Group #19145097 — subgroups

Subgroups — C₂×#14583299 #19145097

Order 5504.

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

normal subgroups only

This group has 360 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	C₂×#13063316	C₂	1	2	yes	maximal
2	#14583299	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063258	C₂	1	2	yes	maximal
4	C₂×#13063257	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#106×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
8	#13063316	—	2	4	no	—
9	#13063316	C₂²	1	8	yes	—
10	C₂×C₄⋊Dic₄₃	—	2	2	no	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	#13063258	C₂²	1	8	yes	—
15	#13063257	C₂²	1	4	yes	—
16	C₈×Dic₄₃	C₂²	1	4	yes	—
17	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
19	#106×C₄₃	C₂²	1	4	yes	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₃	—	2	2	no	—
23	C₂²×Dic₄₃	D₄	1	2	yes	—
24	C₂×C₈×C₄₃	Q₈	1	4	yes	—
25	C₂×C₈×C₄₃	C₂³	1	2	yes	—
26	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₄⋊Dic₄₃	—	2	8	no	—
30	C₄⋊Dic₄₃	C₂³	1	4	yes	—
31	Dic₄₃⋊C₄	—	2	8	no	—
32	C₄×Dic₄₃	D₄	1	2	yes	—
33	C₄×Dic₄₃	C₂³	1	2	yes	—
34	C₂×C₄₃⋊C₈	Q₈	1	4	yes	—
35	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
36	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	4	4	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
42	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
43	C₂×Dic₄₃	—	2	4	no	—
44	C₂×Dic₄₃	—	2	4	no	—
45	C₂×Dic₄₃	—	4	4	no	—
46	C₂×Dic₄₃	C₂×D₄	1	4	yes	—
47	C₈×C₄₃	C₂×Q₈	1	4	yes	—
48	C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
49	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
50	C₂²×C₄₃	#135	1	4	yes	—
51	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
52	C₄×C₄₃	—	4	4	no	—
53	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
54	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
55	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
56	Dic₄₃	—	2	4	no	—
57	Dic₄₃	—	4	4	no	—
58	C₂×#499	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	#499	1	4	yes	complemented
60	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
61	C₂×C₄₃	C₂×#135	1	2	yes	—
62	C₂×#125	—	43	2	no	—
63	#499	—	43	8	no	—
64	C₂×#107	—	43	2	no	—
65	C₂×#106	—	43	1	no	—
66	C₂×#106	D₄₃	1	1	yes	characteristic
67	C₂×C₄×C₈	—	43	1	no	—
68	C₄₃	C₂×#499	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	43	1	no	—
70	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
71	#125	—	43	8	no	—
72	#125	—	86	4	no	—
73	C₂×C₄⋊C₄	—	43	2	no	—
74	C₂×C₄⋊C₄	—	86	2	no	—
75	C₂×C₄⋊C₄	—	86	2	no	—
76	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
77	C₂×C₄²	—	43	1	no	—
78	#107	—	43	8	no	—
79	#106	—	43	4	no	—
80	#106	C₂×D₄₃	1	4	yes	—
81	C₄×C₈	—	43	4	no	—
82	C₂²×C₄	—	2	2	no	—
83	C₂²×C₄	—	43	2	no	—
84	C₂²×C₄	—	86	2	no	—
85	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
86	C₂×C₈	—	43	4	no	—
87	C₂×C₈	—	43	2	no	—
88	C₂×C₈	Dic₈₆	1	4	yes	—
89	C₂×C₈	C₂²×D₄₃	1	2	yes	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	43	4	no	—
92	C₄⋊C₄	—	86	8	no	—
93	C₄⋊C₄	—	86	8	no	—
94	C₄⋊C₄	—	86	2	no	—
95	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
96	C₄²	—	43	2	no	—
97	C₄²	—	43	2	no	—
98	C₂³	D₄×D₄₃	1	1	yes	characteristic
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	4	4	no	—
101	C₂×C₄	—	43	4	no	—
102	C₂×C₄	—	86	4	no	—
103	C₂×C₄	—	86	4	no	—
104	C₂×C₄	—	172	4	no	—
105	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
106	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₄₃	1	2	yes	—
108	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
109	C₈	—	43	4	no	—
110	C₈	C₂×Dic₈₆	1	4	yes	—
111	C₂²	#13063324	1	2	yes	—
112	C₂²	#13063346	1	4	yes	—
113	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
114	C₄	—	4	4	no	—
115	C₄	—	86	4	no	—
116	C₄	—	172	4	no	—
117	C₄	#13063324	1	2	yes	—
118	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
119	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
120	C₂	#14583299	1	4	yes	direct product factor
121	C₂	C₂×#13063324	1	1	yes	characteristic
122	C₂	C₂×#13063346	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063316

C₂

yes

maximal

#14583299

C₂

yes

maximal, direct product factor

C₂×#13063258

C₂

yes

maximal

C₂×#13063257

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₃

C₂

yes

maximal, characteristic

C₂×#106×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063316

—

#13063316

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063258

C₂²

yes

—

#13063257

C₂²

yes

—

C₈×Dic₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#106×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₄₃⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

#135

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂²×Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

C₂×#135

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₂×C₄×C₈

—

C₄₃

C₂×#499

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

#107

—

#106

—

#106

C₂×D₄₃

yes

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄²

—

C₄²

—

C₂³

D₄×D₄₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

172

—

105

C₂×C₄

C₂×Dic₈₆

yes

—

106

C₂×C₄

D₄×D₄₃

yes

characteristic

107

C₂×C₄

Q₈×D₄₃

yes

—

108

C₂×C₄

C₂³×D₄₃

yes

characteristic

109

C₈

—

110

C₈

C₂×Dic₈₆

yes

—

111

C₂²

#13063324

yes

—

112

C₂²

#13063346

yes

—

113

C₂²

C₂×D₄×D₄₃

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

172

—

117

C₄

#13063324

yes

—

118

C₄

C₂×Q₈×D₄₃

yes

characteristic

119

C₄

C₂²×Dic₈₆

yes

characteristic

120

C₂

#14583299

yes

direct product factor

121

C₂

C₂×#13063324

yes

characteristic

122

C₂

C₂×#13063346

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#106×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#106	D₄₃
hypocenter	C₄₃	C₂×#499
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×#106×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
2. #14583299	C₂	direct (N × H)
59. C₂×C₄₃	#499	semidirect
68. C₄₃	C₂×#499	semidirect
120. C₂	#14583299	direct (N × H)

H ≅ G/N

type

2. #14583299

C₂

direct (N × H)

59. C₂×C₄₃

#499

semidirect

68. C₄₃

C₂×#499

semidirect

120. C₂

#14583299

direct (N × H)

Subgroups — C₂×#14583299 #19145097

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583299 #19145097

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583299 #19145097