Finite Group Databasebeta

← #20256164

Subgroups — #20256164

Order 6016.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689848C211yesmaximal, characteristic, complemented
2#15689832C211yesmaximal, characteristic
3#15689491C211yesmaximal, characteristic, complemented
4#15689490C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689431C211yesmaximal, characteristic, complemented
7#15689428C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic
10#15689326C211yesmaximal, characteristic
11#15689252C211yesmaximal, characteristic, complemented
12#15689224C211yesmaximal, characteristic
13#15689223C211yesmaximal, characteristic
14SD16×Dic47C211yesmaximal, characteristic
15C47×#461C211yesmaximal, characteristic
16C2×#10625335C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094022C2211yescharacteristic
19#13094022C2211yescharacteristic
20#13094016C2211yescharacteristic
21#13094015—21no—
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094014—21no—
25#13094003—21no—
26#13094001—21no—
27#13094001—21no—
28Q8×Dic47C2211yescharacteristic
29Q8×Dic47C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×Dic94C2211yescharacteristic
32#13093989—21no—
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35C2×Dic47⋊C4—21no—
36#13093958C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39Dic47⋊C8C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093935C2211yescharacteristic
50#13093934C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C2×Dic94—21no—
66C2×Dic94D411yescharacteristic
67C2×Dic94C2311yescharacteristic
68SD16×C47—22no—
69SD16×C47—22no—
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C22⋊C4×C47—21no—
76C42×C47C2311yescharacteristic
77C22⋊Dic47—21no—
78C22⋊Dic47—21no—
79#10625335—22no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47D411yescharacteristic
84C4⋊Dic47C2311yescharacteristic
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
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×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C23×C47—21no—
106Q8×C47—21no—
107Q8×C47—21no—
108Q8×C47—21no—
109Q8×C47—21no—
110D4×C47—21no—
111D4×C47#4112yes—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—81no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2411yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—42no—
124C2×Dic47—81no—
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129Dic94—22no—
130Dic94—21no—
131Dic94—21no—
132Dic94—81no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C22×C47—22no—
138C22×C47—41no—
139C22×C47—41no—
140C22×C47C22×D411yescharacteristic
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47C2×#4111yescharacteristic
147C4×C472−1+411yescharacteristic
148Dic47—21no—
149Dic47—21no—
150Dic47—21no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47#13712yes—
156#3372—471nomaximal, Sylow
157C2×C47—42no—
158C2×C47#54811yescharacteristic
159C2×C47C2×#13711yescharacteristic
160C2×C47#57711yescharacteristic
161#557—471no—
162#554—471no—
163#491—471no—
164#491—471no—
165#487—471no—
166#479—471no—
167#479—471no—
168#477—471no—
169#461—471no—
170#461—471no—
171#461D4711yescharacteristic
172#446—471no—
173#440—471no—
174#440—471no—
175C4×SD16—471no—
176C47#337211yescharacteristic, complemented, Sylow
177C2×SD16—471no—
178C2×SD16C2×D4711yescharacteristic
179C2×SD16C2×D4711yescharacteristic
180C4⋊Q8—471no—
181C4⋊Q8—471no—
182C4⋊Q8—471no—
183C4⋊Q8C2×D4711yescharacteristic
184#125—471no—
185#125—471no—
186#125—941no—
187#125—941no—
188#125—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C22⋊Q8—941no—
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—471no—
196C4×Q8—941no—
197C4×D4—471no—
198C4×D4—471no—
199C4×D4C2×D4711yescharacteristic
200C2×C4⋊C4—941no—
201#107—471no—
202#107—471no—
203#106—471no—
204C4⋊C8—471no—
205C4⋊C8—471no—
206C4⋊C8C2×D4711yescharacteristic
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#103—471no—
212#103—471no—
213#103—471no—
214#103C2×D4711yescharacteristic
215#103C2×D4711yescharacteristic
216#102—471no—
217#97—471no—
218#97—471no—
219C4×C8—471no—
220C2×Q8—471no—
221C2×Q8—471no—
222C2×Q8—941no—
223C2×Q8C22×D4711yescharacteristic
224C2×Q8C22×D4711yescharacteristic
225C2×D4C22×D4711yescharacteristic
226C22×C4—21no—
227C22×C4—941no—
228C22×C4—941no—
229SD16—22no—
230SD16—22no—
231SD16—942no—
232C2×C8—471no—
233C2×C8—471no—
234C2×C8C22×D4711yescharacteristic
235C2×C8C22×D4711yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—941no—
259C22⋊C4—941no—
260C42—471no—
261C42—471no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42C22×D4711yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—21no—
271Q8—942no—
272Q8—941no—
273Q8—941no—
274Q8—3761no—
275D4—21no—
276D4#1062535212yes—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—471no—
284C2×C4—471no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—3761no—
290C2×C4—1882no—
291C2×C4D4×D4711yescharacteristic
292C2×C4D4×D4711yescharacteristic
293C2×C4C23×D4711yescharacteristic
294C8—21no—
295C8—21no—
296C8—941no—
297C8—941no—
298C22—22no—
299C22—41no—
300C22—41no—
301C22C2×D4×D4711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—472no—
308C4—941no—
309C4—941no—
310C4—941no—
311C4—1881no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4C2×#1062535211yescharacteristic
316C4#1309407111yescharacteristic
317C2—42no—
318C2#1568977911yescharacteristic
319C2#137×D4711yescharacteristic
320C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3372
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
3. #15689491C2semidirect
4. #15689490C2semidirect
5. #15689472C2semidirect
6. #15689431C2semidirect
7. #15689428C2semidirect
8. #15689416C2semidirect
11. #15689252C2semidirect
176. C47#3372semidirect