Finite Group Databasebeta

← #26107338

Subgroups — #26107338

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#20252363C211yesmaximal, characteristic
2#20241974C211yesmaximal, characteristic
3#20241872C211yesmaximal, characteristic
4C8×#10625329C211yesmaximal, characteristic, complemented
5#20241287C211yesmaximal, characteristic, complemented
6#20241281C211yesmaximal, characteristic, complemented
7C47×#1746C211yesmaximal, characteristic, complemented
8#15689657C2211yescharacteristic
9#15689253C411yescharacteristic, complemented
10C8×Dic94C411yescharacteristic, complemented
11#15689202C411yescharacteristic, complemented
12#15689194—21no—
13C8×D188C411yescharacteristic, complemented
14C8×C22⋊D47—21no—
15#15689182—21no—
16#15689180C2211yescharacteristic
17#15689176C2211yescharacteristic
18#15689077—21no—
19C4×#10625329C2211yescharacteristic
20#15688864C412yescomplemented
21#15688862C412yescomplemented
22#15688859C412yes—
23#15688856C412yes—
24#15688845—21no—
25C8×C47⋊C8—21no—
26C2×#97×C47C2211yescharacteristic
27C2×C4×C8×C47C2211yescharacteristic
28C47×#376C2211yescharacteristic
29C47×#336—21no—
30C47×#336—21no—
31C2×#10625329—21no—
32C2×#10625324—21no—
33C2×C8×D47—21no—
34#13094018—21no—
35#13094016C2×C411yescharacteristic
36#13094012C2×C411yescharacteristic
37#13094007—21no—
38#13094003C2×C411yescharacteristic
39#13093998C2×C411yescharacteristic
40C4×Dic94C2×C411yescharacteristic
41C4×D188C2×C411yescharacteristic
42C4×C22⋊D47—21no—
43#13093981—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)C2×C411yescharacteristic
46C4⋊(C47⋊C8)C2×C411yescharacteristic
47Dic47⋊C8—21no—
48Dic47⋊C8—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)C2×C412yes—
51(C2×D47)⋊C8—21no—
52(C2×D47)⋊C8—21no—
53#13093935—21no—
54#13093935C2×C412yes—
55#13093934—21no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8—21no—
58C8×Dic47—21no—
59C22×C8×C47—21no—
60C22×C8×C47D411yescharacteristic
61C22×C8×C47D411yescharacteristic
62C2×C42×C47—21no—
63C2×C42×C47C2311yescharacteristic
64#97×C47—21no—
65#97×C47C2×C412yes—
66C4×C8×C47C2×C411yescharacteristic
67C4×C8×C47C2×C411yescharacteristic
68C4×C8×C47D411yescharacteristic
69C4×C8×C47D411yescharacteristic
70#95×C47—21no—
71#95×C47C2×C412yes—
72C22×C4×C47—22no—
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47#4111yescharacteristic
76C2×C22⋊D47—21no—
77C2×D188C4211yescharacteristic
78C2×C4×D47—21no—
79C2×Dic94C4211yescharacteristic
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C22⋊C411yescharacteristic
86C2×C8×C47C22⋊C411yescharacteristic
87C2×C8×C47C22⋊C411yescharacteristic
88C2×C8×C47C22⋊C411yescharacteristic
89C42×C47—41no—
90C42×C47—41no—
91C42×C47C22×C411yescharacteristic
92C42×C47C22×C411yescharacteristic
93C42×C47C2×D411yescharacteristic
94C42×C47#4111yescharacteristic
95C22⋊Dic47—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47C4211yescharacteristic
101C4⋊Dic47C4211yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107#10625329—24no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—22no—
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×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47C2×C4211yescharacteristic
124C2×C4×C47C2×C22⋊C411yescharacteristic
125C2×C4×C47#11711yescharacteristic
126C2×C4×C47C4×D411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47C4×D411yescharacteristic
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133D188—41no—
134C4×D47—41no—
135C4×D47—41no—
136Dic94—41no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47—21no—
141C8×C47—42no—
142C47⋊C8—24no—
143C47⋊C8—42no—
144C47⋊C8—41no—
145C47⋊C8—41no—
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—82no—
160C4×C47#42111yescharacteristic
161C4×C47#42111yescharacteristic
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165#2966—471no—
166#1746D4711yescharacteristic, complemented
167#1524—471no—
168#1500—471no—
169C8×M16—471no—
170#1302—471no—
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#432—471no—
186#431—471no—
187#405—941no—
188C4×M16—471no—
189C2×#97C2×D4711yescharacteristic
190C2×C4×C8C2×D4711yescharacteristic
191#376C2×D4711yescharacteristic
192#336—21no—
193#336—21no—
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—941no—
205C22×C8C22⋊D4711yescharacteristic
206C22×C8C22⋊D4711yescharacteristic
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—21no—
218C2×C42C22×D4711yescharacteristic
219C4⋊C8—471no—
220C4⋊C8—471no—
221C4⋊C8—941no—
222C4⋊C8—941no—
223C4⋊C8—941no—
224C22⋊C8—472no—
225C22⋊C8—941no—
226C22⋊C8—941no—
227C22⋊C8—941no—
228#97—21no—
229#97—472no—
230#97—941no—
231#97—941no—
232#97C4×D4712yes—
233C4×C8—941no—
234C4×C8—941no—
235C4×C8—941no—
236C4×C8C4×D4711yescharacteristic
237C4×C8C4×D4711yescharacteristic
238C4×C8D18811yescharacteristic
239C4×C8D18811yescharacteristic
240#95—21no—
241#95C4×D4712yes—
242C2×Q8—471no—
243C2×D4—471no—
244C2×D4—941no—
245C22×C4—22no—
246C22×C4—941no—
247C22×C4C2×C4×D4711yescharacteristic
248C22×C4#1062535011yescharacteristic
249C22×C4C2×C22⋊D4711yescharacteristic
250M16—944no—
251M16—1882no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—942no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—942no—
261C2×C8—1882no—
262C2×C8(C2×D47)⋊C411yescharacteristic
263C2×C8(C2×D47)⋊C411yescharacteristic
264C2×C8(C2×D47)⋊C411yescharacteristic
265C2×C8(C2×D47)⋊C411yescharacteristic
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—41no—
278C42—41no—
279C42—941no—
280C42C2×C4×D4711yescharacteristic
281C42C2×C4×D4711yescharacteristic
282C42C2×D18811yescharacteristic
283C42#1062535011yescharacteristic
284C23—941no—
285C23C4×C22⋊D4711yescharacteristic
286Q8—1881no—
287D4—1881no—
288D4—1882no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4C42×D4711yescharacteristic
302C2×C4C2×(C2×D47)⋊C411yescharacteristic
303C2×C4#1309398111yescharacteristic
304C2×C4C4×C22⋊D4711yescharacteristic
305C2×C4C4×D18811yescharacteristic
306C2×C4C4×D18811yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C8—42no—
312C8—944no—
313C8—1882no—
314C8—1881no—
315C8—1881no—
316C22—21no—
317C22—21no—
318C22—1881no—
319C22—1881no—
320C22—1881no—
321C22C4×(C2×D47)⋊C411yescharacteristic
322C22#1568923812yes—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—1881no—
330C4—1881no—
331C4—1881no—
332C4#1568914111yescharacteristic
333C4#1568914111yescharacteristic
334C2—22no—
335C2—3761no—
336C2#2024318911yescharacteristic
337C2#2024319911yescharacteristic
338C2#2024322711yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1746C2
socleC22×C47C4×C22⋊C4
prime radical#13093998C2×C4
cosocleC2×C42×C47C23
hypercenter#1746D47
hypocenterC47#8250
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1746

Complements

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

NH ≅ G/Ntype
4. C8×#10625329C2semidirect
5. #20241287C2semidirect
6. #20241281C2semidirect
7. C47×#1746C2semidirect
9. #15689253C4semidirect
10. C8×Dic94C4semidirect
11. #15689202C4semidirect
13. C8×D188C4semidirect
20. #15688864C4semidirect
21. #15688862C4semidirect
166. #1746D47semidirect
200. C47#8250semidirect

Maximal subgroups

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

subgroupindex
#202523632
#202419742
#202418722
C8×#106253292
#202412872
#202412812
C47×#17462
#825047