Group #19136816 — subgroups

Subgroups — #19136816

Order 5504.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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	#14583158	C₂	1	1	yes	maximal, characteristic
2	#14582946	C₂	1	1	yes	maximal, characteristic
3	#14582721	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582716	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582714	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582680	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#10621872	C₂²	1	1	yes	characteristic
10	M₁₆×D₄₃	—	2	1	no	—
11	#13063305	—	2	1	no	—
12	#13063265	C₂²	1	1	yes	characteristic
13	#13063261	C₂²	1	1	yes	characteristic
14	#13063260	—	2	1	no	—
15	#13063248	—	2	1	no	—
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	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
20	C₂×Dic₈₆	—	2	1	no	—
21	M₁₆×C₄₃	—	2	1	no	—
22	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₄₃	—	2	1	no	—
24	(C₂×D₄₃)⋊C₄	—	4	1	no	—
25	C₄⋊Dic₄₃	—	4	1	no	—
26	#10621877	—	2	1	no	—
27	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
28	Dic₁₇₂	—	2	1	no	—
29	Dic₁₇₂	—	2	1	no	—
30	#10621872	—	2	1	no	—
31	#10621872	—	2	1	no	—
32	#10621872	—	4	1	no	—
33	C₈×D₄₃	—	4	1	no	—
34	C₁₆×C₄₃	—	2	1	no	—
35	C₄₃⋊C₁₆	—	2	1	no	—
36	C₂²×D₄₃	SD₁₆	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₃	—	4	1	no	—
40	C₂×Dic₄₃	SD₁₆	1	1	yes	characteristic
41	C₄×D₄₃	—	2	1	no	—
42	C₄×D₄₃	—	2	1	no	—
43	Dic₈₆	—	4	1	no	—
44	Dic₈₆	—	4	1	no	—
45	C₈×C₄₃	—	4	1	no	—
46	C₈×C₄₃	#41	1	1	yes	characteristic
47	C₈×C₄₃	#41	1	1	yes	characteristic
48	C₄₃⋊C₈	—	2	1	no	—
49	C₄₃⋊C₈	—	4	1	no	—
50	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
51	C₂×D₄₃	—	2	1	no	—
52	C₂×D₄₃	—	4	1	no	—
53	C₄×C₄₃	—	8	1	no	—
54	C₄×C₄₃	#123	1	1	yes	characteristic
55	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
56	Dic₄₃	—	2	1	no	—
57	Dic₄₃	—	8	1	no	—
58	#2239	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	—	2	1	no	—
60	C₂×C₄₃	#481	1	1	yes	characteristic
61	D₄₃	—	4	1	no	—
62	#470	—	43	1	no	—
63	#430	—	43	1	no	—
64	#365	—	43	1	no	—
65	#365	D₄₃	1	1	yes	characteristic, complemented
66	#362	—	43	1	no	—
67	#362	—	43	1	no	—
68	#349	—	43	1	no	—
69	C₄₃	#2239	1	1	yes	characteristic, complemented, Sylow
70	C₂×Q₁₆	—	43	1	no	—
71	C₂×M₁₆	—	43	1	no	—
72	C₂×M₁₆	—	86	1	no	—
73	C₂²⋊Q₈	—	86	1	no	—
74	M₃₂	—	43	1	no	—
75	M₃₂	C₂×D₄₃	1	1	yes	characteristic
76	#108	—	43	1	no	—
77	#108	—	86	1	no	—
78	#108	C₂×D₄₃	1	1	yes	characteristic
79	#106	C₂×D₄₃	1	1	yes	characteristic
80	#103	—	86	1	no	—
81	C₂×Q₈	—	86	1	no	—
82	C₂²×C₄	—	43	1	no	—
83	Q₁₆	—	86	1	no	—
84	Q₁₆	—	86	1	no	—
85	M₁₆	—	2	1	no	—
86	M₁₆	—	86	1	no	—
87	M₁₆	—	86	1	no	—
88	M₁₆	—	86	1	no	—
89	M₁₆	—	172	1	no	—
90	C₂×C₈	—	43	1	no	—
91	C₂×C₈	—	172	1	no	—
92	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	—	172	1	no	—
95	C₂²⋊C₄	—	172	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	86	1	no	—
98	C₂³	—	43	1	no	—
99	Q₈	—	172	1	no	—
100	Q₈	—	172	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	43	1	no	—
103	C₂×C₄	—	86	1	no	—
104	C₂×C₄	—	86	1	no	—
105	C₂×C₄	—	172	1	no	—
106	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
107	C₈	—	4	1	no	—
108	C₈	—	86	1	no	—
109	C₈	—	172	1	no	—
110	C₈	#10621898	1	1	yes	characteristic
111	C₈	#10621902	1	1	yes	characteristic
112	C₂²	—	86	1	no	—
113	C₂²	—	172	1	no	—
114	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
115	C₄	—	8	1	no	—
116	C₄	—	86	1	no	—
117	C₄	—	344	1	no	—
118	C₄	#13063310	1	1	yes	characteristic
119	C₄	#13063352	1	1	yes	characteristic
120	C₂	—	2	1	no	—
121	C₂	—	172	1	no	—
122	C₂	#14583219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583158

C₂

yes

maximal, characteristic

#14582946

C₂

yes

maximal, characteristic

#14582721

C₂

yes

maximal, characteristic, complemented

#14582716

C₂

yes

maximal, characteristic, complemented

#14582714

C₂

yes

maximal, characteristic, complemented

#14582680

C₂

yes

maximal, characteristic

C₄₃×#365

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621872

C₂²

yes

characteristic

M₁₆×D₄₃

—

#13063305

—

#13063265

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063260

—

#13063248

—

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

#106×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

#10621872

—

#10621872

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂²×D₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2239

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#481

yes

characteristic

D₄₃

—

—

—

—

D₄₃

yes

characteristic, complemented

#362

—

#362

—

#349

—

C₄₃

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

#106

C₂×D₄₃

yes

characteristic

#103

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₁₆

—

C₂³

—

Q₈

—

172

—

100

Q₈

—

172

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

172

—

106

C₂×C₄

D₄×D₄₃

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

172

—

110

C₈

#10621898

yes

characteristic

111

C₈

#10621902

yes

characteristic

112

C₂²

—

113

C₂²

—

172

—

114

C₂²

SD₁₆×D₄₃

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

344

—

118

C₄

#13063310

yes

characteristic

119

C₄

#13063352

yes

characteristic

120

C₂

—

121

C₂

—

172

—

122

C₂

#14583219

yes

characteristic

	subgroup	G/H
center	C₂	#14583219
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#365	C₂
socle	C₂×C₄₃	#481
hypercenter	#365	D₄₃
hypocenter	C₄₃	#2239
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#14583219

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
3. #14582721	C₂	semidirect
4. #14582716	C₂	semidirect
5. #14582714	C₂	semidirect
7. C₄₃×#365	C₂	semidirect
65. #365	D₄₃	semidirect
69. C₄₃	#2239	semidirect

H ≅ G/N

type

3. #14582721

C₂

semidirect

4. #14582716

C₂

semidirect

5. #14582714

C₂

semidirect

7. C₄₃×#365

C₂

semidirect

65. #365

D₄₃

semidirect

69. C₄₃

#2239

semidirect

Subgroups — #19136816

Conjugacy classes of subgroups

Complements