Finite Group Databasebeta

← C47×#8519 #26048217

Subgroups — C47×#8519 #26048217

Order 12032.

754 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#542C211yesmaximal, characteristic
2C47×#1822C211yesmaximal, characteristic, complemented
3C47×#1820C211yesmaximal, characteristic, complemented
4C47×#1511C212yesmaximal, complemented
5C47×#1510C212yesmaximal
6C47×#542—24no—
7C47×#542—24no—
8C2×C4⋊Q8×C47C411yescharacteristic, complemented
9C2×#126×C47—21no—
10C2×#124×C47—21no—
11C2×#124×C47C411yescharacteristic, complemented
12C2×#123×C47—21no—
13C2×C22⋊Q8×C47—21no—
14C2×C22⋊Q8×C47C2211yescharacteristic
15C2×#121×C47C2211yescharacteristic
16C2×C4×Q8×C47C411yescharacteristic, complemented
17C2×C4×D4×C47C411yescharacteristic, complemented
18C2×#117×C47C2211yescharacteristic
19C47×#407C2212yes—
20C47×#381C2212yes—
21C47×#343—21no—
22C47×#343—21no—
23C47×#342—21no—
24C47×#342—21no—
25C47×#328—24no—
26C47×#327—24no—
27C22×Q8×C47—21no—
28C22×Q8×C47C2×C411yescharacteristic
29C22×D4×C47—21no—
30C22×D4×C47C2×C411yescharacteristic
31C23×C4×C47—21no—
32C23×C4×C47C2311yescharacteristic
33C2×M16×C47—22no—
34C4⋊Q8×C47—22no—
35C4⋊Q8×C47—22no—
36#126×C47—28no—
37#124×C47—28no—
38#124×C47—22no—
39#124×C47—22no—
40#123×C47—28no—
41C22⋊Q8×C47—28no—
42C22⋊Q8×C47—22no—
43C22⋊Q8×C47D414yes—
44#121×C47—22no—
45#121×C47D414yes—
46C4×Q8×C47—22no—
47C4×Q8×C47—22no—
48C4×D4×C47—22no—
49C4×D4×C47—22no—
50#117×C47—22no—
51#117×C47—22no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47C2×C411yescharacteristic
56C2×C4⋊C4×C47C2×C411yescharacteristic
57C2×C4⋊C4×C47D411yescharacteristic
58C2×C4⋊C4×C47D411yescharacteristic
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—21no—
62C2×C22⋊C4×C47—21no—
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—22no—
65C2×C22⋊C4×C47D411yescharacteristic
66C2×C22⋊C4×C47D411yescharacteristic
67C2×C42×C47—21no—
68C2×C42×C47C2×C411yescharacteristic
69C2×C42×C47C2×C411yescharacteristic
70C22⋊C8×C47—22no—
71C22⋊C8×C47—22no—
72#95×C47—22no—
73#95×C47—22no—
74C24×C47—21no—
75C24×C47C2×D411yescharacteristic
76C2×Q8×C47—24no—
77C2×Q8×C47—21no—
78C2×Q8×C47—42no—
79C2×Q8×C47—82no—
80C2×Q8×C47C22⋊C412yes—
81C2×D4×C47—24no—
82C2×D4×C47—21no—
83C2×D4×C47—42no—
84C2×D4×C47—82no—
85C2×D4×C47C22⋊C412yes—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—24no—
90C22×C4×C47—42no—
91C22×C4×C47—42no—
92C22×C4×C47—82no—
93C22×C4×C47C22⋊C411yescharacteristic
94C22×C4×C47C22⋊C411yescharacteristic
95C22×C4×C47C22⋊C411yescharacteristic
96C22×C4×C47C22⋊C411yescharacteristic
97C22×C4×C47C22×C411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D412yes—
100C22×C4×C47C2×D412yes—
101M16×C47—44no—
102C2×C8×C47—42no—
103C4⋊C4×C47—24no—
104C4⋊C4×C47—24no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—24no—
108C4⋊C4×C47—22no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47C22⋊C412yes—
111C4⋊C4×C47C22⋊C412yes—
112C22⋊C4×C47—24no—
113C22⋊C4×C47—24no—
114C22⋊C4×C47—24no—
115C22⋊C4×C47—24no—
116C22⋊C4×C47—22no—
117C22⋊C4×C47—22no—
118C22⋊C4×C47—24no—
119C22⋊C4×C47—44no—
120C42×C47—24no—
121C42×C47—21no—
122C42×C47—21no—
123C42×C47—21no—
124C42×C47—21no—
125C23×C47—22no—
126C23×C47—22no—
127C23×C47—41no—
128C23×C47—41no—
129C23×C47—42no—
130C23×C47—42no—
131C23×C47—42no—
132C23×C47C2×C22⋊C411yescharacteristic
133C23×C47#12012yes—
134Q8×C47—42no—
135Q8×C47—42no—
136Q8×C47—84no—
137D4×C47—42no—
138D4×C47—42no—
139D4×C47—84no—
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—22no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—22no—
148C2×C4×C47—22no—
149C2×C4×C47—42no—
150C2×C4×C47—42no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—84no—
159C2×C4×C47—82no—
160C2×C4×C47—82no—
161C2×C4×C47—82no—
162C2×C4×C47C2×C22⋊C411yescharacteristic
163C2×C4×C47C2×C22⋊C411yescharacteristic
164C2×C4×C47#12012yes—
165C8×C47—82no—
166#8519C4711yesmaximal, characteristic, direct product factor, Sylow
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—42no—
173C22×C47—42no—
174C22×C47—42no—
175C22×C47—82no—
176C22×C47—84no—
177C22×C47#37911yescharacteristic
178C22×C47#41012yes—
179C4×C47—22no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—42no—
183C4×C47—42no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—42no—
189C4×C47—162no—
190C2×#542C2×C4711yescharacteristic
191#1822C2×C4711yescharacteristic, complemented
192#1820C2×C4711yescharacteristic, complemented
193#1511C2×C4712yescomplemented
194#1510C2×C4712yes—
195C2×C47—22no—
196C2×C47—42no—
197C2×C47—82no—
198C2×C47#178211yescharacteristic
199C2×C47#179511yescharacteristic
200C2×C47#179611yescharacteristic
201#542—24no—
202#542—24no—
203C2×C4⋊Q8C4×C4711yescharacteristic, complemented
204C2×#126—21no—
205C2×#124—21no—
206C2×#124C4×C4711yescharacteristic, complemented
207C2×#123—21no—
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8C22×C4711yescharacteristic
210C2×#121C22×C4711yescharacteristic
211C2×C4×Q8C4×C4711yescharacteristic, complemented
212C2×C4×D4C4×C4711yescharacteristic, complemented
213C2×#117C22×C4711yescharacteristic
214#407C22×C4712yes—
215#381C22×C4712yes—
216#343—21no—
217#343—21no—
218#342—21no—
219#342—21no—
220#328—24no—
221#327—24no—
222C47#851911yescharacteristic, direct product factor, Sylow
223C22×Q8—21no—
224C22×Q8C2×C4×C4711yescharacteristic
225C22×D4—21no—
226C22×D4C2×C4×C4711yescharacteristic
227C23×C4—21no—
228C23×C4C23×C4711yescharacteristic
229C2×M16—22no—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232#126—28no—
233#124—28no—
234#124—22no—
235#124—22no—
236#123—28no—
237C22⋊Q8—28no—
238C22⋊Q8—22no—
239C22⋊Q8D4×C4714yes—
240#121—22no—
241#121D4×C4714yes—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×D4—22no—
245C4×D4—22no—
246#117—22no—
247#117—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C4711yescharacteristic
252C2×C4⋊C4C2×C4×C4711yescharacteristic
253C2×C4⋊C4D4×C4711yescharacteristic
254C2×C4⋊C4D4×C4711yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4D4×C4711yescharacteristic
262C2×C22⋊C4D4×C4711yescharacteristic
263C2×C42—21no—
264C2×C42C2×C4×C4711yescharacteristic
265C2×C42C2×C4×C4711yescharacteristic
266C22⋊C8—22no—
267C22⋊C8—22no—
268#95—22no—
269#95—22no—
270C24—21no—
271C24C2×D4×C4711yescharacteristic
272C2×Q8—24no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C4712yes—
277C2×D4—24no—
278C2×D4—21no—
279C2×D4—42no—
280C2×D4—82no—
281C2×D4C22⋊C4×C4712yes—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—82no—
289C22×C4C22⋊C4×C4711yescharacteristic
290C22×C4C22⋊C4×C4711yescharacteristic
291C22×C4C22⋊C4×C4711yescharacteristic
292C22×C4C22⋊C4×C4711yescharacteristic
293C22×C4C22×C4×C4711yescharacteristic
294C22×C4C2×D4×C4711yescharacteristic
295C22×C4C2×D4×C4712yes—
296C22×C4C2×D4×C4712yes—
297M16—44no—
298C2×C8—42no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4C22⋊C4×C4712yes—
307C4⋊C4C22⋊C4×C4712yes—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C22⋊C4—44no—
316C42—24no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—21no—
321C23—22no—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23C2×C22⋊C4×C4711yescharacteristic
329C23#120×C4712yes—
330Q8—42no—
331Q8—42no—
332Q8—84no—
333D4—42no—
334D4—42no—
335D4—84no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—84no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4C2×C22⋊C4×C4711yescharacteristic
359C2×C4C2×C22⋊C4×C4711yescharacteristic
360C2×C4#120×C4712yes—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22—84no—
372C22C47×#37911yescharacteristic
373C22C47×#41012yes—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—162no—
385C2—22no—
386C2—42no—
387C2—82no—
388C2C47×#178211yescharacteristic
389C2C47×#179511yescharacteristic
390C2C47×#179611yescharacteristic
subgroupG/H
center, socleC22×C47#379
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1822C2semidirect
3. C47×#1820C2semidirect
4. C47×#1511C2semidirect
8. C2×C4⋊Q8×C47C4semidirect
11. C2×#124×C47C4semidirect
16. C2×C4×Q8×C47C4semidirect
17. C2×C4×D4×C47C4semidirect
166. #8519C47direct (N × H)
191. #1822C2×C47semidirect
192. #1820C2×C47semidirect
193. #1511C2×C47semidirect
203. C2×C4⋊Q8C4×C47semidirect
206. C2×#124C4×C47semidirect
211. C2×C4×Q8C4×C47semidirect
212. C2×C4×D4C4×C47semidirect
222. C47#8519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5422
C47×#18222
C47×#18202
C47×#15112
C47×#15102
#851947