Finite Group Databasebeta

← #20254840

Subgroups — #20254840

Order 6016.

322 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#15689734C211yesmaximal, characteristic
2#15689731C211yesmaximal, characteristic
3#15689432C211yesmaximal, characteristic, complemented
4#15689431C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689428C211yesmaximal, characteristic, complemented
7#15689380C211yesmaximal, characteristic
8#15689378C211yesmaximal, characteristic
9#15689363C211yesmaximal, characteristic
10#15689361C211yesmaximal, characteristic
11#15689331C211yesmaximal, characteristic, complemented
12#15689331C211yesmaximal, characteristic, complemented
13#15689330C211yesmaximal, characteristic, complemented
14#15689148C211yesmaximal, characteristic
15C47×#462C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C2×#10625324C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094022C2211yescharacteristic
21#13094019—21no—
22#13094019—21no—
23#13094019—21no—
24#13094018—21no—
25#13094016—21no—
26#13094016C2211yescharacteristic
27#13094015C2211yescharacteristic
28#13094014—21no—
29#13094014—21no—
30#13094014—21no—
31#13094004C2211yescharacteristic
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34#13094000C2211yescharacteristic
35Q8×Dic47C2211yescharacteristic
36Q8×Dic47C2211yescharacteristic
37C4×Dic94C2211yescharacteristic
38#13093981C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093955C2211yescharacteristic
43C4⋊(C47⋊C8)C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093948C2211yescharacteristic
50#13093948C2211yescharacteristic
51#13093948C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C4⋊Q8×C47C2211yescharacteristic
55C4×Q8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C2×C4×D47C2311yescharacteristic
63C2×Dic94C2311yescharacteristic
64Q16×C47—41no—
65Q16×C47—41no—
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47C2311yescharacteristic
72C42×C47—21no—
73C42×C47C2311yescharacteristic
74#10625337—41no—
75#10625337—41no—
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4D411yescharacteristic
81(C2×D47)⋊C4D411yescharacteristic
82C4⋊Dic47—21no—
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⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4D411yescharacteristic
99Dic47⋊C4D411yescharacteristic
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625324—41no—
107C8×D47—41no—
108C22×D47C2×D411yescharacteristic
109Q8×C47—21no—
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C4×D47—21no—
130C4×D47—21no—
131Dic94—21no—
132Dic94—21no—
133C8×C47—21no—
134C8×C47—21no—
135C47⋊C8—21no—
136C47⋊C8—21no—
137C22×C47C22×D411yescharacteristic
138C2×D47—21no—
139C2×D47—21no—
140C2×D47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47—41no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47H(5,𝔽2)11yescharacteristic
148C4×C472−1+411yescharacteristic
149Dic47—21no—
150Dic47—21no—
151Dic47—21no—
152Dic47—41no—
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3261—471nomaximal, Sylow
157C2×C47#53711yescharacteristic
158C2×C47#57811yescharacteristic
159C2×C47#57811yescharacteristic
160D47—41no—
161#541—471no—
162#541—471no—
163#479—471no—
164#479—471no—
165#479—471no—
166#479—471no—
167#470—471no—
168#470—471no—
169#467—471no—
170#467—471no—
171#462—471no—
172#462—471no—
173#462—471no—
174#462D4711yescharacteristic, complemented
175#424—471no—
176C47#326111yescharacteristic, complemented, Sylow
177C2×Q16—471no—
178C2×Q16—471no—
179C2×Q16C2×D4711yescharacteristic
180C2×Q16C2×D4711yescharacteristic
181C2×M16—471no—
182C22×C8—471no—
183C4⋊Q8—471no—
184C4⋊Q8C2×D4711yescharacteristic
185#126—941no—
186#126—941no—
187#126—941no—
188#126—941no—
189#125—471no—
190#125—471no—
191#125—941no—
192#125—941no—
193#125—941no—
194#125—941no—
195C22⋊Q8—471no—
196C22⋊Q8—471no—
197C22⋊Q8—471no—
198C22⋊Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8C2×D4711yescharacteristic
203#117—471no—
204#107—471no—
205#107—471no—
206#106—471no—
207#106—471no—
208C4⋊C8—471no—
209C4⋊C8—471no—
210C4⋊C8—471no—
211C4⋊C8C2×D4711yescharacteristic
212#103—471no—
213#103—471no—
214#103—471no—
215#103—471no—
216#103—471no—
217#103—471no—
218#103C2×D4711yescharacteristic
219#103C2×D4711yescharacteristic
220C2×Q8—471no—
221C2×Q8C22×D4711yescharacteristic
222C2×Q8C22×D4711yescharacteristic
223C2×Q8C22×D4711yescharacteristic
224C22×C4—471no—
225Q16—41no—
226Q16—41no—
227Q16—1881no—
228Q16—1881no—
229M16—1881no—
230C2×C8—471no—
231C2×C8—471no—
232C2×C8—1881no—
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⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4C22×D4711yescharacteristic
257C22⋊C4—471no—
258C22⋊C4—471no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C42—21no—
264C42—471no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42C22×D4711yescharacteristic
269C23—471no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—941no—
277Q8—941no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—471no—
283C2×C4—471no—
284C2×C4—471no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4D4×D4711yescharacteristic
292C2×C4D4×D4711yescharacteristic
293C2×C4C23×D4711yescharacteristic
294C8—21no—
295C8—21no—
296C8—941no—
297C8—941no—
298C22—941no—
299C22—941no—
300C22—941no—
301C22C2×D4×D4711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—941no—
309C4—941no—
310C4—941no—
311C4—1881no—
312C4—1881no—
313C4—1881no—
314C4—1881no—
315C4#1309406911yescharacteristic
316C4#1309407111yescharacteristic
317C2—1881no—
318C2#1568970211yescharacteristic
319C2#1568993611yescharacteristic
320C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#462C2
socleC22×C47C22×D4
hypercenter#462D47
hypocenterC47#3261
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #15689432C2semidirect
4. #15689431C2semidirect
5. #15689430C2semidirect
6. #15689428C2semidirect
11. #15689331C2semidirect
12. #15689331C2semidirect
13. #15689330C2semidirect
15. C47×#462C2semidirect
174. #462D47semidirect
176. C47#3261semidirect