Finite Group Databasebeta

← #20254484

Subgroups — #20254484

Order 6016.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic, complemented
2#15689692C211yesmaximal, characteristic, complemented
3#15689512C211yesmaximal, characteristic, complemented
4#15689507C211yesmaximal, characteristic, complemented
5#15689483C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689324C211yesmaximal, characteristic, complemented
10#15689319C211yesmaximal, characteristic, complemented
11#15689287C211yesmaximal, characteristic, complemented
12#15689276C211yesmaximal, characteristic, complemented
13#15689270C211yesmaximal, characteristic, complemented
14#15689259C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625325C2211yescharacteristic
21C2×#10625325C2211yescharacteristic, complemented
22C2×#10625325C2211yescharacteristic, complemented
23C2×D376C2211yescharacteristic
24C2×D376C2211yescharacteristic
25C2×D376C2211yescharacteristic, complemented
26#13094024C2211yescharacteristic, complemented
27#13094021C2211yescharacteristic
28#13094021C2211yescharacteristic
29#13094019—21no—
30#13094012C2211yescharacteristic
31#13094012C2211yescharacteristic
32#13094012C2211yescharacteristic, complemented
33#13094010—21no—
34#13094006—21no—
35#13094003C2211yescharacteristic
36#13094002—21no—
37#13093999—21no—
38#13093999—21no—
39#13093998C2211yescharacteristic
40#13093994—21no—
41#13093994—21no—
42C4×Dic94C2211yescharacteristic, complemented
43C4×D188C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093949C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic, complemented
51#13093946C2211yescharacteristic, complemented
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic, complemented
54C4⋊C8×C47C2211yescharacteristic, complemented
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic, complemented
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—21no—
62C2×C22⋊D47—21no—
63#10625350—41no—
64#10625350—41no—
65C2×D188—21no—
66C2×D188—21no—
67C2×D188—21no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—41no—
71C2×D188—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×Dic94—21no—
79C2×Dic94C2311yescharacteristic
80C2×Dic94C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47D411yescharacteristic
86C4⋊C4×C47D411yescharacteristic
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47C2311yescharacteristic
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106Dic188—41no—
107D376—41no—
108D376—41no—
109D376—41no—
110#10625325—41no—
111#10625325—41no—
112#10625325—41no—
113#10625325—41no—
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—81no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136D188—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—42no—
145D188—81no—
146D188—81no—
147D188—81no—
148D188—81no—
149C4×D47—42no—
150C4×D47—81no—
151Dic94—21no—
152Dic94—21no—
153Dic94—21no—
154Dic94—21no—
155Dic94—81no—
156C8×C47—21no—
157C8×C47—21no—
158C8×C47—21no—
159C8×C47—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47C22×D411yescharacteristic
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—84no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47H(5,𝔽2)11yescharacteristic
183C4×C47H(5,𝔽2)11yescharacteristic
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188#3224—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47#53511yescharacteristic
191C2×C47#57611yescharacteristic
192C2×C47#57711yescharacteristic
193D47—81no—
194D47—81no—
195D47—81no—
196D47—81no—
197#542—471no—
198#535—471no—
199#496—471no—
200#495—471no—
201#489—471no—
202#486—471no—
203#464—471no—
204#463—471no—
205#460—471no—
206#459—471no—
207#452—471no—
208#450—471no—
209#449—471no—
210#447—471no—
211#433D4711yescharacteristic, complemented
212C47#322411yescharacteristic, complemented, Sylow
213C2×#41—471no—
214C22×D4—471no—
215C2×Q16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×SD16—471no—
219C2×SD16—471no—
220C2×D8—471no—
221C2×D8—471no—
222C2×D8—471no—
223C4⋊Q8—471no—
224#127—471no—
225#127—471no—
226#126—941no—
227#124—471no—
228#124—471no—
229#124—471no—
230#124—941no—
231#123—941no—
232C22⋊Q8—471no—
233C22⋊Q8—941no—
234#121—471no—
235#121—941no—
236#121—941no—
237#120—941no—
238#120—941no—
239C4×Q8—471no—
240C4×D4—471no—
241#117C2×D4711yescharacteristic
242C4⋊C8C2×D4711yescharacteristic, complemented
243C4⋊C8C2×D4711yescharacteristic, complemented
244#103—471no—
245#103—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252C22⋊C8C2×D4711yescharacteristic
253C22⋊C8C2×D4711yescharacteristic
254#97C2×D4711yescharacteristic, complemented
255C4×C8C2×D4711yescharacteristic, complemented
256C24—941no—
257#41—1881no—
258#41—1881no—
259C2×Q8—471no—
260C2×Q8—471no—
261C2×Q8—941no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—1881no—
274C2×D4—1881no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278Q16—1881no—
279SD16—1881no—
280SD16—1881no—
281SD16—1881no—
282SD16—1881no—
283D8—1881no—
284D8—1881no—
285D8—1881no—
286C2×C8C22×D4711yescharacteristic
287C2×C8C22×D4711yescharacteristic
288C2×C8C22×D4711yescharacteristic
289C2×C8C22×D4711yescharacteristic
290C4⋊C4—471no—
291C4⋊C4—471no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4D18811yescharacteristic
296C4⋊C4D18811yescharacteristic
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4D18811yescharacteristic
307C22⋊C4D18811yescharacteristic
308C42—941no—
309C42C22×D4711yescharacteristic
310C42C22×D4711yescharacteristic
311C23—941no—
312C23—941no—
313C23—941no—
314C23—941no—
315C23—3761no—
316C23—3761no—
317C23—1882no—
318C23C2×D18811yescharacteristic
319Q8—941no—
320Q8—941no—
321Q8—941no—
322Q8—941no—
323Q8—3761no—
324D4—941no—
325D4—941no—
326D4—941no—
327D4—941no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—3761no—
333D4—3761no—
334D4—3761no—
335D4—3761no—
336D4—3761no—
337D4—1882no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—3761no—
346C2×C4—1882no—
347C2×C4C2×D18811yescharacteristic
348C2×C4C2×D18811yescharacteristic
349C2×C4C2×D18811yescharacteristic
350C2×C4C2×D18811yescharacteristic
351C2×C4C2×D18811yescharacteristic
352C2×C4C23×D4711yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—3764no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C22×D18811yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—1881no—
380C4—1881no—
381C4—1881no—
382C4—1881no—
383C4#1309407011yescharacteristic
384C4#1309407011yescharacteristic
385C2—41no—
386C2—3761no—
387C2—3761no—
388C2—3761no—
389C2—3761no—
390C2#1568969211yescharacteristic
391C2#1568992811yescharacteristic
392C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689692C2semidirect
3. #15689512C2semidirect
4. #15689507C2semidirect
5. #15689483C2semidirect
6. #15689470C2semidirect
7. #15689346C2semidirect
8. #15689339C2semidirect
9. #15689324C2semidirect
10. #15689319C2semidirect
11. #15689287C2semidirect
12. #15689276C2semidirect
13. #15689270C2semidirect
14. #15689259C2semidirect
15. C47×#433C2semidirect
18. C2×Dic188C22semidirect
21. C2×#10625325C22semidirect
22. C2×#10625325C22semidirect
25. C2×D376C22semidirect
26. #13094024C22semidirect
32. #13094012C22semidirect
42. C4×Dic94C22semidirect
43. C4×D188C22semidirect
44. #13093949C22semidirect
45. #13093949C22semidirect
50. #13093946C22semidirect
51. #13093946C22semidirect
53. C4⋊C8×C47C22semidirect
54. C4⋊C8×C47C22semidirect
57. #97×C47C22semidirect
58. C4×C8×C47C22semidirect
211. #433D47semidirect
212. C47#3224semidirect
242. C4⋊C8C2×D47semidirect
243. C4⋊C8C2×D47semidirect
254. #97C2×D47semidirect
255. C4×C8C2×D47semidirect