Finite Group Databasebeta

← #20255867

Subgroups — #20255867

Order 6016.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689819C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689456C211yesmaximal, characteristic, complemented
5#15689441C211yesmaximal, characteristic, complemented
6#15689436C211yesmaximal, characteristic, complemented
7#15689430C211yesmaximal, characteristic, complemented
8#15689400C211yesmaximal, characteristic, complemented
9#15689371C211yesmaximal, characteristic, complemented
10#15689354C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689163C211yesmaximal, characteristic, complemented
14C2×#13093957C211yesmaximal, characteristic, complemented
15C47×#554C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13094019—21no—
20#13094016C2211yescharacteristic
21#13094006—21no—
22#13093998C2211yescharacteristic
23#13093998C2211yescharacteristic
24#13093996—21no—
25C4×D188C2211yescharacteristic
26(C22⋊D47)⋊C4—21no—
27#13093983C2211yescharacteristic
28C2×C4⋊Dic47C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093957C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093955C2211yescharacteristic
37#13093955C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#125×C47—21no—
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47D411yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47D411yescharacteristic
84C22⋊C4×C47D411yescharacteristic
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625336—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99#10625329—22no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47C2×D411yescharacteristic
106C23×C47C2×D411yescharacteristic
107C22×D47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110Q8×C47—81no—
111D4×C47—22no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—81no—
121C2×C4×C47—81no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—42no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—81no—
133D188—21no—
134D188—21no—
135C4×D47—81no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C47⋊C8—21no—
139C47⋊C8#4112yes—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47#13712yes—
146C22×C47C22×D411yescharacteristic
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C472−1+411yescharacteristic
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3346—471nomaximal, Sylow
164C2×C47—22no—
165C2×C47—41no—
166C2×C47#54711yescharacteristic
167C2×C47C2×#13711yescharacteristic
168C2×C47#57611yescharacteristic
169D47—81no—
170#554D4711yescharacteristic, complemented
171#553—471no—
172#501—471no—
173#485—471no—
174#484—471no—
175#481—471no—
176#480—471no—
177#479—471no—
178#474—471no—
179#468—471no—
180#465—471no—
181#440—471no—
182#435—471no—
183#428—471no—
184C2×#107—471no—
185C47#334611yescharacteristic, complemented, Sylow
186C2×SD16—471no—
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8C2×D4711yescharacteristic
190#126—941no—
191#125—21no—
192#125—471no—
193#123—941no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D4711yescharacteristic
197C22⋊Q8C2×D4711yescharacteristic
198#121—471no—
199#121—471no—
200#121—941no—
201C4×Q8C2×D4711yescharacteristic
202C4×D4—21no—
203C4×D4—471no—
204C4×D4—941no—
205C4×D4C2×D4711yescharacteristic
206#117—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4C2×D4711yescharacteristic
209C2×C4⋊C4C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107—471no—
216#106—471no—
217#106—471no—
218#106—471no—
219C4⋊C8—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#102—471no—
224#102—471no—
225#102—471no—
226C22⋊C8—471no—
227C22⋊C8—471no—
228#97—471no—
229C2×Q8—21no—
230C2×Q8C22×D4711yescharacteristic
231C2×D4—471no—
232C2×D4—941no—
233C2×D4—941no—
234C2×D4C22⋊D4711yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240C22×C4C22×D4711yescharacteristic
241SD16—942no—
242M16—942no—
243C2×C8—471no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8—471no—
247C2×C8—942no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4C22⋊D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C4⋊C4C22×D4711yescharacteristic
263C4⋊C4C22×D4711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4C22⋊D4711yescharacteristic
271C22⋊C4C22⋊D4711yescharacteristic
272C42—21no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—941no—
276C23C2×C22⋊D4711yescharacteristic
277C23C2×C22⋊D4711yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—941no—
283D4—941no—
284D4—3761no—
285D4—1882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4C2×C22⋊D4711yescharacteristic
302C2×C4C2×C22⋊D4711yescharacteristic
303C2×C4C2×C22⋊D4711yescharacteristic
304C2×C4C2×C22⋊D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C8—472no—
307C8—941no—
308C8—941no—
309C8—941no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—1881no—
316C22—1881no—
317C22—1881no—
318C22#1309405512yes—
319C22C22×C22⋊D4711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4#41×D4711yescharacteristic
332C4#1309407111yescharacteristic
333C2—22no—
334C2—41no—
335C2—3761no—
336C2#1568977211yescharacteristic
337C2C2×#1309405511yescharacteristic
338C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#554C2
socleC22×C47C22×D4
hypercenter#554D47
hypocenterC47#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #15689529C2semidirect
3. #15689461C2semidirect
4. #15689456C2semidirect
5. #15689441C2semidirect
6. #15689436C2semidirect
7. #15689430C2semidirect
8. #15689400C2semidirect
9. #15689371C2semidirect
10. #15689354C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689163C2semidirect
14. C2×#13093957C2semidirect
15. C47×#554C2semidirect
170. #554D47semidirect
185. C47#3346semidirect