Finite Group Databasebeta

← #20252787

Subgroups — #20252787

Order 6016.

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

normal subgroups only

This group has 800 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×#13094069C211yesmaximal, characteristic, complemented
2#15689685C212yesmaximal, complemented
3#15689682C211yesmaximal, characteristic, complemented
4#15689314C214yesmaximal, complemented
5#15689311C214yesmaximal, complemented
6C2×#13093938C212yesmaximal, complemented
7C2×#99×C47C211yesmaximal, characteristic, complemented
8#13094069—22no—
9#13094069—24no—
10#13094069C2214yes—
11C2×#10625350—21no—
12C2×#10625352—22no—
13C22×C22⋊D47—21no—
14C22×C22⋊D47C2212yes—
15C22×C22⋊D47C2211yescharacteristic, complemented
16C2×D4×D47—22no—
17#13094008—22no—
18#13094008C2214yescomplemented
19#13094007—21no—
20#13094005C2212yescomplemented
21#13093998—24no—
22#13093996—22no—
23#13093994—22no—
24#13093994C2214yescomplemented
25#13093993—21no—
26#13093992C2212yescomplemented
27C2×C22⋊Dic47C2211yescharacteristic, complemented
28#13093938C2218yescomplemented
29C22×D4×C47C2211yescharacteristic
30C2×C22⋊C4×C47C2212yescomplemented
31#99×C47C2214yescomplemented
32C24×C47D411yescharacteristic, complemented
33C24×C47C2311yescharacteristic
34C23×D47—21no—
35C23×D47D412yescomplemented
36C23×D47C2311yescharacteristic, complemented
37C2×D4×C47—22no—
38C2×D4×C47—22no—
39C2×D4×C47D412yescomplemented
40C2×D4×C47C2312yes—
41C22×C4×C47—22no—
42C22×C4×C47D411yescharacteristic, complemented
43C2×C22⋊D47—22no—
44C2×C22⋊D47—24no—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C2×C22⋊D47—24no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—21no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—21no—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47D414yescomplemented
56C2×C22⋊D47C2314yes—
57C22×Dic47—21no—
58C22×Dic47—21no—
59C22×Dic47D412yescomplemented
60C22×Dic47C2311yescharacteristic, complemented
61#10625352—28no—
62#10625352—28no—
63D4×D47—28no—
64D4×D47—28no—
65#10625350—24no—
66#10625350—24no—
67C2×D188—21no—
68C2×D188—24no—
69C2×C4×D47—22no—
70C2×Dic94—21no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47C2314yescomplemented
73C22⋊Dic47—21no—
74C22⋊Dic47—22no—
75C22⋊Dic47C2312yescomplemented
76(C2×D47)⋊C4—24no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—24no—
79C4⋊Dic47—24no—
80Dic47⋊C4—22no—
81C23×C47—21no—
82C23×C47—21no—
83C23×C47—81no—
84C23×C47—81no—
85C23×C47C2×D412yes—
86C23×C47C2×D411yescharacteristic
87C23×C47C2×D411yescharacteristic
88C23×C47C2×D412yes—
89C23×C47C2×D412yes—
90C23×C47C2411yescharacteristic
91C22×D47—22no—
92C22×D47—24no—
93C22×D47—22no—
94C22×D47—22no—
95C22×D47—21no—
96C22×D47—81no—
97C22×D47—82no—
98C22×D47—82no—
99C22×D47C2×D414yes—
100D4×C47—24no—
101D4×C47—24no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—24no—
105C2×C4×C47—82no—
106C2×C4×C47C2×D412yes—
107C22⋊D47—28no—
108C22⋊D47—24no—
109C22⋊D47—24no—
110C22⋊D47—24no—
111C22⋊D47—24no—
112C22⋊D47—41no—
113C22⋊D47—42no—
114C22⋊D47—41no—
115C22⋊D47—82no—
116C2×Dic47—24no—
117C2×Dic47—22no—
118C2×Dic47—22no—
119C2×Dic47—21no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—81no—
123C2×Dic47C2×D414yes—
124D188—24no—
125D188—84no—
126C4×D47—28no—
127Dic94—24no—
128C22×C47—22no—
129C22×C47—41no—
130C22×C47—42no—
131C22×C47—42no—
132C22×C47—41no—
133C22×C47—41no—
134C22×C47—42no—
135C22×C47—42no—
136C22×C47—81no—
137C22×C47#12011yescharacteristic
138C22×C47#12012yes—
139C22×C47#12011yescharacteristic
140C22×C47C22×D412yes—
141C22×C47C22×D411yescharacteristic
142C2×D47—24no—
143C2×D47—44no—
144C2×D47—44no—
145C2×D47—44no—
146C2×D47—42no—
147C2×D47—41no—
148C2×D47—82no—
149C2×D47—84no—
150C4×C47—22no—
151C4×C47—44no—
152Dic47—24no—
153Dic47—42no—
154Dic47—41no—
155#3026—471nomaximal, Sylow
156C2×C47—21no—
157C2×C47—22no—
158C2×C47—21no—
159C2×C47—22no—
160C2×C47—21no—
161C2×C47—42no—
162C2×C47C2×#12011yescharacteristic
163D47—44no—
164D47—81no—
165C2×H(5,𝔽2)—471no—
166#534—471no—
167#534—472no—
168#458—474no—
169B(4,𝔽2)—474no—
170C2×#99—472no—
171C2×#99D4711yescharacteristic, complemented
172C47#302611yescharacteristic, complemented, Sylow
173H(5,𝔽2)—474no—
174H(5,𝔽2)—944no—
175H(5,𝔽2)—942no—
176C2×#41—942no—
177C2×#41—941no—
178C22×D4—472no—
179C22×D4—471no—
180C22×D4—942no—
181C22×D4—941no—
182C22×D4C2×D4711yescharacteristic
183#123—472no—
184#123—474no—
185#123—942no—
186#123—941no—
187#121—944no—
188#121—942no—
189#120—472no—
190#120—474no—
191#120—942no—
192#120—941no—
193C2×C22⋊C4—471no—
194C2×C22⋊C4C2×D4712yescomplemented
195#99—478no—
196#99C2×D4714yescomplemented
197C24—472no—
198C24—471no—
199C24—941no—
200C24D18811yescharacteristic, complemented
201C24C22×D4711yescharacteristic
202#41—944no—
203#41—948no—
204#41—948no—
205#41—944no—
206C2×Q8—941no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—474no—
210C2×D4—474no—
211C2×D4—941no—
212C2×D4—944no—
213C2×D4—948no—
214C2×D4—948no—
215C2×D4—942no—
216C2×D4—944no—
217C2×D4—942no—
218C2×D4—942no—
219C2×D4—944no—
220C2×D4—942no—
221C2×D4—942no—
222C2×D4—942no—
223C2×D4—941no—
224C2×D4—941no—
225C2×D4—942no—
226C2×D4—942no—
227C2×D4D18812yescomplemented
228C2×D4C22×D4712yes—
229C22×C4—22no—
230C22×C4—472no—
231C22×C4—471no—
232C22×C4—942no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4D18811yescharacteristic, complemented
236C4⋊C4—944no—
237C4⋊C4—942no—
238C22⋊C4—22no—
239C22⋊C4—472no—
240C22⋊C4—944no—
241C22⋊C4—944no—
242C22⋊C4—941no—
243C22⋊C4—942no—
244C22⋊C4—942no—
245C22⋊C4C22×D4714yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—474no—
251C23—944no—
252C23—942no—
253C23—942no—
254C23—942no—
255C23—941no—
256C23—3762no—
257C23—3762no—
258C23—3761no—
259C23C2×D18812yes—
260C23C2×D18811yescharacteristic
261C23C2×D18811yescharacteristic
262C23D4×D4712yes—
263C23D4×D4712yes—
264C23C23×D4711yescharacteristic
265Q8—944no—
266D4—24no—
267D4—24no—
268D4—944no—
269D4—948no—
270D4—944no—
271D4—944no—
272D4—944no—
273D4—944no—
274D4—3764no—
275D4—3762no—
276D4—1881no—
277D4—1881no—
278D4—1882no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—474no—
284C2×C4—948no—
285C2×C4—944no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—941no—
291C2×C4—3761no—
292C2×C4C2×D18812yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—944no—
303C22—3762no—
304C22—3764no—
305C22—1884no—
306C22—1882no—
307C22—1884no—
308C22—1884no—
309C22—1881no—
310C22#1309399411yescharacteristic
311C22#1309399411yescharacteristic
312C22#1309399412yes—
313C22C2×D4×D4712yes—
314C22C22×D18811yescharacteristic
315C4—22no—
316C4—44no—
317C4—944no—
318C4—1882no—
319C4—1881no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—3761no—
327C2—1884no—
328C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC2×#99×C47C2
socleC2×C47C2×#120
hypercenterC2×#99D47
hypocenterC47#3026
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#13094069C2semidirect
2. #15689685C2semidirect
3. #15689682C2semidirect
4. #15689314C2semidirect
5. #15689311C2semidirect
6. C2×#13093938C2semidirect
7. C2×#99×C47C2semidirect
15. C22×C22⋊D47C22semidirect
18. #13094008C22semidirect
20. #13094005C22semidirect
24. #13093994C22semidirect
26. #13093992C22semidirect
27. C2×C22⋊Dic47C22semidirect
28. #13093938C22semidirect
30. C2×C22⋊C4×C47C22semidirect
31. #99×C47C22semidirect
32. C24×C47D4semidirect
35. C23×D47D4semidirect
36. C23×D47C23semidirect
39. C2×D4×C47D4semidirect
42. C22×C4×C47D4semidirect
55. C2×C22⋊D47D4semidirect
59. C22×Dic47D4semidirect
60. C22×Dic47C23semidirect
72. C22⋊C4×C47C23semidirect
75. C22⋊Dic47C23semidirect
171. C2×#99D47semidirect
172. C47#3026semidirect
194. C2×C22⋊C4C2×D47semidirect
196. #99C2×D47semidirect
200. C24D188semidirect
227. C2×D4D188semidirect
235. C22×C4D188semidirect
245. C22⋊C4C22×D47semidirect