Finite Group Databasebeta

← #26104571

Subgroups — #26104571

Order 12032.

402 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243531C211yesmaximal, characteristic
2#20243505C211yesmaximal, characteristic
3#20241214C212yesmaximal
4#20241211C212yesmaximal
5C47×#2295C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7#15688878—21no—
8#15688878—21no—
9#15688878—21no—
10#15688878C2212yes—
11#15688878C2212yes—
12C2×C4×Q8×C47C411yescharacteristic
13C47×#391C411yescharacteristic
14C47×#391C2211yescharacteristic
15C47×#389C411yescharacteristic
16C47×#389C2211yescharacteristic
17C47×#387—21no—
18C47×#387—21no—
19C4×C4⋊C4×C47—21no—
20C4×C4⋊C4×C47C411yescharacteristic
21C47×#376—21no—
22C43×C47C2211yescharacteristic
23C22×C47⋊C8—22no—
24C22×C47⋊C8—22no—
25C4⋊(C47⋊C8)—42no—
26C22×Q8×C47C2×C411yescharacteristic
27C4×Q8×C47—22no—
28C4×Q8×C47—22no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47C2×C411yescharacteristic
33C2×C4⋊C4×C47C2×C411yescharacteristic
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C42×C47—21no—
36C2×C42×C47—21no—
37C2×C42×C47C2×C411yescharacteristic
38C2×C42×C47C2×C411yescharacteristic
39C2×C42×C47D411yescharacteristic
40C2×C42×C47D411yescharacteristic
41C2×C42×C47D411yescharacteristic
42C2×C42×C47D411yescharacteristic
43C2×C42×C47C2311yescharacteristic
44#95×C47—21no—
45#95×C47—21no—
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51C2×Q8×C47—21no—
52C2×Q8×C47—41no—
53C2×Q8×C47—41no—
54C2×Q8×C47M1612yes—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22×C411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C4⋊C4×C47—24no—
67C4⋊C4×C47—21no—
68C4⋊C4×C47—42no—
69C4⋊C4×C47—41no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47—42no—
72C4⋊C4×C47M1612yes—
73C42×C47—24no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—22no—
77C42×C47—41no—
78C42×C47—41no—
79C42×C47—41no—
80C42×C47—41no—
81C42×C47—42no—
82C42×C47SD1612yes—
83C42×C47Q1612yes—
84C2×C47⋊C8—42no—
85C2×C47⋊C8—42no—
86C2×C47⋊C8—42no—
87C2×C47⋊C8—42no—
88C2×C47⋊C8—42no—
89C2×C47⋊C8—42no—
90C23×C47C2×C22⋊C411yescharacteristic
91Q8×C47—42no—
92Q8×C47—42no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
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—21no—
103C2×C4×C47—21no—
104C2×C4×C47—22no—
105C2×C4×C47—22no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
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#10312yes—
122C2×C4×C47#10312yes—
123C2×C4×C47C2×M1611yescharacteristic
124C2×C4×C47C2×M1611yescharacteristic
125C2×C4×C47C2×SD1611yescharacteristic
126C2×C4×C47C2×Q1611yescharacteristic
127C2×C4×C47#13512yes—
128C47⋊C8—82no—
129C47⋊C8—82no—
130#7644—471nomaximal, Sylow
131C22×C47#40711yescharacteristic
132C22×C47#41011yescharacteristic
133C22×C47#41311yescharacteristic
134C22×C47C2×#10311yescharacteristic
135C22×C47#41611yescharacteristic
136C22×C47#42111yescharacteristic
137C22×C47#42111yescharacteristic
138C4×C47—22no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—22no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—22no—
145C4×C47—42no—
146C4×C47—41no—
147C4×C47—42no—
148C4×C47—41no—
149C4×C47—81no—
150C4×C47—81no—
151#2295D4711yescharacteristic
152#1839—471no—
153#1831—471no—
154#1272—472no—
155#1271—472no—
156C2×C47#146411yescharacteristic
157C2×C47#148711yescharacteristic
158C2×C47#148811yescharacteristic
159C2×C47#151811yescharacteristic
160C2×C47#152111yescharacteristic
161C2×C47#153511yescharacteristic
162C2×C47#154211yescharacteristic
163C2×C4×Q8Dic4711yescharacteristic
164C2×C4⋊C8—941no—
165#391Dic4711yescharacteristic
166#391C2×D4711yescharacteristic
167#389Dic4711yescharacteristic
168#389C2×D4711yescharacteristic
169#387—21no—
170#387—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4Dic4711yescharacteristic
173#376—21no—
174C43C2×D4711yescharacteristic
175#336—472no—
176#336—472no—
177#336—941no—
178#336—941no—
179#336—941no—
180C47#764411yescharacteristic, complemented, Sylow
181C22×Q8C2×Dic4711yescharacteristic
182C22×C8—942no—
183C22×C8—942no—
184C4×Q8—22no—
185C4×Q8—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic4711yescharacteristic
190C2×C4⋊C4C2×Dic4711yescharacteristic
191C2×C4⋊C4C2×Dic4711yescharacteristic
192C2×C42—21no—
193C2×C42—21no—
194C2×C42C2×Dic4711yescharacteristic
195C2×C42C2×Dic4711yescharacteristic
196C2×C42C22⋊D4711yescharacteristic
197C2×C42C22⋊D4711yescharacteristic
198C2×C42C22⋊D4711yescharacteristic
199C2×C42C22⋊D4711yescharacteristic
200C2×C42C22×D4711yescharacteristic
201C4⋊C8—1882no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8#1062532912yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊Dic4711yescharacteristic
218C22×C4C22⋊Dic4711yescharacteristic
219C22×C4C22⋊Dic4711yescharacteristic
220C22×C4C22⋊Dic4711yescharacteristic
221C22×C4C22×Dic4711yescharacteristic
222C22×C4C2×C22⋊D4711yescharacteristic
223C22×C4C2×C22⋊D4711yescharacteristic
224C2×C8—1882no—
225C2×C8—1882no—
226C2×C8—1882no—
227C2×C8—1882no—
228C2×C8—1882no—
229C2×C8—1882no—
230C4⋊C4—24no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4#1062532912yes—
237C42—24no—
238C42—21no—
239C42—21no—
240C42—22no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—42no—
246C42#1062533612yes—
247C42#1062533712yes—
248C23C2×C22⋊Dic4711yescharacteristic
249Q8—42no—
250Q8—42no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
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#1309394812yes—
280C2×C4#1309394812yes—
281C2×C4C2×#1062532911yescharacteristic
282C2×C4C2×#1062532911yescharacteristic
283C2×C4C2×#1062533611yescharacteristic
284C2×C4C2×#1062533711yescharacteristic
285C2×C4#1309404412yes—
286C8—3762no—
287C8—3762no—
288C22#1568908711yescharacteristic
289C22#1568909711yescharacteristic
290C22#1568910711yescharacteristic
291C22C2×#1309394811yescharacteristic
292C22#1568911911yescharacteristic
293C22#1568914011yescharacteristic
294C22#1568914011yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—42no—
306C4—81no—
307C4—81no—
308C2#2024172211yescharacteristic
309C2#2024181711yescharacteristic
310C2#2024182211yescharacteristic
311C2#2024195211yescharacteristic
312C2#2024196511yescharacteristic
313C2#2024201911yescharacteristic
314C2#2024204511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2295C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2295D47
hypocenterC47#7644
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
180. C47#7644semidirect

Maximal subgroups

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

subgroupindex
#202435312
#202435052
#202412142
#202412112
C47×#22952
#764447