Group #19143166 — subgroups

Subgroups — C₂²×#13063256 #19143166

Order 5504.

600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 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	C₂³×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063256	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₃	—	2	1	no	—
6	C₂²×C₄₃⋊C₈	C₄	1	8	yes	complemented
7	C₂²×C₄₃⋊C₈	C₂²	1	6	yes	—
8	C₂×C₄⋊Dic₄₃	—	2	3	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	6	yes	—
10	#13063256	C₂²	1	16	yes	direct product factor
11	C₂³×C₄×C₄₃	—	2	1	no	—
12	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₃	—	2	3	no	—
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	6	yes	—
15	C₂⁴×C₄₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	—	2	6	no	—
17	C₂²×C₄×C₄₃	—	4	4	no	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₃	D₄	1	3	yes	—
20	C₂²×C₄×C₄₃	Q₈	1	4	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
22	C₂²×Dic₄₃	—	2	6	no	—
23	C₂²×Dic₄₃	—	4	4	no	—
24	C₄⋊C₄×C₄₃	—	2	6	no	—
25	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
26	C₄⋊Dic₄₃	—	2	6	no	—
27	C₄⋊Dic₄₃	C₂³	1	4	yes	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	24	yes	complemented
29	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
30	C₂³×C₄₃	C₄⋊C₄	1	4	yes	—
31	C₂³×C₄₃	SD₁₆	1	4	yes	—
32	C₂³×C₄₃	SD₁₆	1	4	yes	—
33	C₂³×C₄₃	C₂×D₄	1	3	yes	—
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	—	4	12	no	—
36	C₂×C₄×C₄₃	C₄⋊C₄	1	12	yes	—
37	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
38	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
39	C₂×C₄×C₄₃	C₂×Q₈	1	6	yes	—
40	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	—	4	12	no	—
43	C₄₃⋊C₈	C₂²×C₄	1	8	yes	complemented
44	C₂²×C₄₃	#106	1	16	yes	complemented
45	C₂²×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
46	C₂²×C₄₃	C₂×SD₁₆	1	6	yes	—
47	C₂²×C₄₃	C₂×SD₁₆	1	6	yes	—
48	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
49	C₄×C₄₃	—	4	4	no	—
50	C₄×C₄₃	C₂×C₄⋊C₄	1	6	yes	—
51	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
52	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
53	Dic₄₃	—	4	4	no	—
54	C₂²×#106	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	C₂×#106	1	12	yes	complemented
56	C₂×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
58	C₂×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
59	C₂³×C₈	—	43	1	no	—
60	C₂²×C₄⋊C₄	—	43	1	no	—
61	C₂²×C₄⋊C₄	D₄₃	1	1	yes	characteristic
62	C₂×#106	—	43	12	no	—
63	C₄₃	C₂²×#106	1	1	yes	characteristic, complemented, Sylow
64	C₂³×C₄	—	2	1	no	—
65	C₂³×C₄	—	86	1	no	—
66	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
67	C₂²×C₈	—	43	6	no	—
68	C₂²×C₈	—	43	8	no	—
69	C₂×C₄⋊C₄	—	2	3	no	—
70	C₂×C₄⋊C₄	—	43	6	no	—
71	C₂×C₄⋊C₄	—	86	3	no	—
72	C₂×C₄⋊C₄	C₂×D₄₃	1	6	yes	—
73	#106	—	43	16	no	—
74	C₂⁴	C₂²⋊D₄₃	1	1	yes	characteristic
75	C₂²×C₄	—	2	6	no	—
76	C₂²×C₄	—	4	4	no	—
77	C₂²×C₄	—	86	6	no	—
78	C₂²×C₄	—	172	4	no	—
79	C₂²×C₄	Dic₈₆	1	4	yes	—
80	C₂²×C₄	C₄×D₄₃	1	4	yes	—
81	C₂²×C₄	C₂²⋊D₄₃	1	3	yes	—
82	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
83	C₂×C₈	—	43	24	no	—
84	C₂×C₈	—	43	4	no	—
85	C₄⋊C₄	—	2	6	no	—
86	C₄⋊C₄	—	43	4	no	—
87	C₄⋊C₄	—	86	6	no	—
88	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
89	C₂³	Dic₄₃⋊C₄	1	4	yes	—
90	C₂³	#10621883	1	4	yes	—
91	C₂³	#10621884	1	4	yes	—
92	C₂³	C₂×C₂²⋊D₄₃	1	3	yes	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	4	12	no	—
95	C₂×C₄	—	86	4	no	—
96	C₂×C₄	—	172	12	no	—
97	C₂×C₄	Dic₄₃⋊C₄	1	12	yes	—
98	C₂×C₄	C₂×Dic₈₆	1	6	yes	—
99	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
100	C₂×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
101	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
102	C₈	—	43	8	no	—
103	C₂²	#13063256	1	16	yes	direct product factor
104	C₂²	C₂×Dic₄₃⋊C₄	1	6	yes	—
105	C₂²	C₂×#10621884	1	6	yes	—
106	C₂²	C₂×#10621883	1	6	yes	—
107	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
108	C₄	—	4	4	no	—
109	C₄	—	172	4	no	—
110	C₄	C₂×Dic₄₃⋊C₄	1	6	yes	—
111	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
112	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
113	C₂	C₂×#13063256	1	12	yes	direct product factor
114	C₂	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
115	C₂	C₂²×#10621884	1	1	yes	characteristic
116	C₂	C₂²×#10621883	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

C₂×#13063256

C₂

yes

maximal, direct product factor

C₂²×C₄⋊C₄×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

—

C₂²×C₄₃⋊C₈

C₄

yes

complemented

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063256

C₂²

yes

direct product factor

C₂³×C₄×C₄₃

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

complemented

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₄⋊C₄

yes

—

C₂³×C₄₃

SD₁₆

yes

—

C₂³×C₄₃

SD₁₆

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

C₂²×C₄

yes

complemented

C₂²×C₄₃

#106

yes

complemented

C₂²×C₄₃

C₂×C₄⋊C₄

yes

—

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₂²×C₄₃

C₂×SD₁₆

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂²×Q₈

yes

characteristic

Dic₄₃

—

C₂²×#106

—

maximal, Sylow

C₂×C₄₃

C₂×#106

yes

complemented

C₂×C₄₃

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₃

C₂²×SD₁₆

yes

characteristic

C₂×C₄₃

C₂²×SD₁₆

yes

characteristic

C₂³×C₈

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

D₄₃

yes

characteristic

C₂×#106

—

C₄₃

C₂²×#106

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

#106

—

C₂⁴

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

Dic₈₆

yes

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₂³

Dic₄₃⋊C₄

yes

—

C₂³

#10621883

yes

—

C₂³

#10621884

yes

—

C₂³

C₂×C₂²⋊D₄₃

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

100

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

101

C₂×C₄

C₂³×D₄₃

yes

characteristic

102

C₈

—

103

C₂²

#13063256

yes

direct product factor

104

C₂²

C₂×Dic₄₃⋊C₄

yes

—

105

C₂²

C₂×#10621884

yes

—

106

C₂²

C₂×#10621883

yes

—

107

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

108

C₄

—

109

C₄

—

172

—

110

C₄

C₂×Dic₄₃⋊C₄

yes

—

111

C₄

C₂²×C₄×D₄₃

yes

characteristic

112

C₄

C₂²×Dic₈₆

yes

characteristic

113

C₂

C₂×#13063256

yes

direct product factor

114

C₂

C₂²×Dic₄₃⋊C₄

yes

characteristic

115

C₂

C₂²×#10621884

yes

characteristic

116

C₂

C₂²×#10621883

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂²×C₄⋊C₄×C₄₃	C₂
socle	C₂⁴×C₄₃	D₄
hypercenter	C₂²×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₂²×#106
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₄

subgroup

G/H

center

C₂⁴

C₂²⋊D₄₃

commutator

C₄×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂²×C₄⋊C₄×C₄₃

C₂

socle

C₂⁴×C₄₃

D₄

hypercenter

C₂²×C₄⋊C₄

D₄₃

hypocenter

C₄₃

C₂²×#106

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₄

N	H ≅ G/N	type
3. C₂×#13063256	C₂	direct (N × H)
6. C₂²×C₄₃⋊C₈	C₄	semidirect
10. #13063256	C₂²	direct (N × H)
28. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
43. C₄₃⋊C₈	C₂²×C₄	semidirect
44. C₂²×C₄₃	#106	semidirect
55. C₂×C₄₃	C₂×#106	semidirect
63. C₄₃	C₂²×#106	semidirect
103. C₂²	#13063256	direct (N × H)
113. C₂	C₂×#13063256	direct (N × H)

H ≅ G/N

type

3. C₂×#13063256

C₂

direct (N × H)

6. C₂²×C₄₃⋊C₈

C₄

semidirect

10. #13063256

C₂²

direct (N × H)

28. C₂×C₄₃⋊C₈

C₂×C₄

semidirect

43. C₄₃⋊C₈

C₂²×C₄

semidirect

44. C₂²×C₄₃

#106

semidirect

55. C₂×C₄₃

C₂×#106

semidirect

63. C₄₃

C₂²×#106

semidirect

103. C₂²

#13063256

direct (N × H)

113. C₂

C₂×#13063256

direct (N × H)

Subgroups — C₂²×#13063256 #19143166

Conjugacy classes of subgroups

Complements

Subgroups — C22×#13063256 #19143166

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13063256 #19143166