Group #19132639 — subgroups

Subgroups — #19132639

Order 5504.

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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	#14583283	C₂	1	1	yes	maximal, characteristic
2	#14582650	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic
5	C₂×#10621873	—	2	1	no	—
6	C₂×D₃₄₄	C₄	1	1	yes	characteristic
7	#13063313	—	2	1	no	—
8	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
9	C₂×C₁₆×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×D₁₇₂	—	2	1	no	—
12	C₂×Dic₈₆	—	2	1	no	—
13	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
15	C₄²×C₄₃	D₄	1	1	yes	characteristic
16	(C₂×D₄₃)⋊C₄	—	4	1	no	—
17	(C₂×D₄₃)⋊C₄	—	4	1	no	—
18	C₂×C₄₃⋊C₈	—	4	1	no	—
19	Dic₁₇₂	—	4	1	no	—
20	D₃₄₄	—	4	1	no	—
21	#10621873	—	4	1	no	—
22	#10621873	—	4	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₂²×D₄₃	—	4	1	no	—
25	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
28	C₂×Dic₄₃	—	4	1	no	—
29	D₁₇₂	—	4	1	no	—
30	D₁₇₂	—	4	1	no	—
31	Dic₈₆	—	4	1	no	—
32	Dic₈₆	—	4	1	no	—
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	#102	1	1	yes	characteristic
38	C₂×D₄₃	—	8	1	no	—
39	C₂×D₄₃	—	8	1	no	—
40	C₂×D₄₃	—	8	1	no	—
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	#100	1	1	yes	characteristic
44	C₄×C₄₃	#102	1	1	yes	characteristic
45	Dic₄₃	—	8	1	no	—
46	#1360	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	#331	1	1	yes	characteristic
48	C₂×C₄₃	#359	1	1	yes	characteristic
49	C₂×C₄₃	#360	1	1	yes	characteristic
50	D₄₃	—	16	1	no	—
51	#495	—	43	1	no	—
52	C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
53	#334	—	43	1	no	—
54	C₄₃	#1360	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	43	1	no	—
56	C₂×SD₁₆	—	86	1	no	—
57	C₂×D₈	—	43	1	no	—
58	#124	—	86	1	no	—
59	C₂×C₁₆	—	2	1	no	—
60	C₄⋊C₈	—	86	1	no	—
61	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	86	1	no	—
63	C₂×D₄	—	86	1	no	—
64	Q₁₆	—	172	1	no	—
65	SD₁₆	—	172	1	no	—
66	SD₁₆	—	172	1	no	—
67	D₈	—	172	1	no	—
68	C₂×C₈	—	172	1	no	—
69	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
71	C₂²⋊C₄	—	172	1	no	—
72	C₂²⋊C₄	—	172	1	no	—
73	C₄²	D₁₇₂	1	1	yes	characteristic
74	C₁₆	—	4	1	no	—
75	C₂³	—	172	1	no	—
76	Q₈	—	172	1	no	—
77	Q₈	—	172	1	no	—
78	D₄	—	172	1	no	—
79	D₄	—	172	1	no	—
80	C₂×C₄	—	172	1	no	—
81	C₂×C₄	#10621873	1	1	yes	characteristic
82	C₂×C₄	D₃₄₄	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	344	1	no	—
86	C₈	#10621882	1	1	yes	characteristic
87	C₈	#10621884	1	1	yes	characteristic
88	C₂²	—	344	1	no	—
89	C₂²	—	344	1	no	—
90	C₂²	—	344	1	no	—
91	C₂²	#13063247	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	344	1	no	—
95	C₄	#13063241	1	1	yes	characteristic
96	C₄	#13063245	1	1	yes	characteristic
97	C₂	—	688	1	no	—
98	C₂	#14582642	1	1	yes	characteristic
99	C₂	#14582707	1	1	yes	characteristic
100	C₂	#14582710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583283

C₂

yes

maximal, characteristic

#14582650

C₂

yes

maximal, characteristic, complemented

C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₄

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₄

yes

characteristic

#13063313

—

C₄⋊(C₄₃⋊C₈)

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

D₃₄₄

—

#10621873

—

#10621873

—

C₁₆×C₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

SD₁₆

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

#102

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#495

—

C₄⋊C₁₆

D₄₃

yes

characteristic, complemented

#334

—

C₄₃

#1360

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

172

—

SD₁₆

—

172

—

SD₁₆

—

172

—

D₈

—

172

—

C₂×C₈

—

172

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂²⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

—

C₂³

—

172

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

characteristic

C₂×C₄

D₃₄₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

344

—

C₈

yes

C₈

yes

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

#13063247

yes

characteristic

C₄

—

C₄

—

C₄

—

344

—

C₄

yes

C₄

yes

C₂

—

688

—

C₂

yes

C₂

yes

100

C₂

#14582710

yes

characteristic

	subgroup	G/H
center	C₂²	#13063247
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×C₄⋊C₁₆	C₂
socle	C₂²×C₄₃	#102
hypercenter	C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#1360
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

#13063247

commutator

C₂×C₈×C₄₃

C₂×C₄

Frattini

C₄×C₈

C₂×D₄₃

Fitting

C₄₃×C₄⋊C₁₆

C₂

socle

C₂²×C₄₃

#102

hypercenter

C₄⋊C₁₆

D₄₃

hypocenter

C₄₃

#1360

LCS

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. #14582650	C₂	semidirect
3. C₄₃×C₄⋊C₁₆	C₂	semidirect
52. C₄⋊C₁₆	D₄₃	semidirect
54. C₄₃	#1360	semidirect

H ≅ G/N

type

2. #14582650

C₂

semidirect

3. C₄₃×C₄⋊C₁₆

C₂

semidirect

52. C₄⋊C₁₆

D₄₃

semidirect

54. C₄₃

#1360

semidirect

Subgroups — #19132639

Conjugacy classes of subgroups

Complements