
76	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
77	Q₁₆	—	4	4	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	86	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	43	2	no	—
83	C₄⋊C₄	—	86	4	no	—
84	C₄⋊C₄	—	86	2	no	—
85	C₄²	—	86	2	no	—
86	C₄²	—	86	2	no	—
87	C₄²	C₂²×D₄₃	1	1	yes	characteristic
88	Q₈	—	4	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	—	43	4	no	—
91	Q₈	—	86	2	no	—
92	Q₈	—	344	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	86	2	no	—
96	C₂×C₄	—	86	2	no	—
97	C₂×C₄	D₄×D₄₃	1	2	yes	—
98	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	172	2	no	—
101	C₂²	#13063293	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	4	2	no	—
104	C₄	—	8	1	no	—
105	C₄	—	86	4	no	—
106	C₄	—	172	2	no	—
107	C₄	Q₁₆×D₄₃	1	2	yes	—
108	C₄	#13063357	1	2	yes	—
109	C₂	#14583053	1	2	yes	—
110	C₂	#14583066	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583629

C₂

yes

maximal, characteristic

#14583191

C₂

yes

maximal

#14582648

C₂

yes

maximal, characteristic

#14582631

C₂

yes

maximal

C₄₃×#494

C₂

yes

maximal, characteristic

#13063324

—

#13063323

—

C₄×Dic₈₆

C₂²

yes

—

#13063290

—

#13063258

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063248

—

C₂×Q₁₆×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

Q₁₆

yes

complemented

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

—

C₄×C₄₃

#137

yes

—

Dic₄₃

—

Dic₄₃

—

#1633

—

maximal, Sylow

C₂×C₄₃

#451

yes

—

C₂×C₄₃

#453

yes

characteristic

Q₈²

—

#494

D₄₃

yes

characteristic

#477

—

#333

—

Q₈⋊C₈

—

C₄₃

#1633

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₄₃

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

—

344

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₃

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

100

C₈

—

172

—

101

C₂²

#13063293

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

172

—

107

C₄

Q₁₆×D₄₃

yes

—

108

C₄

#13063357

yes

—

109

C₂

#14583053

yes

—

110

C₂

#14583066

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	#120
hypercenter	#494	D₄₃
hypocenter	C₄₃	#1633
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#13063293

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#494

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
42. Dic₈₆	Q₁₆	semidirect
61. C₄₃	#1633	semidirect

H ≅ G/N

type

42. Dic₈₆

Q₁₆

semidirect

61. C₄₃

#1633

semidirect

Subgroups — #19133733

Conjugacy classes of subgroups

Complements