Group #19147714 — subgroups

Subgroups — C₂×#14583332 #19147714

Order 5504.

368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13063348	C₂	1	2	yes	maximal, complemented
2	#14583332	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063268	C₂	1	2	yes	maximal, complemented
4	C₂×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10621902	—	2	2	no	—
8	#13063348	—	2	4	no	—
9	#13063348	C₂²	1	8	yes	complemented
10	C₂×#10621884	—	2	2	no	—
11	C₂×D₃₄₄	C₂²	1	2	yes	—
12	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
13	#13063268	C₂²	1	8	yes	complemented
14	D₆₈₈	C₂²	1	4	yes	complemented
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₁₆×D₄₃	C₂²	1	4	yes	complemented
17	C₂×Q₁₆×C₄₃	C₂²	1	2	yes	—
18	Q₃₂×C₄₃	C₂²	1	4	yes	complemented
19	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×Q₈×C₄₃	—	2	2	no	—
21	#10621902	—	2	8	no	—
22	#10621902	—	4	4	no	—
23	C₂×D₁₇₂	—	2	2	no	—
24	C₂×D₁₇₂	—	4	2	no	—
25	C₂×C₄×D₄₃	—	4	2	no	—
26	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
27	Q₁₆×C₄₃	—	2	2	no	—
28	Q₁₆×C₄₃	C₂³	1	4	yes	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	#10621884	—	2	8	no	—
31	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
32	D₃₄₄	—	2	2	no	—
33	D₃₄₄	C₂³	1	4	yes	—
34	C₈×D₄₃	D₄	1	2	yes	—
35	C₈×D₄₃	C₂³	1	2	yes	—
36	C₁₆×C₄₃	C₂³	1	2	yes	—
37	C₄₃⋊C₁₆	C₂³	1	2	yes	—
38	C₂²×D₄₃	—	4	2	no	—
39	C₂²×D₄₃	D₈	1	1	yes	characteristic
40	Q₈×C₄₃	—	2	4	no	—
41	Q₈×C₄₃	—	4	2	no	—
42	C₂×C₄×C₄₃	—	4	2	no	—
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×Dic₄₃	D₈	1	1	yes	characteristic
45	D₁₇₂	—	2	4	no	—
46	D₁₇₂	—	4	8	no	—
47	D₁₇₂	—	4	2	no	—
48	C₄×D₄₃	—	4	8	no	—
49	C₄×D₄₃	D₈	1	2	yes	—
50	C₄×D₄₃	C₂×D₄	1	2	yes	—
51	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
52	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
53	C₄₃⋊C₈	C₂×D₄	1	2	yes	—
54	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
55	C₂×D₄₃	—	2	2	no	—
56	C₂×D₄₃	—	4	4	no	—
57	C₂×D₄₃	—	8	4	no	—
58	C₂×D₄₃	C₂×D₈	1	2	yes	—
59	C₄×C₄₃	—	4	4	no	—
60	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
61	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
62	Dic₄₃	C₂×D₈	1	2	yes	—
63	C₂×#508	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	#508	1	2	yes	complemented
65	C₂×C₄₃	C₂²×D₈	1	1	yes	characteristic
66	D₄₃	—	2	2	no	—
67	D₄₃	—	8	4	no	—
68	C₂×#135	—	43	2	no	—
69	#508	—	43	8	no	—
70	C₂×Q₃₂	D₄₃	1	1	yes	characteristic, complemented
71	C₂×SD₃₂	—	43	2	no	—
72	C₂×D₁₆	—	43	1	no	—
73	C₂²×C₁₆	—	43	1	no	—
74	C₄₃	C₂×#508	1	1	yes	characteristic, complemented, Sylow
75	C₂×#41	—	86	2	no	—
76	#135	—	43	8	no	—
77	#135	—	86	4	no	—
78	C₂×Q₁₆	C₂×D₄₃	1	2	yes	—
79	C₂×SD₁₆	—	86	2	no	—
80	C₂×D₈	—	43	2	no	—
81	C₂²×C₈	—	43	1	no	—
82	Q₃₂	C₂×D₄₃	1	4	yes	complemented
83	SD₃₂	—	43	8	no	—
84	D₁₆	—	43	4	no	—
85	C₂×C₁₆	—	43	1	no	—
86	C₂×C₁₆	—	43	4	no	—
87	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
88	#41	—	86	8	no	—
89	#41	—	172	4	no	—
90	C₂×Q₈	—	2	2	no	—
91	C₂×D₄	—	86	2	no	—
92	C₂×D₄	—	172	2	no	—
93	C₂²×C₄	—	43	1	no	—
94	C₂²×C₄	—	172	2	no	—
95	Q₁₆	—	2	2	no	—
96	Q₁₆	C₂²×D₄₃	1	4	yes	—
97	SD₁₆	—	86	8	no	—
98	D₈	—	43	4	no	—
99	D₈	—	86	2	no	—
100	C₂×C₈	—	43	1	no	—
101	C₂×C₈	—	43	2	no	—
102	C₂×C₈	—	43	2	no	—
103	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
104	C₁₆	—	43	2	no	—
105	C₁₆	C₂²×D₄₃	1	2	yes	—
106	C₂³	—	43	1	no	—
107	C₂³	—	172	2	no	—
108	Q₈	—	2	4	no	—
109	Q₈	—	4	2	no	—
110	D₄	—	86	4	no	—
111	D₄	—	172	8	no	—
112	D₄	—	172	2	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	43	1	no	—
115	C₂×C₄	—	43	2	no	—
116	C₂×C₄	—	43	2	no	—
117	C₂×C₄	—	172	8	no	—
118	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
119	C₈	—	43	2	no	—
120	C₈	D₄×D₄₃	1	1	yes	characteristic
121	C₈	C₂³×D₄₃	1	1	yes	characteristic
122	C₂²	—	43	2	no	—
123	C₂²	—	86	2	no	—
124	C₂²	—	344	4	no	—
125	C₂²	—	172	4	no	—
126	C₂²	D₈×D₄₃	1	1	yes	characteristic
127	C₄	—	4	4	no	—
128	C₄	—	43	2	no	—
129	C₄	D₈×D₄₃	1	1	yes	characteristic
130	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
131	C₂	—	86	2	no	—
132	C₂	—	344	4	no	—
133	C₂	#14583332	1	2	yes	direct product factor
134	C₂	C₂×D₈×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063348

C₂

yes

maximal, complemented

#14583332

C₂

yes

maximal, direct product factor

C₂×#13063268

C₂

yes

maximal, complemented

C₂×D₆₈₈

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₃₂×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#10621902

—

#13063348

—

#13063348

C₂²

yes

complemented

C₂×#10621884

—

C₂×D₃₄₄

C₂²

yes

—

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063268

C₂²

yes

complemented

D₆₈₈

C₂²

yes

complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₃

C₂²

yes

complemented

C₂×Q₁₆×C₄₃

C₂²

yes

—

Q₃₂×C₄₃

C₂²

yes

complemented

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

#10621902

—

#10621902

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

#10621884

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

C₂³

yes

—

C₈×D₄₃

D₄

yes

—

C₈×D₄₃

C₂³

yes

—

C₁₆×C₄₃

C₂³

yes

—

C₄₃⋊C₁₆

C₂³

yes

—

C₂²×D₄₃

—

C₂²×D₄₃

D₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

D₈

yes

—

C₄×D₄₃

C₂×D₄

yes

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂⁴

yes

characteristic

C₄₃⋊C₈

C₂×D₄

yes

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂×D₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

C₂²×D₄

yes

characteristic

Dic₄₃

C₂×D₈

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂²×D₈

yes

characteristic

D₄₃

—

D₄₃

—

C₂×#135

—

#508

—

C₂×Q₃₂

D₄₃

yes

characteristic, complemented

C₂×SD₃₂

—

C₂×D₁₆

—

C₂²×C₁₆

—

C₄₃

C₂×#508

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

#135

—

C₂×Q₁₆

C₂×D₄₃

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

—

Q₃₂

C₂×D₄₃

yes

complemented

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#41

—

#41

—

172

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

—

172

—

Q₁₆

—

Q₁₆

C₂²×D₄₃

yes

—

SD₁₆

—

D₈

—

D₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₂²×D₄₃

yes

characteristic

104

C₁₆

—

105

C₁₆

C₂²×D₄₃

yes

—

106

C₂³

—

107

C₂³

—

172

—

108

Q₈

—

109

Q₈

—

110

D₄

—

111

D₄

—

172

—

112

D₄

—

172

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

172

—

118

C₂×C₄

D₄×D₄₃

yes

characteristic

119

C₈

—

120

C₈

D₄×D₄₃

yes

characteristic

121

C₈

C₂³×D₄₃

yes

characteristic

122

C₂²

—

123

C₂²

—

124

C₂²

—

344

—

125

C₂²

—

172

—

126

C₂²

D₈×D₄₃

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

D₈×D₄₃

yes

characteristic

130

C₄

C₂×D₄×D₄₃

yes

characteristic

131

C₂

—

132

C₂

—

344

—

133

C₂

#14583332

yes

direct product factor

134

C₂

C₂×D₈×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₈×C₄₃	C₂⁴
Frattini	C₈	C₂³×D₄₃
Fitting	C₂×Q₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₃
hypocenter	C₄₃	C₂×#508
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₈×C₄₃

C₂⁴

Frattini

C₈

C₂³×D₄₃

Fitting

C₂×Q₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×Q₃₂

D₄₃

hypocenter

C₄₃

C₂×#508

LCS

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
1. C₂×#13063348	C₂	semidirect
2. #14583332	C₂	direct (N × H)
3. C₂×#13063268	C₂	semidirect
4. C₂×D₆₈₈	C₂	semidirect
5. C₂×C₁₆×D₄₃	C₂	semidirect
6. C₂×Q₃₂×C₄₃	C₂	semidirect
9. #13063348	C₂²	semidirect
13. #13063268	C₂²	semidirect
14. D₆₈₈	C₂²	semidirect
16. C₁₆×D₄₃	C₂²	semidirect
18. Q₃₂×C₄₃	C₂²	semidirect
64. C₂×C₄₃	#508	semidirect
70. C₂×Q₃₂	D₄₃	semidirect
74. C₄₃	C₂×#508	semidirect
82. Q₃₂	C₂×D₄₃	semidirect
133. C₂	#14583332	direct (N × H)

H ≅ G/N

type

1. C₂×#13063348

C₂

semidirect

2. #14583332

C₂

direct (N × H)

3. C₂×#13063268

C₂

semidirect

4. C₂×D₆₈₈

C₂

semidirect

5. C₂×C₁₆×D₄₃

C₂

semidirect

6. C₂×Q₃₂×C₄₃

C₂

semidirect

9. #13063348

C₂²

semidirect

13. #13063268

C₂²

semidirect

14. D₆₈₈

C₂²

semidirect

16. C₁₆×D₄₃

C₂²

semidirect

18. Q₃₂×C₄₃

C₂²

semidirect

64. C₂×C₄₃

#508

semidirect

70. C₂×Q₃₂

D₄₃

semidirect

74. C₄₃

C₂×#508

semidirect

82. Q₃₂

C₂×D₄₃

semidirect

133. C₂

#14583332

direct (N × H)

Subgroups — C₂×#14583332 #19147714

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583332 #19147714

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583332 #19147714