Finite Group Databasebeta

← C47×#11853 #26051551

Subgroups — C47×#11853 #26051551

Order 12032.

368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2611C211yesmaximal, characteristic
2C47×#1822C211yesmaximal, characteristic
3C47×#1458C211yesmaximal, characteristic
4C47×#1353C212yesmaximal, complemented
5C47×#1346C212yesmaximal, complemented
6C2×#125×C47C411yescharacteristic
7C2×#117×C47C2211yescharacteristic
8C47×#431—21no—
9C47×#407—21no—
10C47×#400C2211yescharacteristic
11C47×#399C411yescharacteristic
12C47×#398C2211yescharacteristic
13C47×#397C411yescharacteristic
14C47×#389—21no—
15C47×#388—21no—
16C47×#387—21no—
17C47×#385—21no—
18C47×#376C411yescharacteristic
19C47×#343—21no—
20C47×#343C2212yes—
21C47×#324C2212yes—
22C47×#323—21no—
23C23×C4×C47D411yescharacteristic
24C2×M16×C47—22no—
25#125×C47—41no—
26#125×C47—41no—
27#117×C47—41no—
28#117×C47—41no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47C2×C411yescharacteristic
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C4⋊C4×C47D411yescharacteristic
36C2×C4⋊C4×C47C2311yescharacteristic
37C2×C22⋊C4×C47—21no—
38C2×C22⋊C4×C47—21no—
39C2×C22⋊C4×C47C2×C411yescharacteristic
40C2×C22⋊C4×C47D411yescharacteristic
41C2×C42×C47—21no—
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C4⋊C8×C47—41no—
45C22⋊C8×C47—22no—
46C22⋊C8×C47—41no—
47C22⋊C8×C47—41no—
48C4×C8×C47—41no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47C2×C411yescharacteristic
55#95×C47C2×C411yescharacteristic
56C24×C47C22⋊C411yescharacteristic
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—22no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—41no—
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71M16×C47—42no—
72M16×C47—42no—
73C2×C8×C47—42no—
74C2×C8×C47—42no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—42no—
78C4⋊C4×C47—42no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—42no—
84C22⋊C4×C47—41no—
85C22⋊C4×C47—41no—
86C22⋊C4×C47—42no—
87C22⋊C4×C47—42no—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—21no—
91C42×C47—21no—
92C42×C47—42no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—41no—
97C23×C47—41no—
98C23×C47C2×C22⋊C411yescharacteristic
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—22no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47#9911yescharacteristic
126C2×C4×C47#9911yescharacteristic
127C2×C4×C47#13512yes—
128C8×C47—82no—
129C8×C47—82no—
130#11853C4711yesmaximal, characteristic, direct product factor, Sylow
131C22×C47—21no—
132C22×C47—21no—
133C22×C47—42no—
134C22×C47—41no—
135C22×C47—41no—
136C22×C47—41no—
137C22×C47—81no—
138C22×C47C2×#9911yescharacteristic
139C22×C47#41611yescharacteristic
140C22×C47#42111yescharacteristic
141C4×C47—22no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—42no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—81no—
150C4×C47—81no—
151C4×C47—81no—
152#2611C2×C4711yescharacteristic
153#1822C2×C4711yescharacteristic
154#1458C2×C4711yescharacteristic
155#1353C2×C4712yescomplemented
156#1346C2×C4712yescomplemented
157C2×C47—21no—
158C2×C47—21no—
159C2×C47—81no—
160C2×C47#151611yescharacteristic
161C2×C47#212311yescharacteristic
162C2×C47#213211yescharacteristic
163C2×#125C4×C4711yescharacteristic
164C2×#117C22×C4711yescharacteristic
165#431—21no—
166#407—21no—
167#400C22×C4711yescharacteristic
168#399C4×C4711yescharacteristic
169#398C22×C4711yescharacteristic
170#397C4×C4711yescharacteristic
171#389—21no—
172#388—21no—
173#387—21no—
174#385—21no—
175#376C4×C4711yescharacteristic
176#343—21no—
177#343C22×C4712yes—
178#324C22×C4712yes—
179#323—21no—
180C47#1185311yescharacteristic, direct product factor, Sylow
181C23×C4D4×C4711yescharacteristic
182C2×M16—22no—
183#125—41no—
184#125—41no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C4711yescharacteristic
192C2×C4⋊C4C2×C4×C4711yescharacteristic
193C2×C4⋊C4D4×C4711yescharacteristic
194C2×C4⋊C4C23×C4711yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4C2×C4×C4711yescharacteristic
198C2×C22⋊C4D4×C4711yescharacteristic
199C2×C42—21no—
200C2×C42C2×C4×C4711yescharacteristic
201C2×C42D4×C4711yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206C4×C8—41no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95C2×C4×C4711yescharacteristic
213#95C2×C4×C4711yescharacteristic
214C24C22⋊C4×C4711yescharacteristic
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C22⋊C4×C4711yescharacteristic
224C22×C4C22⋊C4×C4711yescharacteristic
225C22×C4C22⋊C4×C4711yescharacteristic
226C22×C4C22×C4×C4711yescharacteristic
227C22×C4C2×D4×C4711yescharacteristic
228C22×C4C2×D4×C4711yescharacteristic
229M16—42no—
230M16—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—42no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×C22⋊C4×C4711yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4#99×C4711yescharacteristic
284C2×C4#99×C4711yescharacteristic
285C2×C4#135×C4712yes—
286C8—82no—
287C8—82no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×#99×C4711yescharacteristic
296C22C47×#41611yescharacteristic
297C22C47×#42111yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—81no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2C47×#151611yescharacteristic
313C2C47×#212311yescharacteristic
314C2C47×#213211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#99
commutatorC22×C4C22×C4×C47
Frattini, cosocleC2×C4⋊C4C23×C47
prime radicalC24×C47C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1353C2semidirect
5. C47×#1346C2semidirect
130. #11853C47direct (N × H)
155. #1353C2×C47semidirect
156. #1346C2×C47semidirect
180. C47#11853direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26112
C47×#18222
C47×#14582
C47×#13532
C47×#13462
#1185347