Finite Group Databasebeta

← #20253354

Subgroups — #20253354

Order 6016.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689696C211yesmaximal, characteristic
2#15689603C211yesmaximal, characteristic
3#15689467C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689462C211yesmaximal, characteristic, complemented
6#15689460C211yesmaximal, characteristic, complemented
7#15689456C211yesmaximal, characteristic, complemented
8#15689454C211yesmaximal, characteristic, complemented
9#15689452C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic, complemented
11#15689158C211yesmaximal, characteristic, complemented
12#15689130C211yesmaximal, characteristic, complemented
13#103×D47C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic
15C47×#485C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023—21no—
21#13094010—21no—
22#13094009—21no—
23#13094006—21no—
24#13094004C2211yescharacteristic
25#13094003C2211yescharacteristic
26#13094000C2211yescharacteristic
27C4×Dic94—21no—
28C4×D188—21no—
29(C22⋊D47)⋊C4—21no—
30(C22⋊D47)⋊C4—21no—
31#13093982C2211yescharacteristic
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34C2×C4⋊Dic47C2211yescharacteristic
35C4⋊C4×D47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47D411yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C22×Dic47—21no—
64Q8×D47—22no—
65Q8×D47—22no—
66#10625350—22no—
67#10625350—22no—
68C2×D188D411yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47C2311yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94D411yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C22⋊Dic47—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—22no—
107C8×D47—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47C2×D411yescharacteristic
110C22×D47C2×D411yescharacteristic
111Q8×C47—21no—
112Q8×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—22no—
122C22⋊D47—22no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—81no—
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130D188—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—42no—
134C4×D47—81no—
135C4×D47—81no—
136C4×D47#4112yes—
137C4×D47#4112yes—
138Dic94—22no—
139Dic94—21no—
140Dic94—21no—
141Dic94—42no—
142C8×C47—21no—
143C8×C47—21no—
144C47⋊C8—21no—
145C47⋊C8—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47C22×D411yescharacteristic
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C2×D47#12312yes—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#4111yescharacteristic
162C4×C47C2×#4111yescharacteristic
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47#12312yes—
169#3097—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47C2×#12311yescharacteristic
172C2×C47#57711yescharacteristic
173C2×C47#57811yescharacteristic
174D47—22no—
175D47—41no—
176#536—471no—
177#520—471no—
178#485—471no—
179#485—471no—
180#485—471no—
181#485D4711yescharacteristic, complemented
182#484—471no—
183#484—471no—
184#483—471no—
185#483—471no—
186#428—471no—
187#427—471no—
188#419—471no—
189C2×#103—471no—
190#408—471no—
191C47#309711yescharacteristic, complemented, Sylow
192C2×#41—471no—
193C22×Q8—471no—
194C2×M16—471no—
195C22×C8—471no—
196C4⋊Q8—941no—
197#124—941no—
198#123—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8C2×D4711yescharacteristic
204C4×Q8—941no—
205C4×D4—941no—
206C4×D4—941no—
207C4×D4—941no—
208#117—471no—
209#117—471no—
210#117—471no—
211#117C2×D4711yescharacteristic
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215#107—471no—
216#107—471no—
217#107—471no—
218#107C2×D4711yescharacteristic
219#106—471no—
220#106—471no—
221#106—471no—
222#106C2×D4711yescharacteristic
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103C2×D4711yescharacteristic
230#103C2×D4711yescharacteristic
231C22⋊C8—471no—
232C22⋊C8—471no—
233C22⋊C8—471no—
234C22⋊C8C2×D4711yescharacteristic
235#41—942no—
236#41—942no—
237C2×Q8—471no—
238C2×Q8—471no—
239C2×Q8—941no—
240C2×Q8—942no—
241C2×Q8—942no—
242C2×Q8C22×D4711yescharacteristic
243C2×D4—471no—
244C2×D4—471no—
245C2×D4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4C22×D4711yescharacteristic
253M16—942no—
254C2×C8—471no—
255C2×C8—471no—
256C2×C8—942no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—471no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4C22×D4711yescharacteristic
270C4⋊C4C22×D4711yescharacteristic
271C4⋊C4C22×D4711yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C42—21no—
281C42—941no—
282C42—941no—
283C42—941no—
284C23—471no—
285C23—471no—
286C23D4×D4711yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—942no—
290Q8—941no—
291Q8—941no—
292Q8—1882no—
293D4—942no—
294D4—942no—
295D4—942no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—471no—
303C2×C4—472no—
304C2×C4—472no—
305C2×C4—471no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4—3761no—
315C2×C4—1882no—
316C2×C4D4×D4711yescharacteristic
317C2×C4C23×D4711yescharacteristic
318C8—21no—
319C8—21no—
320C8—941no—
321C8—941no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—472no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22—941no—
330C22—941no—
331C22C2×D4×D4711yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—472no—
338C4—941no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4#41×D4711yescharacteristic
344C4#41×D4711yescharacteristic
345C2—41no—
346C2—942no—
347C2—1881no—
348C2#123×D4711yescharacteristic
349C2#1568993011yescharacteristic
350C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#485C2
socleC22×C47C22×D4
hypercenter#485D47
hypocenterC47#3097
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #15689467C2semidirect
4. #15689464C2semidirect
5. #15689462C2semidirect
6. #15689460C2semidirect
7. #15689456C2semidirect
8. #15689454C2semidirect
9. #15689452C2semidirect
10. #15689164C2semidirect
11. #15689158C2semidirect
12. #15689130C2semidirect
13. #103×D47C2semidirect
15. C47×#485C2semidirect
181. #485D47semidirect
191. C47#3097semidirect