Finite Group Databasebeta

← #26111506

Subgroups — #26111506

Order 12032.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253948C211yesmaximal, characteristic
2#20244307C211yesmaximal, characteristic
3#20241887C211yesmaximal, characteristic, complemented
4#20241786C211yesmaximal, characteristic
5#20241227C211yesmaximal, characteristic, complemented
6#20241226C211yesmaximal, characteristic, complemented
7C47×#2962C211yesmaximal, characteristic, complemented
8#15689673C2211yescharacteristic
9#15689519C411yescharacteristic, complemented
10#15689497C411yescharacteristic, complemented
11#15689473C411yescharacteristic, complemented
12#15689471C411yescharacteristic, complemented
13#15689354—22no—
14C4×#10625336—22no—
15#15689176C2211yescharacteristic
16C2×#13093950—21no—
17C2×#13093950—21no—
18C2×C4×C47⋊C8C2211yescharacteristic
19C4×C4⋊Dic47C2211yescharacteristic
20#15688860—22no—
21#15688850—21no—
22#15688850—21no—
23C47×#533C2211yescharacteristic
24C47×#446—22no—
25C47×#446—21no—
26C8×Q8×C47—21no—
27C47×#424—21no—
28C2×C4⋊C8×C47C2211yescharacteristic
29C47×#405—21no—
30C4×M16×C47C2211yescharacteristic
31C2×#10625350—21no—
32C2×#10625336—22no—
33C22×C47⋊C8—21no—
34#13094024C2×C411yescharacteristic
35#13094021C2×C411yescharacteristic
36#13094012—21no—
37#13093998—21no—
38#13093998—21no—
39C4×D188—21no—
40C4×D188—21no—
41C2×C4⋊Dic47—21no—
42C2×C4×Dic47—21no—
43#13093955—22no—
44C4⋊(C47⋊C8)—21no—
45#13093950—42no—
46#13093950—42no—
47#13093948—22no—
48#13093944—22no—
49C22⋊(C47⋊C8)—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C4×C47⋊C8C2×C411yescharacteristic
53C4×C47⋊C8C2×C411yescharacteristic
54C47⋊#95—21no—
55C2×M16×C47D411yescharacteristic
56C2×M16×C47D411yescharacteristic
57C22×C8×C47—21no—
58C4⋊Q8×C47C2×C411yescharacteristic
59C4⋊Q8×C47C2×C411yescharacteristic
60#125×C47—21no—
61C22⋊Q8×C47—21no—
62C22⋊Q8×C47D412yes—
63C4×Q8×C47—21no—
64C4×Q8×C47D412yes—
65#117×C47—21no—
66C2×C42×C47C2311yescharacteristic
67C4⋊C8×C47—22no—
68C4⋊C8×C47—22no—
69C4⋊C8×C47—21no—
70C4⋊C8×C47D411yescharacteristic
71C4⋊C8×C47D411yescharacteristic
72#97×C47—22no—
73#97×C47—21no—
74C4×C8×C47—22no—
75C4×C8×C47—21no—
76C2×Q8×C47—21no—
77C2×Q8×C47C22⋊C412yes—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C2×C22⋊D47—41no—
82C22×Dic47—41no—
83#10625350—41no—
84#10625350—41no—
85#10625350—41no—
86#10625350—41no—
87C2×D188—21no—
88C2×D188—21no—
89C2×D188—21no—
90C2×C4×D47—41no—
91C2×Dic94—21no—
92M16×C47—21no—
93M16×C47—21no—
94M16×C47—21no—
95M16×C47SD1612yescomplemented
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—22no—
106C4⋊C4×C47—22no—
107C4⋊C4×C47C22⋊C412yes—
108C22⋊C4×C47—22no—
109C42×C47—22no—
110C42×C47C22×C411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47C2×D411yescharacteristic
113C42×C47#4111yescharacteristic
114#10625336—44no—
115(C2×D47)⋊C4—41no—
116(C2×D47)⋊C4—41no—
117C4⋊Dic47—22no—
118C4⋊Dic47—21no—
119C4⋊Dic47—21no—
120C4⋊Dic47—41no—
121C4×Dic47—41no—
122C4×Dic47—41no—
123C2×C47⋊C8—21no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—42no—
126C2×C47⋊C8—41no—
127C23×C47#12111yescharacteristic
128C22×D47—41no—
129Q8×C47—42no—
130Q8×C47—41no—
131Q8×C47—41no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—22no—
135C2×C4×C47—22no—
136C2×C4×C47—41no—
137C2×C4×C47C2×C22⋊C411yescharacteristic
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47C4×D411yescharacteristic
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12111yescharacteristic
142C2×C4×C47#12311yescharacteristic
143C2×C4×C47C2×SD1611yescharacteristic
144C2×C4×C47#13511yescharacteristic
145C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C47#13711yescharacteristic
147C22⋊D47—81no—
148C22⋊D47—81no—
149C2×Dic47—42no—
150C2×Dic47—41no—
151C2×Dic47—81no—
152C2×Dic47—81no—
153D188—42no—
154D188—41no—
155D188—41no—
156D188—41no—
157D188—41no—
158C4×D47—81no—
159C4×D47—81no—
160Dic94—41no—
161Dic94—41no—
162C8×C47—22no—
163C8×C47—41no—
164C8×C47—41no—
165C8×C47—41no—
166C47⋊C8—22no—
167C47⋊C8—41no—
168C47⋊C8—81no—
169#9054—471nomaximal, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47#38611yescharacteristic
173C22×C47#46011yescharacteristic
174C22×C47#46411yescharacteristic
175C2×D47—81no—
176C2×D47—81no—
177C2×D47—81no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—42no—
183C4×C47C4×SD1611yescharacteristic
184C4×C47#44011yescharacteristic
185C4×C47#44311yescharacteristic
186C4×C47#44411yescharacteristic
187C4×C47#44811yescharacteristic
188C4×C47#44911yescharacteristic
189Dic47—82no—
190Dic47—81no—
191#3167—471no—
192#2962D4711yescharacteristic, complemented
193#1980—471no—
194#1503—471no—
195#1480—471no—
196#1279—471no—
197#1278—471no—
198C2×C47—21no—
199C2×C47—21no—
200C2×C47#187611yescharacteristic
201C2×C47#188011yescharacteristic
202C2×C47#188411yescharacteristic
203D47—161no—
204#533C2×D4711yescharacteristic
205#532—471no—
206#498—471no—
207#492—471no—
208#487—471no—
209#486—471no—
210#465—942no—
211#446—22no—
212#446—21no—
213C8×Q8—21no—
214C4×SD16—942no—
215#431—471no—
216#424—21no—
217C2×C4⋊C8C2×D4711yescharacteristic
218C2×#104—941no—
219C2×#104—941no—
220#405—21no—
221C4×M16C2×D4711yescharacteristic
222C2×C4×C8—471no—
223C4×C4⋊C4—471no—
224#328—942no—
225D4⋊C8—941no—
226D4⋊C8—941no—
227C47#905411yescharacteristic, complemented, Sylow
228C2×#41—941no—
229C2×SD16—942no—
230C2×M16C22⋊D4711yescharacteristic
231C2×M16C22⋊D4711yescharacteristic
232C22×C8—21no—
233C22×C8—941no—
234C4⋊Q8—471no—
235C4⋊Q8C4×D4711yescharacteristic
236C4⋊Q8C4×D4711yescharacteristic
237#127—471no—
238#125—21no—
239#124—941no—
240C22⋊Q8—21no—
241C22⋊Q8D18812yes—
242#121—941no—
243#121—941no—
244C4×Q8—21no—
245C4×Q8C22⋊D4712yes—
246C4×D4—941no—
247C4×D4—941no—
248#117—21no—
249C2×C4⋊C4—941no—
250C2×C42—941no—
251C2×C42C22×D4711yescharacteristic
252#106—942no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—941no—
257C4⋊C8C22⋊D4711yescharacteristic
258C4⋊C8C22⋊D4711yescharacteristic
259#104—1882no—
260#104—1882no—
261#103—942no—
262#102—942no—
263C22⋊C8—941no—
264#97—22no—
265#97—21no—
266C4×C8—22no—
267C4×C8—21no—
268C4×C8—471no—
269C4×C8—471no—
270C4×C8—941no—
271C4×C8—941no—
272#95—941no—
273#41—1881no—
274#41—1881no—
275#41—1881no—
276#41—1881no—
277C2×Q8—21no—
278C2×Q8—941no—
279C2×Q8(C2×D47)⋊C412yes—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—1881no—
284C22×C4—1881no—
285C22×C4—1881no—
286C22×C4C2×D18811yescharacteristic
287C22×C4#1062535011yescharacteristic
288C22×C4C2×C22⋊D4711yescharacteristic
289SD16—1884no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#1062533612yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—941no—
301C2×C8—941no—
302C2×C8—1882no—
303C2×C8—1881no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—942no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4—1881no—
313C4⋊C4(C2×D47)⋊C412yes—
314C22⋊C4—22no—
315C22⋊C4—1881no—
316C22⋊C4—1881no—
317C42—22no—
318C42—1881no—
319C42—1881no—
320C42C2×C4×D4711yescharacteristic
321C42#1062535011yescharacteristic
322C42C2×C22⋊D4711yescharacteristic
323C42C2×C22⋊D4711yescharacteristic
324C23—1881no—
325C23#1309399811yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—1881no—
330Q8—1881no—
331D4—3761no—
332D4—3761no—
333D4—1882no—
334D4—1881no—
335D4—1881no—
336D4—1881no—
337D4—1881no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—3761no—
344C2×C4—3761no—
345C2×C4—3761no—
346C2×C4—3761no—
347C2×C4—1882no—
348C2×C4—1881no—
349C2×C4C2×(C2×D47)⋊C411yescharacteristic
350C2×C4C4×C22⋊D4711yescharacteristic
351C2×C4C4×C22⋊D4711yescharacteristic
352C2×C4#1309399311yescharacteristic
353C2×C4#1309399811yescharacteristic
354C2×C4#1309400711yescharacteristic
355C2×C4C2×#1062533611yescharacteristic
356C2×C4#1309404411yescharacteristic
357C2×C4#1309404911yescharacteristic
358C2×C4#1309405511yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—942no—
364C8—3761no—
365C8—1881no—
366C22—21no—
367C22—21no—
368C22—3761no—
369C22—3761no—
370C22—3761no—
371C22#1568900211yescharacteristic
372C22#1568932311yescharacteristic
373C22#1568934511yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—3762no—
380C4—3761no—
381C4C4×#1062533611yescharacteristic
382C4#1568922111yescharacteristic
383C4#1568923811yescharacteristic
384C4#1568924311yescharacteristic
385C4#1568926211yescharacteristic
386C4#1568926811yescharacteristic
387C2—21no—
388C2—21no—
389C2—7521no—
390C2#2024371511yescharacteristic
391C2#2024374311yescharacteristic
392C2#2024377111yescharacteristic
subgroupG/H
centerC2×C4#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2962C2
socleC22×C47#386
prime radical#15689673C22
cosocleC2×C42×C47C23
hypercenter#2962D47
hypocenterC47#9054
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #20241887C2semidirect
5. #20241227C2semidirect
6. #20241226C2semidirect
7. C47×#2962C2semidirect
9. #15689519C4semidirect
10. #15689497C4semidirect
11. #15689473C4semidirect
12. #15689471C4semidirect
95. M16×C47SD16semidirect
192. #2962D47semidirect
227. C47#9054semidirect
293. M16#10625336semidirect

Maximal subgroups

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

subgroupindex
#202539482
#202443072
#202418872
#202417862
#202412272
#202412262
C47×#29622
#905447