Finite Group Databasebeta

← #20255553

Subgroups — #20255553

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic94C211yesmaximal, characteristic, complemented
2#15689493C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689458C211yesmaximal, characteristic, complemented
5#15689427C211yesmaximal, characteristic, complemented
6#15689367C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689328C211yesmaximal, characteristic, complemented
9#15689261C211yesmaximal, characteristic, complemented
10#15689261C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689131C211yesmaximal, characteristic, complemented
14C2×#13093947C211yesmaximal, characteristic, complemented
15C47×#553C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094024C2211yescharacteristic
24#13094023—21no—
25#13094003C2211yescharacteristic
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13094001—21no—
29C4×Dic94C2211yescharacteristic
30D4×Dic47—21no—
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093947C2211yescharacteristic
36#13093947C2211yescharacteristic
37#13093947C2211yescharacteristic
38#13093947C2211yescharacteristic
39#13093947C2211yescharacteristic
40#13093947C2211yescharacteristic
41#13093947C2211yescharacteristic
42#13093947C2211yescharacteristic
43#13093947C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48#126×C47—21no—
49#125×C47C2211yescharacteristic
50#123×C47—21no—
51#121×C47—21no—
52#121×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54C4×D4×C47—21no—
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57#117×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47D411yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C2×Dic94—22no—
70C2×Dic94—22no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—41no—
74C2×Dic94—41no—
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C42×C47—21no—
92C42×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95#10625335—22no—
96#10625335—41no—
97#10625335—41no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47C2×D411yescharacteristic
113C23×C47C2×D411yescharacteristic
114D4×C47—22no—
115D4×C47—21no—
116D4×C47—21no—
117D4×C47—42no—
118D4×C47—81no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—21no—
143Dic94—21no—
144Dic94—42no—
145Dic94—42no—
146Dic94#4112yes—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47—41no—
159C22×C47#13712yes—
160C22×C47C22×D411yescharacteristic
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—41no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47C2×#4111yescharacteristic
169C4×C47H(5,𝔽2)11yescharacteristic
170Dic47—22no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3320—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—41no—
177C2×C47—81no—
178C2×C47#54611yescharacteristic
179C2×C47C2×#13711yescharacteristic
180C2×C47#57711yescharacteristic
181#553D4711yescharacteristic
182D4×Q8—471no—
183#491—471no—
184#485—471no—
185#484—471no—
186#479—471no—
187#468—471no—
188#465—471no—
189#461—471no—
190#448—471no—
191#448—471no—
192#440—471no—
193#435—471no—
194#419—471no—
195C2×#103—471no—
196C47#332011yescharacteristic, complemented, Sylow
197C22×Q8—471no—
198C22×Q8—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—471no—
205C4⋊Q8—941no—
206#126—21no—
207#125C2×D4711yescharacteristic
208#123—21no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212C22⋊Q8—941no—
213#121—21no—
214#121C2×D4711yescharacteristic
215#121C2×D4711yescharacteristic
216C4×Q8—471no—
217C4×D4—21no—
218C4×D4—941no—
219C4×D4C2×D4711yescharacteristic
220C4×D4C2×D4711yescharacteristic
221#117C2×D4711yescharacteristic
222C2×C4⋊C4C2×D4711yescharacteristic
223#107—471no—
224#107—471no—
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240C2×Q8—471no—
241C2×Q8—471no—
242C2×Q8—471no—
243C2×Q8—942no—
244C2×Q8—942no—
245C2×Q8—941no—
246C2×Q8—941no—
247C2×Q8—1881no—
248C2×Q8—1881no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D4711yescharacteristic
252C2×D4C22×D4711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259SD16—942no—
260SD16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8—471no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—471no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22⋊D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4C22⋊D4711yescharacteristic
288C22⋊C4C22⋊D4711yescharacteristic
289C42—21no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—21no—
293C23C2×C22⋊D4711yescharacteristic
294C23C2×C22⋊D4711yescharacteristic
295Q8—472no—
296Q8—941no—
297Q8—941no—
298Q8—941no—
299Q8—941no—
300Q8—941no—
301Q8—1882no—
302Q8—1882no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C2×C22⋊D4711yescharacteristic
326C2×C4C2×C22⋊D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—941no—
329C8—941no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1309405412yes—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—942no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4#41×D4711yescharacteristic
354C4#1309407011yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1568976111yescharacteristic
359C2C2×#1309405411yescharacteristic
360C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#553C2
socleC22×C47C22×D4
hypercenter#553D47
hypocenterC47#3320
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic94C2semidirect
2. #15689493C2semidirect
3. #15689464C2semidirect
4. #15689458C2semidirect
5. #15689427C2semidirect
6. #15689367C2semidirect
7. #15689350C2semidirect
8. #15689328C2semidirect
9. #15689261C2semidirect
10. #15689261C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689131C2semidirect
14. C2×#13093947C2semidirect
196. C47#3320semidirect