Finite Group Databasebeta

← #20255775

Subgroups — #20255775

Order 6016.

356 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689831C211yesmaximal, characteristic
2#15689828C211yesmaximal, characteristic
3#15689527C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689459C211yesmaximal, characteristic, complemented
6#15689457C211yesmaximal, characteristic, complemented
7#15689417C211yesmaximal, characteristic, complemented
8#15689416C211yesmaximal, characteristic, complemented
9#15689363C211yesmaximal, characteristic, complemented
10#15689362C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic
13C2×#13093957C211yesmaximal, characteristic, complemented
14#107×D47C211yesmaximal, characteristic, complemented
15C47×#484C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C22×C47⋊C8C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094014—21no—
22#13094014—21no—
23#13094004—21no—
24#13094004C2211yescharacteristic
25#13094003—21no—
26#13094003C2211yescharacteristic
27#13094002—21no—
28#13094001—21no—
29#13094000C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31#13093989C2211yescharacteristic
32C4×C22⋊D47—21no—
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093957C2211yescharacteristic
44#13093957C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C22×C4×C47—21no—
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C22×Dic47—21no—
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C22⋊C4×C47—21no—
78C22⋊Dic47—21no—
79C22⋊Dic47D411yescharacteristic
80#10625337—22no—
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4D411yescharacteristic
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47—21no—
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⋊C4—21no—
97Dic47⋊C4D411yescharacteristic
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47C2311yescharacteristic
101C2×C47⋊C8—22no—
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C8×D47—22no—
105C23×C47C2×D411yescharacteristic
106C22×D47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—81no—
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47Q1614yescomplemented
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—81no—
124C2×Dic47C2×D411yescharacteristic
125C2×Dic47C2×D411yescharacteristic
126C2×Dic47C2×D411yescharacteristic
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—81no—
130C4×D47—81no—
131Dic94—21no—
132Dic94—21no—
133Dic94—81no—
134Dic94—81no—
135C8×C47—21no—
136C8×C47—21no—
137C47⋊C8—21no—
138C47⋊C8#4112yes—
139C22×C47—21no—
140C22×C47—21no—
141C22×C47C2×Q1612yes—
142C22×C47C22×D411yescharacteristic
143C2×D47—21no—
144C2×D47—21no—
145C2×D47C2×Q1612yes—
146C4×C47—21no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47C2×#4111yescharacteristic
152C4×C472−1+411yescharacteristic
153Dic47—21no—
154Dic47—21no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47C2×Q1612yes—
160#3338—471nomaximal, Sylow
161C2×C47—22no—
162C2×C47#54711yescharacteristic
163C2×C47C22×Q1611yescharacteristic
164C2×C47#57611yescharacteristic
165D47—22no—
166#554—471no—
167#554—471no—
168#500—471no—
169#484—471no—
170#484—471no—
171#484—471no—
172#484D4711yescharacteristic, complemented
173#477—471no—
174#477—471no—
175#467—471no—
176#467—471no—
177C4×Q16—471no—
178C8×D4—471no—
179C2×#107—471no—
180C2×#107—471no—
181C47#333811yescharacteristic, complemented, Sylow
182C2×Q16—471no—
183C22×C8—471no—
184C22×C8—471no—
185C4⋊Q8—471no—
186C4⋊Q8—471no—
187#125—941no—
188#125—941no—
189C22⋊Q8—471no—
190C22⋊Q8—471no—
191C22⋊Q8—471no—
192C22⋊Q8—941no—
193C22⋊Q8—941no—
194C22⋊Q8—941no—
195C22⋊Q8—941no—
196C22⋊Q8C2×D4711yescharacteristic
197C4×Q8—471no—
198C4×Q8—471no—
199C4×D4—471no—
200C4×D4—941no—
201C4×D4—941no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4C2×D4711yescharacteristic
206#107—471no—
207#107—471no—
208#107—471no—
209#107—471no—
210#107—471no—
211#107—471no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#107C2×D4711yescharacteristic
215C4⋊C8—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103—471no—
220#103C2×D4711yescharacteristic
221#103C2×D4711yescharacteristic
222C22⋊C8—471no—
223C22⋊C8C2×D4711yescharacteristic
224C4×C8—471no—
225C2×Q8—471no—
226C2×Q8—941no—
227C2×Q8—941no—
228C2×Q8C22×D4711yescharacteristic
229C2×D4—471no—
230C22×C4—21no—
231C22×C4—471no—
232C22×C4—941no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4C22×D4711yescharacteristic
236Q16—942no—
237C2×C8—471no—
238C2×C8—471no—
239C2×C8—942no—
240C2×C8—942no—
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—471no—
246C4⋊C4—471no—
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⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4C22×D4711yescharacteristic
260C4⋊C4C22×D4711yescharacteristic
261C4⋊C4C22×D4711yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—471no—
264C22⋊C4—471no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C42—471no—
269C42—941no—
270C42—941no—
271C23—471no—
272C23D4×D4711yescharacteristic
273Q8—21no—
274Q8—21no—
275Q8—941no—
276Q8—941no—
277Q8—3761no—
278Q8—3761no—
279D4—474no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—471no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4D4×D4711yescharacteristic
300C2×C4C23×D4711yescharacteristic
301C8—21no—
302C8—21no—
303C8—472no—
304C8—941no—
305C22—21no—
306C22—21no—
307C22—472no—
308C22—941no—
309C22—941no—
310C22Q16×D4712yes—
311C22C2×D4×D4711yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—472no—
318C4—941no—
319C4—941no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4#41×D4711yescharacteristic
325C4#1309407111yescharacteristic
326C2—22no—
327C2—942no—
328C2#1568977111yescharacteristic
329C2C2×Q16×D4711yescharacteristic
330C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3338
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #15689527C2semidirect
4. #15689460C2semidirect
5. #15689459C2semidirect
6. #15689457C2semidirect
7. #15689417C2semidirect
8. #15689416C2semidirect
9. #15689363C2semidirect
10. #15689362C2semidirect
11. #15689215C2semidirect
13. C2×#13093957C2semidirect
14. #107×D47C2semidirect
15. C47×#484C2semidirect
118. C22⋊D47Q16semidirect
172. #484D47semidirect
181. C47#3338semidirect