Finite Group Databasebeta

← C47×#9431 #26049129

Subgroups — C47×#9431 #26049129

Order 12032.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3181C211yesmaximal, characteristic
2C47×#2968C211yesmaximal, characteristic
3C47×#1531C211yesmaximal, characteristic, complemented
4C47×#1518C211yesmaximal, characteristic, complemented
5C47×#1512C211yesmaximal, characteristic
6C47×#1302C211yesmaximal, characteristic, complemented
7C47×#1295C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#529C2211yescharacteristic
10C47×#501C411yescharacteristic, complemented
11C47×#497C411yescharacteristic, complemented
12C47×#491C411yescharacteristic, complemented
13C47×#489C411yescharacteristic, complemented
14C47×#467—21no—
15C47×#465—21no—
16C47×#446—21no—
17C47×#441—21no—
18C47×#440—21no—
19C47×#435—21no—
20C47×#435—21no—
21C8×D4×C47—21no—
22C47×#433—21no—
23C47×#432C2211yescharacteristic
24C47×#431C2211yescharacteristic
25C47×#405—21no—
26C2×#97×C47C2211yescharacteristic
27C2×#97×C47C2211yescharacteristic
28C47×#382C2211yescharacteristic
29C47×#330—21no—
30C47×#330—21no—
31C47×#328—21no—
32C47×#328—21no—
33C47×#328—21no—
34C47×#327—21no—
35C2×Q16×C47—21no—
36C2×SD16×C47—21no—
37C2×M16×C47—21no—
38C22×C8×C47—21no—
39C22×C8×C47—21no—
40C22×C8×C47—21no—
41C4⋊Q8×C47C2×C411yescharacteristic
42C4⋊Q8×C47C2×C411yescharacteristic
43#126×C47—21no—
44#125×C47—21no—
45#125×C47C2×C411yescharacteristic
46#124×C47C2×C411yescharacteristic
47#123×C47—21no—
48C22⋊Q8×C47—21no—
49C22⋊Q8×C47—21no—
50C22⋊Q8×C47D411yescharacteristic
51#121×C47D411yescharacteristic
52C4×Q8×C47—21no—
53C4×Q8×C47—21no—
54C4×Q8×C47D411yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47D411yescharacteristic
57#117×C47—21no—
58#117×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C42×C47C2311yescharacteristic
61#107×C47—21no—
62#106×C47—21no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67#103×C47—21no—
68#103×C47—21no—
69#103×C47—21no—
70#102×C47—21no—
71C22⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47D411yescharacteristic
75C22⋊C8×C47D411yescharacteristic
76#97×C47—21no—
77#97×C47—21no—
78#97×C47—21no—
79#97×C47—21no—
80#97×C47C2×C411yescharacteristic
81#97×C47C2×C411yescharacteristic
82#97×C47D411yescharacteristic
83#97×C47D411yescharacteristic
84C4×C8×C47—21no—
85C4×C8×C47—21no—
86#95×C47—21no—
87#95×C47—21no—
88C2×Q8×C47—21no—
89C2×Q8×C47—21no—
90C2×Q8×C47C22⋊C411yescharacteristic
91C2×D4×C47—21no—
92C2×D4×C47C22⋊C411yescharacteristic
93C22×C4×C47—21no—
94C22×C4×C47—41no—
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47#4111yescharacteristic
98Q16×C47—42no—
99SD16×C47—42no—
100M16×C47—42no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47—21no—
104C2×C8×C47—21no—
105C2×C8×C47—21no—
106C2×C8×C47—21no—
107C2×C8×C47—42no—
108C2×C8×C47—42no—
109C2×C8×C47—42no—
110C2×C8×C47—41no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47—21no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—41no—
120C4⋊C4×C47—41no—
121C4⋊C4×C47—81no—
122C4⋊C4×C47C22⋊C411yescharacteristic
123C4⋊C4×C47C22⋊C411yescharacteristic
124C22⋊C4×C47—21no—
125C22⋊C4×C47—21no—
126C22⋊C4×C47—21no—
127C22⋊C4×C47—21no—
128C22⋊C4×C47—21no—
129C22⋊C4×C47—41no—
130C42×C47—21no—
131C42×C47—41no—
132C42×C47C22×C411yescharacteristic
133C42×C47C2×D411yescharacteristic
134C42×C47C2×D411yescharacteristic
135C42×C47#4111yescharacteristic
136C23×C47—21no—
137C23×C47#12111yescharacteristic
138Q8×C47—41no—
139Q8×C47—41no—
140Q8×C47—41no—
141Q8×C47—81no—
142D4×C47—41no—
143D4×C47—41no—
144D4×C47—41no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—81no—
157C2×C4×C47—81no—
158C2×C4×C47—81no—
159C2×C4×C47C2×C22⋊C411yescharacteristic
160C2×C4×C47C4×D411yescharacteristic
161C2×C4×C47C4×D411yescharacteristic
162C2×C4×C47#12011yescharacteristic
163C2×C4×C47#12111yescharacteristic
164C2×C4×C47#12311yescharacteristic
165C8×C47—22no—
166C8×C47—22no—
167C8×C47—41no—
168C8×C47—41no—
169C8×C47—41no—
170C8×C47—41no—
171C8×C47—81no—
172#9431C4711yesmaximal, characteristic, direct product factor, Sylow
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47#38611yescharacteristic
179C22×C47#47111yescharacteristic
180C22×C47#47311yescharacteristic
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47—81no—
191C4×C47—81no—
192C4×C47—161no—
193#3181C2×C4711yescharacteristic
194#2968C2×C4711yescharacteristic
195#1531C2×C4711yescharacteristic, complemented
196#1518C2×C4711yescharacteristic, complemented
197#1512C2×C4711yescharacteristic
198#1302C2×C4711yescharacteristic, complemented
199#1295C2×C4711yescharacteristic, complemented
200C2×C47—21no—
201C2×C47—21no—
202C2×C47—81no—
203C2×C47#188411yescharacteristic
204C2×C47#190611yescharacteristic
205C2×C47#190811yescharacteristic
206#533C22×C4711yescharacteristic
207#529C22×C4711yescharacteristic
208#501C4×C4711yescharacteristic, complemented
209#497C4×C4711yescharacteristic, complemented
210#491C4×C4711yescharacteristic, complemented
211#489C4×C4711yescharacteristic, complemented
212#467—21no—
213#465—21no—
214#446—21no—
215#441—21no—
216#440—21no—
217#435—21no—
218#435—21no—
219C8×D4—21no—
220#433—21no—
221#432C22×C4711yescharacteristic
222#431C22×C4711yescharacteristic
223#405—21no—
224C2×#97C22×C4711yescharacteristic
225C2×#97C22×C4711yescharacteristic
226#382C22×C4711yescharacteristic
227#330—21no—
228#330—21no—
229#328—21no—
230#328—21no—
231#328—21no—
232#327—21no—
233C47#943111yescharacteristic, direct product factor, Sylow
234C2×Q16—21no—
235C2×SD16—21no—
236C2×M16—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8C2×C4×C4711yescharacteristic
241C4⋊Q8C2×C4×C4711yescharacteristic
242#126—21no—
243#125—21no—
244#125C2×C4×C4711yescharacteristic
245#124C2×C4×C4711yescharacteristic
246#123—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8D4×C4711yescharacteristic
250#121D4×C4711yescharacteristic
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8D4×C4711yescharacteristic
254C4×D4—21no—
255C4×D4D4×C4711yescharacteristic
256#117—21no—
257#117—21no—
258C2×C4⋊C4—21no—
259C2×C42C23×C4711yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#103—21no—
267#103—21no—
268#103—21no—
269#102—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8D4×C4711yescharacteristic
274C22⋊C8D4×C4711yescharacteristic
275#97—21no—
276#97—21no—
277#97—21no—
278#97—21no—
279#97C2×C4×C4711yescharacteristic
280#97C2×C4×C4711yescharacteristic
281#97D4×C4711yescharacteristic
282#97D4×C4711yescharacteristic
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286#95—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C4711yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C4711yescharacteristic
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C4711yescharacteristic
295C22×C4C2×D4×C4711yescharacteristic
296C22×C4#41×C4711yescharacteristic
297Q16—42no—
298SD16—42no—
299M16—42no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C4⋊C4C22⋊C4×C4711yescharacteristic
322C4⋊C4C22⋊C4×C4711yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—41no—
331C42C22×C4×C4711yescharacteristic
332C42C2×D4×C4711yescharacteristic
333C42C2×D4×C4711yescharacteristic
334C42#41×C4711yescharacteristic
335C23—21no—
336C23#121×C4711yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4C2×C22⋊C4×C4711yescharacteristic
359C2×C4C4×D4×C4711yescharacteristic
360C2×C4C4×D4×C4711yescharacteristic
361C2×C4#120×C4711yescharacteristic
362C2×C4#121×C4711yescharacteristic
363C2×C4#123×C4711yescharacteristic
364C8—22no—
365C8—22no—
366C8—41no—
367C8—41no—
368C8—41no—
369C8—41no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22C47×#38611yescharacteristic
377C22C47×#47111yescharacteristic
378C22C47×#47311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2C47×#188411yescharacteristic
395C2C47×#190611yescharacteristic
396C2C47×#190811yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radical#121×C47D4
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×#1531C2semidirect
4. C47×#1518C2semidirect
6. C47×#1302C2semidirect
7. C47×#1295C2semidirect
10. C47×#501C4semidirect
11. C47×#497C4semidirect
12. C47×#491C4semidirect
13. C47×#489C4semidirect
172. #9431C47direct (N × H)
195. #1531C2×C47semidirect
196. #1518C2×C47semidirect
198. #1302C2×C47semidirect
199. #1295C2×C47semidirect
208. #501C4×C47semidirect
209. #497C4×C47semidirect
210. #491C4×C47semidirect
211. #489C4×C47semidirect
233. C47#9431direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31812
C47×#29682
C47×#15312
C47×#15182
C47×#15122
C47×#13022
C47×#12952
#943147