Group #19132557 — subgroups

Subgroups — #19132557

Order 5504.

110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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×D₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#14582652	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₄₄	C₄	1	1	yes	characteristic
5	C₄×D₁₇₂	—	2	1	no	—
6	#13063259	C₄	1	1	yes	characteristic
7	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	#13063247	—	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×C₄×D₄₃	—	4	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	C₄⋊Dic₄₃	—	2	1	no	—
18	C₂×C₄₃⋊C₈	—	4	1	no	—
19	D₃₄₄	—	2	1	no	—
20	D₃₄₄	C₈	1	2	yes	complemented
21	C₁₆×C₄₃	—	2	2	no	—
22	C₂²×D₄₃	—	4	1	no	—
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
26	C₂×Dic₄₃	—	4	1	no	—
27	D₁₇₂	—	2	2	no	—
28	D₁₇₂	—	4	1	no	—
29	C₄×D₄₃	—	8	1	no	—
30	C₄×D₄₃	—	8	1	no	—
31	C₈×C₄₃	—	2	1	no	—
32	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₄₃	M₁₆	1	1	yes	characteristic
34	C₄₃⋊C₈	—	8	1	no	—
35	C₂²×C₄₃	#102	1	1	yes	characteristic
36	C₂×D₄₃	—	4	2	no	—
37	C₂×D₄₃	—	8	1	no	—
38	C₂×D₄₃	—	8	1	no	—
39	C₄×C₄₃	—	2	1	no	—
40	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₄₃	#104	1	1	yes	characteristic
42	C₄×C₄₃	D₁₆	1	1	yes	characteristic
43	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
44	Dic₄₃	—	8	1	no	—
45	#1331	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₄₃	#357	1	1	yes	characteristic
48	C₂×C₄₃	#359	1	1	yes	characteristic
49	D₄₃	—	8	2	no	—
50	C₄×D₈	—	43	1	no	—
51	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
52	#335	—	43	1	no	—
53	C₄₃	#1331	1	1	yes	characteristic, complemented, Sylow
54	C₂×D₈	—	43	1	no	—
55	C₄×D₄	—	86	1	no	—
56	C₂×C₁₆	—	2	1	no	—
57	#107	—	43	1	no	—
58	C₄⋊C₈	—	86	1	no	—
59	#102	—	86	1	no	—
60	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
61	C₂×D₄	—	86	1	no	—
62	C₂²×C₄	—	172	1	no	—
63	D₈	—	43	2	no	—
64	D₈	—	86	1	no	—
65	C₂×C₈	—	172	1	no	—
66	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
68	C₄⋊C₄	—	86	1	no	—
69	C₂²⋊C₄	—	172	1	no	—
70	C₄²	D₁₇₂	1	1	yes	characteristic
71	C₁₆	—	2	2	no	—
72	C₂³	—	172	1	no	—
73	D₄	—	86	2	no	—
74	D₄	—	172	1	no	—
75	C₂×C₄	—	344	1	no	—
76	C₂×C₄	—	344	1	no	—
77	C₂×C₄	—	172	1	no	—
78	C₂×C₄	#10621873	1	1	yes	characteristic
79	C₂×C₄	D₃₄₄	1	1	yes	characteristic
80	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	344	1	no	—
83	C₈	C₈×D₄₃	1	1	yes	characteristic
84	C₈	#10621872	1	1	yes	characteristic
85	C₂²	—	344	1	no	—
86	C₂²	—	344	1	no	—
87	C₂²	—	172	2	no	—
88	C₂²	#13063247	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	344	1	no	—
91	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
92	C₄	#13063253	1	1	yes	characteristic
93	C₄	D₆₈₈	1	1	yes	characteristic
94	C₄	#13063270	1	1	yes	characteristic
95	C₂	—	344	2	no	—
96	C₂	#14582628	1	1	yes	characteristic
97	C₂	#14582701	1	1	yes	characteristic
98	C₂	#14582707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₃₄₄

C₂

yes

maximal, characteristic

#14582652

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₄

yes

characteristic

C₄×D₁₇₂

—

#13063259

C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

—

#13063247

—

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

D₃₄₄

C₈

yes

complemented

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

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₈

yes

characteristic

C₈×C₄₃

M₁₆

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

#102

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₄×C₄₃

#104

yes

characteristic

C₄×C₄₃

D₁₆

yes

characteristic

C₄×C₄₃

SD₃₂

yes

characteristic

Dic₄₃

—

#1331

—

maximal, Sylow

C₂×C₄₃

D₄⋊C₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

C₄×D₈

—

C₄×C₁₆

D₄₃

yes

characteristic, complemented

#335

—

C₄₃

#1331

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₄×D₄

—

C₂×C₁₆

—

#107

—

C₄⋊C₈

—

#102

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

172

—

D₈

—

D₈

—

C₂×C₈

—

172

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

—

C₂³

—

172

—

D₄

—

D₄

—

172

—

C₂×C₄

—

344

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

characteristic

C₂×C₄

D₃₄₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

344

—

C₈

C₈×D₄₃

yes

characteristic

C₈

#10621872

yes

characteristic

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

172

—

C₂²

#13063247

yes

characteristic

C₄

—

C₄

—

344

—

C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

C₄

#13063253

yes

characteristic

C₄

D₆₈₈

yes

characteristic

C₄

#13063270

yes

characteristic

C₂

—

344

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₃₄₄
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	#102
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#1331
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₄

D₃₄₄

commutator

C₈×C₄₃

C₂×C₈

Frattini

C₄×C₈

C₂×D₄₃

Fitting

C₄×C₁₆×C₄₃

C₂

socle

C₂²×C₄₃

#102

hypercenter

C₄×C₁₆

D₄₃

hypocenter

C₄₃

#1331

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #14582652	C₂	semidirect
3. C₄×C₁₆×C₄₃	C₂	semidirect
20. D₃₄₄	C₈	semidirect
51. C₄×C₁₆	D₄₃	semidirect
53. C₄₃	#1331	semidirect

H ≅ G/N

type

2. #14582652

C₂

semidirect

3. C₄×C₁₆×C₄₃

C₂

semidirect

20. D₃₄₄

C₈

semidirect

51. C₄×C₁₆

D₄₃

semidirect

53. C₄₃

#1331

semidirect

Subgroups — #19132557

Conjugacy classes of subgroups

Complements