Group #19134119 — subgroups

Subgroups — #19134119

Order 5504.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583304	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583190	C₂	1	2	yes	maximal
3	#14582978	C₂	1	1	yes	maximal, characteristic
4	#14582647	C₂	1	2	yes	maximal, complemented
5	C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	—	2	1	no	—
7	#13063325	C₂²	1	2	yes	—
8	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	#13063259	—	2	1	no	—
10	#13063259	—	2	1	no	—
11	#13063257	—	2	2	no	—
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	#13063247	—	2	2	no	—
14	(C₂×D₄₃)⋊C₈	—	2	1	no	—
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₁₇₂	D₄	1	1	yes	characteristic
18	C₂×C₄×D₄₃	—	2	1	no	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	2	1	no	—
25	C₄⋊Dic₄₃	—	2	2	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
28	C₂×C₄₃⋊C₈	—	2	1	no	—
29	#10621872	—	4	2	no	—
30	C₂²×D₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
34	C₂×Dic₄₃	—	2	1	no	—
35	C₂×Dic₄₃	—	4	2	no	—
36	D₁₇₂	—	2	2	no	—
37	C₄×D₄₃	—	4	1	no	—
38	C₄×D₄₃	—	4	1	no	—
39	Dic₈₆	—	8	2	no	—
40	C₈×C₄₃	—	2	1	no	—
41	C₈×C₄₃	—	4	2	no	—
42	C₈×C₄₃	SD₁₆	1	2	yes	—
43	C₄₃⋊C₈	—	4	1	no	—
44	C₂²×C₄₃	#121	1	1	yes	characteristic
45	C₂×D₄₃	—	4	1	no	—
46	C₂×D₄₃	—	4	1	no	—
47	C₂×D₄₃	—	4	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₄×C₄₃	#137	1	2	yes	—
51	C₄×C₄₃	#137	1	1	yes	characteristic
52	Dic₄₃	—	4	1	no	—
53	Dic₄₃	—	8	2	no	—
54	#1695	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	#461	1	1	yes	characteristic
56	C₂×C₄₃	#470	1	1	yes	characteristic
57	C₂×C₄₃	#472	1	1	yes	characteristic
58	D₄₃	—	8	1	no	—
59	#500	—	43	1	no	—
60	#476	—	43	2	no	—
61	#436	—	43	1	no	—
62	#334	D₄₃	1	1	yes	characteristic, complemented
63	#333	—	43	2	no	—
64	C₄₃	#1695	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	86	1	no	—
66	C₄⋊Q₈	—	43	2	no	—
67	C₄×D₄	—	43	1	no	—
68	#107	—	86	1	no	—
69	#107	—	86	1	no	—
70	#106	—	86	2	no	—
71	C₄⋊C₈	—	43	1	no	—
72	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
73	#102	—	86	2	no	—
74	C₂²⋊C₈	—	86	1	no	—
75	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
76	C₂×Q₈	—	86	2	no	—
77	C₂×D₄	—	43	1	no	—
78	C₂²×C₄	—	86	1	no	—
79	M₁₆	—	172	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	86	1	no	—
82	C₂×C₈	D₁₇₂	1	1	yes	characteristic
83	C₂×C₈	D₁₇₂	1	1	yes	characteristic
84	C₄⋊C₄	—	43	1	no	—
85	C₄⋊C₄	—	86	2	no	—
86	C₄⋊C₄	—	86	2	no	—
87	C₂²⋊C₄	—	86	1	no	—
88	C₄²	C₂²×D₄₃	1	1	yes	characteristic
89	C₂³	—	86	1	no	—
90	Q₈	—	344	2	no	—
91	D₄	—	86	2	no	—
92	C₂×C₄	—	86	1	no	—
93	C₂×C₄	—	172	2	no	—
94	C₂×C₄	—	172	1	no	—
95	C₂×C₄	—	172	1	no	—
96	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
97	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
98	C₂×C₄	#10621902	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	2	no	—
101	C₈	—	172	1	no	—
102	C₈	#10621873	1	2	yes	—
103	C₂²	—	172	1	no	—
104	C₂²	—	172	1	no	—
105	C₂²	—	172	1	no	—
106	C₂²	#13063300	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	344	2	no	—
109	C₄	—	172	1	no	—
110	C₄	C₂×#10621873	1	1	yes	characteristic
111	C₄	#13063354	1	2	yes	—
112	C₄	#13063358	1	1	yes	characteristic
113	C₂	—	344	1	no	—
114	C₂	#14583105	1	1	yes	characteristic
115	C₂	#14583158	1	1	yes	characteristic
116	C₂	#14583170	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic, complemented

#14583190

C₂

yes

maximal

#14582978

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, complemented

C₄₃×#334

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

—

#13063325

C₂²

yes

—

C₄×D₁₇₂

C₂²

yes

—

—

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

#13063247

—

(C₂×D₄₃)⋊C₈

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

D₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

—

#10621872

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

#137

yes

—

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#333

—

C₄₃

#1695

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

Q₈

—

344

—

D₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621902

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

172

—

102

C₈

#10621873

yes

—

103

C₂²

—

172

—

104

C₂²

—

172

—

105

C₂²

—

172

—

106

C₂²

#13063300

yes

characteristic

107

C₄

—

108

C₄

—

344

—

109

C₄

—

172

—

110

C₄

C₂×#10621873

yes

characteristic

111

C₄

#13063354

yes

—

112

C₄

#13063358

yes

characteristic

113

C₂

—

344

—

114

C₂

#14583105

yes

characteristic

115

C₂

#14583158

yes

characteristic

116

C₂

#14583170

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1695
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #14583304	C₂	semidirect
4. #14582647	C₂	semidirect
5. C₄₃×#334	C₂	semidirect
62. #334	D₄₃	semidirect
64. C₄₃	#1695	semidirect

H ≅ G/N

type

1. #14583304

C₂

semidirect

4. #14582647

C₂

semidirect

5. C₄₃×#334

C₂

semidirect

62. #334

D₄₃

semidirect

64. C₄₃

#1695

semidirect

Subgroups — #19134119

Conjugacy classes of subgroups

Complements