Finite Group Databasebeta

← C47×#9054 #26048752

Subgroups — C47×#9054 #26048752

Order 12032.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3167C211yesmaximal, characteristic
2C47×#2962C211yesmaximal, characteristic, complemented
3C47×#1980C211yesmaximal, characteristic
4C47×#1503C211yesmaximal, characteristic, complemented
5C47×#1480C211yesmaximal, characteristic
6C47×#1279C211yesmaximal, characteristic, complemented
7C47×#1278C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#498C411yescharacteristic, complemented
11C47×#492C411yescharacteristic, complemented
12C47×#487C411yescharacteristic, complemented
13C47×#486C411yescharacteristic, complemented
14C47×#465—22no—
15C47×#446—22no—
16C47×#446—21no—
17C8×Q8×C47—21no—
18C4×SD16×C47—22no—
19C47×#431C2211yescharacteristic
20C47×#424—21no—
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×#104×C47—21no—
23C2×#104×C47—21no—
24C47×#405—21no—
25C4×M16×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C4×C4⋊C4×C47C2211yescharacteristic
28C47×#328—22no—
29C47×D4⋊C8—21no—
30C47×D4⋊C8—21no—
31C2×#41×C47—21no—
32C2×SD16×C47—22no—
33C2×M16×C47D411yescharacteristic
34C2×M16×C47D411yescharacteristic
35C22×C8×C47—21no—
36C22×C8×C47—21no—
37C4⋊Q8×C47C2×C411yescharacteristic
38C4⋊Q8×C47C2×C411yescharacteristic
39C4⋊Q8×C47C2×C411yescharacteristic
40#127×C47C2×C411yescharacteristic
41#125×C47—21no—
42#124×C47—21no—
43C22⋊Q8×C47—21no—
44C22⋊Q8×C47D412yes—
45#121×C47—21no—
46#121×C47—21no—
47C4×Q8×C47—21no—
48C4×Q8×C47D412yes—
49C4×D4×C47—21no—
50C4×D4×C47—21no—
51#117×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C42×C47—21no—
54C2×C42×C47C2311yescharacteristic
55#106×C47—22no—
56C4⋊C8×C47—22no—
57C4⋊C8×C47—22no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D411yescharacteristic
61C4⋊C8×C47D411yescharacteristic
62#104×C47—42no—
63#104×C47—42no—
64#103×C47—22no—
65#102×C47—22no—
66C22⋊C8×C47—21no—
67#97×C47—22no—
68#97×C47—21no—
69C4×C8×C47—22no—
70C4×C8×C47—21no—
71C4×C8×C47—21no—
72C4×C8×C47—21no—
73C4×C8×C47C2×C411yescharacteristic
74C4×C8×C47C2×C411yescharacteristic
75#95×C47—21no—
76#41×C47—41no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80C2×Q8×C47—21no—
81C2×Q8×C47—21no—
82C2×Q8×C47C22⋊C412yes—
83C2×D4×C47—21no—
84C2×D4×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47#4111yescharacteristic
92SD16×C47—44no—
93M16×C47—21no—
94M16×C47—21no—
95M16×C47—21no—
96M16×C47SD1612yescomplemented
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—21no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47—42no—
104C2×C8×C47—41no—
105C2×C8×C47—41no—
106C2×C8×C47—41no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47—22no—
111C4⋊C4×C47—22no—
112C4⋊C4×C47—22no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—41no—
116C4⋊C4×C47C22⋊C412yes—
117C22⋊C4×C47—22no—
118C22⋊C4×C47—41no—
119C22⋊C4×C47—41no—
120C42×C47—22no—
121C42×C47—41no—
122C42×C47—41no—
123C42×C47C22×C411yescharacteristic
124C42×C47C2×D411yescharacteristic
125C42×C47C2×D411yescharacteristic
126C42×C47#4111yescharacteristic
127C23×C47—41no—
128C23×C47#12111yescharacteristic
129Q8×C47—42no—
130Q8×C47—41no—
131Q8×C47—41no—
132Q8×C47—41no—
133Q8×C47—41no—
134D4×C47—42no—
135D4×C47—41no—
136D4×C47—41no—
137D4×C47—41no—
138D4×C47—41no—
139D4×C47—81no—
140D4×C47—81no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—41no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—81no—
149C2×C4×C47—81no—
150C2×C4×C47—81no—
151C2×C4×C47—81no—
152C2×C4×C47C2×C22⋊C411yescharacteristic
153C2×C4×C47C4×D411yescharacteristic
154C2×C4×C47C4×D411yescharacteristic
155C2×C4×C47#12011yescharacteristic
156C2×C4×C47#12111yescharacteristic
157C2×C4×C47#12311yescharacteristic
158C2×C4×C47C2×SD1611yescharacteristic
159C2×C4×C47#13511yescharacteristic
160C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C47#13711yescharacteristic
162C8×C47—22no—
163C8×C47—22no—
164C8×C47—41no—
165C8×C47—41no—
166C8×C47—41no—
167C8×C47—41no—
168C8×C47—81no—
169#9054C4711yesmaximal, characteristic, direct product factor, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—81no—
173C22×C47—81no—
174C22×C47—81no—
175C22×C47#38611yescharacteristic
176C22×C47#46011yescharacteristic
177C22×C47#46411yescharacteristic
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—42no—
183C4×C47—82no—
184C4×C47—81no—
185C4×C47C4×SD1611yescharacteristic
186C4×C47#44011yescharacteristic
187C4×C47#44311yescharacteristic
188C4×C47#44411yescharacteristic
189C4×C47#44811yescharacteristic
190C4×C47#44911yescharacteristic
191#3167C2×C4711yescharacteristic
192#2962C2×C4711yescharacteristic, complemented
193#1980C2×C4711yescharacteristic
194#1503C2×C4711yescharacteristic, complemented
195#1480C2×C4711yescharacteristic
196#1279C2×C4711yescharacteristic, complemented
197#1278C2×C4711yescharacteristic, complemented
198C2×C47—21no—
199C2×C47—21no—
200C2×C47—161no—
201C2×C47#187611yescharacteristic
202C2×C47#188011yescharacteristic
203C2×C47#188411yescharacteristic
204#533C22×C4711yescharacteristic
205#532C22×C4711yescharacteristic
206#498C4×C4711yescharacteristic, complemented
207#492C4×C4711yescharacteristic, complemented
208#487C4×C4711yescharacteristic, complemented
209#486C4×C4711yescharacteristic, complemented
210#465—22no—
211#446—22no—
212#446—21no—
213C8×Q8—21no—
214C4×SD16—22no—
215#431C22×C4711yescharacteristic
216#424—21no—
217C2×C4⋊C8C22×C4711yescharacteristic
218C2×#104—21no—
219C2×#104—21no—
220#405—21no—
221C4×M16C22×C4711yescharacteristic
222C2×C4×C8C22×C4711yescharacteristic
223C4×C4⋊C4C22×C4711yescharacteristic
224#328—22no—
225D4⋊C8—21no—
226D4⋊C8—21no—
227C47#905411yescharacteristic, direct product factor, Sylow
228C2×#41—21no—
229C2×SD16—22no—
230C2×M16D4×C4711yescharacteristic
231C2×M16D4×C4711yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C4⋊Q8C2×C4×C4711yescharacteristic
235C4⋊Q8C2×C4×C4711yescharacteristic
236C4⋊Q8C2×C4×C4711yescharacteristic
237#127C2×C4×C4711yescharacteristic
238#125—21no—
239#124—21no—
240C22⋊Q8—21no—
241C22⋊Q8D4×C4712yes—
242#121—21no—
243#121—21no—
244C4×Q8—21no—
245C4×Q8D4×C4712yes—
246C4×D4—21no—
247C4×D4—21no—
248#117—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C23×C4711yescharacteristic
252#106—22no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C4711yescharacteristic
258C4⋊C8D4×C4711yescharacteristic
259#104—42no—
260#104—42no—
261#103—22no—
262#102—22no—
263C22⋊C8—21no—
264#97—22no—
265#97—21no—
266C4×C8—22no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270C4×C8C2×C4×C4711yescharacteristic
271C4×C8C2×C4×C4711yescharacteristic
272#95—21no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊C4×C4712yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C4711yescharacteristic
287C22×C4C2×D4×C4711yescharacteristic
288C22×C4#41×C4711yescharacteristic
289SD16—44no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16SD16×C4712yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4C22⋊C4×C4712yes—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42C22×C4×C4711yescharacteristic
321C42C2×D4×C4711yescharacteristic
322C42C2×D4×C4711yescharacteristic
323C42#41×C4711yescharacteristic
324C23—41no—
325C23#121×C4711yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330Q8—41no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4C2×C22⋊C4×C4711yescharacteristic
350C2×C4C4×D4×C4711yescharacteristic
351C2×C4C4×D4×C4711yescharacteristic
352C2×C4#120×C4711yescharacteristic
353C2×C4#121×C4711yescharacteristic
354C2×C4#123×C4711yescharacteristic
355C2×C4C2×SD16×C4711yescharacteristic
356C2×C4#135×C4711yescharacteristic
357C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
358C2×C4#137×C4711yescharacteristic
359C8—22no—
360C8—22no—
361C8—41no—
362C8—41no—
363C8—41no—
364C8—41no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C47×#38611yescharacteristic
372C22C47×#46011yescharacteristic
373C22C47×#46411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—81no—
381C4C4×SD16×C4711yescharacteristic
382C4C47×#44011yescharacteristic
383C4C47×#44311yescharacteristic
384C4C47×#44411yescharacteristic
385C4C47×#44811yescharacteristic
386C4C47×#44911yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2C47×#187611yescharacteristic
391C2C47×#188011yescharacteristic
392C2C47×#188411yescharacteristic
subgroupG/H
centerC2×C4×C47#120
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#386
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ 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×#2962C2semidirect
4. C47×#1503C2semidirect
6. C47×#1279C2semidirect
7. C47×#1278C2semidirect
10. C47×#498C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
96. M16×C47SD16semidirect
169. #9054C47direct (N × H)
192. #2962C2×C47semidirect
194. #1503C2×C47semidirect
196. #1279C2×C47semidirect
197. #1278C2×C47semidirect
206. #498C4×C47semidirect
207. #492C4×C47semidirect
208. #487C4×C47semidirect
209. #486C4×C47semidirect
227. C47#9054direct (N × H)
293. M16SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31672
C47×#29622
C47×#19802
C47×#15032
C47×#14802
C47×#12792
C47×#12782
#905447