Group #19146049 — subgroups

Subgroups — #19146049

Order 5504.

322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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	#14583511	C₂	1	2	yes	maximal
2	#14583207	C₂	1	4	yes	maximal, complemented
3	#14583157	C₂	1	2	yes	maximal
4	#14583140	C₂	1	2	yes	maximal
5	#14583110	C₂	1	4	yes	maximal, complemented
6	C₄₃×#424	C₂	1	1	yes	maximal, characteristic
7	C₂×Dic₁₇₂	C₂²	1	2	yes	—
8	C₂×Dic₁₇₂	C₂²	1	2	yes	—
9	#13063325	C₂²	1	2	yes	—
10	#13063318	—	2	4	no	—
11	#13063317	C₂²	1	2	yes	—
12	#13063315	—	2	4	no	—
13	#13063304	C₂²	1	4	yes	—
14	C₄×Dic₈₆	C₂²	1	4	yes	—
15	#13063259	C₂²	1	2	yes	—
16	#13063257	C₂²	1	2	yes	—
17	#13063250	C₂²	1	4	yes	—
18	#13063250	C₂²	1	4	yes	—
19	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₈₆	C₂³	1	4	yes	—
25	M₁₆×C₄₃	—	4	1	no	—
26	C₂×C₈×C₄₃	—	4	1	no	—
27	C₂×C₈×C₄₃	C₂³	1	2	yes	—
28	C₂×C₈×C₄₃	C₂³	1	2	yes	—
29	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
30	C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
31	C₄²×C₄₃	C₂³	1	2	yes	—
32	C₂²⋊Dic₄₃	—	2	4	no	—
33	C₄⋊Dic₄₃	—	2	4	no	—
34	C₄⋊Dic₄₃	C₂³	1	4	yes	—
35	Dic₄₃⋊C₄	—	2	4	no	—
36	Dic₄₃⋊C₄	—	2	4	no	—
37	Dic₄₃⋊C₄	—	2	4	no	—
38	C₄×Dic₄₃	—	2	4	no	—
39	Dic₁₇₂	—	4	2	no	—
40	Dic₁₇₂	—	4	2	no	—
41	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₄₃	—	2	4	no	—
48	C₂×Dic₄₃	—	2	4	no	—
49	Dic₈₆	—	2	4	no	—
50	Dic₈₆	—	2	4	no	—
51	C₈×C₄₃	—	2	2	no	—
52	C₈×C₄₃	—	2	2	no	—
53	C₂²×C₄₃	—	2	1	no	—
54	C₂²×C₄₃	—	2	2	no	—
55	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	2	4	no	—
58	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
59	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
60	Dic₄₃	—	4	4	no	—
61	Dic₄₃	—	4	4	no	—
62	#3261	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	—	4	1	no	—
64	C₂×C₄₃	#537	1	1	yes	characteristic
65	C₂×C₄₃	#578	1	2	yes	—
66	#541	—	43	2	no	—
67	#479	—	43	4	no	—
68	#470	—	43	2	no	—
69	#467	—	43	2	no	—
70	#462	—	43	4	no	—
71	#424	D₄₃	1	1	yes	characteristic
72	C₄₃	#3261	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₁₆	—	43	2	no	—
74	C₂×Q₁₆	—	43	2	no	—
75	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
76	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₄⋊Q₈	—	43	2	no	—
78	#126	—	86	4	no	—
79	#125	—	43	2	no	—
80	#125	—	86	4	no	—
81	C₂²⋊Q₈	—	43	4	no	—
82	C₄×Q₈	—	43	4	no	—
83	#117	C₂×D₄₃	1	1	yes	characteristic
84	#107	—	43	2	no	—
85	#106	—	43	2	no	—
86	C₄⋊C₈	C₂×D₄₃	1	4	yes	—
87	#103	—	43	4	no	—
88	#103	—	43	4	no	—
89	C₂×Q₈	—	43	4	no	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	Q₁₆	—	172	2	no	—
92	Q₁₆	—	172	2	no	—
93	M₁₆	—	4	1	no	—
94	C₂×C₈	—	4	1	no	—
95	C₂×C₈	C₂²×D₄₃	1	2	yes	—
96	C₂×C₈	C₂²×D₄₃	1	2	yes	—
97	C₄⋊C₄	—	43	4	no	—
98	C₄⋊C₄	—	86	4	no	—
99	C₄⋊C₄	—	86	4	no	—
100	C₄⋊C₄	—	86	4	no	—
101	C₄⋊C₄	—	86	4	no	—
102	C₄⋊C₄	D₁₇₂	1	2	yes	—
103	C₂²⋊C₄	—	86	4	no	—
104	C₂²⋊C₄	D₁₇₂	1	2	yes	—
105	C₄²	—	86	4	no	—
106	C₄²	C₂²×D₄₃	1	2	yes	—
107	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
108	Q₈	—	86	4	no	—
109	Q₈	—	86	4	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	86	4	no	—
113	C₂×C₄	—	86	4	no	—
114	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
115	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
116	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	2	2	no	—
119	C₂²	—	2	2	no	—
120	C₂²	—	2	1	no	—
121	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
122	C₄	—	2	4	no	—
123	C₄	—	2	1	no	—
124	C₄	—	172	4	no	—
125	C₄	—	172	4	no	—
126	C₄	#13063370	1	1	yes	characteristic
127	C₄	#13063373	1	1	yes	characteristic
128	C₂	—	4	1	no	—
129	C₂	#14583480	1	1	yes	characteristic
130	C₂	#14583716	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583511

C₂

yes

maximal

#14583207

C₂

yes

maximal, complemented

#14583157

C₂

yes

maximal

#14583140

C₂

yes

maximal

#14583110

C₂

yes

maximal, complemented

C₄₃×#424

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

—

#13063325

C₂²

yes

—

#13063318

—

#13063317

C₂²

yes

—

#13063315

—

#13063304

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

#13063250

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

C₂³

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

H(5,𝔽₂)

yes

characteristic

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#3261

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#537

yes

characteristic

C₂×C₄₃

#578

yes

—

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#3261

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#126

—

#125

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₄₃

yes

characteristic

#107

—

#106

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

#103

—

C₂×Q₈

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

Q₁₆

—

172

—

Q₁₆

—

172

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

D₁₇₂

yes

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

D₁₇₂

yes

—

105

C₄²

—

106

C₄²

C₂²×D₄₃

yes

—

107

C₂³

C₂×D₁₇₂

yes

characteristic

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×D₁₇₂

yes

—

115

C₂×C₄

C₂×D₁₇₂

yes

characteristic

116

C₂×C₄

C₂³×D₄₃

yes

characteristic

117

C₈

—

118

C₈

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂²×D₁₇₂

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

172

—

125

C₄

—

172

—

126

C₄

#13063370

yes

characteristic

127

C₄

#13063373

yes

characteristic

128

C₂

—

129

C₂

#14583480

yes

characteristic

130

C₂

#14583716

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#424	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#424	D₄₃
hypocenter	C₄₃	#3261
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #424

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#424

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ #117 ◁ #424

N	H ≅ G/N	type
2. #14583207	C₂	semidirect
5. #14583110	C₂	semidirect
72. C₄₃	#3261	semidirect

H ≅ G/N

type

2. #14583207

C₂

semidirect

5. #14583110

C₂

semidirect

72. C₄₃

#3261

semidirect

Subgroups — #19146049

Conjugacy classes of subgroups

Complements