Group #19133654 — subgroups

Subgroups — #19133654

Order 5504.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583275	C₂	1	1	yes	maximal, characteristic
2	#14583099	C₂	1	2	yes	maximal, complemented
3	#14582643	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₄₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621884	—	2	2	no	—
7	C₂×#10621882	—	2	2	no	—
8	#13063322	C₂²	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	#13063245	—	2	2	no	—
11	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	#127×C₄₃	C₂²	1	1	yes	characteristic
13	#124×C₄₃	—	2	2	no	—
14	#123×C₄₃	—	2	2	no	—
15	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
16	C₄×D₄×C₄₃	—	2	2	no	—
17	C₂×Q₈×C₄₃	D₄	1	2	yes	—
18	C₂×D₄×C₄₃	—	2	2	no	—
19	C₂×D₄×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂×D₁₇₂	—	2	2	no	—
22	C₂×D₁₇₂	—	2	1	no	—
23	C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
25	C₂²⋊C₄×C₄₃	—	2	4	no	—
26	C₂²⋊C₄×C₄₃	—	2	2	no	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	#10621884	—	4	4	no	—
30	#10621882	—	4	4	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂³×C₄₃	—	2	2	no	—
34	C₂²×D₄₃	—	4	1	no	—
35	Q₈×C₄₃	—	2	2	no	—
36	Q₈×C₄₃	—	2	2	no	—
37	D₄×C₄₃	—	4	2	no	—
38	D₄×C₄₃	—	4	2	no	—
39	D₄×C₄₃	—	4	2	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	8	2	no	—
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
45	D₁₇₂	—	4	2	no	—
46	D₁₇₂	—	4	2	no	—
47	D₁₇₂	—	4	2	no	—
48	C₄₃⋊C₈	—	2	2	no	—
49	C₄₃⋊C₈	—	4	2	no	—
50	C₂²×C₄₃	—	4	4	no	—
51	C₂²×C₄₃	—	4	2	no	—
52	C₂²×C₄₃	#120	1	1	yes	characteristic
53	C₂×D₄₃	—	8	2	no	—
54	C₂×D₄₃	—	8	1	no	—
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	—	4	2	no	—
57	C₄×C₄₃	—	4	2	no	—
58	C₄×C₄₃	#135	1	2	yes	—
59	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
60	#1620	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	—	8	2	no	—
62	C₂×C₄₃	#449	1	2	yes	—
63	C₂×C₄₃	#453	1	1	yes	characteristic
64	D₄₃	—	16	1	no	—
65	#559	D₄₃	1	1	yes	characteristic, complemented
66	#493	—	43	1	no	—
67	#460	—	43	2	no	—
68	#331	—	43	1	no	—
69	Q₈⋊C₈	—	43	2	no	—
70	C₄₃	#1620	1	1	yes	characteristic, complemented, Sylow
71	C₂×SD₁₆	—	86	2	no	—
72	C₂×D₈	—	86	2	no	—
73	#127	—	43	1	no	—
74	#127	C₂×D₄₃	1	1	yes	characteristic
75	#124	—	2	2	no	—
76	#123	—	2	2	no	—
77	C₄×Q₈	C₂×D₄₃	1	2	yes	—
78	C₄×D₄	—	2	2	no	—
79	C₄⋊C₈	—	43	2	no	—
80	#102	—	86	2	no	—
81	C₄×C₈	—	43	1	no	—
82	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	86	2	no	—
85	C₂×D₄	—	86	1	no	—
86	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
87	C₂²×C₄	—	2	2	no	—
88	SD₁₆	—	172	4	no	—
89	D₈	—	172	4	no	—
90	C₂×C₈	—	86	1	no	—
91	C₂×C₈	—	86	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
94	C₂²⋊C₄	—	2	4	no	—
95	C₂²⋊C₄	—	2	2	no	—
96	C₄²	—	2	2	no	—
97	C₄²	C₂²×D₄₃	1	1	yes	characteristic
98	C₂³	—	2	2	no	—
99	C₂³	—	172	1	no	—
100	Q₈	—	2	2	no	—
101	Q₈	—	2	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	172	2	no	—
106	D₄	—	172	2	no	—
107	D₄	—	172	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	8	2	no	—
111	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
112	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
113	C₈	—	86	2	no	—
114	C₈	—	172	2	no	—
115	C₂²	—	4	4	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	344	2	no	—
118	C₂²	—	344	1	no	—
119	C₂²	#13063294	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	4	2	no	—
123	C₄	#13063345	1	2	yes	—
124	C₄	#13063350	1	2	yes	—
125	C₂	—	8	2	no	—
126	C₂	—	688	1	no	—
127	C₂	#14583044	1	2	yes	—
128	C₂	#14583067	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583275

C₂

yes

maximal, characteristic

#14583099

C₂

yes

maximal, complemented

#14582643

C₂

yes

maximal, characteristic, complemented

Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal, complemented

C₄₃×#559

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

C₂×#10621882

—

#13063322

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063245

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

#124×C₄₃

—

#123×C₄₃

—

C₄×Q₈×C₄₃

C₂²

yes

—

C₄×D₄×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

#10621882

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

#1620

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#449

yes

—

C₂×C₄₃

#453

yes

characteristic

D₄₃

—

#559

D₄₃

yes

characteristic, complemented

#493

—

#460

—

#331

—

Q₈⋊C₈

—

C₄₃

#1620

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

#127

—

#127

C₂×D₄₃

yes

characteristic

#124

—

#123

—

C₄×Q₈

C₂×D₄₃

yes

—

C₄×D₄

—

C₄⋊C₈

—

#102

—

C₄×C₈

—

C₂×Q₈

C₂²⋊D₄₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

—

SD₁₆

—

172

—

D₈

—

172

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

C₂³

—

172

—

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

172

—

106

D₄

—

172

—

107

D₄

—

172

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

112

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

113

C₈

—

114

C₈

—

172

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

344

—

118

C₂²

—

344

—

119

C₂²

#13063294

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

#13063345

yes

—

124

C₄

#13063350

yes

—

125

C₂

—

126

C₂

—

688

—

127

C₂

#14583044

yes

—

128

C₂

#14583067

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#559	C₂
socle	C₂²×C₄₃	#120
hypercenter	#559	D₄₃
hypocenter	C₄₃	#1620
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #559

subgroup

G/H

center

C₂²

#13063294

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#559

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #559

N	H ≅ G/N	type
2. #14583099	C₂	semidirect
3. #14582643	C₂	semidirect
4. Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
5. C₄₃×#559	C₂	semidirect
65. #559	D₄₃	semidirect
70. C₄₃	#1620	semidirect

H ≅ G/N

type

2. #14583099

C₂

semidirect

3. #14582643

C₂

semidirect

4. Q₈⋊(C₄₃⋊C₈)

C₂

semidirect

5. C₄₃×#559

C₂

semidirect

65. #559

D₄₃

semidirect

70. C₄₃

#1620

semidirect

Subgroups — #19133654

Conjugacy classes of subgroups

Complements