Group #19142632 — subgroups

Subgroups — #19142632

Order 5504.

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

normal subgroups only

This group has 444 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	C₂×#13063304	C₂	1	2	yes	maximal
2	#14582839	C₂	1	4	yes	maximal, complemented
3	#14582824	C₂	1	4	yes	maximal
4	#14582820	C₂	1	4	yes	maximal, complemented
5	C₄₃×#381	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	2	yes	—
7	#13063304	—	2	8	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
10	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
11	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
12	C₄₃⋊#95	C₂²	1	8	yes	—
13	C₄₃⋊#95	C₂²	1	4	yes	—
14	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
16	#95×C₄₃	C₂²	1	4	yes	—
17	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	—	4	2	no	—
19	C₂²×C₄×C₄₃	D₄	1	4	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
22	C₂²×Dic₄₃	C₂³	1	4	yes	—
23	C₂²×Dic₄₃	C₂³	1	4	yes	—
24	C₂×Dic₈₆	—	2	4	no	—
25	C₂×Dic₈₆	—	4	4	no	—
26	C₂²⋊C₄×C₄₃	—	4	2	no	—
27	C₂²⋊Dic₄₃	—	2	8	no	—
28	C₄⋊Dic₄₃	—	2	4	no	—
29	C₄⋊Dic₄₃	—	4	4	no	—
30	Dic₄₃⋊C₄	—	2	8	no	—
31	C₂³×C₄₃	—	2	2	no	—
32	C₂³×C₄₃	—	2	4	no	—
33	C₂³×C₄₃	C₂×D₄	1	2	yes	—
34	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	—	2	4	no	—
37	C₂×C₄×C₄₃	—	2	8	no	—
38	C₂×C₄×C₄₃	—	4	4	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
40	C₂×Dic₄₃	—	2	4	no	—
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	—	2	8	no	—
43	C₂×Dic₄₃	—	2	8	no	—
44	Dic₈₆	—	4	8	no	—
45	C₂²×C₄₃	—	2	2	no	—
46	C₂²×C₄₃	—	2	4	no	—
47	C₂²×C₄₃	—	4	4	no	—
48	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
49	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
50	C₂²×C₄₃	2₋¹⁺⁴	1	4	yes	—
51	C₄×C₄₃	—	2	4	no	—
52	C₄×C₄₃	—	4	4	no	—
53	Dic₄₃	—	4	4	no	—
54	Dic₄₃	—	4	4	no	—
55	#2817	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	—	4	2	no	—
57	C₂×C₄₃	#534	1	1	yes	characteristic
58	C₂×C₄₃	#536	1	2	yes	—
59	C₂×C₄₃	#563	1	4	yes	—
60	C₂×C₂²⋊Q₈	—	43	2	no	—
61	#400	—	43	4	no	—
62	#397	—	43	4	no	—
63	#395	—	43	4	no	—
64	#381	D₄₃	1	1	yes	characteristic
65	C₄₃	#2817	1	1	yes	characteristic, complemented, Sylow
66	C₂²×Q₈	—	43	2	no	—
67	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
68	C₂²⋊Q₈	—	86	8	no	—
69	C₂×C₄⋊C₄	—	43	4	no	—
70	C₂×C₄⋊C₄	—	43	2	no	—
71	C₂×C₄⋊C₄	—	43	4	no	—
72	C₂×C₂²⋊C₄	—	43	4	no	—
73	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
74	#95	—	43	8	no	—
75	#95	—	43	4	no	—
76	#95	C₂×D₄₃	1	4	yes	—
77	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
78	C₂×Q₈	—	86	4	no	—
79	C₂×Q₈	—	172	4	no	—
80	C₂²×C₄	—	4	2	no	—
81	C₂²×C₄	—	43	4	no	—
82	C₂²×C₄	—	43	4	no	—
83	C₂²×C₄	D₁₇₂	1	4	yes	—
84	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
85	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
86	C₄⋊C₄	—	86	8	no	—
87	C₄⋊C₄	—	86	4	no	—
88	C₄⋊C₄	—	172	4	no	—
89	C₂²⋊C₄	—	4	2	no	—
90	C₂²⋊C₄	—	86	8	no	—
91	C₂³	—	2	2	no	—
92	C₂³	—	2	4	no	—
93	C₂³	C₂×D₁₇₂	1	2	yes	—
94	C₂³	C₂³×D₄₃	1	1	yes	characteristic
95	Q₈	—	172	8	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	2	8	no	—
99	C₂×C₄	—	4	4	no	—
100	C₂×C₄	—	86	4	no	—
101	C₂×C₄	—	86	4	no	—
102	C₂×C₄	—	86	8	no	—
103	C₂×C₄	—	86	8	no	—
104	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	4	no	—
107	C₂²	—	4	4	no	—
108	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
109	C₂²	#13063370	1	2	yes	—
110	C₂²	#13063372	1	4	yes	—
111	C₄	—	2	4	no	—
112	C₄	—	4	4	no	—
113	C₄	—	172	4	no	—
114	C₄	—	172	4	no	—
115	C₂	—	4	2	no	—
116	C₂	#14583461	1	1	yes	characteristic
117	C₂	#14583475	1	2	yes	—
118	C₂	#14583652	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063304

C₂

yes

maximal

#14582839

C₂

yes

maximal, complemented

#14582824

C₂

yes

maximal

#14582820

C₂

yes

maximal, complemented

C₄₃×#381

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

#13063304

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2817

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#534

yes

characteristic

C₂×C₄₃

#536

yes

—

C₂×C₄₃

#563

yes

—

C₂×C₂²⋊Q₈

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2817

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

#95

—

#95

—

#95

C₂×D₄₃

yes

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

C₂×D₁₇₂

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₁₇₂

yes

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

C₂²×D₁₇₂

yes

characteristic

109

C₂²

#13063370

yes

—

110

C₂²

#13063372

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

172

—

114

C₄

—

172

—

115

C₂

—

116

C₂

#14583461

yes

characteristic

117

C₂

#14583475

yes

—

118

C₂

#14583652

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#381	C₂
hypercenter	#381	D₄₃
hypocenter	C₄₃	#2817
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#381

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
2. #14582839	C₂	semidirect
4. #14582820	C₂	semidirect
65. C₄₃	#2817	semidirect

H ≅ G/N

type

2. #14582839

C₂

semidirect

4. #14582820

C₂

semidirect

65. C₄₃

#2817

semidirect

Subgroups — #19142632

Conjugacy classes of subgroups

Complements