Finite Group Databasebeta

← #20254355

Subgroups — #20254355

Order 6016.

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#15689657C211yesmaximal, characteristic, complemented
2C2×#13094012C211yesmaximal, characteristic, complemented
3#15689507C212yesmaximal, complemented
4#15689478C212yesmaximal, complemented
5#15689346C212yesmaximal, complemented
6#15689339C212yesmaximal, complemented
7#15689281C211yesmaximal, characteristic, complemented
8#15689276C211yesmaximal, characteristic, complemented
9#15689264C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic
11C47×#431C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×D188C2211yescharacteristic
14C2×Dic188C2212yescomplemented
15C2×#10625325C2212yes—
16C2×#10625325C2212yescomplemented
17C2×D376C2212yes—
18#13094018—21no—
19#13094016C2211yescharacteristic, complemented
20#13094012—21no—
21#13094012—21no—
22#13094012C2212yes—
23#13094012C2212yes—
24#13094012C2211yescharacteristic, complemented
25#13094007—21no—
26#13094003C2211yescharacteristic
27#13093998C2211yescharacteristic
28C4×Dic94C2211yescharacteristic, complemented
29C4×D188C2211yescharacteristic, complemented
30C4×C22⋊D47—21no—
31#13093981—21no—
32C2×(C2×D47)⋊C4—21no—
33C2×(C2×D47)⋊C4—21no—
34#13093949C2212yescomplemented
35#13093949C2212yescomplemented
36#13093946C2212yes—
37#13093946C2212yes—
38C2×C42×C47C2211yescharacteristic
39C4⋊C8×C47C2212yescomplemented
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42C4×C8×C47C2212yescomplemented
43C23×D47—21no—
44C22×C4×C47D411yescharacteristic
45C22×C4×C47D411yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49C2×D188—21no—
50C2×D188—42no—
51C2×D188C2312yes—
52C2×D188C2311yescharacteristic
53C2×C4×D47—21no—
54C2×Dic94—21no—
55C2×Dic94—42no—
56C2×Dic94C2312yes—
57C2×Dic94C2311yescharacteristic
58C2×C8×C47C2312yes—
59C2×C8×C47C2312yes—
60C42×C47D411yescharacteristic
61C42×C47D411yescharacteristic
62C42×C47C2311yescharacteristic
63C42×C47C2311yescharacteristic
64C22⋊Dic47—21no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47C2311yescharacteristic
74C4⋊Dic47C2311yescharacteristic
75Dic47⋊C4—21no—
76Dic47⋊C4—21no—
77Dic47⋊C4—21no—
78Dic47⋊C4—21no—
79C4×Dic47—21no—
80Dic188—42no—
81D376—42no—
82#10625325—42no—
83#10625325—42no—
84C23×C47C2×D411yescharacteristic
85C22×D47—21no—
86C22×D47—22no—
87C22×D47—42no—
88C22×D47—42no—
89C22×D47—42no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—41no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—42no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—42no—
105D188—22no—
106D188—22no—
107D188—22no—
108D188—42no—
109C4×D47—42no—
110Dic94—22no—
111Dic94—22no—
112Dic94—22no—
113Dic94—42no—
114C8×C47—22no—
115C8×C47—22no—
116C22×C47—21no—
117C22×C47—21no—
118C22×C47#13512yes—
119C22×C47C22×D411yescharacteristic
120C2×D47—42no—
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—42no—
124C2×D47—41no—
125C2×D47—42no—
126C2×D47—84no—
127C4×C47—21no—
128C4×C47—21no—
129C4×C47—21no—
130C4×C47—21no—
131C4×C47—21no—
132C4×C47H(5,𝔽2)12yes—
133Dic47—42no—
134Dic47—41no—
135Dic47—41no—
136Dic47—41no—
137#3211—471nomaximal, Sylow
138C2×C47—22no—
139C2×C47#53511yescharacteristic
140C2×C47C2×#13511yescharacteristic
141C2×C47#57511yescharacteristic
142D47—81no—
143D47—82no—
144#529—471no—
145C2×#124—471no—
146#495—472no—
147#488—472no—
148#464—472no—
149#463—472no—
150#451—471no—
151#450—471no—
152#448—471no—
153#447—471no—
154#431D4711yescharacteristic, complemented
155C47#321111yescharacteristic, complemented, Sylow
156C22×Q8—471no—
157C22×D4—471no—
158C2×Q16—472no—
159C2×SD16—472no—
160C2×SD16—472no—
161C2×D8—472no—
162#126—941no—
163#125—471no—
164#124—472no—
165#124—472no—
166#124—471no—
167#124—941no—
168#124—941no—
169#123—941no—
170C22⋊Q8—471no—
171#121—471no—
172C4×Q8—471no—
173C4×D4—471no—
174C4×D4—941no—
175#117—941no—
176C2×C22⋊C4—941no—
177C2×C22⋊C4—941no—
178C2×C42C2×D4711yescharacteristic
179C4⋊C8C2×D4712yescomplemented
180#103—472no—
181#103—472no—
182#102—472no—
183#102—472no—
184C22⋊C8C2×D4711yescharacteristic
185C22⋊C8C2×D4711yescharacteristic
186C4×C8C2×D4712yescomplemented
187C24—941no—
188C2×Q8—472no—
189C2×Q8—471no—
190C2×Q8—941no—
191C2×Q8—1882no—
192C2×D4—472no—
193C2×D4—471no—
194C2×D4—941no—
195C2×D4—941no—
196C2×D4—1882no—
197C22×C4—941no—
198C22×C4—941no—
199C22×C4D18811yescharacteristic
200C22×C4D18811yescharacteristic
201C22×C4C22×D4711yescharacteristic
202Q16—1882no—
203SD16—1882no—
204SD16—1882no—
205D8—1882no—
206C2×C8C22×D4712yes—
207C2×C8C22×D4712yes—
208C4⋊C4—471no—
209C4⋊C4—471no—
210C4⋊C4—941no—
211C4⋊C4—941no—
212C4⋊C4—941no—
213C4⋊C4—941no—
214C22⋊C4—941no—
215C22⋊C4—942no—
216C22⋊C4—942no—
217C22⋊C4—942no—
218C22⋊C4—942no—
219C22⋊C4—941no—
220C22⋊C4—941no—
221C22⋊C4—941no—
222C22⋊C4—941no—
223C42—941no—
224C42D18811yescharacteristic
225C42D18811yescharacteristic
226C42C22×D4711yescharacteristic
227C42C22×D4711yescharacteristic
228C23—941no—
229C23—942no—
230C23—1882no—
231C23—1882no—
232C23—1882no—
233C23C2×D18811yescharacteristic
234Q8—942no—
235Q8—942no—
236Q8—942no—
237Q8—1882no—
238D4—942no—
239D4—942no—
240D4—942no—
241D4—1882no—
242D4—1882no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—941no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—941no—
250C2×C4—1882no—
251C2×C4—1882no—
252C2×C4C2×D18811yescharacteristic
253C2×C4C2×D18811yescharacteristic
254C2×C4C2×D18811yescharacteristic
255C2×C4C2×D18811yescharacteristic
256C2×C4C2×D18811yescharacteristic
257C2×C4C23×D4711yescharacteristic
258C8—22no—
259C8—22no—
260C22—21no—
261C22—21no—
262C22—3764no—
263C22—1881no—
264C22—1882no—
265C22—1881no—
266C22—1882no—
267C22—1882no—
268C22—1881no—
269C22#1309404612yes—
270C22C22×D18811yescharacteristic
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—1881no—
277C4—1881no—
278C4—1882no—
279C4—1881no—
280C4#1309407012yes—
281C2—22no—
282C2—3762no—
283C2—3761no—
284C2#1568969211yescharacteristic
285C2C2×#1309404611yescharacteristic
286C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3211
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #15689657C2semidirect
2. C2×#13094012C2semidirect
3. #15689507C2semidirect
4. #15689478C2semidirect
5. #15689346C2semidirect
6. #15689339C2semidirect
7. #15689281C2semidirect
8. #15689276C2semidirect
9. #15689264C2semidirect
11. C47×#431C2semidirect
14. C2×Dic188C22semidirect
16. C2×#10625325C22semidirect
19. #13094016C22semidirect
24. #13094012C22semidirect
28. C4×Dic94C22semidirect
29. C4×D188C22semidirect
34. #13093949C22semidirect
35. #13093949C22semidirect
39. C4⋊C8×C47C22semidirect
42. C4×C8×C47C22semidirect
154. #431D47semidirect
155. C47#3211semidirect
179. C4⋊C8C2×D47semidirect
186. C4×C8C2×D47semidirect