Finite Group Databasebeta

← C2×#20245606 #26371167

Subgroups — C2×#20245606 #26371167

Order 12032.

552 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689378C211yesmaximal, characteristic
2C2×#15689170C211yesmaximal, characteristic
3#20245606C218yesmaximal, direct product factor
4C2×#15688947C211yesmaximal, characteristic, complemented
5C2×#15688946C211yesmaximal, characteristic, complemented
6C2×#15688939C211yesmaximal, characteristic, complemented
7C2×#15688904C211yesmaximal, characteristic
8C2×C47×#362C211yesmaximal, characteristic, complemented
9C22×#10625324C2211yescharacteristic
10C2×M16×D47—21no—
11C2×#13094000—21no—
12C2×#13093964C2211yescharacteristic
13#15689378—22no—
14#15689378C2214yes—
15#15689170—22no—
16#15689170C2214yes—
17C2×#13093960C2211yescharacteristic
18C2×#13093959—21no—
19C2×#13093956C2211yescharacteristic
20C2×#13093948—21no—
21#15688947C2214yescomplemented
22#15688946C2214yescomplemented
23#15688939C2214yescomplemented
24#15688904C2214yes—
25C22×Q16×C47C2211yescharacteristic
26C2×M32×C47C2211yescharacteristic
27C2×#108×C47C2211yescharacteristic
28C47×#362C2214yescomplemented
29C22×C4×D47D411yescharacteristic
30C2×#10625329—21no—
31C2×#10625324—21no—
32C2×#10625324—21no—
33C2×#10625324—21no—
34C2×#10625324—21no—
35C2×#10625324—41no—
36C2×#10625324D412yes—
37C2×#10625324C2312yes—
38M16×D47—24no—
39M16×D47—42no—
40C22×C47⋊C8D411yescharacteristic
41C2×C8×D47—41no—
42#13094000—24no—
43#13094000—42no—
44C2×C4⋊Dic47—21no—
45C2×Dic47⋊C4—41no—
46C2×(C2×D47)⋊C4—41no—
47#13093964—21no—
48#13093964C2312yes—
49C2×C47⋊C16—21no—
50#13093960—21no—
51#13093960C2312yes—
52#13093959—24no—
53#13093956—21no—
54#13093956C2312yes—
55#13093948—24no—
56C22×Q8×C47—21no—
57C2×Q16×C47—21no—
58C2×Q16×C47—21no—
59C2×Q16×C47—21no—
60C2×Q16×C47—21no—
61C2×Q16×C47—21no—
62C2×Q16×C47C2312yes—
63C2×M16×C47—21no—
64C22×C8×C47C2311yescharacteristic
65M32×C47—21no—
66M32×C47C2312yes—
67C2×C16×C47—21no—
68#108×C47—21no—
69#108×C47C2312yes—
70C23×D47SD1611yescharacteristic
71C2×Q8×C47—22no—
72C2×Q8×C47—41no—
73C2×Q8×C47—41no—
74C2×Q8×C47—41no—
75C2×Q8×C47—41no—
76C2×Q8×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47C2×D411yescharacteristic
79C22×Dic47—41no—
80C22×Dic47SD1611yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47SD1612yes—
86C2×C4×D47C2×D412yes—
87Q16×C47—22no—
88Q16×C47—22no—
89Q16×C47—41no—
90Q16×C47—41no—
91M16×C47—22no—
92M16×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C2×C8×C47C2411yescharacteristic
100(C2×D47)⋊C4—44no—
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103Dic47⋊C4—44no—
104#10625329—22no—
105#10625329—41no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—41no—
109C2×C47⋊C8C2×D412yes—
110#10625324—22no—
111#10625324—22no—
112#10625324—22no—
113#10625324—22no—
114#10625324—44no—
115C8×D47—44no—
116C16×C47—22no—
117C47⋊C16—22no—
118C23×C47C2×SD1611yescharacteristic
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—42no—
122C22×D47C2×SD1612yes—
123Q8×C47—42no—
124Q8×C47—42no—
125Q8×C47—81no—
126Q8×C47—81no—
127C2×C4×C47—42no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47#12311yescharacteristic
131C2×C4×C47#12311yescharacteristic
132C2×C4×C47C2×SD1611yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47C22×D411yescharacteristic
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—82no—
140C2×Dic47C2×SD1612yes—
141C4×D47—22no—
142C4×D47—22no—
143C4×D47—22no—
144C4×D47—22no—
145C8×C47—42no—
146C8×C47#12311yescharacteristic
147C8×C47#12311yescharacteristic
148C8×C47C2×#4111yescharacteristic
149C8×C47C2×#4111yescharacteristic
150C47⋊C8—22no—
151C47⋊C8—42no—
152C2×#2239—471nomaximal, Sylow
153C22×C47—22no—
154C22×C47#48111yescharacteristic
155C22×C47#48111yescharacteristic
156C22×C47C22×SD1611yescharacteristic
157C2×D47—22no—
158C2×D47—42no—
159C2×D47—42no—
160C2×D47—81no—
161C4×C47—82no—
162C4×C47#48111yescharacteristic
163C4×C47#48111yescharacteristic
164C4×C47C2×#12311yescharacteristic
165C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
166Dic47—22no—
167Dic47—82no—
168C2×#470—471no—
169C2×#430—471no—
170#2239—478no—
171C2×#365—471no—
172C2×#365—471no—
173C2×#362—471no—
174C2×#362D4711yescharacteristic, complemented
175C2×#349—471no—
176C2×C47—21no—
177C2×C47—21no—
178C2×C47#223912yescomplemented
179C2×C47C2×#48111yescharacteristic
180D47—42no—
181C22×Q16C2×D4711yescharacteristic
182C22×M16—471no—
183C22×M16—941no—
184C2×C22⋊Q8—941no—
185C2×M32—471no—
186C2×M32C2×D4711yescharacteristic
187#470—474no—
188#470—942no—
189#430—474no—
190#430—942no—
191C2×#108—471no—
192C2×#108—941no—
193C2×#108C2×D4711yescharacteristic
194C2×#106—471no—
195C2×#103—941no—
196#365—474no—
197#365—474no—
198#362—474no—
199#362C2×D4714yescomplemented
200#349—474no—
201C47C2×#223911yescharacteristic, complemented, Sylow
202C22×Q8—21no—
203C23×C4—471no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16C22×D4712yes—
210C2×M16—21no—
211C2×M16—472no—
212C2×M16—472no—
213C2×M16—941no—
214C2×M16—941no—
215C2×M16—941no—
216C2×M16—941no—
217C2×M16—944no—
218C2×M16—941no—
219C2×M16—1881no—
220C2×M16—1882no—
221C22×C8—471no—
222C22×C8—1881no—
223C22×C8C22×D4711yescharacteristic
224C22⋊Q8—944no—
225C22⋊Q8—1882no—
226C2×C4⋊C4—941no—
227C2×C4⋊C4—1881no—
228C2×C22⋊C4—1881no—
229M32—21no—
230M32—472no—
231M32—941no—
232M32C22×D4712yes—
233C2×C16—21no—
234C2×C16—941no—
235#108—21no—
236#108—472no—
237#108—944no—
238#108—941no—
239#108C22×D4712yes—
240#106—472no—
241#106—941no—
242#103—944no—
243C24—471no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C22×C4—41no—
251C22×C4—471no—
252C22×C4—472no—
253C22×C4—472no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—1881no—
259C22×C4D4×D4711yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264M16—22no—
265M16—41no—
266M16—942no—
267M16—942no—
268M16—942no—
269M16—942no—
270M16—942no—
271M16—1884no—
272M16—1881no—
273C2×C8—41no—
274C2×C8—472no—
275C2×C8—941no—
276C2×C8—941no—
277C2×C8—1884no—
278C2×C8—1881no—
279C2×C8#1062535011yescharacteristic
280C2×C8#1062535011yescharacteristic
281C2×C8D4×D4711yescharacteristic
282C2×C8#1062535211yescharacteristic
283C2×C8#1062535211yescharacteristic
284C2×C8C23×D4711yescharacteristic
285C4⋊C4—942no—
286C4⋊C4—1884no—
287C4⋊C4—1881no—
288C22⋊C4—1884no—
289C16—22no—
290C16—942no—
291C23—472no—
292C23—941no—
293C23—941no—
294C23—1882no—
295C23SD16×D4711yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—472no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—942no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—3762no—
311C2×C4—1882no—
312C2×C4#1309400611yescharacteristic
313C2×C4#1309400611yescharacteristic
314C2×C4SD16×D4711yescharacteristic
315C2×C4#1309404811yescharacteristic
316C2×C4#1309404811yescharacteristic
317C2×C4C2×D4×D4711yescharacteristic
318C8—42no—
319C8—942no—
320C8—1882no—
321C8#1309400611yescharacteristic
322C8#1309400611yescharacteristic
323C8C2×#1062535211yescharacteristic
324C8C2×#1062535011yescharacteristic
325C22—22no—
326C22—942no—
327C22—3761no—
328C22—1882no—
329C22—1882no—
330C22#1568944011yescharacteristic
331C22#1568944011yescharacteristic
332C22C2×SD16×D4711yescharacteristic
333C4—82no—
334C4—942no—
335C4—3762no—
336C4#1568944011yescharacteristic
337C4#1568944011yescharacteristic
338C4C2×#1309400611yescharacteristic
339C4C2×#1309404811yescharacteristic
340C2—21no—
341C2—21no—
342C2—1882no—
343C2#2024560612yesdirect product factor
344C2C2×#1568944011yescharacteristic
subgroupG/H
centerC22#15689440
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#362C2
socleC22×C47#481
prime radicalC23×D47SD16
hypercenterC2×#362D47
hypocenterC47C2×#2239
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #20245606C2direct (N × H)
4. C2×#15688947C2semidirect
5. C2×#15688946C2semidirect
6. C2×#15688939C2semidirect
8. C2×C47×#362C2semidirect
21. #15688947C22semidirect
22. #15688946C22semidirect
23. #15688939C22semidirect
28. C47×#362C22semidirect
174. C2×#362D47semidirect
178. C2×C47#2239semidirect
199. #362C2×D47semidirect
201. C47C2×#2239semidirect
343. C2#20245606direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893782
C2×#156891702
#202456062
C2×#156889472
C2×#156889462
C2×#156889392
C2×#156889042
C2×C47×#3622
C2×#223947