Finite Group Databasebeta

← #20252607

Subgroups — #20252607

Order 6016.

764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625352C211yesmaximal, characteristic, complemented
2C2×#13094045C212yesmaximal, complemented
3#15689636C211yesmaximal, characteristic, complemented
4#15689282C212yesmaximal, complemented
5#15689278C211yesmaximal, characteristic, complemented
6#15689269C212yesmaximal, complemented
7#15689264C211yesmaximal, characteristic, complemented
8#15689257C211yesmaximal, characteristic, complemented
9#15689116C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#450C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic, complemented
13C2×#10625352—28no—
14C2×#10625352—21no—
15C2×#10625352—21no—
16C2×#10625352C2212yes—
17C2×#10625352C2212yes—
18C22×Dic94C2211yescharacteristic
19C22×C22⋊D47—21no—
20C23×Dic47—21no—
21C22×C4×D47C2211yescharacteristic
22#13094045—28no—
23C2×#10625337C2212yescomplemented
24C2×#10625325C2212yescomplemented
25C2×#10625334C2212yescomplemented
26C2×C8×D47C2212yescomplemented
27#13094009—21no—
28#13094000C2211yescharacteristic, complemented
29#13093999C2211yescharacteristic, complemented
30#13093998C2211yescharacteristic
31#13093994—21no—
32#13093986—21no—
33(C22⋊D47)⋊C4—21no—
34#13093982C2211yescharacteristic, complemented
35#13093949C2212yescomplemented
36#13093947C2212yescomplemented
37#13093945C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic
39(C2×D47)⋊C8C2212yescomplemented
40C22×D4×C47C2211yescharacteristic
41C2×SD16×C47C2212yescomplemented
42C22⋊Q8×C47C2211yescharacteristic
43#102×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic
45C24×C47—21no—
46C23×D47D411yescharacteristic
47C2×Q8×C47C2311yescharacteristic
48C2×D4×C47—24no—
49C2×D4×C47—21no—
50C2×D4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—28no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—21no—
56C22×Dic47—28no—
57C22×Dic47—21no—
58C22×Dic47—22no—
59C22×Dic47—22no—
60C22×Dic47D411yescharacteristic
61#10625354—24no—
62#10625352—28no—
63#10625352—28no—
64#10625352—24no—
65#10625352—24no—
66#10625352—24no—
67#10625352D418yescomplemented
68C2×D188—21no—
69C2×D188—21no—
70C2×D188C2311yescharacteristic
71C2×C4×D47—24no—
72C2×C4×D47—21no—
73C2×C4×D47D411yescharacteristic
74C2×C4×D47D411yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94—21no—
78C2×Dic94—24no—
79C2×Dic94C2312yes—
80SD16×C47—24no—
81C2×C8×C47C2312yes—
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85#10625337—24no—
86#10625334—24no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93C4×Dic47—21no—
94C2×C47⋊C8C2312yes—
95#10625325—24no—
96C8×D47—24no—
97C23×C47—24no—
98C23×C47—22no—
99C23×C47—42no—
100C23×C47—42no—
101C23×C47C2×D411yescharacteristic
102C22×D47—22no—
103C22×D47—22no—
104C22×D47—21no—
105C22×D47—41no—
106C22×D47C2×D411yescharacteristic
107C22×D47C2×D411yescharacteristic
108Q8×C47—22no—
109D4×C47—24no—
110D4×C47—22no—
111D4×C47C2×D414yes—
112C2×C4×C47—22no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C22⋊D47—28no—
118C22⋊D47—28no—
119C22⋊D47—42no—
120C2×Dic47—24no—
121C2×Dic47—28no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—28no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128D188—22no—
129D188—42no—
130D188—42no—
131C4×D47—22no—
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—42no—
135C4×D47C2×D414yes—
136Dic94—24no—
137Dic94—22no—
138Dic94C2×D414yes—
139C8×C47—22no—
140C47⋊C8—22no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—24no—
144C22×C47—48no—
145C22×C47—42no—
146C22×C47—42no—
147C22×C47#13512yescomplemented
148C22×C47C22×D411yescharacteristic
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—44no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47#12012yes—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47C22×D412yes—
163Dic47—24no—
164Dic47—21no—
165Dic47—41no—
166Dic47#12012yes—
167#3002—471nomaximal, Sylow
168C2×C47—22no—
169C2×C47—44no—
170C2×C47C2×#12011yescharacteristic
171C2×C47C2×#13511yescharacteristic
172C2×C47#57511yescharacteristic
173D47—22no—
174D47—41no—
175D47—81no—
176C22×#41—471no—
177C2×#135—472no—
178#525—471no—
179#452—472no—
180#451—471no—
181#450D4711yescharacteristic, complemented
182#449—472no—
183#448—471no—
184#447—471no—
185#416—472no—
186C2×C22⋊C8—471no—
187C47#300211yescharacteristic, complemented, Sylow
188C2×#41—471no—
189C2×#41—472no—
190C2×#41—472no—
191C2×#41—941no—
192C2×#41—941no—
193C2×#41—948no—
194C22×Q8—471no—
195C22×D4—941no—
196C22×D4C2×D4711yescharacteristic
197C23×C4—471no—
198C23×C4—941no—
199#135—948no—
200C2×Q16—472no—
201C2×SD16—472no—
202C2×SD16C2×D4712yescomplemented
203C2×D8—472no—
204C22×C8—472no—
205#123—941no—
206C22⋊Q8—471no—
207C22⋊Q8C2×D4711yescharacteristic
208#121—471no—
209#121—471no—
210#120—941no—
211C4×D4—941no—
212C4×D4—941no—
213#117—471no—
214#103—472no—
215#103—472no—
216#102—472no—
217#102C2×D4712yescomplemented
218C22⋊C8—471no—
219C22⋊C8—472no—
220C22⋊C8C2×D4711yescharacteristic
221C24—21no—
222C24—471no—
223#41—478no—
224#41—944no—
225#41—944no—
226#41—944no—
227#41—948no—
228#41—948no—
229#41—944no—
230C2×Q8—472no—
231C2×Q8—944no—
232C2×Q8—941no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4—24no—
235C2×D4—21no—
236C2×D4—471no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4—942no—
240C2×D4—942no—
241C2×D4—948no—
242C2×D4—941no—
243C2×D4C22×D4712yes—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—944no—
250C22×C4—941no—
251C22×C4—942no—
252C22×C4—942no—
253C22×C4—948no—
254C22×C4—941no—
255C22×C4C22×D4711yescharacteristic
256Q16—944no—
257SD16—24no—
258SD16—944no—
259D8—944no—
260C2×C8—472no—
261C2×C8—944no—
262C2×C8C22×D4712yes—
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—941no—
266C4⋊C4C22×D4711yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C42—941no—
273C23—24no—
274C23—22no—
275C23—42no—
276C23—42no—
277C23—471no—
278C23—471no—
279C23—942no—
280C23—942no—
281C23—941no—
282C23—1881no—
283C23D4×D4711yescharacteristic
284Q8—22no—
285Q8—474no—
286Q8—944no—
287Q8—942no—
288D4—24no—
289D4—22no—
290D4—948no—
291D4—948no—
292D4—942no—
293D4—1882no—
294D4—1882no—
295D4—1882no—
296D4D4×D4714yes—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—471no—
301C2×C4—474no—
302C2×C4—471no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—948no—
307C2×C4—944no—
308C2×C4—948no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—941no—
312C2×C4—1882no—
313C2×C4D4×D4711yescharacteristic
314C2×C4C23×D4711yescharacteristic
315C8—22no—
316C8—942no—
317C22—21no—
318C22—21no—
319C22—24no—
320C22—48no—
321C22—42no—
322C22—42no—
323C22—472no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22—1884no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22#1309404512yescomplemented
334C22C2×D4×D4711yescharacteristic
335C4—21no—
336C4—41no—
337C4—41no—
338C4—472no—
339C4—941no—
340C4—944no—
341C4—1881no—
342C4C2×D4×D4712yes—
343C2—22no—
344C2—44no—
345C2—942no—
346C2—3761no—
347C2—1881no—
348C2#120×D4711yescharacteristic
349C2C2×#1309404511yescharacteristic
350C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3002
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×#13094045C2semidirect
3. #15689636C2semidirect
4. #15689282C2semidirect
5. #15689278C2semidirect
6. #15689269C2semidirect
7. #15689264C2semidirect
8. #15689257C2semidirect
9. #15689116C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#450C2semidirect
12. C2×#10625354C22semidirect
23. C2×#10625337C22semidirect
24. C2×#10625325C22semidirect
25. C2×#10625334C22semidirect
26. C2×C8×D47C22semidirect
28. #13094000C22semidirect
29. #13093999C22semidirect
34. #13093982C22semidirect
35. #13093949C22semidirect
36. #13093947C22semidirect
37. #13093945C22semidirect
39. (C2×D47)⋊C8C22semidirect
41. C2×SD16×C47C22semidirect
43. #102×C47C22semidirect
67. #10625352D4semidirect
147. C22×C47#135semidirect
181. #450D47semidirect
187. C47#3002semidirect
202. C2×SD16C2×D47semidirect
217. #102C2×D47semidirect
333. C22#13094045semidirect