Finite Group Databasebeta

← #26107337

Subgroups — #26107337

Order 12032.

400 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252357C211yesmaximal, characteristic
2#20243141C211yesmaximal, characteristic, complemented
3#20241974C211yesmaximal, characteristic
4#20241875C211yesmaximal, characteristic
5#20241669C211yesmaximal, characteristic, complemented
6#20241280C211yesmaximal, characteristic, complemented
7C47×#1302C211yesmaximal, characteristic, complemented
8#15689657C2211yescharacteristic
9#15689250C411yescharacteristic, complemented
10#15689247C411yescharacteristic, complemented
11#15689200C411yescharacteristic, complemented
12#15689191—21no—
13#15689188C411yescharacteristic, complemented
14(C22⋊D47)⋊C8—21no—
15#15689185—21no—
16#15689080—21no—
17C4×#10625329C2211yescharacteristic
18C2×C4×C47⋊C8C2211yescharacteristic
19#15688969C2211yescharacteristic
20#15688877—21no—
21#15688877—21no—
22#15688864C412yescomplemented
23#15688862C412yescomplemented
24#15688861C412yes—
25#15688858C412yes—
26#15688845—21no—
27C8×C47⋊C8—21no—
28C47×#432C2211yescharacteristic
29C47×#431C2211yescharacteristic
30C2×#97×C47C2211yescharacteristic
31C2×#10625329—21no—
32C2×#10625324—21no—
33C22×C47⋊C8D411yescharacteristic
34C22×C47⋊C8D411yescharacteristic
35C2×C8×D47—21no—
36#13094018—21no—
37#13094016C2×C411yescharacteristic
38#13094012C2×C411yescharacteristic
39#13094007—21no—
40#13094003C2×C411yescharacteristic
41#13093998C2×C411yescharacteristic
42C4×Dic94C2×C411yescharacteristic
43C4×D188C2×C411yescharacteristic
44C4×C22⋊D47—21no—
45#13093981—21no—
46C2×C4×Dic47—21no—
47Dic47⋊C8—21no—
48Dic47⋊C8—21no—
49(C2×D47)⋊C8—21no—
50(C2×D47)⋊C8—21no—
51#13093935C2×C412yes—
52#13093934—21no—
53C4×C47⋊C8—21no—
54C4×C47⋊C8C2×C411yescharacteristic
55C4×C47⋊C8C2×C411yescharacteristic
56C4×C47⋊C8D411yescharacteristic
57C4×C47⋊C8D411yescharacteristic
58C8×Dic47—21no—
59C47⋊#95—21no—
60C47⋊#95C2×C412yes—
61C22×C8×C47—21no—
62C2×C42×C47C2311yescharacteristic
63C4⋊C8×C47—21no—
64C4⋊C8×C47C2×C411yescharacteristic
65C4⋊C8×C47C2×C411yescharacteristic
66C22⋊C8×C47—21no—
67C22⋊C8×C47C2×C412yes—
68#97×C47—21no—
69#97×C47—21no—
70#97×C47C2×C412yes—
71C4×C8×C47—21no—
72C22×C4×C47C22×C411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47#4111yescharacteristic
75C2×C22⋊D47—21no—
76C22×Dic47—22no—
77C2×D188C4211yescharacteristic
78C2×C4×D47—21no—
79C2×Dic94C4211yescharacteristic
80C2×C8×C47—21no—
81C2×C8×C47—21no—
82C2×C8×C47—22no—
83C2×C8×C47—22no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C42×C47C22×C411yescharacteristic
87C42×C47C22×C411yescharacteristic
88C42×C47C2×D411yescharacteristic
89C42×C47#4111yescharacteristic
90C22⋊Dic47—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47C4211yescharacteristic
96C4⋊Dic47C4211yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—41no—
103C4×Dic47—41no—
104#10625329—24no—
105C2×C47⋊C8—22no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8C22⋊C411yescharacteristic
109C2×C47⋊C8C22⋊C411yescharacteristic
110C2×C47⋊C8C22⋊C411yescharacteristic
111C2×C47⋊C8C22⋊C411yescharacteristic
112#10625324—42no—
113C8×D47—42no—
114C23×C47C4×D411yescharacteristic
115C22×D47—21no—
116C2×C4×C47—22no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—41no—
120C2×C4×C47C2×C4211yescharacteristic
121C2×C4×C47C2×C22⋊C411yescharacteristic
122C2×C4×C47#11711yescharacteristic
123C2×C4×C47C4×D411yescharacteristic
124C2×C4×C47C4×D411yescharacteristic
125C2×C4×C47C4×D411yescharacteristic
126C22⋊D47—42no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133D188—41no—
134C4×D47—41no—
135C4×D47—41no—
136Dic94—41no—
137C8×C47—42no—
138C8×C47—42no—
139C8×C47—41no—
140C8×C47—41no—
141C47⋊C8—24no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146#8250—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47C4×C22⋊C411yescharacteristic
150C22×C47#44312yes—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47#42111yescharacteristic
160C4×C47#42111yescharacteristic
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47—82no—
165#2966—471no—
166#1746—471no—
167#1524—471no—
168#1500—471no—
169C8×M16—471no—
170#1302D4711yescharacteristic, complemented
171#1300—471no—
172C2×C47—22no—
173C2×C47#175711yescharacteristic
174C2×C47#175911yescharacteristic
175C2×C47#176411yescharacteristic
176D47—81no—
177#529—471no—
178#446—471no—
179C8×Q8—471no—
180#436—471no—
181#435—941no—
182C8×D4—471no—
183C8×D4—941no—
184#433—941no—
185#432C2×D4711yescharacteristic
186#431C2×D4711yescharacteristic
187#405—941no—
188C4×M16—471no—
189C2×#97C2×D4711yescharacteristic
190C2×C4×C8—471no—
191#376—471no—
192#336—941no—
193#336—941no—
194#330—472no—
195#329—472no—
196#328—472no—
197#327—472no—
198#322—941no—
199C82—941no—
200C47#825011yescharacteristic, complemented, Sylow
201C2×M16—941no—
202C2×M16—941no—
203C22×C8—21no—
204C22×C8—471no—
205C22×C8—471no—
206C22×C8—941no—
207#126—941no—
208#125—471no—
209#124—471no—
210#123—941no—
211C22⋊Q8—471no—
212#121—471no—
213C4×Q8—471no—
214C4×D4—471no—
215C4×D4—941no—
216#117—941no—
217C2×C42—941no—
218C2×C42C22×D4711yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8C4×D4711yescharacteristic
223C4⋊C8C4×D4711yescharacteristic
224C22⋊C8—21no—
225C22⋊C8—941no—
226C22⋊C8—941no—
227C22⋊C8C4×D4712yes—
228#97—21no—
229#97—21no—
230#97—472no—
231#97—941no—
232#97C4×D4712yes—
233C4×C8—21no—
234C4×C8—471no—
235C4×C8—471no—
236C4×C8—471no—
237C4×C8—471no—
238C4×C8—941no—
239C4×C8—941no—
240#95—472no—
241#95—941no—
242C2×Q8—471no—
243C2×D4—471no—
244C2×D4—941no—
245C22×C4—941no—
246C22×C4—942no—
247C22×C4C2×C4×D4711yescharacteristic
248C22×C4D4×D4711yescharacteristic
249C22×C4#1062535411yescharacteristic
250M16—944no—
251M16—1882no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—471no—
262C2×C8—942no—
263C2×C8—1882no—
264C2×C8—1881no—
265C2×C8—1881no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—941no—
278C42—1881no—
279C42—1881no—
280C42C2×C4×D4711yescharacteristic
281C42C2×C4×D4711yescharacteristic
282C42D4×D4711yescharacteristic
283C42#1062535211yescharacteristic
284C23—941no—
285C23#1309398611yescharacteristic
286Q8—1881no—
287D4—1881no—
288D4—1882no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—1882no—
297C2×C4—1882no—
298C2×C4—1882no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4C42×D4711yescharacteristic
302C2×C4C22⋊C4×D4711yescharacteristic
303C2×C4#1309398211yescharacteristic
304C2×C4(C22⋊D47)⋊C411yescharacteristic
305C2×C4(C22⋊D47)⋊C411yescharacteristic
306C2×C4#1309398611yescharacteristic
307C8—42no—
308C8—42no—
309C8—41no—
310C8—41no—
311C8—944no—
312C8—941no—
313C8—941no—
314C8—941no—
315C8—941no—
316C22—21no—
317C22—21no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22#1568897011yescharacteristic
322C22#1568923912yes—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—3762no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4#1568913811yescharacteristic
333C4#1568913811yescharacteristic
334C2—22no—
335C2—3761no—
336C2#2024318711yescharacteristic
337C2#2024319711yescharacteristic
338C2#2024322411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1302C2
socleC22×C47C4×C22⋊C4
prime radical#13093998C2×C4
cosocleC2×C42×C47C23
hypercenter#1302D47
hypocenterC47#8250
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
2. #20243141C2semidirect
5. #20241669C2semidirect
6. #20241280C2semidirect
7. C47×#1302C2semidirect
9. #15689250C4semidirect
10. #15689247C4semidirect
11. #15689200C4semidirect
13. #15689188C4semidirect
22. #15688864C4semidirect
23. #15688862C4semidirect
170. #1302D47semidirect
200. C47#8250semidirect

Maximal subgroups

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

subgroupindex
#202523572
#202431412
#202419742
#202418752
#202416692
#202412802
C47×#13022
#825047