Group #19132520 — subgroups

Subgroups — #19132520

Order 5504.

116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14582865	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621898	C₄	1	1	yes	characteristic
5	C₂×#10621877	C₄	1	1	yes	characteristic
6	C₂×C₄₃⋊C₁₆	—	2	1	no	—
7	(C₂×D₄₃)⋊C₈	—	2	1	no	—
8	(C₂×D₄₃)⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₃	—	2	1	no	—
13	#10621898	—	4	1	no	—
14	#10621898	—	4	1	no	—
15	C₂×D₁₇₂	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₃	—	2	1	no	—
17	C₂×Dic₈₆	C₈	1	1	yes	characteristic
18	C₂×C₈×C₄₃	—	4	1	no	—
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	#10621877	—	4	1	no	—
22	C₂×C₄₃⋊C₈	—	2	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₄₃⋊C₁₆	—	4	1	no	—
25	C₂³×C₄₃	M₁₆	1	1	yes	characteristic
26	C₂²×D₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	—	2	1	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
31	C₂²⋊D₄₃	—	4	2	no	—
32	C₂×Dic₄₃	—	2	1	no	—
33	D₁₇₂	—	4	1	no	—
34	C₄×D₄₃	—	4	1	no	—
35	C₄×D₄₃	—	4	1	no	—
36	Dic₈₆	—	4	1	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₈×C₄₃	—	2	1	no	—
39	C₄₃⋊C₈	—	4	1	no	—
40	C₂²×C₄₃	—	2	1	no	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₂×D₄₃	—	4	1	no	—
45	C₂×D₄₃	—	4	1	no	—
46	C₂×D₄₃	—	4	1	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	#99	1	1	yes	characteristic
49	C₄×C₄₃	#100	1	1	yes	characteristic
50	Dic₄₃	—	4	1	no	—
51	#1315	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	4	1	no	—
53	C₂×C₄₃	#323	1	1	yes	characteristic
54	C₂×C₄₃	#350	1	1	yes	characteristic
55	C₂×C₄₃	#350	1	1	yes	characteristic
56	D₄₃	—	8	1	no	—
57	#408	—	43	1	no	—
58	C₂²⋊C₁₆	—	43	1	no	—
59	C₂²⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
60	C₄₃	#1315	1	1	yes	characteristic, complemented, Sylow
61	C₂×#41	—	43	1	no	—
62	C₂×M₁₆	—	43	1	no	—
63	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
64	C₂×C₁₆	—	2	1	no	—
65	C₂×C₁₆	—	86	1	no	—
66	C₂²⋊C₈	—	86	1	no	—
67	C₂²⋊C₈	—	86	1	no	—
68	#41	—	172	1	no	—
69	#41	—	172	1	no	—
70	C₂×Q₈	—	43	1	no	—
71	C₂×D₄	—	43	1	no	—
72	C₂×D₄	—	86	1	no	—
73	C₂²×C₄	—	86	1	no	—
74	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
75	M₁₆	—	172	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	—	86	1	no	—
78	C₂×C₈	D₁₇₂	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
80	C₁₆	—	4	1	no	—
81	C₁₆	—	172	1	no	—
82	C₂³	—	86	1	no	—
83	C₂³	#10621872	1	1	yes	characteristic
84	Q₈	—	172	1	no	—
85	D₄	—	172	1	no	—
86	D₄	—	172	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	86	1	no	—
90	C₂×C₄	—	172	1	no	—
91	C₂×C₄	—	172	1	no	—
92	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
93	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	2	1	no	—
96	C₈	—	172	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	172	1	no	—
101	C₂²	—	172	1	no	—
102	C₂²	—	172	1	no	—
103	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	172	1	no	—
106	C₄	#13063239	1	1	yes	characteristic
107	C₄	#13063241	1	1	yes	characteristic
108	C₂	—	4	1	no	—
109	C₂	—	344	1	no	—
110	C₂	#14582622	1	1	yes	characteristic
111	C₂	#14582682	1	1	yes	characteristic
112	C₂	#14582684	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582865

C₂

yes

maximal, characteristic

C₂²⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₄₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₄

yes

characteristic

C₂×#10621877

C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

(C₂×D₄₃)⋊C₈

—

(C₂×D₄₃)⋊C₈

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

C₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

C₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

M₁₆

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1315

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#408

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₄₃

yes

characteristic, complemented

C₄₃

#1315

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#41

—

172

—

#41

—

172

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

172

—

C₂³

—

C₂³

#10621872

yes

characteristic

Q₈

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₈×D₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

172

—

101

C₂²

—

172

—

102

C₂²

—

172

—

103

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

104

C₄

—

105

C₄

—

172

—

106

C₄

#13063239

yes

characteristic

107

C₄

#13063241

yes

characteristic

108

C₂

—

109

C₂

—

344

—

110

C₂

#14582622

yes

characteristic

111

C₂

#14582682

yes

characteristic

112

C₂

#14582684

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₄₃×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₃	C₂²⋊C₈
hypercenter	C₂²⋊C₁₆	D₄₃
hypocenter	C₄₃	#1315
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₂×C₈

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₄₃×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₃

C₂²⋊C₈

hypercenter

C₂²⋊C₁₆

D₄₃

hypocenter

C₄₃

#1315

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. C₂²⋊(C₄₃⋊C₁₆)	C₂	semidirect
3. C₄₃×C₂²⋊C₁₆	C₂	semidirect
59. C₂²⋊C₁₆	D₄₃	semidirect
60. C₄₃	#1315	semidirect

H ≅ G/N

type

2. C₂²⋊(C₄₃⋊C₁₆)

C₂

semidirect

3. C₄₃×C₂²⋊C₁₆

C₂

semidirect

59. C₂²⋊C₁₆

D₄₃

semidirect

60. C₄₃

#1315

semidirect

Subgroups — #19132520

Conjugacy classes of subgroups

Complements