Finite Group Databasebeta

← #26104517

Subgroups — #26104517

Order 12032.

434 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243241C211yesmaximal, characteristic
2#20243137C211yesmaximal, characteristic
3#20241214C212yesmaximal
4#20241211C212yesmaximal
5C47×#2295C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7C2×#13093935—21no—
8C2×#13093935—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)—24no—
26#13093935—24no—
27#13093935—42no—
28C22×Q8×C47C2×C411yescharacteristic
29C4×Q8×C47—22no—
30C4×Q8×C47—22no—
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—21no—
34C2×C4⋊C4×C47C2×C411yescharacteristic
35C2×C4⋊C4×C47C2×C411yescharacteristic
36C2×C4⋊C4×C47C2×C411yescharacteristic
37C2×C42×C47—21no—
38C2×C42×C47—21no—
39C2×C42×C47C2×C411yescharacteristic
40C2×C42×C47C2×C411yescharacteristic
41C2×C42×C47D411yescharacteristic
42C2×C42×C47D411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C2×C42×C47C2311yescharacteristic
46#95×C47—21no—
47#95×C47—21no—
48#95×C47—21no—
49#95×C47—21no—
50#95×C47—21no—
51#95×C47—21no—
52#95×C47—21no—
53C2×Q8×C47—21no—
54C2×Q8×C47—41no—
55C2×Q8×C47—41no—
56C2×Q8×C47M1612yes—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C22⋊C411yescharacteristic
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22×C411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C4⋊C4×C47—24no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—41no—
71C4⋊C4×C47—41no—
72C4⋊C4×C47—42no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47M1612yes—
76C42×C47—24no—
77C42×C47—22no—
78C42×C47—22no—
79C42×C47—21no—
80C42×C47—21no—
81C42×C47—21no—
82C42×C47—22no—
83C42×C47—21no—
84C42×C47—41no—
85C42×C47—41no—
86C42×C47—42no—
87C2×C47⋊C8—24no—
88C2×C47⋊C8—24no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C23×C47C2×C22⋊C411yescharacteristic
94Q8×C47—42no—
95Q8×C47—42no—
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—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—22no—
108C2×C4×C47—22no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
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#10412yes—
125C2×C4×C47#10412yes—
126C2×C4×C47C2×M1611yescharacteristic
127C2×C4×C47C2×M1611yescharacteristic
128C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C47#13711yescharacteristic
130C2×C4×C47#13712yes—
131C47⋊C8—44no—
132C47⋊C8—44no—
133#7630—471nomaximal, Sylow
134C22×C47#40711yescharacteristic
135C22×C47#41011yescharacteristic
136C22×C47#41311yescharacteristic
137C22×C47#41711yescharacteristic
138C22×C47#41911yescharacteristic
139C22×C47C2×#10411yescharacteristic
140C22×C47C2×#10411yescharacteristic
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—22no—
144C4×C47—22no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—22no—
148C4×C47—41no—
149C4×C47—42no—
150C4×C47—41no—
151C4×C47—42no—
152C4×C47—81no—
153C4×C47—81no—
154#2295D4711yescharacteristic
155#1767—471no—
156#1745—471no—
157#1272—472no—
158#1271—472no—
159C2×C47#146411yescharacteristic
160C2×C47#148911yescharacteristic
161C2×C47#149111yescharacteristic
162C2×C47#150611yescharacteristic
163C2×C47#150911yescharacteristic
164C2×C47#152411yescharacteristic
165C2×C47#155911yescharacteristic
166C2×C4×Q8Dic4711yescharacteristic
167C2×C4⋊C8—941no—
168C2×#97—941no—
169C2×#97—941no—
170#391Dic4711yescharacteristic
171#391C2×D4711yescharacteristic
172#389Dic4711yescharacteristic
173#389C2×D4711yescharacteristic
174#387—21no—
175#387—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4Dic4711yescharacteristic
178#376—21no—
179C43C2×D4711yescharacteristic
180#336—472no—
181#336—472no—
182#336—941no—
183C47#763011yescharacteristic, complemented, Sylow
184C22×Q8C2×Dic4711yescharacteristic
185C22×C8—942no—
186C22×C8—942no—
187C4×Q8—22no—
188C4×Q8—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×Dic4711yescharacteristic
193C2×C4⋊C4C2×Dic4711yescharacteristic
194C2×C4⋊C4C2×Dic4711yescharacteristic
195C2×C42—21no—
196C2×C42—21no—
197C2×C42C2×Dic4711yescharacteristic
198C2×C42C2×Dic4711yescharacteristic
199C2×C42C22⋊D4711yescharacteristic
200C2×C42C22⋊D4711yescharacteristic
201C2×C42C22⋊D4711yescharacteristic
202C2×C42C22⋊D4711yescharacteristic
203C2×C42C22×D4711yescharacteristic
204C4⋊C8—944no—
205#97—944no—
206#97—1882no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C2×Q8—21no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8#1062532912yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic4711yescharacteristic
223C22×C4C22⋊Dic4711yescharacteristic
224C22×C4C22⋊Dic4711yescharacteristic
225C22×C4C22⋊Dic4711yescharacteristic
226C22×C4C22×Dic4711yescharacteristic
227C22×C4C2×C22⋊D4711yescharacteristic
228C22×C4C2×C22⋊D4711yescharacteristic
229C2×C8—944no—
230C2×C8—944no—
231C2×C8—1882no—
232C2×C8—1882no—
233C2×C8—1882no—
234C2×C8—1882no—
235C4⋊C4—24no—
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4#1062532912yes—
243C42—24no—
244C42—22no—
245C42—22no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—22no—
251C42—41no—
252C42—41no—
253C42—42no—
254C23C2×C22⋊Dic4711yescharacteristic
255Q8—42no—
256Q8—42no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
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—41no—
284C2×C4—41no—
285C2×C4#1309395112yes—
286C2×C4#1309395112yes—
287C2×C4C2×#1062532911yescharacteristic
288C2×C4C2×#1062532911yescharacteristic
289C2×C4#1309404911yescharacteristic
290C2×C4#1309405411yescharacteristic
291C2×C4#1309405512yes—
292C8—1884no—
293C8—1884no—
294C22#1568908711yescharacteristic
295C22#1568909711yescharacteristic
296C22#1568910711yescharacteristic
297C22#1568912411yescharacteristic
298C22#1568913211yescharacteristic
299C22C2×#1309395111yescharacteristic
300C22C2×#1309395111yescharacteristic
301C4—22no—
302C4—21no—
303C4—21no—
304C4—22no—
305C4—22no—
306C4—21no—
307C4—21no—
308C4—42no—
309C4—41no—
310C4—42no—
311C4—41no—
312C4—81no—
313C4—81no—
314C2#2024172211yescharacteristic
315C2#2024182711yescharacteristic
316C2#2024183511yescharacteristic
317C2#2024190011yescharacteristic
318C2#2024191311yescharacteristic
319C2#2024197611yescharacteristic
320C2#2024211811yescharacteristic
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#7630
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
183. C47#7630semidirect

Maximal subgroups

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

subgroupindex
#202432412
#202431372
#202412142
#202412112
C47×#22952
#763047