Finite Group Databasebeta

← #20256235

Subgroups — #20256235

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689852C211yesmaximal, characteristic, complemented
2#15689845C211yesmaximal, characteristic
3#15689490C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic
5#15689479C211yesmaximal, characteristic
6#15689433C211yesmaximal, characteristic, complemented
7#15689422C211yesmaximal, characteristic
8#15689418C211yesmaximal, characteristic, complemented
9#15689347C211yesmaximal, characteristic
10#15689345C211yesmaximal, characteristic
11#15689331C211yesmaximal, characteristic, complemented
12#15689251C211yesmaximal, characteristic, complemented
13#15689226C211yesmaximal, characteristic
14#15689215C211yesmaximal, characteristic, complemented
15C47×#441C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18#13094024—21no—
19#13094024C2211yescharacteristic
20#13094022C2211yescharacteristic
21#13094019—21no—
22#13094018—21no—
23#13094015—21no—
24#13094015—21no—
25#13094015C2211yescharacteristic
26#13094015C2211yescharacteristic
27#13094013C2211yescharacteristic
28#13094012C2211yescharacteristic
29#13094002—21no—
30Q8×Dic47C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32C4×Dic94—21no—
33C4×Dic94C2211yescharacteristic
34#13093989C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093981—21no—
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39C4⋊(C47⋊C8)C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093944C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×Q8×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×Dic94—21no—
64C2×Dic94D411yescharacteristic
65C2×Dic94C2311yescharacteristic
66Q16×C47—22no—
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C42×C47—21no—
74C42×C47—21no—
75C42×C47C2311yescharacteristic
76#10625337—22no—
77#10625336—22no—
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—
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47D411yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4D411yescharacteristic
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C22×D47—21no—
106Q8×C47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47#4112yes—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2411yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C2×Dic47C2×D411yescharacteristic
124D188—21no—
125D188—21no—
126C4×D47—42no—
127Dic94—21no—
128Dic94—21no—
129Dic94—41no—
130Dic94—42no—
131C8×C47—21no—
132C8×C47—21no—
133C47⋊C8—21no—
134C47⋊C8—21no—
135C22×C47C22×D411yescharacteristic
136C2×D47—41no—
137C2×D47—41no—
138C2×D47—41no—
139C4×C47—22no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47C2×#4111yescharacteristic
146C4×C472−1+411yescharacteristic
147Dic47—21no—
148Dic47—21no—
149Dic47—21no—
150Dic47—21no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3377—471nomaximal, Sylow
155C2×C47#54811yescharacteristic
156C2×C47#57511yescharacteristic
157C2×C47#57811yescharacteristic
158D47—81no—
159#557—471no—
160#556—471no—
161#491—471no—
162#489—471no—
163#488—471no—
164#479—471no—
165#478—471no—
166#477—471no—
167#464—471no—
168#464—471no—
169#462—471no—
170#446—471no—
171#441D4711yescharacteristic, complemented
172#440—471no—
173C4×Q16—471no—
174C47#337711yescharacteristic, complemented, Sylow
175C2×Q16—471no—
176C2×Q16C2×D4711yescharacteristic
177C2×SD16—471no—
178C4⋊Q8—471no—
179C4⋊Q8—471no—
180C4⋊Q8—941no—
181#126—941no—
182#126—941no—
183#125—471no—
184#125—471no—
185#125—941no—
186#125—941no—
187#124—471no—
188#124—471no—
189C22⋊Q8—941no—
190C4×Q8—471no—
191C4×Q8—471no—
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—941no—
195C4×Q8C2×D4711yescharacteristic
196C4×Q8C2×D4711yescharacteristic
197C4×D4—471no—
198#117—941no—
199#107—471no—
200#107—471no—
201#106C2×D4711yescharacteristic
202C4⋊C8—471no—
203C4⋊C8—471no—
204C4⋊C8—471no—
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209#103—471no—
210#103C2×D4711yescharacteristic
211#103C2×D4711yescharacteristic
212#102—471no—
213#102—471no—
214#102—471no—
215#97—471no—
216#97C2×D4711yescharacteristic
217C4×C8—471no—
218C2×Q8—471no—
219C2×Q8—471no—
220C2×Q8—941no—
221C2×Q8C22×D4711yescharacteristic
222C2×Q8C22×D4711yescharacteristic
223C2×D4—471no—
224C22×C4—941no—
225Q16—22no—
226Q16—942no—
227SD16—942no—
228C2×C8—471no—
229C2×C8—471no—
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4C22×D4711yescharacteristic
250C4⋊C4C22×D4711yescharacteristic
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C42—21no—
257C42—21no—
258C42—471no—
259C42—471no—
260C42—941no—
261C42—941no—
262C42—941no—
263C42C22×D4711yescharacteristic
264C23—941no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—941no—
269Q8—941no—
270Q8—1881no—
271Q8—1882no—
272Q8#1062535012yes—
273D4—941no—
274D4—941no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—471no—
280C2×C4—471no—
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—1882no—
287C2×C4D4×D4711yescharacteristic
288C2×C4D4×D4711yescharacteristic
289C2×C4C23×D4711yescharacteristic
290C8—21no—
291C8—21no—
292C8—941no—
293C8—941no—
294C22—1881no—
295C22—1881no—
296C22—1881no—
297C22C2×D4×D4711yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—941no—
305C4—941no—
306C4—941no—
307C4—941no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4C2×#1062535011yescharacteristic
312C4#1309407111yescharacteristic
313C2—3761no—
314C2#1568978211yescharacteristic
315C2#1568992211yescharacteristic
316C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3377
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #15689852C2semidirect
3. #15689490C2semidirect
6. #15689433C2semidirect
8. #15689418C2semidirect
11. #15689331C2semidirect
12. #15689251C2semidirect
14. #15689215C2semidirect
15. C47×#441C2semidirect
171. #441D47semidirect
174. C47#3377semidirect