Finite Group Databasebeta

← C2×#20245285 #26369718

Subgroups — C2×#20245285 #26369718

Order 12032.

710 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
1C2×#15689561C211yesmaximal, characteristic
2C2×#15689244C211yesmaximal, characteristic, complemented
3C2×#15689234C211yesmaximal, characteristic, complemented
4#20245285C218yesmaximal, direct product factor
5C2×#15688935C211yesmaximal, characteristic, complemented
6C2×#15688932C211yesmaximal, characteristic, complemented
7C2×#15688900C211yesmaximal, characteristic, complemented
8C2×C47×#365C211yesmaximal, characteristic, complemented
9C2×#13094046C2211yescharacteristic
10C22×D376C2211yescharacteristic
11C2×#13094032—21no—
12C2×#13093986—21no—
13#15689561C414yescomplemented
14#15689561C2214yes—
15C2×#13093969C412yescomplemented
16C2×D752C412yescomplemented
17C2×#13093964C2211yescharacteristic
18#15689244—22no—
19#15689244C2214yescomplemented
20#15689234—22no—
21#15689234C2214yescomplemented
22C2×#13093950—21no—
23C2×#13093944—21no—
24C2×#13093934C2211yescharacteristic
25#15688935C2214yescomplemented
26#15688932C2214yescomplemented
27#15688900C2214yescomplemented
28C2×M32×C47C2211yescharacteristic
29C2×#108×C47C2211yescharacteristic
30C2×#106×C47C2211yescharacteristic
31C47×#365C2214yescomplemented
32C2×#10625350—21no—
33C22×D188—21no—
34C22×C4×D47—41no—
35#13094046—21no—
36#13094046—21no—
37#13094046C2×C412yescomplemented
38#13094046C2312yes—
39C2×Dic188C2×C411yescharacteristic, complemented
40C2×#10625325—21no—
41C2×D376—21no—
42C2×D376—21no—
43C2×D376—21no—
44C2×D376C2×C412yes—
45C2×D376C2×C412yes—
46C2×D376C2×C411yescharacteristic, complemented
47C2×D376C2312yes—
48#13094032—24no—
49#13094032—42no—
50C2×#10625324—41no—
51C22×C47⋊C8D411yescharacteristic
52C2×C8×D47—41no—
53#13093986—24no—
54#13093986—42no—
55C2×(C2×D47)⋊C4—41no—
56C2×C4×Dic47D411yescharacteristic
57#13093969C2×C418yescomplemented
58D752C2×C418yescomplemented
59#13093964—21no—
60#13093964C2312yes—
61C2×C47⋊C16—21no—
62#13093950—24no—
63#13093944—24no—
64#13093934D412yes—
65#13093934C2312yes—
66C2×M16×C47—21no—
67C22×C8×C47C2311yescharacteristic
68C2×C4⋊C4×C47—21no—
69M32×C47C2×C412yescomplemented
70M32×C47C2312yes—
71C2×C16×C47C2×C412yescomplemented
72#108×C47—21no—
73#108×C47C2312yes—
74#106×C47—21no—
75#106×C47C2312yes—
76C23×D47—41no—
77C22×C4×C47—41no—
78C22×C4×C47C2×D411yescharacteristic
79C2×C22⋊D47—41no—
80C22×Dic47—21no—
81#10625350—22no—
82#10625350—22no—
83#10625350—41no—
84#10625350—41no—
85C2×D188—22no—
86C2×D188—22no—
87C2×D188—21no—
88C2×D188—22no—
89C2×D188—41no—
90C2×D188—41no—
91C2×D188—41no—
92C2×C4×D47—41no—
93C2×C4×D47—44no—
94C2×C4×D47—84no—
95C2×Dic94—21no—
96M16×C47—22no—
97M16×C47—41no—
98C2×C8×C47—41no—
99C2×C8×C47C22×C411yescharacteristic
100C2×C8×C47C22×C411yescharacteristic
101C2×C8×C47C2×D411yescharacteristic
102C2×C8×C47#4111yescharacteristic
103C2×C8×C47#4111yescharacteristic
104C2×C8×C47C2411yescharacteristic
105C4⋊C4×C47—22no—
106C4⋊C4×C47—41no—
107(C2×D47)⋊C4—44no—
108C4×Dic47—21no—
109C4×Dic47C2×D412yes—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8C2×D412yes—
113Dic188—21no—
114Dic188C22×C412yescomplemented
115D376—22no—
116D376—22no—
117D376—21no—
118D376—22no—
119D376C22×C414yes—
120D376C22×C412yescomplemented
121#10625325—22no—
122#10625325—22no—
123#10625324—44no—
124C8×D47—44no—
125C16×C47C22×C414yescomplemented
126C47⋊C16—22no—
127C23×C47AGL(1,ℤ/8)11yescharacteristic
128C22×D47—42no—
129C22×D47—41no—
130C22×D47—42no—
131C22×D47—42no—
132C22×D47—82no—
133C22×D47—82no—
134C2×C4×C47—42no—
135C2×C4×C47—82no—
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C47C22×D411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C2×Dic47—22no—
145C2×Dic47—42no—
146C2×Dic47—41no—
147D188—22no—
148D188—24no—
149D188—42no—
150D188—42no—
151D188—42no—
152D188—41no—
153C4×D47—42no—
154C4×D47—42no—
155C4×D47—88no—
156Dic94—22no—
157Dic94—41no—
158C8×C47—42no—
159C8×C47C4×D411yescharacteristic
160C8×C47C4×D411yescharacteristic
161C8×C47C23×C411yescharacteristic
162C8×C47C2×#4111yescharacteristic
163C47⋊C8—22no—
164C2×AGL(1,ℤ/16)—471nomaximal, Sylow
165C22×C47—22no—
166C22×C47#44211yescharacteristic
167C22×C47#44211yescharacteristic
168C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
169C2×D47—42no—
170C2×D47—44no—
171C2×D47—82no—
172C2×D47—82no—
173C2×D47—84no—
174C2×D47—82no—
175C2×D47—84no—
176C4×C47—82no—
177C4×C47#44211yescharacteristic
178C4×C47#44211yescharacteristic
179C4×C47C2×C4×D411yescharacteristic
180C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
181Dic47—42no—
182Dic47—42no—
183C2×#509—471no—
184C2×#444—471no—
185C2×#442—471no—
186AGL(1,ℤ/16)—478no—
187C2×#365D4711yescharacteristic, complemented
188C2×#361—471no—
189C2×#360—471no—
190C2×#347—471no—
191C2×C47—21no—
192C2×C47—21no—
193C2×C47AGL(1,ℤ/16)12yescomplemented
194C2×C47C2×#44211yescharacteristic
195D47—82no—
196D47—84no—
197C2×#135—471no—
198C22×D8—471no—
199C2×#131—941no—
200C2×C4×D4—941no—
201#509—474no—
202#509—474no—
203C2×SD32—472no—
204C2×D16—472no—
205C2×M32—471no—
206C2×M32C2×D4711yescharacteristic
207#444—474no—
208#444—942no—
209#442—474no—
210#442—942no—
211C2×#108C2×D4711yescharacteristic
212C2×#106C2×D4711yescharacteristic
213C2×#104—941no—
214C2×#102—941no—
215C2×#97—471no—
216#365C2×D4714yescomplemented
217#361—474no—
218#360—474no—
219#347—474no—
220C47C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
221C2×#41—941no—
222C22×D4—941no—
223C23×C4—1881no—
224#135—472no—
225#135—472no—
226#135—941no—
227#135—941no—
228C2×Q16—471no—
229C2×SD16—941no—
230C2×D8—472no—
231C2×D8—472no—
232C2×D8—471no—
233C2×D8—472no—
234C2×D8—941no—
235C2×D8—941no—
236C2×D8—941no—
237#131—944no—
238#131—1882no—
239C2×M16—21no—
240C2×M16—1881no—
241C22×C8—471no—
242C22×C8—1881no—
243C22×C8C22×D4711yescharacteristic
244C4×D4—944no—
245C4×D4—1882no—
246C2×C4⋊C4—21no—
247C2×C22⋊C4—1881no—
248C2×C42—471no—
249SD32—478no—
250D16—478no—
251M32—472no—
252M32—941no—
253M32C4×D4712yescomplemented
254M32C22×D4712yes—
255C2×C16—941no—
256C2×C16C4×D4712yescomplemented
257#108—21no—
258#108C22×D4712yes—
259#106—21no—
260#106C22×D4712yes—
261#104—944no—
262#102—944no—
263#97—472no—
264#97—472no—
265C24—1881no—
266#41—942no—
267#41—942no—
268#41—1881no—
269#41—1881no—
270C2×Q8—941no—
271C2×D4—942no—
272C2×D4—942no—
273C2×D4—941no—
274C2×D4—942no—
275C2×D4—1881no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1881no—
279C22×C4—41no—
280C22×C4—941no—
281C22×C4—3764no—
282C22×C4—1884no—
283C22×C4—1881no—
284C22×C4D4×D4711yescharacteristic
285Q16—472no—
286Q16—941no—
287SD16—942no—
288SD16—942no—
289D8—474no—
290D8—472no—
291D8—942no—
292D8—942no—
293D8—941no—
294D8—942no—
295M16—22no—
296M16—41no—
297M16—1884no—
298C2×C8—41no—
299C2×C8—472no—
300C2×C8—941no—
301C2×C8—941no—
302C2×C8—1884no—
303C2×C8C2×C4×D4711yescharacteristic
304C2×C8C2×C4×D4711yescharacteristic
305C2×C8D4×D4711yescharacteristic
306C2×C8#1062535411yescharacteristic
307C2×C8#1062535411yescharacteristic
308C2×C8C23×D4711yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—41no—
311C22⋊C4—1884no—
312C42—472no—
313C42—941no—
314C16—942no—
315C16C2×C4×D4714yescomplemented
316C23—3762no—
317C23—3762no—
318C23—1882no—
319C23—1881no—
320C23—1882no—
321C23—1882no—
322C23#1309405111yescharacteristic
323Q8—942no—
324Q8—1881no—
325D4—944no—
326D4—942no—
327D4—1882no—
328D4—1882no—
329D4—1882no—
330D4—1882no—
331D4—1881no—
332D4—1882no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—942no—
336C2×C4—3768no—
337C2×C4—1882no—
338C2×C4—1881no—
339C2×C4—1882no—
340C2×C4—1882no—
341C2×C4#1309398611yescharacteristic
342C2×C4#1309398611yescharacteristic
343C2×C4#1309405111yescharacteristic
344C2×C4#1309405111yescharacteristic
345C2×C4#1309405111yescharacteristic
346C2×C4C2×D4×D4711yescharacteristic
347C8—42no—
348C8—942no—
349C8#1309398611yescharacteristic
350C8#1309398611yescharacteristic
351C8C22×C4×D4711yescharacteristic
352C8C2×#1062535411yescharacteristic
353C22—22no—
354C22—3762no—
355C22—3762no—
356C22—3764no—
357C22—3764no—
358C22—3762no—
359C22—1882no—
360C22—1884no—
361C22#1568923411yescharacteristic
362C22#1568923411yescharacteristic
363C22C2×#1309405111yescharacteristic
364C4—82no—
365C4—1882no—
366C4—1882no—
367C4#1568923411yescharacteristic
368C4#1568923411yescharacteristic
369C4C2×#1309398611yescharacteristic
370C4C2×#1309405111yescharacteristic
371C2—21no—
372C2—21no—
373C2—3764no—
374C2—3762no—
375C2#2024528512yesdirect product factor
376C2C2×#1568923411yescharacteristic
subgroupG/H
centerC22#15689234
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#365C2
socleC22×C47#442
prime radicalC2×#15689561C2
cosocleC2×C8×C47C24
hypercenterC2×#365D47
hypocenterC47C2×AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. C2×#15689244C2semidirect
3. C2×#15689234C2semidirect
4. #20245285C2direct (N × H)
5. C2×#15688935C2semidirect
6. C2×#15688932C2semidirect
7. C2×#15688900C2semidirect
8. C2×C47×#365C2semidirect
13. #15689561C4semidirect
15. C2×#13093969C4semidirect
16. C2×D752C4semidirect
19. #15689244C22semidirect
21. #15689234C22semidirect
25. #15688935C22semidirect
26. #15688932C22semidirect
27. #15688900C22semidirect
31. C47×#365C22semidirect
37. #13094046C2×C4semidirect
39. C2×Dic188C2×C4semidirect
46. C2×D376C2×C4semidirect
57. #13093969C2×C4semidirect
58. D752C2×C4semidirect
69. M32×C47C2×C4semidirect
71. C2×C16×C47C2×C4semidirect
114. Dic188C22×C4semidirect
120. D376C22×C4semidirect
125. C16×C47C22×C4semidirect
187. C2×#365D47semidirect
193. C2×C47AGL(1,ℤ/16)semidirect
216. #365C2×D47semidirect
220. C47C2×AGL(1,ℤ/16)semidirect
253. M32C4×D47semidirect
256. C2×C16C4×D47semidirect
315. C16C2×C4×D47semidirect
375. C2#20245285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895612
C2×#156892442
C2×#156892342
#202452852
C2×#156889352
C2×#156889322
C2×#156889002
C2×C47×#3652
C2×AGL(1,ℤ/16)47