Finite Group Databasebeta

← C47×#9315 #26049013

Subgroups — C47×#9315 #26049013

Order 12032.

480 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×#3079C211yesmaximal, characteristic
2C47×#2988C211yesmaximal, characteristic
3C47×#1987C211yesmaximal, characteristic, complemented
4C47×#1806C211yesmaximal, characteristic
5C47×#1548C211yesmaximal, characteristic, complemented
6C47×#1303C211yesmaximal, characteristic, complemented
7C47×#1292C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C47C2211yescharacteristic
9C4×#41×C47C2211yescharacteristic
10C47×#477—21no—
11C47×#476—21no—
12C47×#475C412yescomplemented
13C47×#474C412yescomplemented
14C8×Q8×C47—21no—
15C8×D4×C47—22no—
16C8×D4×C47—21no—
17C47×#431—21no—
18C47×#431C2211yescharacteristic
19C47×#428—21no—
20C47×#423C2211yescharacteristic
21C47×#423C2211yescharacteristic
22C2×C4⋊C8×C47—21no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#104×C47—21no—
25C47×#417—21no—
26C4×C4⋊C4×C47C2211yescharacteristic
27C47×#340—22no—
28C47×#339—21no—
29C47×#333—21no—
30C47×#333—21no—
31C2×#41×C47D411yescharacteristic
32C22×Q8×C47—21no—
33C2×M16×C47—21no—
34C2×M16×C47—21no—
35C22×C8×C47—22no—
36C22×C8×C47D412yes—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47C2×C412yes—
41C4×Q8×C47C2×C411yescharacteristic
42C4×Q8×C47D411yescharacteristic
43C4×D4×C47—21no—
44C4×D4×C47—21no—
45C4×D4×C47C2×C411yescharacteristic
46C4×D4×C47D411yescharacteristic
47#117×C47—21no—
48#117×C47D411yescharacteristic
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C42×C47—21no—
53C2×C42×C47—21no—
54C2×C42×C47C2311yescharacteristic
55#107×C47—22no—
56#106×C47—22no—
57C4⋊C8×C47—22no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47C2×C412yes—
64C4⋊C8×C47D411yescharacteristic
65C4⋊C8×C47D411yescharacteristic
66#104×C47—42no—
67#103×C47—22no—
68#102×C47—22no—
69C22⋊C8×C47—22no—
70C22⋊C8×C47—21no—
71C4×C8×C47—22no—
72C4×C8×C47—21no—
73#95×C47—21no—
74#41×C47—21no—
75#41×C47—21no—
76#41×C47SD1612yes—
77#41×C47Q1612yes—
78C2×Q8×C47—22no—
79C2×Q8×C47—41no—
80C2×Q8×C47—82no—
81C2×Q8×C47C22⋊C411yescharacteristic
82C2×D4×C47—21no—
83C2×D4×C47C22⋊C411yescharacteristic
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47#4111yescharacteristic
92M16×C47—41no—
93M16×C47—41no—
94M16×C47—41no—
95M16×C47—41no—
96C2×C8×C47—22no—
97C2×C8×C47—22no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—42no—
101C2×C8×C47—41no—
102C2×C8×C47—82no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—22no—
106C4⋊C4×C47—22no—
107C4⋊C4×C47—22no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C4⋊C4×C47C22⋊C411yescharacteristic
112C4⋊C4×C47C22⋊C411yescharacteristic
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C42×C47—21no—
117C42×C47—21no—
118C42×C47—21no—
119C42×C47—41no—
120C42×C47—41no—
121C42×C47C22×C411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47#4111yescharacteristic
125C23×C47—21no—
126C23×C47#12111yescharacteristic
127Q8×C47—21no—
128Q8×C47—82no—
129Q8×C47—82no—
130Q8×C47#10312yes—
131D4×C47—22no—
132D4×C47—22no—
133D4×C47—21no—
134D4×C47#10312yes—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—81no—
148C2×C4×C47—81no—
149C2×C4×C47—82no—
150C2×C4×C47—81no—
151C2×C4×C47C2×C22⋊C411yescharacteristic
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47C4×D411yescharacteristic
154C2×C4×C47#12011yescharacteristic
155C2×C4×C47#12111yescharacteristic
156C2×C4×C47#12311yescharacteristic
157C2×C4×C47C2×SD1611yescharacteristic
158C2×C4×C47C2×Q1611yescharacteristic
159C2×C4×C47#13511yescharacteristic
160C2×C4×C47#13511yescharacteristic
161C8×C47—42no—
162C8×C47—42no—
163C8×C47—41no—
164C8×C47—41no—
165C8×C47—81no—
166#9315C4711yesmaximal, characteristic, direct product factor, Sylow
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—22no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47#38611yescharacteristic
173C22×C47#46511yescharacteristic
174C22×C47#46711yescharacteristic
175C4×C47—21no—
176C4×C47—22no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—82no—
182C4×C47—82no—
183C4×C47C2×#10311yescharacteristic
184C4×C47#41611yescharacteristic
185C4×C47#45511yescharacteristic
186C4×C47#45611yescharacteristic
187C4×C47#46511yescharacteristic
188C4×C47#46711yescharacteristic
189#3079C2×C4711yescharacteristic
190#2988C2×C4711yescharacteristic
191#1987C2×C4711yescharacteristic, complemented
192#1806C2×C4711yescharacteristic
193#1548C2×C4711yescharacteristic, complemented
194#1303C2×C4711yescharacteristic, complemented
195#1292C2×C4711yescharacteristic, complemented
196C2×C47—21no—
197C2×C47—21no—
198C2×C47—42no—
199C2×C47#188211yescharacteristic
200C2×C47#189211yescharacteristic
201C2×C47#190311yescharacteristic
202C2×C4⋊Q8C22×C4711yescharacteristic
203C4×#41C22×C4711yescharacteristic
204#477—21no—
205#476—21no—
206#475C4×C4712yescomplemented
207#474C4×C4712yescomplemented
208C8×Q8—21no—
209C8×D4—22no—
210C8×D4—21no—
211#431—21no—
212#431C22×C4711yescharacteristic
213#428—21no—
214#423C22×C4711yescharacteristic
215#423C22×C4711yescharacteristic
216C2×C4⋊C8—21no—
217C2×C4⋊C8C22×C4711yescharacteristic
218C2×#104—21no—
219#417—21no—
220C4×C4⋊C4C22×C4711yescharacteristic
221#340—22no—
222#339—21no—
223#333—21no—
224#333—21no—
225C47#931511yescharacteristic, direct product factor, Sylow
226C2×#41D4×C4711yescharacteristic
227C22×Q8—21no—
228C2×M16—21no—
229C2×M16—21no—
230C22×C8—22no—
231C22×C8D4×C4712yes—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C2×C4×C4712yes—
236C4×Q8C2×C4×C4711yescharacteristic
237C4×Q8D4×C4711yescharacteristic
238C4×D4—21no—
239C4×D4—21no—
240C4×D4C2×C4×C4711yescharacteristic
241C4×D4D4×C4711yescharacteristic
242#117—21no—
243#117D4×C4711yescharacteristic
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C23×C4711yescharacteristic
250#107—22no—
251#106—22no—
252C4⋊C8—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8C2×C4×C4712yes—
259C4⋊C8D4×C4711yescharacteristic
260C4⋊C8D4×C4711yescharacteristic
261#104—42no—
262#103—22no—
263#102—22no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266C4×C8—22no—
267C4×C8—21no—
268#95—21no—
269#41—21no—
270#41—21no—
271#41SD16×C4712yes—
272#41Q16×C4712yes—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C4711yescharacteristic
277C2×D4—21no—
278C2×D4C22⋊C4×C4711yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C4711yescharacteristic
285C22×C4C2×D4×C4711yescharacteristic
286C22×C4#41×C4711yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—82no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C4711yescharacteristic
307C4⋊C4C22⋊C4×C4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—41no—
315C42—41no—
316C42C22×C4×C4711yescharacteristic
317C42C2×D4×C4711yescharacteristic
318C42C2×D4×C4711yescharacteristic
319C42#41×C4711yescharacteristic
320C23—21no—
321C23#121×C4711yescharacteristic
322Q8—21no—
323Q8—82no—
324Q8—82no—
325Q8#103×C4712yes—
326D4—22no—
327D4—22no—
328D4—21no—
329D4#103×C4712yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C4711yescharacteristic
347C2×C4C4×D4×C4711yescharacteristic
348C2×C4C4×D4×C4711yescharacteristic
349C2×C4#120×C4711yescharacteristic
350C2×C4#121×C4711yescharacteristic
351C2×C4#123×C4711yescharacteristic
352C2×C4C2×SD16×C4711yescharacteristic
353C2×C4C2×Q16×C4711yescharacteristic
354C2×C4#135×C4711yescharacteristic
355C2×C4#135×C4711yescharacteristic
356C8—42no—
357C8—41no—
358C8—41no—
359C8—42no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22C47×#38611yescharacteristic
367C22C47×#46511yescharacteristic
368C22C47×#46711yescharacteristic
369C4—21no—
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—82no—
376C4—82no—
377C4C2×#103×C4711yescharacteristic
378C4C47×#41611yescharacteristic
379C4C47×#45511yescharacteristic
380C4C47×#45611yescharacteristic
381C4C47×#46511yescharacteristic
382C4C47×#46711yescharacteristic
383C2—21no—
384C2—21no—
385C2—42no—
386C2C47×#188211yescharacteristic
387C2C47×#189211yescharacteristic
388C2C47×#190311yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC2×#41×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
3. C47×#1987C2semidirect
5. C47×#1548C2semidirect
6. C47×#1303C2semidirect
7. C47×#1292C2semidirect
12. C47×#475C4semidirect
13. C47×#474C4semidirect
166. #9315C47direct (N × H)
191. #1987C2×C47semidirect
193. #1548C2×C47semidirect
194. #1303C2×C47semidirect
195. #1292C2×C47semidirect
206. #475C4×C47semidirect
207. #474C4×C47semidirect
225. C47#9315direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30792
C47×#29882
C47×#19872
C47×#18062
C47×#15482
C47×#13032
C47×#12922
#931547