Finite Group Databasebeta

← #20253229

Subgroups — #20253229

Order 6016.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689753C211yesmaximal, characteristic
2#15689599C211yesmaximal, characteristic
3#15689432C211yesmaximal, characteristic, complemented
4#15689429C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689416C211yesmaximal, characteristic, complemented
8#15689408C211yesmaximal, characteristic, complemented
9#15689407C211yesmaximal, characteristic, complemented
10#15689162C211yesmaximal, characteristic
11#15689160C211yesmaximal, characteristic
12#15689148C211yesmaximal, characteristic
13#15689130C211yesmaximal, characteristic
14#103×D47C211yesmaximal, characteristic
15C47×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625324C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094023—21no—
21#13094023C2211yescharacteristic
22#13094015C2211yescharacteristic
23#13094014—21no—
24#13094004—21no—
25#13094002—21no—
26Q8×Dic47C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94C2211yescharacteristic
29#13093989—21no—
30#13093989C2211yescharacteristic
31#13093982—21no—
32#13093982C2211yescharacteristic
33#13093982C2211yescharacteristic
34#13093981—21no—
35#13093981C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
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×D47C2311yescharacteristic
65C2×Dic94—21no—
66C2×Dic94—21no—
67C2×Dic94—21no—
68C2×Dic94C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C4⋊C4×C47C2311yescharacteristic
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81(C2×D47)⋊C4D411yescharacteristic
82(C2×D47)⋊C4D411yescharacteristic
83C4⋊Dic47—21no—
84C4⋊Dic47—21no—
85C4⋊Dic47—21no—
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88C4⋊Dic47C2311yescharacteristic
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4D411yescharacteristic
95Dic47⋊C4D411yescharacteristic
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104#10625324—22no—
105C8×D47—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—81no—
125C4×D47C2×Q812yes—
126C4×D47#4112yes—
127Dic94—21no—
128Dic94—24no—
129Dic94—81no—
130Dic94—81no—
131Dic94C2×Q812yes—
132C8×C47—21no—
133C8×C47—21no—
134C47⋊C8—21no—
135C47⋊C8—21no—
136C22×C47C22×D411yescharacteristic
137C2×D47—21no—
138C2×D47—21no—
139C2×D47C22⋊Q812yes—
140C4×C47—22no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47C22×Q811yescharacteristic
147C4×C47C2×#4111yescharacteristic
148Dic47—22no—
149Dic47—21no—
150Dic47—21no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154Dic47C22⋊Q812yes—
155#3082—471nomaximal, Sylow
156C2×C47C2×C22⋊Q811yescharacteristic
157C2×C47#57711yescharacteristic
158C2×C47#57811yescharacteristic
159D47—22no—
160#544—471no—
161#519—471no—
162#479—471no—
163#479—471no—
164#479—471no—
165#479D4711yescharacteristic, complemented
166#477—471no—
167#477—471no—
168#475—471no—
169#475—471no—
170#428—471no—
171#427—471no—
172#424—471no—
173#419—471no—
174C2×#103—471no—
175C47#308211yescharacteristic, complemented, Sylow
176C22×Q8—471no—
177C2×M16—471no—
178C22×C8—471no—
179C4⋊Q8—471no—
180C4⋊Q8—471no—
181C4⋊Q8—941no—
182#125—471no—
183#125—941no—
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×Q8C2×D4711yescharacteristic
193#117—471no—
194#117—471no—
195#117—471no—
196#117—941no—
197#117—941no—
198C2×C4⋊C4—471no—
199#107—471no—
200#107—471no—
201#107—471no—
202#107C2×D4711yescharacteristic
203#106—471no—
204#106—471no—
205#106—471no—
206#106C2×D4711yescharacteristic
207C4⋊C8—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8C2×D4711yescharacteristic
211#103—471no—
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103C2×D4711yescharacteristic
218#103C2×D4711yescharacteristic
219C2×Q8—474no—
220C2×Q8—471no—
221C2×Q8—941no—
222C2×Q8—941no—
223C2×Q8—942no—
224C2×Q8—941no—
225C2×Q8C22×D4711yescharacteristic
226C22×C4—471no—
227C22×C4—941no—
228C22×C4—941no—
229M16—942no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—942no—
233C2×C8C22×D4711yescharacteristic
234C2×C8C22×D4711yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—471no—
239C4⋊C4—471no—
240C4⋊C4—471no—
241C4⋊C4—471no—
242C4⋊C4—471no—
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—471no—
255C22⋊C4—471no—
256C22⋊C4—941no—
257C22⋊C4—941no—
258C42—21no—
259C42—471no—
260C42—941no—
261C42—941no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42C22×D4711yescharacteristic
266C23—471no—
267Q8—21no—
268Q8—472no—
269Q8—944no—
270Q8—941no—
271Q8—3761no—
272Q8—3761no—
273Q8Q8×D4712yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—471no—
279C2×C4—472no—
280C2×C4—472no—
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—944no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—3761no—
289C2×C4D4×D4711yescharacteristic
290C2×C4D4×D4711yescharacteristic
291C2×C4C23×D4711yescharacteristic
292C8—21no—
293C8—21no—
294C8—941no—
295C8—941no—
296C22—472no—
297C22—941no—
298C22—941no—
299C22C2×D4×D4711yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—472no—
307C4—942no—
308C4—941no—
309C4—941no—
310C4—1881no—
311C4—1881no—
312C4—1881no—
313C4C2×Q8×D4711yescharacteristic
314C4#41×D4711yescharacteristic
315C2—942no—
316C2C22⋊Q8×D4711yescharacteristic
317C2#1568993211yescharacteristic
318C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#479C2
socleC22×C47C22×D4
hypercenter#479D47
hypocenterC47#3082
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. #15689432C2semidirect
4. #15689429C2semidirect
5. #15689427C2semidirect
6. #15689419C2semidirect
7. #15689416C2semidirect
8. #15689408C2semidirect
9. #15689407C2semidirect
15. C47×#479C2semidirect
61. Q8×D47Q8semidirect
165. #479D47semidirect
175. C47#3082semidirect