Finite Group Databasebeta

← C47×#9415 #26049113

Subgroups — C47×#9415 #26049113

Order 12032.

420 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3182C211yesmaximal, characteristic
2C47×#2980C211yesmaximal, characteristic
3C47×#1537C211yesmaximal, characteristic, complemented
4C47×#1515C211yesmaximal, characteristic, complemented
5C47×#1514C211yesmaximal, characteristic
6C47×#1291C211yesmaximal, characteristic, complemented
7C47×#1288C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#500C411yescharacteristic, complemented
11C47×#492C411yescharacteristic, complemented
12C47×#487C411yescharacteristic, complemented
13C47×#486C411yescharacteristic, complemented
14C47×#468—22no—
15C47×#440—22no—
16C47×#435—22no—
17C47×#435—22no—
18C47×#432C2211yescharacteristic
19C47×#432C2211yescharacteristic
20C47×#432C2211yescharacteristic
21C47×#408—22no—
22C4×M16×C47C2211yescharacteristic
23C47×#383C2211yescharacteristic
24C47×#330—22no—
25C47×#328—22no—
26C47×#327—22no—
27C2×#41×C47—21no—
28C2×SD16×C47—22no—
29C2×M16×C47—21no—
30C2×M16×C47—22no—
31C22×C8×C47—22no—
32C4⋊Q8×C47C2×C411yescharacteristic
33C4⋊Q8×C47C2×C411yescharacteristic
34C4⋊Q8×C47C2×C411yescharacteristic
35#127×C47C2×C411yescharacteristic
36#125×C47—21no—
37#124×C47—21no—
38C22⋊Q8×C47—21no—
39C22⋊Q8×C47—21no—
40#121×C47—21no—
41#121×C47D412yes—
42C4×Q8×C47—21no—
43C4×Q8×C47—21no—
44C4×D4×C47—21no—
45C4×D4×C47D412yes—
46#117×C47—21no—
47C2×C42×C47C2311yescharacteristic
48#107×C47—22no—
49C4⋊C8×C47—21no—
50C4⋊C8×C47—21no—
51C4⋊C8×C47—21no—
52#103×C47—22no—
53#102×C47—22no—
54C22⋊C8×C47—24no—
55C22⋊C8×C47—21no—
56C22⋊C8×C47—21no—
57C22⋊C8×C47D412yes—
58#97×C47—21no—
59#97×C47—21no—
60#97×C47—21no—
61#97×C47D412yes—
62C4×C8×C47C2×C411yescharacteristic
63C4×C8×C47C2×C411yescharacteristic
64#95×C47—21no—
65#95×C47—21no—
66#95×C47—21no—
67#41×C47—81no—
68#41×C47—81no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C2×D4×C47—22no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47C22⋊C412yes—
76C22×C4×C47—22no—
77C22×C4×C47—41no—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81SD16×C47—44no—
82M16×C47—42no—
83M16×C47—82no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—22no—
87C2×C8×C47—22no—
88C2×C8×C47—41no—
89C2×C8×C47—82no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47C22⋊C412yes—
98C22⋊C4×C47—22no—
99C22⋊C4×C47—22no—
100C22⋊C4×C47—41no—
101C42×C47—41no—
102C42×C47C22×C411yescharacteristic
103C42×C47C2×D411yescharacteristic
104C42×C47C2×D411yescharacteristic
105C42×C47#4111yescharacteristic
106C23×C47—22no—
107C23×C47#12111yescharacteristic
108Q8×C47—42no—
109Q8×C47—81no—
110Q8×C47—81no—
111D4×C47—42no—
112D4×C47—81no—
113D4×C47—81no—
114D4×C47—82no—
115C2×C4×C47—22no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47C2×C22⋊C411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#12311yescharacteristic
132C8×C47—22no—
133C8×C47—42no—
134C8×C47—42no—
135C8×C47—41no—
136C8×C47—81no—
137#9415C4711yesmaximal, characteristic, direct product factor, Sylow
138C22×C47—21no—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47—42no—
142C22×C47—42no—
143C22×C47—42no—
144C22×C47#38611yescharacteristic
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—42no—
152C4×C47—81no—
153C4×C47—81no—
154C4×C47—161no—
155#3182C2×C4711yescharacteristic
156#2980C2×C4711yescharacteristic
157#1537C2×C4711yescharacteristic, complemented
158#1515C2×C4711yescharacteristic, complemented
159#1514C2×C4711yescharacteristic
160#1291C2×C4711yescharacteristic, complemented
161#1288C2×C4711yescharacteristic, complemented
162C2×C47—41no—
163C2×C47—82no—
164C2×C47#188411yescharacteristic
165C2×C47#190211yescharacteristic
166C2×C47#190411yescharacteristic
167#533C22×C4711yescharacteristic
168#532C22×C4711yescharacteristic
169#500C4×C4711yescharacteristic, complemented
170#492C4×C4711yescharacteristic, complemented
171#487C4×C4711yescharacteristic, complemented
172#486C4×C4711yescharacteristic, complemented
173#468—22no—
174#440—22no—
175#435—22no—
176#435—22no—
177#432C22×C4711yescharacteristic
178#432C22×C4711yescharacteristic
179#432C22×C4711yescharacteristic
180#408—22no—
181C4×M16C22×C4711yescharacteristic
182#383C22×C4711yescharacteristic
183#330—22no—
184#328—22no—
185#327—22no—
186C47#941511yescharacteristic, direct product factor, Sylow
187C2×#41—21no—
188C2×SD16—22no—
189C2×M16—21no—
190C2×M16—22no—
191C22×C8—22no—
192C4⋊Q8C2×C4×C4711yescharacteristic
193C4⋊Q8C2×C4×C4711yescharacteristic
194C4⋊Q8C2×C4×C4711yescharacteristic
195#127C2×C4×C4711yescharacteristic
196#125—21no—
197#124—21no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200#121—21no—
201#121D4×C4712yes—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×D4—21no—
205C4×D4D4×C4712yes—
206#117—21no—
207C2×C42C23×C4711yescharacteristic
208#107—22no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212#103—22no—
213#102—22no—
214C22⋊C8—24no—
215C22⋊C8—21no—
216C22⋊C8—21no—
217C22⋊C8D4×C4712yes—
218#97—21no—
219#97—21no—
220#97—21no—
221#97D4×C4712yes—
222C4×C8C2×C4×C4711yescharacteristic
223C4×C8C2×C4×C4711yescharacteristic
224#95—21no—
225#95—21no—
226#95—21no—
227#41—81no—
228#41—81no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×D4—22no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊C4×C4712yes—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4C2×D4×C4711yescharacteristic
239C22×C4C2×D4×C4711yescharacteristic
240C22×C4#41×C4711yescharacteristic
241SD16—44no—
242M16—42no—
243M16—82no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—82no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4C22⋊C4×C4712yes—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—41no—
261C42—41no—
262C42C22×C4×C4711yescharacteristic
263C42C2×D4×C4711yescharacteristic
264C42C2×D4×C4711yescharacteristic
265C42#41×C4711yescharacteristic
266C23—22no—
267C23#121×C4711yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—81no—
271D4—42no—
272D4—81no—
273D4—81no—
274D4—82no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C2×C22⋊C4×C4711yescharacteristic
287C2×C4C4×D4×C4711yescharacteristic
288C2×C4C4×D4×C4711yescharacteristic
289C2×C4#120×C4711yescharacteristic
290C2×C4#121×C4711yescharacteristic
291C2×C4#123×C4711yescharacteristic
292C8—22no—
293C8—42no—
294C8—42no—
295C8—41no—
296C8—81no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22C47×#38611yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—42no—
311C4—81no—
312C4—81no—
313C4—161no—
314C2—41no—
315C2—82no—
316C2C47×#188411yescharacteristic
317C2C47×#190211yescharacteristic
318C2C47×#190411yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1537C2semidirect
4. C47×#1515C2semidirect
6. C47×#1291C2semidirect
7. C47×#1288C2semidirect
10. C47×#500C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
137. #9415C47direct (N × H)
157. #1537C2×C47semidirect
158. #1515C2×C47semidirect
160. #1291C2×C47semidirect
161. #1288C2×C47semidirect
169. #500C4×C47semidirect
170. #492C4×C47semidirect
171. #487C4×C47semidirect
172. #486C4×C47semidirect
186. C47#9415direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#31822
C47×#29802
C47×#15372
C47×#15152
C47×#15142
C47×#12912
C47×#12882
#941547