Finite Group Databasebeta

← #20256312

Subgroups — #20256312

Order 6016.

360 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#15689849C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic
3#15689531C211yesmaximal, characteristic, complemented
4#15689529C211yesmaximal, characteristic, complemented
5#15689527C211yesmaximal, characteristic, complemented
6#15689426C211yesmaximal, characteristic
7#15689424C211yesmaximal, characteristic
8#15689416C211yesmaximal, characteristic, complemented
9#15689406C211yesmaximal, characteristic, complemented
10#15689402C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689226C211yesmaximal, characteristic
13#15689221C211yesmaximal, characteristic
14#15689208C211yesmaximal, characteristic
15C47×#477C211yesmaximal, characteristic, complemented
16C2×Q8×D47—21no—
17C2×#10625336C2211yescharacteristic
18#13094023—21no—
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094016—21no—
23#13094016C2211yescharacteristic
24#13094015—21no—
25#13094015C2211yescharacteristic
26#13094002—21no—
27#13094002—21no—
28#13094000—21no—
29Q8×Dic47C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31C4×Dic94—21no—
32C4×Dic94C2211yescharacteristic
33C4×D188C2211yescharacteristic
34#13093986C2211yescharacteristic
35#13093986C2211yescharacteristic
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C4⋊Q8×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47C2311yescharacteristic
61Q8×D47—44no—
62C2×D188C2311yescharacteristic
63C2×C4×D47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94D411yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79#10625336Q814yescomplemented
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⋊Dic47D411yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89C4⋊Dic47C2311yescharacteristic
90Dic47⋊C4—21no—
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×Dic47C2311yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C22×D47—21no—
105Q8×C47—21no—
106Q8×C47—42no—
107Q8×C47C2×Q812yescomplemented
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2411yescharacteristic
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47C2×D411yescharacteristic
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122D188—21no—
123D188C2×Q812yes—
124C4×D47—42no—
125C4×D47—42no—
126C4×D47—42no—
127Dic94—22no—
128Dic94—42no—
129Dic94—42no—
130Dic94—42no—
131C8×C47—21no—
132C8×C47—21no—
133C47⋊C8—21no—
134C47⋊C8C2×Q812yescomplemented
135C22×C47C22×D411yescharacteristic
136C2×D47—22no—
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×C47C22×Q811yescharacteristic
146C4×C472−1+411yescharacteristic
147Dic47—21no—
148Dic47—21no—
149Dic47—21no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47AGL(1,ℤ/8)12yes—
154#3386—471nomaximal, Sylow
155C2×C47D4×Q811yescharacteristic
156C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
157C2×C47#57811yescharacteristic
158D47—42no—
159#557—471no—
160D4×Q8—471no—
161#501—471no—
162#501—471no—
163#500—471no—
164#478—471no—
165#478—471no—
166#477—471no—
167#477D4711yescharacteristic, complemented
168#475—471no—
169#474—471no—
170#446—471no—
171#440—471no—
172#440—471no—
173C4×SD16—471no—
174C47#338611yescharacteristic, complemented, Sylow
175C22×Q8—941no—
176C2×SD16—471no—
177C4⋊Q8—471no—
178C4⋊Q8—471no—
179C4⋊Q8—471no—
180C4⋊Q8—941no—
181C4⋊Q8C2×D4711yescharacteristic
182#125—471no—
183#125—471no—
184#125—941no—
185#125—941no—
186C22⋊Q8—941no—
187C22⋊Q8—941no—
188C22⋊Q8—941no—
189C4×Q8—471no—
190C4×Q8—471no—
191C4×Q8—471no—
192C4×Q8—941no—
193C4×Q8C2×D4711yescharacteristic
194C4×D4—471no—
195C4×D4—471no—
196C4×D4—471no—
197#107—471no—
198#107—471no—
199#107—471no—
200#107—471no—
201#107C2×D4711yescharacteristic
202#107C2×D4711yescharacteristic
203#106—471no—
204#106—471no—
205#106—471no—
206C4⋊C8—471no—
207C4⋊C8—471no—
208C4⋊C8C2×D4711yescharacteristic
209#103—471no—
210#103C2×D4711yescharacteristic
211#103C2×D4711yescharacteristic
212#102—471no—
213#102—471no—
214#102—471no—
215#97—471no—
216#97—471no—
217C4×C8—471no—
218C2×Q8—21no—
219C2×Q8—471no—
220C2×Q8—941no—
221C2×Q8—941no—
222C2×Q8—941no—
223C2×Q8—1884no—
224C2×Q8C22×D4711yescharacteristic
225C2×D4—471no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4—941no—
229SD16—474no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8C22×D4711yescharacteristic
233C2×C8C22×D4711yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—471no—
237C4⋊C4—471no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4C22×D4711yescharacteristic
252C4⋊C4C22×D4711yescharacteristic
253C4⋊C4C22×D4711yescharacteristic
254C22⋊C4—941no—
255C22⋊C4—941no—
256C22⋊C4—941no—
257C42—21no—
258C42—471no—
259C42—471no—
260C42—941no—
261C42—941no—
262C42C22×D4711yescharacteristic
263C23—941no—
264Q8—21no—
265Q8—42no—
266Q8—942no—
267Q8—1882no—
268Q8—1882no—
269Q8—1882no—
270Q8Q8×D4712yescomplemented
271D4—472no—
272D4—941no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—471no—
278C2×C4—471no—
279C2×C4—471no—
280C2×C4—471no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—1882no—
285C2×C4—1882no—
286C2×C4—1882no—
287C2×C4D4×D4711yescharacteristic
288C2×C4D4×D4711yescharacteristic
289C2×C4C23×D4711yescharacteristic
290C8—21no—
291C8—21no—
292C8—472no—
293C8—941no—
294C22—942no—
295C22—1881no—
296C22—1881no—
297C22C2×D4×D4711yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—472no—
305C4—941no—
306C4—941no—
307C4—941no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4C2×Q8×D4711yescharacteristic
312C4#1309407111yescharacteristic
313C2—1882no—
314C2#1568978611yescharacteristic
315C2AGL(1,ℤ/8)×D4711yescharacteristic
316C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#477C2
socleC22×C47C22×D4
hypercenter#477D47
hypocenterC47#3386
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #15689849C2semidirect
3. #15689531C2semidirect
4. #15689529C2semidirect
5. #15689527C2semidirect
8. #15689416C2semidirect
9. #15689406C2semidirect
11. #15689252C2semidirect
15. C47×#477C2semidirect
79. #10625336Q8semidirect
107. Q8×C47C2×Q8semidirect
134. C47⋊C8C2×Q8semidirect
167. #477D47semidirect
174. C47#3386semidirect
270. Q8Q8×D47semidirect