Group #19136745 — subgroups

Subgroups — #19136745

Order 5504.

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

normal subgroups only

This group has 130 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	#14583303	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582725	C₂	1	1	yes	maximal, characteristic
4	#14582724	C₂	1	1	yes	maximal, characteristic
5	Dic₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	#14582703	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#358	C₂	1	1	yes	maximal, characteristic
8	#13063324	—	2	1	no	—
9	Q₈×Dic₄₃	—	2	1	no	—
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13063259	C₂²	1	1	yes	characteristic
12	#13063259	C₂²	1	1	yes	characteristic
13	#13063258	—	2	1	no	—
14	#13063249	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	—	2	1	no	—
20	C₂×Dic₈₆	—	4	1	no	—
21	Q₁₆×C₄₃	—	2	1	no	—
22	Q₁₆×C₄₃	Q₈	1	2	yes	complemented
23	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₃	—	2	1	no	—
25	C₄⋊Dic₄₃	—	2	1	no	—
26	C₄⋊Dic₄₃	—	2	1	no	—
27	C₄⋊Dic₄₃	—	4	1	no	—
28	Dic₄₃⋊C₄	—	4	1	no	—
29	C₄×Dic₄₃	—	4	1	no	—
30	C₄×Dic₄₃	D₄	1	1	yes	characteristic
31	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
32	C₁₆×C₄₃	—	2	1	no	—
33	C₄₃⋊C₁₆	—	2	1	no	—
34	Q₈×C₄₃	—	2	2	no	—
35	Q₈×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₃	—	4	1	no	—
40	C₂×Dic₄₃	—	4	1	no	—
41	C₂×Dic₄₃	D₈	1	1	yes	characteristic
42	C₂×Dic₄₃	D₈	1	1	yes	characteristic
43	Dic₈₆	—	8	2	no	—
44	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₃	#41	1	1	yes	characteristic
46	C₄₃⋊C₈	—	2	1	no	—
47	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
48	C₄×C₄₃	—	4	2	no	—
49	C₄×C₄₃	—	8	1	no	—
50	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
51	C₄×C₄₃	#137	1	1	yes	characteristic
52	Dic₄₃	—	2	1	no	—
53	Dic₄₃	—	8	1	no	—
54	Dic₄₃	—	8	1	no	—
55	Dic₄₃	Q₃₂	1	2	yes	—
56	#2227	—	43	1	no	maximal, Sylow
57	C₂×C₄₃	#474	1	1	yes	characteristic
58	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
59	C₂×C₄₃	#509	1	1	yes	characteristic
60	#500	—	43	1	no	—
61	C₄×Q₁₆	—	43	1	no	—
62	#366	—	43	1	no	—
63	#366	—	43	1	no	—
64	C₄⋊C₁₆	—	43	1	no	—
65	#358	—	43	1	no	—
66	#358	D₄₃	1	1	yes	characteristic
67	C₄₃	#2227	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
69	C₄⋊Q₈	—	86	1	no	—
70	C₄×Q₈	—	86	1	no	—
71	C₂×C₁₆	—	43	1	no	—
72	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
73	#107	—	43	1	no	—
74	#107	—	43	1	no	—
75	#107	—	86	1	no	—
76	#107	C₂×D₄₃	1	1	yes	characteristic
77	#103	—	86	1	no	—
78	C₄×C₈	—	43	1	no	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	172	1	no	—
81	Q₁₆	—	2	1	no	—
82	Q₁₆	Dic₈₆	1	2	yes	complemented
83	C₂×C₈	—	43	1	no	—
84	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
85	C₄⋊C₄	—	2	1	no	—
86	C₄⋊C₄	—	86	1	no	—
87	C₄⋊C₄	—	86	1	no	—
88	C₄⋊C₄	—	172	1	no	—
89	C₄⋊C₄	—	172	1	no	—
90	C₄²	—	43	1	no	—
91	C₄²	—	172	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	86	1	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	4	1	no	—
96	Q₈	—	344	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	43	1	no	—
100	C₂×C₄	—	43	1	no	—
101	C₂×C₄	—	172	1	no	—
102	C₂×C₄	—	172	1	no	—
103	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
104	C₈	—	86	1	no	—
105	C₈	C₂×Dic₈₆	1	1	yes	characteristic
106	C₈	#10621900	1	1	yes	characteristic
107	C₂²	D₈×D₄₃	1	1	yes	characteristic
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	43	2	no	—
111	C₄	—	86	1	no	—
112	C₄	—	344	1	no	—
113	C₄	—	344	1	no	—
114	C₄	#13063302	1	1	yes	characteristic
115	C₄	#13063354	1	1	yes	characteristic
116	C₂	#14583177	1	1	yes	characteristic
117	C₂	Q₃₂×D₄₃	1	1	yes	characteristic
118	C₂	#14583336	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583303

C₂

yes

maximal, characteristic

Q₁₆×Dic₄₃

C₂

yes

maximal, characteristic

#14582725

C₂

yes

maximal, characteristic

#14582724

C₂

yes

maximal, characteristic

Dic₄₃⋊C₁₆

C₂

yes

maximal, characteristic

#14582703

C₂

yes

maximal, characteristic

C₄₃×#358

C₂

yes

maximal, characteristic

#13063324

—

Q₈×Dic₄₃

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063258

—

#13063249

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

Q₃₂

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×Q₃₂

yes

C₂×C₄₃

yes

—

C₄×Q₁₆

—

#366

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

D₄₃

yes

characteristic

C₄₃

#2227

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

C₂×D₄₃

yes

characteristic

#103

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

Q₁₆

—

Q₁₆

Dic₈₆

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

—

172

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

344

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

172

—

102

C₂×C₄

—

172

—

103

C₂×C₄

D₄×D₄₃

yes

characteristic

104

C₈

—

105

C₈

C₂×Dic₈₆

yes

characteristic

106

C₈

#10621900

yes

characteristic

107

C₂²

D₈×D₄₃

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

344

—

113

C₄

—

344

—

114

C₄

#13063302

yes

characteristic

115

C₄

#13063354

yes

characteristic

116

C₂

#14583177

yes

characteristic

117

C₂

Q₃₂×D₄₃

yes

characteristic

118

C₂

#14583336

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#358	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#358	D₄₃
hypocenter	C₄₃	#2227
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#358

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
22. Q₁₆×C₄₃	Q₈	semidirect
67. C₄₃	#2227	semidirect
82. Q₁₆	Dic₈₆	semidirect

H ≅ G/N

type

22. Q₁₆×C₄₃

Q₈

semidirect

67. C₄₃

#2227

semidirect

82. Q₁₆

Dic₈₆

semidirect

Subgroups — #19136745

Conjugacy classes of subgroups

Complements