Finite Group Databasebeta

← C47×#8240 #26047938

Subgroups — C47×#8240 #26047938

Order 12032.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2929C211yesmaximal, characteristic
2C47×#1752C211yesmaximal, characteristic, complemented
3C8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
4C47×#1501C211yesmaximal, characteristic
5C47×#1501C211yesmaximal, characteristic
6C47×#1298C211yesmaximal, characteristic, complemented
7C47×#1297C211yesmaximal, characteristic, complemented
8C2×#131×C47C411yescharacteristic, complemented
9C23×C8×C47C2211yescharacteristic
10C47×#525C2211yescharacteristic
11C47×#435—21no—
12C47×#435—21no—
13C8×D4×C47—21no—
14C8×D4×C47—21no—
15C47×#424C411yescharacteristic, complemented
16C47×#408C411yescharacteristic, complemented
17C47×#407C2211yescharacteristic
18C2×C22⋊C8×C47C2211yescharacteristic
19C2×C22⋊C8×C47C2211yescharacteristic
20C47×#405C411yescharacteristic, complemented
21C2×#97×C47—21no—
22C2×C4×C8×C47—21no—
23C4×C22⋊C4×C47C2211yescharacteristic
24C4×C22⋊C4×C47C2211yescharacteristic
25C47×#336—21no—
26C47×#336—21no—
27C47×#328C412yescomplemented
28C47×#328C412yescomplemented
29C47×#327C412yescomplemented
30C47×#327C412yescomplemented
31C2×#41×C47C2×C411yescharacteristic
32C23×C4×C47C2311yescharacteristic
33#131×C47—42no—
34C2×M16×C47—21no—
35C2×M16×C47C2×C411yescharacteristic
36C2×M16×C47C2×C411yescharacteristic
37C22×C8×C47—21no—
38C22×C8×C47—21no—
39C22×C8×C47—21no—
40C22×C8×C47—42no—
41C22×C8×C47C2×C411yescharacteristic
42C22×C8×C47C2×C411yescharacteristic
43C22×C8×C47D411yescharacteristic
44C22×C8×C47D411yescharacteristic
45C22×C8×C47D411yescharacteristic
46C22×C8×C47D411yescharacteristic
47#123×C47—21no—
48C22⋊Q8×C47C2×C411yescharacteristic
49C22⋊Q8×C47C2×C411yescharacteristic
50#121×C47C2×C411yescharacteristic
51#121×C47C2×C411yescharacteristic
52#120×C47—21no—
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55#117×C47C2×C411yescharacteristic
56C2×C22⋊C4×C47—21no—
57C2×C22⋊C4×C47—21no—
58C2×C42×C47—21no—
59C2×C42×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64C22⋊C8×C47—21no—
65C22⋊C8×C47—21no—
66C22⋊C8×C47—21no—
67C22⋊C8×C47—21no—
68C22⋊C8×C47C2×C412yes—
69C22⋊C8×C47C2×C412yes—
70#97×C47—21no—
71#97×C47—42no—
72C4×C8×C47—21no—
73C4×C8×C47—42no—
74#95×C47C2×C412yes—
75#95×C47C2×C412yes—
76C24×C47#4111yescharacteristic
77#41×C47—41no—
78#41×C47—41no—
79C2×Q8×C47C4211yescharacteristic
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47C4211yescharacteristic
84C22×C4×C47—22no—
85C22×C4×C47—21no—
86C22×C4×C47—22no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47C22×C411yescharacteristic
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C22×C411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47C2×D411yescharacteristic
94C22×C4×C47#4111yescharacteristic
95M16×C47—42no—
96M16×C47—41no—
97M16×C47—41no—
98C2×C8×C47—22no—
99C2×C8×C47—22no—
100C2×C8×C47—22no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47—22no—
104C2×C8×C47—22no—
105C2×C8×C47—41no—
106C2×C8×C47—41no—
107C2×C8×C47—41no—
108C2×C8×C47—42no—
109C2×C8×C47—41no—
110C2×C8×C47—41no—
111C2×C8×C47—41no—
112C2×C8×C47—41no—
113C2×C8×C47C22⋊C411yescharacteristic
114C2×C8×C47C22⋊C411yescharacteristic
115C2×C8×C47C22⋊C411yescharacteristic
116C2×C8×C47C22⋊C411yescharacteristic
117C4⋊C4×C47—21no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47C4211yescharacteristic
120C4⋊C4×C47C4211yescharacteristic
121C22⋊C4×C47—24no—
122C22⋊C4×C47—21no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—21no—
126C22⋊C4×C47—21no—
127C22⋊C4×C47—42no—
128C42×C47—21no—
129C42×C47—41no—
130C42×C47—41no—
131C42×C47—41no—
132C42×C47—41no—
133C23×C47—22no—
134C23×C47—22no—
135C23×C47—21no—
136C23×C47—41no—
137C23×C47#11711yescharacteristic
138C23×C47C4×D411yescharacteristic
139C23×C47C4×D411yescharacteristic
140Q8×C47—41no—
141D4×C47—41no—
142D4×C47—42no—
143D4×C47—42no—
144D4×C47—42no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—24no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—42no—
163C2×C4×C47—42no—
164C2×C4×C47—42no—
165C2×C4×C47C2×C4211yescharacteristic
166C2×C4×C47C2×C22⋊C411yescharacteristic
167C2×C4×C47C4×D411yescharacteristic
168C2×C4×C47C4×D411yescharacteristic
169C8×C47—21no—
170C8×C47—21no—
171C8×C47—21no—
172C8×C47—42no—
173C8×C47—42no—
174C8×C47—41no—
175C8×C47—41no—
176C8×C47#9912yes—
177#8240C4711yesmaximal, characteristic, direct product factor, Sylow
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—44no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47C4×C22⋊C411yescharacteristic
190C22×C47#44312yes—
191C22×C47#44412yes—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—44no—
196C4×C47—41no—
197C4×C47—41no—
198C4×C47—41no—
199C4×C47—82no—
200C4×C47C2×#9911yescharacteristic
201C4×C47#41011yescharacteristic
202#2929C2×C4711yescharacteristic
203#1752C2×C4711yescharacteristic, complemented
204C8×C22⋊C4C2×C4711yescharacteristic, complemented
205#1501C2×C4711yescharacteristic
206#1501C2×C4711yescharacteristic
207#1298C2×C4711yescharacteristic, complemented
208#1297C2×C4711yescharacteristic, complemented
209C2×C47—22no—
210C2×C47—22no—
211C2×C47—41no—
212C2×C47—81no—
213C2×C47C4×#9911yescharacteristic
214C2×C47#176411yescharacteristic
215C2×C47#176511yescharacteristic
216C2×#131C4×C4711yescharacteristic, complemented
217C23×C8C22×C4711yescharacteristic
218#525C22×C4711yescharacteristic
219#435—21no—
220#435—21no—
221C8×D4—21no—
222C8×D4—21no—
223#424C4×C4711yescharacteristic, complemented
224#408C4×C4711yescharacteristic, complemented
225#407C22×C4711yescharacteristic
226C2×C22⋊C8C22×C4711yescharacteristic
227C2×C22⋊C8C22×C4711yescharacteristic
228#405C4×C4711yescharacteristic, complemented
229C2×#97—21no—
230C2×C4×C8—21no—
231C4×C22⋊C4C22×C4711yescharacteristic
232C4×C22⋊C4C22×C4711yescharacteristic
233#336—21no—
234#336—21no—
235#328C4×C4712yescomplemented
236#328C4×C4712yescomplemented
237#327C4×C4712yescomplemented
238#327C4×C4712yescomplemented
239C47#824011yescharacteristic, direct product factor, Sylow
240C2×#41C2×C4×C4711yescharacteristic
241C23×C4C23×C4711yescharacteristic
242#131—42no—
243C2×M16—21no—
244C2×M16C2×C4×C4711yescharacteristic
245C2×M16C2×C4×C4711yescharacteristic
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—42no—
250C22×C8C2×C4×C4711yescharacteristic
251C22×C8C2×C4×C4711yescharacteristic
252C22×C8D4×C4711yescharacteristic
253C22×C8D4×C4711yescharacteristic
254C22×C8D4×C4711yescharacteristic
255C22×C8D4×C4711yescharacteristic
256#123—21no—
257C22⋊Q8C2×C4×C4711yescharacteristic
258C22⋊Q8C2×C4×C4711yescharacteristic
259#121C2×C4×C4711yescharacteristic
260#121C2×C4×C4711yescharacteristic
261#120—21no—
262C4×D4—21no—
263C4×D4—21no—
264#117C2×C4×C4711yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8C2×C4×C4712yes—
278C22⋊C8C2×C4×C4712yes—
279#97—21no—
280#97—42no—
281C4×C8—21no—
282C4×C8—42no—
283#95C2×C4×C4712yes—
284#95C2×C4×C4712yes—
285C24#41×C4711yescharacteristic
286#41—41no—
287#41—41no—
288C2×Q8C42×C4711yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C42×C4711yescharacteristic
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C22×C4×C4711yescharacteristic
299C22×C4C22×C4×C4711yescharacteristic
300C22×C4C22×C4×C4711yescharacteristic
301C22×C4C2×D4×C4711yescharacteristic
302C22×C4C2×D4×C4711yescharacteristic
303C22×C4#41×C4711yescharacteristic
304M16—42no—
305M16—41no—
306M16—41no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8C22⋊C4×C4711yescharacteristic
323C2×C8C22⋊C4×C4711yescharacteristic
324C2×C8C22⋊C4×C4711yescharacteristic
325C2×C8C22⋊C4×C4711yescharacteristic
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4C42×C4711yescharacteristic
329C4⋊C4C42×C4711yescharacteristic
330C22⋊C4—24no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—42no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—41no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—41no—
346C23#117×C4711yescharacteristic
347C23C4×D4×C4711yescharacteristic
348C23C4×D4×C4711yescharacteristic
349Q8—41no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—42no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4C2×C42×C4711yescharacteristic
375C2×C4C2×C22⋊C4×C4711yescharacteristic
376C2×C4C4×D4×C4711yescharacteristic
377C2×C4C4×D4×C4711yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—42no—
383C8—41no—
384C8—41no—
385C8#99×C4712yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22C4×C22⋊C4×C4711yescharacteristic
398C22C47×#44312yes—
399C22C47×#44412yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—82no—
408C4C2×#99×C4711yescharacteristic
409C4C47×#41011yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—81no—
414C2C4×#99×C4711yescharacteristic
415C2C47×#176411yescharacteristic
416C2C47×#176511yescharacteristic
subgroupG/H
centerC2×C4×C47C2×C22⋊C4
commutatorC2×C4C2×C42×C47
Frattini, cosocleC23×C4C23×C47
socleC22×C47C4×C22⋊C4
prime radicalC47×#525C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C23×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1752C2semidirect
3. C8×C22⋊C4×C47C2semidirect
6. C47×#1298C2semidirect
7. C47×#1297C2semidirect
8. C2×#131×C47C4semidirect
15. C47×#424C4semidirect
16. C47×#408C4semidirect
20. C47×#405C4semidirect
27. C47×#328C4semidirect
28. C47×#328C4semidirect
29. C47×#327C4semidirect
30. C47×#327C4semidirect
177. #8240C47direct (N × H)
203. #1752C2×C47semidirect
204. C8×C22⋊C4C2×C47semidirect
207. #1298C2×C47semidirect
208. #1297C2×C47semidirect
216. C2×#131C4×C47semidirect
223. #424C4×C47semidirect
224. #408C4×C47semidirect
228. #405C4×C47semidirect
235. #328C4×C47semidirect
236. #328C4×C47semidirect
237. #327C4×C47semidirect
238. #327C4×C47semidirect
239. C47#8240direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29292
C47×#17522
C8×C22⋊C4×C472
C47×#15012
C47×#12982
C47×#12972
#824047