Group #19132638 — subgroups

Subgroups — #19132638

Order 5504.

102 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 41 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	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582650	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#495	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₂×Q₁₆×C₄₃	C₄	1	1	yes	characteristic
7	C₂×SD₁₆×C₄₃	—	2	1	no	—
8	C₂×D₈×C₄₃	C₄	1	1	yes	characteristic
9	#124×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₄₃	—	2	1	no	—
12	C₂×D₄×C₄₃	—	2	1	no	—
13	Q₁₆×C₄₃	—	4	1	no	—
14	SD₁₆×C₄₃	—	4	1	no	—
15	SD₁₆×C₄₃	—	4	1	no	—
16	D₈×C₄₃	—	4	1	no	—
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×C₄₃	—	4	1	no	—
20	C₂²⋊C₄×C₄₃	—	4	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	—	4	1	no	—
23	C₄₃⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₃	—	4	1	no	—
25	Q₈×C₄₃	—	4	1	no	—
26	Q₈×C₄₃	—	4	1	no	—
27	D₄×C₄₃	—	4	1	no	—
28	D₄×C₄₃	—	4	1	no	—
29	C₂×C₄×C₄₃	—	4	1	no	—
30	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
33	C₈×C₄₃	—	2	1	no	—
34	C₈×C₄₃	D₈	1	1	yes	characteristic
35	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
36	C₄₃⋊C₈	—	8	1	no	—
37	C₂²×C₄₃	—	8	1	no	—
38	C₂²×C₄₃	—	8	1	no	—
39	C₂²×C₄₃	—	8	1	no	—
40	C₂²×C₄₃	#102	1	1	yes	characteristic
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	8	1	no	—
44	C₄×C₄₃	#100	1	1	yes	characteristic
45	C₄×C₄₃	#102	1	1	yes	characteristic
46	#1360	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	16	1	no	—
48	C₂×C₄₃	#331	1	1	yes	characteristic
49	C₂×C₄₃	#359	1	1	yes	characteristic
50	C₂×C₄₃	#360	1	1	yes	characteristic
51	#495	D₄₃	1	1	yes	characteristic
52	C₄⋊C₁₆	—	43	1	no	—
53	#334	—	43	1	no	—
54	C₄₃	#1360	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	Dic₄₃	1	1	yes	characteristic
56	C₂×SD₁₆	—	2	1	no	—
57	C₂×D₈	Dic₄₃	1	1	yes	characteristic
58	#124	—	2	1	no	—
59	C₂×C₁₆	—	86	1	no	—
60	C₄⋊C₈	—	86	1	no	—
61	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	2	1	no	—
63	C₂×D₄	—	2	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	4	1	no	—
66	SD₁₆	—	4	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	—	172	1	no	—
69	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
71	C₂²⋊C₄	—	4	1	no	—
72	C₂²⋊C₄	—	4	1	no	—
73	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
74	C₁₆	—	172	1	no	—
75	C₂³	—	4	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	D₄	—	4	1	no	—
79	D₄	—	4	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	#10621882	1	1	yes	characteristic
82	C₂×C₄	#10621883	1	1	yes	characteristic
83	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	344	1	no	—
86	C₈	#10621882	1	1	yes	characteristic
87	C₈	#10621883	1	1	yes	characteristic
88	C₂²	—	8	1	no	—
89	C₂²	—	8	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	#13063246	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	8	1	no	—
95	C₄	#13063242	1	1	yes	characteristic
96	C₄	#13063246	1	1	yes	characteristic
97	C₂	—	16	1	no	—
98	C₂	#14582643	1	1	yes	characteristic
99	C₂	#14582706	1	1	yes	characteristic
100	C₂	#14582709	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

#14582650

C₂

yes

maximal, characteristic, complemented

C₄₃×#495

C₂

yes

maximal, characteristic

C₂×C₄₃⋊C₁₆

—

C₄⋊(C₄₃⋊C₈)

—

C₂×Q₁₆×C₄₃

C₄

yes

characteristic

C₂×SD₁₆×C₄₃

—

C₂×D₈×C₄₃

C₄

yes

characteristic

#124×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

Q₁₆×C₄₃

—

SD₁₆×C₄₃

—

SD₁₆×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

SD₁₆

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

C₄⋊C₁₆

—

#334

—

C₄₃

#1360

yes

characteristic, complemented, Sylow

C₂×Q₁₆

Dic₄₃

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

Dic₄₃

yes

characteristic

#124

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

172

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₈

—

C₈

—

344

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

—

C₂²

#13063246

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

100

C₂

#14582709

yes

characteristic

	subgroup	G/H
center	C₂²	#13063246
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#495	C₂
socle	C₂²×C₄₃	#102
hypercenter	#495	D₄₃
hypocenter	C₄₃	#1360
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

#13063246

commutator

C₂×C₈×C₄₃

C₂×C₄

Frattini

C₄×C₈

C₂×D₄₃

Fitting

C₄₃×#495

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₄⋊(C₄₃⋊C₁₆)	C₂	semidirect
2. #14582650	C₂	semidirect
54. C₄₃	#1360	semidirect

H ≅ G/N

type

1. C₄⋊(C₄₃⋊C₁₆)

C₂

semidirect

2. #14582650

C₂

semidirect

54. C₄₃

#1360

semidirect

Subgroups — #19132638

Conjugacy classes of subgroups

Complements