Finite Group Databasebeta

← #20256217

Subgroups — #20256217

Order 6016.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689846C211yesmaximal, characteristic, complemented
2#15689833C211yesmaximal, characteristic, complemented
3#15689492C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic, complemented
5#15689478C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689424C211yesmaximal, characteristic, complemented
8#15689409C211yesmaximal, characteristic, complemented
9#15689339C211yesmaximal, characteristic
10#15689339C211yesmaximal, characteristic
11#15689329C211yesmaximal, characteristic, complemented
12#15689236C211yesmaximal, characteristic
13#15689225C211yesmaximal, characteristic, complemented
14C4×#10625325C211yesmaximal, characteristic, complemented
15C47×#446C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×D376C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094019—21no—
22#13094019—21no—
23#13094016C2211yescharacteristic
24#13094016C2211yescharacteristic
25#13094012C2211yescharacteristic
26#13094012C2211yescharacteristic
27#13094002—21no—
28#13094002—21no—
29#13094000—21no—
30#13094000—21no—
31C4×Dic94C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic
37#13093982—21no—
38C4⋊C4×D47—21no—
39#13093958C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C4×Q8×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×D188C2311yescharacteristic
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94C2311yescharacteristic
68C2×Dic94C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C4⋊C4×C47D411yescharacteristic
76C42×C47C2311yescharacteristic
77C42×C47C2311yescharacteristic
78C42×C47C2311yescharacteristic
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102D376—22no—
103#10625325—22no—
104#10625325—22no—
105C22×D47—21no—
106C22×D47—21no—
107Q8×C47—41no—
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121D188—21no—
122D188—21no—
123D188—21no—
124D188#4112yes—
125C4×D47—42no—
126C4×D47—42no—
127C4×D47—81no—
128C4×D47—81no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—21no—
133Dic94—81no—
134C8×C47—21no—
135C8×C47—21no—
136C8×C47—21no—
137C8×C47—21no—
138C22×C47C22×D411yescharacteristic
139C2×D47—22no—
140C2×D47—41no—
141C2×D47—41no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47C2×#4111yescharacteristic
152C4×C472−1+411yescharacteristic
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#3376—471nomaximal, Sylow
160C2×C47#54811yescharacteristic
161C2×C47#57511yescharacteristic
162C2×C47#57711yescharacteristic
163D47—42no—
164D47—81no—
165#556—471no—
166#554—471no—
167#491—471no—
168#489—471no—
169#488—471no—
170#479—471no—
171#478—471no—
172#475—471no—
173#463—471no—
174#463—471no—
175#461—471no—
176#446D4711yescharacteristic, complemented
177#442—471no—
178#440—471no—
179C4×SD16—471no—
180C47#337611yescharacteristic, complemented, Sylow
181C2×SD16—471no—
182C2×SD16—471no—
183C2×D8—471no—
184C4⋊Q8—471no—
185C4⋊Q8—471no—
186#126—941no—
187#126—941no—
188#125—471no—
189#125—471no—
190#124—471no—
191#124—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C22⋊Q8—941no—
196C4×Q8—471no—
197C4×Q8—471no—
198C4×Q8C2×D4711yescharacteristic
199C4×D4—471no—
200C4×D4—471no—
201C4×D4—471no—
202C4×D4—471no—
203#117—941no—
204C2×C4⋊C4—941no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8C2×D4711yescharacteristic
209C4⋊C8C2×D4711yescharacteristic
210C4⋊C8C2×D4711yescharacteristic
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#102—471no—
218#102—471no—
219#102—471no—
220#102—471no—
221#97C2×D4711yescharacteristic
222#97C2×D4711yescharacteristic
223C4×C8C2×D4711yescharacteristic
224C2×Q8—471no—
225C2×Q8—471no—
226C2×Q8—941no—
227C2×Q8D18811yescharacteristic
228C2×D4—471no—
229C2×D4—471no—
230C22×C4—941no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4—941no—
234SD16—942no—
235SD16—942no—
236D8—942no—
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C2×C8C22×D4711yescharacteristic
240C2×C8C22×D4711yescharacteristic
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4D18811yescharacteristic
255C4⋊C4D18811yescharacteristic
256C4⋊C4D18811yescharacteristic
257C22⋊C4—941no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C42—941no—
266C42—941no—
267C42C22×D4711yescharacteristic
268C42C22×D4711yescharacteristic
269C42C22×D4711yescharacteristic
270C23—941no—
271C23—941no—
272Q8—41no—
273Q8—941no—
274Q8—941no—
275Q8—941no—
276Q8—941no—
277Q8—3761no—
278D4—472no—
279D4—941no—
280D4—941no—
281D4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—3761no—
289C2×C4—3761no—
290C2×C4—1882no—
291C2×C4—1882no—
292C2×C4C2×D18811yescharacteristic
293C2×C4C2×D18811yescharacteristic
294C2×C4C2×D18811yescharacteristic
295C2×C4C2×D18811yescharacteristic
296C2×C4C2×D18811yescharacteristic
297C2×C4C2×D18811yescharacteristic
298C2×C4C23×D4711yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—942no—
304C22—1881no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22C22×D18811yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—1881no—
317C4—1881no—
318C4—1881no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4#41×D4711yescharacteristic
323C4#1309407211yescharacteristic
324C2—3761no—
325C2—1882no—
326C2#1568978511yescharacteristic
327C2#1568992311yescharacteristic
328C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #15689846C2semidirect
2. #15689833C2semidirect
3. #15689492C2semidirect
4. #15689483C2semidirect
5. #15689478C2semidirect
6. #15689431C2semidirect
7. #15689424C2semidirect
8. #15689409C2semidirect
11. #15689329C2semidirect
13. #15689225C2semidirect
14. C4×#10625325C2semidirect
15. C47×#446C2semidirect
176. #446D47semidirect
180. C47#3376semidirect