Finite Group Databasebeta

← #19145560

Subgroups — #19145560

Order 5504.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583433C211yesmaximal, characteristic, complemented
2#14583281C212yesmaximal, complemented
3#14583253C212yesmaximal, complemented
4#14583118C212yesmaximal, complemented
5#14583111C212yesmaximal, complemented
6#14583055C211yesmaximal, characteristic, complemented
7#14583050C211yesmaximal, characteristic, complemented
8#14583038C211yesmaximal, characteristic, complemented
9#14583033C211yesmaximal, characteristic
10#14582952C211yesmaximal, characteristic, complemented
11C2×#124×C43C211yesmaximal, characteristic, complemented
12C2×#10621885C2212yescomplemented
13C2×#10621883C2212yes—
14C2×#10621884C2212yescomplemented
15C2×#10621882C2212yes—
16#13063319—21no—
17#13063317C2211yescharacteristic, complemented
18#13063313C2211yescharacteristic, complemented
19#13063308—21no—
20#13063304C2211yescharacteristic
21#13063299C2211yescharacteristic
22C4×Dic86C2211yescharacteristic, complemented
23C4×D172C2211yescharacteristic, complemented
24C4×C22⋊D43—21no—
25#13063282—21no—
26C4⋊(C43⋊C8)C2212yescomplemented
27#13063249C2212yescomplemented
28#13063249C2212yescomplemented
29#13063246C2212yes—
30#13063246C2212yes—
31C22⋊(C43⋊C8)C2211yescharacteristic
32C22⋊(C43⋊C8)C2211yescharacteristic
33C4×C43⋊C8C2212yescomplemented
34C22×Q8×C43C2211yescharacteristic
35C22×D4×C43C2211yescharacteristic
36#124×C43—21no—
37#124×C43—21no—
38#124×C43C2212yes—
39#124×C43C2212yes—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—21no—
42C2×C42×C43C2211yescharacteristic
43C24×C43—21no—
44C2×Q8×C43—21no—
45C2×Q8×C43—42no—
46C2×Q8×C43C2312yes—
47C2×D4×C43—21no—
48C2×D4×C43—42no—
49C2×D4×C43C2312yes—
50C22×C4×C43—21no—
51C22×C4×C43D411yescharacteristic
52C22×C4×C43D411yescharacteristic
53C22×C4×C43C2311yescharacteristic
54C2×C22⋊D43—21no—
55C2×D172C2311yescharacteristic
56C2×C4×D43—21no—
57C2×Dic86C2311yescharacteristic
58C22⋊C4×C43—22no—
59C22⋊C4×C43—22no—
60C22⋊C4×C43—22no—
61C22⋊C4×C43—22no—
62C42×C43D411yescharacteristic
63C42×C43D411yescharacteristic
64C42×C43C2311yescharacteristic
65C42×C43C2311yescharacteristic
66C22⋊Dic43—21no—
67#10621885—42no—
68#10621884—42no—
69#10621883—42no—
70#10621882—42no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77Dic43⋊C4—21no—
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82C2×C43⋊C8C2312yes—
83C2×C43⋊C8C2312yes—
84C23×C43—22no—
85C23×C43—42no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43C2×D411yescharacteristic
89C22×D43—21no—
90Q8×C43—22no—
91Q8×C43—22no—
92Q8×C43—42no—
93D4×C43—22no—
94D4×C43—22no—
95D4×C43—42no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2×D411yescharacteristic
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2411yescharacteristic
107C22⋊D43—42no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111D172—22no—
112C4×D43—42no—
113Dic86—22no—
114C43⋊C8—22no—
115C43⋊C8—22no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—42no—
119C22×C43—42no—
120C22×C43—42no—
121C22×C43—84no—
122C22×C43#13512yes—
123C22×C43C22×D411yescharacteristic
124C2×D43—41no—
125C2×D43—41no—
126C2×D43—41no—
127C4×C43—21no—
128C4×C43—21no—
129C4×C43—21no—
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—42no—
133C4×C43H(5,𝔽2)12yes—
134Dic43—41no—
135Dic43—41no—
136Dic43—41no—
137#3211—431nomaximal, Sylow
138C2×C43—22no—
139C2×C43—82no—
140C2×C43#53511yescharacteristic
141C2×C43C2×#13511yescharacteristic
142C2×C43#57511yescharacteristic
143D43—81no—
144#529—431no—
145C2×#124D4311yescharacteristic, complemented
146#495—432no—
147#488—432no—
148#464—432no—
149#463—432no—
150#451—431no—
151#450—431no—
152#448—431no—
153#447—431no—
154#431—431no—
155C43#321111yescharacteristic, complemented, Sylow
156C22×Q8C2×D4311yescharacteristic
157C22×D4C2×D4311yescharacteristic
158C2×Q16—432no—
159C2×SD16—432no—
160C2×SD16—432no—
161C2×D8—432no—
162#126—861no—
163#125—431no—
164#124—21no—
165#124—21no—
166#124—431no—
167#124C2×D4312yes—
168#124C2×D4312yes—
169#123—861no—
170C22⋊Q8—431no—
171#121—431no—
172C4×Q8—431no—
173C4×D4—431no—
174C4×D4—861no—
175#117—861no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42C2×D4311yescharacteristic
179C4⋊C8—432no—
180#103—432no—
181#103—432no—
182#102—432no—
183#102—432no—
184C22⋊C8—431no—
185C22⋊C8—431no—
186C4×C8—432no—
187C24—21no—
188C2×Q8—21no—
189C2×Q8—42no—
190C2×Q8—431no—
191C2×Q8C22×D4312yes—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4—431no—
195C2×D4—861no—
196C2×D4C22×D4312yes—
197C22×C4—21no—
198C22×C4—861no—
199C22×C4C22⋊D4311yescharacteristic
200C22×C4C22⋊D4311yescharacteristic
201C22×C4C22×D4311yescharacteristic
202Q16—1722no—
203SD16—1722no—
204SD16—1722no—
205D8—1722no—
206C2×C8—432no—
207C2×C8—432no—
208C4⋊C4—431no—
209C4⋊C4—431no—
210C4⋊C4—861no—
211C4⋊C4—861no—
212C4⋊C4—861no—
213C4⋊C4—861no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—861no—
219C22⋊C4—861no—
220C22⋊C4—861no—
221C22⋊C4—861no—
222C22⋊C4—861no—
223C42—861no—
224C42C22⋊D4311yescharacteristic
225C42C22⋊D4311yescharacteristic
226C42C22×D4311yescharacteristic
227C42C22×D4311yescharacteristic
228C23—22no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—861no—
233C23C2×C22⋊D4311yescharacteristic
234Q8—22no—
235Q8—22no—
236Q8—42no—
237Q8—862no—
238D4—22no—
239D4—22no—
240D4—42no—
241D4—862no—
242D4—1722no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—861no—
249C2×C4—861no—
250C2×C4—861no—
251C2×C4—1722no—
252C2×C4C2×C22⋊D4311yescharacteristic
253C2×C4C2×C22⋊D4311yescharacteristic
254C2×C4C2×C22⋊D4311yescharacteristic
255C2×C4C2×C22⋊D4311yescharacteristic
256C2×C4C2×C22⋊D4311yescharacteristic
257C2×C4C23×D4311yescharacteristic
258C8—862no—
259C8—862no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—1721no—
267C22—1721no—
268C22—1721no—
269C22#1306334512yes—
270C22C22×C22⋊D4311yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—42no—
277C4—1721no—
278C4—1721no—
279C4—1721no—
280C4#1306337012yes—
281C2—22no—
282C2—82no—
283C2—3441no—
284C2#1458346611yescharacteristic
285C2C2×#1306334511yescharacteristic
286C2#1458369711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#124×C43C2
socleC22×C43C22×D4
hypercenterC2×#124D43
hypocenterC43#3211
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #14583433C2semidirect
2. #14583281C2semidirect
3. #14583253C2semidirect
4. #14583118C2semidirect
5. #14583111C2semidirect
6. #14583055C2semidirect
7. #14583050C2semidirect
8. #14583038C2semidirect
10. #14582952C2semidirect
11. C2×#124×C43C2semidirect
12. C2×#10621885C22semidirect
14. C2×#10621884C22semidirect
17. #13063317C22semidirect
18. #13063313C22semidirect
22. C4×Dic86C22semidirect
23. C4×D172C22semidirect
26. C4⋊(C43⋊C8)C22semidirect
27. #13063249C22semidirect
28. #13063249C22semidirect
33. C4×C43⋊C8C22semidirect
145. C2×#124D43semidirect
155. C43#3211semidirect