Finite Group Databasebeta

← #20254073

Subgroups — #20254073

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#15689744C211yesmaximal, characteristic, complemented
2#15689533C211yesmaximal, characteristic, complemented
3#15689510C211yesmaximal, characteristic, complemented
4#15689480C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689367C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689233C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12C4×#10625335C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689079C211yesmaximal, characteristic, complemented
15C47×#540C211yesmaximal, characteristic, complemented
16C2×#10625335C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625329C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094019—21no—
24#13094012C2211yescharacteristic
25#13094010—21no—
26#13094006—21no—
27#13094003C2211yescharacteristic
28#13094002—21no—
29#13093998C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093957C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093935C2211yescharacteristic
45#13093935C2211yescharacteristic
46C4×C47⋊C8C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48#127×C47C2211yescharacteristic
49#125×C47C2211yescharacteristic
50#123×C47—21no—
51#123×C47—21no—
52#121×C47—21no—
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊C4×C47—21no—
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47D411yescharacteristic
84C22⋊C4×C47D411yescharacteristic
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88#10625335—22no—
89#10625335—22no—
90#10625334—22no—
91#10625334—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102#10625329—22no—
103C2×C47⋊C8—22no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116D4×C47—81no—
117D4×C47—81no—
118D4×C47—81no—
119D4×C47—81no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—81no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136D188—21no—
137D188—21no—
138C4×D47—81no—
139Dic94—21no—
140Dic94—21no—
141Dic94—81no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8#4112yes—
145C47⋊C8#4112yes—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3179—471nomaximal, Sylow
172C2×C47—41no—
173C2×C47—81no—
174C2×C47—81no—
175C2×C47#53211yescharacteristic
176C2×C47#57611yescharacteristic
177C2×C47#57711yescharacteristic
178D47—81no—
179#542—471no—
180#540D4711yescharacteristic, complemented
181#501—471no—
182#496—471no—
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×SD16—471no—
196C2×SD16—471no—
197C2×D8—471no—
198C2×D8—471no—
199C2×M16—471no—
200C22×C8—471no—
201C4⋊Q8—471no—
202#127C2×D4711yescharacteristic
203#126—941no—
204#125C2×D4711yescharacteristic
205#124—471no—
206#124—941no—
207#123—21no—
208#123—21no—
209#123—941no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—21no—
213#121—21no—
214#121—471no—
215#121C2×D4711yescharacteristic
216#121C2×D4711yescharacteristic
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4C2×D4711yescharacteristic
220C4×D4C2×D4711yescharacteristic
221#117C2×D4711yescharacteristic
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#97—471no—
236C4×C8—471no—
237C4×C8—471no—
238C2×Q8—471no—
239C2×Q8—941no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—471no—
245C2×D4—941no—
246C2×D4C22×D4711yescharacteristic
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252SD16—942no—
253SD16—942no—
254D8—942no—
255D8—942no—
256M16—942no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—942no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22⋊D4711yescharacteristic
270C4⋊C4C22⋊D4711yescharacteristic
271C4⋊C4C22×D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4C22⋊D4711yescharacteristic
283C22⋊C4C22⋊D4711yescharacteristic
284C42—941no—
285C42C22×D4711yescharacteristic
286C42C22×D4711yescharacteristic
287C23—21no—
288C23—21no—
289C23—941no—
290C23C2×C22⋊D4711yescharacteristic
291Q8—941no—
292Q8—941no—
293Q8—3761no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—941no—
303D4—941no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—3761no—
315C2×C4C2×C22⋊D4711yescharacteristic
316C2×C4C2×C22⋊D4711yescharacteristic
317C2×C4C2×C22⋊D4711yescharacteristic
318C2×C4C2×C22⋊D4711yescharacteristic
319C2×C4C2×C22⋊D4711yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—472no—
322C8—472no—
323C8—941no—
324C8—941no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C22×C22⋊D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4#41×D4711yescharacteristic
349C4#41×D4711yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—3761no—
354C2#1568966911yescharacteristic
355C2#1568992611yescharacteristic
356C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#540C2
socleC22×C47C22×D4
hypercenter#540D47
hypocenterC47#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689533C2semidirect
3. #15689510C2semidirect
4. #15689480C2semidirect
5. #15689469C2semidirect
6. #15689374C2semidirect
7. #15689367C2semidirect
8. #15689357C2semidirect
9. #15689350C2semidirect
10. #15689233C2semidirect
11. #15689223C2semidirect
12. C4×#10625335C2semidirect
13. C4×#10625334C2semidirect
14. #15689079C2semidirect
15. C47×#540C2semidirect
180. #540D47semidirect
194. C47#3179semidirect