Finite Group Databasebeta

← C47×#9761 #26049459

Subgroups — C47×#9761 #26049459

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3167C211yesmaximal, characteristic
2C47×#1726C211yesmaximal, characteristic, complemented
3C47×#1568C211yesmaximal, characteristic, complemented
4C47×#1531C211yesmaximal, characteristic, complemented
5C47×#1530C211yesmaximal, characteristic
6C47×#1506C211yesmaximal, characteristic, complemented
7C47×#1505C211yesmaximal, characteristic
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×#432C2211yescharacteristic
19C47×#432C2211yescharacteristic
20C2×#97×C47—21no—
21C2×#97×C47C2211yescharacteristic
22C2×C4×C8×C47—21no—
23C2×C4×C8×C47C2211yescharacteristic
24C47×#376C2211yescharacteristic
25C47×#335—21no—
26C47×#334—21no—
27C47×#330—22no—
28C47×#329—22no—
29C47×#328—22no—
30C47×#327—22no—
31C2×#41×C47—21no—
32C2×SD16×C47—21no—
33C2×SD16×C47—21no—
34C22×C8×C47—21no—
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×C42×C47—21no—
53C2×C42×C47C2311yescharacteristic
54#106×C47—21no—
55#106×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58#103×C47—21no—
59#103×C47—21no—
60#102×C47—21no—
61#102×C47—21no—
62C22⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64#97×C47—24no—
65#97×C47—21no—
66#97×C47—21no—
67#97×C47—21no—
68#97×C47D412yes—
69C4×C8×C47—24no—
70C4×C8×C47C2×C411yescharacteristic
71C4×C8×C47C2×C411yescharacteristic
72C4×C8×C47D411yescharacteristic
73C4×C8×C47D411yescharacteristic
74#95×C47—21no—
75#95×C47D412yes—
76#41×C47—82no—
77C2×Q8×C47—21no—
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—41no—
84C22×C4×C47—22no—
85C22×C4×C47—41no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47#4111yescharacteristic
89SD16×C47—42no—
90SD16×C47—42no—
91C2×C8×C47—22no—
92C2×C8×C47—22no—
93C2×C8×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47—41no—
97C2×C8×C47—41no—
98C2×C8×C47C22⋊C411yescharacteristic
99C2×C8×C47C22⋊C411yescharacteristic
100C2×C8×C47C22⋊C411yescharacteristic
101C2×C8×C47C22⋊C411yescharacteristic
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C22⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—41no—
113C42×C47—22no—
114C42×C47—22no—
115C42×C47—41no—
116C42×C47C22×C411yescharacteristic
117C42×C47C2×D411yescharacteristic
118C42×C47C2×D411yescharacteristic
119C42×C47#4111yescharacteristic
120C23×C47—41no—
121C23×C47#12111yescharacteristic
122Q8×C47—41no—
123Q8×C47—41no—
124Q8×C47—81no—
125Q8×C47—81no—
126D4×C47—41no—
127D4×C47—41no—
128D4×C47—81no—
129D4×C47—81no—
130D4×C47—82no—
131C2×C4×C47—22no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—24no—
135C2×C4×C47—41no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—82no—
142C2×C4×C47C2×C22⋊C411yescharacteristic
143C2×C4×C47C4×D411yescharacteristic
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12411yescharacteristic
147C2×C4×C47#12711yescharacteristic
148C8×C47—24no—
149C8×C47—21no—
150C8×C47—21no—
151C8×C47—81no—
152C8×C47—81no—
153C8×C47#10412yes—
154C8×C47#10412yes—
155#9761C4711yesmaximal, characteristic, direct product factor, Sylow
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—81no—
159C22×C47—81no—
160C22×C47—81no—
161C22×C47#39011yescharacteristic
162C22×C47#47112yes—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—44no—
169C4×C47—81no—
170C4×C47—81no—
171C4×C47—81no—
172C4×C47C2×#10411yescharacteristic
173C4×C47C2×#10411yescharacteristic
174#3167C2×C4711yescharacteristic
175#1726C2×C4711yescharacteristic, complemented
176#1568C2×C4711yescharacteristic, complemented
177#1531C2×C4711yescharacteristic, complemented
178#1530C2×C4711yescharacteristic
179#1506C2×C4711yescharacteristic, complemented
180#1505C2×C4711yescharacteristic
181C2×C47—22no—
182C2×C47—161no—
183C2×C47#196211yescharacteristic
184C2×C47#197611yescharacteristic
185C2×C47#197711yescharacteristic
186#533C22×C4711yescharacteristic
187#532C22×C4711yescharacteristic
188#498C4×C4711yescharacteristic, complemented
189#492C4×C4711yescharacteristic, complemented
190#487C4×C4711yescharacteristic, complemented
191#486C4×C4711yescharacteristic, complemented
192#465—21no—
193#465—21no—
194C4×SD16—21no—
195C4×SD16—21no—
196#432C22×C4711yescharacteristic
197#432C22×C4711yescharacteristic
198C2×#97—21no—
199C2×#97C22×C4711yescharacteristic
200C2×C4×C8—21no—
201C2×C4×C8C22×C4711yescharacteristic
202#376C22×C4711yescharacteristic
203#335—21no—
204#334—21no—
205#330—22no—
206#329—22no—
207#328—22no—
208#327—22no—
209C47#976111yescharacteristic, direct product factor, Sylow
210C2×#41—21no—
211C2×SD16—21no—
212C2×SD16—21no—
213C22×C8—21no—
214C22×C8D4×C4711yescharacteristic
215C22×C8D4×C4711yescharacteristic
216C4⋊Q8C2×C4×C4711yescharacteristic
217C4⋊Q8C2×C4×C4711yescharacteristic
218C4⋊Q8C2×C4×C4711yescharacteristic
219#127C2×C4×C4711yescharacteristic
220#125—21no—
221#124—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224#121—21no—
225#121—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×D4—21no—
229C4×D4—21no—
230#117—21no—
231C2×C42—21no—
232C2×C42C23×C4711yescharacteristic
233#106—21no—
234#106—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#97—24no—
244#97—21no—
245#97—21no—
246#97—21no—
247#97D4×C4712yes—
248C4×C8—24no—
249C4×C8C2×C4×C4711yescharacteristic
250C4×C8C2×C4×C4711yescharacteristic
251C4×C8D4×C4711yescharacteristic
252C4×C8D4×C4711yescharacteristic
253#95—21no—
254#95D4×C4712yes—
255#41—82no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4C2×D4×C4711yescharacteristic
266C22×C4C2×D4×C4711yescharacteristic
267C22×C4#41×C4711yescharacteristic
268SD16—42no—
269SD16—42no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22⋊C4×C4711yescharacteristic
278C2×C8C22⋊C4×C4711yescharacteristic
279C2×C8C22⋊C4×C4711yescharacteristic
280C2×C8C22⋊C4×C4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C42—22no—
293C42—22no—
294C42—41no—
295C42C22×C4×C4711yescharacteristic
296C42C2×D4×C4711yescharacteristic
297C42C2×D4×C4711yescharacteristic
298C42#41×C4711yescharacteristic
299C23—41no—
300C23#121×C4711yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—81no—
304Q8—81no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—82no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—24no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4C2×C22⋊C4×C4711yescharacteristic
322C2×C4C4×D4×C4711yescharacteristic
323C2×C4C4×D4×C4711yescharacteristic
324C2×C4#121×C4711yescharacteristic
325C2×C4#124×C4711yescharacteristic
326C2×C4#127×C4711yescharacteristic
327C8—24no—
328C8—21no—
329C8—21no—
330C8—81no—
331C8—81no—
332C8#104×C4712yes—
333C8#104×C4712yes—
334C22—21no—
335C22—21no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22C47×#39011yescharacteristic
340C22C47×#47112yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4C2×#104×C4711yescharacteristic
351C4C2×#104×C4711yescharacteristic
352C2—22no—
353C2—161no—
354C2C47×#196211yescharacteristic
355C2C47×#197611yescharacteristic
356C2C47×#197711yescharacteristic
subgroupG/H
center, socleC22×C47#390
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
2. C47×#1726C2semidirect
3. C47×#1568C2semidirect
4. C47×#1531C2semidirect
6. C47×#1506C2semidirect
10. C47×#498C4semidirect
11. C47×#492C4semidirect
12. C47×#487C4semidirect
13. C47×#486C4semidirect
155. #9761C47direct (N × H)
175. #1726C2×C47semidirect
176. #1568C2×C47semidirect
177. #1531C2×C47semidirect
179. #1506C2×C47semidirect
188. #498C4×C47semidirect
189. #492C4×C47semidirect
190. #487C4×C47semidirect
191. #486C4×C47semidirect
209. C47#9761direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31672
C47×#17262
C47×#15682
C47×#15312
C47×#15302
C47×#15062
C47×#15052
#976147