Group #19136960 — subgroups

Subgroups — #19136960

Order 5504.

628 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 389 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×Q₈×Dic₄₃	C₂	1	2	yes	maximal
2	C₄⋊C₄×Dic₄₃	C₂	1	6	yes	maximal
3	C₄×C₄⋊Dic₄₃	C₂	1	3	yes	maximal
4	#14582745	C₂	1	3	yes	maximal
5	C₂×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₄₃	C₄	1	16	yes	complemented
7	C₂×C₄⋊Dic₄₃	C₂²	1	6	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
10	C₄₃⋊#95	C₂²	1	1	yes	characteristic
11	C₄₃⋊#95	C₂²	1	3	yes	—
12	C₄₃⋊#95	C₂²	1	6	yes	—
13	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
16	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
17	C₂×Q₈×C₄₃	C₂×C₄	1	8	yes	—
18	C₂×Q₈×C₄₃	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
22	C₂²×Dic₄₃	C₂³	1	2	yes	—
23	C₂²×Dic₄₃	C₂³	1	6	yes	—
24	C₄⋊C₄×C₄₃	C₂×C₄	1	12	yes	—
25	C₄²×C₄₃	C₂×C₄	1	12	yes	—
26	C₄⋊Dic₄₃	C₂×C₄	1	24	yes	—
27	C₄×Dic₄₃	—	4	6	no	—
28	C₄×Dic₄₃	C₂×C₄	1	24	yes	—
29	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
30	Q₈×C₄₃	C₄²	1	16	yes	complemented
31	C₂×C₄×C₄₃	—	2	3	no	—
32	C₂×C₄×C₄₃	—	2	3	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	12	yes	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
37	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
38	C₂×Dic₄₃	—	2	6	no	—
39	C₂×Dic₄₃	—	2	2	no	—
40	C₂×Dic₄₃	—	2	2	no	—
41	C₂×Dic₄₃	—	2	6	no	—
42	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
43	C₂×Dic₄₃	C₂²×C₄	1	12	yes	—
44	C₂²×C₄₃	C₂³×C₄	1	2	yes	—
45	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
48	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
49	C₄×C₄₃	—	2	2	no	—
50	C₄×C₄₃	—	2	6	no	—
51	C₄×C₄₃	C₂×C₄²	1	12	yes	—
52	Dic₄₃	—	2	4	no	—
53	Dic₄₃	—	2	12	no	—
54	#2276	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
56	C₂×C₄₃	#519	1	2	yes	—
57	C₂×C₄₃	#519	1	1	yes	characteristic
58	C₂×C₄₃	#520	1	2	yes	—
59	C₂×C₄₃	#520	1	1	yes	characteristic
60	C₂×C₄×Q₈	—	43	2	no	—
61	C₂×C₄×Q₈	D₄₃	1	1	yes	characteristic
62	C₄×C₄⋊C₄	—	43	6	no	—
63	C₄×C₄⋊C₄	—	43	3	no	—
64	#376	—	43	3	no	—
65	C₄₃	#2276	1	1	yes	characteristic, complemented, Sylow
66	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
67	C₄×Q₈	—	43	16	no	—
68	C₄×Q₈	Dic₄₃	1	8	yes	complemented
69	C₂×C₄⋊C₄	—	43	6	no	—
70	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
71	C₂×C₄²	—	43	6	no	—
72	C₂×C₄²	—	43	6	no	—
73	C₂×C₄²	C₂×D₄₃	1	3	yes	—
74	#95	—	43	1	no	—
75	#95	—	43	6	no	—
76	#95	—	43	3	no	—
77	C₂×Q₈	C₄×D₄₃	1	8	yes	—
78	C₂×Q₈	C₂×Dic₄₃	1	4	yes	—
79	C₂²×C₄	—	43	2	no	—
80	C₂²×C₄	—	43	6	no	—
81	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
83	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
84	C₄⋊C₄	—	43	24	no	—
85	C₄⋊C₄	C₂×Dic₄₃	1	12	yes	—
86	C₄²	—	43	24	no	—
87	C₄²	—	172	6	no	—
88	C₄²	C₂×Dic₄₃	1	12	yes	—
89	C₂³	C₂³×D₄₃	1	1	yes	characteristic
90	Q₈	C₄×Dic₄₃	1	16	yes	complemented
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	43	4	no	—
95	C₂×C₄	—	43	12	no	—
96	C₂×C₄	—	86	6	no	—
97	C₂×C₄	—	86	2	no	—
98	C₂×C₄	—	86	2	no	—
99	C₂×C₄	—	86	6	no	—
100	C₂×C₄	C₂×C₄×D₄₃	1	12	yes	—
101	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
102	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
103	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
104	C₂²	C₂²×C₄×D₄₃	1	2	yes	—
105	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
106	C₂²	#13063371	1	1	yes	characteristic
107	C₂²	#13063372	1	1	yes	characteristic
108	C₂²	#13063373	1	2	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	2	6	no	—
111	C₄	—	86	4	no	—
112	C₄	—	86	12	no	—
113	C₄	C₂×C₄×Dic₄₃	1	12	yes	—
114	C₂	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
115	C₂	#14583375	1	2	yes	—
116	C₂	#14583377	1	1	yes	characteristic
117	C₂	#14583381	1	2	yes	—
118	C₂	#14583382	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₄₃

C₂

yes

maximal

C₄⋊C₄×Dic₄₃

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal

#14582745

C₂

yes

maximal

C₂×C₄×Q₈×C₄₃

C₂

yes

maximal, characteristic

Q₈×Dic₄₃

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

characteristic

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

C₄²

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

—

Dic₄₃

—

Dic₄₃

—

#2276

—

maximal, Sylow

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

#519

yes

—

C₂×C₄₃

#519

yes

characteristic

C₂×C₄₃

#520

yes

—

C₂×C₄₃

#520

yes

characteristic

C₂×C₄×Q₈

—

C₂×C₄×Q₈

D₄₃

yes

characteristic

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

#376

—

C₄₃

#2276

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

Dic₄₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

#95

—

#95

—

#95

—

C₂×Q₈

C₄×D₄₃

yes

—

C₂×Q₈

C₂×Dic₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄²

—

C₄²

—

172

—

C₄²

C₂×Dic₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

C₄×Dic₄₃

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×C₄×D₄₃

yes

—

101

C₂×C₄

C₂²×Dic₄₃

yes

—

102

C₂×C₄

C₂²×Dic₄₃

yes

—

103

C₂×C₄

C₂²×Dic₄₃

yes

—

104

C₂²

C₂²×C₄×D₄₃

yes

—

105

C₂²

C₂³×Dic₄₃

yes

characteristic

106

C₂²

#13063371

yes

characteristic

107

C₂²

#13063372

yes

characteristic

108

C₂²

#13063373

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₂×C₄×Dic₄₃

yes

—

114

C₂

C₂²×C₄×Dic₄₃

yes

characteristic

115

C₂

#14583375

yes

—

116

C₂

#14583377

yes

characteristic

117

C₂

#14583381

yes

—

118

C₂

#14583382

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Fitting	C₂×C₄×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₃
hypocenter	C₄₃	#2276
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Fitting

C₂×C₄×Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₂×C₄×Q₈

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
6. Q₈×Dic₄₃	C₄	semidirect
14. C₄×Q₈×C₄₃	C₄	semidirect
30. Q₈×C₄₃	C₄²	semidirect
65. C₄₃	#2276	semidirect
68. C₄×Q₈	Dic₄₃	semidirect
90. Q₈	C₄×Dic₄₃	semidirect

H ≅ G/N

type

6. Q₈×Dic₄₃

C₄

semidirect

14. C₄×Q₈×C₄₃

C₄

semidirect

30. Q₈×C₄₃

C₄²

semidirect

65. C₄₃

#2276

semidirect

68. C₄×Q₈

Dic₄₃

semidirect

90. Q₈

C₄×Dic₄₃

semidirect

Subgroups — #19136960

Conjugacy classes of subgroups

Complements