Group #19139837 — subgroups

Subgroups — #19139837

Order 5504.

380 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 165 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	#14582838	C₂	1	4	yes	maximal
2	#14582798	C₂	1	4	yes	maximal
3	#14582764	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₄₃	C₂	1	2	yes	maximal
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
10	C₄₃⋊#95	C₂²	1	8	yes	—
11	C₄₃⋊#95	C₂²	1	4	yes	—
12	C₄₃⋊#95	C₂²	1	4	yes	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
19	C₂²×Dic₄₃	C₂³	1	4	yes	—
20	C₂²×Dic₄₃	C₂³	1	4	yes	—
21	C₄⋊C₄×C₄₃	—	2	8	no	—
22	C₄⋊C₄×C₄₃	—	4	2	no	—
23	C₄²×C₄₃	Q₈	1	4	yes	—
24	C₄⋊Dic₄₃	—	2	4	no	—
25	C₄⋊Dic₄₃	—	2	4	no	—
26	C₄⋊Dic₄₃	—	4	4	no	—
27	C₄×Dic₄₃	—	2	8	no	—
28	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	2	8	no	—
32	C₂×C₄×C₄₃	—	2	4	no	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₄₃	#41	1	4	yes	—
36	C₂×C₄×C₄₃	#41	1	4	yes	—
37	C₂×Dic₄₃	—	2	4	no	—
38	C₂×Dic₄₃	—	2	4	no	—
39	C₂×Dic₄₃	—	2	4	no	—
40	C₂×Dic₄₃	—	2	4	no	—
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	—	2	4	no	—
43	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×C₄₃	C₂×#41	1	2	yes	—
45	C₂²×C₄₃	C₂×#41	1	2	yes	—
46	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
48	C₄×C₄₃	—	2	2	no	—
49	C₄×C₄₃	—	4	4	no	—
50	C₄×C₄₃	#125	1	8	yes	—
51	Dic₄₃	—	4	4	no	—
52	Dic₄₃	—	4	4	no	—
53	#2571	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	C₂×#125	1	2	yes	—
55	C₂×C₄₃	#544	1	1	yes	characteristic
56	C₂×C₄₃	#555	1	1	yes	characteristic
57	C₂×C₄₃	#556	1	2	yes	—
58	C₂×C₄₃	#559	1	1	yes	characteristic
59	#400	—	43	4	no	—
60	#389	—	43	4	no	—
61	#384	D₄₃	1	1	yes	characteristic
62	#382	—	43	4	no	—
63	C₄×C₄⋊C₄	—	43	2	no	—
64	C₄₃	#2571	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄⋊C₄	—	43	2	no	—
66	C₂×C₄⋊C₄	—	43	2	no	—
67	C₂×C₄⋊C₄	—	43	4	no	—
68	C₂×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
69	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
70	C₂×C₄²	—	43	4	no	—
71	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
72	#95	—	43	4	no	—
73	#95	—	43	4	no	—
74	#95	—	43	8	no	—
75	C₂²×C₄	—	43	4	no	—
76	C₂²×C₄	—	43	4	no	—
77	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
78	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
80	C₄⋊C₄	—	2	8	no	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄⋊C₄	—	86	4	no	—
83	C₄⋊C₄	—	86	4	no	—
84	C₄⋊C₄	—	172	4	no	—
85	C₄²	—	86	8	no	—
86	C₄²	Dic₈₆	1	4	yes	—
87	C₂³	C₂³×D₄₃	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	86	4	no	—
93	C₂×C₄	—	86	4	no	—
94	C₂×C₄	—	86	4	no	—
95	C₂×C₄	—	86	4	no	—
96	C₂×C₄	—	86	4	no	—
97	C₂×C₄	—	86	4	no	—
98	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
99	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
100	C₂×C₄	#10621900	1	4	yes	—
101	C₂×C₄	#10621902	1	4	yes	—
102	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
103	C₂²	C₂×#10621900	1	2	yes	—
104	C₂²	C₂×#10621902	1	2	yes	—
105	C₂²	#13063370	1	1	yes	characteristic
106	C₂²	#13063373	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	172	4	no	—
110	C₄	—	172	4	no	—
111	C₄	#13063316	1	8	yes	—
112	C₂	C₂×#13063316	1	2	yes	—
113	C₂	#14583530	1	1	yes	characteristic
114	C₂	#14583615	1	1	yes	characteristic
115	C₂	#14583623	1	2	yes	—
116	C₂	#14583635	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582838

C₂

yes

maximal

#14582798

C₂

yes

maximal

#14582764

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal

C₄₃×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

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

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

—

Dic₄₃

—

Dic₄₃

—

#2571

—

maximal, Sylow

C₂×C₄₃

C₂×#125

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

#382

—

C₄×C₄⋊C₄

—

C₄₃

#2571

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

Dic₈₆

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

100

C₂×C₄

#10621900

yes

—

101

C₂×C₄

#10621902

yes

—

102

C₂²

C₂²×Dic₈₆

yes

characteristic

103

C₂²

C₂×#10621900

yes

—

104

C₂²

C₂×#10621902

yes

—

105

C₂²

#13063370

yes

characteristic

106

C₂²

#13063373

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

172

—

110

C₄

—

172

—

111

C₄

#13063316

yes

—

112

C₂

C₂×#13063316

yes

—

113

C₂

#14583530

yes

characteristic

114

C₂

#14583615

yes

characteristic

115

C₂

#14583623

yes

—

116

C₂

#14583635

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#384	C₂
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2571
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
64. C₄₃	#2571	semidirect

H ≅ G/N

type

64. C₄₃

#2571

semidirect

Subgroups — #19139837

Conjugacy classes of subgroups

Complements