Finite Group Databasebeta

← #20252659

Subgroups — #20252659

Order 6016.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#13094070C211yesmaximal, characteristic, complemented
2C2×#13094049C211yesmaximal, characteristic, complemented
3C22×D376C211yesmaximal, characteristic, complemented
4#15689692C211yesmaximal, characteristic, complemented
5#15689271C214yesmaximal, complemented
6#15689258C214yesmaximal, complemented
7#15689127C211yesmaximal, characteristic, complemented
8#15689089C211yesmaximal, characteristic, complemented
9C47×#416C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354C2212yescomplemented
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×D188—21no—
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic, complemented
18C2×D4×D47—22no—
19C2×D4×D47C2212yescomplemented
20#13094049—24no—
21C2×#10625336C2212yescomplemented
22C2×D376—24no—
23C2×D376C2214yescomplemented
24C2×#10625334C2212yescomplemented
25C2×#10625329C2211yescharacteristic, complemented
26#13094021—21no—
27#13094012—21no—
28#13093999C2214yescomplemented
29#13093994—22no—
30#13093944C2214yescomplemented
31(C2×D47)⋊C8C2214yescomplemented
32C2×#41×C47C2211yescharacteristic
33C22×C8×C47C2211yescharacteristic, complemented
34#117×C47C2211yescharacteristic, complemented
35#103×C47C2212yescomplemented
36#102×C47C2212yescomplemented
37C23×D47—21no—
38C23×D47—22no—
39C23×D47—21no—
40#41×C47—22no—
41#41×C47D414yescomplemented
42C2×Q8×C47C2311yescharacteristic
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—22no—
48C2×C22⋊D47D412yes—
49#10625354—24no—
50#10625354—24no—
51D4×D47—216no—
52D4×D47—24no—
53D4×D47—24no—
54#10625350—28no—
55#10625350—22no—
56#10625350—22no—
57C2×D188—28no—
58C2×D188—22no—
59C2×D188—21no—
60C2×D188—22no—
61C2×D188—22no—
62C2×D188—22no—
63C2×D188—21no—
64C2×D188—24no—
65C2×D188D411yescharacteristic
66C2×D188D414yescomplemented
67C2×D188C2312yes—
68C2×D188C2312yes—
69C2×C4×D47—22no—
70C2×C4×D47C2312yes—
71C2×Dic94D411yescharacteristic
72C2×C8×C47—22no—
73C2×C8×C47C2312yes—
74C4⋊C4×C47C2312yes—
75C22⋊C4×C47—21no—
76C42×C47—21no—
77#10625336—24no—
78#10625334—24no—
79(C2×D47)⋊C4—24no—
80#10625329—22no—
81C2×C47⋊C8C2312yes—
82D376—28no—
83C23×C47—21no—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—28no—
87C22×D47—24no—
88C22×D47—22no—
89C22×D47—42no—
90C22×D47—84no—
91C22×D47—82no—
92C22×D47—82no—
93C22×D47C2×D412yes—
94Q8×C47—21no—
95Q8×C47C2×D412yes—
96D4×C47—24no—
97D4×C47—21no—
98D4×C47C2×D412yes—
99C2×C4×C47—21no—
100C2×C4×C47—24no—
101C2×C4×C47—22no—
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2411yescharacteristic
106C22⋊D47—28no—
107C22⋊D47—24no—
108C2×Dic47C2×D412yes—
109D188—28no—
110D188—22no—
111D188—24no—
112D188—22no—
113D188—22no—
114D188—22no—
115D188—42no—
116D188—84no—
117D188C2×D414yes—
118C4×D47—28no—
119C4×D47—22no—
120C4×D47—22no—
121Dic94—22no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—42no—
127C22×C47#12012yes—
128C22×C47C22×D411yescharacteristic
129C2×D47—22no—
130C2×D47—24no—
131C2×D47—24no—
132C2×D47—44no—
133C2×D47—42no—
134C2×D47—44no—
135C2×D47—84no—
136C2×D47—88no—
137C2×D47—84no—
138C4×C47—22no—
139C4×C47—42no—
140C4×C47#12012yes—
141C4×C47C22×D411yescharacteristic
142C4×C47C22×D411yescharacteristic
143Dic47—22no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—42no—
147C2×C47C2×#12011yescharacteristic
148C2×C47#57612yes—
149D47—42no—
150D47—44no—
151D47—82no—
152C2×H(5,𝔽2)—471no—
153C2×AGL(1,ℤ/8)—471no—
154C22×D8—471no—
155#535—471no—
156#449—474no—
157#447—474no—
158#418—471no—
159#416D4711yescharacteristic, complemented
160#408—471no—
161C47#300811yescharacteristic, complemented, Sylow
162H(5,𝔽2)—944no—
163H(5,𝔽2)—944no—
164C2×#41—471no—
165C2×#41—472no—
166C2×#41—941no—
167C2×#41C2×D4711yescharacteristic
168C22×D4—472no—
169C22×D4—471no—
170C22×D4—471no—
171C22×D4—941no—
172C22×D4—942no—
173AGL(1,ℤ/8)—944no—
174C2×SD16—472no—
175C2×D8—472no—
176C2×D8—474no—
177C2×D8—944no—
178C2×M16—471no—
179C22×C8C2×D4711yescharacteristic, complemented
180#127—941no—
181#124—941no—
182#121—474no—
183#120—942no—
184#117C2×D4711yescharacteristic, complemented
185#103C2×D4712yescomplemented
186#102—474no—
187#102C2×D4712yescomplemented
188C22⋊C8—474no—
189C24—942no—
190C24—941no—
191C24—941no—
192#41—22no—
193#41—948no—
194#41—944no—
195#41—944no—
196#41—942no—
197#41—942no—
198#41D18814yescomplemented
199C2×Q8—471no—
200C2×Q8C22×D4711yescharacteristic
201C2×D4—21no—
202C2×D4—472no—
203C2×D4—474no—
204C2×D4—471no—
205C2×D4—472no—
206C2×D4—472no—
207C2×D4—942no—
208C2×D4—948no—
209C2×D4—944no—
210C2×D4—942no—
211C2×D4—944no—
212C2×D4—9416no—
213C2×D4—944no—
214C2×D4—942no—
215C2×D4—942no—
216C2×D4—941no—
217C2×D4—942no—
218C2×D4—941no—
219C2×D4C22×D4711yescharacteristic
220C22×C4—21no—
221C22×C4—472no—
222C22×C4—942no—
223C22×C4C22×D4711yescharacteristic
224SD16—944no—
225D8—948no—
226D8—944no—
227M16—942no—
228C2×C8—22no—
229C2×C8—472no—
230C2×C8C22×D4712yes—
231C4⋊C4C22×D4712yes—
232C22⋊C4—21no—
233C22⋊C4—944no—
234C42—21no—
235C23—21no—
236C23—472no—
237C23—948no—
238C23—944no—
239C23—942no—
240C23—942no—
241C23—3762no—
242C23—3762no—
243C23—3764no—
244C23—1882no—
245C23D4×D4711yescharacteristic
246Q8—21no—
247Q8—942no—
248Q8C2×D18812yes—
249D4—24no—
250D4—21no—
251D4—474no—
252D4—948no—
253D4—948no—
254D4—944no—
255D4—944no—
256D4—942no—
257D4—942no—
258D4—942no—
259D4—942no—
260D4—3764no—
261D4—1882no—
262D4C2×D18812yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—472no—
267C2×C4—948no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4C2×D18812yes—
271C2×C4D4×D4711yescharacteristic
272C2×C4D4×D4712yes—
273C2×C4C23×D4711yescharacteristic
274C8—22no—
275C8—942no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—944no—
280C22—942no—
281C22—944no—
282C22—3764no—
283C22—3764no—
284C22—3768no—
285C22—1882no—
286C22—1884no—
287C22—1884no—
288C22#1309399412yes—
289C22C2×D4×D4711yescharacteristic
290C4—22no—
291C4—42no—
292C4—942no—
293C4#1309399412yes—
294C4C2×D4×D4711yescharacteristic
295C4C22×D18811yescharacteristic
296C2—22no—
297C2—42no—
298C2—3762no—
299C2—1882no—
300C2—1884no—
301C2C2×#1309399411yescharacteristic
302C2#1568992512yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#416C2
socleC22×C47C22×D4
hypercenter#416D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094049C2semidirect
3. C22×D376C2semidirect
4. #15689692C2semidirect
5. #15689271C2semidirect
6. #15689258C2semidirect
7. #15689127C2semidirect
8. #15689089C2semidirect
9. C47×#416C2semidirect
12. C2×#10625354C22semidirect
17. C22×D188C22semidirect
19. C2×D4×D47C22semidirect
21. C2×#10625336C22semidirect
23. C2×D376C22semidirect
24. C2×#10625334C22semidirect
25. C2×#10625329C22semidirect
28. #13093999C22semidirect
30. #13093944C22semidirect
31. (C2×D47)⋊C8C22semidirect
33. C22×C8×C47C22semidirect
34. #117×C47C22semidirect
35. #103×C47C22semidirect
36. #102×C47C22semidirect
41. #41×C47D4semidirect
66. C2×D188D4semidirect
159. #416D47semidirect
161. C47#3008semidirect
179. C22×C8C2×D47semidirect
184. #117C2×D47semidirect
185. #103C2×D47semidirect
187. #102C2×D47semidirect
198. #41D188semidirect