Group #19136452 — subgroups

Subgroups — C₄×#13063271 #19136452

Order 5504.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13063271	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#14582724	C₂	1	1	yes	maximal, characteristic
4	#14582703	C₂	1	1	yes	maximal, characteristic
5	#14582702	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₄×Dic₈₆	—	2	1	no	—
10	#13063271	C₄	1	4	yes	direct product factor
11	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13063259	C₂²	1	1	yes	characteristic
14	#13063250	—	2	1	no	—
15	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₄×Q₈×C₄₃	—	2	1	no	—
17	#107×C₄₃	C₂²	1	1	yes	characteristic
18	#103×C₄₃	—	2	1	no	—
19	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×Q₈×C₄₃	—	2	1	no	—
21	C₂×Dic₈₆	—	2	1	no	—
22	Q₁₆×C₄₃	—	2	1	no	—
23	Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₄₃	—	2	1	no	—
27	C₄⋊C₄×C₄₃	—	4	1	no	—
28	C₄²×C₄₃	—	4	1	no	—
29	C₄²×C₄₃	D₄	1	1	yes	characteristic
30	C₄⋊Dic₄₃	—	2	1	no	—
31	Dic₄₃⋊C₄	—	4	1	no	—
32	C₄×Dic₄₃	—	4	1	no	—
33	Dic₁₇₂	—	2	1	no	—
34	Dic₁₇₂	C₂×C₄	1	2	yes	—
35	C₄₃⋊C₁₆	—	2	1	no	—
36	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
37	Q₈×C₄₃	—	2	2	no	—
38	Q₈×C₄₃	—	4	1	no	—
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
42	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×Dic₄₃	—	4	1	no	—
45	C₂×Dic₄₃	—	4	1	no	—
46	Dic₈₆	—	2	2	no	—
47	Dic₈₆	—	4	1	no	—
48	C₈×C₄₃	—	2	1	no	—
49	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₈×C₄₃	#41	1	1	yes	characteristic
51	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₄×C₄₃	—	2	1	no	—
53	C₄×C₄₃	—	4	2	no	—
54	C₄×C₄₃	—	8	1	no	—
55	C₄×C₄₃	Q₃₂	1	2	yes	complemented
56	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
57	C₄×C₄₃	#135	1	1	yes	characteristic
58	Dic₄₃	—	4	2	no	—
59	Dic₄₃	—	8	1	no	—
60	C₄×Q₃₂	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
62	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
63	C₂×C₄₃	#508	1	1	yes	characteristic
64	C₂×Q₃₂	—	43	1	no	—
65	C₄×Q₁₆	—	43	1	no	—
66	C₄×Q₁₆	D₄₃	1	1	yes	characteristic
67	#366	—	43	1	no	—
68	#358	—	43	1	no	—
69	#358	—	43	1	no	—
70	C₄×C₁₆	—	43	1	no	—
71	C₄₃	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₁₆	—	43	1	no	—
73	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
74	C₄×Q₈	—	2	1	no	—
75	C₄×Q₈	—	86	1	no	—
76	Q₃₂	—	43	4	no	—
77	C₂×C₁₆	—	43	1	no	—
78	C₂×C₁₆	—	43	1	no	—
79	#107	—	43	1	no	—
80	#107	C₂×D₄₃	1	1	yes	characteristic
81	#103	—	2	1	no	—
82	#103	—	86	1	no	—
83	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	86	1	no	—
86	Q₁₆	—	2	1	no	—
87	Q₁₆	—	43	2	no	—
88	Q₁₆	—	86	1	no	—
89	Q₁₆	C₄×D₄₃	1	2	yes	—
90	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
91	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
92	C₄⋊C₄	—	2	1	no	—
93	C₄⋊C₄	—	4	1	no	—
94	C₄⋊C₄	—	86	1	no	—
95	C₄⋊C₄	—	172	1	no	—
96	C₄²	—	4	1	no	—
97	C₄²	—	172	1	no	—
98	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
99	C₁₆	—	43	2	no	—
100	C₁₆	—	86	1	no	—
101	Q₈	—	2	2	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	86	2	no	—
104	Q₈	—	172	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	172	1	no	—
108	C₂×C₄	—	172	1	no	—
109	C₂×C₄	#10621882	1	1	yes	characteristic
110	C₂×C₄	#10621882	1	1	yes	characteristic
111	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
112	C₈	—	2	1	no	—
113	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
114	C₈	#10621898	1	1	yes	characteristic
115	C₂²	C₂×#10621882	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	4	2	no	—
118	C₄	—	8	1	no	—
119	C₄	—	344	1	no	—
120	C₄	—	172	2	no	—
121	C₄	#13063271	1	2	yes	direct product factor
122	C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
123	C₄	#13063345	1	1	yes	characteristic
124	C₂	C₄×#10621882	1	1	yes	characteristic
125	C₂	C₂×#13063271	1	1	yes	characteristic
126	C₂	#14583329	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063271

C₂

yes

maximal, characteristic

C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

#14582724

C₂

yes

maximal, characteristic

#14582703

C₂

yes

maximal, characteristic

#14582702

C₂

yes

maximal, characteristic

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₄×Dic₈₆

—

#13063271

C₄

yes

direct product factor

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063250

—

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

—

#107×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

C₂×C₄

yes

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

C₂×C₄

yes

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

Q₃₂

yes

complemented

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

Dic₄₃

—

C₄×Q₃₂

—

maximal, Sylow

C₂×C₄₃

C₄×D₈

yes

characteristic

C₂×C₄₃

C₂×Q₃₂

yes

characteristic

C₂×C₄₃

#508

yes

characteristic

C₂×Q₃₂

—

C₄×Q₁₆

—

C₄×Q₁₆

D₄₃

yes

—

—

—

C₄×C₁₆

—

C₄₃

C₄×Q₃₂

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₃

yes

characteristic

#103

—

#103

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

100

C₁₆

—

101

Q₈

—

102

Q₈

—

103

Q₈

—

104

Q₈

—

172

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

172

—

108

C₂×C₄

—

172

—

109

C₂×C₄

#10621882

yes

characteristic

110

C₂×C₄

#10621882

yes

characteristic

111

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

112

C₈

—

113

C₈

C₂×C₄×D₄₃

yes

characteristic

114

C₈

#10621898

yes

characteristic

115

C₂²

C₂×#10621882

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

344

—

120

C₄

—

172

—

121

C₄

#13063271

yes

direct product factor

122

C₄

C₄×C₂²⋊D₄₃

yes

characteristic

123

C₄

#13063345

yes

characteristic

124

C₂

C₄×#10621882

yes

characteristic

125

C₂

C₂×#13063271

yes

characteristic

126

C₂

#14583329

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10621882
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×Q₁₆	D₄₃
hypocenter	C₄₃	C₄×Q₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

#10621882

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄×Q₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₄×Q₁₆

D₄₃

hypocenter

C₄₃

C₄×Q₃₂

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

N	H ≅ G/N	type
10. #13063271	C₄	direct (N × H)
55. C₄×C₄₃	Q₃₂	semidirect
71. C₄₃	C₄×Q₃₂	semidirect
121. C₄	#13063271	direct (N × H)

H ≅ G/N

type

10. #13063271

C₄

direct (N × H)

55. C₄×C₄₃

Q₃₂

semidirect

71. C₄₃

C₄×Q₃₂

semidirect

121. C₄

#13063271

direct (N × H)

Subgroups — C₄×#13063271 #19136452

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13063271 #19136452

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063271 #19136452