Finite Group Databasebeta

← #26109769

Subgroups — #26109769

Order 12032.

384 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#20245886C211yesmaximal, characteristic
2#20241722C211yesmaximal, characteristic
3#20241245C212yesmaximal, complemented
4#20241243C212yesmaximal, complemented
5C47×#1464C211yesmaximal, characteristic
6#15689180C2212yes—
7#15689016—21no—
8#15689016—21no—
9#15689009—21no—
10#15689009—21no—
11C4×C4⋊Dic47C2211yescharacteristic
12C4×C4⋊Dic47C2211yescharacteristic
13C4×C22⋊Dic47C411yescharacteristic
14C4×C22⋊Dic47C411yescharacteristic
15#15688969C411yescharacteristic
16C42×Dic47C411yescharacteristic
17#15688849—21no—
18#15688847—21no—
19C2×#117×C47C2211yescharacteristic
20C47×#432C2212yes—
21C47×#324—21no—
22C47×#323—21no—
23C2×C4⋊Dic47—21no—
24C2×C4⋊Dic47—21no—
25C2×C22⋊Dic47—21no—
26C2×C22⋊Dic47—21no—
27C2×C4×Dic47—21no—
28C2×C4×Dic47—21no—
29C2×C4×Dic47C2×C411yescharacteristic
30C2×C4×Dic47C2×C411yescharacteristic
31C2×C4×Dic47C2×C411yescharacteristic
32C2×C4×Dic47C2×C411yescharacteristic
33C4⋊(C47⋊C8)—22no—
34C22⋊(C47⋊C8)—22no—
35#13093935—22no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C23×C4×C47C2×C411yescharacteristic
43#117×C47—22no—
44#117×C47—22no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C22⋊C4×C47D411yescharacteristic
48C2×C22⋊C4×C47D411yescharacteristic
49C2×C42×C47C2×C411yescharacteristic
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—22no—
52C22⋊C8×C47—22no—
53#97×C47—22no—
54C24×C47C22⋊C411yescharacteristic
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47—21no—
69C2×C8×C47—42no—
70C4⋊C4×C47—22no—
71C4⋊C4×C47—22no—
72C22⋊C4×C47—22no—
73C22⋊C4×C47—22no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47#4112yes—
77C42×C47#4112yes—
78C22⋊Dic47—42no—
79C22⋊Dic47—42no—
80C4⋊Dic47—42no—
81C4⋊Dic47—42no—
82C4×Dic47—42no—
83C4×Dic47—42no—
84C4×Dic47—41no—
85C4×Dic47—41no—
86C4×Dic47—41no—
87C4×Dic47—41no—
88C2×C47⋊C8—42no—
89C23×C47—21no—
90C23×C47—21no—
91C23×C47—21no—
92C23×C47—41no—
93C23×C47—41no—
94C23×C47C2×C22⋊C411yescharacteristic
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—42no—
105C2×C4×C47—42no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47#11711yescharacteristic
109C2×C4×C47#11711yescharacteristic
110C2×C4×C47#12312yes—
111C2×C4×C47#12312yes—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—41no—
115C2×Dic47—41no—
116C2×Dic47—41no—
117C2×Dic47—41no—
118C2×Dic47—41no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C8×C47—82no—
125C47⋊C8—82no—
126#8744—471nomaximal, Sylow
127C22×C47—21no—
128C22×C47—21no—
129C22×C47—41no—
130C22×C47—41no—
131C22×C47—41no—
132C22×C47—81no—
133C22×C47—81no—
134C22×C47#38111yescharacteristic
135C22×C47#41311yescharacteristic
136C22×C47#41311yescharacteristic
137C4×C47—21no—
138C4×C47—21no—
139C4×C47—22no—
140C4×C47—22no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144Dic47—42no—
145Dic47—42no—
146Dic47—81no—
147Dic47—81no—
148#2298—471no—
149#1464—471no—
150#1464D4711yescharacteristic
151#1285—472no—
152#1285—472no—
153C2×C47—21no—
154C2×C47—21no—
155C2×C47—81no—
156C2×C47#182211yescharacteristic
157C2×C47#182711yescharacteristic
158C2×C47#182711yescharacteristic
159C2×#117C2×D4711yescharacteristic
160#432—472no—
161#432C2×D4712yes—
162#388—941no—
163#388—941no—
164#387—941no—
165#387—941no—
166C4×C4⋊C4—471no—
167C4×C4⋊C4—471no—
168C4×C22⋊C4—471no—
169C4×C22⋊C4—471no—
170#376—471no—
171C43—471no—
172#324—21no—
173#324—941no—
174#323—21no—
175#323—941no—
176C47#874411yescharacteristic, complemented, Sylow
177C23×C4C4×D4711yescharacteristic
178#117—22no—
179#117—22no—
180C2×C4⋊C4—941no—
181C2×C4⋊C4—941no—
182C2×C4⋊C4D18811yescharacteristic
183C2×C4⋊C4C22⋊D4711yescharacteristic
184C2×C22⋊C4—941no—
185C2×C22⋊C4—941no—
186C2×C22⋊C4D18811yescharacteristic
187C2×C22⋊C4C22⋊D4711yescharacteristic
188C2×C42—471no—
189C2×C42—471no—
190C2×C42—471no—
191C2×C42—471no—
192C2×C42—941no—
193C2×C42—941no—
194C2×C42C4×D4711yescharacteristic
195C2×C42C22×D4711yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—942no—
198C22⋊C8—22no—
199C22⋊C8—942no—
200#97—22no—
201#97—942no—
202#95—941no—
203#95—941no—
204#95—941no—
205#95—941no—
206#95—941no—
207#95—941no—
208C24(C2×D47)⋊C411yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—941no—
214C22×C4—941no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4(C2×D47)⋊C411yescharacteristic
218C22×C4(C2×D47)⋊C411yescharacteristic
219C22×C4(C2×D47)⋊C411yescharacteristic
220C22×C4C2×C4×D4711yescharacteristic
221C22×C4C2×D18811yescharacteristic
222C22×C4C2×C22⋊D4711yescharacteristic
223C2×C8—42no—
224C2×C8—1882no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—1882no—
228C4⋊C4—1882no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—1882no—
232C22⋊C4—1882no—
233C42—21no—
234C42—21no—
235C42—1881no—
236C42—1881no—
237C42—1881no—
238C42—1881no—
239C42—1882no—
240C42—1882no—
241C42#1062535212yes—
242C42#1062535212yes—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×(C2×D47)⋊C411yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—942no—
263C2×C4—942no—
264C2×C4—1881no—
265C2×C4—1881no—
266C2×C4—1881no—
267C2×C4—1881no—
268C2×C4—1881no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4—1881no—
272C2×C4—1881no—
273C2×C4—1881no—
274C2×C4#1309398011yescharacteristic
275C2×C4#1309398011yescharacteristic
276C2×C4#1309400512yes—
277C2×C4#1309400812yes—
278C8—82no—
279C8—3762no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1568898411yescharacteristic
288C22#1568910511yescharacteristic
289C22#1568910511yescharacteristic
290C4—21no—
291C4—21no—
292C4—22no—
293C4—22no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—3761no—
298C4—3761no—
299C4—1882no—
300C4—1882no—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#2024346911yescharacteristic
305C2#2024348911yescharacteristic
306C2#2024349311yescharacteristic
subgroupG/H
centerC22#15688984
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1464C2
socleC22×C47#381
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1464D47
hypocenterC47#8744
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #20241245C2semidirect
4. #20241243C2semidirect
176. C47#8744semidirect

Maximal subgroups

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

subgroupindex
#202458862
#202417222
#202412452
#202412432
C47×#14642
#874447