Finite Group Databasebeta

← #26369726

Subgroups — #26369726

Order 12032.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256522C211yesmaximal, characteristic
2C2×#15689246C211yesmaximal, characteristic, complemented
3#20245284C214yesmaximal, complemented
4#20245277C214yesmaximal, complemented
5#20245160C211yesmaximal, characteristic, complemented
6#20245137C211yesmaximal, characteristic, complemented
7#20245123C211yesmaximal, characteristic, complemented
8C2×#15688901C211yesmaximal, characteristic, complemented
9C47×#2943C211yesmaximal, characteristic, complemented
10C2×#13094046C2211yescharacteristic
11C2×#13094030—21no—
12#15689564C2212yes—
13#15689563C412yescomplemented
14#15689559C2212yes—
15#15689558C412yescomplemented
16#15689553C414yescomplemented
17C2×#13093964C2211yescharacteristic
18C2×#13093964C2211yescharacteristic
19#15689246—22no—
20#15689246C2214yes—
21C2×#13093960C2211yescharacteristic
22C2×#13093952—21no—
23#15688945C2214yescomplemented
24#15688939C2212yescomplemented
25#15688936C2212yescomplemented
26#15688932C2214yes—
27#15688901C2214yescomplemented
28C2×#135×C47C2211yescharacteristic
29C4×#41×C47—21no—
30C47×#442C2212yescomplemented
31C47×#441C2212yescomplemented
32C47×#440—22no—
33C47×#427C2211yescharacteristic
34C47×#416—21no—
35C2×#97×C47C2211yescharacteristic
36C2×#10625350—21no—
37#13094046—21no—
38#13094046—21no—
39#13094046C2×C412yescomplemented
40#13094046C2312yes—
41C2×Dic188C2×C411yescharacteristic, complemented
42C2×#10625325—21no—
43C2×D376C2×C411yescharacteristic, complemented
44#13094030—24no—
45#13094030—42no—
46C2×#10625329—21no—
47C2×#10625324—41no—
48C2×C8×D47—41no—
49#13093970C2×C414yescomplemented
50#13093968C2×C414yescomplemented
51#13093967C2×C414yescomplemented
52#13093965C2×C414yescomplemented
53#13093964—21no—
54#13093964C2×C412yescomplemented
55#13093964C2312yes—
56#13093964C2312yes—
57C2×C47⋊C16—21no—
58C2×C47⋊C16C2×C412yescomplemented
59#13093960—21no—
60#13093960C2312yes—
61#13093952—24no—
62C2×#41×C47—21no—
63#135×C47—21no—
64#135×C47—21no—
65#135×C47C2×C412yes—
66#135×C47C2×C412yes—
67C2×Q16×C47C2311yescharacteristic
68C2×SD16×C47—21no—
69C2×D8×C47C2311yescharacteristic
70C22×C8×C47D411yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C4×Q8×C47—22no—
73C4×D4×C47—22no—
74C4×D4×C47—42no—
75#117×C47—21no—
76#117×C47—41no—
77C2×C42×C47—41no—
78C2×C42×C47D411yescharacteristic
79#107×C47—21no—
80#106×C47C2312yes—
81#103×C47—22no—
82#102×C47—22no—
83#97×C47D412yes—
84#97×C47C2312yes—
85#41×C47—22no—
86#41×C47—22no—
87#41×C47—41no—
88#41×C47—41no—
89C2×Q8×C47—21no—
90C2×D4×C47—21no—
91C2×D4×C47—41no—
92C22×C4×C47—21no—
93C22×C4×C47—42no—
94C22×C4×C47—41no—
95C22×C4×C47C2×D411yescharacteristic
96C2×C22⋊D47—41no—
97#10625350—22no—
98#10625350—22no—
99#10625350—41no—
100#10625350—41no—
101C2×D188—21no—
102C2×C4×D47—41no—
103C2×Dic94—21no—
104Q16×C47—21no—
105Q16×C47C22×C412yes—
106SD16×C47—22no—
107SD16×C47—22no—
108D8×C47—21no—
109D8×C47C22×C412yes—
110C2×C8×C47—21no—
111C2×C8×C47—21no—
112C2×C8×C47C22×C411yescharacteristic
113C2×C8×C47C22×C411yescharacteristic
114C2×C8×C47C2×D412yes—
115C2×C8×C47C2×D411yescharacteristic
116C2×C8×C47#4111yescharacteristic
117C2×C8×C47#4111yescharacteristic
118C2×C8×C47C2411yescharacteristic
119C4⋊C4×C47—22no—
120C4⋊C4×C47—42no—
121C22⋊C4×C47—42no—
122C22⋊C4×C47—41no—
123C42×C47—21no—
124C42×C47—42no—
125C42×C47—41no—
126C42×C47C2×D412yes—
127#10625329—22no—
128#10625329—41no—
129C2×C47⋊C8—41no—
130Dic188—21no—
131Dic188C22×C412yes—
132D376—21no—
133D376C22×C412yes—
134#10625325—22no—
135#10625325—22no—
136#10625324—44no—
137C8×D47—44no—
138C47⋊C16—22no—
139C47⋊C16C22×C414yes—
140C23×C47—41no—
141C23×C47AGL(1,ℤ/8)11yescharacteristic
142C22×D47—41no—
143Q8×C47—22no—
144Q8×C47—41no—
145D4×C47—22no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47—41no—
149C2×C4×C47—22no—
150C2×C4×C47—41no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—81no—
155C2×C4×C47—84no—
156C2×C4×C47C4×D411yescharacteristic
157C2×C4×C47C4×D411yescharacteristic
158C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C47C22×D411yescharacteristic
162C22⋊D47—42no—
163C22⋊D47—42no—
164C2×Dic47—41no—
165D188—22no—
166D188—41no—
167C4×D47—42no—
168C4×D47—42no—
169Dic94—22no—
170Dic94—41no—
171C8×C47—22no—
172C8×C47C4×D411yescharacteristic
173C8×C47C4×D411yescharacteristic
174C8×C47C23×C411yescharacteristic
175C8×C47C2×#4111yescharacteristic
176C47⋊C8—42no—
177#33468—471nomaximal, Sylow
178C22×C47—41no—
179C22×C47—42no—
180C22×C47—82no—
181C22×C47#44211yescharacteristic
182C22×C47#44211yescharacteristic
183C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
184C2×D47—42no—
185C2×D47—82no—
186C4×C47—42no—
187C4×C47—42no—
188C4×C47—82no—
189C4×C47#44211yescharacteristic
190C4×C47#44211yescharacteristic
191C4×C47C2×C4×D411yescharacteristic
192C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
193Dic47—42no—
194#3414—471no—
195C2×#444—471no—
196#2943D4711yescharacteristic, complemented
197AGL(1,ℤ/16)—474no—
198#2180—474no—
199#2155—471no—
200#2148—471no—
201#2145—471no—
202C2×#347—471no—
203C2×C47—21no—
204C2×C47—21no—
205C2×C47—21no—
206C2×C47—82no—
207C2×C47C2×#44211yescharacteristic
208D47—82no—
209C2×#135—471no—
210C2×#135C2×D4711yescharacteristic
211C2×#131—941no—
212C4×#41—21no—
213#510—472no—
214#510—472no—
215#509—472no—
216#509—472no—
217#508—474no—
218C2×M32—471no—
219C2×M32—471no—
220#444—474no—
221#444—942no—
222#442C2×D4712yescomplemented
223#441C2×D4712yescomplemented
224#440—22no—
225C2×#108—471no—
226#427C2×D4711yescharacteristic
227C2×#104—941no—
228#416—21no—
229C2×#97C2×D4711yescharacteristic
230#365—474no—
231#362—472no—
232#361—472no—
233#360—474no—
234#347—474no—
235C47#3346811yescharacteristic, complemented, Sylow
236C2×#41—21no—
237C2×#41—941no—
238#135—21no—
239#135—21no—
240#135—472no—
241#135—472no—
242#135—941no—
243#135—941no—
244#135C4×D4712yes—
245#135C4×D4712yes—
246C2×Q16—471no—
247C2×Q16C22×D4711yescharacteristic
248C2×SD16—21no—
249C2×SD16—941no—
250C2×D8—471no—
251C2×D8C22×D4711yescharacteristic
252#131—944no—
253#131—1882no—
254C2×M16—941no—
255C2×M16—1881no—
256C22×C8—1881no—
257C22×C8C22⋊D4711yescharacteristic
258C22×C8C22×D4711yescharacteristic
259C4×Q8—22no—
260C4×D4—22no—
261C4×D4—42no—
262#117—21no—
263#117—41no—
264C2×C42—41no—
265C2×C42C22⋊D4711yescharacteristic
266Q32—474no—
267SD32—474no—
268SD32—474no—
269D16—474no—
270M32—472no—
271M32—472no—
272M32—472no—
273M32—941no—
274C2×C16—472no—
275C2×C16—941no—
276#108—472no—
277#108—941no—
278#107—21no—
279#106C22×D4712yes—
280#104—944no—
281#103—22no—
282#102—22no—
283#97C22⋊D4712yes—
284#97C22×D4712yes—
285#41—22no—
286#41—22no—
287#41—41no—
288#41—41no—
289#41—942no—
290#41—942no—
291#41—1881no—
292#41—1881no—
293C2×Q8—21no—
294C2×Q8—941no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—941no—
298C2×D4—1881no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—1881no—
303C22×C4C2×C22⋊D4711yescharacteristic
304Q16—21no—
305Q16—472no—
306Q16—941no—
307Q16C2×C4×D4712yes—
308SD16—22no—
309SD16—22no—
310SD16—942no—
311SD16—942no—
312D8—21no—
313D8—472no—
314D8—941no—
315D8C2×C4×D4712yes—
316M16—942no—
317M16—1884no—
318M16—1881no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—1884no—
322C2×C8—1881no—
323C2×C8C2×C4×D4711yescharacteristic
324C2×C8C2×C4×D4711yescharacteristic
325C2×C8#1062535011yescharacteristic
326C2×C8#1062535011yescharacteristic
327C2×C8C2×C22⋊D4712yes—
328C2×C8C2×C22⋊D4711yescharacteristic
329C2×C8C23×D4711yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C42—21no—
335C42—42no—
336C42—41no—
337C42C2×C22⋊D4712yes—
338C16—474no—
339C16—942no—
340C23—41no—
341C23—1881no—
342C23#1309405011yescharacteristic
343Q8—22no—
344Q8—41no—
345Q8—942no—
346Q8—1881no—
347D4—22no—
348D4—42no—
349D4—42no—
350D4—41no—
351D4—942no—
352D4—1882no—
353D4—1882no—
354D4—1881no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—84no—
362C2×C4—1881no—
363C2×C4—1882no—
364C2×C4—1882no—
365C2×C4C4×C22⋊D4711yescharacteristic
366C2×C4C4×C22⋊D4711yescharacteristic
367C2×C4#1309404911yescharacteristic
368C2×C4#1309404911yescharacteristic
369C2×C4#1309405011yescharacteristic
370C2×C4C22×C22⋊D4711yescharacteristic
371C8—22no—
372C8—1882no—
373C8C4×C22⋊D4711yescharacteristic
374C8C4×C22⋊D4711yescharacteristic
375C8C22×C4×D4711yescharacteristic
376C8C2×#1062535011yescharacteristic
377C22—41no—
378C22—42no—
379C22—82no—
380C22—3762no—
381C22—1882no—
382C22#1568923311yescharacteristic
383C22#1568923311yescharacteristic
384C22C2×#1309405011yescharacteristic
385C4—42no—
386C4—42no—
387C4—82no—
388C4—1882no—
389C4#1568923311yescharacteristic
390C4#1568923311yescharacteristic
391C4C2×C4×C22⋊D4711yescharacteristic
392C4C2×#1309404911yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—3762no—
398C2C2×#1568923311yescharacteristic
subgroupG/H
centerC4#15689233
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2943C2
socleC2×C47C2×#442
prime radical#20256522C2
cosocleC2×C8×C47C24
hypercenter#2943D47
hypocenterC47#33468
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C2×#15689246C2semidirect
3. #20245284C2semidirect
4. #20245277C2semidirect
5. #20245160C2semidirect
6. #20245137C2semidirect
7. #20245123C2semidirect
8. C2×#15688901C2semidirect
9. C47×#2943C2semidirect
13. #15689563C4semidirect
15. #15689558C4semidirect
16. #15689553C4semidirect
23. #15688945C22semidirect
24. #15688939C22semidirect
25. #15688936C22semidirect
27. #15688901C22semidirect
30. C47×#442C22semidirect
31. C47×#441C22semidirect
39. #13094046C2×C4semidirect
41. C2×Dic188C2×C4semidirect
43. C2×D376C2×C4semidirect
49. #13093970C2×C4semidirect
50. #13093968C2×C4semidirect
51. #13093967C2×C4semidirect
52. #13093965C2×C4semidirect
54. #13093964C2×C4semidirect
58. C2×C47⋊C16C2×C4semidirect
196. #2943D47semidirect
222. #442C2×D47semidirect
223. #441C2×D47semidirect
235. C47#33468semidirect

Maximal subgroups

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

subgroupindex
#202565222
C2×#156892462
#202452842
#202452772
#202451602
#202451372
#202451232
C2×#156889012
C47×#29432
#3346847