Finite Group Databasebeta

← #20255978

Subgroups — #20255978

Order 6016.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689837C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic, complemented
3#15689520C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689440C211yesmaximal, characteristic, complemented
7#15689439C211yesmaximal, characteristic, complemented
8#15689411C211yesmaximal, characteristic, complemented
9#15689401C211yesmaximal, characteristic, complemented
10#15689373C211yesmaximal, characteristic, complemented
11D8×Dic47C211yesmaximal, characteristic, complemented
12#15689199C211yesmaximal, characteristic, complemented
13#15689165C211yesmaximal, characteristic, complemented
14#15689162C211yesmaximal, characteristic, complemented
15C47×#469C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625324C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094011—21no—
21#13094010—21no—
22#13094006—21no—
23#13094005—21no—
24#13094001—21no—
25#13093996—21no—
26#13093995C2211yescharacteristic
27#13093995C2211yescharacteristic
28D4×Dic47C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30C4×C22⋊D47C2211yescharacteristic
31#13093983C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093980—21no—
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093955C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×D8×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47D411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70#10625352—44no—
71C2×C4×D47—21no—
72C2×C4×D47C2311yescharacteristic
73C2×Dic94—21no—
74C2×Dic94—21no—
75D8×C47—22no—
76M16×C47—22no—
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47D411yescharacteristic
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625324—22no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47C2×D411yescharacteristic
109C22×D47C2×D411yescharacteristic
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—21no—
114D4×C47—42no—
115D4×C47—81no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—22no—
123C22⋊D47—42no—
124C22⋊D47—81no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—42no—
130C2×Dic47—42no—
131C2×Dic47—42no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—42no—
138Dic94—42no—
139Dic94—81no—
140C8×C47—21no—
141C8×C47#4112yescomplemented
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—21no—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47C2×#4111yescharacteristic
161C4×C472−1+411yescharacteristic
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47AGL(1,ℤ/8)12yes—
169#3354—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47—81no—
172C2×C47—81no—
173C2×C47#54711yescharacteristic
174C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C47#57711yescharacteristic
176D47—41no—
177#555—471no—
178#547—471no—
179#498—471no—
180#482—471no—
181#482—471no—
182#481—471no—
183#481—471no—
184#476—471no—
185#474—471no—
186#469—471no—
187#469D4711yescharacteristic, complemented
188C4×D8—471no—
189#436—471no—
190#428—471no—
191#428—471no—
192C47#335411yescharacteristic, complemented, Sylow
193C2×#41—941no—
194C2×D8C2×D4711yescharacteristic
195C2×M16—471no—
196C2×M16C2×D4711yescharacteristic
197C4⋊Q8—471no—
198C4⋊Q8—471no—
199#124—941no—
200#124—941no—
201#123—941no—
202#123—941no—
203C22⋊Q8—941no—
204#121—471no—
205#121—471no—
206#121—941no—
207#121C2×D4711yescharacteristic
208#121C2×D4711yescharacteristic
209C4×D4—471no—
210C4×D4—471no—
211C4×D4—471no—
212#117—471no—
213#117—471no—
214#117—941no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217#107—471no—
218#107—471no—
219#107—471no—
220#106—471no—
221#106—471no—
222#106—471no—
223#106—471no—
224#106—471no—
225#106C2×D4711yescharacteristic
226C4⋊C8—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102C2×D4711yescharacteristic
232#102C2×D4711yescharacteristic
233C22⋊C8—471no—
234C22⋊C8—471no—
235C4×C8—471no—
236#41—1884no—
237C2×Q8—941no—
238C2×Q8—941no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—471no—
242C2×D4—941no—
243C2×D4—941no—
244C2×D4C22×D4711yescharacteristic
245C2×D4C22×D4711yescharacteristic
246C22×C4—471no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252D8—22no—
253M16—22no—
254M16—942no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4C22×D4711yescharacteristic
269C4⋊C4C22×D4711yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—471no—
273C22⋊C4—471no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—471no—
281C42—941no—
282C42—941no—
283C23—21no—
284C23—21no—
285C23—471no—
286C23D4×D4711yescharacteristic
287Q8—3761no—
288Q8—1882no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—81no—
295D4—942no—
296D4—3761no—
297D4—1882no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—471no—
303C2×C4—471no—
304C2×C4—471no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4D4×D4711yescharacteristic
316C2×C4C23×D4711yescharacteristic
317C8—21no—
318C8—941no—
319C8—941no—
320C8#1062535212yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—941no—
331C22—941no—
332C22—941no—
333C22C2×D4×D4711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—472no—
338C4—941no—
339C4—941no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4—1881no—
344C4C2×#1062535211yescharacteristic
345C4#1309407111yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—1881no—
350C2#1568977311yescharacteristic
351C2AGL(1,ℤ/8)×D4711yescharacteristic
352C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3354
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #15689837C2semidirect
2. #15689773C2semidirect
3. #15689520C2semidirect
4. #15689445C2semidirect
5. #15689444C2semidirect
6. #15689440C2semidirect
7. #15689439C2semidirect
8. #15689411C2semidirect
9. #15689401C2semidirect
10. #15689373C2semidirect
11. D8×Dic47C2semidirect
12. #15689199C2semidirect
13. #15689165C2semidirect
14. #15689162C2semidirect
15. C47×#469C2semidirect
141. C8×C47#41semidirect
187. #469D47semidirect
192. C47#3354semidirect
320. C8#10625352semidirect