Finite Group Databasebeta

← C47×#9722 #26049420

Subgroups — C47×#9722 #26049420

Order 12032.

460 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3167C211yesmaximal, characteristic
2C47×#1986C211yesmaximal, characteristic, complemented
3C47×#1980C211yesmaximal, characteristic
4C4×#107×C47C211yesmaximal, characteristic, complemented
5C47×#1503C211yesmaximal, characteristic, complemented
6C47×#1502C211yesmaximal, characteristic
7C47×#1451C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#498C411yescharacteristic, complemented
11C47×#492C411yescharacteristic, complemented
12C47×#487C411yescharacteristic, complemented
13C47×#486C411yescharacteristic, complemented
14C47×#465—21no—
15C47×#465—21no—
16C4×SD16×C47—21no—
17C4×SD16×C47—21no—
18C47×#431C2211yescharacteristic
19C2×#107×C47—21no—
20C2×#104×C47—22no—
21C4×M16×C47C2211yescharacteristic
22C2×C4×C8×C47C2211yescharacteristic
23C4×C4⋊C4×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C47×#340—21no—
26C47×#339—22no—
27C47×#328—22no—
28C47×#327—22no—
29C47×#322—21no—
30C47×#322—21no—
31C2×#41×C47—21no—
32C2×SD16×C47—21no—
33C2×SD16×C47—21no—
34C2×M16×C47D412yes—
35C22×C8×C47D411yescharacteristic
36C22×C8×C47D411yescharacteristic
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×C47—21no—
45#121×C47—21no—
46#121×C47—21no—
47C4×Q8×C47—21no—
48C4×Q8×C47—21no—
49C4×D4×C47—21no—
50C4×D4×C47—21no—
51#117×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C42×C47—21no—
55C2×C42×C47—21no—
56C2×C42×C47C2311yescharacteristic
57#107×C47—24no—
58#106×C47—21no—
59#106×C47—21no—
60C4⋊C8×C47—21no—
61#104×C47—44no—
62#103×C47—21no—
63#103×C47—21no—
64#102×C47—21no—
65#102×C47—21no—
66C22⋊C8×C47D412yes—
67#97×C47—21no—
68C4×C8×C47—21no—
69C4×C8×C47—21no—
70C4×C8×C47C2×C411yescharacteristic
71C4×C8×C47C2×C411yescharacteristic
72C4×C8×C47D411yescharacteristic
73C4×C8×C47D411yescharacteristic
74#95×C47—21no—
75#95×C47—21no—
76#41×C47—42no—
77#41×C47—42no—
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—21no—
84C2×D4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91SD16×C47—42no—
92SD16×C47—42no—
93M16×C47—22no—
94M16×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47—22no—
97C2×C8×C47—22no—
98C2×C8×C47—41no—
99C2×C8×C47C22⋊C411yescharacteristic
100C2×C8×C47C22⋊C411yescharacteristic
101C2×C8×C47C22⋊C411yescharacteristic
102C2×C8×C47C22⋊C411yescharacteristic
103C4⋊C4×C47—22no—
104C4⋊C4×C47—22no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47—41no—
113C4⋊C4×C47—41no—
114C4⋊C4×C47—41no—
115C22⋊C4×C47—41no—
116C22⋊C4×C47—41no—
117C22⋊C4×C47—41no—
118C42×C47—41no—
119C42×C47—42no—
120C42×C47—42no—
121C42×C47C22×C411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47#4111yescharacteristic
124C42×C47#4111yescharacteristic
125C23×C47—41no—
126C23×C47#12711yescharacteristic
127Q8×C47—41no—
128Q8×C47—41no—
129Q8×C47—42no—
130Q8×C47—81no—
131D4×C47—41no—
132D4×C47—41no—
133D4×C47—42no—
134D4×C47—81no—
135D4×C47—81no—
136D4×C47—81no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—41no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—81no—
146C2×C4×C47—81no—
147C2×C4×C47—81no—
148C2×C4×C47—81no—
149C2×C4×C47—82no—
150C2×C4×C47C2×C22⋊C411yescharacteristic
151C2×C4×C47C4×D411yescharacteristic
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47#12111yescharacteristic
155C2×C4×C47#12411yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)12yes—
157C2×C4×C47#13712yes—
158C8×C47—21no—
159C8×C47—21no—
160C8×C47—21no—
161C8×C47—42no—
162C8×C47—42no—
163C8×C47#10412yescomplemented
164#9722C4711yesmaximal, characteristic, direct product factor, Sylow
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—81no—
168C22×C47—81no—
169C22×C47—81no—
170C22×C47#39011yescharacteristic
171C22×C47#49611yescharacteristic
172C22×C47#49711yescharacteristic
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—82no—
177C4×C47—82no—
178C4×C47—81no—
179C4×C47—81no—
180C4×C47—81no—
181C4×C47C2×#10411yescharacteristic
182C4×C47#42111yescharacteristic
183C4×C47#44012yes—
184C4×C47#46812yes—
185#3167C2×C4711yescharacteristic
186#1986C2×C4711yescharacteristic, complemented
187#1980C2×C4711yescharacteristic
188C4×#107C2×C4711yescharacteristic, complemented
189#1503C2×C4711yescharacteristic, complemented
190#1502C2×C4711yescharacteristic
191#1451C2×C4711yescharacteristic, complemented
192C2×C47—21no—
193C2×C47—21no—
194C2×C47—161no—
195C2×C47#197311yescharacteristic
196C2×C47#197611yescharacteristic
197C2×C47#198011yescharacteristic
198#533C22×C4711yescharacteristic
199#532C22×C4711yescharacteristic
200#498C4×C4711yescharacteristic, complemented
201#492C4×C4711yescharacteristic, complemented
202#487C4×C4711yescharacteristic, complemented
203#486C4×C4711yescharacteristic, complemented
204#465—21no—
205#465—21no—
206C4×SD16—21no—
207C4×SD16—21no—
208#431C22×C4711yescharacteristic
209C2×#107—21no—
210C2×#104—22no—
211C4×M16C22×C4711yescharacteristic
212C2×C4×C8C22×C4711yescharacteristic
213C4×C4⋊C4C22×C4711yescharacteristic
214C4×C4⋊C4C22×C4711yescharacteristic
215#340—21no—
216#339—22no—
217#328—22no—
218#327—22no—
219#322—21no—
220#322—21no—
221C47#972211yescharacteristic, direct product factor, Sylow
222C2×#41—21no—
223C2×SD16—21no—
224C2×SD16—21no—
225C2×M16D4×C4712yes—
226C22×C8D4×C4711yescharacteristic
227C22×C8D4×C4711yescharacteristic
228C4⋊Q8C2×C4×C4711yescharacteristic
229C4⋊Q8C2×C4×C4711yescharacteristic
230C4⋊Q8C2×C4×C4711yescharacteristic
231#127C2×C4×C4711yescharacteristic
232#125—21no—
233#124—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C23×C4711yescharacteristic
248#107—24no—
249#106—21no—
250#106—21no—
251C4⋊C8—21no—
252#104—44no—
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257C22⋊C8D4×C4712yes—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8C2×C4×C4711yescharacteristic
262C4×C8C2×C4×C4711yescharacteristic
263C4×C8D4×C4711yescharacteristic
264C4×C8D4×C4711yescharacteristic
265#95—21no—
266#95—21no—
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C2×D4×C4711yescharacteristic
280C22×C4C2×D4×C4711yescharacteristic
281C22×C4C2×D4×C4711yescharacteristic
282SD16—42no—
283SD16—42no—
284M16—22no—
285M16—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8C22⋊C4×C4711yescharacteristic
291C2×C8C22⋊C4×C4711yescharacteristic
292C2×C8C22⋊C4×C4711yescharacteristic
293C2×C8C22⋊C4×C4711yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42—42no—
311C42—42no—
312C42C22×C4×C4711yescharacteristic
313C42C2×D4×C4711yescharacteristic
314C42#41×C4711yescharacteristic
315C42#41×C4711yescharacteristic
316C23—41no—
317C23#127×C4711yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4C2×C22⋊C4×C4711yescharacteristic
342C2×C4C4×D4×C4711yescharacteristic
343C2×C4C4×D4×C4711yescharacteristic
344C2×C4#121×C4711yescharacteristic
345C2×C4#121×C4711yescharacteristic
346C2×C4#124×C4711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C4712yes—
348C2×C4#137×C4712yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—42no—
353C8—42no—
354C8#104×C4712yescomplemented
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C47×#39011yescharacteristic
361C22C47×#49611yescharacteristic
362C22C47×#49711yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4C2×#104×C4711yescharacteristic
372C4C47×#42111yescharacteristic
373C4C47×#44012yes—
374C4C47×#46812yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2C47×#197311yescharacteristic
379C2C47×#197611yescharacteristic
380C2C47×#198011yescharacteristic
subgroupG/H
centerC2×C4×C47#121
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
socleC22×C47#390
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×#1986C2semidirect
4. C4×#107×C47C2semidirect
5. C47×#1503C2semidirect
7. C47×#1451C2semidirect
10. C47×#498C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
163. C8×C47#104semidirect
164. #9722C47direct (N × H)
186. #1986C2×C47semidirect
188. C4×#107C2×C47semidirect
189. #1503C2×C47semidirect
191. #1451C2×C47semidirect
200. #498C4×C47semidirect
201. #492C4×C47semidirect
202. #487C4×C47semidirect
203. #486C4×C47semidirect
221. C47#9722direct (N × H)
354. C8#104×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31672
C47×#19862
C47×#19802
C4×#107×C472
C47×#15032
C47×#15022
C47×#14512
#972247