Finite Group Databasebeta

← #20252747

Subgroups — #20252747

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#15689923C211yesmaximal, characteristic, complemented
3#15689921C211yesmaximal, characteristic, complemented
4#15689692C211yesmaximal, characteristic, complemented
5#15689302C214yesmaximal, complemented
6#15689292C214yesmaximal, complemented
7#15689141C211yesmaximal, characteristic, complemented
8C2×#13093940C211yesmaximal, characteristic, complemented
9C47×#421C211yesmaximal, characteristic, complemented
10#13094070—22no—
11#13094070—22no—
12#13094070—22no—
13#13094070C2214yes—
14C2×#10625354—21no—
15C2×#10625350—21no—
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic, complemented
18C22×D188—21no—
19C22×D188C2211yescharacteristic
20C2×D4×D47—22no—
21C2×D4×D47—21no—
22#13094057—21no—
23#13094057C2212yescomplemented
24#13094055—21no—
25#13094054C2212yescomplemented
26#13094052—21no—
27#13094052C2212yescomplemented
28#13094050—21no—
29#13094049C2212yescomplemented
30#13094046—22no—
31#13094044—22no—
32C2×#10625329C2211yescharacteristic, complemented
33#13094021C2212yescomplemented
34#13094012C2212yescomplemented
35#13093999—22no—
36#13093994—22no—
37#13093952C2214yescomplemented
38#13093940C2214yescomplemented
39C2×#41×C47C2211yescharacteristic
40C2×M16×C47C2211yescharacteristic, complemented
41#117×C47C2211yescharacteristic, complemented
42#104×C47C2214yescomplemented
43C23×D47—22no—
44C23×D47D412yes—
45#41×C47—21no—
46#41×C47—21no—
47#41×C47D412yescomplemented
48#41×C47C2312yes—
49C2×Q8×C47D411yescharacteristic, complemented
50C2×D4×C47—21no—
51C2×D4×C47D411yescharacteristic, complemented
52C22×C4×C47—21no—
53C22×C4×C47C2311yescharacteristic
54C2×C22⋊D47—22no—
55C2×C22⋊D47—21no—
56C2×C22⋊D47—21no—
57#10625354—24no—
58#10625354—24no—
59D4×D47—28no—
60D4×D47—24no—
61D4×D47—28no—
62D4×D47—24no—
63#10625350—24no—
64#10625350—21no—
65#10625350—21no—
66#10625350—21no—
67#10625350—21no—
68#10625350—21no—
69#10625350—21no—
70#10625350—24no—
71#10625350D412yescomplemented
72#10625350C2312yes—
73C2×D188—22no—
74C2×D188—24no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188—21no—
79C2×D188—24no—
80C2×D188—24no—
81C2×D188D412yes—
82C2×D188D411yescharacteristic, complemented
83C2×D188C2312yes—
84C2×D188C2311yescharacteristic, complemented
85C2×C4×D47—22no—
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×Dic94D411yescharacteristic, complemented
89C2×Dic94C2311yescharacteristic, complemented
90M16×C47—21no—
91M16×C47C2312yescomplemented
92C2×C8×C47—21no—
93C4⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C42×C47C2312yescomplemented
96#10625337—22no—
97#10625336—22no—
98#10625335—22no—
99#10625334—22no—
100(C2×D47)⋊C4—24no—
101#10625329—21no—
102#10625329C2312yescomplemented
103C2×C47⋊C8—21no—
104Dic188—22no—
105D376—22no—
106#10625325—22no—
107#10625325—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110C22×D47—22no—
111C22×D47—21no—
112C22×D47—28no—
113C22×D47—22no—
114C22×D47—21no—
115C22×D47—82no—
116C22×D47—84no—
117C22×D47C2×D414yes—
118Q8×C47—21no—
119Q8×C47C2×D412yes—
120D4×C47—22no—
121D4×C47—22no—
122D4×C47—21no—
123D4×C47C2×D412yes—
124C2×C4×C47—21no—
125C2×C4×C47—22no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2411yescharacteristic
134C22⋊D47—28no—
135C22⋊D47—22no—
136C22⋊D47—22no—
137C22⋊D47—41no—
138C22⋊D47—41no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141D188—28no—
142D188—22no—
143D188—21no—
144D188—22no—
145D188—22no—
146D188—22no—
147D188—21no—
148D188—21no—
149D188—84no—
150D188C2×D412yes—
151C4×D47—28no—
152C4×D47—22no—
153C4×D47—22no—
154C4×D47—41no—
155C4×D47—41no—
156Dic94—21no—
157Dic94—21no—
158Dic94—21no—
159Dic94C2×D412yes—
160C8×C47—22no—
161C47⋊C8—22no—
162C22×C47—22no—
163C22×C47—41no—
164C22×C47—42no—
165C22×C47#12011yescharacteristic
166C22×C47#12011yescharacteristic
167C22×C47C22×D411yescharacteristic
168C2×D47—24no—
169C2×D47—22no—
170C2×D47—44no—
171C2×D47—42no—
172C2×D47—44no—
173C2×D47—42no—
174C2×D47—41no—
175C2×D47—82no—
176C2×D47—88no—
177C4×C47—22no—
178C4×C47—42no—
179C4×C47#12011yescharacteristic
180C4×C47#12011yescharacteristic
181C4×C47C22×D411yescharacteristic
182C4×C47C22×D411yescharacteristic
183Dic47—22no—
184Dic47—41no—
185#3019—471nomaximal, Sylow
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—21no—
189C2×C47—42no—
190C2×C47C2×#12011yescharacteristic
191D47—44no—
192D47—42no—
193D47—81no—
194C2×H(5,𝔽2)—471no—
195#575—471no—
196#575—471no—
197#535—471no—
198#455—474no—
199#453—474no—
200#421—471no—
201#421D4711yescharacteristic, complemented
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—471no—
210C2×#41—941no—
211C2×#41—941no—
212C2×#41C2×D4711yescharacteristic
213C22×D4—471no—
214C22×D4—941no—
215C22×D4—942no—
216C22×D4—941no—
217#137—472no—
218#137—472no—
219#137—941no—
220#137—941no—
221AGL(1,ℤ/8)—472no—
222AGL(1,ℤ/8)—472no—
223AGL(1,ℤ/8)—941no—
224AGL(1,ℤ/8)—941no—
225#135—942no—
226#135—942no—
227C2×M16—471no—
228C2×M16C2×D4711yescharacteristic, complemented
229#127—472no—
230#124—472no—
231#121—942no—
232#120—942no—
233#117C2×D4711yescharacteristic, complemented
234#104—474no—
235#104C2×D4714yescomplemented
236#100—474no—
237C24—472no—
238C24—942no—
239#41—21no—
240#41—21no—
241#41—472no—
242#41—472no—
243#41—944no—
244#41—944no—
245#41—944no—
246#41—944no—
247#41—941no—
248#41—941no—
249#41—941no—
250#41—941no—
251#41—941no—
252#41—941no—
253#41D18812yescomplemented
254#41C22×D4712yes—
255C2×Q8—471no—
256C2×Q8—471no—
257C2×Q8D18811yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—471no—
260C2×D4—472no—
261C2×D4—472no—
262C2×D4—471no—
263C2×D4—944no—
264C2×D4—942no—
265C2×D4—944no—
266C2×D4—944no—
267C2×D4—948no—
268C2×D4—948no—
269C2×D4—944no—
270C2×D4—942no—
271C2×D4—941no—
272C2×D4—944no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—941no—
278C2×D4D18811yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—942no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4C22×D4711yescharacteristic
284Q16—942no—
285Q16—942no—
286SD16—942no—
287SD16—942no—
288SD16—942no—
289SD16—942no—
290D8—942no—
291D8—942no—
292M16—21no—
293M16—472no—
294M16—941no—
295M16C22×D4712yescomplemented
296C2×C8—21no—
297C2×C8—941no—
298C4⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—944no—
301C42C22×D4712yescomplemented
302C23—21no—
303C23—474no—
304C23—948no—
305C23—942no—
306C23—941no—
307C23—942no—
308C23—941no—
309C23—3764no—
310C23—3762no—
311C23D4×D4711yescharacteristic
312Q8—21no—
313Q8—472no—
314Q8—941no—
315Q8—941no—
316Q8—941no—
317Q8C2×D18812yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—472no—
322D4—948no—
323D4—948no—
324D4—942no—
325D4—942no—
326D4—941no—
327D4—942no—
328D4—942no—
329D4—942no—
330D4—941no—
331D4—942no—
332D4—941no—
333D4—3764no—
334D4—1881no—
335D4—1881no—
336D4C2×D18812yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—948no—
342C2×C4—941no—
343C2×C4—942no—
344C2×C4—942no—
345C2×C4—941no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4C2×D18811yescharacteristic
349C2×C4C2×D18811yescharacteristic
350C2×C4D4×D4711yescharacteristic
351C2×C4D4×D4711yescharacteristic
352C2×C4D4×D4711yescharacteristic
353C2×C4C23×D4711yescharacteristic
354C8—22no—
355C8—942no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—942no—
360C22—944no—
361C22—3762no—
362C22—3768no—
363C22—1882no—
364C22—1884no—
365C22—1882no—
366C22—1884no—
367C22—1881no—
368C22#1309399411yescharacteristic
369C22#1309399411yescharacteristic
370C22C2×D4×D4711yescharacteristic
371C4—22no—
372C4—42no—
373C4—942no—
374C4—1881no—
375C4#1309399411yescharacteristic
376C4#1309399411yescharacteristic
377C4C2×D4×D4711yescharacteristic
378C4C22×D18811yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—3761no—
384C2—1882no—
385C2—1884no—
386C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#421C2
socleC2×C47C2×#120
hypercenter#421D47
hypocenterC47#3019
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. C2×#13094070C2semidirect
2. #15689923C2semidirect
3. #15689921C2semidirect
4. #15689692C2semidirect
5. #15689302C2semidirect
6. #15689292C2semidirect
7. #15689141C2semidirect
8. C2×#13093940C2semidirect
9. C47×#421C2semidirect
17. C2×#10625350C22semidirect
23. #13094057C22semidirect
25. #13094054C22semidirect
27. #13094052C22semidirect
29. #13094049C22semidirect
32. C2×#10625329C22semidirect
33. #13094021C22semidirect
34. #13094012C22semidirect
37. #13093952C22semidirect
38. #13093940C22semidirect
40. C2×M16×C47C22semidirect
41. #117×C47C22semidirect
42. #104×C47C22semidirect
47. #41×C47D4semidirect
49. C2×Q8×C47D4semidirect
51. C2×D4×C47D4semidirect
71. #10625350D4semidirect
82. C2×D188D4semidirect
84. C2×D188C23semidirect
88. C2×Dic94D4semidirect
89. C2×Dic94C23semidirect
91. M16×C47C23semidirect
95. C42×C47C23semidirect
102. #10625329C23semidirect
201. #421D47semidirect
203. C47#3019semidirect
228. C2×M16C2×D47semidirect
233. #117C2×D47semidirect
235. #104C2×D47semidirect
253. #41D188semidirect
257. C2×Q8D188semidirect
278. C2×D4D188semidirect
295. M16C22×D47semidirect
301. C42C22×D47semidirect