Finite Group Databasebeta

← #20253557

Subgroups — #20253557

Order 6016.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689655C211yesmaximal, characteristic
2C4×Q8×D47C211yesmaximal, characteristic, complemented
3#15689460C211yesmaximal, characteristic, complemented
4#15689440C211yesmaximal, characteristic
5#15689429C211yesmaximal, characteristic, complemented
6#15689428C211yesmaximal, characteristic, complemented
7#15689344C211yesmaximal, characteristic, complemented
8#15689343C211yesmaximal, characteristic, complemented
9#15689280C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic
11#15689231C211yesmaximal, characteristic, complemented
12#15689228C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689178C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20#13094017—21no—
21#13094015C2211yescharacteristic
22#13094011C2211yescharacteristic
23#13094006—21no—
24#13094004C2211yescharacteristic
25#13093995C2211yescharacteristic
26Q8×Dic47C2211yescharacteristic
27C4×Dic94—21no—
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30#13093989—21no—
31#13093989C2211yescharacteristic
32C4×C22⋊D47—21no—
33#13093983—21no—
34C4⋊C4×D47—21no—
35C4⋊C4×D47C2211yescharacteristic
36C42×D47—21no—
37C42×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093947C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093945C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63Q8×D47—22no—
64Q8×D47—22no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47D411yescharacteristic
68C2×C4×D47D411yescharacteristic
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—21no—
71C2×Dic94C2311yescharacteristic
72C2×Dic94C2311yescharacteristic
73SD16×C47—22no—
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C4⋊C4×C47—21no—
77C4⋊C4×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C42×C47—21no—
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47—21no—
85#10625337—22no—
86#10625335—22no—
87(C2×D47)⋊C4—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—22no—
108C23×C47—21no—
109C22×D47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47#4112yes—
112D4×C47—21no—
113D4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—42no—
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—42no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129C4×D47—24no—
130C4×D47—22no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—41no—
134C4×D47—42no—
135Dic94—24no—
136Dic94—21no—
137Dic94—21no—
138Dic94—21no—
139Dic94#4112yes—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47C22×D411yescharacteristic
148C2×D47—21no—
149C2×D47—21no—
150C2×D47#13712yes—
151C4×C47—22no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47C2×#4111yescharacteristic
157C4×C47C2×#4111yescharacteristic
158Dic47—21no—
159Dic47—22no—
160Dic47—21no—
161Dic47—21no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165#3117—471nomaximal, Sylow
166C2×C47—81no—
167C2×C47#52511yescharacteristic
168C2×C47C2×#13711yescharacteristic
169C2×C47#57511yescharacteristic
170D47—22no—
171#529—471no—
172C2×C4×Q8—471no—
173#484—471no—
174#481—471no—
175#479—471no—
176#479—471no—
177#464—471no—
178#464—471no—
179#451—471no—
180#448—471no—
181#441—471no—
182#441—471no—
183#440—471no—
184#440D4711yescharacteristic, complemented
185#432—471no—
186C47#311711yescharacteristic, complemented, Sylow
187C22×Q8—471no—
188C2×Q16—471no—
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192#126—941no—
193#125—471no—
194#124—471no—
195#123—941no—
196C22⋊Q8—471no—
197#121—471no—
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×Q8—941no—
204C4×Q8C2×D4711yescharacteristic
205C4×D4—941no—
206C4×D4C2×D4711yescharacteristic
207#117—941no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210C2×C42—471no—
211C2×C42—941no—
212#107—471no—
213#107C2×D4711yescharacteristic
214#106—471no—
215#106—471no—
216C4⋊C8—471no—
217C4⋊C8—471no—
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#103C2×D4711yescharacteristic
224#102—471no—
225#102C2×D4711yescharacteristic
226C22⋊C8—471no—
227C22⋊C8—471no—
228#97—471no—
229#97C2×D4711yescharacteristic
230C2×Q8—471no—
231C2×Q8—471no—
232C2×Q8—941no—
233C2×Q8—942no—
234C2×Q8—942no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—941no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—941no—
243C22×C4—941no—
244Q16—942no—
245Q16—942no—
246SD16—22no—
247SD16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8C22×D4711yescharacteristic
251C2×C8C22×D4711yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—471no—
254C4⋊C4—471no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—21no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42C22×D4711yescharacteristic
279C23—21no—
280C23—471no—
281Q8—21no—
282Q8—472no—
283Q8—944no—
284Q8—941no—
285Q8—941no—
286Q8—941no—
287Q8#1062535012yes—
288D4—21no—
289D4—21no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—944no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1881no—
307C2×C4—1882no—
308C2×C4D4×D4711yescharacteristic
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—472no—
319C22—941no—
320C22—941no—
321C22C2×D4×D4711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—941no—
328C4—942no—
329C4—941no—
330C4—941no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C4#41×D4711yescharacteristic
335C4C2×#1062535011yescharacteristic
336C2—81no—
337C2—942no—
338C2#1568963211yescharacteristic
339C2#137×D4711yescharacteristic
340C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3117
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D47C2semidirect
3. #15689460C2semidirect
5. #15689429C2semidirect
6. #15689428C2semidirect
7. #15689344C2semidirect
8. #15689343C2semidirect
9. #15689280C2semidirect
11. #15689231C2semidirect
12. #15689228C2semidirect
13. #15689223C2semidirect
14. #15689178C2semidirect
15. C47×#440C2semidirect
184. #440D47semidirect
186. C47#3117semidirect