Finite Group Databasebeta

← C47×#3242 #20240852

Subgroups — C47×#3242 #20240852

Order 6016.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#544C211yesmaximal, characteristic
2C47×#541C211yesmaximal, characteristic
3C47×#501C211yesmaximal, characteristic, complemented
4C47×#499C211yesmaximal, characteristic, complemented
5C47×#491C211yesmaximal, characteristic, complemented
6C47×#487C211yesmaximal, characteristic, complemented
7C47×#485C211yesmaximal, characteristic
8C47×#485C211yesmaximal, characteristic
9C47×#484C211yesmaximal, characteristic
10C47×#483C211yesmaximal, characteristic
11C47×#479C211yesmaximal, characteristic, complemented
12C47×#479C211yesmaximal, characteristic, complemented
13C47×#477C211yesmaximal, characteristic, complemented
14C47×#475C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic
16C4⋊Q8×C47—21no—
17C4⋊Q8×C47C2211yescharacteristic
18C4⋊Q8×C47C2211yescharacteristic
19C4⋊Q8×C47C2211yescharacteristic
20#126×C47—21no—
21#126×C47—21no—
22#125×C47—21no—
23#125×C47—21no—
24#125×C47—21no—
25#125×C47C2211yescharacteristic
26#125×C47C2211yescharacteristic
27#125×C47C2211yescharacteristic
28C22⋊Q8×C47—21no—
29C22⋊Q8×C47—21no—
30C22⋊Q8×C47C2211yescharacteristic
31C22⋊Q8×C47C2211yescharacteristic
32C4×Q8×C47C2211yescharacteristic
33C4×Q8×C47C2211yescharacteristic
34#117×C47C2211yescharacteristic
35#117×C47C2211yescharacteristic
36C2×C4⋊C4×C47C2211yescharacteristic
37#107×C47C2211yescharacteristic
38#107×C47C2211yescharacteristic
39#107×C47C2211yescharacteristic
40#107×C47C2211yescharacteristic
41#106×C47C2211yescharacteristic
42#106×C47C2211yescharacteristic
43#106×C47C2211yescharacteristic
44#106×C47C2211yescharacteristic
45C4⋊C8×C47C2211yescharacteristic
46C4⋊C8×C47C2211yescharacteristic
47#103×C47C2211yescharacteristic
48#103×C47C2211yescharacteristic
49#103×C47C2211yescharacteristic
50#103×C47C2211yescharacteristic
51#103×C47C2211yescharacteristic
52#103×C47C2211yescharacteristic
53#103×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47D411yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47D411yescharacteristic
96C22⋊C4×C47D411yescharacteristic
97C42×C47—21no—
98C42×C47—21no—
99C42×C47—21no—
100C42×C47C2311yescharacteristic
101C42×C47C2311yescharacteristic
102C23×C47C2×D411yescharacteristic
103Q8×C47—21no—
104Q8×C47—21no—
105Q8×C47—21no—
106Q8×C47—21no—
107Q8×C47—81no—
108Q8×C47—81no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—81no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C8×C47—21no—
127C8×C47—21no—
128C8×C47—21no—
129C8×C47—21no—
130C22×C47—21no—
131C22×C47—21no—
132C22×C47—21no—
133C22×C47C22×D411yescharacteristic
134C4×C47—21no—
135C4×C47—21no—
136C4×C47—21no—
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C472−1+411yescharacteristic
148C4×C472−1+411yescharacteristic
149#3242C4711yesmaximal, characteristic, direct product factor, Sylow
150C2×C47—41no—
151C2×C47#53611yescharacteristic
152C2×C47#57711yescharacteristic
153C2×C47#57811yescharacteristic
154#544C2×C4711yescharacteristic
155#541C2×C4711yescharacteristic
156#501C2×C4711yescharacteristic, complemented
157#499C2×C4711yescharacteristic, complemented
158#491C2×C4711yescharacteristic, complemented
159#487C2×C4711yescharacteristic, complemented
160#485C2×C4711yescharacteristic
161#485C2×C4711yescharacteristic
162#484C2×C4711yescharacteristic
163#483C2×C4711yescharacteristic
164#479C2×C4711yescharacteristic, complemented
165#479C2×C4711yescharacteristic, complemented
166#477C2×C4711yescharacteristic, complemented
167#475C2×C4711yescharacteristic, complemented
168#433C2×C4711yescharacteristic
169C47#324211yescharacteristic, direct product factor, Sylow
170C4⋊Q8—21no—
171C4⋊Q8C22×C4711yescharacteristic
172C4⋊Q8C22×C4711yescharacteristic
173C4⋊Q8C22×C4711yescharacteristic
174#126—21no—
175#126—21no—
176#125—21no—
177#125—21no—
178#125—21no—
179#125C22×C4711yescharacteristic
180#125C22×C4711yescharacteristic
181#125C22×C4711yescharacteristic
182C22⋊Q8—21no—
183C22⋊Q8—21no—
184C22⋊Q8C22×C4711yescharacteristic
185C22⋊Q8C22×C4711yescharacteristic
186C4×Q8C22×C4711yescharacteristic
187C4×Q8C22×C4711yescharacteristic
188#117C22×C4711yescharacteristic
189#117C22×C4711yescharacteristic
190C2×C4⋊C4C22×C4711yescharacteristic
191#107C22×C4711yescharacteristic
192#107C22×C4711yescharacteristic
193#107C22×C4711yescharacteristic
194#107C22×C4711yescharacteristic
195#106C22×C4711yescharacteristic
196#106C22×C4711yescharacteristic
197#106C22×C4711yescharacteristic
198#106C22×C4711yescharacteristic
199C4⋊C8C22×C4711yescharacteristic
200C4⋊C8C22×C4711yescharacteristic
201#103C22×C4711yescharacteristic
202#103C22×C4711yescharacteristic
203#103C22×C4711yescharacteristic
204#103C22×C4711yescharacteristic
205#103C22×C4711yescharacteristic
206#103C22×C4711yescharacteristic
207#103C22×C4711yescharacteristic
208#103C22×C4711yescharacteristic
209C22⋊C8C22×C4711yescharacteristic
210C22⋊C8C22×C4711yescharacteristic
211#97C22×C4711yescharacteristic
212C4×C8C22×C4711yescharacteristic
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8C23×C4711yescharacteristic
216C2×Q8C23×C4711yescharacteristic
217C22×C4—21no—
218C22×C4C23×C4711yescharacteristic
219C2×C8C23×C4711yescharacteristic
220C2×C8C23×C4711yescharacteristic
221C2×C8C23×C4711yescharacteristic
222C2×C8C23×C4711yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4D4×C4711yescharacteristic
239C4⋊C4D4×C4711yescharacteristic
240C4⋊C4C23×C4711yescharacteristic
241C4⋊C4C23×C4711yescharacteristic
242C4⋊C4C23×C4711yescharacteristic
243C4⋊C4C23×C4711yescharacteristic
244C4⋊C4C23×C4711yescharacteristic
245C4⋊C4C23×C4711yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4D4×C4711yescharacteristic
250C22⋊C4D4×C4711yescharacteristic
251C42—21no—
252C42—21no—
253C42—21no—
254C42C23×C4711yescharacteristic
255C42C23×C4711yescharacteristic
256C23C2×D4×C4711yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—21no—
260Q8—21no—
261Q8—81no—
262Q8—81no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—81no—
274C2×C4C2×D4×C4711yescharacteristic
275C2×C4C2×D4×C4711yescharacteristic
276C2×C4C2×D4×C4711yescharacteristic
277C2×C4C2×D4×C4711yescharacteristic
278C2×C4C2×D4×C4711yescharacteristic
279C2×C4C24×C4711yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D4×C4711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C42−1+4×C4711yescharacteristic
302C42−1+4×C4711yescharacteristic
303C2—41no—
304C2C47×#53611yescharacteristic
305C2C47×#57711yescharacteristic
306C2C47×#57811yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radicalC23×C47C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ #117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#501C2semidirect
4. C47×#499C2semidirect
5. C47×#491C2semidirect
6. C47×#487C2semidirect
11. C47×#479C2semidirect
12. C47×#479C2semidirect
13. C47×#477C2semidirect
14. C47×#475C2semidirect
149. #3242C47direct (N × H)
156. #501C2×C47semidirect
157. #499C2×C47semidirect
158. #491C2×C47semidirect
159. #487C2×C47semidirect
164. #479C2×C47semidirect
165. #479C2×C47semidirect
166. #477C2×C47semidirect
167. #475C2×C47semidirect
169. C47#3242direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5442
C47×#5412
C47×#5012
C47×#4992
C47×#4912
C47×#4872
C47×#4852
C47×#4842
C47×#4832
C47×#4792
C47×#4772
C47×#4752
C47×#4332
#324247