Group #19136668 — subgroups

Subgroups — #19136668

Order 5504.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14583335	C₂	1	2	yes	maximal, complemented
2	#14583017	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582712	C₂	1	2	yes	maximal, complemented
5	C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₂²	1	1	yes	characteristic
7	#13063331	—	2	1	no	—
8	#13063269	—	2	2	no	—
9	#13063266	—	2	2	no	—
10	#13063265	C₂²	1	2	yes	—
11	#13063261	C₂²	1	1	yes	characteristic
12	#13063253	—	2	1	no	—
13	C₂×D₈×C₄₃	—	2	1	no	—
14	C₂×D₈×C₄₃	C₂²	1	2	yes	—
15	#127×C₄₃	—	2	1	no	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₃	—	2	2	no	—
18	C₂×D₄×C₄₃	—	4	2	no	—
19	#10621898	—	2	1	no	—
20	D₈×C₄₃	—	2	2	no	—
21	D₈×C₄₃	—	2	2	no	—
22	D₈×C₄₃	—	4	1	no	—
23	D₈×C₄₃	—	4	1	no	—
24	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₄²×C₄₃	D₄	1	1	yes	characteristic
27	#10621877	—	2	1	no	—
28	Dic₁₇₂	D₄	1	1	yes	characteristic, complemented
29	D₃₄₄	D₄	1	1	yes	characteristic, complemented
30	#10621873	—	2	1	no	—
31	#10621872	—	4	1	no	—
32	C₈×D₄₃	—	4	1	no	—
33	C₄₃⋊C₁₆	—	2	2	no	—
34	C₂³×C₄₃	—	4	2	no	—
35	D₄×C₄₃	—	4	2	no	—
36	D₄×C₄₃	—	4	2	no	—
37	D₄×C₄₃	—	8	4	no	—
38	C₂×C₄×C₄₃	—	2	1	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂²⋊D₄₃	—	4	1	no	—
41	D₁₇₂	—	2	1	no	—
42	C₄×D₄₃	—	4	1	no	—
43	Dic₈₆	—	2	1	no	—
44	C₈×C₄₃	D₈	1	1	yes	characteristic
45	C₈×C₄₃	D₈	1	1	yes	characteristic
46	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₈×C₄₃	#41	1	1	yes	characteristic
48	C₄₃⋊C₈	—	4	1	no	—
49	C₂²×C₄₃	—	8	4	no	—
50	C₂²×C₄₃	—	8	2	no	—
51	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
52	C₂×D₄₃	—	4	1	no	—
53	C₄×C₄₃	—	2	2	no	—
54	C₄×C₄₃	#121	1	1	yes	characteristic
55	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
56	Dic₄₃	—	4	1	no	—
57	#2213	—	43	1	no	maximal, Sylow
58	C₂×C₄₃	—	2	1	no	—
59	C₂×C₄₃	—	16	2	no	—
60	C₂×C₄₃	#459	1	1	yes	characteristic
61	D₄₃	—	8	1	no	—
62	#509	—	43	2	no	—
63	#493	D₄₃	1	1	yes	characteristic, complemented
64	#443	—	43	1	no	—
65	#364	—	43	1	no	—
66	#361	—	43	2	no	—
67	C₄₃	#2213	1	1	yes	characteristic, complemented, Sylow
68	#135	—	43	1	no	—
69	C₂×D₈	—	2	1	no	—
70	C₂×D₈	C₂×D₄₃	1	2	yes	—
71	#131	—	86	1	no	—
72	#127	—	2	1	no	—
73	SD₃₂	—	86	2	no	—
74	D₁₆	—	86	2	no	—
75	M₃₂	—	43	2	no	—
76	#108	—	43	1	no	—
77	#104	—	86	1	no	—
78	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
79	#41	—	86	1	no	—
80	C₂×D₄	—	2	2	no	—
81	C₂×D₄	—	4	2	no	—
82	Q₁₆	—	43	1	no	—
83	SD₁₆	—	86	1	no	—
84	D₈	—	2	2	no	—
85	D₈	—	2	2	no	—
86	D₈	—	4	1	no	—
87	D₈	—	4	1	no	—
88	D₈	—	43	1	no	—
89	M₁₆	—	86	1	no	—
90	M₁₆	—	172	1	no	—
91	C₂×C₈	—	172	1	no	—
92	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
93	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
94	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
95	C₁₆	—	86	2	no	—
96	C₂³	—	4	2	no	—
97	Q₈	—	86	1	no	—
98	D₄	—	4	2	no	—
99	D₄	—	4	2	no	—
100	D₄	—	8	4	no	—
101	D₄	—	86	1	no	—
102	D₄	—	172	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	172	1	no	—
105	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
106	C₈	—	172	1	no	—
107	C₈	#10621882	1	1	yes	characteristic
108	C₈	#10621882	1	1	yes	characteristic
109	C₈	D₄×D₄₃	1	1	yes	characteristic
110	C₈	#10621900	1	1	yes	characteristic
111	C₂²	—	8	4	no	—
112	C₂²	—	8	2	no	—
113	C₂²	—	172	1	no	—
114	C₂²	#13063351	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	172	1	no	—
117	C₄	#13063296	1	1	yes	characteristic
118	C₄	C₂×#10621882	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	16	2	no	—
121	C₂	—	344	1	no	—
122	C₂	#14583091	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583335

C₂

yes

maximal, complemented

#14583017

C₂

yes

maximal, characteristic, complemented

#14582720

C₂

yes

maximal, characteristic, complemented

#14582712

C₂

yes

maximal, complemented

C₄₃×#493

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

—

—

—

C₂²

yes

—

#13063261

C₂²

yes

characteristic

#13063253

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

—

#127×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

#10621898

—

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

#10621877

—

Dic₁₇₂

D₄

yes

characteristic, complemented

D₃₄₄

D₄

yes

characteristic, complemented

#10621873

—

#10621872

—

C₈×D₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

#2213

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

D₄₃

—

#509

—

#493

D₄₃

yes

characteristic, complemented

#443

—

#364

—

#361

—

C₄₃

#2213

yes

characteristic, complemented, Sylow

#135

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

—

#131

—

#127

—

SD₃₂

—

D₁₆

—

M₃₂

—

#108

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

D₄

—

D₄

—

100

D₄

—

101

D₄

—

102

D₄

—

172

—

103

C₂×C₄

—

104

C₂×C₄

—

172

—

105

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

106

C₈

—

172

—

107

C₈

#10621882

yes

characteristic

108

C₈

#10621882

yes

characteristic

109

C₈

D₄×D₄₃

yes

characteristic

110

C₈

#10621900

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

172

—

114

C₂²

#13063351

yes

characteristic

115

C₄

—

116

C₄

—

172

—

117

C₄

#13063296

yes

characteristic

118

C₄

C₂×#10621882

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

—

344

—

122

C₂

#14583091

yes

characteristic

	subgroup	G/H
center	C₂	#14583091
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#493	C₂
socle	C₂×C₄₃	#459
hypercenter	#493	D₄₃
hypocenter	C₄₃	#2213
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂

#14583091

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#493

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. #14583335	C₂	semidirect
2. #14583017	C₂	semidirect
3. #14582720	C₂	semidirect
4. #14582712	C₂	semidirect
5. C₄₃×#493	C₂	semidirect
28. Dic₁₇₂	D₄	semidirect
29. D₃₄₄	D₄	semidirect
63. #493	D₄₃	semidirect
67. C₄₃	#2213	semidirect

H ≅ G/N

type

1. #14583335

C₂

semidirect

2. #14583017

C₂

semidirect

3. #14582720

C₂

semidirect

4. #14582712

C₂

semidirect

5. C₄₃×#493

C₂

semidirect

28. Dic₁₇₂

D₄

semidirect

29. D₃₄₄

D₄

semidirect

63. #493

D₄₃

semidirect

67. C₄₃

#2213

semidirect

Subgroups — #19136668

Conjugacy classes of subgroups

Complements