Group #19142940 — subgroups

Subgroups — #19142940

Order 5504.

924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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, complemented
2	C₂×#13063299	C₂	1	6	yes	maximal, complemented
3	#14582801	C₂	1	6	yes	maximal, complemented
4	#14582769	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	6	yes	—
7	C₂²×C₂²⋊D₄₃	C₂²	1	4	yes	—
8	#13063322	—	2	4	no	—
9	#13063299	—	2	24	no	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	6	yes	—
11	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	—
12	C₂³×C₄×C₄₃	C₂²	1	3	yes	—
13	C₂×C₄²×C₄₃	—	2	4	no	—
14	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
17	C₂³×D₄₃	C₂³	1	4	yes	—
18	C₂²×C₄×C₄₃	—	2	6	no	—
19	C₂²×C₄×C₄₃	—	2	6	no	—
20	C₂²×C₄×C₄₃	D₄	1	12	yes	complemented
21	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
23	C₂×C₂²⋊D₄₃	—	2	24	no	—
24	C₂²×Dic₄₃	C₂³	1	4	yes	—
25	C₂×D₁₇₂	—	2	12	no	—
26	C₂×D₁₇₂	—	2	12	no	—
27	C₂×D₁₇₂	—	2	12	no	—
28	C₄²×C₄₃	—	2	6	no	—
29	C₄²×C₄₃	D₄	1	4	yes	complemented
30	(C₂×D₄₃)⋊C₄	—	2	24	no	—
31	C₄⋊Dic₄₃	—	2	12	no	—
32	C₂³×C₄₃	—	2	1	no	—
33	C₂³×C₄₃	—	2	3	no	—
34	C₂³×C₄₃	C₂×D₄	1	6	yes	—
35	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
36	C₂²×D₄₃	—	2	12	no	—
37	C₂²×D₄₃	—	2	4	no	—
38	C₂²×D₄₃	—	2	12	no	—
39	C₂×C₄×C₄₃	—	2	3	no	—
40	C₂×C₄×C₄₃	—	2	3	no	—
41	C₂×C₄×C₄₃	—	2	24	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
43	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
44	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
45	C₂×C₄×C₄₃	#41	1	6	yes	—
46	C₂²⋊D₄₃	—	4	16	no	—
47	C₂×Dic₄₃	—	2	12	no	—
48	D₁₇₂	—	4	24	no	—
49	C₂²×C₄₃	—	2	6	no	—
50	C₂²×C₄₃	—	2	6	no	—
51	C₂²×C₄₃	#127	1	4	yes	complemented
52	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
53	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
54	C₂²×C₄₃	C₂×#41	1	3	yes	—
55	C₂×D₄₃	—	4	12	no	—
56	C₂×D₄₃	—	4	4	no	—
57	C₂×D₄₃	—	4	12	no	—
58	C₄×C₄₃	—	2	6	no	—
59	C₄×C₄₃	#121	1	12	yes	complemented
60	Dic₄₃	—	4	4	no	—
61	#2856	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	4	no	—
63	C₂×C₄₃	C₂×#121	1	3	yes	—
64	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
65	C₂×C₄₃	#532	1	3	yes	—
66	D₄₃	—	8	4	no	—
67	C₂×#127	—	43	1	no	—
68	C₂×#121	—	43	6	no	—
69	C₂²×C₄²	D₄₃	1	1	yes	characteristic, complemented
70	#390	—	43	6	no	—
71	#384	—	43	1	no	—
72	C₄₃	#2856	1	1	yes	characteristic, complemented, Sylow
73	C₂²×D₄	—	43	4	no	—
74	C₂²×D₄	—	43	6	no	—
75	C₂³×C₄	C₂×D₄₃	1	3	yes	—
76	#127	—	86	4	no	—
77	#121	—	86	24	no	—
78	C₂×C₄⋊C₄	—	43	6	no	—
79	C₂×C₂²⋊C₄	—	43	12	no	—
80	C₂×C₄²	—	2	4	no	—
81	C₂×C₄²	C₂×D₄₃	1	3	yes	—
82	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
83	C₂⁴	—	43	4	no	—
84	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
85	C₂×D₄	—	86	24	no	—
86	C₂×D₄	—	86	12	no	—
87	C₂×D₄	—	86	12	no	—
88	C₂×D₄	—	86	12	no	—
89	C₂²×C₄	—	2	6	no	—
90	C₂²×C₄	—	2	6	no	—
91	C₂²×C₄	—	43	4	no	—
92	C₂²×C₄	D₁₇₂	1	12	yes	complemented
93	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
94	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
95	C₄⋊C₄	—	86	12	no	—
96	C₂²⋊C₄	—	86	24	no	—
97	C₄²	—	2	6	no	—
98	C₄²	C₂²⋊D₄₃	1	4	yes	complemented
99	C₂³	—	2	1	no	—
100	C₂³	—	2	3	no	—
101	C₂³	—	86	4	no	—
102	C₂³	—	86	12	no	—
103	C₂³	—	86	12	no	—
104	C₂³	C₂×D₁₇₂	1	6	yes	—
105	C₂³	C₂³×D₄₃	1	1	yes	characteristic
106	D₄	—	172	16	no	—
107	D₄	—	172	24	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	24	no	—
111	C₂×C₄	—	86	12	no	—
112	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
113	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
114	C₂×C₄	#10621898	1	6	yes	—
115	C₂×C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
116	C₂²	—	2	6	no	—
117	C₂²	—	2	6	no	—
118	C₂²	—	172	12	no	—
119	C₂²	—	172	4	no	—
120	C₂²	—	172	12	no	—
121	C₂²	#13063322	1	4	yes	complemented
122	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
123	C₂²	C₂²×D₁₇₂	1	3	yes	—
124	C₂²	C₂×#10621898	1	3	yes	—
125	C₄	—	2	6	no	—
126	C₄	—	172	4	no	—
127	C₄	#13063299	1	12	yes	complemented
128	C₂	—	2	4	no	—
129	C₂	—	344	4	no	—
130	C₂	C₂×#13063299	1	3	yes	—
131	C₂	C₂×#13063322	1	1	yes	characteristic
132	C₂	#14583449	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063322

C₂

yes

maximal, characteristic, complemented

C₂×#13063299

C₂

yes

maximal, complemented

#14582801

C₂

yes

maximal, complemented

#14582769

C₂

yes

maximal, characteristic, complemented

C₂²×C₄²×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

—

C₂²×C₂²⋊D₄₃

C₂²

yes

—

#13063322

—

#13063299

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂⁴

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

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#127

yes

complemented

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

complemented

Dic₄₃

—

#2856

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#121

yes

—

C₂×C₄₃

C₂×#127

yes

characteristic

C₂×C₄₃

#532

yes

—

D₄₃

—

C₂×#127

—

C₂×#121

—

C₂²×C₄²

D₄₃

yes

characteristic, complemented

#390

—

#384

—

C₄₃

#2856

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂×D₄₃

yes

—

#127

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂⁴

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

complemented

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₄₃

yes

complemented

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₂×D₁₇₂

yes

—

105

C₂³

C₂³×D₄₃

yes

characteristic

106

D₄

—

172

—

107

D₄

—

172

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂×D₁₇₂

yes

—

113

C₂×C₄

C₂×D₁₇₂

yes

—

114

C₂×C₄

#10621898

yes

—

115

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

172

—

119

C₂²

—

172

—

120

C₂²

—

172

—

121

C₂²

#13063322

yes

complemented

122

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

123

C₂²

C₂²×D₁₇₂

yes

—

124

C₂²

C₂×#10621898

yes

—

125

C₄

—

126

C₄

—

172

—

127

C₄

#13063299

yes

complemented

128

C₂

—

129

C₂

—

344

—

130

C₂

C₂×#13063299

yes

—

131

C₂

C₂×#13063322

yes

characteristic

132

C₂

#14583449

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂²×C₄²×C₄₃	C₂
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	#2856
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂²×C₄²×C₄₃

C₂

hypercenter

C₂²×C₄²

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂²×C₄²

N	H ≅ G/N	type
1. C₂×#13063322	C₂	semidirect
2. C₂×#13063299	C₂	semidirect
3. #14582801	C₂	semidirect
4. #14582769	C₂	semidirect
5. C₂²×C₄²×C₄₃	C₂	semidirect
20. C₂²×C₄×C₄₃	D₄	semidirect
29. C₄²×C₄₃	D₄	semidirect
51. C₂²×C₄₃	#127	semidirect
59. C₄×C₄₃	#121	semidirect
69. C₂²×C₄²	D₄₃	semidirect
72. C₄₃	#2856	semidirect
92. C₂²×C₄	D₁₇₂	semidirect
98. C₄²	C₂²⋊D₄₃	semidirect
121. C₂²	#13063322	semidirect
127. C₄	#13063299	semidirect

H ≅ G/N

type

1. C₂×#13063322

C₂

semidirect

2. C₂×#13063299

C₂

semidirect

3. #14582801

C₂

semidirect

4. #14582769

C₂

semidirect

5. C₂²×C₄²×C₄₃

C₂

semidirect

20. C₂²×C₄×C₄₃

D₄

semidirect

29. C₄²×C₄₃

D₄

semidirect

51. C₂²×C₄₃

#127

semidirect

59. C₄×C₄₃

#121

semidirect

69. C₂²×C₄²

D₄₃

semidirect

72. C₄₃

#2856

semidirect

92. C₂²×C₄

D₁₇₂

semidirect

98. C₄²

C₂²⋊D₄₃

semidirect

121. C₂²

#13063322

semidirect

127. C₄

#13063299

semidirect

Subgroups — #19142940

Conjugacy classes of subgroups

Complements