Finite Group Databasebeta

← #19145780

Subgroups — #19145780

Order 5504.

368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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#14583447C211yesmaximal, characteristic
2#125×D43C211yesmaximal, characteristic, complemented
3#14583309C211yesmaximal, characteristic, complemented
4#14583308C211yesmaximal, characteristic, complemented
5#14583263C211yesmaximal, characteristic, complemented
6#14583216C212yesmaximal, complemented
7#14583211C212yesmaximal, complemented
8#14583201C212yesmaximal, complemented
9#14583197C212yesmaximal, complemented
10#14582954C211yesmaximal, characteristic, complemented
11C43×#490C211yesmaximal, characteristic, complemented
12C2×#10621900—21no—
13#13063325C2211yescharacteristic
14#13063317C2211yescharacteristic
15#13063316C2211yescharacteristic
16#13063316C2211yescharacteristic
17#13063315—21no—
18#13063315—21no—
19#13063312—21no—
20#13063296—21no—
21#13063296C2212yes—
22D4×Dic43—21no—
23D4×Dic43C2212yes—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C4⋊C4×D43C2211yescharacteristic
27C4⋊C4×D43C2211yescharacteristic
28C42×D43C2211yescharacteristic
29#13063259C2212yes—
30#13063258C2212yes—
31#13063257C2212yes—
32#13063256C2212yes—
33Dic43⋊C8C2212yes—
34#13063246C2212yes—
35#13063246C2212yes—
36(C2×D43)⋊C8C2212yes—
37#13063236C2211yescharacteristic
38#127×C43C2211yescharacteristic
39#125×C43C2211yescharacteristic
40#102×C43C2212yes—
41#102×C43C2212yes—
42#97×C43C2211yescharacteristic
43C2×D4×C43—21no—
44C2×D4×C43—21no—
45C2×D4×C43C2312yes—
46C2×C22⋊D43—22no—
47C22×Dic43—22no—
48#10621900—44no—
49C2×C4×D43—21no—
50C2×C4×D43—21no—
51C2×C4×D43D411yescharacteristic
52C2×C4×D43D411yescharacteristic
53C2×C4×D43C2311yescharacteristic
54C2×Dic86—21no—
55C2×C8×C43C2312yes—
56C4⋊C4×C43—21no—
57C4⋊C4×C43—21no—
58C4⋊C4×C43C2311yescharacteristic
59C4⋊C4×C43C2311yescharacteristic
60C42×C43C2311yescharacteristic
61C22⋊Dic43—22no—
62C22⋊Dic43—22no—
63C4⋊Dic43—21no—
64C4⋊Dic43—21no—
65C4⋊Dic43—21no—
66C4⋊Dic43C2311yescharacteristic
67C4⋊Dic43C2311yescharacteristic
68C4⋊Dic43C2312yes—
69Dic43⋊C4—21no—
70Dic43⋊C4—21no—
71Dic43⋊C4—21no—
72Dic43⋊C4—21no—
73Dic43⋊C4—21no—
74Dic43⋊C4—21no—
75C4×Dic43D411yescharacteristic
76C4×Dic43D411yescharacteristic
77C4×Dic43C2311yescharacteristic
78C2×C43⋊C8C2312yes—
79C23×C43—22no—
80C22×D43C2×D411yescharacteristic
81D4×C43—24no—
82D4×C43—42no—
83D4×C43—42no—
84C2×C4×C43—21no—
85C2×C4×C43—21no—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2411yescharacteristic
89C22⋊D43—44no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—44no—
94C2×Dic43C2×D411yescharacteristic
95C2×Dic43C2×D411yescharacteristic
96C2×Dic43C2×D411yescharacteristic
97C4×D43—22no—
98C4×D43—22no—
99C4×D43—41no—
100C4×D43—42no—
101C4×D43—42no—
102Dic86—42no—
103C8×C43—22no—
104C43⋊C8—22no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—42no—
108C22×C43C22×D411yescharacteristic
109C2×D43—21no—
110C2×D43—21no—
111C2×D43AGL(1,ℤ/8)12yes—
112C4×C43—21no—
113C4×C43—21no—
114C4×C43—41no—
115C4×C43—41no—
116C4×C432−1+412yes—
117Dic43—21no—
118Dic43—21no—
119Dic43—21no—
120Dic43—42no—
121Dic43—41no—
122Dic43—41no—
123#3234—431nomaximal, Sylow
124C2×C43—82no—
125C2×C43#53611yescharacteristic
126C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C43#57511yescharacteristic
128D43—22no—
129#532—431no—
130C2×#125—431no—
131#501—431no—
132#501—431no—
133#490—431no—
134#490D4311yescharacteristic, complemented
135#481—432no—
136#480—432no—
137#478—432no—
138#478—432no—
139#432—431no—
140C43#323411yescharacteristic, complemented, Sylow
141C2×#41—861no—
142C4⋊Q8—431no—
143#127C2×D4311yescharacteristic
144#125—431no—
145#125—431no—
146#125—431no—
147#125—861no—
148#125—861no—
149#125C2×D4311yescharacteristic
150#124—861no—
151#121—432no—
152#121—861no—
153C4×D4—432no—
154C4×D4—861no—
155C2×C4⋊C4—431no—
156C2×C4⋊C4—431no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—861no—
159C2×C42—431no—
160#107—432no—
161#107—432no—
162#106—432no—
163#106—432no—
164C4⋊C8—432no—
165#102—432no—
166#102—432no—
167#102C2×D4312yes—
168#102C2×D4312yes—
169C22⋊C8—432no—
170#97—431no—
171#97C2×D4311yescharacteristic
172#41—1724no—
173C2×Q8—861no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—862no—
177C2×D4C22×D4312yes—
178C22×C4—431no—
179C22×C4—431no—
180C22×C4—431no—
181C22×C4—861no—
182C22×C4—861no—
183C22×C4—862no—
184C2×C8—432no—
185C2×C8C22×D4312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—431no—
189C4⋊C4—431no—
190C4⋊C4—432no—
191C4⋊C4—861no—
192C4⋊C4—861no—
193C4⋊C4—861no—
194C4⋊C4—861no—
195C4⋊C4—861no—
196C4⋊C4—861no—
197C4⋊C4—861no—
198C4⋊C4—861no—
199C4⋊C4—861no—
200C4⋊C4C22×D4311yescharacteristic
201C4⋊C4C22×D4311yescharacteristic
202C22⋊C4—862no—
203C22⋊C4—862no—
204C42—431no—
205C42—431no—
206C42—431no—
207C42C22×D4311yescharacteristic
208C23—22no—
209C23—431no—
210Q8—1722no—
211D4—24no—
212D4—42no—
213D4—42no—
214D4—1724no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—431no—
218C2×C4—431no—
219C2×C4—431no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—861no—
224C2×C4—861no—
225C2×C4—1721no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1724no—
229C2×C4D4×D4311yescharacteristic
230C2×C4D4×D4311yescharacteristic
231C2×C4C23×D4311yescharacteristic
232C8—22no—
233C8—862no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—432no—
238C22—861no—
239C22—861no—
240C22C2×D4×D4311yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—41no—
245C4—861no—
246C4—861no—
247C4—861no—
248C4—1722no—
249C4—1721no—
250C4—1721no—
251C4#1306337212yes—
252C2—82no—
253C2—862no—
254C2#1458346911yescharacteristic
255C2AGL(1,ℤ/8)×D4311yescharacteristic
256C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3234
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D43C2semidirect
3. #14583309C2semidirect
4. #14583308C2semidirect
5. #14583263C2semidirect
6. #14583216C2semidirect
7. #14583211C2semidirect
8. #14583201C2semidirect
9. #14583197C2semidirect
10. #14582954C2semidirect
11. C43×#490C2semidirect
134. #490D43semidirect
140. C43#3234semidirect