Group #19136687 — subgroups

Subgroups — #19136687

Order 5504.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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	C₂×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14583141	C₂	1	2	yes	maximal
4	#14582702	C₂	1	2	yes	maximal, complemented
5	C₄₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	#13063305	—	2	2	no	—
9	Dic₃₄₄	—	2	2	no	—
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₁₆×D₄₃	—	2	2	no	—
12	#13063248	—	2	2	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	#107×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
16	C₂×Dic₈₆	—	2	2	no	—
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₄₃	—	2	2	no	—
19	(C₂×D₄₃)⋊C₄	—	4	2	no	—
20	C₄⋊Dic₄₃	—	4	2	no	—
21	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
22	Dic₁₇₂	—	2	2	no	—
23	Dic₁₇₂	—	2	2	no	—
24	C₈×D₄₃	—	2	1	no	—
25	C₈×D₄₃	—	2	1	no	—
26	C₁₆×C₄₃	D₄	1	2	yes	—
27	C₄₃⋊C₁₆	—	2	1	no	—
28	C₂²×D₄₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	4	2	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₄₃	—	4	2	no	—
32	C₂×Dic₄₃	D₈	1	1	yes	characteristic
33	C₄×D₄₃	—	2	1	no	—
34	C₄×D₄₃	—	2	1	no	—
35	Dic₈₆	—	4	2	no	—
36	Dic₈₆	—	4	2	no	—
37	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₄₃	#41	1	1	yes	characteristic
39	C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₃	—	2	1	no	—
42	C₂×D₄₃	—	2	1	no	—
43	C₂×D₄₃	Q₃₂	1	2	yes	complemented
44	C₄×C₄₃	—	8	2	no	—
45	C₄×C₄₃	#121	1	1	yes	characteristic
46	C₄×C₄₃	#135	1	1	yes	characteristic
47	Dic₄₃	—	2	1	no	—
48	Dic₄₃	—	8	2	no	—
49	#2216	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	#466	1	1	yes	characteristic
51	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
52	C₂×C₄₃	#508	1	1	yes	characteristic
53	D₄₃	—	2	2	no	—
54	C₂×Q₃₂	—	43	1	no	—
55	C₂²×C₁₆	—	43	1	no	—
56	#467	—	43	2	no	—
57	#366	D₄₃	1	1	yes	characteristic, complemented
58	#358	—	43	2	no	—
59	C₄₃	#2216	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₁₆	—	43	2	no	—
61	C₂²×C₈	—	43	1	no	—
62	C₂²⋊Q₈	—	86	2	no	—
63	Q₃₂	—	86	2	no	—
64	C₂×C₁₆	—	43	1	no	—
65	C₂×C₁₆	—	86	2	no	—
66	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
67	#107	C₂×D₄₃	1	2	yes	—
68	#103	—	86	2	no	—
69	C₂×Q₈	—	86	2	no	—
70	C₂²×C₄	—	43	1	no	—
71	Q₁₆	—	86	2	no	—
72	Q₁₆	—	86	2	no	—
73	C₂×C₈	—	43	1	no	—
74	C₂×C₈	—	86	1	no	—
75	C₂×C₈	—	86	1	no	—
76	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	172	2	no	—
79	C₂²⋊C₄	—	172	2	no	—
80	C₁₆	—	86	1	no	—
81	C₁₆	D₁₇₂	1	2	yes	—
82	C₂³	—	43	1	no	—
83	Q₈	—	172	2	no	—
84	Q₈	—	172	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	43	1	no	—
87	C₂×C₄	—	86	1	no	—
88	C₂×C₄	—	86	1	no	—
89	C₂×C₄	—	172	2	no	—
90	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
91	C₈	—	86	1	no	—
92	C₈	C₂×D₁₇₂	1	1	yes	characteristic
93	C₈	#10621902	1	1	yes	characteristic
94	C₂²	—	43	2	no	—
95	C₂²	—	86	1	no	—
96	C₂²	—	86	1	no	—
97	C₂²	D₈×D₄₃	1	1	yes	characteristic
98	C₄	—	8	2	no	—
99	C₄	—	86	1	no	—
100	C₄	—	344	2	no	—
101	C₄	#13063300	1	1	yes	characteristic
102	C₄	#13063348	1	1	yes	characteristic
103	C₂	—	86	2	no	—
104	C₂	#14583136	1	1	yes	characteristic
105	C₂	Q₃₂×D₄₃	1	1	yes	characteristic
106	C₂	#14583328	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₄₄

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₄₃

C₂

yes

maximal, characteristic

#14583141

C₂

yes

maximal

#14582702

C₂

yes

maximal, complemented

C₄₃×#366

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

—

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063305

—

Dic₃₄₄

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₃

—

#13063248

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

Q₃₂

yes

complemented

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×Q₃₂

yes

characteristic

C₂×C₄₃

#508

yes

characteristic

D₄₃

—

C₂×Q₃₂

—

C₂²×C₁₆

—

#467

—

#366

D₄₃

yes

characteristic, complemented

#358

—

C₄₃

#2216

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂²×C₈

—

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

C₂×D₄₃

yes

—

#103

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₁₆

D₁₇₂

yes

—

C₂³

—

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₈

—

C₈

C₂×D₁₇₂

yes

characteristic

C₈

#10621902

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₄₃

yes

characteristic

C₄

—

C₄

—

100

C₄

—

344

—

101

C₄

#13063300

yes

characteristic

102

C₄

#13063348

yes

characteristic

103

C₂

—

104

C₂

#14583136

yes

characteristic

105

C₂

Q₃₂×D₄₃

yes

characteristic

106

C₂

#14583328

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#366	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#366	D₄₃
hypocenter	C₄₃	#2216
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#366

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
1. C₂×Dic₃₄₄	C₂	semidirect
4. #14582702	C₂	semidirect
5. C₄₃×#366	C₂	semidirect
43. C₂×D₄₃	Q₃₂	semidirect
57. #366	D₄₃	semidirect
59. C₄₃	#2216	semidirect

H ≅ G/N

type

1. C₂×Dic₃₄₄

C₂

semidirect

4. #14582702

C₂

semidirect

5. C₄₃×#366

C₂

semidirect

43. C₂×D₄₃

Q₃₂

semidirect

57. #366

D₄₃

semidirect

59. C₄₃

#2216

semidirect

Subgroups — #19136687

Conjugacy classes of subgroups

Complements