Finite Group Databasebeta

← #20254061

Subgroups — #20254061

Order 6016.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689747C211yesmaximal, characteristic
2#15689736C211yesmaximal, characteristic, complemented
3#15689517C211yesmaximal, characteristic, complemented
4#15689480C211yesmaximal, characteristic, complemented
5#15689475C211yesmaximal, characteristic, complemented
6#15689382C211yesmaximal, characteristic, complemented
7#15689370C211yesmaximal, characteristic
8#15689365C211yesmaximal, characteristic, complemented
9#15689353C211yesmaximal, characteristic
10#15689229C211yesmaximal, characteristic, complemented
11#15689222C211yesmaximal, characteristic, complemented
12#15689217C211yesmaximal, characteristic, complemented
13#15689210C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#501C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094024C2211yescharacteristic
23#13094019—21no—
24#13094019—21no—
25#13094019—21no—
26#13094015—21no—
27#13094015—21no—
28#13094013—21no—
29#13094012C2211yescharacteristic
30#13094009—21no—
31#13094004C2211yescharacteristic
32#13094004C2211yescharacteristic
33#13094004C2211yescharacteristic
34#13094000—21no—
35#13093999C2211yescharacteristic
36#13093989C2211yescharacteristic
37#13093989C2211yescharacteristic
38#13093989C2211yescharacteristic
39#13093986C2211yescharacteristic
40#13093981C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093947C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53#125×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic
57#106×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×D188—21no—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×C4×D47C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66C2×Dic94C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47C2311yescharacteristic
73C4⋊C4×C47C2311yescharacteristic
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C42×C47C2311yescharacteristic
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4D411yescharacteristic
85(C2×D47)⋊C4D411yescharacteristic
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4D411yescharacteristic
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102Dic188—22no—
103Dic188—22no—
104#10625325—22no—
105#10625325—22no—
106#10625324—22no—
107C8×D47—22no—
108C22×D47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—81no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188—21no—
126D188—81no—
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—81no—
130Dic94—21no—
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—21no—
135Dic94—21no—
136C8×C47#4112yes—
137C8×C47#4112yes—
138C47⋊C8—21no—
139C47⋊C8—21no—
140C22×C47C22×D411yescharacteristic
141C2×D47—21no—
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C2×#4111yescharacteristic
154C4×C47C2×#4111yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3178—471nomaximal, Sylow
162C2×C47#53211yescharacteristic
163C2×C47#57711yescharacteristic
164C2×C47#57811yescharacteristic
165D47—41no—
166D47—81no—
167#542—471no—
168#541—471no—
169#501D4711yescharacteristic, complemented
170#497—471no—
171#488—471no—
172#487—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#441—471no—
178#440—471no—
179C4×Q16—471no—
180C4×SD16—471no—
181#405—471no—
182C47#317811yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×Q16—471no—
185C2×SD16—471no—
186C2×SD16—471no—
187C2×M16—471no—
188C22×C8—471no—
189C4⋊Q8—471no—
190C4⋊Q8C2×D4711yescharacteristic
191#126—941no—
192#126—941no—
193#126—941no—
194#125—941no—
195#125—941no—
196#125C2×D4711yescharacteristic
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—941no—
204#121—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×D4—471no—
209#117—471no—
210#107C2×D4711yescharacteristic
211#107C2×D4711yescharacteristic
212#106C2×D4711yescharacteristic
213#106C2×D4711yescharacteristic
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#102—471no—
221#102—471no—
222#97—471no—
223#97C2×D4711yescharacteristic
224C4×C8—471no—
225C4×C8—471no—
226C2×Q8—21no—
227C2×Q8—471no—
228C2×Q8—471no—
229C2×Q8—471no—
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—471no—
233C22×C4—941no—
234Q16—942no—
235Q16—942no—
236SD16—942no—
237SD16—942no—
238M16—942no—
239C2×C8—471no—
240C2×C8—471no—
241C2×C8—942no—
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—471no—
248C4⋊C4—471no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4C22×D4711yescharacteristic
258C4⋊C4C22×D4711yescharacteristic
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C22⋊C4—471no—
262C22⋊C4—471no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—471no—
271C42—941no—
272C42—941no—
273C42—941no—
274C42C22×D4711yescharacteristic
275C23—471no—
276C23—941no—
277Q8—81no—
278Q8—941no—
279Q8—941no—
280Q8—941no—
281Q8—941no—
282Q8—941no—
283Q8—941no—
284D4—941no—
285D4—941no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—471no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—3761no—
300C2×C4D4×D4711yescharacteristic
301C2×C4D4×D4711yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—941no—
304C8—941no—
305C8#1062535412yes—
306C8#1062535412yes—
307C22—941no—
308C22—941no—
309C22—941no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C2×D4×D4711yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—941no—
321C4—941no—
322C4—941no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4C2×#1062535411yescharacteristic
327C4C2×#1062535411yescharacteristic
328C2—3761no—
329C2—1881no—
330C2#1568967411yescharacteristic
331C2#1568993311yescharacteristic
332C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #15689736C2semidirect
3. #15689517C2semidirect
4. #15689480C2semidirect
5. #15689475C2semidirect
6. #15689382C2semidirect
8. #15689365C2semidirect
10. #15689229C2semidirect
11. #15689222C2semidirect
12. #15689217C2semidirect
13. #15689210C2semidirect
14. #15689080C2semidirect
15. C47×#501C2semidirect
169. #501D47semidirect
182. C47#3178semidirect