Finite Group Databasebeta

← #20254234

Subgroups — #20254234

Order 6016.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689687C211yesmaximal, characteristic, complemented
2#15689461C211yesmaximal, characteristic, complemented
3#15689444C211yesmaximal, characteristic, complemented
4#15689441C211yesmaximal, characteristic, complemented
5#15689436C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689371C211yesmaximal, characteristic, complemented
8#15689357C211yesmaximal, characteristic, complemented
9#15689354C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689268C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689256C211yesmaximal, characteristic, complemented
14#15689090C211yesmaximal, characteristic, complemented
15C47×#537C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625329C2211yescharacteristic, complemented
22C22×C47⋊C8C2211yescharacteristic, complemented
23#13094020—21no—
24#13094013—21no—
25#13093998C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093998C2211yescharacteristic
29#13093992—21no—
30#13093992—21no—
31#13093983C2211yescharacteristic
32#13093957C2211yescharacteristic, complemented
33#13093957C2211yescharacteristic, complemented
34#13093955C2211yescharacteristic, complemented
35#13093955C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic, complemented
39#13093945C2211yescharacteristic, complemented
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C2×#41×C47C2211yescharacteristic, complemented
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic, complemented
53#121×C47—21no—
54#121×C47—21no—
55#121×C47—21no—
56#121×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic, complemented
58C2×C4⋊C4×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60#41×C47—41no—
61#41×C47—41no—
62#41×C47—41no—
63#41×C47—41no—
64C2×Q8×C47D411yescharacteristic
65C2×Q8×C47C2311yescharacteristic
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47D411yescharacteristic
70C2×D4×C47D411yescharacteristic
71C2×D4×C47D411yescharacteristic
72C2×D4×C47C2311yescharacteristic
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47—21no—
82C2×D188—21no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188C2311yescharacteristic
86C2×D188C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47C2311yescharacteristic
91C4⋊C4×C47C2311yescharacteristic
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊Dic47—21no—
97#10625336—41no—
98#10625336—41no—
99#10625334—41no—
100#10625334—41no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105C4⋊Dic47C2311yescharacteristic
106C4⋊Dic47C2311yescharacteristic
107C4×Dic47—21no—
108#10625329—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—21no—
115C23×C47C2×D411yescharacteristic
116C23×C47C2×D411yescharacteristic
117C23×C47C2×D411yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123Q8×C47—21no—
124Q8×C47—21no—
125Q8×C47—41no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—41no—
129D4×C47—41no—
130D4×C47—41no—
131D4×C47—42no—
132D4×C47—81no—
133D4×C47—81no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—42no—
144C2×C4×C47—81no—
145C2×C4×C47C2×D411yescharacteristic
146C2×C4×C47C2×D411yescharacteristic
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—81no—
150C22⋊D47—81no—
151C22⋊D47—81no—
152C22⋊D47—81no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155D188—21no—
156D188—21no—
157D188—21no—
158D188—21no—
159D188—42no—
160C47⋊C8—21no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C47⋊C8—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—21no—
172C22×C47—21no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C22×D411yescharacteristic
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47H(5,𝔽2)11yescharacteristic
191C4×C47H(5,𝔽2)11yescharacteristic
192Dic47—41no—
193Dic47—41no—
194#3198—471nomaximal, Sylow
195C2×C47—41no—
196C2×C47—41no—
197C2×C47—41no—
198C2×C47—81no—
199C2×C47#53411yescharacteristic
200C2×C47#57611yescharacteristic
201C2×C47#57711yescharacteristic
202D47—81no—
203D47—81no—
204#537D4711yescharacteristic, complemented
205#535—471no—
206#485—471no—
207#482—471no—
208#481—471no—
209#480—471no—
210#469—471no—
211#468—471no—
212#466—471no—
213#465—471no—
214#450—471no—
215#449—471no—
216#449—471no—
217#447—471no—
218#408—471no—
219C47#319811yescharacteristic, complemented, Sylow
220C2×#41C2×D4711yescharacteristic
221C2×#41C2×D4711yescharacteristic, complemented
222C22×D4—471no—
223C2×SD16—471no—
224C2×SD16—471no—
225C2×D8—471no—
226C2×D8—471no—
227C2×M16—471no—
228C22×C8—471no—
229#127—941no—
230#124—941no—
231C22⋊Q8—21no—
232C22⋊Q8C2×D4711yescharacteristic
233C22⋊Q8C2×D4711yescharacteristic, complemented
234#121—21no—
235#121—21no—
236#121—21no—
237#121—471no—
238#121—471no—
239#121—471no—
240#121—471no—
241#121C2×D4711yescharacteristic
242#121C2×D4711yescharacteristic, complemented
243#120—941no—
244#120—941no—
245#117—471no—
246C2×C4⋊C4C2×D4711yescharacteristic, complemented
247#107—471no—
248#107—471no—
249#106—471no—
250#106—471no—
251#103—471no—
252#103—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102—471no—
259C22⋊C8—471no—
260C22⋊C8—471no—
261C22⋊C8—471no—
262C22⋊C8—471no—
263C24—941no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8C22⋊D4711yescharacteristic
269C2×Q8C22×D4711yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—471no—
274C2×D4—471no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4—941no—
279C2×D4—941no—
280C2×D4—1881no—
281C2×D4—1881no—
282C2×D4C22⋊D4711yescharacteristic
283C2×D4C22⋊D4711yescharacteristic
284C2×D4C22⋊D4711yescharacteristic
285C2×D4C22×D4711yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291SD16—1881no—
292SD16—1881no—
293D8—1881no—
294D8—1881no—
295M16—1881no—
296C2×C8—471no—
297C2×C8—471no—
298C2×C8—471no—
299C2×C8—471no—
300C2×C8—1881no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—471no—
305C4⋊C4—471no—
306C4⋊C4C22×D4711yescharacteristic
307C4⋊C4C22×D4711yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—941no—
313C22⋊C4—941no—
314C22⋊C4—941no—
315C22⋊C4—941no—
316C22⋊C4—941no—
317C42—941no—
318C23—21no—
319C23—941no—
320C23—941no—
321C23—3761no—
322C23—3761no—
323C23—1882no—
324C23C2×C22⋊D4711yescharacteristic
325C23C2×C22⋊D4711yescharacteristic
326C23C2×C22⋊D4711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—41no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—42no—
336D4—81no—
337D4—81no—
338D4—941no—
339D4—941no—
340D4—941no—
341D4—941no—
342D4—3761no—
343D4—3761no—
344D4—3761no—
345D4—3761no—
346D4—1882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4C2×C22⋊D4711yescharacteristic
361C2×C4C2×C22⋊D4711yescharacteristic
362C2×C4C2×C22⋊D4711yescharacteristic
363C2×C4C23×D4711yescharacteristic
364C8—941no—
365C8—941no—
366C8—941no—
367C8—941no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3764no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22—1881no—
385C22—1881no—
386C22—1881no—
387C22C22×C22⋊D4711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—1881no—
395C4—1881no—
396C4#1309406911yescharacteristic
397C4#1309406911yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—3761no—
403C2—3761no—
404C2#1568968211yescharacteristic
405C2#1568992611yescharacteristic
406C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#537C2
socleC22×C47C22×D4
hypercenter#537D47
hypocenterC47#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #15689687C2semidirect
2. #15689461C2semidirect
3. #15689444C2semidirect
4. #15689441C2semidirect
5. #15689436C2semidirect
6. #15689374C2semidirect
7. #15689371C2semidirect
8. #15689357C2semidirect
9. #15689354C2semidirect
10. #15689273C2semidirect
11. #15689268C2semidirect
12. #15689268C2semidirect
13. #15689256C2semidirect
14. #15689090C2semidirect
15. C47×#537C2semidirect
21. C2×#10625329C22semidirect
22. C22×C47⋊C8C22semidirect
32. #13093957C22semidirect
33. #13093957C22semidirect
34. #13093955C22semidirect
35. #13093955C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
38. #13093945C22semidirect
39. #13093945C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. C22⋊(C47⋊C8)C22semidirect
49. C2×#41×C47C22semidirect
52. C22⋊Q8×C47C22semidirect
57. #121×C47C22semidirect
58. C2×C4⋊C4×C47C22semidirect
204. #537D47semidirect
219. C47#3198semidirect
221. C2×#41C2×D47semidirect
233. C22⋊Q8C2×D47semidirect
242. #121C2×D47semidirect
246. C2×C4⋊C4C2×D47semidirect