Group #19146399 — subgroups

Subgroups — #19146399

Order 5504.

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

normal subgroups only

This group has 444 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	#14583712	C₂	1	4	yes	maximal, complemented
2	#14583171	C₂	1	4	yes	maximal, complemented
3	#14583081	C₂	1	4	yes	maximal, complemented
4	#14583017	C₂	1	2	yes	maximal, complemented
5	C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063373	C₂²	1	4	yes	—
7	#13063357	—	2	8	no	—
8	#13063356	C₂²	1	8	yes	—
9	#13063348	—	2	4	no	—
10	#13063347	C₂²	1	2	yes	—
11	Q₁₆×D₄₃	—	2	4	no	—
12	#13063331	C₂²	1	4	yes	—
13	#13063261	C₂²	1	2	yes	—
14	#13063253	C₂²	1	4	yes	—
15	#13063244	C₂²	1	4	yes	—
16	C₂×Q₁₆×C₄₃	C₂²	1	4	yes	—
17	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
20	#10621902	—	2	8	no	—
21	Q₈×D₄₃	—	2	8	no	—
22	#10621898	—	4	4	no	—
23	#10621898	C₂³	1	4	yes	—
24	Q₁₆×C₄₃	—	2	4	no	—
25	Q₁₆×C₄₃	—	2	4	no	—
26	C₂×C₈×C₄₃	C₂³	1	2	yes	—
27	C₄⋊C₄×C₄₃	—	4	2	no	—
28	C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	#10621885	—	2	8	no	—
30	#10621884	—	2	8	no	—
31	#10621877	C₂³	1	4	yes	—
32	Dic₁₇₂	D₄	1	2	yes	—
33	D₃₄₄	D₄	1	2	yes	—
34	#10621873	D₄	1	4	yes	—
35	#10621872	—	2	4	no	—
36	C₈×D₄₃	—	2	4	no	—
37	Q₈×C₄₃	—	2	8	no	—
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₂²⋊D₄₃	—	2	4	no	—
42	D₁₇₂	—	4	4	no	—
43	D₁₇₂	C₂×D₄	1	4	yes	—
44	C₄×D₄₃	—	2	4	no	—
45	C₄×D₄₃	—	4	8	no	—
46	Dic₈₆	—	4	4	no	—
47	Dic₈₆	C₂×D₄	1	4	yes	—
48	C₈×C₄₃	C₂×D₄	1	2	yes	—
49	C₈×C₄₃	C₂×D₄	1	2	yes	—
50	C₄₃⋊C₈	—	2	4	no	—
51	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
52	C₂×D₄₃	—	2	4	no	—
53	C₄×C₄₃	—	2	2	no	—
54	C₄×C₄₃	—	4	4	no	—
55	C₄×C₄₃	C₂²×D₄	1	2	yes	—
56	Dic₄₃	—	2	4	no	—
57	#3293	—	43	1	no	maximal, Sylow
58	C₂×C₄₃	—	2	1	no	—
59	C₂×C₄₃	D₄²	1	1	yes	characteristic
60	D₄₃	—	4	4	no	—
61	#578	—	43	4	no	—
62	#494	D₄₃	1	1	yes	characteristic, complemented
63	#473	—	43	4	no	—
64	#456	—	43	4	no	—
65	#443	—	43	2	no	—
66	C₄₃	#3293	1	1	yes	characteristic, complemented, Sylow
67	2₋¹⁺⁴	—	43	4	no	—
68	#137	—	43	8	no	—
69	#137	—	86	8	no	—
70	#135	—	43	2	no	—
71	#135	—	86	4	no	—
72	C₂×Q₁₆	—	86	4	no	—
73	C₂×Q₁₆	C₂×D₄₃	1	4	yes	—
74	#131	—	43	4	no	—
75	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
76	#108	—	43	2	no	—
77	#104	—	43	4	no	—
78	#101	—	43	4	no	—
79	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
80	#41	—	43	4	no	—
81	#41	—	86	8	no	—
82	#41	—	172	4	no	—
83	C₂×Q₈	—	86	8	no	—
84	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
85	Q₁₆	—	2	4	no	—
86	Q₁₆	—	2	4	no	—
87	Q₁₆	—	43	2	no	—
88	Q₁₆	—	86	8	no	—
89	SD₁₆	—	43	4	no	—
90	SD₁₆	—	86	8	no	—
91	D₈	—	43	2	no	—
92	M₁₆	—	43	4	no	—
93	M₁₆	—	86	4	no	—
94	C₂×C₈	—	86	4	no	—
95	C₂×C₈	C₂²×D₄₃	1	2	yes	—
96	C₄⋊C₄	—	4	2	no	—
97	C₄²	C₂²×D₄₃	1	1	yes	characteristic
98	Q₈	—	2	8	no	—
99	Q₈	—	43	4	no	—
100	Q₈	—	172	4	no	—
101	D₄	—	43	4	no	—
102	D₄	—	86	4	no	—
103	D₄	—	172	4	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	86	4	no	—
107	C₂×C₄	—	172	8	no	—
108	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
109	C₈	—	86	4	no	—
110	C₈	D₄×D₄₃	1	2	yes	—
111	C₈	D₄×D₄₃	1	2	yes	—
112	C₂²	—	86	4	no	—
113	C₂²	#13063370	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	—	86	4	no	—
117	C₄	C₂×D₄×D₄₃	1	2	yes	—
118	C₂	—	2	1	no	—
119	C₂	—	172	4	no	—
120	C₂	#14583534	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583712

C₂

yes

maximal, complemented

#14583171

C₂

yes

maximal, complemented

#14583081

C₂

yes

maximal, complemented

#14583017

C₂

yes

maximal, complemented

C₄₃×#494

C₂

yes

maximal, characteristic, complemented

#13063373

C₂²

yes

—

#13063357

—

#13063356

C₂²

yes

—

#13063348

—

#13063347

C₂²

yes

—

Q₁₆×D₄₃

—

#13063331

C₂²

yes

—

#13063261

C₂²

yes

—

#13063253

C₂²

yes

—

#13063244

C₂²

yes

—

C₂×Q₁₆×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

C₂³

yes

—

#10621902

—

Q₈×D₄₃

—

#10621898

—

#10621898

C₂³

yes

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

—

—

C₂³

yes

—

Dic₁₇₂

D₄

yes

—

D₃₄₄

D₄

yes

—

#10621873

D₄

yes

—

#10621872

—

C₈×D₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

D₁₇₂

C₂×D₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

C₂×D₄

yes

—

C₈×C₄₃

C₂×D₄

yes

—

C₈×C₄₃

C₂×D₄

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²×D₄

yes

—

Dic₄₃

—

#3293

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

D₄²

yes

characteristic

D₄₃

—

#578

—

#494

D₄₃

yes

characteristic, complemented

#473

—

#456

—

#443

—

C₄₃

#3293

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

—

#131

—

C₄⋊Q₈

C₂×D₄₃

yes

—

#108

—

#104

—

#101

—

C₄×C₈

C₂×D₄₃

yes

—

—

—

172

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₃

yes

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

172

—

101

D₄

—

102

D₄

—

103

D₄

—

172

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

172

—

108

C₂×C₄

C₂³×D₄₃

yes

characteristic

109

C₈

—

110

C₈

D₄×D₄₃

yes

—

111

C₈

D₄×D₄₃

yes

—

112

C₂²

—

113

C₂²

#13063370

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×D₄×D₄₃

yes

—

118

C₂

—

119

C₂

—

172

—

120

C₂

#14583534

yes

characteristic

	subgroup	G/H
center	C₂	#14583534
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂×C₄₃	D₄²
hypercenter	#494	D₄₃
hypocenter	C₄₃	#3293
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

subgroup

G/H

center

C₂

#14583534

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#494

C₂

socle

C₂×C₄₃

D₄²

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

N	H ≅ G/N	type
1. #14583712	C₂	semidirect
2. #14583171	C₂	semidirect
3. #14583081	C₂	semidirect
4. #14583017	C₂	semidirect
5. C₄₃×#494	C₂	semidirect
62. #494	D₄₃	semidirect
66. C₄₃	#3293	semidirect

H ≅ G/N

type

1. #14583712

C₂

semidirect

2. #14583171

C₂

semidirect

3. #14583081

C₂

semidirect

4. #14583017

C₂

semidirect

5. C₄₃×#494

C₂

semidirect

62. #494

D₄₃

semidirect

66. C₄₃

#3293

semidirect

Subgroups — #19146399

Conjugacy classes of subgroups

Complements