Group #19136677 — subgroups

Subgroups — #19136677

Order 5504.

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

normal subgroups only

This group has 150 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	#14583342	C₂	1	2	yes	maximal
2	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583017	C₂	1	1	yes	maximal, characteristic
4	#14582716	C₂	1	2	yes	maximal, complemented
5	C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₇₂	—	2	1	no	—
8	C₂×Dic₁₇₂	C₂²	1	2	yes	—
9	#13063331	—	2	1	no	—
10	#13063325	—	2	1	no	—
11	Dic₃₄₄	—	2	2	no	—
12	#13063270	—	2	2	no	—
13	#13063261	C₂²	1	1	yes	characteristic
14	#13063253	—	2	1	no	—
15	M₃₂×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	#10621898	—	2	1	no	—
18	C₂×Dic₈₆	—	2	2	no	—
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₄⋊Dic₄₃	—	4	2	no	—
23	#10621877	—	2	1	no	—
24	Dic₁₇₂	—	2	2	no	—
25	Dic₁₇₂	—	2	2	no	—
26	Dic₁₇₂	—	4	1	no	—
27	Dic₁₇₂	—	4	1	no	—
28	Dic₁₇₂	D₄	1	1	yes	characteristic
29	D₃₄₄	D₄	1	1	yes	characteristic
30	#10621873	—	2	1	no	—
31	#10621872	—	4	1	no	—
32	C₈×D₄₃	—	4	1	no	—
33	C₁₆×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂²⋊D₄₃	—	4	1	no	—
37	C₂×Dic₄₃	—	4	2	no	—
38	D₁₇₂	—	2	1	no	—
39	C₄×D₄₃	—	4	1	no	—
40	Dic₈₆	—	2	1	no	—
41	Dic₈₆	—	4	2	no	—
42	Dic₈₆	—	4	2	no	—
43	C₈×C₄₃	D₈	1	1	yes	characteristic
44	C₈×C₄₃	D₈	1	1	yes	characteristic
45	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₈×C₄₃	#41	1	1	yes	characteristic
47	C₄₃⋊C₈	—	4	1	no	—
48	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
49	C₂×D₄₃	—	4	1	no	—
50	C₄×C₄₃	—	2	2	no	—
51	C₄×C₄₃	#121	1	1	yes	characteristic
52	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
53	Dic₄₃	—	4	1	no	—
54	Dic₄₃	—	8	2	no	—
55	#2214	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	—	2	1	no	—
57	C₂×C₄₃	#459	1	1	yes	characteristic
58	D₄₃	—	8	1	no	—
59	#510	—	43	2	no	—
60	#494	—	43	1	no	—
61	#443	—	43	1	no	—
62	#364	D₄₃	1	1	yes	characteristic, complemented
63	#362	—	43	2	no	—
64	C₄₃	#2214	1	1	yes	characteristic, complemented, Sylow
65	#135	—	43	1	no	—
66	C₂×Q₁₆	—	43	2	no	—
67	C₂×Q₁₆	—	86	1	no	—
68	#131	—	86	1	no	—
69	C₄⋊Q₈	—	86	1	no	—
70	Q₃₂	—	86	2	no	—
71	SD₃₂	—	86	2	no	—
72	M₃₂	C₂×D₄₃	1	2	yes	—
73	#108	—	43	1	no	—
74	#104	—	86	1	no	—
75	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
76	#41	—	86	1	no	—
77	C₂×Q₈	—	86	2	no	—
78	Q₁₆	—	43	1	no	—
79	Q₁₆	—	86	2	no	—
80	Q₁₆	—	86	2	no	—
81	Q₁₆	—	172	1	no	—
82	Q₁₆	—	172	1	no	—
83	SD₁₆	—	86	1	no	—
84	D₈	—	43	1	no	—
85	M₁₆	—	86	1	no	—
86	M₁₆	—	172	1	no	—
87	C₂×C₈	—	172	1	no	—
88	C₂×C₈	D₁₇₂	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
90	C₄⋊C₄	—	172	2	no	—
91	C₄²	D₁₇₂	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	Q₈	—	86	1	no	—
94	Q₈	—	172	2	no	—
95	Q₈	—	172	2	no	—
96	D₄	—	86	1	no	—
97	D₄	—	172	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	172	2	no	—
100	C₂×C₄	—	172	1	no	—
101	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
102	C₈	—	172	1	no	—
103	C₈	D₃₄₄	1	1	yes	characteristic
104	C₈	D₃₄₄	1	1	yes	characteristic
105	C₈	D₄×D₄₃	1	1	yes	characteristic
106	C₈	#10621902	1	1	yes	characteristic
107	C₂²	—	172	1	no	—
108	C₂²	#13063353	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	344	2	no	—
111	C₄	—	172	1	no	—
112	C₄	#13063300	1	1	yes	characteristic
113	C₄	C₂×D₃₄₄	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	344	1	no	—
116	C₂	#14583095	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583342

C₂

yes

maximal

#14583279

C₂

yes

maximal, characteristic, complemented

#14583017

C₂

yes

maximal, characteristic

#14582716

C₂

yes

maximal, complemented

C₄₃×#364

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂²

yes

—

#13063331

—

#13063325

—

Dic₃₄₄

—

#13063270

—

#13063261

C₂²

yes

characteristic

#13063253

—

M₃₂×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

#10621898

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

#10621877

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

characteristic

D₃₄₄

D₄

yes

characteristic

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

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

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2214

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#362

—

C₄₃

#2214

yes

characteristic, complemented, Sylow

#135

—

C₂×Q₁₆

—

C₂×Q₁₆

—

#131

—

C₄⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

C₂×D₄₃

yes

—

#108

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

172

—

Q₁₆

—

172

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

172

—

C₄²

D₁₇₂

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

172

—

100

C₂×C₄

—

172

—

101

C₂×C₄

C₂×D₁₇₂

yes

characteristic

102

C₈

—

172

—

103

C₈

D₃₄₄

yes

characteristic

104

C₈

D₃₄₄

yes

characteristic

105

C₈

D₄×D₄₃

yes

characteristic

106

C₈

#10621902

yes

characteristic

107

C₂²

—

172

—

108

C₂²

#13063353

yes

characteristic

109

C₄

—

110

C₄

—

344

—

111

C₄

—

172

—

112

C₄

#13063300

yes

characteristic

113

C₄

C₂×D₃₄₄

yes

characteristic

114

C₂

—

115

C₂

—

344

—

116

C₂

#14583095

yes

characteristic

	subgroup	G/H
center	C₂	#14583095
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#364	C₂
socle	C₂×C₄₃	#459
hypercenter	#364	D₄₃
hypocenter	C₄₃	#2214
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

subgroup

G/H

center

C₂

#14583095

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#364

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

N	H ≅ G/N	type
2. #14583279	C₂	semidirect
4. #14582716	C₂	semidirect
5. C₄₃×#364	C₂	semidirect
62. #364	D₄₃	semidirect
64. C₄₃	#2214	semidirect

H ≅ G/N

type

2. #14583279

C₂

semidirect

4. #14582716

C₂

semidirect

5. C₄₃×#364

C₂

semidirect

62. #364

D₄₃

semidirect

64. C₄₃

#2214

semidirect

Subgroups — #19136677

Conjugacy classes of subgroups

Complements