Group #19136712 — subgroups

Subgroups — #19136712

Order 5504.

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

normal subgroups only

This group has 148 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	#14583315	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583166	C₂	1	2	yes	maximal, complemented
3	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582712	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063351	—	2	2	no	—
7	#13063331	C₂²	1	1	yes	characteristic
8	#13063265	C₂²	1	1	yes	characteristic
9	#13063264	—	2	1	no	—
10	C₁₆×D₄₃	—	2	1	no	—
11	#13063261	C₂²	1	2	yes	—
12	#13063242	—	2	2	no	—
13	C₂×D₈×C₄₃	C₂²	1	2	yes	—
14	D₁₆×C₄₃	—	2	1	no	—
15	D₁₆×C₄₃	—	2	1	no	—
16	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₃	—	2	2	no	—
18	#10621898	D₄	1	1	yes	characteristic
19	D₈×C₄₃	—	2	2	no	—
20	D₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	#10621883	—	4	2	no	—
23	#10621882	—	4	2	no	—
24	#10621877	—	2	2	no	—
25	#10621877	D₄	1	1	yes	characteristic
26	#10621872	—	2	1	no	—
27	C₈×D₄₃	—	2	1	no	—
28	C₁₆×C₄₃	D₄	1	1	yes	characteristic
29	C₁₆×C₄₃	D₄	1	1	yes	characteristic
30	C₄₃⋊C₁₆	—	2	1	no	—
31	C₂³×C₄₃	—	4	2	no	—
32	D₄×C₄₃	—	4	2	no	—
33	D₄×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²⋊D₄₃	—	2	1	no	—
36	D₁₇₂	D₈	1	1	yes	characteristic
37	C₄×D₄₃	—	2	1	no	—
38	Dic₈₆	D₈	1	1	yes	characteristic
39	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₈×C₄₃	#41	1	1	yes	characteristic
41	C₄₃⋊C₈	—	2	1	no	—
42	C₄₃⋊C₈	—	4	2	no	—
43	C₂²×C₄₃	—	8	2	no	—
44	C₂²×C₄₃	—	16	2	no	—
45	C₂²×C₄₃	#135	1	1	yes	characteristic
46	C₂×D₄₃	—	2	1	no	—
47	C₄×C₄₃	#121	1	1	yes	characteristic
48	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
49	Dic₄₃	—	2	1	no	—
50	#2221	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	—	16	2	no	—
53	C₂×C₄₃	#466	1	1	yes	characteristic
54	D₄₃	—	4	1	no	—
55	C₂×D₁₆	D₄₃	1	1	yes	characteristic, complemented
56	#504	—	43	1	no	—
57	#472	—	43	2	no	—
58	#368	—	43	1	no	—
59	#361	—	43	2	no	—
60	C₄₃	#2221	1	1	yes	characteristic, complemented, Sylow
61	AGL(1,ℤ/8)	—	86	2	no	—
62	C₂×D₈	C₂×D₄₃	1	2	yes	—
63	#131	—	43	1	no	—
64	D₁₆	—	2	1	no	—
65	D₁₆	—	2	1	no	—
66	M₃₂	—	43	1	no	—
67	M₃₂	—	86	1	no	—
68	C₂×C₁₆	—	86	1	no	—
69	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
70	#108	—	43	2	no	—
71	#100	—	86	2	no	—
72	#41	—	43	1	no	—
73	C₂×D₄	—	2	2	no	—
74	SD₁₆	—	172	2	no	—
75	D₈	—	2	2	no	—
76	D₈	—	2	2	no	—
77	D₈	—	172	2	no	—
78	M₁₆	—	43	1	no	—
79	M₁₆	—	86	1	no	—
80	M₁₆	—	86	2	no	—
81	C₂×C₈	—	86	1	no	—
82	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
83	C₁₆	—	86	1	no	—
84	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
85	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
86	C₂³	—	4	2	no	—
87	Q₈	—	43	1	no	—
88	D₄	—	4	2	no	—
89	D₄	—	4	2	no	—
90	D₄	—	43	1	no	—
91	D₄	—	86	1	no	—
92	C₂×C₄	—	86	1	no	—
93	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
94	C₈	—	86	1	no	—
95	C₈	—	172	2	no	—
96	C₈	#10621900	1	1	yes	characteristic
97	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
98	C₂²	—	8	2	no	—
99	C₂²	—	16	2	no	—
100	C₂²	—	86	1	no	—
101	C₂²	#13063344	1	1	yes	characteristic
102	C₄	—	86	1	no	—
103	C₄	#13063296	1	1	yes	characteristic
104	C₄	D₈×D₄₃	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	16	2	no	—
107	C₂	—	172	1	no	—
108	C₂	#14583132	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583315

C₂

yes

maximal, characteristic, complemented

#14583166

C₂

yes

maximal, complemented

#14582729

C₂

yes

maximal, characteristic, complemented

#14582712

C₂

yes

maximal, complemented

C₂×D₁₆×C₄₃

C₂

yes

maximal, characteristic, complemented

#13063351

—

#13063331

C₂²

yes

characteristic

#13063265

C₂²

yes

characteristic

#13063264

—

C₁₆×D₄₃

—

#13063261

C₂²

yes

—

#13063242

—

C₂×D₈×C₄₃

C₂²

yes

—

D₁₆×C₄₃

—

D₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

#10621898

D₄

yes

characteristic

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

D₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

D₄

yes

characteristic

C₁₆×C₄₃

D₄

yes

characteristic

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

D₈

yes

characteristic

C₄×D₄₃

—

Dic₈₆

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2221

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#466

yes

characteristic

D₄₃

—

C₂×D₁₆

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄₃

#2221

yes

characteristic, complemented, Sylow

AGL(1,ℤ/8)

—

C₂×D₈

C₂×D₄₃

yes

—

#131

—

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

C₂×D₄

—

SD₁₆

—

172

—

D₈

—

D₈

—

D₈

—

172

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₁₆

—

C₁₆

C₂²⋊D₄₃

yes

characteristic

C₁₆

C₂²⋊D₄₃

yes

characteristic

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₈

—

C₈

—

172

—

C₈

#10621900

yes

characteristic

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

#13063344

yes

characteristic

102

C₄

—

103

C₄

#13063296

yes

characteristic

104

C₄

D₈×D₄₃

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

172

—

108

C₂

#14583132

yes

characteristic

	subgroup	G/H
center	C₂	#14583132
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×D₁₆×C₄₃	C₂
socle	C₂×C₄₃	#466
hypercenter	C₂×D₁₆	D₄₃
hypocenter	C₄₃	#2221
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂

#14583132

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×D₁₆×C₄₃

C₂

socle

C₂×C₄₃

#466

hypercenter

C₂×D₁₆

D₄₃

hypocenter

C₄₃

#2221

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. #14583315	C₂	semidirect
2. #14583166	C₂	semidirect
3. #14582729	C₂	semidirect
4. #14582712	C₂	semidirect
5. C₂×D₁₆×C₄₃	C₂	semidirect
55. C₂×D₁₆	D₄₃	semidirect
60. C₄₃	#2221	semidirect

H ≅ G/N

type

1. #14583315

C₂

semidirect

2. #14583166

C₂

semidirect

3. #14582729

C₂

semidirect

4. #14582712

C₂

semidirect

5. C₂×D₁₆×C₄₃

C₂

semidirect

55. C₂×D₁₆

D₄₃

semidirect

60. C₄₃

#2221

semidirect

Subgroups — #19136712

Conjugacy classes of subgroups

Complements