Group #19133188 — subgroups

Subgroups — #19133188

Order 5504.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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	#14583455	C₂	1	1	yes	maximal, characteristic
2	#14582851	C₂	1	2	yes	maximal
3	#14582641	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582640	C₂	1	2	yes	maximal, complemented
5	C₄₃×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621872	—	2	2	no	—
7	#13063324	C₄	1	2	yes	—
8	#13063317	C₂²	1	1	yes	characteristic
9	#13063303	—	2	2	no	—
10	#13063290	—	2	2	no	—
11	#13063283	C₄	1	2	yes	—
12	C₄²×D₄₃	C₂²	1	1	yes	characteristic
13	#13063236	C₂²	1	2	yes	—
14	C₈×Dic₄₃	—	2	2	no	—
15	#125×C₄₃	C₂²	1	1	yes	characteristic
16	#97×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₄₃	D₄	1	2	yes	—
19	C₂×Dic₈₆	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	(C₂×D₄₃)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
26	Dic₄₃⋊C₄	—	2	2	no	—
27	Dic₄₃⋊C₄	—	2	2	no	—
28	C₄×Dic₄₃	—	2	2	no	—
29	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₄₃	D₄	1	2	yes	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	#10621872	—	2	8	no	—
33	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
37	C₂×Dic₄₃	—	2	2	no	—
38	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
40	C₄×D₄₃	—	2	2	no	—
41	C₄×D₄₃	—	2	4	no	—
42	Dic₈₆	—	4	4	no	—
43	C₈×C₄₃	—	2	4	no	—
44	C₄₃⋊C₈	—	2	4	no	—
45	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₄₃	—	2	1	no	—
47	C₂×D₄₃	—	2	2	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	2	no	—
50	C₄×C₄₃	—	4	2	no	—
51	Dic₄₃	—	4	2	no	—
52	Dic₄₃	#101	1	2	yes	—
53	Dic₄₃	#104	1	4	yes	—
54	#1526	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	C₂×#101	1	1	yes	characteristic
56	C₂×C₄₃	C₂×#104	1	2	yes	—
57	D₄₃	—	4	1	no	—
58	#533	—	43	1	no	—
59	C₄×M₁₆	—	43	2	no	—
60	#330	—	43	1	no	—
61	#330	—	43	2	no	—
62	#330	D₄₃	1	1	yes	characteristic, complemented
63	C₄₃	#1526	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	86	2	no	—
65	C₄⋊Q₈	—	43	2	no	—
66	#125	—	43	1	no	—
67	#125	C₂×D₄₃	1	1	yes	characteristic
68	C₂²⋊Q₈	—	86	2	no	—
69	C₄×Q₈	—	86	2	no	—
70	#117	—	43	2	no	—
71	C₂×C₄²	—	43	1	no	—
72	#97	—	43	2	no	—
73	#97	C₂×D₄₃	1	2	yes	—
74	C₄×C₈	—	86	2	no	—
75	C₂×Q₈	—	86	2	no	—
76	C₂²×C₄	—	43	1	no	—
77	C₂²×C₄	—	43	2	no	—
78	M₁₆	—	86	8	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	86	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	43	2	no	—
83	C₄⋊C₄	—	86	2	no	—
84	C₄⋊C₄	—	86	2	no	—
85	C₄⋊C₄	C₄×D₄₃	1	2	yes	—
86	C₂²⋊C₄	—	86	2	no	—
87	C₄²	—	43	1	no	—
88	C₄²	—	43	2	no	—
89	C₄²	—	86	2	no	—
90	C₄²	C₂²×D₄₃	1	1	yes	characteristic
91	C₂³	—	43	1	no	—
92	Q₈	—	172	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	43	1	no	—
95	C₂×C₄	—	43	2	no	—
96	C₂×C₄	—	86	4	no	—
97	C₂×C₄	—	86	2	no	—
98	C₂×C₄	—	86	2	no	—
99	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
100	C₂×C₄	D₄×D₄₃	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	—	86	4	no	—
103	C₂²	—	86	1	no	—
104	C₂²	—	86	2	no	—
105	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	2	no	—
108	C₄	—	4	2	no	—
109	C₄	—	43	2	no	—
110	C₄	—	43	4	no	—
111	C₄	—	172	2	no	—
112	C₂	—	172	1	no	—
113	C₂	#101×D₄₃	1	1	yes	characteristic
114	C₂	#104×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583455

C₂

yes

maximal, characteristic

#14582851

C₂

yes

maximal

#14582641

C₂

yes

maximal, characteristic, complemented

#14582640

C₂

yes

maximal, complemented

C₄₃×#330

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

—

#13063324

C₄

yes

—

#13063317

C₂²

yes

—

—

C₄

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

#13063236

C₂²

yes

—

C₈×Dic₄₃

—

#125×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

#10621872

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

#101

yes

—

Dic₄₃

#104

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

#533

—

C₄×M₁₆

—

#330

—

#330

—

#330

D₄₃

yes

characteristic, complemented

C₄₃

#1526

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#97

—

#97

C₂×D₄₃

yes

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

100

C₂×C₄

D₄×D₄₃

yes

—

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

172

—

112

C₂

—

172

—

113

C₂

#101×D₄₃

yes

characteristic

114

C₂

#104×D₄₃

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#330	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#330	D₄₃
hypocenter	C₄₃	#1526
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#330

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #14582641	C₂	semidirect
4. #14582640	C₂	semidirect
5. C₄₃×#330	C₂	semidirect
62. #330	D₄₃	semidirect
63. C₄₃	#1526	semidirect

H ≅ G/N

type

3. #14582641

C₂

semidirect

4. #14582640

C₂

semidirect

5. C₄₃×#330

C₂

semidirect

62. #330

D₄₃

semidirect

63. C₄₃

#1526

semidirect

Subgroups — #19133188

Conjugacy classes of subgroups

Complements