Finite Group Databasebeta

← #20252658

Subgroups — #20252658

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×#13094052C211yesmaximal, characteristic, complemented
3C22×D376C211yesmaximal, characteristic, complemented
4#15689687C211yesmaximal, characteristic, complemented
5#15689270C214yesmaximal, complemented
6#15689259C214yesmaximal, complemented
7#15689129C211yesmaximal, characteristic, complemented
8#15689120C211yesmaximal, characteristic, complemented
9C47×#408C211yesmaximal, characteristic, complemented
10#13094070—24no—
11#13094070—24no—
12C2×#10625354—21no—
13C2×#10625350C2211yescharacteristic
14C2×#10625350C2212yescomplemented
15C22×D188C2211yescharacteristic
16C22×D188C2212yescomplemented
17C22×D188C2211yescharacteristic, complemented
18C2×D4×D47—21no—
19C2×D4×D47—22no—
20#13094052—24no—
21C2×#10625325C2212yescomplemented
22C2×D376—24no—
23C2×D376C2212yescomplemented
24C2×D376C2214yescomplemented
25#13094020—21no—
26#13094013—21no—
27#13093998C2214yescomplemented
28#13093992—22no—
29#13093983C2211yescharacteristic, complemented
30#13093949C2212yescomplemented
31#13093946C2212yescomplemented
32#13093946C2214yescomplemented
33C2×#41×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic, complemented
35C22×C8×C47C2211yescharacteristic, complemented
36C22⋊C8×C47C2214yescomplemented
37C23×D47—21no—
38C23×D47—22no—
39C23×D47—21no—
40#41×C47—22no—
41#41×C47—22no—
42C2×Q8×C47D411yescharacteristic
43C2×D4×C47D412yes—
44C2×D4×C47D411yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—24no—
50#10625354—28no—
51D4×D47—216no—
52D4×D47—28no—
53#10625350—22no—
54#10625350—24no—
55#10625350—24no—
56#10625350D414yescomplemented
57C2×D188—21no—
58C2×D188—22no—
59C2×D188—22no—
60C2×D188—24no—
61C2×D188—24no—
62C2×D188—22no—
63C2×D188—22no—
64C2×D188—21no—
65C2×D188D414yescomplemented
66C2×D188C2312yes—
67C2×D188C2312yes—
68C2×D188C2311yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—22no—
71C2×Dic94C2311yescharacteristic
72M16×C47—22no—
73C2×C8×C47—22no—
74C2×C8×C47C2312yes—
75C2×C8×C47C2312yes—
76C22⋊Dic47—21no—
77(C2×D47)⋊C4—24no—
78C4⋊Dic47C2312yes—
79C4×Dic47—21no—
80D376—28no—
81D376—24no—
82#10625325—24no—
83C23×C47C2×D412yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—21no—
86C22×D47—22no—
87C22×D47—28no—
88C22×D47—24no—
89C22×D47—22no—
90C22×D47—42no—
91C22×D47—82no—
92C22×D47—84no—
93C22×D47—82no—
94Q8×C47—22no—
95D4×C47—24no—
96D4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2411yescharacteristic
104C22⋊D47—28no—
105C22⋊D47—24no—
106C22⋊D47—84no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109D188—28no—
110D188—24no—
111D188—21no—
112D188—22no—
113D188—22no—
114D188—22no—
115D188—42no—
116D188C2×D412yes—
117D188C2×D414yes—
118C4×D47—28no—
119C4×D47—24no—
120Dic94—21no—
121Dic94C2×D412yes—
122C8×C47—22no—
123C8×C47—22no—
124C22×C47—22no—
125C22×C47—22no—
126C22×C47—24no—
127C22×C47#12012yes—
128C22×C47C22×D411yescharacteristic
129C2×D47—24no—
130C2×D47—22no—
131C2×D47—44no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—44no—
135C2×D47—84no—
136C2×D47—88no—
137C2×D47—84no—
138C4×C47—22no—
139C4×C47#12012yes—
140C4×C47C22×D411yescharacteristic
141C4×C47C22×D411yescharacteristic
142Dic47—22no—
143Dic47—42no—
144#3008—471nomaximal, Sylow
145C2×C47—22no—
146C2×C47—42no—
147C2×C47C2×#12011yescharacteristic
148C2×C47#57612yes—
149D47—44no—
150D47—42no—
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#416—471no—
160#408D4711yescharacteristic, complemented
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—471no—
169C22×D4—471no—
170C22×D4—472no—
171C22×D4—942no—
172C22×D4—941no—
173AGL(1,ℤ/8)—944no—
174C2×SD16—472no—
175C2×D8—474no—
176C2×D8—472no—
177C2×D8—944no—
178C2×M16C2×D4711yescharacteristic, complemented
179C22×C8C2×D4711yescharacteristic, complemented
180#127—941no—
181#124—941no—
182#121—474no—
183#120—942no—
184#117—471no—
185#103—472no—
186#102—472no—
187#102—474no—
188C22⋊C8C2×D4714yescomplemented
189C24—942no—
190C24—941no—
191C24—941no—
192#41—22no—
193#41—22no—
194#41—474no—
195#41—944no—
196#41—944no—
197#41—948no—
198#41—942no—
199C2×Q8—471no—
200C2×Q8D18811yescharacteristic
201C2×D4—474no—
202C2×D4—472no—
203C2×D4—471no—
204C2×D4—472no—
205C2×D4—944no—
206C2×D4—944no—
207C2×D4—9416no—
208C2×D4—948no—
209C2×D4—942no—
210C2×D4—941no—
211C2×D4—944no—
212C2×D4—942no—
213C2×D4—941no—
214C2×D4—941no—
215C2×D4—942no—
216C2×D4—942no—
217C2×D4—942no—
218C2×D4D18812yes—
219C2×D4D18811yescharacteristic
220C22×C4—942no—
221C22×C4—941no—
222C22×C4C22×D4712yes—
223C22×C4C22×D4711yescharacteristic
224SD16—944no—
225D8—948no—
226D8—944no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D4712yes—
230C2×C8C22×D4712yes—
231C4⋊C4—472no—
232C22⋊C4—941no—
233C22⋊C4—944no—
234C42—941no—
235C23—948no—
236C23—944no—
237C23—942no—
238C23—941no—
239C23—942no—
240C23—3762no—
241C23—3762no—
242C23—3764no—
243C23—1882no—
244C23C2×D18812yes—
245C23C2×D18811yescharacteristic
246Q8—22no—
247Q8—472no—
248Q8—941no—
249D4—24no—
250D4—22no—
251D4—474no—
252D4—472no—
253D4—948no—
254D4—948no—
255D4—944no—
256D4—944no—
257D4—941no—
258D4—942no—
259D4—942no—
260D4—942no—
261D4—3764no—
262D4—1882no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—948no—
266C2×C4—941no—
267C2×C4—944no—
268C2×C4—942no—
269C2×C4C2×D18812yes—
270C2×C4C2×D18811yescharacteristic
271C2×C4D4×D4712yes—
272C2×C4D4×D4712yes—
273C2×C4C23×D4711yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—944no—
280C22—942no—
281C22—3764no—
282C22—3764no—
283C22—3768no—
284C22—1882no—
285C22—1884no—
286C22—1884no—
287C22—1882no—
288C22#1309399412yes—
289C22C22×D18811yescharacteristic
290C4—22no—
291C4—942no—
292C4—1882no—
293C4#1309399412yes—
294C4C2×D4×D4711yescharacteristic
295C4C2×D4×D4711yescharacteristic
296C2—22no—
297C2—42no—
298C2—3762no—
299C2—1884no—
300C2—1882no—
301C2C2×#1309399411yescharacteristic
302C2#1568992812yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3008
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. C2×#13094052C2semidirect
3. C22×D376C2semidirect
4. #15689687C2semidirect
5. #15689270C2semidirect
6. #15689259C2semidirect
7. #15689129C2semidirect
8. #15689120C2semidirect
9. C47×#408C2semidirect
14. C2×#10625350C22semidirect
16. C22×D188C22semidirect
17. C22×D188C22semidirect
21. C2×#10625325C22semidirect
23. C2×D376C22semidirect
24. C2×D376C22semidirect
27. #13093998C22semidirect
29. #13093983C22semidirect
30. #13093949C22semidirect
31. #13093946C22semidirect
32. #13093946C22semidirect
34. C2×M16×C47C22semidirect
35. C22×C8×C47C22semidirect
36. C22⋊C8×C47C22semidirect
56. #10625350D4semidirect
65. C2×D188D4semidirect
160. #408D47semidirect
161. C47#3008semidirect
178. C2×M16C2×D47semidirect
179. C22×C8C2×D47semidirect
188. C22⋊C8C2×D47semidirect