Finite Group Databasebeta

← #20248635

Subgroups — #20248635

Order 6016.

476 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689061C211yesmaximal, characteristic, complemented
2#15689038C211yesmaximal, characteristic
3#15689036C211yesmaximal, characteristic, complemented
4#15689035C211yesmaximal, characteristic, complemented
5#15689027C211yesmaximal, characteristic, complemented
6#15689013C211yesmaximal, characteristic, complemented
7#15689000C211yesmaximal, characteristic
8#15688999C211yesmaximal, characteristic
9#15688991C211yesmaximal, characteristic, complemented
10#15688990C211yesmaximal, characteristic, complemented
11#15688985C211yesmaximal, characteristic, complemented
12#15688984C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C2×C4⋊C4×C47C2211yescharacteristic
45C2×C22⋊C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C23×D47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C2×C22⋊D47—22no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—41no—
62C22×Dic47—22no—
63C22×Dic47—22no—
64C22×Dic47—41no—
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—41no—
75C2×Dic94—22no—
76C2×Dic94—41no—
77C2×Dic94—41no—
78C4⋊C4×C47—41no—
79C22⋊C4×C47—22no—
80C22⋊C4×C47—22no—
81C22⋊C4×C47—41no—
82C42×C47—22no—
83C22⋊Dic47—22no—
84C22⋊Dic47—41no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—41no—
89(C2×D47)⋊C4—41no—
90Dic47⋊C4—41no—
91C4×Dic47—22no—
92C4×Dic47—41no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47#4112yes—
100C23×C47C2411yescharacteristic
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47#4112yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
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#4112yes—
126C22⋊D47—44no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—44no—
147C2×Dic47#4112yes—
148C2×Dic47#4112yes—
149C4×D47—44no—
150Dic94—44no—
151C22×C47—22no—
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C2×#4111yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47C2×#4111yescharacteristic
162C22×C47C2×#4111yescharacteristic
163C22×C47H(5,𝔽2)11yescharacteristic
164C22×C47H(5,𝔽2)11yescharacteristic
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C4×C47—22no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47—41no—
178Dic47—22no—
179Dic47—22no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185#2572—471nomaximal, Sylow
186C2×C47—42no—
187C2×C47#52911yescharacteristic
188C2×C47#52911yescharacteristic
189C2×C47#53811yescharacteristic
190C2×C47#55111yescharacteristic
191C2×C47#55111yescharacteristic
192C2×C47#55111yescharacteristic
193C2×C47#55511yescharacteristic
194D47—42no—
195#400—471no—
196#394—471no—
197#393—471no—
198#393—471no—
199#391—471no—
200#388—471no—
201#388D4711yescharacteristic, complemented
202#386—471no—
203#386—471no—
204#383—471no—
205#383—471no—
206#381—471no—
207#381—471no—
208C4×C22⋊C4—471no—
209C4×C22⋊C4—471no—
210C47#257211yescharacteristic, complemented, Sylow
211C22×Q8—471no—
212C22×D4—471no—
213C23×C4—471no—
214C23×C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4C2×D4711yescharacteristic
217C2×C22⋊C4—471no—
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C22⋊C4—471no—
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4C2×D4711yescharacteristic
225C2×C22⋊C4C2×D4711yescharacteristic
226C2×C22⋊C4C2×D4711yescharacteristic
227C2×C42—471no—
228C2×C42—471no—
229C2×C42C2×D4711yescharacteristic
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95—471no—
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95C2×D4711yescharacteristic
245#95C2×D4711yescharacteristic
246C24—471no—
247C24C22×D4711yescharacteristic
248C2×Q8—942no—
249C2×Q8—1881no—
250C2×Q8—1881no—
251C2×D4—942no—
252C2×D4—942no—
253C2×D4—1881no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—942no—
262C22×C4—942no—
263C22×C4—942no—
264C22×C4—942no—
265C22×C4—1881no—
266C22×C4—1881no—
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—1881no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—41no—
278C22⋊C4—942no—
279C22⋊C4—942no—
280C22⋊C4—942no—
281C22⋊C4—942no—
282C22⋊C4—1881no—
283C22⋊C4—1881no—
284C22⋊C4—1881no—
285C42—22no—
286C42—942no—
287C42—1881no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—472no—
295C23—941no—
296C23—941no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23#1062535012yes—
302C23C23×D4711yescharacteristic
303Q8—1884no—
304D4—1884no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—472no—
323C2×C4—472no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—1884no—
344C2×C4—1884no—
345C2×C4#1062535212yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—942no—
354C22—942no—
355C22—942no—
356C22—1881no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22#41×D4711yescharacteristic
361C22#41×D4711yescharacteristic
362C22#41×D4711yescharacteristic
363C22C2×#1062535211yescharacteristic
364C22C2×#1062535011yescharacteristic
365C22#1309406911yescharacteristic
366C22#1309407011yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—942no—
374C4—942no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4—1881no—
380C2—42no—
381C2—1882no—
382C2#1568965311yescharacteristic
383C2#1568965611yescharacteristic
384C2#1568970711yescharacteristic
385C2#1568979611yescharacteristic
386C2#1568979711yescharacteristic
387C2#1568980211yescharacteristic
388C2#1568983711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2572
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #15689061C2semidirect
3. #15689036C2semidirect
4. #15689035C2semidirect
5. #15689027C2semidirect
6. #15689013C2semidirect
9. #15688991C2semidirect
10. #15688990C2semidirect
11. #15688985C2semidirect
12. #15688984C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C47×#388C2semidirect
201. #388D47semidirect
210. C47#2572semidirect