Group #19136149 — subgroups

Subgroups — #19136149

Order 5504.

210 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14582948	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582926	C₂	1	2	yes	maximal, complemented
3	#14582917	C₂	1	2	yes	maximal
4	#14582867	C₂	1	1	yes	maximal, characteristic
5	C₄₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	#13063261	—	2	2	no	—
10	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
11	#13063253	—	2	4	no	—
12	(C₂×D₄₃)⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	#117×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×C₂²⋊D₄₃	—	2	1	no	—
17	#10621898	—	2	2	no	—
18	#10621898	—	2	2	no	—
19	C₂×D₁₇₂	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₄₃	—	2	1	no	—
21	C₂×Dic₈₆	Q₈	1	1	yes	characteristic
22	M₁₆×C₄₃	—	2	2	no	—
23	C₂×C₈×C₄₃	D₄	1	2	yes	—
24	C₄⋊C₄×C₄₃	—	2	2	no	—
25	C₂²⋊C₄×C₄₃	—	2	2	no	—
26	C₄²×C₄₃	D₄	1	4	yes	—
27	#10621877	—	2	2	no	—
28	#10621877	—	2	2	no	—
29	C₂×C₄₃⋊C₈	—	2	1	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂³×C₄₃	#41	1	1	yes	characteristic
33	C₂²×D₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#41	1	2	yes	—
39	C₂²⋊D₄₃	—	4	2	no	—
40	C₂×Dic₄₃	—	2	1	no	—
41	D₁₇₂	—	2	2	no	—
42	C₄×D₄₃	—	4	1	no	—
43	C₄×D₄₃	—	4	1	no	—
44	Dic₈₆	—	2	2	no	—
45	C₈×C₄₃	—	2	2	no	—
46	C₄₃⋊C₈	—	4	1	no	—
47	C₄₃⋊C₈	—	4	2	no	—
48	C₂²×C₄₃	—	4	1	no	—
49	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₃	#123	1	2	yes	—
51	C₂×D₄₃	—	4	2	no	—
52	C₂×D₄₃	—	4	1	no	—
53	C₄×C₄₃	—	4	4	no	—
54	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
55	C₄×C₄₃	#123	1	1	yes	characteristic
56	C₄×C₄₃	#127	1	1	yes	characteristic
57	Dic₄₃	—	4	1	no	—
58	#2098	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	—	2	2	no	—
60	C₂×C₄₃	—	2	1	no	—
61	C₂×C₄₃	#399	1	1	yes	characteristic
62	D₄₃	—	8	1	no	—
63	#430	—	43	1	no	—
64	#424	—	43	2	no	—
65	#421	—	43	2	no	—
66	#408	—	43	1	no	—
67	H(3,ℤ/4)	D₄₃	1	1	yes	characteristic, complemented
68	C₄₃	#2098	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	—	43	1	no	—
70	C₂×M₁₆	—	43	2	no	—
71	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
72	C₂²×C₈	—	43	1	no	—
73	#117	C₂×D₄₃	1	2	yes	—
74	#108	—	86	2	no	—
75	C₄⋊C₈	—	86	4	no	—
76	#104	—	86	4	no	—
77	C₂²⋊C₈	—	86	2	no	—
78	#41	—	86	2	no	—
79	#41	—	86	2	no	—
80	C₂×Q₈	—	43	1	no	—
81	C₂×D₄	—	43	1	no	—
82	C₂×D₄	—	86	1	no	—
83	C₂²×C₄	—	86	1	no	—
84	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	86	2	no	—
87	M₁₆	—	86	2	no	—
88	C₂×C₈	—	86	1	no	—
89	C₂×C₈	—	86	2	no	—
90	C₂×C₈	—	86	2	no	—
91	C₂×C₈	D₁₇₂	1	2	yes	—
92	C₄⋊C₄	—	2	2	no	—
93	C₂²⋊C₄	—	2	2	no	—
94	C₄²	D₁₇₂	1	4	yes	—
95	C₂³	—	86	1	no	—
96	C₂³	#10621900	1	1	yes	characteristic
97	Q₈	—	86	2	no	—
98	D₄	—	86	2	no	—
99	D₄	—	172	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	86	1	no	—
102	C₂×C₄	—	172	1	no	—
103	C₂×C₄	—	172	1	no	—
104	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
105	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
106	C₂×C₄	#10621900	1	2	yes	—
107	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	172	1	no	—
110	C₈	—	172	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	172	2	no	—
113	C₂²	—	172	1	no	—
114	C₂²	#13063305	1	1	yes	characteristic
115	C₂²	#13063309	1	2	yes	—
116	C₄	—	4	4	no	—
117	C₄	—	172	1	no	—
118	C₄	#13063305	1	2	yes	—
119	C₄	#13063309	1	1	yes	characteristic
120	C₄	#13063322	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	344	1	no	—
124	C₂	#14582836	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic, complemented

#14582926

C₂

yes

maximal, complemented

#14582917

C₂

yes

maximal

#14582867

C₂

yes

maximal, characteristic

C₄₃×H(3,ℤ/4)

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

#13063253

—

(C₂×D₄₃)⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

Q₈

yes

characteristic

C₂×C₄×D₄₃

—

C₂×Dic₈₆

Q₈

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

#123

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2098

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#399

yes

characteristic

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2098

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

#117

C₂×D₄₃

yes

—

#108

—

C₄⋊C₈

—

#104

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₁₇₂

yes

—

C₂³

—

C₂³

#10621900

yes

characteristic

Q₈

—

D₄

—

D₄

—

172

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

172

—

103

C₂×C₄

—

172

—

104

C₂×C₄

C₂×D₁₇₂

yes

—

105

C₂×C₄

C₂×D₁₇₂

yes

characteristic

106

C₂×C₄

#10621900

yes

—

107

C₂×C₄

Q₈×D₄₃

yes

characteristic

108

C₈

—

109

C₈

—

172

—

110

C₈

—

172

—

111

C₂²

—

112

C₂²

—

172

—

113

C₂²

—

172

—

114

C₂²

#13063305

yes

characteristic

115

C₂²

#13063309

yes

—

116

C₄

—

117

C₄

—

172

—

118

C₄

#13063305

yes

—

119

C₄

#13063309

yes

characteristic

120

C₄

#13063322

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

344

—

124

C₂

#14582836

yes

characteristic

	subgroup	G/H
center	C₄	#13063322
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×H(3,ℤ/4)	C₂
socle	C₂×C₄₃	#399
hypercenter	H(3,ℤ/4)	D₄₃
hypocenter	C₄₃	#2098
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#13063322

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×H(3,ℤ/4)

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
1. #14582948	C₂	semidirect
2. #14582926	C₂	semidirect
5. C₄₃×H(3,ℤ/4)	C₂	semidirect
67. H(3,ℤ/4)	D₄₃	semidirect
68. C₄₃	#2098	semidirect

H ≅ G/N

type

1. #14582948

C₂

semidirect

2. #14582926

C₂

semidirect

5. C₄₃×H(3,ℤ/4)

C₂

semidirect

67. H(3,ℤ/4)

D₄₃

semidirect

68. C₄₃

#2098

semidirect

Subgroups — #19136149

Conjugacy classes of subgroups

Complements