Finite Group Databasebeta

← C47×#9162 #26048860

Subgroups — C47×#9162 #26048860

Order 12032.

472 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3115C211yesmaximal, characteristic
2C47×#2971C211yesmaximal, characteristic, complemented
3C47×#1759C211yesmaximal, characteristic, complemented
4C47×#1525C211yesmaximal, characteristic, complemented
5C47×#1505C211yesmaximal, characteristic, complemented
6C47×#1300C211yesmaximal, characteristic, complemented
7C47×#1291C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C4×#41×C47C2211yescharacteristic
10C47×#482—21no—
11C47×#475C411yescharacteristic, complemented
12C47×#474C411yescharacteristic, complemented
13C47×#460C411yescharacteristic, complemented
14C47×#459C411yescharacteristic, complemented
15C47×#449—21no—
16C8×Q8×C47—21no—
17C47×#442—21no—
18C47×#440—21no—
19C47×#436—22no—
20C47×#436—21no—
21C47×#432—21no—
22C47×#432C2211yescharacteristic
23C47×#432C2211yescharacteristic
24C2×#104×C47—21no—
25C4×M16×C47—21no—
26C4×M16×C47C2211yescharacteristic
27C4×M16×C47C2211yescharacteristic
28C47×#376C2211yescharacteristic
29C47×#339—21no—
30C47×#329—21no—
31C47×#329—21no—
32C47×#327—22no—
33C2×#41×C47—21no—
34C2×#41×C47D411yescharacteristic
35C2×SD16×C47—21no—
36C2×D8×C47—21no—
37C2×M16×C47—22no—
38C2×M16×C47—21no—
39C2×M16×C47—21no—
40C4⋊Q8×C47C2×C411yescharacteristic
41#127×C47C2×C411yescharacteristic
42#124×C47—21no—
43#121×C47—21no—
44#121×C47—21no—
45C4×Q8×C47C2×C411yescharacteristic
46C4×Q8×C47D411yescharacteristic
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47—21no—
50C4×D4×C47—21no—
51C4×D4×C47C2×C411yescharacteristic
52C4×D4×C47D411yescharacteristic
53#117×C47—21no—
54#117×C47D411yescharacteristic
55C2×C42×C47—21no—
56C2×C42×C47—21no—
57C2×C42×C47C2311yescharacteristic
58#107×C47—21no—
59#106×C47—21no—
60C4⋊C8×C47—22no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47C2×C411yescharacteristic
63C4⋊C8×C47C2×C411yescharacteristic
64#104×C47—24no—
65#103×C47—21no—
66#102×C47—21no—
67#102×C47—21no—
68#102×C47—21no—
69C22⋊C8×C47—22no—
70C22⋊C8×C47—21no—
71C22⋊C8×C47D412yes—
72#97×C47—21no—
73#97×C47—21no—
74#97×C47—21no—
75#97×C47D411yescharacteristic
76#97×C47D411yescharacteristic
77C4×C8×C47—22no—
78C4×C8×C47—21no—
79C4×C8×C47—21no—
80#95×C47—21no—
81#95×C47—21no—
82#41×C47—22no—
83#41×C47—41no—
84#41×C47—82no—
85C2×Q8×C47—21no—
86C2×Q8×C47C22⋊C411yescharacteristic
87C2×D4×C47—21no—
88C2×D4×C47—21no—
89C2×D4×C47—21no—
90C2×D4×C47—21no—
91C2×D4×C47—41no—
92C2×D4×C47C22⋊C411yescharacteristic
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47#4111yescharacteristic
101SD16×C47—42no—
102D8×C47—42no—
103M16×C47—22no—
104M16×C47—42no—
105M16×C47—44no—
106M16×C47—41no—
107C2×C8×C47—21no—
108C2×C8×C47—21no—
109C2×C8×C47—21no—
110C2×C8×C47—22no—
111C2×C8×C47—21no—
112C2×C8×C47—41no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47C22⋊C411yescharacteristic
118C4⋊C4×C47C22⋊C411yescharacteristic
119C22⋊C4×C47—21no—
120C22⋊C4×C47—21no—
121C22⋊C4×C47—21no—
122C22⋊C4×C47—41no—
123C22⋊C4×C47—41no—
124C42×C47—21no—
125C42×C47—21no—
126C42×C47—21no—
127C42×C47—22no—
128C42×C47—41no—
129C42×C47C22×C411yescharacteristic
130C42×C47C2×D411yescharacteristic
131C42×C47C2×D411yescharacteristic
132C42×C47#4111yescharacteristic
133C23×C47—21no—
134C23×C47—41no—
135C23×C47#12111yescharacteristic
136Q8×C47—21no—
137Q8×C47—81no—
138Q8×C47#10412yes—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—42no—
142D4×C47—41no—
143D4×C47—41no—
144D4×C47—81no—
145D4×C47—81no—
146D4×C47—82no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—42no—
155C2×C4×C47—42no—
156C2×C4×C47—42no—
157C2×C4×C47—41no—
158C2×C4×C47—81no—
159C2×C4×C47—82no—
160C2×C4×C47—81no—
161C2×C4×C47—81no—
162C2×C4×C47C2×C22⋊C411yescharacteristic
163C2×C4×C47C4×D411yescharacteristic
164C2×C4×C47C4×D411yescharacteristic
165C2×C4×C47#12011yescharacteristic
166C2×C4×C47#12111yescharacteristic
167C2×C4×C47#12311yescharacteristic
168C8×C47—22no—
169C8×C47—42no—
170C8×C47—41no—
171C8×C47—42no—
172C8×C47—41no—
173C8×C47—41no—
174#9162C4711yesmaximal, characteristic, direct product factor, Sylow
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—81no—
182C22×C47—81no—
183C22×C47—81no—
184C22×C47#38611yescharacteristic
185C4×C47—21no—
186C4×C47—22no—
187C4×C47—21no—
188C4×C47—21no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—82no—
194C4×C47—81no—
195C4×C47C2×#10411yescharacteristic
196C4×C47#42111yescharacteristic
197#3115C2×C4711yescharacteristic
198#2971C2×C4711yescharacteristic, complemented
199#1759C2×C4711yescharacteristic, complemented
200#1525C2×C4711yescharacteristic, complemented
201#1505C2×C4711yescharacteristic, complemented
202#1300C2×C4711yescharacteristic, complemented
203#1291C2×C4711yescharacteristic, complemented
204C2×C47—41no—
205C2×C47—81no—
206C2×C47—161no—
207C2×C47#187111yescharacteristic
208C2×C47#190311yescharacteristic
209C2×C47#190611yescharacteristic
210#532C22×C4711yescharacteristic
211C4×#41C22×C4711yescharacteristic
212#482—21no—
213#475C4×C4711yescharacteristic, complemented
214#474C4×C4711yescharacteristic, complemented
215#460C4×C4711yescharacteristic, complemented
216#459C4×C4711yescharacteristic, complemented
217#449—21no—
218C8×Q8—21no—
219#442—21no—
220#440—21no—
221#436—21no—
222#436—22no—
223#432—21no—
224#432C22×C4711yescharacteristic
225#432C22×C4711yescharacteristic
226C2×#104—21no—
227C4×M16—21no—
228C4×M16C22×C4711yescharacteristic
229C4×M16C22×C4711yescharacteristic
230#376C22×C4711yescharacteristic
231#339—21no—
232#329—21no—
233#329—21no—
234#327—22no—
235C47#916211yescharacteristic, direct product factor, Sylow
236C2×#41—21no—
237C2×#41D4×C4711yescharacteristic
238C2×SD16—21no—
239C2×D8—21no—
240C2×M16—22no—
241C2×M16—21no—
242C2×M16—21no—
243C4⋊Q8C2×C4×C4711yescharacteristic
244#127C2×C4×C4711yescharacteristic
245#124—21no—
246#121—21no—
247#121—21no—
248C4×Q8C2×C4×C4711yescharacteristic
249C4×Q8D4×C4711yescharacteristic
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4C2×C4×C4711yescharacteristic
255C4×D4D4×C4711yescharacteristic
256#117—21no—
257#117D4×C4711yescharacteristic
258C2×C42—21no—
259C2×C42—21no—
260C2×C42C23×C4711yescharacteristic
261#107—21no—
262#106—21no—
263C4⋊C8—22no—
264C4⋊C8—21no—
265C4⋊C8C2×C4×C4711yescharacteristic
266C4⋊C8C2×C4×C4711yescharacteristic
267#104—24no—
268#103—21no—
269#102—21no—
270#102—21no—
271#102—21no—
272C22⋊C8—22no—
273C22⋊C8—21no—
274C22⋊C8D4×C4712yes—
275#97—21no—
276#97—21no—
277#97—21no—
278#97D4×C4711yescharacteristic
279#97D4×C4711yescharacteristic
280C4×C8—22no—
281C4×C8—21no—
282C4×C8—21no—
283#95—21no—
284#95—21no—
285#41—22no—
286#41—41no—
287#41—82no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C4711yescharacteristic
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4C22⋊C4×C4711yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C4711yescharacteristic
302C22×C4C2×D4×C4711yescharacteristic
303C22×C4#41×C4711yescharacteristic
304SD16—42no—
305D8—42no—
306M16—22no—
307M16—42no—
308M16—44no—
309M16—41no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—21no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4C22⋊C4×C4711yescharacteristic
321C4⋊C4C22⋊C4×C4711yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42—22no—
331C42—41no—
332C42C22×C4×C4711yescharacteristic
333C42C2×D4×C4711yescharacteristic
334C42C2×D4×C4711yescharacteristic
335C42#41×C4711yescharacteristic
336C23—21no—
337C23—41no—
338C23#121×C4711yescharacteristic
339Q8—21no—
340Q8—81no—
341Q8#104×C4712yes—
342D4—21no—
343D4—21no—
344D4—42no—
345D4—41no—
346D4—41no—
347D4—81no—
348D4—81no—
349D4—82no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×C22⋊C4×C4711yescharacteristic
366C2×C4C4×D4×C4711yescharacteristic
367C2×C4C4×D4×C4711yescharacteristic
368C2×C4#120×C4711yescharacteristic
369C2×C4#121×C4711yescharacteristic
370C2×C4#123×C4711yescharacteristic
371C8—22no—
372C8—42no—
373C8—41no—
374C8—42no—
375C8—41no—
376C8—41no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C47×#38611yescharacteristic
387C4—21no—
388C4—22no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—81no—
397C4C2×#104×C4711yescharacteristic
398C4C47×#42111yescharacteristic
399C2—41no—
400C2—81no—
401C2—161no—
402C2C47×#187111yescharacteristic
403C2C47×#190311yescharacteristic
404C2C47×#190611yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#3115C2
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
2. C47×#2971C2semidirect
3. C47×#1759C2semidirect
4. C47×#1525C2semidirect
5. C47×#1505C2semidirect
6. C47×#1300C2semidirect
7. C47×#1291C2semidirect
11. C47×#475C4semidirect
12. C47×#474C4semidirect
13. C47×#460C4semidirect
14. C47×#459C4semidirect
174. #9162C47direct (N × H)
198. #2971C2×C47semidirect
199. #1759C2×C47semidirect
200. #1525C2×C47semidirect
201. #1505C2×C47semidirect
202. #1300C2×C47semidirect
203. #1291C2×C47semidirect
213. #475C4×C47semidirect
214. #474C4×C47semidirect
215. #460C4×C47semidirect
216. #459C4×C47semidirect
235. C47#9162direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31152
C47×#29712
C47×#17592
C47×#15252
C47×#15052
C47×#13002
C47×#12912
#916247