Finite Group Databasebeta

← #19144694

Subgroups — #19144694

Order 5504.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583456C211yesmaximal, characteristic, complemented
2#14583234C212yesmaximal, complemented
3#14583179C212yesmaximal, complemented
4#14583104C212yesmaximal, complemented
5#14583050C212yesmaximal
6#14582999C214yesmaximal, complemented
7#14582956C211yesmaximal, characteristic, complemented
8C2×C4×D4×C43C211yesmaximal, characteristic
9C2×#10621883C2214yes—
10#13063325C2211yescharacteristic, complemented
11#13063325C2211yescharacteristic, complemented
12#13063317—21no—
13#13063304—21no—
14#13063304C2212yes—
15C4×Dic86—21no—
16C4×Dic86C2212yescomplemented
17#13063284—21no—
18#13063258C2214yescomplemented
19C4⋊(C43⋊C8)C2212yescomplemented
20#13063248C2214yescomplemented
21#13063246C2214yes—
22C22⋊(C43⋊C8)C2212yes—
23#13063236C2212yescomplemented
24C22×D4×C43C2211yescharacteristic
25C23×C4×C43—21no—
26C4×D4×C43—21no—
27C4×D4×C43—21no—
28C4×D4×C43C2212yes—
29C4×D4×C43C2212yes—
30C2×C4⋊C4×C43C2211yescharacteristic
31C2×C22⋊C4×C43—21no—
32C2×C42×C43C2211yescharacteristic
33C24×C43—21no—
34C2×D4×C43—24no—
35C2×D4×C43—21no—
36C2×D4×C43C2312yes—
37C22×C4×C43—22no—
38C22×C4×C43—22no—
39C22×C4×C43—21no—
40C22×C4×C43—44no—
41C22×C4×C43D411yescharacteristic
42C22×C4×C43D411yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C2×Dic86—21no—
45C2×Dic86C2312yes—
46C4⋊C4×C43—21no—
47C4⋊C4×C43C2312yes—
48C22⋊C4×C43—22no—
49C22⋊C4×C43—22no—
50C42×C43D411yescharacteristic
51C42×C43D411yescharacteristic
52C42×C43C2311yescharacteristic
53C42×C43C2311yescharacteristic
54C22⋊Dic43—22no—
55#10621883—28no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58C4⋊Dic43—21no—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C2×C43⋊C8C2314yes—
64C23×C43—24no—
65C23×C43—22no—
66C23×C43—42no—
67C23×C43—42no—
68C23×C43C2×D411yescharacteristic
69D4×C43—24no—
70D4×C43—22no—
71D4×C43#4114yes—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—44no—
77C2×C4×C43—42no—
78C2×C4×C43—44no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2411yescharacteristic
85C2×Dic43—22no—
86C2×Dic43—22no—
87Dic86—24no—
88Dic86—42no—
89C43⋊C8—24no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—24no—
93C22×C43—48no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43#13712yes—
97C22×C43C22×D411yescharacteristic
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—42no—
103C4×C43AGL(1,ℤ/8)12yes—
104C4×C43C2×#4112yes—
105Dic43—42no—
106Dic43—42no—
107#3110—431nomaximal, Sylow
108C2×C43—22no—
109C2×C43—44no—
110C2×C43#52511yescharacteristic
111C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C43C2×#13711yescharacteristic
113#533—431no—
114C2×C4×D4D4311yescharacteristic
115#484—432no—
116#474—432no—
117#461—432no—
118#450—432no—
119#440—434no—
120#432—431no—
121C43#311011yescharacteristic, complemented, Sylow
122C22×D4C2×D4311yescharacteristic
123C23×C4—21no—
124C2×SD16—434no—
125C4⋊Q8—431no—
126C4⋊Q8—431no—
127#125—861no—
128C22⋊Q8—432no—
129C22⋊Q8—861no—
130C4×Q8—432no—
131C4×Q8—861no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D4312yes—
135C4×D4C2×D4312yes—
136#117—861no—
137C2×C4⋊C4C2×D4311yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D4311yescharacteristic
140#107—434no—
141C4⋊C8—432no—
142#103—434no—
143#102—434no—
144C22⋊C8—432no—
145#97—432no—
146C24—21no—
147C2×Q8—432no—
148C2×Q8—861no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D4312yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D4311yescharacteristic
157C22×C4C22⋊D4311yescharacteristic
158C22×C4C22×D4311yescharacteristic
159SD16—868no—
160C2×C8—434no—
161C4⋊C4—21no—
162C4⋊C4—432no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—861no—
168C4⋊C4C22×D4312yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—862no—
172C42—862no—
173C42C22⋊D4311yescharacteristic
174C42C22⋊D4311yescharacteristic
175C42C22×D4311yescharacteristic
176C42C22×D4311yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D4311yescharacteristic
182Q8—864no—
183Q8—1722no—
184D4—24no—
185D4—22no—
186D4#1062189814yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4C2×C22⋊D4311yescharacteristic
197C2×C4C2×C22⋊D4311yescharacteristic
198C2×C4C2×C22⋊D4311yescharacteristic
199C2×C4C2×C22⋊D4311yescharacteristic
200C2×C4C2×C22⋊D4311yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—864no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1306335512yes—
210C22C22×C22⋊D4311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—1722no—
217C4—1722no—
218C4#1306335112yes—
219C4C2×#1062189812yes—
220C2—22no—
221C2—44no—
222C2#1458341011yescharacteristic
223C2C2×#1306335111yescharacteristic
224C2C2×#1306335511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×C4×D4×C43C2
socleC22×C43C22×D4
hypercenterC2×C4×D4D43
hypocenterC43#3110
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583456C2semidirect
2. #14583234C2semidirect
3. #14583179C2semidirect
4. #14583104C2semidirect
6. #14582999C2semidirect
7. #14582956C2semidirect
10. #13063325C22semidirect
11. #13063325C22semidirect
16. C4×Dic86C22semidirect
18. #13063258C22semidirect
19. C4⋊(C43⋊C8)C22semidirect
20. #13063248C22semidirect
23. #13063236C22semidirect
121. C43#3110semidirect