Finite Group Databasebeta

← C47×#9287 #26048985

Subgroups — C47×#9287 #26048985

Order 12032.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3227C211yesmaximal, characteristic
2C47×#2932C211yesmaximal, characteristic
3C47×#1993C211yesmaximal, characteristic, complemented
4C47×#1548C211yesmaximal, characteristic, complemented
5C47×#1517C211yesmaximal, characteristic
6C47×#1286C211yesmaximal, characteristic, complemented
7C47×#1275C211yesmaximal, characteristic, complemented
8C2×#131×C47—21no—
9C47×#532C2211yescharacteristic
10C2×C4⋊Q8×C47C2211yescharacteristic
11C47×#498C412yescomplemented
12C47×#486C412yescomplemented
13C47×#481—22no—
14C47×#476—22no—
15C47×#435—22no—
16C47×#435—22no—
17C47×#431C2211yescharacteristic
18C47×#431C2211yescharacteristic
19C47×#423C2211yescharacteristic
20C47×#408—21no—
21C2×#97×C47C2211yescharacteristic
22C47×#382C2211yescharacteristic
23C47×#340—21no—
24C47×#340—21no—
25C47×#333—22no—
26C47×#327—22no—
27C2×#41×C47—21no—
28C22×Q8×C47—21no—
29#131×C47—42no—
30#131×C47—42no—
31C2×M16×C47—22no—
32C2×M16×C47—21no—
33C22×C8×C47—22no—
34C22×C8×C47D411yescharacteristic
35C22×C8×C47D411yescharacteristic
36C4⋊Q8×C47—21no—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47C2×C412yes—
40C4⋊Q8×C47C2×C411yescharacteristic
41#127×C47C2×C411yescharacteristic
42#124×C47—21no—
43#121×C47—21no—
44#121×C47D412yes—
45C4×D4×C47—21no—
46C4×D4×C47D412yes—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C42×C47C2311yescharacteristic
51#106×C47—24no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47D412yes—
56#102×C47—24no—
57C22⋊C8×C47—24no—
58C22⋊C8×C47—21no—
59C22⋊C8×C47—21no—
60#97×C47—21no—
61#97×C47—21no—
62C4×C8×C47—21no—
63C4×C8×C47C2×C412yes—
64#95×C47—21no—
65#95×C47—21no—
66#41×C47—41no—
67#41×C47—41no—
68#41×C47—41no—
69#41×C47—41no—
70C2×Q8×C47—21no—
71C2×Q8×C47—22no—
72C2×Q8×C47—41no—
73C2×Q8×C47—82no—
74C2×D4×C47—22no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47C22⋊C412yes—
78C22×C4×C47—22no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47#4111yescharacteristic
84M16×C47—44no—
85M16×C47—41no—
86M16×C47—41no—
87C2×C8×C47—21no—
88C2×C8×C47—21no—
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47—44no—
95C2×C8×C47—41no—
96C2×C8×C47SD1612yes—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47C22⋊C412yes—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—22no—
107C42×C47C22×C411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47C2×D411yescharacteristic
110C42×C47#4111yescharacteristic
111C23×C47—22no—
112C23×C47#12111yescharacteristic
113Q8×C47—41no—
114Q8×C47—41no—
115Q8×C47—82no—
116Q8×C47—82no—
117D4×C47—42no—
118D4×C47—42no—
119D4×C47—42no—
120D4×C47—41no—
121D4×C47—41no—
122D4×C47—81no—
123C2×C4×C47—22no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—82no—
130C2×C4×C47—81no—
131C2×C4×C47—81no—
132C2×C4×C47—81no—
133C2×C4×C47C2×C22⋊C411yescharacteristic
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47#12011yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12311yescharacteristic
139C2×C4×C47C2×SD1611yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C47#13711yescharacteristic
143C8×C47—22no—
144C8×C47—42no—
145C8×C47—42no—
146C8×C47—41no—
147C8×C47—81no—
148#9287C4711yesmaximal, characteristic, direct product factor, Sylow
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47#38611yescharacteristic
155C22×C47#46111yescharacteristic
156C22×C47#46311yescharacteristic
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—42no—
162C4×C47—82no—
163C4×C47—161no—
164C4×C47C4×SD1611yescharacteristic
165C4×C47#44011yescharacteristic
166C4×C47#45011yescharacteristic
167C4×C47#45211yescharacteristic
168#3227C2×C4711yescharacteristic
169#2932C2×C4711yescharacteristic
170#1993C2×C4711yescharacteristic, complemented
171#1548C2×C4711yescharacteristic, complemented
172#1517C2×C4711yescharacteristic
173#1286C2×C4711yescharacteristic, complemented
174#1275C2×C4711yescharacteristic, complemented
175C2×C47—21no—
176C2×C47—21no—
177C2×C47—82no—
178C2×C47#187711yescharacteristic
179C2×C47#190311yescharacteristic
180C2×C47#190911yescharacteristic
181C2×#131—21no—
182#532C22×C4711yescharacteristic
183C2×C4⋊Q8C22×C4711yescharacteristic
184#498C4×C4712yescomplemented
185#486C4×C4712yescomplemented
186#481—22no—
187#476—22no—
188#435—22no—
189#435—22no—
190#431C22×C4711yescharacteristic
191#431C22×C4711yescharacteristic
192#423C22×C4711yescharacteristic
193#408—21no—
194C2×#97C22×C4711yescharacteristic
195#382C22×C4711yescharacteristic
196#340—21no—
197#340—21no—
198#333—22no—
199#327—22no—
200C47#928711yescharacteristic, direct product factor, Sylow
201C2×#41—21no—
202C22×Q8—21no—
203#131—42no—
204#131—42no—
205C2×M16—22no—
206C2×M16—21no—
207C22×C8—22no—
208C22×C8D4×C4711yescharacteristic
209C22×C8D4×C4711yescharacteristic
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8C2×C4×C4712yes—
214C4⋊Q8C2×C4×C4711yescharacteristic
215#127C2×C4×C4711yescharacteristic
216#124—21no—
217#121—21no—
218#121D4×C4712yes—
219C4×D4—21no—
220C4×D4D4×C4712yes—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C42C23×C4711yescharacteristic
225#106—24no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8D4×C4712yes—
230#102—24no—
231C22⋊C8—24no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234#97—21no—
235#97—21no—
236C4×C8—21no—
237C4×C8C2×C4×C4712yes—
238#95—21no—
239#95—21no—
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊C4×C4712yes—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C4711yescharacteristic
256C22×C4C2×D4×C4711yescharacteristic
257C22×C4#41×C4711yescharacteristic
258M16—44no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—22no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—44no—
269C2×C8—41no—
270C2×C8SD16×C4712yes—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4C22⋊C4×C4712yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C22×C4×C4711yescharacteristic
282C42C2×D4×C4711yescharacteristic
283C42C2×D4×C4711yescharacteristic
284C42#41×C4711yescharacteristic
285C23—22no—
286C23#121×C4711yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—82no—
290Q8—82no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×C22⋊C4×C4711yescharacteristic
308C2×C4C4×D4×C4711yescharacteristic
309C2×C4C4×D4×C4711yescharacteristic
310C2×C4#120×C4711yescharacteristic
311C2×C4#121×C4711yescharacteristic
312C2×C4#123×C4711yescharacteristic
313C2×C4C2×SD16×C4711yescharacteristic
314C2×C4#135×C4711yescharacteristic
315C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
316C2×C4#137×C4711yescharacteristic
317C8—22no—
318C8—42no—
319C8—42no—
320C8—41no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22C47×#38611yescharacteristic
328C22C47×#46111yescharacteristic
329C22C47×#46311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—82no—
336C4—161no—
337C4C4×SD16×C4711yescharacteristic
338C4C47×#44011yescharacteristic
339C4C47×#45011yescharacteristic
340C4C47×#45211yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2C47×#187711yescharacteristic
345C2C47×#190311yescharacteristic
346C2C47×#190911yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
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×#1993C2semidirect
4. C47×#1548C2semidirect
6. C47×#1286C2semidirect
7. C47×#1275C2semidirect
11. C47×#498C4semidirect
12. C47×#486C4semidirect
148. #9287C47direct (N × H)
170. #1993C2×C47semidirect
171. #1548C2×C47semidirect
173. #1286C2×C47semidirect
174. #1275C2×C47semidirect
184. #498C4×C47semidirect
185. #486C4×C47semidirect
200. C47#9287direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32272
C47×#29322
C47×#19932
C47×#15482
C47×#15172
C47×#12862
C47×#12752
#928747