Finite Group Databasebeta

← C47×#8841 #26048539

Subgroups — C47×#8841 #26048539

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2989C211yesmaximal, characteristic
2C47×#1842C211yesmaximal, characteristic, complemented
3C4×#104×C47C211yesmaximal, characteristic
4C47×#1565C211yesmaximal, characteristic, complemented
5C47×#1477C211yesmaximal, characteristic
6C47×#1283C211yesmaximal, characteristic, complemented
7C47×#1276C211yesmaximal, characteristic, complemented
8C4×#41×C47C2211yescharacteristic
9C47×#446—21no—
10C47×#436—21no—
11C47×#435—22no—
12C47×#432—21no—
13C47×#431C2211yescharacteristic
14C47×#431C2211yescharacteristic
15C47×#423—21no—
16C2×C4⋊C8×C47—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×#104×C47C411yescharacteristic
20C2×#104×C47C411yescharacteristic
21C4×M16×C47C2211yescharacteristic
22C43×C47C2211yescharacteristic
23C47×#339C411yescharacteristic
24C47×#339C411yescharacteristic
25C47×#335—21no—
26C47×#334—21no—
27C47×Q8⋊C8—21no—
28C47×D4⋊C8—21no—
29C2×#41×C47C2×C411yescharacteristic
30C2×M16×C47—22no—
31C2×M16×C47C2×C411yescharacteristic
32C2×M16×C47C2×C411yescharacteristic
33C22×C8×C47—21no—
34C22×C8×C47D412yes—
35C4×Q8×C47D411yescharacteristic
36C4×Q8×C47Q811yescharacteristic
37C4×D4×C47—21no—
38C4×D4×C47—21no—
39C4×D4×C47D411yescharacteristic
40C4×D4×C47Q811yescharacteristic
41#117×C47—21no—
42#117×C47C2×C411yescharacteristic
43C2×C42×C47—21no—
44C2×C42×C47—21no—
45C2×C42×C47—21no—
46C2×C42×C47C2×C411yescharacteristic
47C2×C42×C47C2×C411yescharacteristic
48C2×C42×C47C2311yescharacteristic
49C4⋊C8×C47—22no—
50C4⋊C8×C47—21no—
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—44no—
56C4⋊C8×C47D411yescharacteristic
57C4⋊C8×C47D411yescharacteristic
58#104×C47—22no—
59#104×C47—22no—
60C22⋊C8×C47—22no—
61C22⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63#97×C47—22no—
64#97×C47—21no—
65C4×C8×C47—21no—
66C4×C8×C47—21no—
67C4×C8×C47—21no—
68#41×C47—21no—
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—21no—
72C2×Q8×C47C4⋊C411yescharacteristic
73C2×D4×C47—21no—
74C2×D4×C47C4⋊C411yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47C22×C411yescharacteristic
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47#4111yescharacteristic
83M16×C47—21no—
84M16×C47—21no—
85M16×C47—21no—
86M16×C47—82no—
87M16×C47M1612yescomplemented
88C2×C8×C47—21no—
89C2×C8×C47—21no—
90C2×C8×C47—22no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C2×C8×C47—42no—
94C2×C8×C47—42no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47C4⋊C411yescharacteristic
100C4⋊C4×C47C4⋊C411yescharacteristic
101C22⋊C4×C47—21no—
102C22⋊C4×C47—21no—
103C22⋊C4×C47—21no—
104C42×C47—22no—
105C42×C47—22no—
106C42×C47—21no—
107C42×C47—21no—
108C42×C47—21no—
109C42×C47—21no—
110C42×C47—21no—
111C42×C47—21no—
112C42×C47—42no—
113C42×C47M1612yescomplemented
114C42×C47C2×D411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47C2×Q811yescharacteristic
117C42×C47#4111yescharacteristic
118C23×C47—21no—
119C23×C47C4×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—41no—
125D4×C47—41no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—22no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—81no—
143C2×C4×C47C2×C4⋊C411yescharacteristic
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47#12011yescharacteristic
146C2×C4×C47C22⋊Q811yescharacteristic
147C2×C4×C47C22⋊Q811yescharacteristic
148C2×C4×C47#12311yescharacteristic
149C2×C4×C47C2×M1611yescharacteristic
150C2×C4×C47C2×M1611yescharacteristic
151C2×C4×C47#13111yescharacteristic
152C2×C4×C47#13111yescharacteristic
153C8×C47—22no—
154C8×C47—41no—
155C8×C47—42no—
156C8×C47—41no—
157C8×C47—41no—
158C8×C47—81no—
159C8×C47—81no—
160#8841C4711yesmaximal, characteristic, direct product factor, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47#38511yescharacteristic
167C22×C47#43511yescharacteristic
168C22×C47#43611yescharacteristic
169C4×C47—24no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—42no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47#42311yescharacteristic
178C4×C47#42411yescharacteristic
179C4×C47#43511yescharacteristic
180C4×C47#43611yescharacteristic
181C4×C47#45311yescharacteristic
182C4×C47#45611yescharacteristic
183#2989C2×C4711yescharacteristic
184#1842C2×C4711yescharacteristic, complemented
185C4×#104C2×C4711yescharacteristic
186#1565C2×C4711yescharacteristic, complemented
187#1477C2×C4711yescharacteristic
188#1283C2×C4711yescharacteristic, complemented
189#1276C2×C4711yescharacteristic, complemented
190C2×C47—21no—
191C2×C47—21no—
192C2×C47—81no—
193C2×C47#185111yescharacteristic
194C2×C47#185911yescharacteristic
195C2×C47#186111yescharacteristic
196C4×#41C22×C4711yescharacteristic
197#446—21no—
198#436—21no—
199#435—22no—
200#432—21no—
201#431C22×C4711yescharacteristic
202#431C22×C4711yescharacteristic
203#423—21no—
204C2×C4⋊C8—22no—
205C2×C4⋊C8C22×C4711yescharacteristic
206C2×C4⋊C8C22×C4711yescharacteristic
207C2×#104C4×C4711yescharacteristic
208C2×#104C4×C4711yescharacteristic
209C4×M16C22×C4711yescharacteristic
210C43C22×C4711yescharacteristic
211#339C4×C4711yescharacteristic
212#339C4×C4711yescharacteristic
213#335—21no—
214#334—21no—
215Q8⋊C8—21no—
216D4⋊C8—21no—
217C47#884111yescharacteristic, direct product factor, Sylow
218C2×#41C2×C4×C4711yescharacteristic
219C2×M16—22no—
220C2×M16C2×C4×C4711yescharacteristic
221C2×M16C2×C4×C4711yescharacteristic
222C22×C8—21no—
223C22×C8D4×C4712yes—
224C4×Q8D4×C4711yescharacteristic
225C4×Q8Q8×C4711yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4D4×C4711yescharacteristic
229C4×D4Q8×C4711yescharacteristic
230#117—21no—
231#117C2×C4×C4711yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42C2×C4×C4711yescharacteristic
236C2×C42C2×C4×C4711yescharacteristic
237C2×C42C23×C4711yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—44no—
245C4⋊C8D4×C4711yescharacteristic
246C4⋊C8D4×C4711yescharacteristic
247#104—22no—
248#104—22no—
249C22⋊C8—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252#97—22no—
253#97—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257#41—21no—
258#41—21no—
259#41—21no—
260#41—21no—
261C2×Q8C4⋊C4×C4711yescharacteristic
262C2×D4—21no—
263C2×D4C4⋊C4×C4711yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22×C4×C4711yescharacteristic
270C22×C4C2×D4×C4711yescharacteristic
271C22×C4#41×C4711yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—82no—
276M16M16×C4712yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C4⋊C4×C4711yescharacteristic
289C4⋊C4C4⋊C4×C4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—22no—
294C42—22no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—42no—
302C42M16×C4712yescomplemented
303C42C2×D4×C4711yescharacteristic
304C42C2×D4×C4711yescharacteristic
305C42C2×Q8×C4711yescharacteristic
306C42#41×C4711yescharacteristic
307C23—21no—
308C23C4×D4×C4711yescharacteristic
309Q8—21no—
310Q8—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—41no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4C2×C4⋊C4×C4711yescharacteristic
333C2×C4C4×D4×C4711yescharacteristic
334C2×C4#120×C4711yescharacteristic
335C2×C4C22⋊Q8×C4711yescharacteristic
336C2×C4C22⋊Q8×C4711yescharacteristic
337C2×C4#123×C4711yescharacteristic
338C2×C4C2×M16×C4711yescharacteristic
339C2×C4C2×M16×C4711yescharacteristic
340C2×C4#131×C4711yescharacteristic
341C2×C4#131×C4711yescharacteristic
342C8—22no—
343C8—42no—
344C8—41no—
345C8—41no—
346C8—41no—
347C8—81no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22C47×#38511yescharacteristic
355C22C47×#43511yescharacteristic
356C22C47×#43611yescharacteristic
357C4—24no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4C47×#42311yescharacteristic
366C4C47×#42411yescharacteristic
367C4C47×#43511yescharacteristic
368C4C47×#43611yescharacteristic
369C4C47×#45311yescharacteristic
370C4C47×#45611yescharacteristic
371C2—21no—
372C2—21no—
373C2—81no—
374C2C47×#185111yescharacteristic
375C2C47×#185911yescharacteristic
376C2C47×#186111yescharacteristic
subgroupG/H
centerC2×C4×C47#120
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#385
prime radicalC2×#41×C47C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ 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×#1842C2semidirect
4. C47×#1565C2semidirect
6. C47×#1283C2semidirect
7. C47×#1276C2semidirect
87. M16×C47M16semidirect
113. C42×C47M16semidirect
160. #8841C47direct (N × H)
184. #1842C2×C47semidirect
186. #1565C2×C47semidirect
188. #1283C2×C47semidirect
189. #1276C2×C47semidirect
217. C47#8841direct (N × H)
276. M16M16×C47semidirect
302. C42M16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#29892
C47×#18422
C4×#104×C472
C47×#15652
C47×#14772
C47×#12832
C47×#12762
#884147