Finite Group Databasebeta

← C47×#11688 #26051386

Subgroups — C47×#11688 #26051386

Order 12032.

432 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×#3054C211yesmaximal, characteristic
2C2×C47×#349C211yesmaximal, characteristic, complemented
3C2×C47×#338C211yesmaximal, characteristic, complemented
4C47×#1342C212yesmaximal, complemented
5C47×#1341C212yesmaximal, complemented
6C2×#135×C47C411yescharacteristic
7C22×M16×C47—21no—
8C22×M16×C47C2211yescharacteristic
9C47×#525—21no—
10C2×M32×C47—21no—
11C47×#470C411yescharacteristic
12C47×#470C2211yescharacteristic
13C47×#469C411yescharacteristic
14C47×#469C2211yescharacteristic
15C47×#468—21no—
16C47×#468—21no—
17C47×#427C411yescharacteristic
18C47×#416—21no—
19C47×#349—21no—
20C47×#349C2212yes—
21C47×#338—21no—
22C47×#338C2212yes—
23C2×#41×C47—21no—
24C23×C4×C47D411yescharacteristic
25#135×C47—41no—
26#135×C47—41no—
27C2×Q16×C47C2×C411yescharacteristic
28C2×SD16×C47—21no—
29C2×D8×C47C2×C411yescharacteristic
30C2×M16×C47—22no—
31C2×M16×C47—22no—
32C2×M16×C47—41no—
33C2×M16×C47—41no—
34C2×M16×C47—41no—
35C2×M16×C47—41no—
36C2×M16×C47—41no—
37C2×M16×C47—41no—
38C2×M16×C47C2×C411yescharacteristic
39C2×M16×C47D411yescharacteristic
40C2×M16×C47D411yescharacteristic
41C2×M16×C47C2311yescharacteristic
42C22×C8×C47—22no—
43C22×C8×C47C2×C411yescharacteristic
44C22×C8×C47D411yescharacteristic
45#123×C47—41no—
46C22⋊Q8×C47—21no—
47C22⋊Q8×C47—21no—
48#121×C47—21no—
49#121×C47—21no—
50#120×C47—41no—
51C4×D4×C47—41no—
52C4×D4×C47—41no—
53#117×C47—21no—
54M32×C47—22no—
55M32×C47—41no—
56C2×C16×C47—41no—
57#107×C47—21no—
58#106×C47C2×C411yescharacteristic
59#106×C47C2×C411yescharacteristic
60#103×C47—21no—
61#103×C47—21no—
62#102×C47—21no—
63#102×C47—21no—
64C24×C47SD1611yescharacteristic
65#41×C47—41no—
66#41×C47—41no—
67#41×C47—41no—
68#41×C47—41no—
69C2×Q8×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—41no—
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47D811yescharacteristic
82C22×C4×C47D811yescharacteristic
83C22×C4×C47SD1611yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85Q16×C47—41no—
86SD16×C47—42no—
87D8×C47—41no—
88M16×C47—41no—
89M16×C47—41no—
90M16×C47—41no—
91M16×C47—41no—
92M16×C47—42no—
93M16×C47—42no—
94M16×C47—42no—
95M16×C47—42no—
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—24no—
101C2×C8×C47—42no—
102C2×C8×C47—42no—
103C2×C8×C47C22⋊C411yescharacteristic
104C2×C8×C47C22⋊C411yescharacteristic
105C2×C8×C47C22×C411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—41no—
113C22⋊C4×C47—41no—
114C22⋊C4×C47—41no—
115C22⋊C4×C47—41no—
116C42×C47—41no—
117C16×C47—42no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—41no—
121C23×C47—81no—
122C23×C47#10211yescharacteristic
123C23×C47#10211yescharacteristic
124C23×C47C2×SD1611yescharacteristic
125Q8×C47—41no—
126Q8×C47—41no—
127D4×C47—41no—
128D4×C47—41no—
129D4×C47—82no—
130D4×C47—82no—
131D4×C47—81no—
132D4×C47—81no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—81no—
147C2×C4×C47—81no—
148C2×C4×C47#9911yescharacteristic
149C2×C4×C47#9911yescharacteristic
150C2×C4×C47#10211yescharacteristic
151C2×C4×C47#10211yescharacteristic
152C2×C4×C47#10411yescharacteristic
153C2×C4×C47#10411yescharacteristic
154C2×C4×C47C2×C22⋊C411yescharacteristic
155C2×C4×C47C2×D811yescharacteristic
156C8×C47—21no—
157C8×C47—21no—
158C8×C47—21no—
159C8×C47—21no—
160C8×C47—44no—
161#11688C4711yesmaximal, characteristic, direct product factor, Sylow
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—42no—
168C22×C47—81no—
169C22×C47—81no—
170C22×C47—81no—
171C22×C47—81no—
172C22×C47#32711yescharacteristic
173C22×C47#32711yescharacteristic
174C22×C47C2×#10211yescharacteristic
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—81no—
178C4×C47—81no—
179C4×C47—81no—
180C4×C47#32711yescharacteristic
181C4×C47#32711yescharacteristic
182C4×C47C2×#9911yescharacteristic
183C4×C47C2×#10411yescharacteristic
184#3054C2×C4711yescharacteristic
185C2×#349C2×C4711yescharacteristic, complemented
186C2×#338C2×C4711yescharacteristic, complemented
187#1342C2×C4712yescomplemented
188#1341C2×C4712yescomplemented
189C2×C47—21no—
190C2×C47—21no—
191C2×C47—21no—
192C2×C47—41no—
193C2×C47—41no—
194C2×C47—161no—
195C2×C47C2×#32711yescharacteristic
196C2×#135C4×C4711yescharacteristic
197C22×M16—21no—
198C22×M16C22×C4711yescharacteristic
199#525—21no—
200C2×M32—21no—
201#470C4×C4711yescharacteristic
202#470C22×C4711yescharacteristic
203#469C4×C4711yescharacteristic
204#469C22×C4711yescharacteristic
205#468—21no—
206#468—21no—
207#427C4×C4711yescharacteristic
208#416—21no—
209#349—21no—
210#349C22×C4712yes—
211#338—21no—
212#338C22×C4712yes—
213C47#1168811yescharacteristic, direct product factor, Sylow
214C2×#41—21no—
215C23×C4D4×C4711yescharacteristic
216#135—41no—
217#135—41no—
218C2×Q16C2×C4×C4711yescharacteristic
219C2×SD16—21no—
220C2×D8C2×C4×C4711yescharacteristic
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—41no—
224C2×M16—41no—
225C2×M16—41no—
226C2×M16—41no—
227C2×M16—41no—
228C2×M16—41no—
229C2×M16C2×C4×C4711yescharacteristic
230C2×M16D4×C4711yescharacteristic
231C2×M16D4×C4711yescharacteristic
232C2×M16C23×C4711yescharacteristic
233C22×C8—22no—
234C22×C8C2×C4×C4711yescharacteristic
235C22×C8D4×C4711yescharacteristic
236#123—41no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239#121—21no—
240#121—21no—
241#120—41no—
242C4×D4—41no—
243C4×D4—41no—
244#117—21no—
245M32—22no—
246M32—41no—
247C2×C16—41no—
248#107—21no—
249#106C2×C4×C4711yescharacteristic
250#106C2×C4×C4711yescharacteristic
251#103—21no—
252#103—21no—
253#102—21no—
254#102—21no—
255C24SD16×C4711yescharacteristic
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C22⋊C4×C4711yescharacteristic
271C22×C4C22⋊C4×C4711yescharacteristic
272C22×C4D8×C4711yescharacteristic
273C22×C4D8×C4711yescharacteristic
274C22×C4SD16×C4711yescharacteristic
275C22×C4C2×D4×C4711yescharacteristic
276Q16—41no—
277SD16—42no—
278D8—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—42no—
284M16—42no—
285M16—42no—
286M16—42no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8C22⋊C4×C4711yescharacteristic
295C2×C8C22⋊C4×C4711yescharacteristic
296C2×C8C22×C4×C4711yescharacteristic
297C2×C8C2×D4×C4711yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C16—42no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—81no—
313C23#102×C4711yescharacteristic
314C23#102×C4711yescharacteristic
315C23C2×SD16×C4711yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#99×C4711yescharacteristic
340C2×C4#99×C4711yescharacteristic
341C2×C4#102×C4711yescharacteristic
342C2×C4#102×C4711yescharacteristic
343C2×C4#104×C4711yescharacteristic
344C2×C4#104×C4711yescharacteristic
345C2×C4C2×C22⋊C4×C4711yescharacteristic
346C2×C4C2×D8×C4711yescharacteristic
347C8—21no—
348C8—21no—
349C8—21no—
350C8—21no—
351C8—44no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22C47×#32711yescharacteristic
363C22C47×#32711yescharacteristic
364C22C2×#102×C4711yescharacteristic
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4C47×#32711yescharacteristic
371C4C47×#32711yescharacteristic
372C4C2×#99×C4711yescharacteristic
373C4C2×#104×C4711yescharacteristic
374C2—21no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—41no—
379C2—161no—
380C2C2×C47×#32711yescharacteristic
subgroupG/H
centerC4×C47#327
commutatorC2×C8C22×C4×C47
Frattini, cosocleC2×M16C23×C47
socleC2×C47C2×#327
prime radicalC47×#3054C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C47 ◁ C22×C4×C47 ◁ C22×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#349C2semidirect
3. C2×C47×#338C2semidirect
4. C47×#1342C2semidirect
5. C47×#1341C2semidirect
161. #11688C47direct (N × H)
185. C2×#349C2×C47semidirect
186. C2×#338C2×C47semidirect
187. #1342C2×C47semidirect
188. #1341C2×C47semidirect
213. C47#11688direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30542
C2×C47×#3492
C2×C47×#3382
C47×#13422
C47×#13412
#1168847