Finite Group Databasebeta

← #20253543

Subgroups — #20253543

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#15689675C211yesmaximal, characteristic, complemented
2#41×Dic47C211yesmaximal, characteristic
3#15689465C211yesmaximal, characteristic, complemented
4#15689461C211yesmaximal, characteristic, complemented
5#15689416C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689331C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic
10#15689230C211yesmaximal, characteristic, complemented
11#15689227C211yesmaximal, characteristic, complemented
12#15689224C211yesmaximal, characteristic, complemented
13#15689220C211yesmaximal, characteristic, complemented
14#15689177C211yesmaximal, characteristic, complemented
15C47×#452C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic
17C2×#10625335C2211yescharacteristic
18#13094023C2211yescharacteristic
19#13094022C2211yescharacteristic
20#13094014—21no—
21#13094003C2211yescharacteristic
22#13094001—21no—
23Q8×Dic47C2211yescharacteristic
24Q8×Dic47C2211yescharacteristic
25Q8×Dic47C2211yescharacteristic
26#13093989—21no—
27#13093989C2211yescharacteristic
28D4×Dic47—21no—
29D4×Dic47—21no—
30D4×Dic47C2211yescharacteristic
31D4×Dic47C2211yescharacteristic
32#13093983—21no—
33#13093983C2211yescharacteristic
34#13093980—21no—
35C2×C4×Dic47—21no—
36C2×C4×Dic47C2211yescharacteristic
37#13093958C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093956C2211yescharacteristic
40#13093955C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093945C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50#13093934C2211yescharacteristic
51#13093934C2211yescharacteristic
52C2×#41×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59#41×C47—22no—
60#41×C47—22no—
61C2×Q8×C47C2311yescharacteristic
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47D411yescharacteristic
70C22×Dic47D411yescharacteristic
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73Q16×C47—22no—
74SD16×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47C2311yescharacteristic
79C22⋊C4×C47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84#10625337—22no—
85#10625335—22no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102C4×Dic47D411yescharacteristic
103C4×Dic47D411yescharacteristic
104C4×Dic47C2311yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C23×C47—21no—
109C23×C47C2×D411yescharacteristic
110Q8×C47—21no—
111Q8×C47—21no—
112Q8×C47—21no—
113Q8×C47#4112yes—
114D4×C47—24no—
115D4×C47—21no—
116D4×C47#4112yes—
117C2×C4×C47—24no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C2×Dic47—22no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—41no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137Dic94—21no—
138Dic94—21no—
139Dic94—42no—
140C8×C47—21no—
141C8×C47—21no—
142C47⋊C8—21no—
143C47⋊C8—21no—
144C22×C47—21no—
145C22×C47—22no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47C22×D411yescharacteristic
151C4×C47—21no—
152C4×C47—22no—
153C4×C47—41no—
154C4×C47—41no—
155C4×C47C2×#4111yescharacteristic
156C4×C47C2×#4111yescharacteristic
157Dic47—21no—
158Dic47—21no—
159Dic47—21no—
160Dic47—41no—
161Dic47—41no—
162Dic47—41no—
163Dic47—41no—
164Dic47#13712yes—
165#3116—471nomaximal, Sylow
166C2×C47—41no—
167C2×C47—42no—
168C2×C47#52511yescharacteristic
169C2×C47C2×#13711yescharacteristic
170C2×C47#57511yescharacteristic
171#533—471no—
172C4×#41—471no—
173#485—471no—
174#485—471no—
175#477—471no—
176#476—471no—
177#462—471no—
178#461—471no—
179#452—471no—
180#452D4711yescharacteristic
181#441—471no—
182#441—471no—
183#440—471no—
184#440—471no—
185#432—471no—
186C47#311611yescharacteristic, complemented, Sylow
187C2×#41C2×D4711yescharacteristic
188C2×Q16—471no—
189C2×Q16C2×D4711yescharacteristic
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192C4⋊Q8—471no—
193C4⋊Q8—471no—
194#125—941no—
195C22⋊Q8—471no—
196C22⋊Q8—941no—
197C22⋊Q8C2×D4711yescharacteristic
198C4×Q8—471no—
199C4×Q8—471no—
200C4×Q8—471no—
201C4×Q8—471no—
202C4×Q8—941no—
203C4×D4—471no—
204C4×D4—471no—
205C4×D4—941no—
206C4×D4—941no—
207#117—471no—
208#117—941no—
209#117—941no—
210C2×C42—471no—
211C2×C42—941no—
212#107—471no—
213#107—471no—
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⋊C8C2×D4711yescharacteristic
228#97—471no—
229#97—471no—
230#41—22no—
231#41—22no—
232C2×Q8—471no—
233C2×Q8—941no—
234C2×Q8C22×D4711yescharacteristic
235C2×Q8C22×D4711yescharacteristic
236C2×D4—21no—
237C2×D4C22×D4711yescharacteristic
238C22×C4—21no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4C22×D4711yescharacteristic
244Q16—22no—
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—471no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C42—471no—
271C42—471no—
272C42—471no—
273C42—471no—
274C42—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42—941no—
279C23—21no—
280C23D4×D4711yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—941no—
285Q8—941no—
286Q8—1882no—
287Q8#1062535212yes—
288D4—24no—
289D4—21no—
290D4#1062535212yes—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—471no—
298C2×C4—471no—
299C2×C4—471no—
300C2×C4—471no—
301C2×C4—942no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—1882no—
307C2×C4—1881no—
308C2×C4—1882no—
309C2×C4D4×D4711yescharacteristic
310C2×C4C23×D4711yescharacteristic
311C8—21no—
312C8—21no—
313C8—941no—
314C8—941no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22C2×D4×D4711yescharacteristic
322C4—21no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—472no—
327C4—941no—
328C4—941no—
329C4—941no—
330C4—1881no—
331C4—1881no—
332C4—1881no—
333C4—1881no—
334C4C2×#1062535211yescharacteristic
335C4C2×#1062535211yescharacteristic
336C2—41no—
337C2—42no—
338C2#1568962911yescharacteristic
339C2#137×D4711yescharacteristic
340C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#452C2
socleC22×C47C22×D4
hypercenter#452D47
hypocenterC47#3116
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #15689675C2semidirect
3. #15689465C2semidirect
4. #15689461C2semidirect
5. #15689416C2semidirect
6. #15689411C2semidirect
7. #15689331C2semidirect
8. #15689326C2semidirect
10. #15689230C2semidirect
11. #15689227C2semidirect
12. #15689224C2semidirect
13. #15689220C2semidirect
14. #15689177C2semidirect
186. C47#3116semidirect