Finite Group Databasebeta

← C47×#8911 #26048609

Subgroups — C47×#8911 #26048609

Order 12032.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2379C211yesmaximal, characteristic
2C47×#1959C211yesmaximal, characteristic
3C47×#1847C211yesmaximal, characteristic, complemented
4C47×#1836C211yesmaximal, characteristic, complemented
5C2×C47×#329C211yesmaximal, characteristic
6C47×#1295C211yesmaximal, characteristic, complemented
7C47×#1295C211yesmaximal, characteristic, complemented
8C2×#124×C47C2211yescharacteristic
9C2×#107×C47—21no—
10C2×#106×C47—21no—
11C2×#103×C47—21no—
12C2×#102×C47—21no—
13C2×#97×C47C2211yescharacteristic
14C2×#97×C47C2211yescharacteristic
15C2×#97×C47C2211yescharacteristic
16C47×#391—21no—
17C47×#388—21no—
18C47×#388—21no—
19C47×#386—21no—
20C47×#385—21no—
21C47×#385—21no—
22C47×#384C2211yescharacteristic
23C47×#382C2211yescharacteristic
24C47×#382C2211yescharacteristic
25C47×#340—21no—
26C47×#340—21no—
27C47×#329C414yescomplemented
28C22×Q8×C47D411yescharacteristic
29C22×D4×C47D411yescharacteristic
30C23×C4×C47—21no—
31C22×C8×C47—21no—
32C22×C8×C47—21no—
33C22×C8×C47—21no—
34#124×C47—21no—
35#124×C47—21no—
36#124×C47C2×C412yes—
37#124×C47Q812yes—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47D411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—21no—
51C2×C42×C47—21no—
52C2×C42×C47C2311yescharacteristic
53#107×C47—42no—
54#106×C47—42no—
55#103×C47—42no—
56#102×C47—42no—
57#97×C47—21no—
58#97×C47—21no—
59#97×C47—21no—
60#97×C47—21no—
61#97×C47C2×C412yescomplemented
62#97×C47C2×C412yescomplemented
63#95×C47—21no—
64#95×C47—21no—
65#95×C47—21no—
66#95×C47—21no—
67#95×C47—21no—
68#95×C47—21no—
69C24×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C2×Q8×C47C4⋊C412yes—
74C2×D4×C47—21no—
75C2×D4×C47—41no—
76C2×D4×C47—41no—
77C2×D4×C47C4⋊C412yes—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—41no—
84C22×C4×C47—81no—
85C22×C4×C47—81no—
86C22×C4×C47—81no—
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C2×C8×C47—22no—
91C2×C8×C47—22no—
92C2×C8×C47—22no—
93C2×C8×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—42no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—81no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47—22no—
112C22⋊C4×C47—22no—
113C22⋊C4×C47—81no—
114C22⋊C4×C47—81no—
115C22⋊C4×C47—81no—
116C42×C47—81no—
117C42×C47C22×C411yescharacteristic
118C42×C47C2×Q811yescharacteristic
119C42×C47#4111yescharacteristic
120C42×C47#4111yescharacteristic
121C23×C47—22no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47#12011yescharacteristic
129Q8×C47—42no—
130Q8×C47—81no—
131D4×C47—42no—
132D4×C47—81no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—22no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—84no—
155C2×C4×C47—81no—
156C2×C4×C47—81no—
157C2×C4×C47—81no—
158C2×C4×C47C2×C4⋊C411yescharacteristic
159C2×C4×C47C4×D411yescharacteristic
160C2×C4×C47C4×D411yescharacteristic
161C2×C4×C47C22⋊Q811yescharacteristic
162C2×C4×C47C22⋊Q811yescharacteristic
163C2×C4×C47#12311yescharacteristic
164C8×C47—24no—
165C8×C47—42no—
166C8×C47—42no—
167#8911C4711yesmaximal, characteristic, direct product factor, Sylow
168C22×C47—42no—
169C22×C47—42no—
170C22×C47—42no—
171C22×C47—81no—
172C22×C47—81no—
173C22×C47—81no—
174C22×C47—81no—
175C22×C47#38511yescharacteristic
176C22×C47#45311yescharacteristic
177C22×C47#45311yescharacteristic
178C22×C47#45411yescharacteristic
179C22×C47#45511yescharacteristic
180C22×C47#45511yescharacteristic
181C22×C47#45611yescharacteristic
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—42no—
189C4×C47—81no—
190C4×C47—81no—
191C4×C47—81no—
192C4×C47—81no—
193C4×C47—161no—
194#2379C2×C4711yescharacteristic
195#1959C2×C4711yescharacteristic
196#1847C2×C4711yescharacteristic, complemented
197#1836C2×C4711yescharacteristic, complemented
198C2×#329C2×C4711yescharacteristic
199#1295C2×C4711yescharacteristic, complemented
200#1295C2×C4711yescharacteristic, complemented
201C2×C47—82no—
202C2×C47#165611yescharacteristic
203C2×C47#165911yescharacteristic
204C2×C47#166111yescharacteristic
205C2×C47#166411yescharacteristic
206C2×C47#185611yescharacteristic
207C2×C47#185911yescharacteristic
208C2×C47#186011yescharacteristic
209C2×#124C22×C4711yescharacteristic
210C2×#107—21no—
211C2×#106—21no—
212C2×#103—21no—
213C2×#102—21no—
214C2×#97C22×C4711yescharacteristic
215C2×#97C22×C4711yescharacteristic
216C2×#97C22×C4711yescharacteristic
217#391—21no—
218#388—21no—
219#388—21no—
220#386—21no—
221#385—21no—
222#385—21no—
223#384C22×C4711yescharacteristic
224#382C22×C4711yescharacteristic
225#382C22×C4711yescharacteristic
226#340—21no—
227#340—21no—
228#329C4×C4714yescomplemented
229C47#891111yescharacteristic, direct product factor, Sylow
230C22×Q8D4×C4711yescharacteristic
231C22×D4D4×C4711yescharacteristic
232C23×C4—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236#124—21no—
237#124—21no—
238#124C2×C4×C4712yes—
239#124Q8×C4712yes—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C4711yescharacteristic
245C2×C4⋊C4D4×C4711yescharacteristic
246C2×C4⋊C4D4×C4711yescharacteristic
247C2×C4⋊C4D4×C4711yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42—21no—
254C2×C42C23×C4711yescharacteristic
255#107—42no—
256#106—42no—
257#103—42no—
258#102—42no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97—21no—
263#97C2×C4×C4712yescomplemented
264#97C2×C4×C4712yescomplemented
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271C24—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C4⋊C4×C4712yes—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4C4⋊C4×C4712yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C4711yescharacteristic
290C22×C4C2×D4×C4711yescharacteristic
291C22×C4C2×D4×C4711yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C42—81no—
319C42C22×C4×C4711yescharacteristic
320C42C2×Q8×C4711yescharacteristic
321C42#41×C4711yescharacteristic
322C42#41×C4711yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#120×C4711yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—42no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C2×C4⋊C4×C4711yescharacteristic
361C2×C4C4×D4×C4711yescharacteristic
362C2×C4C4×D4×C4711yescharacteristic
363C2×C4C22⋊Q8×C4711yescharacteristic
364C2×C4C22⋊Q8×C4711yescharacteristic
365C2×C4#123×C4711yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C47×#38511yescharacteristic
377C22C47×#45311yescharacteristic
378C22C47×#45311yescharacteristic
379C22C47×#45411yescharacteristic
380C22C47×#45511yescharacteristic
381C22C47×#45511yescharacteristic
382C22C47×#45611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—161no—
395C2—82no—
396C2C47×#165611yescharacteristic
397C2C47×#165911yescharacteristic
398C2C47×#166111yescharacteristic
399C2C47×#166411yescharacteristic
400C2C47×#185611yescharacteristic
401C2C47×#185911yescharacteristic
402C2C47×#186011yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1847C2semidirect
4. C47×#1836C2semidirect
6. C47×#1295C2semidirect
7. C47×#1295C2semidirect
27. C47×#329C4semidirect
61. #97×C47C2×C4semidirect
62. #97×C47C2×C4semidirect
167. #8911C47direct (N × H)
196. #1847C2×C47semidirect
197. #1836C2×C47semidirect
199. #1295C2×C47semidirect
200. #1295C2×C47semidirect
228. #329C4×C47semidirect
229. C47#8911direct (N × H)
263. #97C2×C4×C47semidirect
264. #97C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#23792
C47×#19592
C47×#18472
C47×#18362
C2×C47×#3292
C47×#12952
#891147