Finite Group Databasebeta

← #20247639

Subgroups — #20247639

Order 6016.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094019C211yesmaximal, characteristic, complemented
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic
3#15689052C211yesmaximal, characteristic, complemented
4#15689050C211yesmaximal, characteristic, complemented
5#15689049C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689015C211yesmaximal, characteristic, complemented
8#15689013C211yesmaximal, characteristic, complemented
9#15689012C211yesmaximal, characteristic, complemented
10#15688998C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688978C211yesmaximal, characteristic
13#15688978C211yesmaximal, characteristic
14C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#380C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18#13094019—24no—
19C2×C4⋊Dic47C2211yescharacteristic, complemented
20C2×C4⋊Dic47C2211yescharacteristic, complemented
21C2×Dic47⋊C4C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2211yescharacteristic, complemented
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4—24no—
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic, complemented
39C2×C4×Dic47C2211yescharacteristic, complemented
40C47⋊#95C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C23×C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C4⋊C4×C47C2211yescharacteristic, complemented
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53C24×C47C2311yescharacteristic
54C23×D47—22no—
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47C2311yescharacteristic
62C23×D47C2311yescharacteristic
63C22×C4×C47—22no—
64C22×C4×C47—22no—
65C22×C4×C47—41no—
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×Dic47—22no—
73C22×Dic47—22no—
74C22×Dic47—41no—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C4⋊C4×C47—22no—
82C4⋊C4×C47—41no—
83C22⋊C4×C47—22no—
84C22⋊C4×C47—22no—
85C22⋊Dic47—22no—
86C22⋊Dic47—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4—41no—
96(C2×D47)⋊C4—41no—
97(C2×D47)⋊C4—41no—
98(C2×D47)⋊C4D414yes—
99C4⋊Dic47—22no—
100C4⋊Dic47—41no—
101Dic47⋊C4—22no—
102Dic47⋊C4—41no—
103C4×Dic47—22no—
104C4×Dic47—41no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47#4112yes—
110C23×C47#4112yes—
111C23×C47#4112yes—
112C23×C47C2411yescharacteristic
113C22×D47—28no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—44no—
127C22×D47—44no—
128C22×D47—44no—
129C22×D47—44no—
130C22×D47—44no—
131C22×D47—44no—
132C22×D47C2×D412yes—
133C22×D47#4112yes—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—44no—
152C2×C4×C47C2×D412yes—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—44no—
171C2×Dic47C2×D412yes—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—22no—
178C22×C47#12614yescomplemented
179C22×C47C22×D411yescharacteristic
180C22×C47C2×#4111yescharacteristic
181C22×C47C2×#4111yescharacteristic
182C22×C47C2×#4111yescharacteristic
183C22×C47C2×#4111yescharacteristic
184C22×C47H(5,𝔽2)11yescharacteristic
185C22×C47H(5,𝔽2)11yescharacteristic
186C2×D47—22no—
187C2×D47—22no—
188C2×D47—22no—
189C2×D47—22no—
190C2×D47—22no—
191C2×D47—22no—
192C2×D47—416no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C4×C47—22no—
202C4×C47—41no—
203C4×C47—41no—
204C4×C47—41no—
205C4×C47—41no—
206C4×C47—41no—
207Dic47—22no—
208Dic47—41no—
209Dic47—41no—
210Dic47—41no—
211Dic47—41no—
212Dic47—41no—
213#2480—471nomaximal, Sylow
214C2×C47—24no—
215C2×C47#52511yescharacteristic
216C2×C47C2×#12611yescharacteristic
217C2×C47#53811yescharacteristic
218C2×C47#54611yescharacteristic
219C2×C47#54611yescharacteristic
220C2×C47#55111yescharacteristic
221C2×C47#55111yescharacteristic
222D47—42no—
223D47—42no—
224C2×#126—471no—
225C22×C22⋊C4—471no—
226#397—471no—
227#397—471no—
228#397—471no—
229#396—471no—
230#388—471no—
231#388—471no—
232#388—471no—
233#385—471no—
234#385—471no—
235#380D4711yescharacteristic, complemented
236#379—471no—
237#379—471no—
238C4×C22⋊C4—471no—
239C47#248011yescharacteristic, complemented, Sylow
240C25—471no—
241C23×C4—471no—
242C23×C4C2×D4711yescharacteristic
243#126—944no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—471no—
248C2×C4⋊C4C2×D4711yescharacteristic, complemented
249C2×C4⋊C4C2×D4711yescharacteristic, complemented
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—471no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—944no—
265C2×C22⋊C4C2×D4711yescharacteristic
266C2×C22⋊C4C2×D4711yescharacteristic
267C2×C42—471no—
268C2×C42—471no—
269#95—471no—
270#95—471no—
271#95—471no—
272#95—471no—
273#95—471no—
274#95—471no—
275#95C2×D4711yescharacteristic, complemented
276#95C2×D4711yescharacteristic, complemented
277C24—471no—
278C24—471no—
279C24—942no—
280C24—942no—
281C24—942no—
282C24—942no—
283C24—942no—
284C24—1881no—
285C24—1881no—
286C24C22×D4711yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—471no—
296C22×C4—942no—
297C22×C4—942no—
298C22×C4—1881no—
299C22×C4C22×D4711yescharacteristic
300C22×C4C22×D4711yescharacteristic
301C22×C4C22×D4711yescharacteristic
302C22×C4C22×D4711yescharacteristic
303C22×C4C22×D4711yescharacteristic
304C22×C4C22×D4711yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—942no—
308C4⋊C4—942no—
309C4⋊C4—1881no—
310C4⋊C4—1881no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—474no—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—942no—
318C22⋊C4—942no—
319C22⋊C4—942no—
320C22⋊C4—942no—
321C22⋊C4—942no—
322C22⋊C4—942no—
323C22⋊C4—1881no—
324C22⋊C4—1881no—
325C22⋊C4—1881no—
326C22⋊C4—1881no—
327C42—942no—
328C42—1881no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—472no—
334C23—472no—
335C23—948no—
336C23—941no—
337C23—941no—
338C23—941no—
339C23—941no—
340C23—941no—
341C23—941no—
342C23—941no—
343C23—941no—
344C23—941no—
345C23—941no—
346C23—941no—
347C23—941no—
348C23—1884no—
349C23—1884no—
350C23—1884no—
351C23—1884no—
352C23—1884no—
353C23—1884no—
354C23#1062535012yes—
355C23#1062535212yes—
356C23#1062535412yes—
357C23C23×D4711yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—472no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—1884no—
395C2×C4D4×D4712yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—942no—
403C22—942no—
404C22—942no—
405C22—942no—
406C22—942no—
407C22—942no—
408C22—18816no—
409C22—1881no—
410C22—1881no—
411C22—1881no—
412C22—1881no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22#1309401914yescomplemented
418C22C2×D4×D4711yescharacteristic
419C22#41×D4711yescharacteristic
420C22C2×#1062535211yescharacteristic
421C22C2×#1062535011yescharacteristic
422C22C2×#1062535411yescharacteristic
423C22#1309406911yescharacteristic
424C22#1309407011yescharacteristic
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—942no—
432C4—1881no—
433C4—1881no—
434C4—1881no—
435C4—1881no—
436C4—1881no—
437C2—24no—
438C2—1882no—
439C2—1882no—
440C2#1568963311yescharacteristic
441C2C2×#1309401911yescharacteristic
442C2#1568971011yescharacteristic
443C2#1568976311yescharacteristic
444C2#1568976411yescharacteristic
445C2#1568979711yescharacteristic
446C2#1568980011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#380C2
hypercenter#380D47
hypocenterC47#2480
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
3. #15689052C2semidirect
4. #15689050C2semidirect
5. #15689049C2semidirect
6. #15689045C2semidirect
7. #15689015C2semidirect
8. #15689013C2semidirect
9. #15689012C2semidirect
10. #15688998C2semidirect
11. #15688996C2semidirect
14. C22⋊C4×Dic47C2semidirect
15. C47×#380C2semidirect
19. C2×C4⋊Dic47C22semidirect
20. C2×C4⋊Dic47C22semidirect
21. C2×Dic47⋊C4C22semidirect
22. C2×Dic47⋊C4C22semidirect
38. C2×C4×Dic47C22semidirect
39. C2×C4×Dic47C22semidirect
40. C47⋊#95C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
47. C2×C4⋊C4×C47C22semidirect
48. C2×C4⋊C4×C47C22semidirect
51. #95×C47C22semidirect
52. #95×C47C22semidirect
178. C22×C47#126semidirect
235. #380D47semidirect
239. C47#2480semidirect
248. C2×C4⋊C4C2×D47semidirect
249. C2×C4⋊C4C2×D47semidirect
275. #95C2×D47semidirect
276. #95C2×D47semidirect
417. C22#13094019semidirect