Finite Group Databasebeta

← #20252743

Subgroups — #20252743

Order 6016.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094070C211yesmaximal, characteristic, complemented
2#15689921C211yesmaximal, characteristic, complemented
3#15689687C211yesmaximal, characteristic, complemented
4#15689299C214yesmaximal, complemented
5#15689289C214yesmaximal, complemented
6#15689140C211yesmaximal, characteristic, complemented
7#15689139C211yesmaximal, characteristic, complemented
8C2×#13093940C211yesmaximal, characteristic, complemented
9C47×#575C211yesmaximal, characteristic, complemented
10#13094070—22no—
11#13094070—22no—
12#13094070—22no—
13#13094070C2214yes—
14C2×#10625354—21no—
15C2×#10625350—21no—
16C2×#10625350C2211yescharacteristic
17C22×D188—21no—
18C22×D188C2211yescharacteristic
19C2×D4×D47—22no—
20C2×D4×D47—21no—
21#13094055C2212yescomplemented
22#13094054—21no—
23#13094050C2212yescomplemented
24#13094049—21no—
25#13094044—22no—
26C2×#10625329C2211yescharacteristic, complemented
27#13094020C2212yescomplemented
28#13094013C2212yescomplemented
29#13093998—22no—
30#13093992—22no—
31#13093983C2211yescharacteristic, complemented
32#13093951C2214yescomplemented
33#13093950C2214yescomplemented
34#13093940C2214yescomplemented
35C2×#41×C47C2211yescharacteristic
36C2×#41×C47C2211yescharacteristic, complemented
37#137×C47—21no—
38#137×C47C2212yescomplemented
39AGL(1,ℤ/8)×C47—21no—
40AGL(1,ℤ/8)×C47C2212yescomplemented
41#135×C47—22no—
42C2×M16×C47C2211yescharacteristic, complemented
43C23×D47—22no—
44C23×D47D412yes—
45#41×C47—21no—
46#41×C47—21no—
47#41×C47—21no—
48#41×C47—21no—
49#41×C47—21no—
50#41×C47—21no—
51#41×C47D412yescomplemented
52#41×C47C2312yes—
53C2×Q8×C47D411yescharacteristic, complemented
54C2×Q8×C47C2311yescharacteristic, complemented
55C2×D4×C47—21no—
56C2×D4×C47—21no—
57C2×D4×C47D411yescharacteristic, complemented
58C2×D4×C47C2311yescharacteristic, complemented
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—22no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—24no—
65#10625354—24no—
66#10625354—24no—
67D4×D47—28no—
68D4×D47—24no—
69D4×D47—28no—
70D4×D47—24no—
71#10625350—24no—
72#10625350—21no—
73#10625350—21no—
74#10625350—24no—
75#10625350D412yescomplemented
76#10625350C2312yes—
77C2×D188—22no—
78C2×D188—24no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—24no—
84C2×D188D412yes—
85C2×D188D411yescharacteristic, complemented
86C2×D188C2312yes—
87C2×C4×D47—22no—
88C2×C4×D47—21no—
89C2×Dic94D411yescharacteristic, complemented
90Q16×C47—22no—
91SD16×C47—22no—
92SD16×C47—22no—
93D8×C47—22no—
94M16×C47—21no—
95M16×C47C2312yescomplemented
96C2×C8×C47—21no—
97C22⋊Dic47—21no—
98#10625337—22no—
99#10625336—22no—
100#10625335—22no—
101#10625334—22no—
102(C2×D47)⋊C4—24no—
103C4⋊Dic47—21no—
104C4×Dic47C2312yescomplemented
105#10625329—21no—
106#10625329C2312yescomplemented
107C2×C47⋊C8—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47C2×D411yescharacteristic
111C22×D47—22no—
112C22×D47—21no—
113C22×D47—28no—
114C22×D47—22no—
115C22×D47—82no—
116C22×D47—84no—
117C22×D47C2×D414yes—
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47C2×D412yes—
122D4×C47—22no—
123D4×C47—22no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—41no—
128D4×C47—41no—
129D4×C47C2×D412yes—
130C2×C4×C47—21no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—21no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—28no—
143C22⋊D47—22no—
144C22⋊D47—22no—
145C22⋊D47—84no—
146C2×Dic47—21no—
147C2×Dic47—22no—
148D188—28no—
149D188—22no—
150D188—21no—
151D188—22no—
152D188—22no—
153D188—22no—
154D188C2×D412yes—
155C4×D47—28no—
156C4×D47—22no—
157C4×D47—22no—
158Dic94—21no—
159Dic94C2×D412yes—
160C8×C47—22no—
161C47⋊C8—22no—
162C22×C47—22no—
163C22×C47—41no—
164C22×C47—42no—
165C22×C47—42no—
166C22×C47—41no—
167C22×C47#12011yescharacteristic
168C22×C47#12011yescharacteristic
169C22×C47C22×D411yescharacteristic
170C2×D47—24no—
171C2×D47—22no—
172C2×D47—44no—
173C2×D47—42no—
174C2×D47—44no—
175C2×D47—82no—
176C2×D47—88no—
177C4×C47—22no—
178C4×C47—41no—
179C4×C47#12011yescharacteristic
180C4×C47#12011yescharacteristic
181C4×C47C22×D411yescharacteristic
182C4×C47C22×D411yescharacteristic
183Dic47—22no—
184Dic47—42no—
185#3019—471nomaximal, Sylow
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—21no—
189C2×C47—42no—
190C2×C47—81no—
191C2×C47C2×#12011yescharacteristic
192D47—44no—
193D47—42no—
194C2×H(5,𝔽2)—471no—
195#575—471no—
196#575D4711yescharacteristic, complemented
197#535—471no—
198#455—474no—
199#453—474no—
200#421—471no—
201#421—471no—
202C2×#100—471no—
203C47#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—474no—
205H(5,𝔽2)—942no—
206H(5,𝔽2)—942no—
207H(5,𝔽2)—942no—
208C2×#41—471no—
209C2×#41—941no—
210C2×#41—941no—
211C2×#41C2×D4711yescharacteristic
212C2×#41C2×D4711yescharacteristic, complemented
213C22×D4—471no—
214C22×D4—941no—
215C22×D4—942no—
216C22×D4—941no—
217#137—21no—
218#137—472no—
219#137—941no—
220#137C2×D4712yescomplemented
221AGL(1,ℤ/8)—21no—
222AGL(1,ℤ/8)—472no—
223AGL(1,ℤ/8)—941no—
224AGL(1,ℤ/8)C2×D4712yescomplemented
225#135—22no—
226#135—942no—
227C2×M16—471no—
228C2×M16C2×D4711yescharacteristic, complemented
229#127—472no—
230#124—472no—
231#121—942no—
232#120—942no—
233#117—471no—
234#104—474no—
235#104—474no—
236#100—474no—
237C24—472no—
238C24—942no—
239#41—21no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—472no—
246#41—472no—
247#41—944no—
248#41—944no—
249#41—944no—
250#41—944no—
251#41—941no—
252#41—941no—
253#41C22⋊D4712yescomplemented
254#41C22×D4712yes—
255C2×Q8—471no—
256C2×Q8C22⋊D4711yescharacteristic, complemented
257C2×Q8C22×D4711yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—471no—
261C2×D4—472no—
262C2×D4—472no—
263C2×D4—944no—
264C2×D4—942no—
265C2×D4—944no—
266C2×D4—948no—
267C2×D4—948no—
268C2×D4—944no—
269C2×D4—942no—
270C2×D4—941no—
271C2×D4—944no—
272C2×D4—944no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4C22⋊D4711yescharacteristic, complemented
278C2×D4C22×D4711yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—942no—
282C22×C4—941no—
283C22×C4C22×D4711yescharacteristic
284Q16—22no—
285Q16—942no—
286SD16—22no—
287SD16—22no—
288SD16—942no—
289SD16—942no—
290D8—22no—
291D8—942no—
292M16—21no—
293M16—472no—
294M16—941no—
295M16C22×D4712yescomplemented
296C2×C8—21no—
297C2×C8—941no—
298C4⋊C4—941no—
299C22⋊C4—944no—
300C22⋊C4—941no—
301C42—472no—
302C23—21no—
303C23—21no—
304C23—474no—
305C23—948no—
306C23—942no—
307C23—941no—
308C23—942no—
309C23—3764no—
310C23—3762no—
311C23D4×D4711yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—472no—
316Q8—941no—
317Q8C2×C22⋊D4712yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—472no—
326D4—948no—
327D4—948no—
328D4—942no—
329D4—942no—
330D4—941no—
331D4—942no—
332D4—942no—
333D4—942no—
334D4—942no—
335D4—3764no—
336D4C2×C22⋊D4712yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—948no—
344C2×C4—941no—
345C2×C4—942no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4D4×D4711yescharacteristic
349C2×C4D4×D4711yescharacteristic
350C2×C4D4×D4711yescharacteristic
351C2×C4C2×C22⋊D4711yescharacteristic
352C2×C4C2×C22⋊D4711yescharacteristic
353C2×C4C23×D4711yescharacteristic
354C8—22no—
355C8—942no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—942no—
362C22—944no—
363C22—3762no—
364C22—3768no—
365C22—1884no—
366C22—1882no—
367C22—1884no—
368C22#1309399211yescharacteristic
369C22#1309399211yescharacteristic
370C22C2×D4×D4711yescharacteristic
371C4—22no—
372C4—41no—
373C4—942no—
374C4—1882no—
375C4#1309399211yescharacteristic
376C4#1309399211yescharacteristic
377C4C2×D4×D4711yescharacteristic
378C4C22×C22⋊D4711yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—81no—
384C2—1882no—
385C2—1884no—
386C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#575C2
socleC2×C47C2×#120
hypercenter#575D47
hypocenterC47#3019
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. #15689921C2semidirect
3. #15689687C2semidirect
4. #15689299C2semidirect
5. #15689289C2semidirect
6. #15689140C2semidirect
7. #15689139C2semidirect
8. C2×#13093940C2semidirect
9. C47×#575C2semidirect
21. #13094055C22semidirect
23. #13094050C22semidirect
26. C2×#10625329C22semidirect
27. #13094020C22semidirect
28. #13094013C22semidirect
31. #13093983C22semidirect
32. #13093951C22semidirect
33. #13093950C22semidirect
34. #13093940C22semidirect
36. C2×#41×C47C22semidirect
38. #137×C47C22semidirect
40. AGL(1,ℤ/8)×C47C22semidirect
42. C2×M16×C47C22semidirect
51. #41×C47D4semidirect
53. C2×Q8×C47D4semidirect
54. C2×Q8×C47C23semidirect
57. C2×D4×C47D4semidirect
58. C2×D4×C47C23semidirect
75. #10625350D4semidirect
85. C2×D188D4semidirect
89. C2×Dic94D4semidirect
95. M16×C47C23semidirect
104. C4×Dic47C23semidirect
106. #10625329C23semidirect
196. #575D47semidirect
203. C47#3019semidirect
212. C2×#41C2×D47semidirect
220. #137C2×D47semidirect
224. AGL(1,ℤ/8)C2×D47semidirect
228. C2×M16C2×D47semidirect
253. #41C22⋊D47semidirect
256. C2×Q8C22⋊D47semidirect
257. C2×Q8C22×D47semidirect
277. C2×D4C22⋊D47semidirect
278. C2×D4C22×D47semidirect
295. M16C22×D47semidirect