Finite Group Databasebeta

← #20254068

Subgroups — #20254068

Order 6016.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689742C211yesmaximal, characteristic, complemented
2#15689727C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689477C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic, complemented
7#15689366C211yesmaximal, characteristic, complemented
8#15689356C211yesmaximal, characteristic, complemented
9#15689349C211yesmaximal, characteristic, complemented
10#15689235C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12SD16×Dic47C211yesmaximal, characteristic, complemented
13D8×Dic47C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#496C211yesmaximal, characteristic, complemented
16C2×#10625324C2211yescharacteristic
17C2×C8×D47C2211yescharacteristic
18#13094024C2211yescharacteristic
19#13094017—21no—
20#13094016C2211yescharacteristic
21#13094010—21no—
22#13094008—21no—
23#13094005—21no—
24#13094005—21no—
25#13094001—21no—
26#13094000C2211yescharacteristic
27#13093996—21no—
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093995C2211yescharacteristic
31#13093995C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35D4×Dic47C2211yescharacteristic
36#13093981C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56#127×C47C2211yescharacteristic
57#124×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C2×C4×D47C2311yescharacteristic
72C2×Dic94—21no—
73SD16×C47—22no—
74SD16×C47—22no—
75D8×C47—22no—
76D8×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4D411yescharacteristic
101Dic47⋊C4D411yescharacteristic
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—21no—
113Q8×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47—21no—
120D4×C47—81no—
121D4×C47—81no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2411yescharacteristic
126C22⋊D47—81no—
127C22⋊D47—81no—
128C22⋊D47—81no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C2×Dic47C2×D411yescharacteristic
139C4×D47—21no—
140C4×D47—21no—
141Dic94—81no—
142C8×C47#4112yes—
143C8×C47#4112yes—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47C2×#4111yescharacteristic
163C4×C47C2×#4111yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3179—471nomaximal, Sylow
172C2×C47—81no—
173C2×C47—81no—
174C2×C47—81no—
175C2×C47#53211yescharacteristic
176C2×C47#57611yescharacteristic
177C2×C47#57711yescharacteristic
178D47—41no—
179#542—471no—
180#540—471no—
181#501—471no—
182#496D4711yescharacteristic, complemented
183#488—471no—
184#486—471no—
185#469—471no—
186#468—471no—
187#466—471no—
188#465—471no—
189#442—471no—
190#440—471no—
191C4×SD16—471no—
192C4×D8—471no—
193#405—471no—
194C47#317911yescharacteristic, complemented, Sylow
195C2×SD16C2×D4711yescharacteristic
196C2×SD16C2×D4711yescharacteristic
197C2×D8C2×D4711yescharacteristic
198C2×D8C2×D4711yescharacteristic
199C2×M16—471no—
200C22×C8—471no—
201C4⋊Q8—471no—
202#127C2×D4711yescharacteristic
203#126—941no—
204#125—471no—
205#124—941no—
206#124C2×D4711yescharacteristic
207#123—941no—
208#123—941no—
209#123—941no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—471no—
214#121—471no—
215#121—941no—
216#121—941no—
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221#117—471no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226#103—471no—
227#103—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#97—471no—
235#97C2×D4711yescharacteristic
236C4×C8—471no—
237C4×C8—471no—
238C2×Q8—941no—
239C2×Q8C22×D4711yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4C22×D4711yescharacteristic
246C2×D4C22×D4711yescharacteristic
247C2×D4C22×D4711yescharacteristic
248C22×C4—471no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—942no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—942no—
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—471no—
276C22⋊C4—471no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C42—471no—
285C42—941no—
286C42C22×D4711yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—471no—
291Q8—21no—
292Q8—21no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—471no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—3761no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—941no—
322C8—941no—
323C8#1062535212yes—
324C8#1062535212yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—941no—
335C22—941no—
336C22—941no—
337C22C2×D4×D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—941no—
342C4—941no—
343C4—941no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4C2×#1062535211yescharacteristic
349C4C2×#1062535211yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—1881no—
354C2#1568967111yescharacteristic
355C2#1568992711yescharacteristic
356C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#496C2
socleC22×C47C22×D4
hypercenter#496D47
hypocenterC47#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #15689742C2semidirect
2. #15689727C2semidirect
3. #15689532C2semidirect
4. #15689477C2semidirect
5. #15689469C2semidirect
6. #15689373C2semidirect
7. #15689366C2semidirect
8. #15689356C2semidirect
9. #15689349C2semidirect
10. #15689235C2semidirect
11. #15689224C2semidirect
12. SD16×Dic47C2semidirect
13. D8×Dic47C2semidirect
14. #15689080C2semidirect
15. C47×#496C2semidirect
182. #496D47semidirect
194. C47#3179semidirect