Group #19143383 — subgroups

Subgroups — C₂×#14583007 #19143383

Order 5504.

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂²×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₈₆	C₂	1	2	yes	maximal
3	#14583007	C₂	1	8	yes	maximal, direct product factor
4	C₂×#13063257	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063250	C₂	1	2	yes	maximal
6	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₈₆	C₂²	1	2	yes	—
8	C₂×Dic₁₇₂	C₄	1	8	yes	complemented
9	C₂×Dic₁₇₂	C₂²	1	4	yes	—
10	C₄×Dic₈₆	—	2	4	no	—
11	C₄×Dic₈₆	C₂²	1	8	yes	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×Dic₄₃⋊C₄	—	2	2	no	—
14	C₂×C₄×Dic₄₃	—	2	2	no	—
15	#13063257	C₂²	1	4	yes	—
16	#13063250	C₂²	1	8	yes	—
17	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	#97×C₄₃	C₂²	1	4	yes	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×Dic₄₃	—	2	2	no	—
24	C₂²×Dic₄₃	—	2	2	no	—
25	C₂×Dic₈₆	—	2	2	no	—
26	C₂×Dic₈₆	—	2	4	no	—
27	C₂×Dic₈₆	C₂×C₄	1	8	yes	—
28	C₂×Dic₈₆	C₂³	1	4	yes	—
29	C₂×C₈×C₄₃	—	2	2	no	—
30	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
31	C₂×C₈×C₄₃	C₂³	1	2	yes	—
32	C₂×C₈×C₄₃	C₂³	1	2	yes	—
33	C₄²×C₄₃	D₄	1	2	yes	—
34	C₄²×C₄₃	C₂³	1	2	yes	—
35	C₄⋊Dic₄₃	—	2	2	no	—
36	C₄⋊Dic₄₃	C₂³	1	4	yes	—
37	Dic₄₃⋊C₄	—	2	8	no	—
38	C₄×Dic₄₃	—	2	8	no	—
39	Dic₁₇₂	C₂×C₄	1	16	yes	complemented
40	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#41	1	2	yes	—
46	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₄₃	—	2	8	no	—
48	C₂×Dic₄₃	—	2	4	no	—
49	C₂×Dic₄₃	—	2	4	no	—
50	C₂×Dic₄₃	—	4	4	no	—
51	Dic₈₆	—	2	8	no	—
52	Dic₈₆	—	2	4	no	—
53	Dic₈₆	C₂²×C₄	1	8	yes	—
54	C₈×C₄₃	—	2	2	no	—
55	C₈×C₄₃	C₂²×C₄	1	4	yes	—
56	C₂²×C₄₃	C₄×D₄	1	2	yes	—
57	C₂²×C₄₃	#137	1	4	yes	—
58	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₄₃	—	2	4	no	—
60	C₄×C₄₃	C₄×D₄	1	2	yes	—
61	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
63	Dic₄₃	—	2	8	no	—
64	Dic₄₃	—	4	4	no	—
65	C₂×#441	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	#441	1	4	yes	complemented
67	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
68	C₂×C₄₃	C₂×#137	1	2	yes	—
69	C₂²×Q₁₆	—	43	1	no	—
70	C₂×C₄×Q₈	—	43	2	no	—
71	#441	—	43	8	no	—
72	C₂×#106	—	43	1	no	—
73	C₂×#103	—	43	2	no	—
74	C₂×#97	D₄₃	1	1	yes	characteristic
75	C₄₃	C₂×#441	1	1	yes	characteristic, complemented, Sylow
76	C₂²×Q₈	—	43	2	no	—
77	C₂×Q₁₆	—	43	4	no	—
78	C₂×Q₁₆	—	43	8	no	—
79	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
80	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
81	C₄×Q₈	—	43	8	no	—
82	C₄×Q₈	—	86	4	no	—
83	C₂×C₄⋊C₄	—	43	2	no	—
84	C₂×C₄⋊C₄	—	86	2	no	—
85	C₂×C₄²	—	86	2	no	—
86	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
87	#106	—	43	4	no	—
88	#103	—	43	8	no	—
89	#97	C₂×D₄₃	1	4	yes	—
90	C₂×Q₈	—	43	8	no	—
91	C₂×Q₈	—	43	4	no	—
92	C₂×Q₈	—	86	2	no	—
93	C₂×Q₈	—	86	4	no	—
94	C₂²×C₄	—	86	2	no	—
95	C₂²×C₄	—	86	2	no	—
96	C₂²×C₄	D₁₇₂	1	2	yes	—
97	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
98	Q₁₆	—	43	16	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₄×D₄₃	1	4	yes	—
101	C₂×C₈	C₂²×D₄₃	1	2	yes	—
102	C₂×C₈	C₂²×D₄₃	1	2	yes	—
103	C₄⋊C₄	—	43	4	no	—
104	C₄⋊C₄	—	86	2	no	—
105	C₄⋊C₄	—	86	8	no	—
106	C₄²	—	86	8	no	—
107	C₄²	D₁₇₂	1	2	yes	—
108	C₄²	C₂²×D₄₃	1	2	yes	—
109	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
110	Q₈	—	43	8	no	—
111	Q₈	—	86	8	no	—
112	Q₈	—	86	4	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	86	8	no	—
115	C₂×C₄	—	86	4	no	—
116	C₂×C₄	—	86	4	no	—
117	C₂×C₄	—	172	4	no	—
118	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
119	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
120	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
121	C₂×C₄	#10621898	1	2	yes	—
122	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₂×C₄×D₄₃	1	4	yes	—
125	C₂²	C₄×D₁₇₂	1	2	yes	—
126	C₂²	#13063358	1	4	yes	—
127	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	86	8	no	—
130	C₄	—	172	4	no	—
131	C₄	C₄×D₁₇₂	1	2	yes	—
132	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
133	C₄	C₂×#10621898	1	1	yes	characteristic
134	C₂	#14583007	1	4	yes	direct product factor
135	C₂	C₂×C₄×D₁₇₂	1	1	yes	characteristic
136	C₂	C₂×#13063358	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₇₂

C₂

yes

maximal, characteristic

C₂×C₄×Dic₈₆

C₂

yes

maximal

#14583007

C₂

yes

maximal, direct product factor

C₂×#13063257

C₂

yes

maximal, characteristic

C₂×#13063250

C₂

yes

maximal

C₂×#97×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂×Dic₁₇₂

C₄

yes

complemented

C₂×Dic₁₇₂

C₂²

yes

—

C₄×Dic₈₆

—

C₄×Dic₈₆

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

#13063257

C₂²

yes

—

#13063250

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×Dic₈₆

C₂³

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

C₂²×C₄

yes

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

#137

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄×D₄

yes

characteristic

C₂×C₄₃

C₂×#137

yes

—

C₂²×Q₁₆

—

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₄₃

yes

characteristic

C₄₃

C₂×#441

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

C₄×D₄₃

yes

—

101

C₂×C₈

C₂²×D₄₃

yes

—

102

C₂×C₈

C₂²×D₄₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

D₁₇₂

yes

—

108

C₄²

C₂²×D₄₃

yes

—

109

C₂³

C₂×D₁₇₂

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

172

—

118

C₂×C₄

C₂×C₄×D₄₃

yes

—

119

C₂×C₄

C₂×D₁₇₂

yes

—

120

C₂×C₄

C₂×D₁₇₂

yes

characteristic

121

C₂×C₄

#10621898

yes

—

122

C₂×C₄

C₂³×D₄₃

yes

characteristic

123

C₈

—

124

C₈

C₂×C₄×D₄₃

yes

—

125

C₂²

C₄×D₁₇₂

yes

—

126

C₂²

#13063358

yes

—

127

C₂²

C₂²×D₁₇₂

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

172

—

131

C₄

C₄×D₁₇₂

yes

—

132

C₄

C₂²×C₄×D₄₃

yes

characteristic

133

C₄

C₂×#10621898

yes

characteristic

134

C₂

#14583007

yes

direct product factor

135

C₂

C₂×C₄×D₁₇₂

yes

characteristic

136

C₂

C₂×#13063358

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	C₂×#441
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₄×C₄₃

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×#97×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×#97

D₄₃

hypocenter

C₄₃

C₂×#441

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #14583007	C₂	direct (N × H)
8. C₂×Dic₁₇₂	C₄	semidirect
39. Dic₁₇₂	C₂×C₄	semidirect
66. C₂×C₄₃	#441	semidirect
75. C₄₃	C₂×#441	semidirect
134. C₂	#14583007	direct (N × H)

H ≅ G/N

type

3. #14583007

C₂

direct (N × H)

8. C₂×Dic₁₇₂

C₄

semidirect

39. Dic₁₇₂

C₂×C₄

semidirect

66. C₂×C₄₃

#441

semidirect

75. C₄₃

C₂×#441

semidirect

134. C₂

#14583007

direct (N × H)

Subgroups — C₂×#14583007 #19143383

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583007 #19143383

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583007 #19143383