Finite Group Databasebeta

← D4×#10625334 #20255061

Subgroups — D4×#10625334 #20255061

Order 6016.

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

normal subgroups only

This group has 620 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
1C22×#10625334C212yesmaximal, complemented
2D4×D188C211yesmaximal, characteristic, complemented
3#15689499C211yesmaximal, characteristic, complemented
4#15689357C212yesmaximal, complemented
5#15689318C211yesmaximal, characteristic, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689257C212yesmaximal, complemented
8#15689256C212yesmaximal, complemented
9C4×#10625334C211yesmaximal, characteristic, complemented
10D4×C47⋊C8C211yesmaximal, characteristic, complemented
11D42×C47C211yesmaximal, characteristic, complemented
12C22×D188C2212yescomplemented
13C2×D4×D47—21no—
14C2×#10625334—28no—
15C2×#10625334C2211yescharacteristic
16C2×#10625334C2212yescomplemented
17C2×#10625334C2212yescomplemented
18C2×#10625334C2212yescomplemented
19C2×#10625334C2212yescomplemented
20C22×C47⋊C8C2212yescomplemented
21#13094021C2211yescharacteristic, complemented
22#13093999—21no—
23#13093998C2212yescomplemented
24#13093994—22no—
25C4×D188C2211yescharacteristic, complemented
26#13093957C2211yescharacteristic, complemented
27C4⋊(C47⋊C8)C2211yescharacteristic, complemented
28#13093945C2211yescharacteristic, complemented
29#13093945C2212yescomplemented
30#13093944C2211yescharacteristic, complemented
31#13093944C2212yescomplemented
32C22⋊(C47⋊C8)C2212yescomplemented
33C4×C47⋊C8C2211yescharacteristic, complemented
34C22×D4×C47—21no—
35C22×D4×C47C2212yescomplemented
36#127×C47C2211yescharacteristic, complemented
37#121×C47—21no—
38#121×C47C2212yescomplemented
39#120×C47—22no—
40C4×D4×C47C2211yescharacteristic
41C4×D4×C47C2211yescharacteristic, complemented
42C24×C47—22no—
43C23×D47—22no—
44C2×D4×C47—24no—
45C2×D4×C47—22no—
46C2×D4×C47—22no—
47C2×D4×C47—21no—
48C2×D4×C47—21no—
49C2×D4×C47—42no—
50C2×D4×C47—44no—
51C2×D4×C47D411yescharacteristic
52C2×D4×C47C2312yes—
53C2×D4×C47C2311yescharacteristic
54C22×C4×C47—21no—
55C22×C4×C47C2312yes—
56C2×C22⋊D47—22no—
57D4×D47—44no—
58C2×D188—24no—
59C2×D188—22no—
60C2×D188—21no—
61C2×D188—21no—
62C2×D188—42no—
63C2×D188C2312yes—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C4⋊C4×C47D411yescharacteristic
67C4⋊C4×C47C2311yescharacteristic
68C22⋊C4×C47—21no—
69C22⋊C4×C47—22no—
70C22⋊C4×C47D412yes—
71C42×C47C2311yescharacteristic
72#10625334—24no—
73#10625334—24no—
74#10625334—24no—
75#10625334—42no—
76#10625334D414yesdirect product factor
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—22no—
79C4⋊Dic47C2311yescharacteristic
80C2×C47⋊C8—24no—
81C2×C47⋊C8C2311yescharacteristic
82C2×C47⋊C8C2312yes—
83C2×C47⋊C8C2311yescharacteristic
84C23×C47—21no—
85C23×C47—22no—
86C23×C47—44no—
87C23×C47—44no—
88C23×C47—82no—
89C23×C47C2×D412yes—
90C22×D47—21no—
91C22×D47—22no—
92C22×D47—44no—
93C22×D47—44no—
94C22×D47—82no—
95D4×C47—22no—
96D4×C47—21no—
97D4×C47—22no—
98D4×C47—44no—
99D4×C47—44no—
100D4×C47—42no—
101D4×C47—81no—
102D4×C47D814yescomplemented
103D4×C47C2×D412yescomplemented
104C2×C4×C47—22no—
105C2×C4×C47—22no—
106C2×C4×C47—21no—
107C2×C4×C47—42no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D412yes—
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2411yescharacteristic
112C22⋊D47—44no—
113C2×Dic47—21no—
114D188—22no—
115D188—21no—
116D188—22no—
117D188—44no—
118D188—42no—
119D188—81no—
120D188C2×D412yescomplemented
121C4×D47—42no—
122C47⋊C8—22no—
123C47⋊C8—21no—
124C47⋊C8C2×D412yescomplemented
125C22×C47—22no—
126C22×C47—22no—
127C22×C47—22no—
128C22×C47—41no—
129C22×C47—41no—
130C22×C47—42no—
131C22×C47—42no—
132C22×C47—42no—
133C22×C47—88no—
134C22×C47C2×D814yescomplemented
135C22×C47C22×D411yescharacteristic
136C2×D47—22no—
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—42no—
140C2×D47—42no—
141C2×D47—42no—
142C2×D47—88no—
143C4×C47—22no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47C2×D812yescomplemented
147C4×C47C22×D411yescharacteristic
148C4×C47H(5,𝔽2)11yescharacteristic
149Dic47—41no—
150D4×D8—471nomaximal, Sylow
151C2×C47—24no—
152C2×C47—42no—
153C2×C47—82no—
154C2×C47D4211yescharacteristic
155C2×C47C22×D811yescharacteristic
156C2×C47#57611yescharacteristic
157D47—42no—
158D47—82no—
159C22×D8—472no—
160D42—471no—
161D42D4711yescharacteristic, complemented
162#493—471no—
163#466—472no—
164#459—471no—
165#459—471no—
166#447—472no—
167#447—472no—
168C4×D8—471no—
169C8×D4—471no—
170C47D4×D811yescharacteristic, complemented, Sylow
171C22×D4—21no—
172C22×D4—472no—
173C22×D4—941no—
174C22×D4C2×D4712yescomplemented
175C2×D8—471no—
176C2×D8—472no—
177C2×D8—472no—
178C2×D8—472no—
179C2×D8—472no—
180C2×D8—948no—
181C22×C8—472no—
182#127—471no—
183#127C2×D4711yescharacteristic, complemented
184#121—21no—
185#121—472no—
186#121—941no—
187#121C2×D4712yescomplemented
188#120—22no—
189#120—942no—
190C4×D4—471no—
191C4×D4C2×D4711yescharacteristic
192C4×D4C2×D4711yescharacteristic, complemented
193#107—471no—
194C4⋊C8—471no—
195#102—471no—
196#102—472no—
197#102—471no—
198#102—472no—
199C22⋊C8—472no—
200C4×C8—471no—
201C24—22no—
202C24—942no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—471no—
211C2×D4—472no—
212C2×D4—944no—
213C2×D4—942no—
214C2×D4—941no—
215C2×D4—942no—
216C2×D4—941no—
217C2×D4—1882no—
218C2×D4—1884no—
219C2×D4C22⋊D4711yescharacteristic
220C2×D4C22×D4712yes—
221C2×D4C22×D4711yescharacteristic
222C22×C4—21no—
223C22×C4—941no—
224C22×C4C22×D4712yes—
225D8—474no—
226D8—944no—
227D8—944no—
228D8—944no—
229D8—1882no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—472no—
233C2×C8—944no—
234C4⋊C4—471no—
235C4⋊C4C22⋊D4711yescharacteristic
236C4⋊C4C22×D4711yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—941no—
240C22⋊C4—942no—
241C22⋊C4C22⋊D4712yes—
242C42C22×D4711yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—941no—
249C23—942no—
250C23—3762no—
251C23—1884no—
252C23—1884no—
253C23C2×C22⋊D4712yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—472no—
262D4—942no—
263D4—941no—
264D4—942no—
265D4—3761no—
266D4—1884no—
267D4—1884no—
268D4—1882no—
269D4#1062533414yesdirect product factor
270D4D4×D4712yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—941no—
276C2×C4—1882no—
277C2×C4C2×C22⋊D4711yescharacteristic
278C2×C4C2×C22⋊D4712yes—
279C2×C4C2×C22⋊D4711yescharacteristic
280C2×C4C23×D4711yescharacteristic
281C8—472no—
282C8—942no—
283C8—941no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—942no—
294C22—3768no—
295C22—1882no—
296C22—1882no—
297C22—1882no—
298C22—1881no—
299C22—1881no—
300C22C2×#1062533414yescomplemented
301C22C22×C22⋊D4711yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—1881no—
306C4C2×#1062533412yescomplemented
307C4C2×D4×D4711yescharacteristic
308C4#1309406911yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—3762no—
313C2—1882no—
314C2D4×C22⋊D4711yescharacteristic
315C2C22×#1062533411yescharacteristic
316C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD42×C47C2
socleC22×C47C22×D4
hypercenterD42D47
hypocenterC47D4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#10625334C2semidirect
2. D4×D188C2semidirect
3. #15689499C2semidirect
4. #15689357C2semidirect
5. #15689318C2semidirect
6. #15689315C2semidirect
7. #15689257C2semidirect
8. #15689256C2semidirect
9. C4×#10625334C2semidirect
10. D4×C47⋊C8C2semidirect
11. D42×C47C2semidirect
12. C22×D188C22semidirect
16. C2×#10625334C22semidirect
17. C2×#10625334C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625334C22semidirect
20. C22×C47⋊C8C22semidirect
21. #13094021C22semidirect
23. #13093998C22semidirect
25. C4×D188C22semidirect
26. #13093957C22semidirect
27. C4⋊(C47⋊C8)C22semidirect
28. #13093945C22semidirect
29. #13093945C22semidirect
30. #13093944C22semidirect
31. #13093944C22semidirect
32. C22⋊(C47⋊C8)C22semidirect
33. C4×C47⋊C8C22semidirect
35. C22×D4×C47C22semidirect
36. #127×C47C22semidirect
38. #121×C47C22semidirect
41. C4×D4×C47C22semidirect
76. #10625334D4direct (N × H)
102. D4×C47D8semidirect
103. D4×C47C2×D4semidirect
120. D188C2×D4semidirect
124. C47⋊C8C2×D4semidirect
134. C22×C47C2×D8semidirect
146. C4×C47C2×D8semidirect
161. D42D47semidirect
170. C47D4×D8semidirect
174. C22×D4C2×D47semidirect
183. #127C2×D47semidirect
187. #121C2×D47semidirect
192. C4×D4C2×D47semidirect
269. D4#10625334direct (N × H)
270. D4D4×D47semidirect
300. C22C2×#10625334semidirect
306. C4C2×#10625334semidirect