Finite Group Databasebeta

← #19143857

Subgroups — #19143857

Order 5504.

754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×#10621898C211yesmaximal, characteristic
2C2×#13063358C212yesmaximal, complemented
3C2×#13063304C211yesmaximal, characteristic, complemented
4#14583063C214yesmaximal, complemented
5#14583057C212yesmaximal, complemented
6#14583052C212yesmaximal, complemented
7#14582901C212yesmaximal, complemented
8C43×#407C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10C2×#10621898—21no—
11C2×#10621898—28no—
12C2×#10621898C2212yes—
13C2×#10621898C2212yes—
14C22×Dic86C2211yescharacteristic
15C22×Dic86C2211yescharacteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C22⋊D43—21no—
18C22×C4×D43—21no—
19#13063358—28no—
20C2×Dic172C2214yescomplemented
21C2×#10621873C2214yescomplemented
22#13063304—21no—
23#13063304—21no—
24#13063304C2212yes—
25#13063304C2212yescomplemented
26C2×C4⋊Dic43C2211yescharacteristic, complemented
27C2×Dic43⋊C4—21no—
28C2×C22⋊Dic43—21no—
29#13063250C2214yescomplemented
30#13063247C2214yescomplemented
31C23×C4×C43C2211yescharacteristic
32C2×M16×C43C2212yescomplemented
33C22⋊C8×C43C2212yes—
34C22⋊C8×C43C2212yescomplemented
35C24×C43D411yescharacteristic
36C23×D43—21no—
37C22×C4×C43—24no—
38C22×C4×C43D411yescharacteristic
39C22×C4×C43D411yescharacteristic
40C22×C4×C43D411yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—28no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C22×Dic43—21no—
48C22×Dic43—21no—
49C22×Dic43—21no—
50#10621898—28no—
51#10621898—28no—
52#10621898—24no—
53#10621898—24no—
54#10621898—24no—
55#10621898D418yes—
56C2×D172—21no—
57C2×D172—24no—
58C2×D172C2312yes—
59C2×C4×D43—28no—
60C2×C4×D43—22no—
61C2×C4×D43—22no—
62C2×Dic86—21no—
63C2×Dic86—24no—
64C2×Dic86—24no—
65C2×Dic86—21no—
66C2×Dic86C2312yes—
67C2×Dic86C2312yes—
68M16×C43—24no—
69C2×C8×C43C2314yes—
70C22⋊Dic43—22no—
71C22⋊Dic43—22no—
72C4⋊Dic43—21no—
73C4⋊Dic43C2312yes—
74Dic43⋊C4—22no—
75Dic43⋊C4—22no—
76Dic172—28no—
77#10621873—28no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—41no—
81C23×C43C2×D411yescharacteristic
82C23×C43C2×D411yescharacteristic
83C23×C43C2×D411yescharacteristic
84C22×D43—24no—
85C22×D43—22no—
86C22×D43—42no—
87C22×D43—42no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D414yes—
97C2×C4×C43C2411yescharacteristic
98C22⋊D43—28no—
99C22⋊D43—28no—
100C2×Dic43—24no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106D172—24no—
107D172—22no—
108D172C2×D414yes—
109C4×D43—28no—
110C4×D43—28no—
111Dic86—24no—
112Dic86—22no—
113Dic86—24no—
114Dic86—42no—
115Dic86C2×D414yes—
116C8×C43—24no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—44no—
125C22×C43#12012yes—
126C22×C43#13712yescomplemented
127C22×C43C22×D411yescharacteristic
128C2×D43—24no—
129C2×D43—48no—
130C2×D43—42no—
131C2×D43—42no—
132C4×C43—21no—
133C4×C43—21no—
134C4×C43#12012yes—
135C4×C43C22×D412yes—
136Dic43—24no—
137Dic43—42no—
138Dic43—42no—
139#3007—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—22no—
142C2×C43—41no—
143C2×C43C2×#12011yescharacteristic
144C2×C43C2×#13711yescharacteristic
145C2×C43#57511yescharacteristic
146D43—44no—
147C22×#41—431no—
148C2×#137—432no—
149C2×C22⋊Q8—431no—
150#452—434no—
151#451—432no—
152#450—432no—
153#417—432no—
154#407D4311yescharacteristic, complemented
155C43#300711yescharacteristic, complemented, Sylow
156C2×#41—432no—
157C2×#41—432no—
158C2×#41—868no—
159C2×#41—861no—
160C2×#41—861no—
161C22×Q8—431no—
162C22×Q8—431no—
163C22×D4—431no—
164C22×D4—861no—
165C23×C4—861no—
166C23×C4C2×D4311yescharacteristic
167#137—868no—
168C2×Q16—434no—
169C2×SD16—434no—
170C2×M16C2×D4312yescomplemented
171C22⋊Q8—432no—
172C22⋊Q8—432no—
173C22⋊Q8—861no—
174C22⋊Q8—861no—
175C2×C4⋊C4—431no—
176C2×C4⋊C4—861no—
177C2×C22⋊C4—861no—
178#103—434no—
179#102—434no—
180C22⋊C8C2×D4312yes—
181C22⋊C8C2×D4312yescomplemented
182C24—861no—
183C24D17211yescharacteristic
184#41—438no—
185#41—864no—
186#41—864no—
187#41—868no—
188#41—868no—
189#41—864no—
190C2×Q8—432no—
191C2×Q8—432no—
192C2×Q8—864no—
193C2×Q8—861no—
194C2×Q8—861no—
195C2×Q8—864no—
196C2×D4—432no—
197C2×D4—864no—
198C2×D4—868no—
199C2×D4—862no—
200C2×D4—862no—
201C2×D4—861no—
202C22×C4—24no—
203C22×C4—868no—
204C22×C4—861no—
205C22×C4—862no—
206C22×C4—862no—
207C22×C4—861no—
208C22×C4—861no—
209C22×C4D17211yescharacteristic
210C22×C4D17211yescharacteristic
211C22×C4D17211yescharacteristic
212C22×C4C22×D4311yescharacteristic
213C22×C4C22×D4311yescharacteristic
214C22×C4C22×D4311yescharacteristic
215Q16—868no—
216SD16—868no—
217M16—24no—
218C2×C8C22×D4314yes—
219C4⋊C4—432no—
220C4⋊C4—861no—
221C4⋊C4—862no—
222C4⋊C4—862no—
223C22⋊C4—862no—
224C22⋊C4—862no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—864no—
229C23—862no—
230C23—1722no—
231C23—1722no—
232C23C2×D17211yescharacteristic
233C23C2×D17211yescharacteristic
234C23C2×D17211yescharacteristic
235Q8—434no—
236Q8—864no—
237Q8—862no—
238Q8—864no—
239Q8—1722no—
240D4—434no—
241D4—864no—
242D4—868no—
243D4—868no—
244D4—862no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—868no—
251C2×C4—864no—
252C2×C4—862no—
253C2×C4—868no—
254C2×C4—862no—
255C2×C4—862no—
256C2×C4—1722no—
257C2×C4—1722no—
258C2×C4C2×D17211yescharacteristic
259C2×C4C2×D17211yescharacteristic
260C2×C4C2×D17211yescharacteristic
261C2×C4D4×D4314yes—
262C2×C4C23×D4311yescharacteristic
263C8—24no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—44no—
272C22—864no—
273C22—1728no—
274C22—1722no—
275C22—1722no—
276C22#1306329512yes—
277C22#1306335812yescomplemented
278C22C22×D17211yescharacteristic
279C4—21no—
280C4—21no—
281C4—864no—
282C4—1722no—
283C4—1722no—
284C4#1306329512yes—
285C4C2×D4×D4312yes—
286C2—22no—
287C2—22no—
288C2—41no—
289C2—1724no—
290C2C2×#1306329511yescharacteristic
291C2C2×#1306335811yescharacteristic
292C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3007
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#13063358C2semidirect
3. C2×#13063304C2semidirect
4. #14583063C2semidirect
5. #14583057C2semidirect
6. #14583052C2semidirect
7. #14582901C2semidirect
8. C43×#407C2semidirect
15. C22×Dic86C22semidirect
20. C2×Dic172C22semidirect
21. C2×#10621873C22semidirect
25. #13063304C22semidirect
26. C2×C4⋊Dic43C22semidirect
29. #13063250C22semidirect
30. #13063247C22semidirect
32. C2×M16×C43C22semidirect
34. C22⋊C8×C43C22semidirect
126. C22×C43#137semidirect
154. #407D43semidirect
155. C43#3007semidirect
170. C2×M16C2×D43semidirect
181. C22⋊C8C2×D43semidirect
277. C22#13063358semidirect