Finite Group Databasebeta

← #20256009

Subgroups — #20256009

Order 6016.

354 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#15689837C211yesmaximal, characteristic
2#15689831C211yesmaximal, characteristic, complemented
3#15689527C211yesmaximal, characteristic, complemented
4#15689462C211yesmaximal, characteristic, complemented
5#15689461C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689434C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689411C211yesmaximal, characteristic, complemented
10#15689366C211yesmaximal, characteristic, complemented
11SD16×Dic47C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689164C211yesmaximal, characteristic, complemented
15C47×#468C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094014—21no—
20#13094011—21no—
21#13094010—21no—
22#13094004—21no—
23#13094001—21no—
24#13094000C2211yescharacteristic
25#13093996—21no—
26#13093995C2211yescharacteristic
27Q8×Dic47C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29C4×C22⋊D47C2211yescharacteristic
30(C22⋊D47)⋊C4—21no—
31#13093983C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093980—21no—
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C2×C4×D47—21no—
68C2×C4×D47C2311yescharacteristic
69C2×Dic94—21no—
70C2×Dic94—21no—
71SD16×C47—22no—
72M16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C22⋊C4×C47—21no—
79C22⋊C4×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47D411yescharacteristic
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4D411yescharacteristic
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C23×C47—21no—
106C23×C47C2×D411yescharacteristic
107C22×D47C2×D411yescharacteristic
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—81no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—22no—
121C22⋊D47—81no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—42no—
127C2×Dic47—81no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—81no—
134Dic94—81no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—21no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47—41no—
154C4×C47C2×#4111yescharacteristic
155C4×C472−1+411yescharacteristic
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47#13712yes—
163#3357—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47—81no—
166C2×C47#54711yescharacteristic
167C2×C47C2×#13711yescharacteristic
168C2×C47#57611yescharacteristic
169D47—41no—
170#555—471no—
171#554—471no—
172#500—471no—
173#485—471no—
174#485—471no—
175#480—471no—
176#480—471no—
177#477—471no—
178#476—471no—
179#468—471no—
180#468D4711yescharacteristic, complemented
181C4×SD16—471no—
182#436—471no—
183#428—471no—
184#428—471no—
185C47#335711yescharacteristic, complemented, Sylow
186C2×SD16C2×D4711yescharacteristic
187C2×M16—471no—
188C2×M16C2×D4711yescharacteristic
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191#125—941no—
192#124—941no—
193#124—941no—
194C22⋊Q8—471no—
195C22⋊Q8—941no—
196C22⋊Q8—941no—
197C22⋊Q8C2×D4711yescharacteristic
198#121—471no—
199#121—941no—
200#121C2×D4711yescharacteristic
201C4×Q8—471no—
202C4×D4—471no—
203C4×D4—471no—
204C4×D4—941no—
205#117—471no—
206#117—471no—
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210#107—471no—
211#107—471no—
212#107—471no—
213#107—471no—
214#107—471no—
215#107C2×D4711yescharacteristic
216#106—471no—
217#106—471no—
218#106—471no—
219C4⋊C8—471no—
220#103—471no—
221#103—471no—
222#103C2×D4711yescharacteristic
223#102—471no—
224#102—471no—
225#102C2×D4711yescharacteristic
226C22⋊C8—471no—
227C22⋊C8—471no—
228C4×C8—471no—
229C2×Q8—941no—
230C2×Q8—941no—
231C2×Q8C22×D4711yescharacteristic
232C2×D4—21no—
233C2×D4—471no—
234C2×D4—941no—
235C2×D4C22×D4711yescharacteristic
236C22×C4—471no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4C22×D4711yescharacteristic
241SD16—22no—
242M16—22no—
243M16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—471no—
252C4⋊C4—471no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—471no—
265C22⋊C4—471no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C42—471no—
272C42—941no—
273C42—941no—
274C42—941no—
275C23—21no—
276C23—471no—
277C23D4×D4711yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—3761no—
281Q8—3761no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—942no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—471no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—3761no—
302C2×C4—3761no—
303C2×C4—1882no—
304C2×C4D4×D4711yescharacteristic
305C2×C4C23×D4711yescharacteristic
306C8—21no—
307C8—941no—
308C8—941no—
309C8#1062535212yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—941no—
317C22—941no—
318C22—941no—
319C22C2×D4×D4711yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—472no—
325C4—941no—
326C4—941no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4—1881no—
331C4C2×#1062535211yescharacteristic
332C4#1309407111yescharacteristic
333C2—41no—
334C2—81no—
335C2—1881no—
336C2#1568977311yescharacteristic
337C2#137×D4711yescharacteristic
338C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#468C2
socleC22×C47C22×D4
hypercenter#468D47
hypocenterC47#3357
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #15689831C2semidirect
3. #15689527C2semidirect
4. #15689462C2semidirect
5. #15689461C2semidirect
6. #15689435C2semidirect
7. #15689434C2semidirect
8. #15689416C2semidirect
9. #15689411C2semidirect
10. #15689366C2semidirect
11. SD16×Dic47C2semidirect
12. #15689199C2semidirect
13. #15689165C2semidirect
14. #15689164C2semidirect
15. C47×#468C2semidirect
180. #468D47semidirect
185. C47#3357semidirect