Finite Group Databasebeta

← C47×#9108 #26048806

Subgroups — C47×#9108 #26048806

Order 12032.

586 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2972C211yesmaximal, characteristic
2C47×#2322C211yesmaximal, characteristic
3C47×#1459C211yesmaximal, characteristic
4C2×C47×#324C212yesmaximal, complemented
5C47×#1282C212yesmaximal, complemented
6C2×#123×C47C411yescharacteristic
7C2×C4×D4×C47C2211yescharacteristic
8C22×C4⋊C4×C47C2211yescharacteristic
9C8×D4×C47—24no—
10C47×#431—21no—
11C2×C22⋊C8×C47—21no—
12C2×C22⋊C8×C47C2212yes—
13C2×C22⋊C8×C47C2212yes—
14C47×#389—21no—
15C47×#388—21no—
16C47×#387—21no—
17C47×#386C411yescharacteristic
18C47×#385—21no—
19C47×#385C411yescharacteristic
20C47×#381C411yescharacteristic
21C4×C22⋊C4×C47C2211yescharacteristic
22C47×#324—24no—
23C47×#324—21no—
24C47×#323—21no—
25C22×D4×C47C2×C411yescharacteristic
26C23×C4×C47C2×C411yescharacteristic
27C23×C4×C47C2×C411yescharacteristic
28C23×C4×C47D411yescharacteristic
29C23×C4×C47C2311yescharacteristic
30C22×C8×C47—22no—
31C22×C8×C47—22no—
32C22×C8×C47—22no—
33#123×C47—22no—
34#123×C47C814yescomplemented
35C4×D4×C47—22no—
36C4×D4×C47—22no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—22no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47C2×C411yescharacteristic
47C2×C22⋊C4×C47C2×C411yescharacteristic
48C2×C22⋊C4×C47C2×C411yescharacteristic
49C2×C22⋊C4×C47D411yescharacteristic
50C2×C42×C47—21no—
51C2×C42×C47D411yescharacteristic
52C4⋊C8×C47—22no—
53C22⋊C8×C47—22no—
54C22⋊C8×C47—22no—
55C22⋊C8×C47—22no—
56C22⋊C8×C47—22no—
57C22⋊C8×C47D414yes—
58C4×C8×C47—22no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47—21no—
62#95×C47—21no—
63#95×C47—21no—
64C24×C47C22⋊C411yescharacteristic
65C24×C47C22×C411yescharacteristic
66C2×D4×C47—22no—
67C2×D4×C47—22no—
68C2×D4×C47C2×C812yes—
69C2×D4×C47M1612yes—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—22no—
73C22×C4×C47—21no—
74C22×C4×C47—22no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—22no—
80C22×C4×C47—81no—
81C22×C4×C47—81no—
82C22×C4×C47—81no—
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47C22⋊C411yescharacteristic
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C2×C812yescomplemented
87C22×C4×C47C2×D412yes—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47#4112yes—
91C2×C8×C47—24no—
92C2×C8×C47—42no—
93C2×C8×C47—82no—
94C2×C8×C47—82no—
95C2×C8×C47—82no—
96C4⋊C4×C47—24no—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—42no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—81no—
102C22⋊C4×C47—24no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—21no—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—22no—
107C22⋊C4×C47—81no—
108C22⋊C4×C47C2×C812yescomplemented
109C42×C47—21no—
110C42×C47—21no—
111C42×C47—81no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47C22⋊C812yes—
119C23×C47C2×C22⋊C411yescharacteristic
120C23×C47C4×D412yes—
121C23×C47C22×C811yescharacteristic
122C23×C47C2×M1611yescharacteristic
123C23×C47#13112yes—
124D4×C47—24no—
125D4×C47—24no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—24no—
133C2×C4×C47—41no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—42no—
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—41no—
150C2×C4×C47—41no—
151C2×C4×C47—81no—
152C2×C4×C47—82no—
153C2×C4×C47C22⋊C812yes—
154C2×C4×C47#12011yescharacteristic
155C2×C4×C47#12112yes—
156C2×C4×C47#12311yescharacteristic
157C8×C47—44no—
158C8×C47—82no—
159#9108C4711yesmaximal, characteristic, direct product factor, Sylow
160C22×C47—21no—
161C22×C47—22no—
162C22×C47—21no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—42no—
168C22×C47—42no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—81no—
172C22×C47#38611yescharacteristic
173C22×C47C2×C22⋊C811yescharacteristic
174C22×C47#40811yescharacteristic
175C22×C47C8×D412yes—
176C22×C47#43512yes—
177C4×C47—22no—
178C4×C47—21no—
179C4×C47—22no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—42no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—81no—
186C4×C47—81no—
187#2972C2×C4711yescharacteristic
188#2322C2×C4711yescharacteristic
189#1459C2×C4711yescharacteristic
190C2×#324C2×C4712yescomplemented
191#1282C2×C4712yescomplemented
192C2×C47—21no—
193C2×C47—21no—
194C2×C47—22no—
195C2×C47—22no—
196C2×C47—42no—
197C2×C47#186911yescharacteristic
198C2×C47#191311yescharacteristic
199C2×C47#191511yescharacteristic
200C2×#123C4×C4711yescharacteristic
201C2×C4×D4C22×C4711yescharacteristic
202C22×C4⋊C4C22×C4711yescharacteristic
203C8×D4—24no—
204#431—21no—
205C2×C22⋊C8—21no—
206C2×C22⋊C8C22×C4712yes—
207C2×C22⋊C8C22×C4712yes—
208#389—21no—
209#388—21no—
210#387—21no—
211#386C4×C4711yescharacteristic
212#385—21no—
213#385C4×C4711yescharacteristic
214#381C4×C4711yescharacteristic
215C4×C22⋊C4C22×C4711yescharacteristic
216#324—21no—
217#324—24no—
218#323—21no—
219C47#910811yescharacteristic, direct product factor, Sylow
220C22×D4C2×C4×C4711yescharacteristic
221C23×C4C2×C4×C4711yescharacteristic
222C23×C4C2×C4×C4711yescharacteristic
223C23×C4D4×C4711yescharacteristic
224C23×C4C23×C4711yescharacteristic
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228#123—22no—
229#123C8×C4714yescomplemented
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C4711yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4C2×C4×C4711yescharacteristic
242C2×C22⋊C4C2×C4×C4711yescharacteristic
243C2×C22⋊C4C2×C4×C4711yescharacteristic
244C2×C22⋊C4D4×C4711yescharacteristic
245C2×C42—21no—
246C2×C42D4×C4711yescharacteristic
247C4⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—22no—
252C22⋊C8D4×C4714yes—
253C4×C8—22no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259C24C22⋊C4×C4711yescharacteristic
260C24C22×C4×C4711yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4C2×C8×C4712yes—
264C2×D4M16×C4712yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4C22⋊C4×C4711yescharacteristic
279C22×C4C22⋊C4×C4711yescharacteristic
280C22×C4C22⋊C4×C4711yescharacteristic
281C22×C4C2×C8×C4712yescomplemented
282C22×C4C2×D4×C4712yes—
283C22×C4C2×D4×C4711yescharacteristic
284C22×C4C2×D4×C4711yescharacteristic
285C22×C4#41×C4712yes—
286C2×C8—24no—
287C2×C8—42no—
288C2×C8—82no—
289C2×C8—82no—
290C2×C8—82no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C22⋊C4—22no—
298C22⋊C4—21no—
299C22⋊C4—24no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—81no—
303C22⋊C4C2×C8×C4712yescomplemented
304C42—21no—
305C42—21no—
306C42—81no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C22⋊C8×C4712yes—
314C23C2×C22⋊C4×C4711yescharacteristic
315C23C4×D4×C4712yes—
316C23C22×C8×C4711yescharacteristic
317C23C2×M16×C4711yescharacteristic
318C23#131×C4712yes—
319D4—24no—
320D4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4C22⋊C8×C4712yes—
349C2×C4#120×C4711yescharacteristic
350C2×C4#121×C4712yes—
351C2×C4#123×C4711yescharacteristic
352C8—44no—
353C8—82no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22C47×#38611yescharacteristic
367C22C2×C22⋊C8×C4711yescharacteristic
368C22C47×#40811yescharacteristic
369C22C8×D4×C4712yes—
370C22C47×#43512yes—
371C4—22no—
372C4—21no—
373C4—22no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—42no—
386C2C47×#186911yescharacteristic
387C2C47×#191311yescharacteristic
388C2C47×#191511yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC23C22×C8×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC22×D4×C47C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C47×#324C2semidirect
5. C47×#1282C2semidirect
34. #123×C47C8semidirect
86. C22×C4×C47C2×C8semidirect
108. C22⋊C4×C47C2×C8semidirect
159. #9108C47direct (N × H)
190. C2×#324C2×C47semidirect
191. #1282C2×C47semidirect
219. C47#9108direct (N × H)
229. #123C8×C47semidirect
281. C22×C4C2×C8×C47semidirect
303. C22⋊C4C2×C8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#29722
C47×#23222
C47×#14592
C2×C47×#3242
C47×#12822
#910847