Finite Group Databasebeta

← #20254476

Subgroups — #20254476

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#15689692C211yesmaximal, characteristic, complemented
2#15689513C211yesmaximal, characteristic, complemented
3#15689505C211yesmaximal, characteristic, complemented
4#15689485C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689345C211yesmaximal, characteristic, complemented
7#15689338C211yesmaximal, characteristic, complemented
8#15689323C211yesmaximal, characteristic, complemented
9#15689318C211yesmaximal, characteristic, complemented
10#15689283C211yesmaximal, characteristic, complemented
11#15689273C211yesmaximal, characteristic, complemented
12#15689266C211yesmaximal, characteristic, complemented
13#15689256C211yesmaximal, characteristic, complemented
14#15689184C211yesmaximal, characteristic, complemented
15C47×#542C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625336C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625336C2211yescharacteristic, complemented
23C2×#10625334C2211yescharacteristic
24C2×#10625334C2211yescharacteristic
25C2×#10625334C2211yescharacteristic, complemented
26#13094021C2211yescharacteristic
27#13094021C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094012C2211yescharacteristic
30#13093999—21no—
31#13093999—21no—
32#13093994—21no—
33#13093994—21no—
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35C4⋊(C47⋊C8)C2211yescharacteristic, complemented
36#13093947C2211yescharacteristic, complemented
37#13093947C2211yescharacteristic, complemented
38#13093944C2211yescharacteristic
39#13093944C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic, complemented
43#13093944C2211yescharacteristic, complemented
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46#13093935C2211yescharacteristic, complemented
47C4×C47⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C47C2211yescharacteristic, complemented
49#126×C47—21no—
50#124×C47—21no—
51#124×C47C2211yescharacteristic, complemented
52#123×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic, complemented
57C4×D4×C47C2211yescharacteristic, complemented
58#117×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—21no—
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67#10625350—41no—
68#10625350—41no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×C4×D47—21no—
80C2×Dic94C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47D411yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47D411yescharacteristic
94C22⋊C4×C47D411yescharacteristic
95C42×C47—21no—
96C42×C47C2311yescharacteristic
97C42×C47C2311yescharacteristic
98#10625337—41no—
99#10625336—41no—
100#10625336—41no—
101#10625336—41no—
102#10625335—41no—
103#10625334—41no—
104#10625334—41no—
105#10625334—41no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122Q8×C47—21no—
123Q8×C47—21no—
124Q8×C47—81no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—81no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—81no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2411yescharacteristic
140C22⋊D47—42no—
141C2×Dic47—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—21no—
146D188—21no—
147D188—21no—
148D188—42no—
149D188—81no—
150D188—81no—
151D188—81no—
152D188—81no—
153C4×D47—42no—
154Dic94—21no—
155Dic94—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47C22×D411yescharacteristic
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×C47—41no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47H(5,𝔽2)11yescharacteristic
186C4×C47H(5,𝔽2)11yescharacteristic
187Dic47—41no—
188#3224—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47—81no—
191C2×C47#53511yescharacteristic
192C2×C47#57611yescharacteristic
193C2×C47#57711yescharacteristic
194D47—81no—
195D47—81no—
196D47—81no—
197#542D4711yescharacteristic, complemented
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#433—471no—
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⋊Q8C2×D4711yescharacteristic, complemented
224#127—471no—
225#127—471no—
226#126—21no—
227#124—21no—
228#124—471no—
229#124—471no—
230#124C2×D4711yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D4711yescharacteristic
234#121—941no—
235#121—941no—
236#121C2×D4711yescharacteristic
237#120—941no—
238#120—941no—
239C4×Q8C2×D4711yescharacteristic, complemented
240C4×D4C2×D4711yescharacteristic, complemented
241#117C2×D4711yescharacteristic
242C4⋊C8—471no—
243C4⋊C8—471no—
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⋊C8—471no—
253C22⋊C8—471no—
254#97—471no—
255C4×C8—471no—
256C24—941no—
257#41—1881no—
258#41—1881no—
259C2×Q8—21no—
260C2×Q8—471no—
261C2×Q8C22×D4711yescharacteristic
262C2×D4—21no—
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—1881no—
273C2×D4—1881no—
274C2×D4C22×D4711yescharacteristic
275C22×C4—21no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278Q16—1881no—
279SD16—1881no—
280SD16—1881no—
281SD16—1881no—
282SD16—1881no—
283D8—1881no—
284D8—1881no—
285D8—1881no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—471no—
289C2×C8—471no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D4711yescharacteristic
294C4⋊C4C22⋊D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C4⋊C4C22×D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4C22⋊D4711yescharacteristic
307C22⋊C4C22⋊D4711yescharacteristic
308C42—21no—
309C42C22×D4711yescharacteristic
310C42C22×D4711yescharacteristic
311C23—21no—
312C23—941no—
313C23—941no—
314C23—941no—
315C23—3761no—
316C23—3761no—
317C23—1882no—
318C23C2×C22⋊D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—941no—
323Q8—941no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—941no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—941no—
333D4—3761no—
334D4—3761no—
335D4—3761no—
336D4—3761no—
337D4—1882no—
338D4—1882no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—941no—
346C2×C4—1882no—
347C2×C4C2×C22⋊D4711yescharacteristic
348C2×C4C2×C22⋊D4711yescharacteristic
349C2×C4C2×C22⋊D4711yescharacteristic
350C2×C4C2×C22⋊D4711yescharacteristic
351C2×C4C2×C22⋊D4711yescharacteristic
352C2×C4C23×D4711yescharacteristic
353C8—941no—
354C8—941no—
355C8—941no—
356C8—941no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3764no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22—1881no—
372C22—1881no—
373C22C22×C22⋊D4711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—1881no—
383C4#1309407011yescharacteristic
384C4#1309407011yescharacteristic
385C2—41no—
386C2—81no—
387C2—3761no—
388C2—3761no—
389C2—3761no—
390C2#1568968711yescharacteristic
391C2#1568992611yescharacteristic
392C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#542C2
socleC22×C47C22×D4
hypercenter#542D47
hypocenterC47#3224
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #15689692C2semidirect
2. #15689513C2semidirect
3. #15689505C2semidirect
4. #15689485C2semidirect
5. #15689471C2semidirect
6. #15689345C2semidirect
7. #15689338C2semidirect
8. #15689323C2semidirect
9. #15689318C2semidirect
10. #15689283C2semidirect
11. #15689273C2semidirect
12. #15689266C2semidirect
13. #15689256C2semidirect
14. #15689184C2semidirect
15. C47×#542C2semidirect
18. C2×#10625337C22semidirect
19. C2×#10625335C22semidirect
22. C2×#10625336C22semidirect
25. C2×#10625334C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. C4⋊(C47⋊C8)C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
46. #13093935C22semidirect
47. C4×C47⋊C8C22semidirect
48. C4⋊Q8×C47C22semidirect
51. #124×C47C22semidirect
56. C4×Q8×C47C22semidirect
57. C4×D4×C47C22semidirect
197. #542D47semidirect
212. C47#3224semidirect
223. C4⋊Q8C2×D47semidirect
230. #124C2×D47semidirect
239. C4×Q8C2×D47semidirect
240. C4×D4C2×D47semidirect