Finite Group Databasebeta

← C47×#9846 #26049544

Subgroups — C47×#9846 #26049544

Order 12032.

460 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3167C211yesmaximal, characteristic
2C47×#1994C211yesmaximal, characteristic, complemented
3C47×#1962C211yesmaximal, characteristic
4C47×#1744C211yesmaximal, characteristic, complemented
5C47×#1566C211yesmaximal, characteristic, complemented
6C47×#1493C211yesmaximal, characteristic, complemented
7C47×#1492C211yesmaximal, characteristic
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#498C411yescharacteristic, complemented
11C47×#492C411yescharacteristic, complemented
12C47×#487C411yescharacteristic, complemented
13C47×#486C411yescharacteristic, complemented
14C47×#465—22no—
15C4×SD16×C47—22no—
16C47×#423C2211yescharacteristic
17C47×#423C2211yescharacteristic
18C2×#104×C47—22no—
19C2×C4×C8×C47C2211yescharacteristic
20C2×C4×C8×C47C2211yescharacteristic
21C43×C47C2211yescharacteristic
22C47×#339—22no—
23C47×#336—22no—
24C47×#334—22no—
25C47×Q8⋊C8—22no—
26C47×D4⋊C8—22no—
27C2×#41×C47—21no—
28C2×SD16×C47—22no—
29C2×M16×C47—21no—
30C2×M16×C47—21no—
31C22×C8×C47—21no—
32C22×C8×C47D412yes—
33C4⋊Q8×C47C2×C411yescharacteristic
34C4⋊Q8×C47C2×C411yescharacteristic
35C4⋊Q8×C47C2×C411yescharacteristic
36#127×C47C2×C411yescharacteristic
37#125×C47—21no—
38#124×C47—21no—
39C22⋊Q8×C47—21no—
40C22⋊Q8×C47—21no—
41#121×C47—21no—
42#121×C47—21no—
43C4×Q8×C47—21no—
44C4×Q8×C47—21no—
45C4×D4×C47—21no—
46C4×D4×C47—21no—
47#117×C47—21no—
48C2×C42×C47—21no—
49C2×C42×C47—21no—
50C2×C42×C47D412yes—
51C2×C42×C47C2311yescharacteristic
52#106×C47—22no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57#104×C47—44no—
58#103×C47—22no—
59#102×C47—22no—
60C4×C8×C47—21no—
61C4×C8×C47C2×C411yescharacteristic
62C4×C8×C47C2×C411yescharacteristic
63C4×C8×C47D412yes—
64C4×C8×C47D412yes—
65#41×C47—42no—
66#41×C47—42no—
67C2×Q8×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—41no—
74C22×C4×C47—22no—
75C22×C4×C47—41no—
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47#4111yescharacteristic
79SD16×C47—44no—
80M16×C47—42no—
81M16×C47—42no—
82C2×C8×C47—22no—
83C2×C8×C47—42no—
84C2×C8×C47—42no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47C22⋊C412yes—
88C2×C8×C47C22⋊C412yes—
89C4⋊C4×C47—21no—
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—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C42×C47—22no—
101C42×C47—42no—
102C42×C47—42no—
103C42×C47—41no—
104C42×C47SD1614yescomplemented
105C42×C47C22×C411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47#4111yescharacteristic
109C23×C47—41no—
110C23×C47#12111yescharacteristic
111Q8×C47—42no—
112Q8×C47—42no—
113Q8×C47—42no—
114D4×C47—42no—
115D4×C47—42no—
116D4×C47—42no—
117D4×C47—82no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—24no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C2×C22⋊C411yescharacteristic
129C2×C4×C47C4×D411yescharacteristic
130C2×C4×C47C4×D411yescharacteristic
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12411yescharacteristic
133C2×C4×C47#12711yescharacteristic
134C2×C4×C47C2×SD1612yes—
135C2×C4×C47#13512yes—
136C8×C47—22no—
137C8×C47—22no—
138C8×C47—42no—
139C8×C47—81no—
140C8×C47—81no—
141#9846C4711yesmaximal, characteristic, direct product factor, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—81no—
145C22×C47—81no—
146C22×C47—81no—
147C22×C47#39011yescharacteristic
148C22×C47#46512yes—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—44no—
152C4×C47—81no—
153C4×C47—81no—
154C4×C47—81no—
155C4×C47#42112yes—
156C4×C47C4×SD1612yes—
157C4×C47#44412yes—
158C4×C47#49211yescharacteristic
159C4×C47#49511yescharacteristic
160#3167C2×C4711yescharacteristic
161#1994C2×C4711yescharacteristic, complemented
162#1962C2×C4711yescharacteristic
163#1744C2×C4711yescharacteristic, complemented
164#1566C2×C4711yescharacteristic, complemented
165#1493C2×C4711yescharacteristic, complemented
166#1492C2×C4711yescharacteristic
167C2×C47—22no—
168C2×C47—161no—
169C2×C47#196311yescharacteristic
170C2×C47#196811yescharacteristic
171C2×C47#197511yescharacteristic
172#533C22×C4711yescharacteristic
173#532C22×C4711yescharacteristic
174#498C4×C4711yescharacteristic, complemented
175#492C4×C4711yescharacteristic, complemented
176#487C4×C4711yescharacteristic, complemented
177#486C4×C4711yescharacteristic, complemented
178#465—22no—
179C4×SD16—22no—
180#423C22×C4711yescharacteristic
181#423C22×C4711yescharacteristic
182C2×#104—22no—
183C2×C4×C8C22×C4711yescharacteristic
184C2×C4×C8C22×C4711yescharacteristic
185C43C22×C4711yescharacteristic
186#339—22no—
187#336—22no—
188#334—22no—
189Q8⋊C8—22no—
190D4⋊C8—22no—
191C47#984611yescharacteristic, direct product factor, Sylow
192C2×#41—21no—
193C2×SD16—22no—
194C2×M16—21no—
195C2×M16—21no—
196C22×C8—21no—
197C22×C8D4×C4712yes—
198C4⋊Q8C2×C4×C4711yescharacteristic
199C4⋊Q8C2×C4×C4711yescharacteristic
200C4⋊Q8C2×C4×C4711yescharacteristic
201#127C2×C4×C4711yescharacteristic
202#125—21no—
203#124—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206#121—21no—
207#121—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×D4—21no—
211C4×D4—21no—
212#117—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42D4×C4712yes—
216C2×C42C23×C4711yescharacteristic
217#106—22no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222#104—44no—
223#103—22no—
224#102—22no—
225C4×C8—21no—
226C4×C8C2×C4×C4711yescharacteristic
227C4×C8C2×C4×C4711yescharacteristic
228C4×C8D4×C4712yes—
229C4×C8D4×C4712yes—
230#41—42no—
231#41—42no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—41no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4C2×D4×C4711yescharacteristic
242C22×C4C2×D4×C4711yescharacteristic
243C22×C4#41×C4711yescharacteristic
244SD16—44no—
245M16—42no—
246M16—42no—
247C2×C8—22no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8C22⋊C4×C4712yes—
253C2×C8C22⋊C4×C4712yes—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C42—22no—
266C42—42no—
267C42—42no—
268C42—41no—
269C42SD16×C4714yescomplemented
270C42C22×C4×C4711yescharacteristic
271C42C2×D4×C4711yescharacteristic
272C42C2×D4×C4711yescharacteristic
273C42#41×C4711yescharacteristic
274C23—41no—
275C23#121×C4711yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—42no—
279D4—42no—
280D4—42no—
281D4—42no—
282D4—82no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4C2×C22⋊C4×C4711yescharacteristic
294C2×C4C4×D4×C4711yescharacteristic
295C2×C4C4×D4×C4711yescharacteristic
296C2×C4#121×C4711yescharacteristic
297C2×C4#124×C4711yescharacteristic
298C2×C4#127×C4711yescharacteristic
299C2×C4C2×SD16×C4712yes—
300C2×C4#135×C4712yes—
301C8—22no—
302C8—22no—
303C8—42no—
304C8—81no—
305C8—81no—
306C22—21no—
307C22—21no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22C47×#39011yescharacteristic
312C22C47×#46512yes—
313C4—21no—
314C4—21no—
315C4—44no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4C47×#42112yes—
320C4C4×SD16×C4712yes—
321C4C47×#44412yes—
322C4C47×#49211yescharacteristic
323C4C47×#49511yescharacteristic
324C2—22no—
325C2—161no—
326C2C47×#196311yescharacteristic
327C2C47×#196811yescharacteristic
328C2C47×#197511yescharacteristic
subgroupG/H
centerC2×C4×C47#127
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#390
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1994C2semidirect
4. C47×#1744C2semidirect
5. C47×#1566C2semidirect
6. C47×#1493C2semidirect
10. C47×#498C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
104. C42×C47SD16semidirect
141. #9846C47direct (N × H)
161. #1994C2×C47semidirect
163. #1744C2×C47semidirect
164. #1566C2×C47semidirect
165. #1493C2×C47semidirect
174. #498C4×C47semidirect
175. #492C4×C47semidirect
176. #487C4×C47semidirect
177. #486C4×C47semidirect
191. C47#9846direct (N × H)
269. C42SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31672
C47×#19942
C47×#19622
C47×#17442
C47×#15662
C47×#14932
C47×#14922
#984647