Finite Group Databasebeta

← #20253612

Subgroups — #20253612

Order 6016.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689740C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689417C211yesmaximal, characteristic, complemented
5#15689407C211yesmaximal, characteristic, complemented
6#15689344C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689281C211yesmaximal, characteristic, complemented
9#15689261C211yesmaximal, characteristic
10#15689229C211yesmaximal, characteristic, complemented
11#15689220C211yesmaximal, characteristic, complemented
12#15689217C211yesmaximal, characteristic, complemented
13#15689214C211yesmaximal, characteristic, complemented
14#15689181C211yesmaximal, characteristic, complemented
15C47×#482C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×Dic188C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094017—21no—
23#13094011—21no—
24#13094011C2211yescharacteristic
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13094001—21no—
28C4×Dic94—21no—
29C4×Dic94—21no—
30#13093989C2211yescharacteristic
31#13093989C2211yescharacteristic
32#13093989C2211yescharacteristic
33#13093989C2211yescharacteristic
34#13093989C2211yescharacteristic
35D4×Dic47C2211yescharacteristic
36#13093983C2211yescharacteristic
37#13093980—21no—
38#13093980—21no—
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C2×Dic94—21no—
65C2×Dic94—22no—
66C2×Dic94—22no—
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69C2×Dic94C2311yescharacteristic
70C2×Dic94C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C22⋊C4×C47—21no—
78C42×C47—21no—
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47D411yescharacteristic
84C22⋊Dic47D411yescharacteristic
85#10625335—22no—
86#10625335—22no—
87C4⋊Dic47D411yescharacteristic
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106Dic188—22no—
107Dic188—22no—
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110D4×C47—21no—
111D4×C47—21no—
112D4×C47—81no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C2×Dic47—24no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—81no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C2×Dic47C2×D411yescharacteristic
130Dic94—24no—
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136Dic94#4112yes—
137Dic94#4112yes—
138C8×C47—21no—
139C8×C47—21no—
140C47⋊C8—21no—
141C47⋊C8—21no—
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47C22×D411yescharacteristic
149C4×C47—21no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C47C2×#4111yescharacteristic
155Dic47—22no—
156Dic47—22no—
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—21no—
161Dic47—41no—
162Dic47—41no—
163#3121—471nomaximal, Sylow
164C2×C47—41no—
165C2×C47—81no—
166C2×C47#52511yescharacteristic
167C2×C47#57711yescharacteristic
168C2×C47#57811yescharacteristic
169#542—471no—
170#519—471no—
171#485—471no—
172#482D4711yescharacteristic
173#477—471no—
174#475—471no—
175#464—471no—
176#464—471no—
177#451—471no—
178#448—471no—
179#441—471no—
180#440—471no—
181C4×Q16—471no—
182C4×SD16—471no—
183#433—471no—
184C47#312111yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C2×Q16—471no—
187C2×Q16—471no—
188C2×SD16—471no—
189C2×SD16—471no—
190C4⋊Q8—471no—
191#126—941no—
192#124—471no—
193#124—941no—
194#123—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197#121C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—471no—
203C4×Q8—941no—
204C4×Q8—941no—
205C4×D4—471no—
206#117—471no—
207#117—941no—
208#117—941no—
209#117C2×D4711yescharacteristic
210#107—471no—
211#107C2×D4711yescharacteristic
212#106—471no—
213#106C2×D4711yescharacteristic
214C4⋊C8—471no—
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#102C2×D4711yescharacteristic
223#102C2×D4711yescharacteristic
224C22⋊C8—471no—
225C22⋊C8C2×D4711yescharacteristic
226#97—471no—
227C4×C8—471no—
228C2×Q8—471no—
229C2×Q8—471no—
230C2×Q8—471no—
231C2×Q8—941no—
232C2×Q8—942no—
233C2×Q8—942no—
234C2×Q8—941no—
235C2×D4—21no—
236C2×D4C22×D4711yescharacteristic
237C22×C4—941no—
238C22×C4—941no—
239C22×C4C22×D4711yescharacteristic
240Q16—942no—
241Q16—942no—
242SD16—942no—
243SD16—942no—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8C22×D4711yescharacteristic
247C2×C8C22×D4711yescharacteristic
248C4⋊C4—471no—
249C4⋊C4—471no—
250C4⋊C4—471no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C42—21no—
270C42—471no—
271C42—471no—
272C42—941no—
273C42—941no—
274C42—941no—
275C42—941no—
276C42—941no—
277C23—21no—
278C23D4×D4711yescharacteristic
279Q8—472no—
280Q8—472no—
281Q8—944no—
282Q8—941no—
283Q8—941no—
284Q8—941no—
285Q8—941no—
286Q8—3761no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—944no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—3761no—
305C2×C4D4×D4711yescharacteristic
306C2×C4C23×D4711yescharacteristic
307C8—21no—
308C8—21no—
309C8—941no—
310C8—941no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D4711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—942no—
323C4—942no—
324C4—941no—
325C4—941no—
326C4—941no—
327C4—941no—
328C4—1881no—
329C4—1881no—
330C4#41×D4711yescharacteristic
331C4#41×D4711yescharacteristic
332C2—41no—
333C2—81no—
334C2#1568963111yescharacteristic
335C2#1568993311yescharacteristic
336C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#482C2
socleC22×C47C22×D4
hypercenter#482D47
hypocenterC47#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
3. #15689464C2semidirect
4. #15689417C2semidirect
5. #15689407C2semidirect
6. #15689344C2semidirect
7. #15689344C2semidirect
8. #15689281C2semidirect
10. #15689229C2semidirect
11. #15689220C2semidirect
12. #15689217C2semidirect
13. #15689214C2semidirect
14. #15689181C2semidirect
184. C47#3121semidirect