Finite Group Databasebeta

← C2×#20245454 #26370647

Subgroups — C2×#20245454 #26370647

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689564C211yesmaximal, characteristic, complemented
2C2×#15689559C211yesmaximal, characteristic
3C2×#15689241C211yesmaximal, characteristic, complemented
4#20245454C218yesmaximal, direct product factor
5C2×#15688944C211yesmaximal, characteristic, complemented
6C2×#15688939C211yesmaximal, characteristic, complemented
7C2×#15688936C211yesmaximal, characteristic, complemented
8C2×C47×#495C211yesmaximal, characteristic, complemented
9C2×#13094046C2211yescharacteristic
10C2×#13094030—21no—
11#15689564—22no—
12#15689564C2214yescomplemented
13#15689559—22no—
14#15689559C2214yes—
15C2×#13093970—21no—
16C2×#13093968—21no—
17C2×#13093967—21no—
18C2×#13093965—21no—
19C2×#13093964C2211yescharacteristic
20C2×#13093964C2211yescharacteristic
21#15689241—22no—
22#15689241C2214yescomplemented
23C2×#13093960C2211yescharacteristic
24C2×#13093952—21no—
25#15688944C2214yescomplemented
26#15688939C2214yescomplemented
27#15688936C2214yescomplemented
28C22×Q16×C47C2211yescharacteristic
29C22×SD16×C47—21no—
30C22×D8×C47C2211yescharacteristic
31C2×#124×C47—21no—
32C47×#495—22no—
33C47×#495C2214yescomplemented
34C2×C4×C8×C47C2211yescharacteristic
35C2×#10625350—21no—
36#13094046—21no—
37#13094046—21no—
38#13094046D412yes—
39#13094046C2312yes—
40C2×Dic188D411yescharacteristic
41C2×#10625325—21no—
42C2×D376D411yescharacteristic
43#13094030—24no—
44#13094030—42no—
45C2×#10625329—21no—
46C2×#10625324—41no—
47C2×C8×D47—41no—
48#13093970—24no—
49#13093968—24no—
50#13093967—24no—
51#13093965—24no—
52#13093964—21no—
53#13093964—21no—
54#13093964C2312yes—
55#13093964C2312yes—
56C2×C47⋊C16—21no—
57C2×C47⋊C16—21no—
58#13093960—21no—
59#13093960C2312yes—
60#13093952—24no—
61C22×Q8×C47—21no—
62C22×D4×C47—21no—
63C2×Q16×C47—21no—
64C2×Q16×C47—21no—
65C2×Q16×C47—21no—
66C2×Q16×C47—21no—
67C2×Q16×C47—21no—
68C2×Q16×C47C2312yes—
69C2×SD16×C47—24no—
70C2×SD16×C47—41no—
71C2×SD16×C47—41no—
72C2×SD16×C47—42no—
73C2×D8×C47—21no—
74C2×D8×C47—21no—
75C2×D8×C47—21no—
76C2×D8×C47—21no—
77C2×D8×C47—21no—
78C2×D8×C47C2312yes—
79C22×C8×C47D411yescharacteristic
80C22×C8×C47C2311yescharacteristic
81#124×C47—24no—
82#124×C47—42no—
83C2×C22⋊C4×C47—42no—
84C2×C42×C47D411yescharacteristic
85C4×C8×C47D412yes—
86C4×C8×C47C2312yes—
87C24×C47—41no—
88C2×Q8×C47—22no—
89C2×Q8×C47—41no—
90C2×Q8×C47—41no—
91C2×Q8×C47—41no—
92C2×Q8×C47—41no—
93C2×Q8×C47—41no—
94C2×D4×C47—22no—
95C2×D4×C47—41no—
96C2×D4×C47—41no—
97C2×D4×C47—41no—
98C2×D4×C47—41no—
99C2×D4×C47—41no—
100C22×C4×C47—21no—
101C22×C4×C47—41no—
102C22×C4×C47C2×D411yescharacteristic
103C2×C22⋊D47—41no—
104#10625350—22no—
105#10625350—22no—
106#10625350—41no—
107#10625350—41no—
108C2×D188—21no—
109C2×C4×D47—41no—
110C2×Dic94—21no—
111Q16×C47—22no—
112Q16×C47—22no—
113Q16×C47—41no—
114Q16×C47—41no—
115SD16×C47—44no—
116SD16×C47—44no—
117D8×C47—22no—
118D8×C47—22no—
119D8×C47—41no—
120D8×C47—41no—
121C2×C8×C47D811yescharacteristic
122C2×C8×C47D811yescharacteristic
123C2×C8×C47D812yes—
124C2×C8×C47C2×D411yescharacteristic
125C2×C8×C47C2×D411yescharacteristic
126C2×C8×C47C2×D411yescharacteristic
127C2×C8×C47C2×D412yes—
128C2×C8×C47#4111yescharacteristic
129C2×C8×C47#4111yescharacteristic
130C2×C8×C47C2411yescharacteristic
131C22⋊C4×C47—48no—
132C42×C47—21no—
133C42×C47C2×D412yes—
134#10625329—22no—
135#10625329—41no—
136C2×C47⋊C8—41no—
137Dic188—21no—
138Dic188C2×D412yes—
139D376—21no—
140D376C2×D412yes—
141#10625325—22no—
142#10625325—22no—
143#10625324—44no—
144C8×D47—44no—
145C47⋊C16—22no—
146C47⋊C16—22no—
147C23×C47—42no—
148C23×C47—84no—
149C23×C47—81no—
150C23×C47—81no—
151C23×C47AGL(1,ℤ/8)11yescharacteristic
152C22×D47—41no—
153Q8×C47—42no—
154Q8×C47—42no—
155Q8×C47—81no—
156Q8×C47—81no—
157D4×C47—42no—
158D4×C47—42no—
159D4×C47—81no—
160D4×C47—81no—
161C2×C4×C47—22no—
162C2×C4×C47—42no—
163C2×C4×C47—42no—
164C2×C4×C47—81no—
165C2×C4×C47—81no—
166C2×C4×C47#12111yescharacteristic
167C2×C4×C47#12111yescharacteristic
168C2×C4×C47C2×D811yescharacteristic
169C2×C4×C47C2×D811yescharacteristic
170C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C47C22×D411yescharacteristic
172C22⋊D47—42no—
173C22⋊D47—42no—
174C2×Dic47—41no—
175D188—22no—
176D188—41no—
177C4×D47—42no—
178C4×D47—42no—
179Dic94—22no—
180Dic94—41no—
181C8×C47#12111yescharacteristic
182C8×C47#12111yescharacteristic
183C8×C47C2×D812yes—
184C8×C47C2×D812yes—
185C8×C47C22×D411yescharacteristic
186C8×C47C2×#4111yescharacteristic
187C47⋊C8—42no—
188C2×#2212—471nomaximal, Sylow
189C22×C47—22no—
190C22×C47—84no—
191C22×C47—82no—
192C22×C47—162no—
193C22×C47—162no—
194C22×C47#45911yescharacteristic
195C22×C47#45911yescharacteristic
196C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
197C2×D47—42no—
198C2×D47—82no—
199C4×C47—42no—
200C4×C47—82no—
201C4×C47#45911yescharacteristic
202C4×C47#45911yescharacteristic
203C4×C47C2×#12111yescharacteristic
204C4×C47C22×D811yescharacteristic
205Dic47—42no—
206C2×#510—471no—
207C2×#509—471no—
208C2×#495D4711yescharacteristic, complemented
209C2×#443—471no—
210#2212—478no—
211C2×#364—471no—
212C2×#362—471no—
213C2×#361—471no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—162no—
217C2×C47#221212yescomplemented
218C2×C47C2×#45911yescharacteristic
219D47—82no—
220C2×#135—471no—
221C22×Q16C2×D4711yescharacteristic
222C22×SD16—21no—
223C22×D8C2×D4711yescharacteristic
224C2×#131—941no—
225C2×#124—21no—
226#510—474no—
227#510—942no—
228#509—474no—
229#509—942no—
230C2×Q32—941no—
231C2×SD32—941no—
232C2×SD32—941no—
233C2×D16—941no—
234C2×M32—471no—
235C2×M32—471no—
236#495—22no—
237#495C2×D4714yescomplemented
238#443—474no—
239#443—942no—
240C2×#108—471no—
241C2×#104—941no—
242C2×C4×C8C2×D4711yescharacteristic
243#364—474no—
244#362—474no—
245#361—474no—
246C47C2×#221211yescharacteristic, complemented, Sylow
247C2×#41—941no—
248C22×Q8—21no—
249C22×D4—21no—
250#135—472no—
251#135—472no—
252#135—941no—
253#135—941no—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—471no—
260C2×Q16C22×D4712yes—
261C2×SD16—24no—
262C2×SD16—41no—
263C2×SD16—41no—
264C2×SD16—42no—
265C2×SD16—941no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8—471no—
272C2×D8C22×D4712yes—
273#131—944no—
274#131—1882no—
275C2×M16—941no—
276C2×M16—1881no—
277C22×C8—1881no—
278C22×C8C22⋊D4711yescharacteristic
279C22×C8C22×D4711yescharacteristic
280#124—24no—
281#124—42no—
282C2×C22⋊C4—42no—
283C2×C42C22⋊D4711yescharacteristic
284Q32—944no—
285SD32—944no—
286SD32—944no—
287D16—944no—
288M32—472no—
289M32—472no—
290M32—941no—
291M32—941no—
292C2×C16—941no—
293C2×C16—941no—
294#108—472no—
295#108—941no—
296#104—944no—
297C4×C8C22⋊D4712yes—
298C4×C8C22×D4712yes—
299C24—41no—
300#41—942no—
301#41—942no—
302#41—1881no—
303#41—1881no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—941no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—941no—
318C2×D4—1881no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—1881no—
322C22×C4C2×C22⋊D4711yescharacteristic
323Q16—22no—
324Q16—22no—
325Q16—41no—
326Q16—41no—
327Q16—472no—
328Q16—941no—
329SD16—44no—
330SD16—44no—
331SD16—942no—
332SD16—942no—
333D8—22no—
334D8—22no—
335D8—41no—
336D8—41no—
337D8—472no—
338D8—941no—
339M16—942no—
340M16—1881no—
341M16—1884no—
342C2×C8—1881no—
343C2×C8—1884no—
344C2×C8#1062533411yescharacteristic
345C2×C8#1062533411yescharacteristic
346C2×C8#1062533412yes—
347C2×C8D4×D4711yescharacteristic
348C2×C8D4×D4711yescharacteristic
349C2×C8#1062535211yescharacteristic
350C2×C8#1062535211yescharacteristic
351C2×C8C2×C22⋊D4711yescharacteristic
352C2×C8C2×C22⋊D4712yes—
353C2×C8C23×D4711yescharacteristic
354C22⋊C4—48no—
355C42—21no—
356C42C2×C22⋊D4712yes—
357C16—942no—
358C16—942no—
359C23—42no—
360C23—84no—
361C23—81no—
362C23—81no—
363C23—1881no—
364C23#1309405011yescharacteristic
365Q8—42no—
366Q8—42no—
367Q8—81no—
368Q8—81no—
369Q8—942no—
370Q8—1881no—
371D4—42no—
372D4—42no—
373D4—81no—
374D4—81no—
375D4—942no—
376D4—1882no—
377D4—1882no—
378D4—1881no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—1881no—
385C2×C4—1882no—
386C2×C4—1882no—
387C2×C4#1309399511yescharacteristic
388C2×C4#1309399511yescharacteristic
389C2×C4C2×#1062533411yescharacteristic
390C2×C4C2×#1062533411yescharacteristic
391C2×C4#1309405011yescharacteristic
392C2×C4C22×C22⋊D4711yescharacteristic
393C8—1882no—
394C8#1309399511yescharacteristic
395C8#1309399511yescharacteristic
396C8C2×#1062533412yes—
397C8C2×#1062533412yes—
398C8C2×D4×D4711yescharacteristic
399C8C2×#1062535211yescharacteristic
400C22—22no—
401C22—84no—
402C22—82no—
403C22—162no—
404C22—162no—
405C22—3762no—
406C22—1882no—
407C22#1568931511yescharacteristic
408C22#1568931511yescharacteristic
409C22C2×#1309405011yescharacteristic
410C4—42no—
411C4—82no—
412C4—1882no—
413C4#1568931511yescharacteristic
414C4#1568931511yescharacteristic
415C4C2×#1309399511yescharacteristic
416C4C22×#1062533411yescharacteristic
417C2—21no—
418C2—21no—
419C2—162no—
420C2—3762no—
421C2#2024545412yesdirect product factor
422C2C2×#1568931511yescharacteristic
subgroupG/H
centerC22#15689315
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#495C2
socleC22×C47#459
prime radicalC2×#15689559C2
hypercenterC2×#495D47
hypocenterC47C2×#2212
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#15689564C2semidirect
3. C2×#15689241C2semidirect
4. #20245454C2direct (N × H)
5. C2×#15688944C2semidirect
6. C2×#15688939C2semidirect
7. C2×#15688936C2semidirect
8. C2×C47×#495C2semidirect
12. #15689564C22semidirect
22. #15689241C22semidirect
25. #15688944C22semidirect
26. #15688939C22semidirect
27. #15688936C22semidirect
33. C47×#495C22semidirect
208. C2×#495D47semidirect
217. C2×C47#2212semidirect
237. #495C2×D47semidirect
246. C47C2×#2212semidirect
421. C2#20245454direct (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×#156895592
C2×#156892412
#202454542
C2×#156889442
C2×#156889392
C2×#156889362
C2×C47×#4952
C2×#221247