Finite Group Databasebeta

← #20246850

Subgroups — #20246850

Order 6016.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094006C211yesmaximal, characteristic, complemented
2C2×#13093993C211yesmaximal, characteristic
3C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689051C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689038C211yesmaximal, characteristic, complemented
8#15689017C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689002C211yesmaximal, characteristic, complemented
11#15688999C211yesmaximal, characteristic, complemented
12#15688996C211yesmaximal, characteristic, complemented
13#15688983C211yesmaximal, characteristic, complemented
14#15688979C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic, complemented
20#13094006—24no—
21#13093993—24no—
22C4×C22⋊D47—24no—
23C2×C4⋊Dic47C2211yescharacteristic, complemented
24C2×C4⋊Dic47C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C25×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47—24no—
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—22no—
60C24×C47—41no—
61C24×C47—41no—
62C24×C47C2311yescharacteristic
63C24×C47C2311yescharacteristic
64C24×C47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—22no—
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—41no—
83C2×C22⋊D47—41no—
84C2×C22⋊D47D414yes—
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C2×C4×D47—22no—
93C2×C4×D47—22no—
94C2×C4×D47—41no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—22no—
98C22⋊C4×C47D414yescomplemented
99C22⋊Dic47—22no—
100C22⋊Dic47—22no—
101C22⋊Dic47—22no—
102C22⋊Dic47—22no—
103C22⋊Dic47—22no—
104C22⋊Dic47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47—41no—
107C22⋊Dic47—41no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—41no—
111C4⋊Dic47—22no—
112C4⋊Dic47—41no—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115Dic47⋊C4—41no—
116C4×Dic47—22no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—28no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—44no—
135C23×C47—44no—
136C23×C47—44no—
137C23×C47—44no—
138C23×C47—44no—
139C23×C47—44no—
140C23×C47C2×D412yes—
141C23×C47C2×D412yes—
142C23×C47#4112yes—
143C23×C47#4112yes—
144C23×C47#4112yes—
145C23×C47C2411yescharacteristic
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47—21no—
152C22×D47C2×D412yes—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—44no—
164C2×C4×C47—44no—
165C2×C4×C47C2×D412yes—
166C2×C4×C47C2×D412yes—
167C22⋊D47—28no—
168C22⋊D47—44no—
169C22⋊D47—44no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47C2×D412yes—
191C4×D47—44no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—416no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47—41no—
212C22×C47—41no—
213C22×C47#12314yescomplemented
214C22×C47C22×D411yescharacteristic
215C22×C47C22×D411yescharacteristic
216C22×C47C2×#4111yescharacteristic
217C22×C47C2×#4111yescharacteristic
218C22×C47C2×#4111yescharacteristic
219C22×C47H(5,𝔽2)11yescharacteristic
220C22×C47H(5,𝔽2)11yescharacteristic
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C4×C47—22no—
229C4×C47—22no—
230C4×C47—41no—
231C4×C47—41no—
232Dic47—22no—
233Dic47—41no—
234Dic47—41no—
235Dic47—41no—
236Dic47—41no—
237Dic47—41no—
238Dic47—41no—
239#2418—471nomaximal, Sylow
240C2×C47—24no—
241C2×C47—42no—
242C2×C47—42no—
243C2×C47C2×#12311yescharacteristic
244C2×C47#52511yescharacteristic
245C2×C47#53811yescharacteristic
246C2×C47D4211yescharacteristic
247C2×C47#54611yescharacteristic
248C2×C47#54611yescharacteristic
249C2×C47#55111yescharacteristic
250D47—42no—
251C2×#123—471no—
252C2×#120—471no—
253C2×C4×D4—471no—
254C22×C22⋊C4D4711yescharacteristic, complemented
255#399—471no—
256#397—471no—
257#394—471no—
258#394—471no—
259#388—471no—
260#388—471no—
261#386—471no—
262#386—471no—
263#385—471no—
264#380—471no—
265#379—471no—
266C47#241811yescharacteristic, complemented, Sylow
267C25C2×D4711yescharacteristic
268C22×D4—471no—
269C22×D4—471no—
270C22×D4—471no—
271C23×C4—471no—
272C23×C4C2×D4711yescharacteristic
273C23×C4C2×D4711yescharacteristic
274#123—944no—
275#120—944no—
276C4×D4—944no—
277C2×C4⋊C4—471no—
278C2×C4⋊C4—471no—
279C2×C4⋊C4—471no—
280C2×C4⋊C4—471no—
281C2×C4⋊C4—471no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4—471no—
286C2×C22⋊C4—471no—
287C2×C22⋊C4—471no—
288C2×C22⋊C4—471no—
289C2×C22⋊C4—471no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—471no—
294C2×C22⋊C4—471no—
295C2×C22⋊C4C2×D4711yescharacteristic
296C2×C22⋊C4C2×D4711yescharacteristic
297C2×C22⋊C4C2×D4711yescharacteristic
298C2×C22⋊C4C2×D4711yescharacteristic
299C2×C42—471no—
300#95—471no—
301#95—471no—
302#95—471no—
303#95—471no—
304#95—471no—
305#95—471no—
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24—471no—
314C24C22×D4711yescharacteristic
315C24C22×D4711yescharacteristic
316C24C22×D4711yescharacteristic
317C2×D4—474no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—942no—
324C2×D4—1881no—
325C2×D4—1881no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—471no—
333C22×C4—471no—
334C22×C4—471no—
335C22×C4—471no—
336C22×C4—471no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—942no—
340C22×C4—942no—
341C22×C4—1881no—
342C22×C4C22×D4711yescharacteristic
343C22×C4C22×D4711yescharacteristic
344C22×C4C22×D4711yescharacteristic
345C22×C4C22×D4711yescharacteristic
346C4⋊C4—942no—
347C4⋊C4—942no—
348C4⋊C4—942no—
349C4⋊C4—1881no—
350C4⋊C4—1881no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4—942no—
360C22⋊C4—942no—
361C22⋊C4—942no—
362C22⋊C4—942no—
363C22⋊C4—1881no—
364C22⋊C4—1881no—
365C22⋊C4—1881no—
366C22⋊C4C22⋊D4714yescomplemented
367C42—942no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—44no—
386C23—44no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—472no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23#1062535012yes—
399C23#1062535012yes—
400C23D4×D4712yes—
401C23#1062535212yes—
402C23C2×C22⋊D4712yes—
403C23C23×D4711yescharacteristic
404D4—948no—
405D4—1884no—
406D4—1884no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—472no—
420C2×C4—941no—
421C2×C4—941no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—1884no—
441C2×C4C2×C22⋊D4712yes—
442C2×C4C2×C22⋊D4712yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—416no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—942no—
465C22—942no—
466C22—942no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22#1309400614yescomplemented
472C22C2×D4×D4711yescharacteristic
473C22C22×C22⋊D4711yescharacteristic
474C22C2×#1062535211yescharacteristic
475C22C2×#1062535011yescharacteristic
476C22C2×#1062535011yescharacteristic
477C22#1309406911yescharacteristic
478C22#1309406911yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—942no—
484C4—1881no—
485C4—1881no—
486C4—1881no—
487C4—1881no—
488C4—1881no—
489C4—1881no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—1882no—
494C2C2×#1309400611yescharacteristic
495C2#1568963411yescharacteristic
496C2#1568971111yescharacteristic
497C2D4×C22⋊D4711yescharacteristic
498C2#1568976311yescharacteristic
499C2#1568976711yescharacteristic
500C2#1568979911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2418
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094006C2semidirect
3. C2×C4×C22⋊D47C2semidirect
4. #15689059C2semidirect
5. #15689051C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689017C2semidirect
9. #15689016C2semidirect
10. #15689002C2semidirect
11. #15688999C2semidirect
12. #15688996C2semidirect
13. #15688983C2semidirect
14. #15688979C2semidirect
15. C22×C22⋊C4×C47C2semidirect
19. C22×C4×D47C22semidirect
23. C2×C4⋊Dic47C22semidirect
24. C2×C4⋊Dic47C22semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×C4×Dic47C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
98. C22⋊C4×C47D4semidirect
213. C22×C47#123semidirect
254. C22×C22⋊C4D47semidirect
266. C47#2418semidirect
366. C22⋊C4C22⋊D47semidirect
471. C22#13094006semidirect