Group #19132879 — subgroups

Subgroups — #19132879

Order 5504.

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

normal subgroups only

This group has 212 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	#14582952	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#14582621	C₂	1	2	yes	maximal, complemented
4	C₈×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄₃×#431	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₄	1	2	yes	—
7	C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
8	C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
9	C₄×C₄₃⋊C₈	C₄	1	2	yes	—
10	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	C₄	1	2	yes	—
15	C₂²⋊C₈×C₄₃	C₄	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
21	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄₃⋊C₈	C₈	1	8	yes	complemented
26	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂³×C₄₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	2	no	—
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₈×C₄₃	—	2	4	no	—
40	C₄₃⋊C₈	—	2	4	no	—
41	C₄₃⋊C₈	C₂×C₈	1	4	yes	—
42	C₄₃⋊C₈	C₂×C₈	1	4	yes	—
43	C₂²×C₄₃	—	2	1	no	—
44	C₂²×C₄₃	—	2	1	no	—
45	C₂²×C₄₃	C₄×C₈	1	2	yes	—
46	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	C₄×C₈	1	2	yes	—
50	C₄×C₄₃	C₂²×C₈	1	2	yes	—
51	C₄×C₄₃	#131	1	2	yes	—
52	C₄×C₄₃	#131	1	2	yes	—
53	#1450	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	2	no	—
55	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
56	C₂×C₄₃	#405	1	1	yes	characteristic
57	C₂×C₄₃	#405	1	1	yes	characteristic
58	#431	—	43	1	no	—
59	#431	D₄₃	1	1	yes	characteristic
60	C₂×C₄×C₈	—	43	1	no	—
61	#322	—	43	2	no	—
62	C₈²	—	43	2	no	—
63	C₄₃	#1450	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	43	2	no	—
65	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
66	C₄⋊C₈	—	43	2	no	—
67	C₄⋊C₈	Dic₄₃	1	2	yes	—
68	C₂²⋊C₈	—	43	2	no	—
69	C₂²⋊C₈	Dic₄₃	1	2	yes	—
70	C₄×C₈	—	43	1	no	—
71	C₄×C₈	—	43	2	no	—
72	C₄×C₈	—	43	1	no	—
73	C₄×C₈	—	43	2	no	—
74	C₄×C₈	C₂×D₄₃	1	2	yes	—
75	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
76	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
77	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
78	C₂×C₈	—	43	8	no	—
79	C₂×C₈	—	43	2	no	—
80	C₂×C₈	—	43	2	no	—
81	C₂×C₈	—	43	4	no	—
82	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
83	C₄²	C₄×D₄₃	1	1	yes	characteristic
84	C₄²	C₄×D₄₃	1	1	yes	characteristic
85	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
86	C₄²	C₂²×D₄₃	1	1	yes	characteristic
87	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	C₈×D₄₃	1	4	yes	—
91	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
92	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
93	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
96	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
97	C₈	—	2	4	no	—
98	C₈	—	43	4	no	—
99	C₈	—	43	4	no	—
100	C₈	—	86	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	C₈×Dic₄₃	1	2	yes	—
104	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	C₈×Dic₄₃	1	2	yes	—
108	C₄	C₂×C₈×D₄₃	1	2	yes	—
109	C₄	#13063332	1	2	yes	—
110	C₄	#13063333	1	2	yes	—
111	C₂	—	2	2	no	—
112	C₂	C₂×C₈×Dic₄₃	1	1	yes	characteristic
113	C₂	#14582855	1	1	yes	characteristic
114	C₂	#14582857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582952

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#14582621

C₂

yes

maximal, complemented

C₈×C₄₃⋊C₈

C₂

yes

maximal, complemented

C₄₃×#431

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

—

C₂²⋊(C₄₃⋊C₈)

C₄

yes

—

C₄×C₄₃⋊C₈

C₄

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₄

yes

—

C₂²⋊C₈×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₈

yes

complemented

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂×C₈

yes

—

C₄₃⋊C₈

C₂×C₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×C₈

yes

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×C₈

yes

—

C₄×C₄₃

C₂²×C₈

yes

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

#131

yes

—

#1450

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄×C₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₂×C₄×C₈

—

#322

—

C₈²

—

C₄₃

#1450

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

Dic₄₃

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₄×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

—

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₈×Dic₄₃

yes

—

104

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

C₈×Dic₄₃

yes

—

108

C₄

C₂×C₈×D₄₃

yes

—

109

C₄

#13063332

yes

—

110

C₄

#13063333

yes

—

111

C₂

—

112

C₂

C₂×C₈×Dic₄₃

yes

characteristic

113

C₂

#14582855

yes

characteristic

114

C₂

#14582857

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Fitting	C₄₃×#431	C₂
socle	C₂²×C₄₃	C₂×C₄²
hypercenter	#431	D₄₃
hypocenter	C₄₃	#1450
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #431

subgroup

G/H

center, Frattini

C₄²

C₂²×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Fitting

C₄₃×#431

C₂

socle

C₂²×C₄₃

C₂×C₄²

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₄² ◁ #431

N	H ≅ G/N	type
3. #14582621	C₂	semidirect
4. C₈×C₄₃⋊C₈	C₂	semidirect
25. C₂×C₄₃⋊C₈	C₈	semidirect
63. C₄₃	#1450	semidirect

H ≅ G/N

type

3. #14582621

C₂

semidirect

4. C₈×C₄₃⋊C₈

C₂

semidirect

25. C₂×C₄₃⋊C₈

C₈

semidirect

63. C₄₃

#1450

semidirect

Subgroups — #19132879

Conjugacy classes of subgroups

Complements