Finite Group Databasebeta

← #20253610

Subgroups — #20253610

Order 6016.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689740C211yesmaximal, characteristic
2#15689601C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689444C211yesmaximal, characteristic
5#15689416C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689343C211yesmaximal, characteristic, complemented
8#15689343C211yesmaximal, characteristic, complemented
9#15689279C211yesmaximal, characteristic, complemented
10#15689227C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689215C211yesmaximal, characteristic, complemented
13SD16×Dic47C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#448C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094017—21no—
20#13094011—21no—
21#13094011C2211yescharacteristic
22#13094005—21no—
23#13094003C2211yescharacteristic
24#13094001—21no—
25Q8×Dic47—21no—
26Q8×Dic47—21no—
27Q8×Dic47C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31#13093989C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093983—21no—
34#13093983—21no—
35#13093983C2211yescharacteristic
36#13093983C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47—22no—
60C2×Q8×C47—22no—
61C2×Q8×C47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×D4×C47—21no—
65C2×D4×C47C2311yescharacteristic
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C22×Dic47—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71SD16×C47—22no—
72SD16×C47—22no—
73C2×C8×C47C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47D411yescharacteristic
83C22⋊Dic47D411yescharacteristic
84#10625337—22no—
85#10625337—22no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47D411yescharacteristic
91C4⋊Dic47D411yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110Q8×C47—24no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114Q8×C47#4112yes—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—81no—
118C2×C4×C47—24no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—81no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135Dic94—21no—
136Dic94—21no—
137Dic94—81no—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C4×C47—22no—
150C4×C47—22no—
151C4×C47—21no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C47C2×#4111yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—21no—
159Dic47—41no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163#3121—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47—81no—
166C2×C47#52511yescharacteristic
167C2×C47#57711yescharacteristic
168C2×C47#57811yescharacteristic
169#542—471no—
170#519—471no—
171#485—471no—
172#482—471no—
173#477—471no—
174#475—471no—
175#464—471no—
176#464—471no—
177#451—471no—
178#448D4711yescharacteristic
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312111yescharacteristic, complemented, Sylow
185C22×Q8C2×D4711yescharacteristic
186C2×Q16—471no—
187C2×Q16—471no—
188C2×SD16C2×D4711yescharacteristic
189C2×SD16C2×D4711yescharacteristic
190C4⋊Q8—471no—
191#126—941no—
192#124—471no—
193#124—941no—
194#123—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197#121C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×Q8—941no—
204C4×Q8—941no—
205C4×D4—471no—
206#117—471no—
207#117—471no—
208#117—941no—
209#117—941no—
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8—471no—
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222#102—471no—
223#102—471no—
224C22⋊C8—471no—
225C22⋊C8C2×D4711yescharacteristic
226#97—471no—
227C4×C8—471no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×Q8C22×D4711yescharacteristic
234C2×Q8C22×D4711yescharacteristic
235C2×D4—21no—
236C2×D4C22×D4711yescharacteristic
237C22×C4—21no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240Q16—942no—
241Q16—942no—
242SD16—22no—
243SD16—22no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
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—471no—
263C22⋊C4—471no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—471no—
270C42—471no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42—941no—
277C23—21no—
278C23D4×D4711yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—941no—
283Q8—941no—
284Q8—3761no—
285Q8#1062535212yes—
286Q8#1062535212yes—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—471no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—3761no—
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D4711yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—941no—
323C4—941no—
324C4—941no—
325C4—941no—
326C4—1881no—
327C4—1881no—
328C4—1881no—
329C4—1881no—
330C4C2×#1062535211yescharacteristic
331C4C2×#1062535211yescharacteristic
332C2—41no—
333C2—81no—
334C2#1568962911yescharacteristic
335C2#1568992911yescharacteristic
336C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#448C2
socleC22×C47C22×D4
hypercenter#448D47
hypocenterC47#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #15689601C2semidirect
3. #15689465C2semidirect
5. #15689416C2semidirect
6. #15689406C2semidirect
7. #15689343C2semidirect
8. #15689343C2semidirect
9. #15689279C2semidirect
10. #15689227C2semidirect
11. #15689224C2semidirect
12. #15689215C2semidirect
13. SD16×Dic47C2semidirect
14. #15689181C2semidirect
184. C47#3121semidirect