Group #19144931 — subgroups

Subgroups — C₂×#14583265 #19144931

Order 5504.

488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063322	C₂	1	1	yes	maximal, characteristic
2	#14583265	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063245	C₂	1	4	yes	maximal, complemented
4	C₂×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	—	2	2	no	—
7	C₂²×D₁₇₂	C₂²	1	2	yes	—
8	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
9	#13063322	—	2	2	no	—
10	#13063322	C₂²	1	4	yes	—
11	#13063245	C₂²	1	16	yes	complemented
12	#13063236	C₂²	1	4	yes	complemented
13	#125×C₄₃	—	2	2	no	—
14	#125×C₄₃	C₂²	1	4	yes	complemented
15	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
16	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄₃	—	2	2	no	—
19	C₂²×C₄×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×D₁₇₂	—	2	2	no	—
23	C₂×D₁₇₂	—	2	8	no	—
24	C₂×D₁₇₂	—	2	8	no	—
25	C₂×D₁₇₂	—	4	8	no	—
26	C₂×D₁₇₂	C₂³	1	4	yes	—
27	C₄⋊C₄×C₄₃	—	2	8	no	—
28	C₄⋊C₄×C₄₃	—	2	2	no	—
29	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
30	C₄²×C₄₃	D₄	1	2	yes	—
31	C₄²×C₄₃	C₂³	1	2	yes	—
32	C₂×C₄₃⋊C₈	—	2	4	no	—
33	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
34	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×D₄₃	—	2	4	no	—
36	C₂²×D₄₃	—	4	4	no	—
37	C₂²×D₄₃	—	4	8	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	4	4	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	4	yes	—
44	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
45	D₁₇₂	—	2	8	no	—
46	D₁₇₂	—	4	16	no	—
47	D₁₇₂	—	4	4	no	—
48	C₄₃⋊C₈	—	2	4	no	—
49	C₂²×C₄₃	#124	1	2	yes	—
50	C₂²×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
51	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
52	C₂×D₄₃	—	4	4	no	—
53	C₂×D₄₃	—	4	8	no	—
54	C₂×D₄₃	—	8	8	no	—
55	C₄×C₄₃	—	2	4	no	—
56	C₄×C₄₃	—	4	4	no	—
57	C₄×C₄₃	#124	1	2	yes	—
58	C₄×C₄₃	C₂×#41	1	2	yes	—
59	C₂×#490	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	#490	1	4	yes	complemented
61	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
62	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
63	D₄₃	—	8	4	no	—
64	C₂×#127	—	43	1	no	—
65	C₂×#125	D₄₃	1	1	yes	characteristic, complemented
66	#490	—	43	8	no	—
67	C₂×#102	—	43	4	no	—
68	C₂×#97	—	43	1	no	—
69	C₄₃	C₂×#490	1	1	yes	characteristic, complemented, Sylow
70	C₂²×D₄	—	43	2	no	—
71	C₂²×D₄	—	86	2	no	—
72	C₂²×C₈	—	43	2	no	—
73	#127	—	43	4	no	—
74	#127	—	86	2	no	—
75	#125	—	2	2	no	—
76	#125	C₂×D₄₃	1	4	yes	complemented
77	C₂×C₄⋊C₄	—	2	2	no	—
78	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
79	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
80	#102	—	43	16	no	—
81	#97	—	43	4	no	—
82	C₂⁴	—	86	2	no	—
83	C₂×D₄	—	43	4	no	—
84	C₂×D₄	—	86	8	no	—
85	C₂×D₄	—	86	8	no	—
86	C₂×D₄	—	86	2	no	—
87	C₂×D₄	—	172	8	no	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	C₂×C₈	—	43	4	no	—
92	C₂×C₈	—	86	4	no	—
93	C₄⋊C₄	—	2	8	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
96	C₄²	C₂²⋊D₄₃	1	2	yes	—
97	C₄²	C₂²×D₄₃	1	2	yes	—
98	C₂³	—	86	4	no	—
99	C₂³	—	172	4	no	—
100	C₂³	—	172	8	no	—
101	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
102	D₄	—	86	8	no	—
103	D₄	—	172	16	no	—
104	D₄	—	172	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	#10621902	1	4	yes	—
109	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
111	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
112	C₈	—	86	4	no	—
113	C₂²	—	344	8	no	—
114	C₂²	—	172	4	no	—
115	C₂²	—	172	8	no	—
116	C₂²	#13063314	1	2	yes	—
117	C₂²	#13063350	1	4	yes	—
118	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	4	4	no	—
121	C₄	#13063314	1	2	yes	—
122	C₄	C₂×#10621902	1	2	yes	—
123	C₂	—	344	4	no	—
124	C₂	#14583265	1	4	yes	direct product factor
125	C₂	C₂×#13063314	1	1	yes	characteristic
126	C₂	C₂×#13063350	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063322

C₂

yes

maximal, characteristic

#14583265

C₂

yes

maximal, direct product factor

C₂×#13063245

C₂

yes

maximal, complemented

C₂×#13063236

C₂

yes

maximal, characteristic, complemented

C₂×#125×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

—

C₂²×D₁₇₂

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063322

—

#13063322

C₂²

yes

—

#13063245

C₂²

yes

complemented

#13063236

C₂²

yes

complemented

#125×C₄₃

—

#125×C₄₃

C₂²

yes

complemented

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄₃⋊C₈

—

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

—

C₄×C₄₃

C₂×#41

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

—

C₂×#127

—

C₂×#125

D₄₃

yes

characteristic, complemented

#490

—

C₂×#102

—

C₂×#97

—

C₄₃

C₂×#490

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

—

—

—

—

C₂×D₄₃

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#102

—

#97

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄²

C₂²⋊D₄₃

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

—

C₂³

—

172

—

100

C₂³

—

172

—

101

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

102

D₄

—

103

D₄

—

172

—

104

D₄

—

172

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

#10621902

yes

—

109

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

111

C₂×C₄

C₂³×D₄₃

yes

characteristic

112

C₈

—

113

C₂²

—

344

—

114

C₂²

—

172

—

115

C₂²

—

172

—

116

C₂²

#13063314

yes

—

117

C₂²

#13063350

yes

—

118

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

#13063314

yes

—

122

C₄

C₂×#10621902

yes

—

123

C₂

—

344

—

124

C₂

#14583265

yes

direct product factor

125

C₂

C₂×#13063314

yes

characteristic

126

C₂

C₂×#13063350

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	C₂×#490
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×#125×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
2. #14583265	C₂	direct (N × H)
3. C₂×#13063245	C₂	semidirect
4. C₂×#13063236	C₂	semidirect
5. C₂×#125×C₄₃	C₂	semidirect
11. #13063245	C₂²	semidirect
12. #13063236	C₂²	semidirect
14. #125×C₄₃	C₂²	semidirect
60. C₂×C₄₃	#490	semidirect
65. C₂×#125	D₄₃	semidirect
69. C₄₃	C₂×#490	semidirect
76. #125	C₂×D₄₃	semidirect
124. C₂	#14583265	direct (N × H)

H ≅ G/N

type

2. #14583265

C₂

direct (N × H)

3. C₂×#13063245

C₂

semidirect

4. C₂×#13063236

C₂

semidirect

5. C₂×#125×C₄₃

C₂

semidirect

11. #13063245

C₂²

semidirect

12. #13063236

C₂²

semidirect

14. #125×C₄₃

C₂²

semidirect

60. C₂×C₄₃

#490

semidirect

65. C₂×#125

D₄₃

semidirect

69. C₄₃

C₂×#490

semidirect

76. #125

C₂×D₄₃

semidirect

124. C₂

#14583265

direct (N × H)

Subgroups — C₂×#14583265 #19144931

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583265 #19144931

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583265 #19144931