Finite Group Databasebeta

← #20253673

Subgroups — #20253673

Order 6016.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689726C211yesmaximal, characteristic
2#15689601C211yesmaximal, characteristic, complemented
3#15689448C211yesmaximal, characteristic, complemented
4#15689444C211yesmaximal, characteristic, complemented
5#15689432C211yesmaximal, characteristic, complemented
6#15689428C211yesmaximal, characteristic, complemented
7#15689321C211yesmaximal, characteristic, complemented
8#15689321C211yesmaximal, characteristic, complemented
9#15689262C211yesmaximal, characteristic, complemented
10#15689226C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13#15689208C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#448C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18#13094020C2211yescharacteristic
19#13094015C2211yescharacteristic
20#13094008—21no—
21#13094006—21no—
22#13093998C2211yescharacteristic
23#13093996—21no—
24#13093995—21no—
25Q8×Dic47—21no—
26Q8×Dic47—21no—
27Q8×Dic47C2211yescharacteristic
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093986C2211yescharacteristic
33#13093983—21no—
34#13093983—21no—
35#13093983C2211yescharacteristic
36#13093983C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
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
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C22×Dic47—21no—
72C2×D188C2311yescharacteristic
73C2×C4×D47—21no—
74SD16×C47—22no—
75SD16×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47D411yescharacteristic
83C22⋊Dic47D411yescharacteristic
84#10625336—22no—
85#10625336—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47D411yescharacteristic
94C4⋊Dic47D411yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—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
110C22×D47—21no—
111Q8×C47—24no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47#4112yes—
115Q8×C47#4112yes—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—81no—
119C2×C4×C47—24no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—81no—
128C22⋊D47—81no—
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—21no—
139D188—21no—
140C4×D47—81no—
141C8×C47—21no—
142C8×C47—21no—
143C47⋊C8—21no—
144C47⋊C8—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—22no—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47C2×#4111yescharacteristic
160C4×C47C2×#4111yescharacteristic
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47—21no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168#3126—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47—81no—
171C2×C47#52511yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57711yescharacteristic
174D47—81no—
175#540—471no—
176#519—471no—
177#482—471no—
178#482—471no—
179#479—471no—
180#479—471no—
181#460—471no—
182#460—471no—
183#448—471no—
184#448D4711yescharacteristic, complemented
185#440—471no—
186#440—471no—
187C4×SD16—471no—
188C4×SD16—471no—
189#433—471no—
190C47#312611yescharacteristic, complemented, Sylow
191C22×Q8C2×D4711yescharacteristic
192C2×SD16—471no—
193C2×SD16—471no—
194C2×SD16C2×D4711yescharacteristic
195C2×SD16C2×D4711yescharacteristic
196#127—471no—
197#125—471no—
198#123—941no—
199#123—941no—
200#121—471no—
201#121—941no—
202#121—941no—
203#121C2×D4711yescharacteristic
204C4×Q8—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×Q8—941no—
209C4×Q8—941no—
210C4×D4—471no—
211C4×D4—471no—
212#117—471no—
213#117—471no—
214#117—941no—
215#117—941no—
216#107—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221C4⋊C8—471no—
222#103—471no—
223#103—471no—
224#103C2×D4711yescharacteristic
225#103C2×D4711yescharacteristic
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8—471no—
231C22⋊C8C2×D4711yescharacteristic
232#97—471no—
233C4×C8—471no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—21no—
237C2×Q8C22×D4711yescharacteristic
238C2×Q8C22×D4711yescharacteristic
239C2×D4—21no—
240C2×D4—471no—
241C2×D4—941no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4C22×D4711yescharacteristic
245C22×C4—21no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4C22×D4711yescharacteristic
249SD16—22no—
250SD16—22no—
251SD16—942no—
252SD16—942no—
253C2×C8—471no—
254C2×C8—471no—
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—471no—
271C22⋊C4—471no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C42—471no—
277C42—471no—
278C42—941no—
279C42—941no—
280C42—941no—
281C42—941no—
282C42—941no—
283C23—21no—
284C23—941no—
285C23D4×D4711yescharacteristic
286Q8—24no—
287Q8—21no—
288Q8—21no—
289Q8#1062535212yes—
290Q8#1062535212yes—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—941no—
295D4—941no—
296D4—3761no—
297D4—3761no—
298D4—3761no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—471no—
306C2×C4—471no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4D4×D4711yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—941no—
319C8—941no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22C2×D4×D4711yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—941no—
335C4—941no—
336C4—941no—
337C4—941no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4C2×#1062535211yescharacteristic
342C4C2×#1062535211yescharacteristic
343C2—41no—
344C2—81no—
345C2—3761no—
346C2#1568962911yescharacteristic
347C2#1568992911yescharacteristic
348C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#448C2
socleC22×C47C22×D4
hypercenter#448D47
hypocenterC47#3126
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. #15689448C2semidirect
4. #15689444C2semidirect
5. #15689432C2semidirect
6. #15689428C2semidirect
7. #15689321C2semidirect
8. #15689321C2semidirect
9. #15689262C2semidirect
10. #15689226C2semidirect
11. #15689224C2semidirect
12. SD16×Dic47C2semidirect
13. #15689208C2semidirect
14. #15689181C2semidirect
15. C47×#448C2semidirect
184. #448D47semidirect
190. C47#3126semidirect