Finite Group Databasebeta

← C2×#20245277 #26369709

Subgroups — C2×#20245277 #26369709

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689564C211yesmaximal, characteristic
2C2×#15689246C211yesmaximal, characteristic
3#20245277C218yesmaximal, direct product factor
4C2×#15688945C211yesmaximal, characteristic, complemented
5C2×#15688939C211yesmaximal, characteristic, complemented
6C2×#15688932C211yesmaximal, characteristic
7C2×#15688901C211yesmaximal, characteristic, complemented
8C2×C47×#441C211yesmaximal, characteristic, complemented
9C2×#13094046C2211yescharacteristic
10C2×#13094030—21no—
11#15689564C414yescomplemented
12#15689564C2214yes—
13C2×#13093970C412yescomplemented
14C2×#13093967C412yescomplemented
15C2×#13093964C2211yescharacteristic
16C2×#13093964C2211yescharacteristic
17#15689246—22no—
18#15689246C2214yes—
19C2×#13093960C2211yescharacteristic
20C2×#13093952—21no—
21#15688945C2214yescomplemented
22#15688939C2214yescomplemented
23#15688932C2214yes—
24#15688901C2214yescomplemented
25C22×Q16×C47C2211yescharacteristic
26C2×C4×Q8×C47—21no—
27C47×#441—22no—
28C47×#441C2214yescomplemented
29C2×#106×C47C2211yescharacteristic
30C2×#103×C47—21no—
31C2×#97×C47C2211yescharacteristic
32C2×#10625350—21no—
33#13094046—21no—
34#13094046—21no—
35#13094046C2×C412yes—
36#13094046C2312yes—
37C2×Dic188C2×C411yescharacteristic
38C2×#10625325—21no—
39C2×D376C2×C411yescharacteristic
40#13094030—24no—
41#13094030—42no—
42C2×#10625329—21no—
43C2×#10625324—41no—
44C2×C8×D47—41no—
45#13093970C2×C418yescomplemented
46#13093967C2×C418yescomplemented
47#13093964—21no—
48#13093964C2×C412yes—
49#13093964C2312yes—
50#13093964C2312yes—
51C2×C47⋊C16—21no—
52C2×C47⋊C16C2×C412yes—
53#13093960—21no—
54#13093960C2312yes—
55#13093952—24no—
56C22×Q8×C47—21no—
57C2×Q16×C47—21no—
58C2×Q16×C47—21no—
59C2×Q16×C47—21no—
60C2×Q16×C47C2×C412yes—
61C2×Q16×C47C2×C412yes—
62C2×Q16×C47C2312yes—
63C22×C8×C47D411yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C4×Q8×C47—24no—
66C4×Q8×C47—42no—
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47—41no—
69C2×C42×C47—41no—
70C2×C42×C47D411yescharacteristic
71#106×C47—21no—
72#106×C47C2312yes—
73#103×C47—24no—
74#97×C47D412yes—
75#97×C47C2312yes—
76C2×Q8×C47—22no—
77C2×Q8×C47—22no—
78C2×Q8×C47—22no—
79C2×Q8×C47—41no—
80C2×Q8×C47—41no—
81C2×Q8×C47—41no—
82C22×C4×C47—21no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47C2×D411yescharacteristic
86C2×C22⋊D47—41no—
87#10625350—22no—
88#10625350—22no—
89#10625350—41no—
90#10625350—41no—
91C2×D188—21no—
92C2×C4×D47—41no—
93C2×Dic94—21no—
94Q16×C47—22no—
95Q16×C47—22no—
96Q16×C47—22no—
97Q16×C47C22×C414yes—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47C22×C411yescharacteristic
101C2×C8×C47C22×C411yescharacteristic
102C2×C8×C47C2×D412yes—
103C2×C8×C47C2×D411yescharacteristic
104C2×C8×C47#4111yescharacteristic
105C2×C8×C47#4111yescharacteristic
106C2×C8×C47C2411yescharacteristic
107C4⋊C4×C47—22no—
108C4⋊C4×C47—44no—
109C4⋊C4×C47—41no—
110C42×C47—21no—
111C42×C47—44no—
112C42×C47C2×D412yes—
113#10625329—22no—
114#10625329—41no—
115C2×C47⋊C8—41no—
116Dic188—21no—
117Dic188C22×C412yes—
118D376—21no—
119D376C22×C412yes—
120#10625325—22no—
121#10625325—22no—
122#10625324—44no—
123C8×D47—44no—
124C47⋊C16—22no—
125C47⋊C16C22×C414yes—
126C23×C47AGL(1,ℤ/8)11yescharacteristic
127C22×D47—41no—
128Q8×C47—24no—
129Q8×C47—42no—
130Q8×C47—42no—
131Q8×C47—42no—
132C2×C4×C47—22no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—82no—
139C2×C4×C47C4×D411yescharacteristic
140C2×C4×C47C4×D411yescharacteristic
141C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C47C22×D411yescharacteristic
145C22⋊D47—42no—
146C22⋊D47—42no—
147C2×Dic47—41no—
148D188—22no—
149D188—41no—
150C4×D47—42no—
151C4×D47—42no—
152Dic94—22no—
153Dic94—41no—
154C8×C47—22no—
155C8×C47C4×D411yescharacteristic
156C8×C47C4×D411yescharacteristic
157C8×C47C23×C411yescharacteristic
158C8×C47C2×#4111yescharacteristic
159C47⋊C8—42no—
160C2×#2180—471nomaximal, Sylow
161C22×C47—22no—
162C22×C47#44211yescharacteristic
163C22×C47#44211yescharacteristic
164C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
165C2×D47—42no—
166C2×D47—82no—
167C4×C47—42no—
168C4×C47—44no—
169C4×C47—82no—
170C4×C47#44211yescharacteristic
171C4×C47#44211yescharacteristic
172C4×C47C2×C4×D411yescharacteristic
173C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
174Dic47—42no—
175C2×#510—471no—
176C2×#444—471no—
177C2×#441D4711yescharacteristic, complemented
178#2180—478no—
179C2×#365—471no—
180C2×#362—471no—
181C2×#360—471no—
182C2×#347—471no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47#218012yescomplemented
186C2×C47C2×#44211yescharacteristic
187D47—82no—
188C2×#135—471no—
189C22×Q16C2×D4711yescharacteristic
190C2×#131—941no—
191C2×C4×Q8—21no—
192#510—474no—
193#510—474no—
194C2×Q32—472no—
195C2×SD32—472no—
196C2×M32—471no—
197C2×M32—471no—
198#444—474no—
199#444—942no—
200#441—22no—
201#441C2×D4714yescomplemented
202C2×#108—471no—
203C2×#106C2×D4711yescharacteristic
204C2×#104—941no—
205C2×#103—21no—
206C2×#97C2×D4711yescharacteristic
207#365—474no—
208#362—474no—
209#360—474no—
210#347—474no—
211C47C2×#218011yescharacteristic, complemented, Sylow
212C2×#41—941no—
213C22×Q8—21no—
214#135—472no—
215#135—472no—
216#135—941no—
217#135—941no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—471no—
222C2×Q16C4×D4712yes—
223C2×Q16C4×D4712yes—
224C2×Q16C22×D4712yes—
225C2×SD16—941no—
226C2×D8—471no—
227#131—944no—
228#131—1882no—
229C2×M16—941no—
230C2×M16—1881no—
231C22×C8—1881no—
232C22×C8C22⋊D4711yescharacteristic
233C22×C8C22×D4711yescharacteristic
234C4×Q8—24no—
235C4×Q8—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C42—41no—
239C2×C42C22⋊D4711yescharacteristic
240Q32—478no—
241SD32—478no—
242M32—472no—
243M32—472no—
244M32—472no—
245M32—941no—
246C2×C16—472no—
247C2×C16—941no—
248#108—472no—
249#108—941no—
250#106—21no—
251#106C22×D4712yes—
252#104—944no—
253#103—24no—
254#97C22⋊D4712yes—
255#97C22×D4712yes—
256#41—942no—
257#41—942no—
258#41—1881no—
259#41—1881no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—941no—
267C2×D4—941no—
268C2×D4—1881no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—1881no—
273C22×C4C2×C22⋊D4711yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—22no—
277Q16—472no—
278Q16—941no—
279Q16C2×C4×D4714yes—
280SD16—942no—
281SD16—942no—
282D8—472no—
283D8—941no—
284M16—942no—
285M16—1884no—
286M16—1881no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—1884no—
290C2×C8—1881no—
291C2×C8C2×C4×D4711yescharacteristic
292C2×C8C2×C4×D4711yescharacteristic
293C2×C8#1062535011yescharacteristic
294C2×C8#1062535011yescharacteristic
295C2×C8C2×C22⋊D4712yes—
296C2×C8C2×C22⋊D4711yescharacteristic
297C2×C8C23×D4711yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C42—21no—
302C42—44no—
303C42C2×C22⋊D4712yes—
304C16—474no—
305C16—942no—
306C23—1881no—
307C23#1309405011yescharacteristic
308Q8—24no—
309Q8—42no—
310Q8—42no—
311Q8—42no—
312Q8—942no—
313Q8—1881no—
314D4—942no—
315D4—1882no—
316D4—1882no—
317D4—1881no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—1881no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4C4×C22⋊D4711yescharacteristic
329C2×C4C4×C22⋊D4711yescharacteristic
330C2×C4#1309404911yescharacteristic
331C2×C4#1309404911yescharacteristic
332C2×C4#1309405011yescharacteristic
333C2×C4C22×C22⋊D4711yescharacteristic
334C8—22no—
335C8—1882no—
336C8C4×C22⋊D4711yescharacteristic
337C8C4×C22⋊D4711yescharacteristic
338C8C22×C4×D4711yescharacteristic
339C8C2×#1062535011yescharacteristic
340C22—22no—
341C22—3762no—
342C22—1882no—
343C22#1568923311yescharacteristic
344C22#1568923311yescharacteristic
345C22C2×#1309405011yescharacteristic
346C4—42no—
347C4—44no—
348C4—82no—
349C4—1882no—
350C4#1568923311yescharacteristic
351C4#1568923311yescharacteristic
352C4C2×C4×C22⋊D4711yescharacteristic
353C4C2×#1309404911yescharacteristic
354C2—21no—
355C2—21no—
356C2—3762no—
357C2#2024527712yesdirect product factor
358C2C2×#1568923311yescharacteristic
subgroupG/H
centerC22#15689233
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#441C2
socleC22×C47#442
prime radicalC2×#13094046C22
cosocleC2×C8×C47C24
hypercenterC2×#441D47
hypocenterC47C2×#2180
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #20245277C2direct (N × H)
4. C2×#15688945C2semidirect
5. C2×#15688939C2semidirect
7. C2×#15688901C2semidirect
8. C2×C47×#441C2semidirect
11. #15689564C4semidirect
13. C2×#13093970C4semidirect
14. C2×#13093967C4semidirect
21. #15688945C22semidirect
22. #15688939C22semidirect
24. #15688901C22semidirect
28. C47×#441C22semidirect
45. #13093970C2×C4semidirect
46. #13093967C2×C4semidirect
177. C2×#441D47semidirect
185. C2×C47#2180semidirect
201. #441C2×D47semidirect
211. C47C2×#2180semidirect
357. C2#20245277direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895642
C2×#156892462
#202452772
C2×#156889452
C2×#156889392
C2×#156889322
C2×#156889012
C2×C47×#4412
C2×#218047