Finite Group Databasebeta

← C4×#15688932 #26131529

Subgroups — C4×#15688932 #26131529

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094046C211yesmaximal, characteristic
2C2×#15688932C212yesmaximal
3C4×#13093964C211yesmaximal, characteristic, complemented
4#20241495C212yesmaximal, complemented
5C4×#106×C47C211yesmaximal, characteristic, complemented
6C2×#13094046C2211yescharacteristic
7C4×#10625350—21no—
8C2×#13093964C2212yes—
9C4×Dic188C411yescharacteristic, complemented
10C4×Dic188C411yescharacteristic, complemented
11C4×#10625325—21no—
12C4×#10625325—21no—
13C4×D376C411yescharacteristic, complemented
14C4×D376C411yescharacteristic, complemented
15#15689161C2211yescharacteristic
16#15689120—21no—
17#15688932C418yesdirect product factor
18#15688899—21no—
19C4×C47⋊C16—21no—
20C2×#106×C47C2212yes—
21C2×C4×C8×C47C2211yescharacteristic
22C4×C4⋊C4×C47—21no—
23C47×#340—21no—
24C2×#10625350—21no—
25#13094046—22no—
26#13094046C2×C414yes—
27C2×Dic188C2×C411yescharacteristic
28C2×#10625325—21no—
29C2×D376C2×C411yescharacteristic
30C4×Dic94—21no—
31C4×Dic94—21no—
32C4×D188—21no—
33C4×D188—21no—
34C4×C22⋊D47—41no—
35C4×C22⋊D47—41no—
36#13093983—21no—
37#13093981—41no—
38C42×D47—41no—
39#13093964—22no—
40#13093964C2×C414yescomplemented
41C2×C47⋊C16—22no—
42#13093958C2×C411yescharacteristic
43#13093958C2×C411yescharacteristic
44#13093956—21no—
45#13093949—21no—
46#13093949—21no—
47#13093946—21no—
48#13093946—21no—
49C22×C8×C47D411yescharacteristic
50C22×C8×C47C2311yescharacteristic
51C2×C4⋊C4×C47—22no—
52C2×C42×C47—41no—
53C2×C42×C47D411yescharacteristic
54#106×C47—22no—
55#106×C47C2×C414yescomplemented
56C4×C8×C47C2×C411yescharacteristic
57C4×C8×C47C2×C411yescharacteristic
58C4×C8×C47D411yescharacteristic
59C4×C8×C47D411yescharacteristic
60#95×C47—41no—
61C22×C4×C47—42no—
62C22×C4×C47D811yescharacteristic
63C22×C4×C47D811yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C2×C22⋊D47—41no—
66#10625350—24no—
67#10625350—42no—
68C2×D188—21no—
69C2×C4×D47—41no—
70C2×C4×D47—41no—
71C2×C4×D47—41no—
72C2×Dic94—21no—
73C2×C8×C47—22no—
74C2×C8×C47C22⋊C411yescharacteristic
75C2×C8×C47C22⋊C411yescharacteristic
76C2×C8×C47C22×C411yescharacteristic
77C2×C8×C47C22×C412yes—
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47#4112yes—
80C4⋊C4×C47—24no—
81C4⋊C4×C47—42no—
82C42×C47—82no—
83C42×C47C22⋊C411yescharacteristic
84C42×C47C22⋊C411yescharacteristic
85C42×C47SD1611yescharacteristic
86C42×C47SD1611yescharacteristic
87C22⋊Dic47—41no—
88(C2×D47)⋊C4—41no—
89(C2×D47)⋊C4—41no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94C4×Dic47—41no—
95C4×Dic47—41no—
96C4×Dic47—41no—
97Dic188—21no—
98Dic188C4212yescomplemented
99D376—21no—
100D376C4212yescomplemented
101#10625325—24no—
102C47⋊C16—24no—
103C23×C47C2×D811yescharacteristic
104C22×D47—41no—
105C2×C4×C47—22no—
106C2×C4×C47—41no—
107C2×C4×C47—44no—
108C2×C4×C47—82no—
109C2×C4×C47—82no—
110C2×C4×C47#10211yescharacteristic
111C2×C4×C47#10211yescharacteristic
112C2×C4×C47#10211yescharacteristic
113C2×C4×C47#10211yescharacteristic
114C2×C4×C47C2×C22⋊C411yescharacteristic
115C2×C4×C47C4×D412yes—
116C2×C4×C47C2×SD1611yescharacteristic
117C2×C4×C47#13512yes—
118C22⋊D47—44no—
119C2×Dic47—41no—
120C2×Dic47—41no—
121C2×Dic47—41no—
122D188—22no—
123D188—41no—
124C4×D47—44no—
125C4×D47—82no—
126C4×D47—82no—
127Dic94—22no—
128Dic94—41no—
129C8×C47—21no—
130C8×C47—21no—
131C8×C47C2×C4211yescharacteristic
132C8×C47#11711yescharacteristic
133C8×C47C4×D412yes—
134C4×#360—471nomaximal, Sylow
135C22×C47—21no—
136C22×C47—21no—
137C22×C47C2×#10211yescharacteristic
138C22×C47C4×D812yes—
139C2×D47—42no—
140C2×D47—81no—
141C2×D47—81no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—84no—
146C4×C47#36012yescomplemented
147C4×C47C4×C22⋊C411yescharacteristic
148C4×C47#41611yescharacteristic
149C4×C47C4×SD1612yes—
150Dic47—42no—
151Dic47—81no—
152Dic47—81no—
153C4×#135—471no—
154C2×#360—472no—
155C4×M32—471no—
156C4×#106D4711yescharacteristic, complemented
157#1386—472no—
158C2×C47—22no—
159C2×C47C4×#10211yescharacteristic
160C2×C47C2×#36011yescharacteristic
161C2×C47#214511yescharacteristic
162D47—82no—
163C2×#135—471no—
164C4×#41—941no—
165C2×M32—472no—
166C4×Q16—471no—
167C4×Q16—471no—
168C4×SD16—941no—
169C4×SD16—941no—
170C4×D8—471no—
171C4×D8—471no—
172#427—471no—
173C2×#106C2×D4712yes—
174#416—941no—
175C2×C4×C8C2×D4711yescharacteristic
176C4×C4⋊C4—21no—
177#360—478no—
178#346—941no—
179C4×C16—941no—
180#340—21no—
181C47C4×#36011yescharacteristic, complemented, Sylow
182C2×#41—941no—
183#135—474no—
184#135—942no—
185C2×Q16—471no—
186C2×SD16—941no—
187C2×D8—471no—
188C22×C8C22⋊D4711yescharacteristic
189C22×C8C22×D4711yescharacteristic
190C4×Q8—941no—
191C4×Q8—941no—
192C4×D4—941no—
193C4×D4—941no—
194C4×D4—1881no—
195C4×D4—1881no—
196#117—941no—
197#117—1881no—
198C2×C4⋊C4—22no—
199C2×C42—41no—
200C2×C42—1881no—
201C2×C42C22⋊D4711yescharacteristic
202M32—474no—
203M32—942no—
204C2×C16—942no—
205#107—471no—
206#107—471no—
207#106—22no—
208#106—941no—
209#106C4×D4714yescomplemented
210#103—941no—
211#103—941no—
212#102—941no—
213#102—941no—
214C4×C8C4×D4711yescharacteristic
215C4×C8C4×D4711yescharacteristic
216C4×C8D18811yescharacteristic
217C4×C8D18811yescharacteristic
218#95—41no—
219#41—944no—
220#41—1882no—
221C2×Q8—941no—
222C2×D4—941no—
223C2×D4—1881no—
224C22×C4—42no—
225C22×C4—1881no—
226C22×C4—1881no—
227C22×C4—1881no—
228C22×C4#1062533411yescharacteristic
229C22×C4#1062533411yescharacteristic
230C22×C4C2×C22⋊D4711yescharacteristic
231Q16—472no—
232Q16—941no—
233SD16—944no—
234D8—472no—
235D8—941no—
236C2×C8—22no—
237C2×C8(C2×D47)⋊C411yescharacteristic
238C2×C8(C2×D47)⋊C411yescharacteristic
239C2×C8C2×C4×D4711yescharacteristic
240C2×C8C2×C4×D4712yes—
241C2×C8C2×D18811yescharacteristic
242C2×C8#1062535012yes—
243C4⋊C4—24no—
244C4⋊C4—42no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—1881no—
248C4⋊C4—1881no—
249C22⋊C4—1881no—
250C22⋊C4—1881no—
251C22⋊C4—1881no—
252C42—82no—
253C42—1881no—
254C42—1881no—
255C42—1881no—
256C42(C2×D47)⋊C411yescharacteristic
257C42(C2×D47)⋊C411yescharacteristic
258C42#1062533611yescharacteristic
259C42#1062533611yescharacteristic
260C16—944no—
261C23—1881no—
262C23C2×#1062533411yescharacteristic
263Q8—942no—
264Q8—1881no—
265D4—942no—
266D4—1884no—
267D4—1881no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—3762no—
274C2×C4—3762no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4—1884no—
279C2×C4#1309394411yescharacteristic
280C2×C4#1309394411yescharacteristic
281C2×C4#1309394411yescharacteristic
282C2×C4#1309394411yescharacteristic
283C2×C4C2×(C2×D47)⋊C411yescharacteristic
284C2×C4C4×C22⋊D4712yes—
285C2×C4C2×#1062533611yescharacteristic
286C2×C4#1309404412yes—
287C8—21no—
288C8—21no—
289C8C42×D4711yescharacteristic
290C8#1309398111yescharacteristic
291C8C4×D18812yes—
292C22—21no—
293C22—21no—
294C22—3761no—
295C22—3761no—
296C22—1882no—
297C22C2×#1309394411yescharacteristic
298C22C4×#1062533412yes—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—84no—
303C4—3761no—
304C4—3761no—
305C4—1882no—
306C4#1568893212yesdirect product factor
307C4C4×(C2×D47)⋊C411yescharacteristic
308C4#1568911711yescharacteristic
309C4C4×#1062533612yes—
310C2—22no—
311C2—3762no—
312C2C4×#1309394411yescharacteristic
313C2C2×#1568893211yescharacteristic
314C2#2024512311yescharacteristic
subgroupG/H
centerC2×C4#13093944
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC4×#106×C47C2
socleC22×C47C2×#102
prime radicalC2×#13094046C22
cosocleC22×C8×C47C23
hypercenterC4×#106D47
hypocenterC47C4×#360
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
3. C4×#13093964C2semidirect
4. #20241495C2semidirect
5. C4×#106×C47C2semidirect
9. C4×Dic188C4semidirect
10. C4×Dic188C4semidirect
13. C4×D376C4semidirect
14. C4×D376C4semidirect
17. #15688932C4direct (N × H)
40. #13093964C2×C4semidirect
55. #106×C47C2×C4semidirect
98. Dic188C42semidirect
100. D376C42semidirect
146. C4×C47#360semidirect
156. C4×#106D47semidirect
181. C47C4×#360semidirect
209. #106C4×D47semidirect
306. C4#15688932direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130940462
C2×#156889322
C4×#130939642
#202414952
C4×#106×C472
C4×#36047