Group #19136827 — subgroups

Subgroups — #19136827

Order 5504.

138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583301	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583283	C₂	1	1	yes	maximal, characteristic
3	#14582704	C₂	1	2	yes	maximal, complemented
4	#14582701	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×#10621873	—	2	1	no	—
8	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
9	#13063317	—	2	1	no	—
10	#13063313	—	2	1	no	—
11	#13063259	C₂²	1	2	yes	—
12	#13063257	—	2	1	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×D₁₇₂	—	2	1	no	—
16	C₂×Dic₈₆	—	2	1	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	(C₂×D₄₃)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₄₃	—	2	2	no	—
22	Dic₄₃⋊C₄	—	4	2	no	—
23	Dic₁₇₂	—	2	2	no	—
24	D₃₄₄	—	2	2	no	—
25	#10621873	—	4	2	no	—
26	C₁₆×C₄₃	—	2	2	no	—
27	C₂²×D₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	D₈	1	2	yes	—
29	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₄₃	—	4	2	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	D₁₇₂	—	4	1	no	—
33	D₁₇₂	—	4	1	no	—
34	Dic₈₆	—	4	1	no	—
35	Dic₈₆	—	4	1	no	—
36	C₈×C₄₃	SD₁₆	1	2	yes	—
37	C₈×C₄₃	#41	1	2	yes	—
38	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
39	C₂×D₄₃	—	8	1	no	—
40	C₂×D₄₃	—	8	2	no	—
41	C₄×C₄₃	—	2	2	no	—
42	C₄×C₄₃	#124	1	1	yes	characteristic
43	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
44	Dic₄₃	—	8	1	no	—
45	Dic₄₃	—	8	2	no	—
46	#2242	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	#486	1	1	yes	characteristic
48	C₂×C₄₃	#508	1	2	yes	—
49	D₄₃	—	16	1	no	—
50	#499	—	43	1	no	—
51	#495	—	43	1	no	—
52	#358	—	43	2	no	—
53	#357	—	43	2	no	—
54	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
55	C₄₃	#2242	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	—	43	1	no	—
57	C₂×SD₁₆	—	86	1	no	—
58	C₂×D₈	—	43	1	no	—
59	#125	—	86	1	no	—
60	#124	—	86	1	no	—
61	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
62	#107	—	43	2	no	—
63	#106	—	86	1	no	—
64	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	C₂×Q₈	—	86	1	no	—
66	C₂×D₄	—	86	1	no	—
67	Q₁₆	—	86	2	no	—
68	SD₁₆	—	172	2	no	—
69	D₈	—	86	2	no	—
70	C₂×C₈	D₁₇₂	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
72	C₄⋊C₄	—	86	2	no	—
73	C₄⋊C₄	—	172	2	no	—
74	C₂²⋊C₄	—	172	2	no	—
75	C₄²	D₁₇₂	1	1	yes	characteristic
76	C₁₆	—	2	2	no	—
77	C₂³	—	172	1	no	—
78	Q₈	—	172	1	no	—
79	Q₈	—	172	1	no	—
80	D₄	—	172	1	no	—
81	D₄	—	172	1	no	—
82	C₂×C₄	—	172	1	no	—
83	C₂×C₄	—	172	2	no	—
84	C₂×C₄	D₃₄₄	1	2	yes	—
85	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
86	C₈	#10621873	1	2	yes	—
87	C₈	#10621898	1	2	yes	—
88	C₂²	—	344	2	no	—
89	C₂²	—	344	1	no	—
90	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	344	2	no	—
93	C₄	—	344	1	no	—
94	C₄	#13063313	1	1	yes	characteristic
95	C₄	C₂×#10621873	1	1	yes	characteristic
96	C₂	—	688	1	no	—
97	C₂	#14583246	1	1	yes	characteristic
98	C₂	#14583331	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583301

C₂

yes

maximal, characteristic, complemented

#14583283

C₂

yes

maximal, characteristic

#14582704

C₂

yes

maximal, complemented

#14582701

C₂

yes

maximal

C₄×C₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₂²

yes

—

—

C₂²

yes

—

#13063257

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

D₃₄₄

—

#10621873

—

C₁₆×C₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

SD₁₆

yes

—

C₈×C₄₃

#41

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

—

—

—

—

C₄×C₁₆

D₄₃

yes

characteristic, complemented

C₄₃

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#125

—

#124

—

C₂×C₁₆

C₂×D₄₃

yes

—

#107

—

#106

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

172

—

D₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊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

—

172

—

C₂×C₄

D₃₄₄

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

#10621873

yes

—

C₈

#10621898

yes

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

C₂×D₃₄₄

yes

characteristic

C₄

—

C₄

—

344

—

C₄

—

344

—

C₄

yes

C₄

yes

C₂

—

688

—

C₂

#14583246

yes

characteristic

C₂

#14583331

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#2242
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×C₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₄×C₁₆

D₄₃

hypocenter

C₄₃

#2242

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. #14583301	C₂	semidirect
3. #14582704	C₂	semidirect
5. C₄×C₁₆×C₄₃	C₂	semidirect
54. C₄×C₁₆	D₄₃	semidirect
55. C₄₃	#2242	semidirect

H ≅ G/N

type

1. #14583301

C₂

semidirect

3. #14582704

C₂

semidirect

5. C₄×C₁₆×C₄₃

C₂

semidirect

54. C₄×C₁₆

D₄₃

semidirect

55. C₄₃

#2242

semidirect

Subgroups — #19136827

Conjugacy classes of subgroups

Complements