Finite Group Databasebeta

← C47×#8454 #26048152

Subgroups — C47×#8454 #26048152

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3492C211yesmaximal, characteristic
2C47×#1821C211yesmaximal, characteristic, complemented
3C47×#1504C212yesmaximal, complemented
4C47×#1504C212yesmaximal, complemented
5C47×#1445C211yesmaximal, characteristic, complemented
6C47×#554—22no—
7C47×#553—22no—
8C47×#552—22no—
9C47×#547—22no—
10C47×#544C411yescharacteristic, complemented
11C47×#539—22no—
12C47×#537C411yescharacteristic, complemented
13C47×#525—22no—
14C47×#525C2212yes—
15C47×#520C412yescomplemented
16C22×C4⋊C4×C47C2211yescharacteristic
17C47×#407C2212yes—
18C2×#95×C47—22no—
19C2×#95×C47C2211yescharacteristic
20C2×#95×C47C2211yescharacteristic
21C47×#343—22no—
22C47×#328—22no—
23C47×#328—22no—
24C47×#327—22no—
25C47×#327—22no—
26C2×#41×C47—22no—
27C2×#41×C47C2×C412yes—
28C23×C4×C47—21no—
29C23×C4×C47—21no—
30C23×C4×C47D412yes—
31C23×C4×C47C2311yescharacteristic
32C2×M16×C47—22no—
33C4⋊Q8×C47—22no—
34#126×C47—24no—
35#125×C47—24no—
36#125×C47—22no—
37#123×C47—24no—
38#123×C47—24no—
39#123×C47—22no—
40C22⋊Q8×C47—22no—
41C22⋊Q8×C47—24no—
42C22⋊Q8×C47—22no—
43C22⋊Q8×C47—22no—
44C22⋊Q8×C47D412yes—
45C22⋊Q8×C47D412yes—
46#121×C47—22no—
47#121×C47—22no—
48#121×C47—22no—
49#121×C47D412yes—
50#121×C47D412yes—
51#120×C47—22no—
52C4×Q8×C47—22no—
53C4×D4×C47—24no—
54C4×D4×C47—22no—
55C4×D4×C47—24no—
56C4×D4×C47—22no—
57C4×D4×C47—22no—
58#117×C47—22no—
59#117×C47—22no—
60#117×C47C2×C412yes—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47C2×C411yescharacteristic
65C2×C4⋊C4×C47C2×C411yescharacteristic
66C2×C4⋊C4×C47D412yes—
67C22⋊C8×C47—22no—
68C22⋊C8×C47—22no—
69#95×C47—22no—
70#95×C47—22no—
71#95×C47—44no—
72C24×C47C2×D411yescharacteristic
73#41×C47—44no—
74#41×C47—82no—
75#41×C47—82no—
76C2×Q8×C47—22no—
77C2×Q8×C47C22⋊C412yes—
78C2×D4×C47—22no—
79C2×D4×C47—22no—
80C2×D4×C47—22no—
81C2×D4×C47—22no—
82C2×D4×C47C22⋊C412yes—
83C22×C4×C47—22no—
84C22×C4×C47—24no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—42no—
90C22×C4×C47—42no—
91C22×C4×C47—42no—
92C22×C4×C47—42no—
93C22×C4×C47—42no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—42no—
97C22×C4×C47—42no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47C22⋊C412yes—
101C22×C4×C47C22⋊C412yes—
102C22×C4×C47C22×C411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D412yes—
105C22×C4×C47C2×D412yes—
106M16×C47—44no—
107C2×C8×C47—42no—
108C4⋊C4×C47—24no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—22no—
111C4⋊C4×C47—24no—
112C4⋊C4×C47—22no—
113C4⋊C4×C47—22no—
114C4⋊C4×C47—24no—
115C4⋊C4×C47—22no—
116C4⋊C4×C47—22no—
117C4⋊C4×C47C22⋊C412yes—
118C4⋊C4×C47C22⋊C412yes—
119C22⋊C4×C47—24no—
120C22⋊C4×C47—24no—
121C22⋊C4×C47—22no—
122C22⋊C4×C47—22no—
123C22⋊C4×C47—22no—
124C22⋊C4×C47—22no—
125C22⋊C4×C47—22no—
126C42×C47—24no—
127C42×C47—22no—
128C23×C47—22no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—22no—
134C23×C47C2×C22⋊C411yescharacteristic
135C23×C47#12011yescharacteristic
136C23×C47#12011yescharacteristic
137Q8×C47—42no—
138Q8×C47—82no—
139D4×C47—42no—
140D4×C47—44no—
141D4×C47—42no—
142D4×C47—42no—
143D4×C47—42no—
144D4×C47—42no—
145D4×C47—82no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—22no—
149C2×C4×C47—22no—
150C2×C4×C47—22no—
151C2×C4×C47—22no—
152C2×C4×C47—22no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—44no—
156C2×C4×C47—42no—
157C2×C4×C47—42no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—44no—
161C2×C4×C47—44no—
162C2×C4×C47—42no—
163C2×C4×C47—42no—
164C2×C4×C47—82no—
165C2×C4×C47—84no—
166C2×C4×C47—82no—
167C2×C4×C47—82no—
168C2×C4×C47—81no—
169C2×C4×C47—81no—
170C2×C4×C47—81no—
171C2×C4×C47—81no—
172C2×C4×C47C2×C22⋊C412yes—
173C2×C4×C47#12012yes—
174C8×C47—82no—
175#8454C4711yesmaximal, characteristic, direct product factor, Sylow
176C22×C47—22no—
177C22×C47—22no—
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—42no—
187C22×C47—42no—
188C22×C47—42no—
189C22×C47#37911yescharacteristic
190C22×C47#41012yes—
191C22×C47#45311yescharacteristic
192C22×C47#45411yescharacteristic
193C22×C47#45511yescharacteristic
194C22×C47#45611yescharacteristic
195C4×C47—22no—
196C4×C47—22no—
197C4×C47—42no—
198C4×C47—42no—
199C4×C47—42no—
200C4×C47—42no—
201C4×C47—42no—
202C4×C47—82no—
203C4×C47—82no—
204#3492C2×C4711yescharacteristic
205#1821C2×C4711yescharacteristic, complemented
206#1504C2×C4712yescomplemented
207#1504C2×C4712yescomplemented
208#1445C2×C4711yescharacteristic, complemented
209C2×C47—21no—
210C2×C47—21no—
211C2×C47—22no—
212C2×C47—21no—
213C2×C47—21no—
214C2×C47—82no—
215C2×C47#178211yescharacteristic
216C2×C47#179211yescharacteristic
217C2×C47#179311yescharacteristic
218#554—22no—
219#553—22no—
220#552—22no—
221#547—22no—
222#544C4×C4711yescharacteristic, complemented
223#539—22no—
224#537C4×C4711yescharacteristic, complemented
225#525—22no—
226#525C22×C4712yes—
227#520C4×C4712yescomplemented
228C22×C4⋊C4C22×C4711yescharacteristic
229#407C22×C4712yes—
230C2×#95—22no—
231C2×#95C22×C4711yescharacteristic
232C2×#95C22×C4711yescharacteristic
233#343—22no—
234#328—22no—
235#328—22no—
236#327—22no—
237#327—22no—
238C47#845411yescharacteristic, direct product factor, Sylow
239C2×#41—22no—
240C2×#41C2×C4×C4712yes—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4D4×C4712yes—
244C23×C4C23×C4711yescharacteristic
245C2×M16—22no—
246C4⋊Q8—22no—
247#126—24no—
248#125—24no—
249#125—22no—
250#123—24no—
251#123—24no—
252#123—22no—
253C22⋊Q8—22no—
254C22⋊Q8—24no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8D4×C4712yes—
258C22⋊Q8D4×C4712yes—
259#121—22no—
260#121—22no—
261#121—22no—
262#121D4×C4712yes—
263#121D4×C4712yes—
264#120—22no—
265C4×Q8—22no—
266C4×D4—24no—
267C4×D4—22no—
268C4×D4—24no—
269C4×D4—22no—
270C4×D4—22no—
271#117—22no—
272#117—22no—
273#117C2×C4×C4712yes—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4C2×C4×C4711yescharacteristic
278C2×C4⋊C4C2×C4×C4711yescharacteristic
279C2×C4⋊C4D4×C4712yes—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—22no—
283#95—22no—
284#95—44no—
285C24C2×D4×C4711yescharacteristic
286#41—44no—
287#41—82no—
288#41—82no—
289C2×Q8—22no—
290C2×Q8C22⋊C4×C4712yes—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4C22⋊C4×C4712yes—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C22⋊C4×C4712yes—
314C22×C4C22⋊C4×C4712yes—
315C22×C4C22×C4×C4711yescharacteristic
316C22×C4C2×D4×C4711yescharacteristic
317C22×C4C2×D4×C4712yes—
318C22×C4C2×D4×C4712yes—
319M16—44no—
320C2×C8—42no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4C22⋊C4×C4712yes—
331C4⋊C4C22⋊C4×C4712yes—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C42—24no—
340C42—22no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—22no—
346C23—22no—
347C23C2×C22⋊C4×C4711yescharacteristic
348C23#120×C4711yescharacteristic
349C23#120×C4711yescharacteristic
350Q8—42no—
351Q8—82no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—82no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—84no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C4712yes—
386C2×C4#120×C4712yes—
387C8—82no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22C47×#37911yescharacteristic
402C22C47×#41012yes—
403C22C47×#45311yescharacteristic
404C22C47×#45411yescharacteristic
405C22C47×#45511yescharacteristic
406C22C47×#45611yescharacteristic
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—42no—
412C4—42no—
413C4—42no—
414C4—82no—
415C4—82no—
416C2—21no—
417C2—21no—
418C2—21no—
419C2—21no—
420C2—22no—
421C2—82no—
422C2C47×#178211yescharacteristic
423C2C47×#179211yescharacteristic
424C2C47×#179311yescharacteristic
subgroupG/H
center, socleC22×C47#379
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC47×#3492C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1821C2semidirect
3. C47×#1504C2semidirect
4. C47×#1504C2semidirect
5. C47×#1445C2semidirect
10. C47×#544C4semidirect
12. C47×#537C4semidirect
15. C47×#520C4semidirect
175. #8454C47direct (N × H)
205. #1821C2×C47semidirect
206. #1504C2×C47semidirect
207. #1504C2×C47semidirect
208. #1445C2×C47semidirect
222. #544C4×C47semidirect
224. #537C4×C47semidirect
227. #520C4×C47semidirect
238. C47#8454direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34922
C47×#18212
C47×#15042
C47×#14452
#845447