Group #19142669 — subgroups

Subgroups — #19142669

Order 5504.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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	C₂×#13063319	C₂	1	2	yes	maximal, complemented
2	#14582829	C₂	1	3	yes	maximal, complemented
3	#14582821	C₂	1	6	yes	maximal, complemented
4	#14582816	C₂	1	3	yes	maximal
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
7	#13063319	—	2	8	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
9	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
10	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
11	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
12	C₄₃⋊#95	C₂²	1	3	yes	—
13	C₄₃⋊#95	C₂²	1	3	yes	—
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
15	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄₃	C₂³	1	2	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
21	C₂²×Dic₄₃	C₂³	1	6	yes	—
22	C₂×D₁₇₂	—	4	3	no	—
23	C₄⋊C₄×C₄₃	—	4	3	no	—
24	C₄⋊C₄×C₄₃	—	4	3	no	—
25	C₄²×C₄₃	D₄	1	4	yes	complemented
26	(C₂×D₄₃)⋊C₄	—	2	12	no	—
27	(C₂×D₄₃)⋊C₄	—	4	6	no	—
28	C₄⋊Dic₄₃	—	4	3	no	—
29	Dic₄₃⋊C₄	—	2	12	no	—
30	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂²×D₄₃	—	2	2	no	—
32	C₂²×D₄₃	—	2	6	no	—
33	C₂²×D₄₃	—	2	6	no	—
34	C₂×C₄×C₄₃	—	2	3	no	—
35	C₂×C₄×C₄₃	—	2	3	no	—
36	C₂×C₄×C₄₃	—	2	3	no	—
37	C₂×C₄×C₄₃	—	2	6	no	—
38	C₂×C₄×C₄₃	—	2	3	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
40	C₂×Dic₄₃	—	2	6	no	—
41	C₂×Dic₄₃	—	2	6	no	—
42	C₂×Dic₄₃	—	2	6	no	—
43	D₁₇₂	—	4	4	no	—
44	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
45	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
46	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
47	C₂×D₄₃	—	4	6	no	—
48	C₂×D₄₃	—	4	2	no	—
49	C₂×D₄₃	—	4	6	no	—
50	C₄×C₄₃	—	2	6	no	—
51	C₄×C₄₃	—	4	1	no	—
52	C₄×C₄₃	—	4	3	no	—
53	Dic₄₃	—	4	6	no	—
54	#2823	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	#537	1	3	yes	—
56	C₂×C₄₃	#560	1	1	yes	characteristic
57	C₂×C₄₃	#563	1	3	yes	—
58	D₄₃	—	8	2	no	—
59	C₂×#126	—	43	2	no	—
60	#398	—	43	3	no	—
61	#396	—	43	6	no	—
62	#394	—	43	3	no	—
63	#384	D₄₃	1	1	yes	characteristic, complemented
64	C₄₃	#2823	1	1	yes	characteristic, complemented, Sylow
65	C₂²×D₄	—	43	1	no	—
66	#126	—	86	8	no	—
67	C₂×C₄⋊C₄	—	43	6	no	—
68	C₂×C₄⋊C₄	—	43	3	no	—
69	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
70	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
71	C₂×C₂²⋊C₄	—	43	6	no	—
72	C₂×C₂²⋊C₄	—	43	6	no	—
73	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
74	#95	—	43	3	no	—
75	#95	—	43	3	no	—
76	C₂⁴	—	43	2	no	—
77	C₂×D₄	—	172	3	no	—
78	C₂²×C₄	—	43	6	no	—
79	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
80	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
81	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
82	C₄⋊C₄	—	4	3	no	—
83	C₄⋊C₄	—	4	3	no	—
84	C₄⋊C₄	—	86	12	no	—
85	C₄⋊C₄	—	172	3	no	—
86	C₂²⋊C₄	—	86	12	no	—
87	C₂²⋊C₄	—	172	6	no	—
88	C₄²	D₁₇₂	1	4	yes	complemented
89	C₂³	—	86	2	no	—
90	C₂³	—	86	6	no	—
91	C₂³	—	86	6	no	—
92	C₂³	C₂³×D₄₃	1	1	yes	characteristic
93	D₄	—	172	4	no	—
94	C₂×C₄	—	2	3	no	—
95	C₂×C₄	—	2	3	no	—
96	C₂×C₄	—	2	6	no	—
97	C₂×C₄	—	2	3	no	—
98	C₂×C₄	—	2	3	no	—
99	C₂×C₄	—	86	6	no	—
100	C₂×C₄	—	86	6	no	—
101	C₂×C₄	—	86	6	no	—
102	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
103	C₂²	—	172	2	no	—
104	C₂²	—	172	6	no	—
105	C₂²	—	172	6	no	—
106	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
107	C₂²	#13063370	1	3	yes	—
108	C₂²	#13063373	1	3	yes	—
109	C₄	—	2	6	no	—
110	C₄	—	4	1	no	—
111	C₄	—	4	3	no	—
112	C₄	—	172	6	no	—
113	C₂	—	344	2	no	—
114	C₂	#14583480	1	3	yes	—
115	C₂	#14583636	1	1	yes	characteristic
116	C₂	#14583648	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063319

C₂

yes

maximal, complemented

#14582829

C₂

yes

maximal, complemented

#14582821

C₂

yes

maximal, complemented

#14582816

C₂

yes

maximal

C₄₃×#384

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

characteristic

#13063319

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#2823

—

maximal, Sylow

C₂×C₄₃

#537

yes

—

C₂×C₄₃

#560

yes

characteristic

C₂×C₄₃

#563

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2823

yes

characteristic, complemented, Sylow

C₂²×D₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

#95

—

C₂⁴

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₃

yes

characteristic

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂×D₁₇₂

yes

—

103

C₂²

—

172

—

104

C₂²

—

172

—

105

C₂²

—

172

—

106

C₂²

C₂²×D₁₇₂

yes

characteristic

107

C₂²

#13063370

yes

—

108

C₂²

#13063373

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

172

—

113

C₂

—

344

—

114

C₂

#14583480

yes

—

115

C₂

#14583636

yes

characteristic

116

C₂

#14583648

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#384	C₂
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2823
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#384

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
1. C₂×#13063319	C₂	semidirect
2. #14582829	C₂	semidirect
3. #14582821	C₂	semidirect
5. C₄₃×#384	C₂	semidirect
25. C₄²×C₄₃	D₄	semidirect
63. #384	D₄₃	semidirect
64. C₄₃	#2823	semidirect
88. C₄²	D₁₇₂	semidirect

H ≅ G/N

type

1. C₂×#13063319

C₂

semidirect

2. #14582829

C₂

semidirect

3. #14582821

C₂

semidirect

5. C₄₃×#384

C₂

semidirect

25. C₄²×C₄₃

D₄

semidirect

63. #384

D₄₃

semidirect

64. C₄₃

#2823

semidirect

88. C₄²

D₁₇₂

semidirect

Subgroups — #19142669

Conjugacy classes of subgroups

Complements