Group #19142862 — subgroups

Subgroups — #19142862

Order 5504.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	#14582841	C₂	1	3	yes	maximal
2	#14582833	C₂	1	3	yes	maximal
3	#14582831	C₂	1	3	yes	maximal
4	#14582820	C₂	1	3	yes	maximal
5	#14582769	C₂	1	1	yes	maximal, characteristic
6	#14582767	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#383	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
14	C₄₃⋊#95	C₂²	1	3	yes	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	#95×C₄₃	C₂²	1	3	yes	—
20	#95×C₄₃	C₂²	1	3	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×Dic₄₃	C₂³	1	3	yes	—
25	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂×Dic₈₆	—	4	3	no	—
29	C₄²×C₄₃	Q₈	1	4	yes	complemented
30	C₄⋊Dic₄₃	—	4	3	no	—
31	C₄⋊Dic₄₃	—	4	3	no	—
32	C₄⋊Dic₄₃	—	4	3	no	—
33	Dic₄₃⋊C₄	—	4	3	no	—
34	Dic₄₃⋊C₄	—	4	3	no	—
35	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	3	no	—
37	C₂×C₄×C₄₃	—	2	3	no	—
38	C₂×C₄×C₄₃	—	2	3	no	—
39	C₂×C₄×C₄₃	—	2	3	no	—
40	C₂×C₄×C₄₃	—	2	6	no	—
41	C₂×C₄×C₄₃	C₂×Q₈	1	6	yes	—
42	C₂×Dic₄₃	—	2	3	no	—
43	C₂×Dic₄₃	—	2	3	no	—
44	C₂×Dic₄₃	—	2	3	no	—
45	C₂×Dic₄₃	—	2	3	no	—
46	C₂×Dic₄₃	—	2	3	no	—
47	C₂×Dic₄₃	—	2	3	no	—
48	C₂×Dic₄₃	—	2	6	no	—
49	Dic₈₆	—	4	4	no	—
50	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
52	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
53	C₄×C₄₃	—	2	6	no	—
54	C₄×C₄₃	—	4	1	no	—
55	C₄×C₄₃	—	4	3	no	—
56	Dic₄₃	—	4	1	no	—
57	Dic₄₃	—	4	1	no	—
58	Dic₄₃	—	4	3	no	—
59	Dic₄₃	—	4	3	no	—
60	#2843	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	#544	1	3	yes	—
62	C₂×C₄₃	#560	1	1	yes	characteristic
63	C₂×C₄₃	#563	1	3	yes	—
64	#400	—	43	3	no	—
65	#398	—	43	3	no	—
66	#398	—	43	3	no	—
67	#395	—	43	3	no	—
68	#384	—	43	1	no	—
69	#383	—	43	1	no	—
70	#383	D₄₃	1	1	yes	characteristic
71	C₄₃	#2843	1	1	yes	characteristic, complemented, Sylow
72	C₂²×Q₈	—	43	1	no	—
73	C₂×C₄⋊C₄	—	43	3	no	—
74	C₂×C₄⋊C₄	—	43	3	no	—
75	C₂×C₄⋊C₄	—	43	3	no	—
76	C₂×C₄⋊C₄	—	43	3	no	—
77	C₂×C₄⋊C₄	—	43	3	no	—
78	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
79	#95	—	43	3	no	—
80	#95	—	43	3	no	—
81	#95	—	43	3	no	—
82	#95	—	43	3	no	—
83	#95	C₂×D₄₃	1	3	yes	—
84	#95	C₂×D₄₃	1	3	yes	—
85	C₂×Q₈	—	172	3	no	—
86	C₂²×C₄	—	43	3	no	—
87	C₂²×C₄	—	43	1	no	—
88	C₂²×C₄	—	43	1	no	—
89	C₂²×C₄	—	43	3	no	—
90	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
91	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
93	C₄⋊C₄	—	172	3	no	—
94	C₄⋊C₄	—	172	3	no	—
95	C₄⋊C₄	—	172	3	no	—
96	C₄⋊C₄	—	172	3	no	—
97	C₄⋊C₄	—	172	3	no	—
98	C₄²	Dic₈₆	1	4	yes	complemented
99	C₂³	C₂³×D₄₃	1	1	yes	characteristic
100	Q₈	—	172	4	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	3	no	—
105	C₂×C₄	—	2	6	no	—
106	C₂×C₄	—	86	3	no	—
107	C₂×C₄	—	86	3	no	—
108	C₂×C₄	—	86	3	no	—
109	C₂×C₄	—	86	3	no	—
110	C₂×C₄	—	86	3	no	—
111	C₂×C₄	—	86	3	no	—
112	C₂×C₄	—	86	6	no	—
113	C₂×C₄	C₂×Dic₈₆	1	6	yes	—
114	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
115	C₂²	#13063371	1	3	yes	—
116	C₂²	#13063372	1	3	yes	—
117	C₄	—	2	6	no	—
118	C₄	—	4	1	no	—
119	C₄	—	4	3	no	—
120	C₄	—	172	1	no	—
121	C₄	—	172	1	no	—
122	C₄	—	172	3	no	—
123	C₄	—	172	3	no	—
124	C₂	#14583527	1	3	yes	—
125	C₂	#14583640	1	1	yes	characteristic
126	C₂	#14583651	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582841

C₂

yes

maximal

#14582833

C₂

yes

maximal

#14582831

C₂

yes

maximal

#14582820

C₂

yes

maximal

#14582769

C₂

yes

maximal, characteristic

#14582767

C₂

yes

maximal, characteristic

C₄₃×#383

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₄²×C₄₃

Q₈

yes

complemented

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2843

—

maximal, Sylow

C₂×C₄₃

#544

yes

—

C₂×C₄₃

#560

yes

characteristic

C₂×C₄₃

#563

yes

—

—

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2843

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

—

#95

C₂×D₄₃

yes

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

Dic₈₆

yes

complemented

C₂³

C₂³×D₄₃

yes

characteristic

100

Q₈

—

172

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂×Dic₈₆

yes

—

114

C₂²

C₂²×Dic₈₆

yes

characteristic

115

C₂²

#13063371

yes

—

116

C₂²

#13063372

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

172

—

121

C₄

—

172

—

122

C₄

—

172

—

123

C₄

—

172

—

124

C₂

#14583527

yes

—

125

C₂

#14583640

yes

characteristic

126

C₂

#14583651

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#383	C₂
hypercenter	#383	D₄₃
hypocenter	C₄₃	#2843
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#383

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
29. C₄²×C₄₃	Q₈	semidirect
71. C₄₃	#2843	semidirect
98. C₄²	Dic₈₆	semidirect

H ≅ G/N

type

29. C₄²×C₄₃

Q₈

semidirect

71. C₄₃

#2843

semidirect

98. C₄²

Dic₈₆

semidirect

Subgroups — #19142862

Conjugacy classes of subgroups

Complements