Finite Group Databasebeta

← #20253191

Subgroups — #20253191

Order 6016.

376 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689679C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic
3#15689431C211yesmaximal, characteristic, complemented
4#15689430C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689417C211yesmaximal, characteristic, complemented
7#15689416C211yesmaximal, characteristic, complemented
8#15689407C211yesmaximal, characteristic, complemented
9#15689406C211yesmaximal, characteristic, complemented
10#15689164C211yesmaximal, characteristic
11#15689162C211yesmaximal, characteristic
12#15689145C211yesmaximal, characteristic
13#15689130C211yesmaximal, characteristic
14#15689130C211yesmaximal, characteristic
15C47×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19#13094023C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094016C2211yescharacteristic
22#13094002—21no—
23#13094002—21no—
24Q8×Dic47C2211yescharacteristic
25C4×Dic94—21no—
26C4×Dic94C2211yescharacteristic
27#13093989—21no—
28#13093989—21no—
29#13093989—21no—
30#13093989C2211yescharacteristic
31#13093982C2211yescharacteristic
32#13093982C2211yescharacteristic
33C4⋊C4×D47—21no—
34C4⋊C4×D47C2211yescharacteristic
35C42×D47—21no—
36C42×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093948C2211yescharacteristic
50#13093947C2211yescharacteristic
51#13093947C2211yescharacteristic
52#125×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#106×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60Q8×D47—22no—
61Q8×D47Q814yescomplemented
62C2×C4×D47—21no—
63C2×C4×D47—21no—
64C2×C4×D47D411yescharacteristic
65C2×C4×D47D411yescharacteristic
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94—21no—
70C2×Dic94C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47C2311yescharacteristic
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C42×C47—21no—
80C42×C47C2311yescharacteristic
81(C2×D47)⋊C4—21no—
82(C2×D47)⋊C4—21no—
83C4⋊Dic47—21no—
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—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47D411yescharacteristic
100C4×Dic47D411yescharacteristic
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105#10625324—22no—
106C22×D47C2×D411yescharacteristic
107Q8×C47—21no—
108Q8×C47C2×Q812yes—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2411yescharacteristic
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47C2×D411yescharacteristic
121C2×Dic47C2×D411yescharacteristic
122C2×Dic47C2×D411yescharacteristic
123C4×D47—24no—
124C4×D47—22no—
125C4×D47—41no—
126C4×D47—42no—
127C4×D47C2×Q812yes—
128C4×D47#4112yes—
129Dic94—21no—
130Dic94—24no—
131Dic94—42no—
132Dic94—42no—
133Dic94C2×Q812yes—
134C8×C47—21no—
135C8×C47—21no—
136C47⋊C8—21no—
137C47⋊C8—21no—
138C22×C47C22×D411yescharacteristic
139C2×D47—21no—
140C2×D47—21no—
141C2×D47C22⋊Q812yes—
142C4×C47—22no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47C22×Q811yescharacteristic
149C4×C47C2×#4111yescharacteristic
150Dic47—22no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47C22⋊Q812yes—
156Dic47#13712yes—
157#3078—471nomaximal, Sylow
158C2×C47C2×C22⋊Q811yescharacteristic
159C2×C47C2×#13711yescharacteristic
160C2×C47#57511yescharacteristic
161D47—22no—
162#533—471no—
163C2×C4×Q8—471no—
164#479—471no—
165#479—471no—
166#479—471no—
167#479D4711yescharacteristic, complemented
168#477—471no—
169#477—471no—
170#475—471no—
171#475—471no—
172#428—471no—
173#428—471no—
174#423—471no—
175#419—471no—
176#419—471no—
177C47#307811yescharacteristic, complemented, Sylow
178C22×Q8—471no—
179C2×M16—471no—
180C2×M16—471no—
181C4⋊Q8—471no—
182C4⋊Q8—471no—
183#125—471no—
184#125C2×D4711yescharacteristic
185C22⋊Q8—941no—
186C22⋊Q8—941no—
187C4×Q8—471no—
188C4×Q8—471no—
189C4×Q8—471no—
190C4×Q8—941no—
191C4×Q8—941no—
192C4×Q8—941no—
193C4×Q8—941no—
194C4×Q8C2×D4711yescharacteristic
195#117—471no—
196#117—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—941no—
199C2×C42—471no—
200C2×C42—941no—
201#107—471no—
202#107—471no—
203#107—471no—
204#107C2×D4711yescharacteristic
205#106—471no—
206#106—471no—
207#106—471no—
208#106C2×D4711yescharacteristic
209C4⋊C8—471no—
210C4⋊C8—471no—
211C4⋊C8—471no—
212C4⋊C8C2×D4711yescharacteristic
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103—471no—
219#103C2×D4711yescharacteristic
220#103C2×D4711yescharacteristic
221C2×Q8—474no—
222C2×Q8—471no—
223C2×Q8—941no—
224C2×Q8—941no—
225C2×Q8—941no—
226C2×Q8—942no—
227C2×Q8C22×D4711yescharacteristic
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—941no—
232C22×C4—941no—
233M16—942no—
234M16—942no—
235C2×C8—471no—
236C2×C8—471no—
237C2×C8C22×D4711yescharacteristic
238C2×C8C22×D4711yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
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⋊C4C22×D4711yescharacteristic
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C22⋊C4—941no—
257C22⋊C4—941no—
258C42—21no—
259C42—471no—
260C42—471no—
261C42—471no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42—941no—
266C42—941no—
267C42C22×D4711yescharacteristic
268C23—471no—
269Q8—21no—
270Q8—472no—
271Q8—944no—
272Q8—941no—
273Q8—1882no—
274Q8—1882no—
275Q8Q8×D4712yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—471no—
281C2×C4—471no—
282C2×C4—472no—
283C2×C4—472no—
284C2×C4—471no—
285C2×C4—942no—
286C2×C4—944no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—1881no—
292C2×C4—1882no—
293C2×C4D4×D4711yescharacteristic
294C2×C4D4×D4711yescharacteristic
295C2×C4C23×D4711yescharacteristic
296C8—21no—
297C8—21no—
298C8—941no—
299C8—941no—
300C22—472no—
301C22—941no—
302C22—941no—
303C22C2×D4×D4711yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—472no—
311C4—472no—
312C4—942no—
313C4—941no—
314C4—1881no—
315C4—1881no—
316C4—1881no—
317C4C2×Q8×D4711yescharacteristic
318C4#41×D4711yescharacteristic
319C2—942no—
320C2C22⋊Q8×D4711yescharacteristic
321C2#137×D4711yescharacteristic
322C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3078
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #15689431C2semidirect
4. #15689430C2semidirect
5. #15689427C2semidirect
6. #15689417C2semidirect
7. #15689416C2semidirect
8. #15689407C2semidirect
9. #15689406C2semidirect
15. C47×#479C2semidirect
61. Q8×D47Q8semidirect
167. #479D47semidirect
177. C47#3078semidirect