Finite Group Databasebeta

← #20256101

Subgroups — #20256101

Order 6016.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689842C211yesmaximal, characteristic, complemented
2D4×Dic94C211yesmaximal, characteristic, complemented
3#15689482C211yesmaximal, characteristic, complemented
4#15689481C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689416C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic
10#15689326C211yesmaximal, characteristic, complemented
11#15689252C211yesmaximal, characteristic, complemented
12#15689224C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14D8×Dic47C211yesmaximal, characteristic
15C47×#463C211yesmaximal, characteristic
16C22×Dic94—21no—
17C2×#10625335C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022C2211yescharacteristic
22#13094017—21no—
23#13094017—21no—
24#13094011C2211yescharacteristic
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28#13094001—21no—
29Q8×Dic47C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35#13093980—21no—
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54#124×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—44no—
70C2×Dic94D411yescharacteristic
71C2×Dic94C2311yescharacteristic
72SD16×C47—22no—
73D8×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C42×C47C2311yescharacteristic
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86#10625335—22no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47D411yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C23×C47—21no—
107C23×C47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47#4112yes—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—42no—
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—42no—
125C2×Dic47—42no—
126C2×Dic47—42no—
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131Dic94—22no—
132Dic94—21no—
133Dic94—21no—
134Dic94—42no—
135Dic94—42no—
136Dic94—42no—
137C8×C47—21no—
138C8×C47—21no—
139C47⋊C8—21no—
140C47⋊C8—21no—
141C22×C47—22no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47C2×#4111yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—21no—
155Dic47—21no—
156Dic47—21no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47AGL(1,ℤ/8)12yes—
162#3367—471nomaximal, Sylow
163C2×C47—42no—
164C2×C47—81no—
165C2×C47#54811yescharacteristic
166C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C47#57811yescharacteristic
168#556—471no—
169D4×Q8—471no—
170#489—471no—
171#489—471no—
172#487—471no—
173#477—471no—
174#477—471no—
175#474—471no—
176#463—471no—
177#463D4711yescharacteristic
178#461—471no—
179#446—471no—
180#440—471no—
181#440—471no—
182C4×D8—471no—
183C47#336711yescharacteristic, complemented, Sylow
184C22×Q8—941no—
185C2×SD16—471no—
186C2×SD16C2×D4711yescharacteristic
187C2×D8C2×D4711yescharacteristic
188C4⋊Q8—471no—
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191C4⋊Q8—471no—
192#126—941no—
193#126—941no—
194#124—471no—
195#124C2×D4711yescharacteristic
196C22⋊Q8—941no—
197C22⋊Q8—941no—
198C22⋊Q8—941no—
199C22⋊Q8—941no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—471no—
206C4×D4C2×D4711yescharacteristic
207#117—941no—
208#107—471no—
209#107—471no—
210#107—471no—
211C4⋊C8—471no—
212C4⋊C8—471no—
213C4⋊C8C2×D4711yescharacteristic
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103C2×D4711yescharacteristic
220#102—471no—
221#102—471no—
222#102—471no—
223#102C2×D4711yescharacteristic
224#97—471no—
225#97—471no—
226C4×C8—471no—
227C2×Q8—471no—
228C2×Q8—471no—
229C2×Q8—941no—
230C2×Q8—941no—
231C2×Q8—941no—
232C2×Q8—1884no—
233C2×Q8C22×D4711yescharacteristic
234C2×D4C22×D4711yescharacteristic
235C2×D4C22×D4711yescharacteristic
236C22×C4—21no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240SD16—22no—
241SD16—942no—
242D8—22no—
243C2×C8—471no—
244C2×C8—471no—
245C2×C8C22×D4711yescharacteristic
246C2×C8C22×D4711yescharacteristic
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—471no—
270C42—471no—
271C42—941no—
272C42—941no—
273C42C22×D4711yescharacteristic
274C23—21no—
275C23—21no—
276Q8—21no—
277Q8—21no—
278Q8—942no—
279Q8—941no—
280Q8—941no—
281Q8—1882no—
282Q8—1882no—
283Q8—1882no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4#1062535212yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4D4×D4711yescharacteristic
303C2×C4D4×D4711yescharacteristic
304C2×C4C23×D4711yescharacteristic
305C8—21no—
306C8—21no—
307C8—941no—
308C8—941no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C2×D4×D4711yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—472no—
321C4—941no—
322C4—941no—
323C4—941no—
324C4—1881no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C4C2×#1062535211yescharacteristic
329C4#1309407111yescharacteristic
330C2—42no—
331C2—81no—
332C2#1568977911yescharacteristic
333C2AGL(1,ℤ/8)×D4711yescharacteristic
334C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#463C2
socleC22×C47C22×D4
hypercenter#463D47
hypocenterC47#3367
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #15689842C2semidirect
2. D4×Dic94C2semidirect
3. #15689482C2semidirect
4. #15689481C2semidirect
5. #15689472C2semidirect
6. #15689419C2semidirect
7. #15689416C2semidirect
8. #15689401C2semidirect
10. #15689326C2semidirect
11. #15689252C2semidirect
12. #15689224C2semidirect
13. #15689223C2semidirect
183. C47#3367semidirect