Finite Group Databasebeta

← #26115626

Subgroups — #26115626

Order 12032.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253713C211yesmaximal, characteristic
2C4⋊C4×C47⋊C8C211yesmaximal, characteristic, complemented
3#20242134C211yesmaximal, characteristic, complemented
4#20241882C211yesmaximal, characteristic
5#20241791C211yesmaximal, characteristic, complemented
6#20241788C211yesmaximal, characteristic
7C47×#1503C211yesmaximal, characteristic, complemented
8#15689673C2211yescharacteristic
9#15689480—21no—
10#15689480—21no—
11#15689475C411yescharacteristic, complemented
12#15689475C411yescharacteristic, complemented
13#15689471C411yescharacteristic, complemented
14#15689471C411yescharacteristic, complemented
15#15689176C2211yescharacteristic
16C2×C4⋊(C47⋊C8)C2211yescharacteristic
17#15689117—21no—
18#15689117—21no—
19C2×C4×C47⋊C8—21no—
20C2×C4×C47⋊C8C2211yescharacteristic
21#15688878—21no—
22#15688875—21no—
23#15688873—21no—
24#15688856—22no—
25Q8⋊(C47⋊C8)—22no—
26#15688852—22no—
27C47×#533C2211yescharacteristic
28C47×#431C2211yescharacteristic
29C4×C4⋊C4×C47C2211yescharacteristic
30C47×#328—22no—
31C2×#10625350—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8D411yescharacteristic
34C22×C47⋊C8D411yescharacteristic
35#13094024C2×C411yescharacteristic
36#13094021C2×C411yescharacteristic
37#13094012—21no—
38#13093998—21no—
39#13093998—21no—
40C4×D188—21no—
41C4×D188—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)D412yes—
45#13093947—21no—
46#13093947—21no—
47#13093947—21no—
48#13093947—21no—
49#13093944—21no—
50#13093944—21no—
51#13093944—21no—
52#13093944—21no—
53C22⋊(C47⋊C8)—21no—
54C4×C47⋊C8—21no—
55C4×C47⋊C8—42no—
56C4×C47⋊C8C2×C411yescharacteristic
57C4×C47⋊C8C2×C411yescharacteristic
58C4×C47⋊C8D411yescharacteristic
59C4×C47⋊C8D411yescharacteristic
60C4⋊Q8×C47C2×C411yescharacteristic
61C4⋊Q8×C47C2×C411yescharacteristic
62#125×C47—21no—
63C22⋊Q8×C47—21no—
64C22⋊Q8×C47—21no—
65C4×Q8×C47—21no—
66C4×Q8×C47—21no—
67#117×C47—21no—
68C2×C4⋊C4×C47—21no—
69C2×C42×C47—21no—
70C2×C42×C47C2311yescharacteristic
71C4⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C4×C8×C47—21no—
74#95×C47D412yes—
75C2×Q8×C47—21no—
76C2×Q8×C47—21no—
77C22×C4×C47—22no—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C2×C22⋊D47—41no—
82#10625350—41no—
83#10625350—41no—
84#10625350—41no—
85#10625350—41no—
86C2×D188—21no—
87C2×D188—21no—
88C2×D188—21no—
89C2×C4×D47—41no—
90C2×Dic94—21no—
91C2×C8×C47—41no—
92C4⋊C4×C47—24no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C42×C47—41no—
101C42×C47—41no—
102C42×C47—41no—
103C42×C47C22×C411yescharacteristic
104C42×C47C2×D411yescharacteristic
105C42×C47C2×D411yescharacteristic
106C42×C47#4111yescharacteristic
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109C4⋊Dic47—21no—
110C4⋊Dic47—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—21no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8C22⋊C411yescharacteristic
120C2×C47⋊C8C22⋊C411yescharacteristic
121C2×C47⋊C8C22⋊C411yescharacteristic
122C2×C47⋊C8C22⋊C411yescharacteristic
123C23×C47#12111yescharacteristic
124C22×D47—41no—
125Q8×C47—42no—
126Q8×C47—81no—
127C2×C4×C47—22no—
128C2×C4×C47—24no—
129C2×C4×C47—41no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47C2×C22⋊C411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12411yescharacteristic
139C2×C4×C47#12711yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47#13711yescharacteristic
144C22⋊D47—81no—
145C22⋊D47—81no—
146C2×Dic47—41no—
147D188—41no—
148D188—41no—
149D188—42no—
150D188—81no—
151C4×D47—81no—
152C4×D47—81no—
153Dic94—41no—
154Dic94—41no—
155C8×C47—81no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—42no—
161C47⋊C8—81no—
162#9751—471nomaximal, Sylow
163C22×C47—21no—
164C22×C47—21no—
165C22×C47#39011yescharacteristic
166C22×C47#46311yescharacteristic
167C22×C47#46411yescharacteristic
168C2×D47—81no—
169C2×D47—81no—
170C2×D47—81no—
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—44no—
175C4×C47—81no—
176C4×C47—81no—
177C4×C47#41611yescharacteristic
178C4×C47#41711yescharacteristic
179C4×C47#44312yes—
180C4×C47#46311yescharacteristic
181C4×C47#46411yescharacteristic
182Dic47—81no—
183#3131—471no—
184C8×C4⋊C4—471no—
185#1564—471no—
186#1503D4711yescharacteristic, complemented
187#1502—471no—
188#1481—471no—
189#1480—471no—
190C2×C47—21no—
191C2×C47—21no—
192C2×C47#197411yescharacteristic
193C2×C47#197611yescharacteristic
194C2×C47#198311yescharacteristic
195D47—161no—
196#533C2×D4711yescharacteristic
197#532—471no—
198#488—941no—
199#488—941no—
200#487—471no—
201#487—471no—
202#486—471no—
203#486—471no—
204#431—471no—
205#431C2×D4711yescharacteristic
206C2×C4⋊C8—471no—
207#416—941no—
208#416—941no—
209C2×C4×C8—471no—
210C2×C4×C8—941no—
211C4×C4⋊C4C2×D4711yescharacteristic
212#336—941no—
213#335—941no—
214#334—941no—
215#328—22no—
216#327—942no—
217Q8⋊C8—942no—
218D4⋊C8—942no—
219C47#975111yescharacteristic, complemented, Sylow
220C2×#41—941no—
221C22×C8—471no—
222C22×C8—471no—
223C22×C8—941no—
224C4⋊Q8—471no—
225C4⋊Q8C4×D4711yescharacteristic
226C4⋊Q8C4×D4711yescharacteristic
227#127—471no—
228#125—21no—
229#124—941no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—941no—
233#121—941no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—941no—
237C4×D4—941no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D4711yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—472no—
244C4⋊C8—941no—
245C4⋊C8—941no—
246#103—941no—
247#103—941no—
248#103—941no—
249#103—941no—
250#102—941no—
251#102—941no—
252#102—941no—
253#102—941no—
254C22⋊C8—21no—
255C22⋊C8—941no—
256C4×C8—21no—
257C4×C8—471no—
258C4×C8—471no—
259C4×C8—471no—
260C4×C8—471no—
261C4×C8—941no—
262C4×C8—1882no—
263#95C22⋊D4712yes—
264#41—1881no—
265#41—1881no—
266#41—1881no—
267#41—1881no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—1881no—
275C22×C4—22no—
276C22×C4—1881no—
277C22×C4D4×D4711yescharacteristic
278C22×C4#1062535211yescharacteristic
279C22×C4C2×C22⋊D4711yescharacteristic
280C2×C8—41no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—941no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8—941no—
289C2×C8—942no—
290C2×C8—1881no—
291C2×C8—1881no—
292C2×C8—1881no—
293C4⋊C4—24no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C22⋊C4—41no—
303C22⋊C4—1881no—
304C22⋊C4—1881no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×C4×D4711yescharacteristic
309C42#1062535011yescharacteristic
310C42D4×D4711yescharacteristic
311C42D4×D4711yescharacteristic
312C23—1881no—
313C23#1309399611yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—1881no—
317Q8—1881no—
318D4—3761no—
319D4—3761no—
320D4—3761no—
321D4—1882no—
322D4—1881no—
323D4—1881no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—3761no—
332C2×C4—3761no—
333C2×C4—1881no—
334C2×C4C22⋊C4×D4711yescharacteristic
335C2×C4(C22⋊D47)⋊C411yescharacteristic
336C2×C4C4×C22⋊D4711yescharacteristic
337C2×C4#1309399711yescharacteristic
338C2×C4#1309401011yescharacteristic
339C2×C4#1309402011yescharacteristic
340C2×C4#1309404511yescharacteristic
341C2×C4#1309404711yescharacteristic
342C2×C4#1309405111yescharacteristic
343C2×C4#1309405611yescharacteristic
344C8—81no—
345C8—941no—
346C8—941no—
347C8—941no—
348C8—941no—
349C8—3761no—
350C8—1882no—
351C22—21no—
352C22—21no—
353C22—3761no—
354C22—3761no—
355C22—3761no—
356C22#1568902311yescharacteristic
357C22#1568934011yescharacteristic
358C22#1568934711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—81no—
364C4—81no—
365C4—3761no—
366C4#1568911811yescharacteristic
367C4#1568912311yescharacteristic
368C4#1568923712yes—
369C4#1568934111yescharacteristic
370C4#1568934811yescharacteristic
371C2—21no—
372C2—21no—
373C2—7521no—
374C2#2024427311yescharacteristic
375C2#2024428311yescharacteristic
376C2#2024431711yescharacteristic
subgroupG/H
centerC2×C4#13093997
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1503C2
socleC22×C47#390
prime radical#15689673C22
cosocleC2×C42×C47C23
hypercenter#1503D47
hypocenterC47#9751
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C47⋊C8C2semidirect
3. #20242134C2semidirect
5. #20241791C2semidirect
7. C47×#1503C2semidirect
11. #15689475C4semidirect
12. #15689475C4semidirect
13. #15689471C4semidirect
14. #15689471C4semidirect
186. #1503D47semidirect
219. C47#9751semidirect

Maximal subgroups

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

subgroupindex
#202537132
C4⋊C4×C47⋊C82
#202421342
#202418822
#202417912
#202417882
C47×#15032
#975147