Finite Group Databasebeta

← C47×#9369 #26049067

Subgroups — C47×#9369 #26049067

Order 12032.

390 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3240C211yesmaximal, characteristic
2C47×#2967C211yesmaximal, characteristic
3C47×#1521C211yesmaximal, characteristic
4C47×#1515C211yesmaximal, characteristic, complemented
5C47×#1485C211yesmaximal, characteristic, complemented
6C47×#1288C211yesmaximal, characteristic, complemented
7C47×#1287C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#529C2211yescharacteristic
10C47×#501C411yescharacteristic, complemented
11C47×#501C411yescharacteristic, complemented
12C47×#489C411yescharacteristic, complemented
13C47×#489C411yescharacteristic, complemented
14C47×#485—21no—
15C47×#482—21no—
16C47×#479—21no—
17C47×#478—21no—
18C47×#446—21no—
19C47×#436—21no—
20C47×#435—21no—
21C47×#435—21no—
22C47×#433—21no—
23C47×#432C2211yescharacteristic
24C47×#432C2211yescharacteristic
25C47×#431C2211yescharacteristic
26C47×#405—21no—
27C4×M16×C47C2211yescharacteristic
28C47×#383C2211yescharacteristic
29C47×#328—21no—
30C47×#328—21no—
31C47×#328—21no—
32C47×#327—21no—
33C47×Q8⋊C8—21no—
34C47×Q8⋊C8—21no—
35C2×M16×C47—21no—
36C2×M16×C47—21no—
37C22×C8×C47—21no—
38C4⋊Q8×C47C2×C411yescharacteristic
39C4⋊Q8×C47C2×C411yescharacteristic
40#126×C47—21no—
41#125×C47—21no—
42#125×C47C2×C411yescharacteristic
43#124×C47C2×C411yescharacteristic
44#123×C47—21no—
45C22⋊Q8×C47—21no—
46C22⋊Q8×C47—21no—
47C22⋊Q8×C47D411yescharacteristic
48#121×C47D411yescharacteristic
49C4×Q8×C47—21no—
50C4×Q8×C47—21no—
51C4×Q8×C47D411yescharacteristic
52C4×D4×C47—21no—
53C4×D4×C47D411yescharacteristic
54#117×C47—21no—
55#117×C47—21no—
56C2×C42×C47C2311yescharacteristic
57#107×C47—21no—
58#107×C47—21no—
59#106×C47—21no—
60#106×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66#103×C47—21no—
67#103×C47—21no—
68#102×C47—21no—
69#102×C47—21no—
70C22⋊C8×C47—21no—
71C22⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47D411yescharacteristic
75C22⋊C8×C47D411yescharacteristic
76#97×C47—21no—
77#97×C47—21no—
78#97×C47—21no—
79#97×C47C2×C411yescharacteristic
80#97×C47C2×C411yescharacteristic
81C4×C8×C47—21no—
82C4×C8×C47—21no—
83C4×C8×C47D411yescharacteristic
84C4×C8×C47D411yescharacteristic
85#95×C47—21no—
86#95×C47—21no—
87#95×C47—21no—
88C2×Q8×C47—21no—
89C2×Q8×C47—21no—
90C2×Q8×C47C22⋊C411yescharacteristic
91C2×D4×C47—21no—
92C2×D4×C47C22⋊C411yescharacteristic
93C22×C4×C47—21no—
94C22×C4×C47—41no—
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47#4111yescharacteristic
98M16×C47—42no—
99M16×C47—42no—
100C2×C8×C47—21no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47—21no—
104C2×C8×C47—21no—
105C2×C8×C47—21no—
106C2×C8×C47—42no—
107C2×C8×C47—41no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—41no—
117C4⋊C4×C47—41no—
118C4⋊C4×C47C22⋊C411yescharacteristic
119C4⋊C4×C47C22⋊C411yescharacteristic
120C22⋊C4×C47—21no—
121C22⋊C4×C47—21no—
122C22⋊C4×C47—21no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—41no—
126C42×C47—21no—
127C42×C47—41no—
128C42×C47C22×C411yescharacteristic
129C42×C47C2×D411yescharacteristic
130C42×C47C2×D411yescharacteristic
131C42×C47#4111yescharacteristic
132C23×C47—21no—
133C23×C47#12111yescharacteristic
134Q8×C47—41no—
135Q8×C47—42no—
136Q8×C47—81no—
137D4×C47—41no—
138D4×C47—81no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
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—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
158C8×C47—22no—
159C8×C47—41no—
160C8×C47—41no—
161C8×C47—41no—
162C8×C47—41no—
163C8×C47—41no—
164C8×C47—81no—
165#9369C4711yesmaximal, characteristic, direct product factor, Sylow
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47#38611yescharacteristic
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—81no—
183C4×C47—81no—
184C4×C47—161no—
185#3240C2×C4711yescharacteristic
186#2967C2×C4711yescharacteristic
187#1521C2×C4711yescharacteristic
188#1515C2×C4711yescharacteristic, complemented
189#1485C2×C4711yescharacteristic, complemented
190#1288C2×C4711yescharacteristic, complemented
191#1287C2×C4711yescharacteristic, complemented
192C2×C47—41no—
193C2×C47—81no—
194C2×C47#188111yescharacteristic
195C2×C47#190611yescharacteristic
196C2×C47#190911yescharacteristic
197#533C22×C4711yescharacteristic
198#529C22×C4711yescharacteristic
199#501C4×C4711yescharacteristic, complemented
200#501C4×C4711yescharacteristic, complemented
201#489C4×C4711yescharacteristic, complemented
202#489C4×C4711yescharacteristic, complemented
203#485—21no—
204#482—21no—
205#479—21no—
206#478—21no—
207#446—21no—
208#436—21no—
209#435—21no—
210#435—21no—
211#433—21no—
212#432C22×C4711yescharacteristic
213#432C22×C4711yescharacteristic
214#431C22×C4711yescharacteristic
215#405—21no—
216C4×M16C22×C4711yescharacteristic
217#383C22×C4711yescharacteristic
218#328—21no—
219#328—21no—
220#328—21no—
221#327—21no—
222Q8⋊C8—21no—
223Q8⋊C8—21no—
224C47#936911yescharacteristic, direct product factor, Sylow
225C2×M16—21no—
226C2×M16—21no—
227C22×C8—21no—
228C4⋊Q8C2×C4×C4711yescharacteristic
229C4⋊Q8C2×C4×C4711yescharacteristic
230#126—21no—
231#125—21no—
232#125C2×C4×C4711yescharacteristic
233#124C2×C4×C4711yescharacteristic
234#123—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8D4×C4711yescharacteristic
238#121D4×C4711yescharacteristic
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8D4×C4711yescharacteristic
242C4×D4—21no—
243C4×D4D4×C4711yescharacteristic
244#117—21no—
245#117—21no—
246C2×C42C23×C4711yescharacteristic
247#107—21no—
248#107—21no—
249#106—21no—
250#106—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256#103—21no—
257#103—21no—
258#102—21no—
259#102—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8D4×C4711yescharacteristic
265C22⋊C8D4×C4711yescharacteristic
266#97—21no—
267#97—21no—
268#97—21no—
269#97C2×C4×C4711yescharacteristic
270#97C2×C4×C4711yescharacteristic
271C4×C8—21no—
272C4×C8—21no—
273C4×C8D4×C4711yescharacteristic
274C4×C8D4×C4711yescharacteristic
275#95—21no—
276#95—21no—
277#95—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C22⋊C4×C4711yescharacteristic
281C2×D4—21no—
282C2×D4C22⋊C4×C4711yescharacteristic
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C2×D4×C4711yescharacteristic
286C22×C4C2×D4×C4711yescharacteristic
287C22×C4#41×C4711yescharacteristic
288M16—42no—
289M16—42no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—42no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C22⋊C4×C4711yescharacteristic
309C4⋊C4C22⋊C4×C4711yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C42—21no—
317C42—41no—
318C42C22×C4×C4711yescharacteristic
319C42C2×D4×C4711yescharacteristic
320C42C2×D4×C4711yescharacteristic
321C42#41×C4711yescharacteristic
322C23—21no—
323C23#121×C4711yescharacteristic
324Q8—41no—
325Q8—42no—
326Q8—81no—
327D4—41no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C2×C22⋊C4×C4711yescharacteristic
343C2×C4C4×D4×C4711yescharacteristic
344C2×C4C4×D4×C4711yescharacteristic
345C2×C4#120×C4711yescharacteristic
346C2×C4#121×C4711yescharacteristic
347C2×C4#123×C4711yescharacteristic
348C8—22no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—41no—
353C8—41no—
354C8—81no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C47×#38611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—161no—
374C2—41no—
375C2—81no—
376C2C47×#188111yescharacteristic
377C2C47×#190611yescharacteristic
378C2C47×#190911yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radical#121×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1515C2semidirect
5. C47×#1485C2semidirect
6. C47×#1288C2semidirect
7. C47×#1287C2semidirect
10. C47×#501C4semidirect
11. C47×#501C4semidirect
12. C47×#489C4semidirect
13. C47×#489C4semidirect
165. #9369C47direct (N × H)
188. #1515C2×C47semidirect
189. #1485C2×C47semidirect
190. #1288C2×C47semidirect
191. #1287C2×C47semidirect
199. #501C4×C47semidirect
200. #501C4×C47semidirect
201. #489C4×C47semidirect
202. #489C4×C47semidirect
224. C47#9369direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32402
C47×#29672
C47×#15212
C47×#15152
C47×#14852
C47×#12882
C47×#12872
#936947