Group #19134457 — subgroups

Subgroups — C₈×C₄⋊Dic₄₃ #19134457

Order 5504.

296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₄₃	C₂	1	2	yes	maximal
3	C₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#14582653	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₄	1	2	yes	—
8	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
9	C₄⋊(C₄₃⋊C₈)	C₄	1	4	yes	complemented
10	C₈×Dic₄₃	—	2	4	no	—
11	C₄₃⋊#95	C₄	1	2	yes	—
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₄	1	4	yes	complemented
16	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₄₃	—	2	1	no	—
21	C₂×C₈×C₄₃	—	2	1	no	—
22	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₃	D₄	1	2	yes	—
25	C₂×C₈×C₄₃	Q₈	1	2	yes	—
26	C₄²×C₄₃	C₂×C₄	1	2	yes	—
27	C₄²×C₄₃	C₂×C₄	1	2	yes	—
28	C₄⋊Dic₄₃	C₈	1	8	yes	direct product factor
29	C₄×Dic₄₃	—	2	2	no	—
30	C₄×Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
34	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	C₄²	1	2	yes	—
37	C₂×C₄×C₄₃	C₄²	1	2	yes	—
38	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×Dic₄₃	—	2	4	no	—
46	C₂×Dic₄₃	—	2	4	no	—
47	C₂×Dic₄₃	C₂×C₈	1	8	yes	—
48	C₈×C₄₃	—	2	2	no	—
49	C₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
50	C₄₃⋊C₈	—	2	4	no	—
51	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
52	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
53	C₂²×C₄₃	C₄×Q₈	1	1	yes	characteristic
54	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
55	C₂²×C₄₃	#131	1	2	yes	—
56	C₄×C₄₃	—	2	2	no	—
57	C₄×C₄₃	C₄×C₈	1	4	yes	complemented
58	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×C₄₃	#117	1	1	yes	characteristic
60	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
61	C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
62	Dic₄₃	—	2	8	no	—
63	C₈×C₄⋊C₄	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
66	C₂×C₄₃	#405	1	1	yes	characteristic
67	C₂×C₄₃	C₈×D₄	1	2	yes	—
68	C₂×C₄₃	C₈×Q₈	1	2	yes	—
69	C₂×C₄⋊C₈	—	43	1	no	—
70	C₂×C₄×C₈	—	43	2	no	—
71	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
72	C₄×C₄⋊C₄	—	43	1	no	—
73	#336	—	43	2	no	—
74	C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₈	—	43	2	no	—
76	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
77	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂×C₄⋊C₄	—	43	2	no	—
79	C₂×C₄²	—	43	2	no	—
80	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
81	C₄⋊C₈	—	43	4	no	—
82	C₄×C₈	—	86	4	no	—
83	C₄×C₈	Dic₄₃	1	4	yes	complemented
84	#95	—	43	2	no	—
85	C₂²×C₄	—	43	4	no	—
86	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
88	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	43	4	no	—
92	C₂×C₈	—	86	2	no	—
93	C₂×C₈	—	86	2	no	—
94	C₂×C₈	Dic₈₆	1	2	yes	—
95	C₂×C₈	D₁₇₂	1	2	yes	—
96	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
97	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
98	C₄⋊C₄	—	43	8	no	—
99	C₄²	—	86	2	no	—
100	C₄²	—	86	2	no	—
101	C₄²	C₄×D₄₃	1	2	yes	—
102	C₄²	C₂×Dic₄₃	1	2	yes	—
103	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	43	8	no	—
106	C₂×C₄	—	86	4	no	—
107	C₂×C₄	—	86	4	no	—
108	C₂×C₄	C₈×D₄₃	1	4	yes	—
109	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
110	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
111	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
113	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
114	C₂×C₄	#10621898	1	1	yes	characteristic
115	C₂×C₄	#10621898	1	1	yes	characteristic
116	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	86	4	no	—
119	C₈	C₄⋊Dic₄₃	1	4	yes	direct product factor
120	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
121	C₂²	C₄×D₁₇₂	1	1	yes	characteristic
122	C₂²	C₄×Dic₈₆	1	1	yes	characteristic
123	C₂²	C₂×C₈×D₄₃	1	2	yes	—
124	C₂²	#13063331	1	2	yes	—
125	C₄	—	2	2	no	—
126	C₄	—	86	8	no	—
127	C₄	C₈×Dic₄₃	1	4	yes	complemented
128	C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
129	C₄	#13063284	1	1	yes	characteristic
130	C₄	C₄×D₁₇₂	1	1	yes	characteristic
131	C₄	C₄×Dic₈₆	1	1	yes	characteristic
132	C₂	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
133	C₂	C₂×C₈×Dic₄₃	1	1	yes	characteristic
134	C₂	#14582854	1	1	yes	characteristic
135	C₂	C₈×D₁₇₂	1	2	yes	—
136	C₂	C₈×Dic₈₆	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₃

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582653

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

complemented

C₈×Dic₄₃

—

C₄₃⋊#95

C₄

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₈

yes

direct product factor

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×C₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₄⋊C₄

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₂²×C₄₃

C₄×Q₈

yes

characteristic

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

#131

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₄×C₈

yes

complemented

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

#117

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

C₄×Q₈

yes

characteristic

Dic₄₃

—

C₈×C₄⋊C₄

—

maximal, Sylow

C₂×C₄₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₄₃

C₂×C₄×C₈

yes

characteristic

C₂×C₄₃

#405

yes

characteristic

C₂×C₄₃

C₈×D₄

yes

—

C₂×C₄₃

C₈×Q₈

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄×C₄⋊C₄

—

#336

—

C₄₃

C₈×C₄⋊C₄

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

Dic₄₃

yes

complemented

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

D₁₇₂

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄⋊C₄

—

C₄²

—

100

C₄²

—

101

C₄²

C₄×D₄₃

yes

—

102

C₄²

C₂×Dic₄₃

yes

—

103

C₂³

C₂×C₄×D₄₃

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₈×D₄₃

yes

—

109

C₂×C₄

C₄×Dic₄₃

yes

—

110

C₂×C₄

C₄×Dic₄₃

yes

—

111

C₂×C₄

C₂×Dic₈₆

yes

characteristic

112

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

113

C₂×C₄

C₂×D₁₇₂

yes

characteristic

114

C₂×C₄

#10621898

yes

characteristic

115

C₂×C₄

#10621898

yes

characteristic

116

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

C₄⋊Dic₄₃

yes

direct product factor

120

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

121

C₂²

C₄×D₁₇₂

yes

characteristic

122

C₂²

C₄×Dic₈₆

yes

characteristic

123

C₂²

C₂×C₈×D₄₃

yes

—

124

C₂²

#13063331

yes

—

125

C₄

—

126

C₄

—

127

C₄

C₈×Dic₄₃

yes

complemented

128

C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

129

C₄

#13063284

yes

characteristic

130

C₄

C₄×D₁₇₂

yes

characteristic

131

C₄

C₄×Dic₈₆

yes

characteristic

132

C₂

C₄×C₄⋊Dic₄₃

yes

characteristic

133

C₂

C₂×C₈×Dic₄₃

yes

characteristic

134

C₂

#14582854

yes

characteristic

135

C₂

C₈×D₁₇₂

yes

—

136

C₂

C₈×Dic₈₆

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	C₈×C₄⋊C₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₄₃

commutator

C₂×C₄₃

C₂×C₄×C₈

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂²×C₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

C₈×C₄⋊C₄

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄⋊(C₄₃⋊C₈)	C₄	semidirect
15. C₄×C₈×C₄₃	C₄	semidirect
28. C₄⋊Dic₄₃	C₈	direct (N × H)
49. C₈×C₄₃	C₄⋊C₄	semidirect
57. C₄×C₄₃	C₄×C₈	semidirect
74. C₄₃	C₈×C₄⋊C₄	semidirect
83. C₄×C₈	Dic₄₃	semidirect
119. C₈	C₄⋊Dic₄₃	direct (N × H)
127. C₄	C₈×Dic₄₃	semidirect

H ≅ G/N

type

9. C₄⋊(C₄₃⋊C₈)

C₄

semidirect

15. C₄×C₈×C₄₃

C₄

semidirect

28. C₄⋊Dic₄₃

C₈

direct (N × H)

49. C₈×C₄₃

C₄⋊C₄

semidirect

57. C₄×C₄₃

C₄×C₈

semidirect

74. C₄₃

C₈×C₄⋊C₄

semidirect

83. C₄×C₈

Dic₄₃

semidirect

119. C₈

C₄⋊Dic₄₃

direct (N × H)

127. C₄

C₈×Dic₄₃

semidirect

Subgroups — C₈×C₄⋊Dic₄₃ #19134457

Conjugacy classes of subgroups

Complements

Subgroups — C8×C4⋊Dic43 #19134457

Conjugacy classes of subgroups

Complements

Subgroups — C₈×C₄⋊Dic₄₃ #19134457