Finite Group Databasebeta

← #20244453

Subgroups — #20244453

Order 6016.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#15689921C211yesmaximal, characteristic, complemented
2#15689634C211yesmaximal, characteristic, complemented
3#15689141C211yesmaximal, characteristic, complemented
4#15689140C211yesmaximal, characteristic, complemented
5#15689087C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#525C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—21no—
10#13094054—21no—
11#13094050—21no—
12#13094049—21no—
13#13094044—22no—
14C2×#10625329C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13094007—21no—
17#13094003—21no—
18#13093998—21no—
19#13093993—21no—
20C4×C22⋊D47—22no—
21#13093983C2211yescharacteristic
22#13093952—22no—
23#13093951—22no—
24C22⋊(C47⋊C8)—22no—
25C2×#41×C47C2211yescharacteristic
26C23×C4×C47C2211yescharacteristic
27#123×C47—21no—
28C22⋊Q8×C47—21no—
29#121×C47—21no—
30#120×C47—21no—
31C4×D4×C47—22no—
32#117×C47C2211yescharacteristic
33C24×C47D411yescharacteristic
34#41×C47—21no—
35#41×C47—21no—
36#41×C47—21no—
37#41×C47—21no—
38C2×Q8×C47D411yescharacteristic, complemented
39C2×D4×C47—22no—
40C2×D4×C47—21no—
41C2×D4×C47D411yescharacteristic, complemented
42C22×C4×C47—21no—
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47D411yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—22no—
52C2×C22⋊D47—21no—
53#10625350—21no—
54#10625350—21no—
55#10625350—21no—
56#10625350—21no—
57C2×D188D411yescharacteristic, complemented
58C2×C4×D47—21no—
59C2×Dic94D411yescharacteristic, complemented
60C4⋊C4×C47—22no—
61C4⋊C4×C47—21no—
62C22⋊C4×C47—22no—
63C22⋊C4×C47—22no—
64C22⋊C4×C47—21no—
65C42×C47D412yescomplemented
66C22⋊Dic47—22no—
67C22⋊Dic47—21no—
68#10625337—22no—
69#10625336—22no—
70#10625335—22no—
71#10625334—22no—
72(C2×D47)⋊C4—22no—
73C4⋊Dic47—21no—
74Dic47⋊C4—22no—
75C4×Dic47D412yescomplemented
76#10625329—21no—
77#10625329—21no—
78#10625329—21no—
79#10625329—21no—
80C2×C47⋊C8—21no—
81C2×C47⋊C8D412yescomplemented
82C23×C47—21no—
83C23×C47—21no—
84C23×C47—21no—
85C23×C47—21no—
86C23×C47—42no—
87C23×C47C2×D411yescharacteristic
88C22×D47—21no—
89Q8×C47—21no—
90Q8×C47—21no—
91D4×C47—21no—
92D4×C47—21no—
93D4×C47—44no—
94D4×C47—41no—
95D4×C47—41no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47#4111yescharacteristic
113C22⋊D47—44no—
114C22⋊D47—41no—
115C22⋊D47—41no—
116C2×Dic47—22no—
117C2×Dic47—21no—
118D188—21no—
119D188—21no—
120C4×D47—41no—
121C4×D47—41no—
122Dic94—21no—
123Dic94—21no—
124C47⋊C8—22no—
125C47⋊C8—41no—
126C22×C47—22no—
127C22×C47—22no—
128C22×C47—22no—
129C22×C47—41no—
130C22×C47—41no—
131C22×C47—41no—
132C22×C47—41no—
133C22×C47—42no—
134C22×C47—41no—
135C22×C47—41no—
136C22×C47#12011yescharacteristic
137C22×C47#12011yescharacteristic
138C22×C47#12111yescharacteristic
139C2×D47—42no—
140C2×D47—41no—
141C4×C47—42no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47#12011yescharacteristic
145C4×C47#12111yescharacteristic
146C4×C47#12111yescharacteristic
147C4×C47#12711yescharacteristic
148Dic47—42no—
149Dic47—41no—
150#2010—471nomaximal, Sylow
151C2×C47—21no—
152C2×C47—21no—
153C2×C47—21no—
154C2×C47—42no—
155C2×C47—81no—
156C2×C47#39211yescharacteristic
157D47—81no—
158#575—471no—
159#525—471no—
160#525D4711yescharacteristic, complemented
161#421—471no—
162#421—471no—
163#407—471no—
164H(3,ℤ/4)—471no—
165C47#201011yescharacteristic, complemented, Sylow
166C2×#41—471no—
167C2×#41C2×D4711yescharacteristic
168C23×C4C2×D4711yescharacteristic
169#137—941no—
170#137—941no—
171AGL(1,ℤ/8)—941no—
172AGL(1,ℤ/8)—941no—
173#135—942no—
174C2×M16—471no—
175C2×M16—471no—
176#123—21no—
177#123—941no—
178C22⋊Q8—21no—
179C22⋊Q8—941no—
180#121—21no—
181#121—941no—
182#120—21no—
183#120—941no—
184C4×D4—22no—
185C4×D4—942no—
186#117—471no—
187#117C2×D4711yescharacteristic
188#104—942no—
189#104—942no—
190C22⋊C8—942no—
191C24C22⋊D4711yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—941no—
197#41—941no—
198#41—941no—
199#41—941no—
200C2×Q8—471no—
201C2×Q8C22⋊D4711yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—471no—
205C2×D4—942no—
206C2×D4—941no—
207C2×D4C22⋊D4711yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—941no—
216C22×C4C22⋊D4711yescharacteristic
217C22×C4C22×D4711yescharacteristic
218Q16—942no—
219SD16—942no—
220SD16—942no—
221D8—942no—
222M16—941no—
223M16—941no—
224M16—941no—
225M16—941no—
226C2×C8—472no—
227C2×C8—941no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—942no—
231C4⋊C4—941no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—942no—
236C22⋊C4—942no—
237C22⋊C4—941no—
238C42—472no—
239C42C22⋊D4712yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—941no—
246C23C2×C22⋊D4711yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—941no—
250Q8—941no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—941no—
257D4—941no—
258D4—1884no—
259D4—1881no—
260D4—1881no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—942no—
273C2×C4—941no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4D4×D4711yescharacteristic
277C2×C4D4×D4711yescharacteristic
278C2×C4D4×D4711yescharacteristic
279C2×C4#1062535211yescharacteristic
280C2×C4C2×C22⋊D4711yescharacteristic
281C2×C4C2×C22⋊D4711yescharacteristic
282C8—942no—
283C8—1881no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—1882no—
295C22—1881no—
296C22#1309399211yescharacteristic
297C22#1309399311yescharacteristic
298C22#1309399611yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—1882no—
303C4—1881no—
304C4#1309399211yescharacteristic
305C4#1309399511yescharacteristic
306C4#1309399611yescharacteristic
307C4#1309402011yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—3761no—
314C2#1568903111yescharacteristic
subgroupG/H
centerC4#13094020
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#525C2
socleC2×C47#392
hypercenter#525D47
hypocenterC47#2010
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #15689921C2semidirect
2. #15689634C2semidirect
3. #15689141C2semidirect
4. #15689140C2semidirect
5. #15689087C2semidirect
6. #15688879C2semidirect
7. C47×#525C2semidirect
38. C2×Q8×C47D4semidirect
41. C2×D4×C47D4semidirect
57. C2×D188D4semidirect
59. C2×Dic94D4semidirect
65. C42×C47D4semidirect
75. C4×Dic47D4semidirect
81. C2×C47⋊C8D4semidirect
160. #525D47semidirect
165. C47#2010semidirect
201. C2×Q8C22⋊D47semidirect
207. C2×D4C22⋊D47semidirect
239. C42C22⋊D47semidirect