Group #19136770 — subgroups

Subgroups — #19136770

Order 5504.

120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14583299	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583015	C₂	1	1	yes	maximal, characteristic
3	#14582723	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582719	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582710	C₂	1	1	yes	maximal, characteristic
6	#14582708	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	#13063333	—	2	1	no	—
10	#13063316	—	2	1	no	—
11	#13063265	C₂²	1	1	yes	characteristic
12	#13063258	—	2	1	no	—
13	#13063257	C₂²	1	1	yes	characteristic
14	#13063251	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
17	#108×C₄₃	C₂²	1	1	yes	characteristic
18	#106×C₄₃	C₂²	1	1	yes	characteristic
19	#10621898	—	2	1	no	—
20	M₁₆×C₄₃	—	2	1	no	—
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄⋊Dic₄₃	—	2	1	no	—
24	C₄⋊Dic₄₃	—	4	1	no	—
25	Dic₄₃⋊C₄	—	4	1	no	—
26	C₄×Dic₄₃	D₄	1	1	yes	characteristic
27	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
28	Dic₁₇₂	Q₈	1	1	yes	characteristic
29	D₃₄₄	Q₈	1	1	yes	characteristic
30	#10621873	—	2	1	no	—
31	#10621872	—	4	1	no	—
32	C₈×D₄₃	—	4	1	no	—
33	C₁₆×C₄₃	—	2	1	no	—
34	C₄₃⋊C₁₆	—	2	1	no	—
35	C₂×C₄×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂²⋊D₄₃	—	4	1	no	—
38	C₂×Dic₄₃	—	2	1	no	—
39	C₂×Dic₄₃	—	4	1	no	—
40	D₁₇₂	—	2	1	no	—
41	C₄×D₄₃	—	4	1	no	—
42	Dic₈₆	—	2	1	no	—
43	C₈×C₄₃	—	4	1	no	—
44	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₃	#41	1	1	yes	characteristic
46	C₄₃⋊C₈	SD₁₆	1	1	yes	characteristic
47	C₄₃⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
49	C₂×D₄₃	—	4	1	no	—
50	C₄×C₄₃	—	8	1	no	—
51	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
52	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
53	Dic₄₃	—	4	1	no	—
54	Dic₄₃	—	4	1	no	—
55	Dic₄₃	—	8	1	no	—
56	#2231	—	43	1	no	maximal, Sylow
57	C₂×C₄₃	—	2	1	no	—
58	C₂×C₄₃	#476	1	1	yes	characteristic
59	D₄₃	—	8	1	no	—
60	#499	—	43	1	no	—
61	#443	—	43	1	no	—
62	#365	—	43	1	no	—
63	#365	D₄₃	1	1	yes	characteristic, complemented
64	#364	—	43	1	no	—
65	#360	—	43	1	no	—
66	#360	—	43	1	no	—
67	C₄₃	#2231	1	1	yes	characteristic, complemented, Sylow
68	#135	—	43	1	no	—
69	#131	—	86	1	no	—
70	#125	—	86	1	no	—
71	M₃₂	—	43	1	no	—
72	M₃₂	C₂×D₄₃	1	1	yes	characteristic
73	#108	C₂×D₄₃	1	1	yes	characteristic
74	#107	—	86	1	no	—
75	#106	—	43	1	no	—
76	#106	C₂×D₄₃	1	1	yes	characteristic
77	#104	—	86	1	no	—
78	C₄×C₈	—	43	1	no	—
79	#41	—	86	1	no	—
80	Q₁₆	—	43	1	no	—
81	SD₁₆	—	86	1	no	—
82	D₈	—	43	1	no	—
83	M₁₆	—	2	1	no	—
84	M₁₆	—	172	1	no	—
85	C₂×C₈	—	43	1	no	—
86	C₂×C₈	—	172	1	no	—
87	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
88	C₄⋊C₄	—	2	1	no	—
89	C₄⋊C₄	—	86	1	no	—
90	C₄⋊C₄	—	172	1	no	—
91	C₄⋊C₄	—	172	1	no	—
92	C₄²	—	43	1	no	—
93	C₁₆	—	2	1	no	—
94	C₁₆	—	86	1	no	—
95	Q₈	—	86	1	no	—
96	D₄	—	86	1	no	—
97	D₄	—	172	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	86	1	no	—
100	C₂×C₄	—	172	1	no	—
101	C₂×C₄	—	172	1	no	—
102	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
103	C₈	—	4	1	no	—
104	C₈	—	43	1	no	—
105	C₈	—	43	1	no	—
106	C₈	#10621898	1	1	yes	characteristic
107	C₈	Q₈×D₄₃	1	1	yes	characteristic
108	C₂²	—	172	1	no	—
109	C₂²	#13063352	1	1	yes	characteristic
110	C₄	—	8	1	no	—
111	C₄	—	344	1	no	—
112	C₄	—	172	1	no	—
113	C₄	—	172	1	no	—
114	C₄	#13063303	1	1	yes	characteristic
115	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
116	C₂	—	2	1	no	—
117	C₂	—	344	1	no	—
118	C₂	#14583188	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583299

C₂

yes

maximal, characteristic, complemented

#14583015

C₂

yes

maximal, characteristic

#14582723

C₂

yes

maximal, characteristic, complemented

#14582719

C₂

yes

maximal, characteristic, complemented

#14582710

C₂

yes

maximal, characteristic

#14582708

C₂

yes

maximal, characteristic

C₄₃×#365

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

—

—

C₂²

yes

characteristic

#13063258

—

#13063257

C₂²

yes

characteristic

#13063251

—

C₈×Dic₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

#106×C₄₃

C₂²

yes

characteristic

#10621898

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

Q₈

yes

characteristic

D₃₄₄

Q₈

yes

characteristic

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

SD₁₆

yes

characteristic

C₄₃⋊C₈

SD₁₆

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2231

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#476

yes

characteristic

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#364

—

#360

—

#360

—

C₄₃

#2231

yes

characteristic, complemented, Sylow

#135

—

#131

—

#125

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

#108

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

#104

—

C₄×C₈

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

C₁₆

—

C₁₆

—

Q₈

—

D₄

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

172

—

101

C₂×C₄

—

172

—

102

C₂×C₄

D₄×D₄₃

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

#10621898

yes

characteristic

107

C₈

Q₈×D₄₃

yes

characteristic

108

C₂²

—

172

—

109

C₂²

#13063352

yes

characteristic

110

C₄

—

111

C₄

—

344

—

112

C₄

—

172

—

113

C₄

—

172

—

114

C₄

#13063303

yes

characteristic

115

C₄

SD₁₆×D₄₃

yes

characteristic

116

C₂

—

117

C₂

—

344

—

118

C₂

#14583188

yes

characteristic

	subgroup	G/H
center	C₂	#14583188
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#365	C₂
socle	C₂×C₄₃	#476
hypercenter	#365	D₄₃
hypocenter	C₄₃	#2231
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#14583188

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#365

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

N	H ≅ G/N	type
1. #14583299	C₂	semidirect
3. #14582723	C₂	semidirect
4. #14582719	C₂	semidirect
7. C₄₃×#365	C₂	semidirect
63. #365	D₄₃	semidirect
67. C₄₃	#2231	semidirect

H ≅ G/N

type

1. #14583299

C₂

semidirect

3. #14582723

C₂

semidirect

4. #14582719

C₂

semidirect

7. C₄₃×#365

C₂

semidirect

63. #365

D₄₃

semidirect

67. C₄₃

#2231

semidirect

Subgroups — #19136770

Conjugacy classes of subgroups

Complements