Finite Group Databasebeta

← C2×#20245459 #26370652

Subgroups — C2×#20245459 #26370652

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×#15689558C211yesmaximal, characteristic
2C2×#15689508C211yesmaximal, characteristic, complemented
3C2×#15689240C211yesmaximal, characteristic, complemented
4#20245459C218yesmaximal, direct product factor
5C2×#15688943C211yesmaximal, characteristic, complemented
6C2×#15688939C211yesmaximal, characteristic, complemented
7C2×#15688937C211yesmaximal, characteristic, complemented
8C2×C47×#510C211yesmaximal, characteristic, complemented
9C22×#10625336—21no—
10C22×D376C2211yescharacteristic
11C2×#13094031—21no—
12C2×#13094013—21no—
13#15689558—22no—
14#15689558C2214yes—
15C2×#13093967—21no—
16C2×#13093965—21no—
17C2×#13093964C2211yescharacteristic
18#15689508—22no—
19#15689508C2214yescomplemented
20#15689240—22no—
21#15689240C2214yescomplemented
22C2×#13093960C2211yescharacteristic
23C2×#13093951—21no—
24C2×C8×Dic47C2211yescharacteristic
25#15688943C2214yescomplemented
26#15688939C2214yescomplemented
27#15688937C2214yescomplemented
28C2×#135×C47C2211yescharacteristic
29C22×Q16×C47C2211yescharacteristic
30C47×#510—22no—
31C47×#510C2214yescomplemented
32C2×Q32×C47—21no—
33C2×SD32×C47—21no—
34C2×M32×C47C2211yescharacteristic
35C22×D188—21no—
36C2×#10625336—24no—
37C2×#10625336—41no—
38C2×#10625336—41no—
39C2×#10625336—42no—
40C2×D376—21no—
41C2×D376—21no—
42C2×D376—21no—
43C2×D376—21no—
44C2×D376—21no—
45C2×D376C2312yes—
46#13094031—24no—
47#13094031—42no—
48C2×#10625329—21no—
49C2×#10625329—41no—
50C22×C47⋊C8—41no—
51C22×C47⋊C8D411yescharacteristic
52#13094013—24no—
53#13094013—42no—
54C2×(C2×D47)⋊C4—42no—
55C2×C4×Dic47D411yescharacteristic
56#13093967—24no—
57#13093965—24no—
58#13093964—21no—
59#13093964C2312yes—
60C2×C47⋊C16—21no—
61#13093960—21no—
62#13093960C2312yes—
63#13093951—24no—
64C8×Dic47D412yes—
65C8×Dic47C2312yes—
66C2×#41×C47—21no—
67C22×Q8×C47—21no—
68#135×C47—21no—
69#135×C47—21no—
70#135×C47D412yes—
71#135×C47C2312yes—
72C2×Q16×C47—21no—
73C2×Q16×C47—21no—
74C2×Q16×C47—21no—
75C2×Q16×C47—21no—
76C2×Q16×C47—21no—
77C2×Q16×C47D411yescharacteristic
78C2×Q16×C47C2312yes—
79C2×SD16×C47—21no—
80C2×D8×C47D411yescharacteristic
81C22×C8×C47C2311yescharacteristic
82Q32×C47—24no—
83SD32×C47—24no—
84M32×C47—21no—
85M32×C47C2312yes—
86C2×C16×C47—21no—
87C23×D47—41no—
88#41×C47—22no—
89#41×C47—22no—
90#41×C47—41no—
91#41×C47—41no—
92C2×Q8×C47—21no—
93C2×Q8×C47—22no—
94C2×Q8×C47—41no—
95C2×Q8×C47—41no—
96C2×Q8×C47—41no—
97C2×Q8×C47—41no—
98C2×Q8×C47—41no—
99C2×D4×C47—21no—
100C2×D4×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47—41no—
103C22×C4×C47C2×D411yescharacteristic
104C22×Dic47—21no—
105C2×D188—22no—
106C2×D188—41no—
107C2×D188—41no—
108C2×D188—41no—
109C2×D188—41no—
110C2×D188—41no—
111Q16×C47—21no—
112Q16×C47—22no—
113Q16×C47—22no—
114Q16×C47—41no—
115Q16×C47—41no—
116Q16×C47C2×D412yes—
117SD16×C47—22no—
118SD16×C47—22no—
119D8×C47—21no—
120D8×C47C2×D412yes—
121C2×C8×C47C2×D411yescharacteristic
122C2×C8×C47C2×D411yescharacteristic
123C2×C8×C47C2×D411yescharacteristic
124C2×C8×C47#4111yescharacteristic
125C2×C8×C47#4111yescharacteristic
126C2×C8×C47C2411yescharacteristic
127#10625336—44no—
128#10625336—44no—
129(C2×D47)⋊C4—48no—
130C4×Dic47—21no—
131C4×Dic47C2×D412yes—
132#10625329—22no—
133#10625329—41no—
134#10625329—44no—
135C2×C47⋊C8—41no—
136C2×C47⋊C8—44no—
137C2×C47⋊C8D811yescharacteristic
138C2×C47⋊C8D811yescharacteristic
139C2×C47⋊C8D812yes—
140C2×C47⋊C8C2×D412yes—
141D376—22no—
142D376—22no—
143D376—41no—
144D376—41no—
145C16×C47—22no—
146C47⋊C16—22no—
147C23×C47—41no—
148C23×C47AGL(1,ℤ/8)11yescharacteristic
149C22×D47—42no—
150C22×D47—84no—
151C22×D47—81no—
152C22×D47—81no—
153Q8×C47—22no—
154Q8×C47—41no—
155Q8×C47—42no—
156Q8×C47—42no—
157Q8×C47—81no—
158Q8×C47—81no—
159D4×C47—22no—
160D4×C47—42no—
161D4×C47—42no—
162D4×C47—41no—
163C2×C4×C47—41no—
164C2×C4×C47—42no—
165C2×C4×C47—42no—
166C2×C4×C47—42no—
167C2×C4×C47—81no—
168C2×C4×C47—81no—
169C2×C4×C47#12111yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47C2×D811yescharacteristic
172C2×C4×C47C2×D811yescharacteristic
173C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C47C22×D411yescharacteristic
175C2×Dic47—22no—
176C2×Dic47—42no—
177D188—42no—
178D188—42no—
179D188—81no—
180D188—81no—
181C8×C47#12111yescharacteristic
182C8×C47#12111yescharacteristic
183C8×C47C22×D411yescharacteristic
184C8×C47C2×#4111yescharacteristic
185C47⋊C8—42no—
186C47⋊C8C2×D812yes—
187C47⋊C8C2×D812yes—
188C2×#2212—471nomaximal, Sylow
189C22×C47—22no—
190C22×C47—42no—
191C22×C47—82no—
192C22×C47#45911yescharacteristic
193C22×C47#45911yescharacteristic
194C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
195C2×D47—84no—
196C2×D47—82no—
197C2×D47—162no—
198C2×D47—162no—
199C4×C47—42no—
200C4×C47—82no—
201C4×C47#45911yescharacteristic
202C4×C47#45911yescharacteristic
203C4×C47C2×#12111yescharacteristic
204C4×C47C22×D811yescharacteristic
205Dic47—42no—
206C2×#510D4711yescharacteristic, complemented
207C2×#509—471no—
208C2×#495—471no—
209C2×#443—471no—
210#2212—478no—
211C2×#364—471no—
212C2×#362—471no—
213C2×#361—471no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—82no—
217C2×C47#221212yescomplemented
218C2×C47C2×#45911yescharacteristic
219D47—162no—
220C2×#135C2×D4711yescharacteristic
221C22×Q16C2×D4711yescharacteristic
222C22×SD16—941no—
223C22×D8—471no—
224C2×#131—941no—
225C2×#124—941no—
226#510—22no—
227#510C2×D4714yescomplemented
228#509—474no—
229#509—942no—
230C2×Q32—21no—
231C2×SD32—21no—
232C2×SD32—941no—
233C2×D16—941no—
234C2×M32—471no—
235C2×M32C2×D4711yescharacteristic
236#495—474no—
237#495—942no—
238#443—474no—
239#443—942no—
240C2×#108—471no—
241C2×#104—941no—
242C2×C4×C8—471no—
243#364—474no—
244#362—474no—
245#361—474no—
246C47C2×#221211yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C22×Q8—21no—
249C22×D4—941no—
250#135—21no—
251#135—21no—
252#135C22⋊D4712yes—
253#135C22×D4712yes—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16C22⋊D4711yescharacteristic
260C2×Q16C22×D4712yes—
261C2×SD16—21no—
262C2×SD16—944no—
263C2×SD16—1881no—
264C2×SD16—1881no—
265C2×SD16—1882no—
266C2×D8—472no—
267C2×D8—941no—
268C2×D8—941no—
269C2×D8—941no—
270C2×D8—941no—
271C2×D8—941no—
272C2×D8C22⋊D4711yescharacteristic
273#131—944no—
274#131—1882no—
275C2×M16—941no—
276C2×M16—1881no—
277C22×C8—471no—
278C22×C8—1881no—
279C22×C8C22×D4711yescharacteristic
280#124—944no—
281#124—1882no—
282C2×C22⋊C4—1882no—
283C2×C42—471no—
284Q32—24no—
285SD32—24no—
286SD32—944no—
287D16—944no—
288M32—21no—
289M32—472no—
290M32—941no—
291M32C22×D4712yes—
292C2×C16—21no—
293C2×C16—941no—
294#108—472no—
295#108—941no—
296#104—944no—
297C4×C8—472no—
298C4×C8—472no—
299C24—1881no—
300#41—22no—
301#41—22no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—942no—
314C2×D4—1881no—
315C2×D4—1881no—
316C2×D4—1881no—
317C2×D4—1881no—
318C2×D4—1881no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—941no—
322C22×C4D4×D4711yescharacteristic
323Q16—21no—
324Q16—22no—
325Q16—22no—
326Q16—41no—
327Q16—41no—
328Q16C2×C22⋊D4712yes—
329SD16—22no—
330SD16—22no—
331SD16—1884no—
332SD16—1884no—
333D8—21no—
334D8—942no—
335D8—942no—
336D8—1881no—
337D8—1881no—
338D8C2×C22⋊D4712yes—
339M16—942no—
340M16—1884no—
341M16—1881no—
342C2×C8—471no—
343C2×C8—471no—
344C2×C8—472no—
345C2×C8—472no—
346C2×C8—1884no—
347C2×C8—1881no—
348C2×C8D4×D4711yescharacteristic
349C2×C8#1062535211yescharacteristic
350C2×C8#1062535211yescharacteristic
351C2×C8C2×C22⋊D4711yescharacteristic
352C2×C8C2×C22⋊D4711yescharacteristic
353C2×C8C23×D4711yescharacteristic
354C22⋊C4—1888no—
355C42—472no—
356C42—941no—
357C16—22no—
358C16—942no—
359C23—41no—
360C23—3764no—
361C23—3761no—
362C23—3761no—
363C23—1882no—
364C23#1309404811yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—3761no—
376D4—3761no—
377D4—1882no—
378D4—1882no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—942no—
386C2×C4—1882no—
387C2×C4#1309399611yescharacteristic
388C2×C4#1309399611yescharacteristic
389C2×C4D8×D4711yescharacteristic
390C2×C4D8×D4711yescharacteristic
391C2×C4#1309404811yescharacteristic
392C2×C4C2×D4×D4711yescharacteristic
393C8—472no—
394C8—472no—
395C8—1882no—
396C8#1309399611yescharacteristic
397C8#1309399611yescharacteristic
398C8C22×C22⋊D4711yescharacteristic
399C8C2×#1062535211yescharacteristic
400C22—22no—
401C22—42no—
402C22—82no—
403C22—3764no—
404C22—3762no—
405C22—7522no—
406C22—7522no—
407C22#1568931611yescharacteristic
408C22#1568931611yescharacteristic
409C22C2×#1309404811yescharacteristic
410C4—42no—
411C4—82no—
412C4—1882no—
413C4#1568931611yescharacteristic
414C4#1568931611yescharacteristic
415C4C2×#1309399611yescharacteristic
416C4C2×D8×D4711yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—7522no—
421C2#2024545912yesdirect product factor
422C2C2×#1568931611yescharacteristic
subgroupG/H
centerC22#15689316
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#510C2
socleC22×C47#459
prime radicalC2×#15689558C2
hypercenterC2×#510D47
hypocenterC47C2×#2212
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. C2×#15689508C2semidirect
3. C2×#15689240C2semidirect
4. #20245459C2direct (N × H)
5. C2×#15688943C2semidirect
6. C2×#15688939C2semidirect
7. C2×#15688937C2semidirect
8. C2×C47×#510C2semidirect
19. #15689508C22semidirect
21. #15689240C22semidirect
25. #15688943C22semidirect
26. #15688939C22semidirect
27. #15688937C22semidirect
31. C47×#510C22semidirect
206. C2×#510D47semidirect
217. C2×C47#2212semidirect
227. #510C2×D47semidirect
246. C47C2×#2212semidirect
421. C2#20245459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895582
C2×#156895082
C2×#156892402
#202454592
C2×#156889432
C2×#156889392
C2×#156889372
C2×C47×#5102
C2×#221247