Finite Group Databasebeta

← #20243353

Subgroups — #20243353

Order 6016.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#15689959C211yesmaximal, characteristic
2#15689141C211yesmaximal, characteristic, complemented
3#15689140C211yesmaximal, characteristic, complemented
4#15689120C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15689089C211yesmaximal, characteristic, complemented
7C47×#416C211yesmaximal, characteristic, complemented
8#13094072—21no—
9#13094071—21no—
10#13094071C412yescomplemented
11#13094070—21no—
12#13094070C412yescomplemented
13#13094069—21no—
14#13094069—22no—
15C2×#10625350—22no—
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18#41×D47—22no—
19#41×D47—22no—
20C2×#10625329C2211yescharacteristic, complemented
21#13093983C2211yescharacteristic, complemented
22#13093952—22no—
23#13093951—22no—
24#13093949—21no—
25#13093946—21no—
26#13093938—22no—
27(C2×D47)⋊C8—22no—
28C2×#41×C47C2211yescharacteristic
29C22×C8×C47C2211yescharacteristic, complemented
30#117×C47C2211yescharacteristic, complemented
31#103×C47—21no—
32#102×C47—21no—
33#41×C47—21no—
34#41×C47—21no—
35#41×C47C2×C412yes—
36#41×C47D412yes—
37C2×Q8×C47D411yescharacteristic
38C2×D4×C47—21no—
39C2×D4×C47D411yescharacteristic
40C22×C4×C47—21no—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—24no—
43C2×C22⋊D47—21no—
44C2×C22⋊D47D412yes—
45#10625354—22no—
46#10625354—22no—
47Q8×D47—22no—
48Q8×D47—22no—
49#10625352—24no—
50#10625352—22no—
51#10625352—22no—
52#10625352—24no—
53D4×D47—24no—
54D4×D47—22no—
55D4×D47—24no—
56D4×D47—22no—
57#10625350—24no—
58#10625350—24no—
59#10625350—21no—
60#10625350—21no—
61#10625350—21no—
62#10625350—21no—
63#10625350—21no—
64#10625350—21no—
65#10625350—22no—
66#10625350—22no—
67#10625350C2×C412yes—
68#10625350D412yes—
69C2×D188—22no—
70C2×D188C2×C411yescharacteristic
71C2×D188D411yescharacteristic
72C2×C4×D47—24no—
73C2×C4×D47—21no—
74C2×C4×D47D412yes—
75C2×Dic94—22no—
76C2×Dic94C2×C411yescharacteristic
77C2×Dic94D411yescharacteristic
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—21no—
81C4⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C42×C47—21no—
84C22⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4×Dic47—21no—
87#10625329—21no—
88#10625329—21no—
89C2×C47⋊C8—21no—
90C23×C47—21no—
91C23×C47C2×D411yescharacteristic
92C22×D47—24no—
93C22×D47—21no—
94C22×D47C22⋊C412yes—
95Q8×C47—21no—
96Q8×C47C22⋊C412yes—
97D4×C47—22no—
98D4×C47—22no—
99D4×C47—21no—
100D4×C47C22⋊C412yes—
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—41no—
105C2×C4×C47C22×C411yescharacteristic
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C22⋊D47—24no—
112C22⋊D47—24no—
113C22⋊D47—22no—
114C22⋊D47—22no—
115C22⋊D47—22no—
116C22⋊D47—22no—
117C2×Dic47—24no—
118C2×Dic47—21no—
119C2×Dic47—41no—
120C2×Dic47C22⋊C412yes—
121D188—24no—
122D188—21no—
123D188—21no—
124D188—21no—
125D188C22⋊C412yes—
126C4×D47—24no—
127C4×D47—24no—
128C4×D47—22no—
129C4×D47—22no—
130C4×D47—22no—
131C4×D47—22no—
132Dic94—24no—
133Dic94—21no—
134Dic94—21no—
135Dic94—21no—
136Dic94C22⋊C412yes—
137C8×C47—41no—
138C47⋊C8—41no—
139C22×C47—22no—
140C22×C47—41no—
141C22×C47—81no—
142C22×C47C2×C22⋊C411yescharacteristic
143C22×C47#12011yescharacteristic
144C22×C47#12011yescharacteristic
145C2×D47—22no—
146C2×D47—22no—
147C2×D47—42no—
148C2×D47—81no—
149C2×D47—84no—
150C4×C47—22no—
151C4×C47—81no—
152C4×C47C2×C22⋊C411yescharacteristic
153C4×C47C2×C22⋊C411yescharacteristic
154C4×C47#12011yescharacteristic
155C4×C47#12011yescharacteristic
156Dic47—22no—
157Dic47—22no—
158Dic47—81no—
159#1794—471nomaximal, Sylow
160C2×C47—21no—
161C2×C47—21no—
162C2×C47—21no—
163C2×C47—42no—
164C2×C47#37911yescharacteristic
165D47—42no—
166D47—42no—
167#585—471no—
168#421—471no—
169#421—471no—
170#416—471no—
171#416D4711yescharacteristic, complemented
172#410—471no—
173#408—471no—
174C47#179411yescharacteristic, complemented, Sylow
1752−1+4—472no—
1762−1+4—941no—
1772−1+4—941no—
178H(5,𝔽2)—472no—
179H(5,𝔽2)—942no—
180H(5,𝔽2)—941no—
181H(5,𝔽2)—941no—
182C2×#41—471no—
183C2×#41—471no—
184C2×#41—942no—
185C2×#41—942no—
186C2×#41—942no—
187C2×#41C2×D4711yescharacteristic
188C2×M16—471no—
189C22×C8C2×D4711yescharacteristic, complemented
190#117—471no—
191#117C2×D4711yescharacteristic, complemented
192#104—942no—
193#104—942no—
194#103—21no—
195#103—941no—
196#102—21no—
197#102—941no—
198#99—942no—
199C22⋊C8—942no—
200#41—21no—
201#41—21no—
202#41—472no—
203#41—472no—
204#41—942no—
205#41—942no—
206#41—944no—
207#41—944no—
208#41—944no—
209#41—944no—
210#41—942no—
211#41—942no—
212#41—942no—
213#41—942no—
214#41—941no—
215#41—941no—
216#41—941no—
217#41—941no—
218#41—941no—
219#41—941no—
220#41C4×D4712yes—
221#41D18812yes—
222C2×Q8—471no—
223C2×Q8—471no—
224C2×Q8—942no—
225C2×Q8—942no—
226C2×Q8—942no—
227C2×Q8C22⋊D4711yescharacteristic
228C2×D4—21no—
229C2×D4—472no—
230C2×D4—471no—
231C2×D4—471no—
232C2×D4—942no—
233C2×D4—944no—
234C2×D4—944no—
235C2×D4—942no—
236C2×D4—944no—
237C2×D4—941no—
238C2×D4—942no—
239C2×D4C22⋊D4711yescharacteristic
240C22×C4—21no—
241C22×C4—472no—
242C22×C4—944no—
243C22×C4—941no—
244C22×C4C22×D4711yescharacteristic
245M16—941no—
246M16—941no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—941no—
251C4⋊C4—21no—
252C4⋊C4—941no—
253C22⋊C4—21no—
254C22⋊C4—941no—
255C42—21no—
256C42—941no—
257C23—21no—
258C23—472no—
259C23—944no—
260C23—941no—
261C23D4×D4711yescharacteristic
262Q8—21no—
263Q8—472no—
264Q8—944no—
265Q8—941no—
266Q8—941no—
267Q8—941no—
268Q8(C2×D47)⋊C412yes—
269D4—22no—
270D4—22no—
271D4—21no—
272D4—472no—
273D4—944no—
274D4—944no—
275D4—944no—
276D4—942no—
277D4—942no—
278D4—942no—
279D4—942no—
280D4—941no—
281D4—941no—
282D4—941no—
283D4(C2×D47)⋊C412yes—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—472no—
289C2×C4—944no—
290C2×C4—944no—
291C2×C4—944no—
292C2×C4—941no—
293C2×C4—942no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—942no—
297C2×C4—1881no—
298C2×C4C2×C4×D4711yescharacteristic
299C2×C4C2×D18811yescharacteristic
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4D4×D4711yescharacteristic
303C2×C4C2×C22⋊D4711yescharacteristic
304C8—41no—
305C8—1881no—
306C22—22no—
307C22—41no—
308C22—81no—
309C22—942no—
310C22—942no—
311C22—3761no—
312C22—3764no—
313C22—1882no—
314C22C22⋊C4×D4711yescharacteristic
315C22#1309399211yescharacteristic
316C22#1309399411yescharacteristic
317C4—22no—
318C4—81no—
319C4—942no—
320C4—942no—
321C4—3761no—
322C4C22⋊C4×D4711yescharacteristic
323C4C2×(C2×D47)⋊C411yescharacteristic
324C4#1309399211yescharacteristic
325C4#1309399411yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—42no—
330C2—1882no—
331C2—1882no—
332C2#1568897811yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#416C2
socleC2×C47#379
hypercenter#416D47
hypocenterC47#1794
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #15689141C2semidirect
3. #15689140C2semidirect
4. #15689120C2semidirect
5. #15689096C2semidirect
6. #15689089C2semidirect
7. C47×#416C2semidirect
10. #13094071C4semidirect
12. #13094070C4semidirect
20. C2×#10625329C22semidirect
21. #13093983C22semidirect
29. C22×C8×C47C22semidirect
30. #117×C47C22semidirect
171. #416D47semidirect
174. C47#1794semidirect
189. C22×C8C2×D47semidirect
191. #117C2×D47semidirect