Finite Group Databasebeta

← #20254545

Subgroups — #20254545

Order 6016.

326 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689676C211yesmaximal, characteristic
2#15689675C211yesmaximal, characteristic
3#15689527C211yesmaximal, characteristic, complemented
4#15689520C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689472C211yesmaximal, characteristic, complemented
7#15689465C211yesmaximal, characteristic
8#15689464C211yesmaximal, characteristic
9#15689461C211yesmaximal, characteristic
10#15689433C211yesmaximal, characteristic, complemented
11#15689432C211yesmaximal, characteristic, complemented
12#15689429C211yesmaximal, characteristic, complemented
13#15689428C211yesmaximal, characteristic, complemented
14#15689173C211yesmaximal, characteristic
15C47×#485C211yesmaximal, characteristic
16#13094023C2211yescharacteristic
17#13094023C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094022C2211yescharacteristic
20#13094015C2211yescharacteristic
21#13094015C2211yescharacteristic
22#13094014—21no—
23#13094003C2211yescharacteristic
24#13094001—21no—
25#13094001—21no—
26#13094001—21no—
27Q8×Dic47C2211yescharacteristic
28C4×Dic94—21no—
29C4×Dic94—21no—
30#13093989—21no—
31#13093989C2211yescharacteristic
32#13093983C2211yescharacteristic
33#13093980—21no—
34C2×C4×Dic47C2211yescharacteristic
35#13093958C2211yescharacteristic
36#13093957C2211yescharacteristic
37#13093957C2211yescharacteristic
38#13093956C2211yescharacteristic
39#13093955C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#117×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47D411yescharacteristic
62C22×Dic47D411yescharacteristic
63C2×Dic94—21no—
64C2×Dic94—21no—
65C2×Dic94—21no—
66C2×Dic94C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C4⋊C4×C47—21no—
70C4⋊C4×C47C2311yescharacteristic
71C4⋊C4×C47C2311yescharacteristic
72C4⋊C4×C47C2311yescharacteristic
73C22⋊C4×C47—21no—
74C22⋊C4×C47—21no—
75C42×C47—21no—
76C22⋊Dic47—21no—
77C22⋊Dic47—21no—
78C4⋊Dic47—21no—
79C4⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47C2311yescharacteristic
82C4⋊Dic47C2311yescharacteristic
83C4⋊Dic47C2311yescharacteristic
84Dic47⋊C4—21no—
85Dic47⋊C4—21no—
86Dic47⋊C4—21no—
87Dic47⋊C4—21no—
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93C4×Dic47—21no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47D411yescharacteristic
97C4×Dic47D411yescharacteristic
98C4×Dic47C2311yescharacteristic
99C4×Dic47C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C23×C47C2×D411yescharacteristic
103Q8×C47—21no—
104Q8×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2411yescharacteristic
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123Dic94—21no—
124Dic94—21no—
125Dic94—42no—
126Dic94—42no—
127Dic94—42no—
128C8×C47—21no—
129C8×C47—21no—
130C47⋊C8—21no—
131C47⋊C8—21no—
132C22×C47—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47C22×D411yescharacteristic
136C4×C47—21no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47—41no—
141C4×C472−1+411yescharacteristic
142C4×C472−1+411yescharacteristic
143Dic47—21no—
144Dic47—21no—
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148Dic47—41no—
149Dic47#13512yes—
150Dic47#13712yes—
151#3231—471nomaximal, Sylow
152C2×C47—41no—
153C2×C47#53611yescharacteristic
154C2×C47C2×#13511yescharacteristic
155C2×C47C2×#13711yescharacteristic
156#533—471no—
157#533—471no—
158#500—471no—
159#498—471no—
160#487—471no—
161#487—471no—
162#485—471no—
163#485—471no—
164#485—471no—
165#485D4711yescharacteristic
166#479—471no—
167#479—471no—
168#479—471no—
169#479—471no—
170#431—471no—
171C47#323111yescharacteristic, complemented, Sylow
172C4⋊Q8—471no—
173C4⋊Q8—471no—
174C4⋊Q8—471no—
175C4⋊Q8—471no—
176#125—471no—
177#125—471no—
178#125—941no—
179C22⋊Q8—471no—
180C22⋊Q8—941no—
181C22⋊Q8—941no—
182C22⋊Q8—941no—
183C22⋊Q8C2×D4711yescharacteristic
184C4×Q8—471no—
185C4×Q8—471no—
186C4×Q8—941no—
187C4×Q8—941no—
188C4×Q8—941no—
189#117—471no—
190#117—941no—
191#117C2×D4711yescharacteristic
192C2×C42—471no—
193#107—471no—
194#107—471no—
195#107—471no—
196#107C2×D4711yescharacteristic
197#106—471no—
198#106—471no—
199#106—471no—
200#106C2×D4711yescharacteristic
201C4⋊C8—471no—
202C4⋊C8—471no—
203#103—471no—
204#103—471no—
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209#103C2×D4711yescharacteristic
210#103C2×D4711yescharacteristic
211C22⋊C8—471no—
212C22⋊C8C2×D4711yescharacteristic
213C4×C8—471no—
214C4×C8—471no—
215C2×Q8—471no—
216C2×Q8—941no—
217C2×Q8—941no—
218C2×Q8—941no—
219C2×Q8C22×D4711yescharacteristic
220C22×C4—471no—
221C22×C4—471no—
222C22×C4C22×D4711yescharacteristic
223C2×C8—471no—
224C2×C8—471no—
225C2×C8C22×D4711yescharacteristic
226C2×C8C22×D4711yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—471no—
229C4⋊C4—471no—
230C4⋊C4—471no—
231C4⋊C4—941no—
232C4⋊C4—941no—
233C4⋊C4—941no—
234C4⋊C4—941no—
235C4⋊C4—941no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4C22×D4711yescharacteristic
244C4⋊C4C22×D4711yescharacteristic
245C4⋊C4C22×D4711yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—941no—
249C22⋊C4—941no—
250C42—21no—
251C42—471no—
252C42—471no—
253C42—471no—
254C42—471no—
255C42—941no—
256C42—941no—
257C42—941no—
258C23D4×D4711yescharacteristic
259Q8—21no—
260Q8—21no—
261Q8—941no—
262Q8—941no—
263Q8—1882no—
264Q8—1882no—
265Q8—1882no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—471no—
273C2×C4—471no—
274C2×C4—471no—
275C2×C4—471no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4D4×D4711yescharacteristic
283C2×C4C23×D4711yescharacteristic
284C8—21no—
285C8—21no—
286C8—941no—
287C8—941no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22C2×D4×D4711yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—472no—
298C4—472no—
299C4—941no—
300C4—941no—
301C4—1881no—
302C4—1881no—
303C4—1881no—
304C4—1881no—
305C4#1309407111yescharacteristic
306C4#1309407111yescharacteristic
307C2—41no—
308C2#1568969511yescharacteristic
309C2#135×D4711yescharacteristic
310C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#485C2
socleC22×C47C22×D4
hypercenter#485D47
hypocenterC47#3231
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #15689527C2semidirect
4. #15689520C2semidirect
5. #15689472C2semidirect
6. #15689472C2semidirect
10. #15689433C2semidirect
11. #15689432C2semidirect
12. #15689429C2semidirect
13. #15689428C2semidirect
171. C47#3231semidirect