Group #19133362 — subgroups

Subgroups — #19133362

Order 5504.

166 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14582956	C₂	1	1	yes	maximal, characteristic
2	#14582923	C₂	1	1	yes	maximal, characteristic
3	#14582652	C₂	1	2	yes	maximal, complemented
4	#14582650	C₂	1	2	yes	maximal, complemented
5	C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	—	2	1	no	—
7	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
12	#13063236	—	2	1	no	—
13	C₂×M₁₆×C₄₃	C₄	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	#97×C₄₃	C₄	1	1	yes	characteristic
16	#97×C₄₃	C₄	1	1	yes	characteristic
17	C₄×C₈×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
21	M₁₆×C₄₃	—	2	4	no	—
22	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
24	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₄₃	D₄	1	1	yes	characteristic
26	C₄²×C₄₃	Q₈	1	1	yes	characteristic
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	#10621877	—	4	2	no	—
29	C₂×C₄₃⋊C₈	—	2	1	no	—
30	C₂×C₄₃⋊C₈	—	2	1	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₄⋊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	C₈×C₄₃	—	2	2	no	—
44	C₈×C₄₃	M₁₆	1	4	yes	complemented
45	C₄₃⋊C₈	—	4	1	no	—
46	C₄₃⋊C₈	—	4	2	no	—
47	C₄₃⋊C₈	—	4	1	no	—
48	C₂²×C₄₃	—	2	1	no	—
49	C₂²×C₄₃	—	2	1	no	—
50	C₂²×C₄₃	—	2	1	no	—
51	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₄₃	—	2	1	no	—
53	C₄×C₄₃	—	2	1	no	—
54	C₄×C₄₃	—	2	1	no	—
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	C₂×M₁₆	1	2	yes	—
57	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
58	C₄×C₄₃	#137	1	1	yes	characteristic
59	#1569	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	—	4	1	no	—
61	C₂×C₄₃	#423	1	1	yes	characteristic
62	C₂×C₄₃	#428	1	1	yes	characteristic
63	C₂×C₄₃	#430	1	1	yes	characteristic
64	#432	—	43	1	no	—
65	#423	—	43	1	no	—
66	C₄×M₁₆	D₄₃	1	1	yes	characteristic
67	#335	—	43	2	no	—
68	#334	—	43	2	no	—
69	C₄₃	#1569	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	86	1	no	—
71	C₂×M₁₆	Dic₄₃	1	2	yes	—
72	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
73	C₄⋊C₈	—	43	1	no	—
74	C₄⋊C₈	—	43	2	no	—
75	C₄⋊C₈	—	43	1	no	—
76	C₄⋊C₈	—	86	1	no	—
77	C₂²⋊C₈	—	86	1	no	—
78	#97	—	86	1	no	—
79	#97	Dic₄₃	1	1	yes	characteristic
80	#97	Dic₄₃	1	1	yes	characteristic
81	C₄×C₈	C₂×D₄₃	1	2	yes	—
82	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
83	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
84	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
85	M₁₆	—	2	4	no	—
86	M₁₆	—	172	2	no	—
87	C₂×C₈	—	86	1	no	—
88	C₂×C₈	—	86	1	no	—
89	C₂×C₈	—	86	2	no	—
90	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
91	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
92	C₄²	Dic₈₆	1	1	yes	characteristic
93	C₄²	D₁₇₂	1	1	yes	characteristic
94	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
95	C₄²	C₂²×D₄₃	1	1	yes	characteristic
96	C₂³	C₄⋊Dic₄₃	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
102	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
103	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
104	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
105	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
106	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	172	2	no	—
109	C₈	—	172	1	no	—
110	C₈	—	172	1	no	—
111	C₈	#10621877	1	4	yes	complemented
112	C₂²	—	2	1	no	—
113	C₂²	—	2	1	no	—
114	C₂²	—	2	1	no	—
115	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	2	1	no	—
119	C₄	—	2	1	no	—
120	C₄	C₂×#10621877	1	2	yes	—
121	C₄	#13063353	1	1	yes	characteristic
122	C₄	#13063358	1	1	yes	characteristic
123	C₂	—	4	1	no	—
124	C₂	#14582923	1	1	yes	characteristic
125	C₂	#14582941	1	1	yes	characteristic
126	C₂	#14582948	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582956

C₂

yes

maximal, characteristic

#14582923

C₂

yes

maximal, characteristic

#14582652

C₂

yes

maximal, complemented

#14582650

C₂

yes

maximal, complemented

C₄×M₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₂×M₁₆×C₄₃

C₄

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₄

yes

characteristic

#97×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

M₁₆

yes

complemented

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×M₁₆

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₄×M₁₆

D₄₃

yes

characteristic

#335

—

#334

—

C₄₃

#1569

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

Dic₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

Dic₄₃

yes

characteristic

#97

Dic₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

Dic₈₆

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

102

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

103

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

104

C₂×C₄

C₂×Dic₈₆

yes

characteristic

105

C₂×C₄

C₂×D₁₇₂

yes

characteristic

106

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

107

C₈

—

108

C₈

—

172

—

109

C₈

—

172

—

110

C₈

—

172

—

111

C₈

#10621877

yes

complemented

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂×#10621877

yes

—

121

C₄

#13063353

yes

characteristic

122

C₄

#13063358

yes

characteristic

123

C₂

—

124

C₂

#14582923

yes

characteristic

125

C₂

#14582941

yes

characteristic

126

C₂

#14582948

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₄×M₁₆	D₄₃
hypocenter	C₄₃	#1569
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄×M₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

hypercenter

C₄×M₁₆

D₄₃

hypocenter

C₄₃

#1569

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
3. #14582652	C₂	semidirect
4. #14582650	C₂	semidirect
44. C₈×C₄₃	M₁₆	semidirect
69. C₄₃	#1569	semidirect
111. C₈	#10621877	semidirect

H ≅ G/N

type

3. #14582652

C₂

semidirect

4. #14582650

C₂

semidirect

44. C₈×C₄₃

M₁₆

semidirect

69. C₄₃

#1569

semidirect

111. C₈

#10621877

semidirect

Subgroups — #19133362

Conjugacy classes of subgroups

Complements