Finite Group Databasebeta

← #20246367

Subgroups — #20246367

Order 6016.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093993C211yesmaximal, characteristic
2C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic47C211yesmaximal, characteristic, complemented
5#15689023C211yesmaximal, characteristic, complemented
6#15689017C211yesmaximal, characteristic, complemented
7#15689011C211yesmaximal, characteristic, complemented
8#15689002C211yesmaximal, characteristic, complemented
9#15689000C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688995C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic, complemented
22#13093993C418yescomplemented
23C4×C22⋊D47—24no—
24(C22⋊D47)⋊C4—24no—
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic47—24no—
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic47C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C2×C4×Dic47C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C25×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47—24no—
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—22no—
60C24×C47—41no—
61C24×C47—41no—
62C24×C47C2×C414yescomplemented
63C24×C47C2311yescharacteristic
64C24×C47C2311yescharacteristic
65C24×C47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—41no—
82C2×C22⋊D47—41no—
83C2×C22⋊D47C2×C414yescomplemented
84C2×C22⋊D47C2×C414yescomplemented
85C2×C22⋊D47C2×C414yescomplemented
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—22no—
89C22×Dic47—22no—
90C22×Dic47—41no—
91C22×Dic47—41no—
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95C22×Dic47C2311yescharacteristic
96C22×Dic47C2311yescharacteristic
97C22×Dic47C2311yescharacteristic
98C22×Dic47C2311yescharacteristic
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47—41no—
102C22⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—22no—
105C22⋊C4×C47D414yescomplemented
106C22⋊Dic47—22no—
107C22⋊Dic47—22no—
108C22⋊Dic47—22no—
109C22⋊Dic47C2×C414yescomplemented
110C22⋊Dic47C2×C414yescomplemented
111C22⋊Dic47C2×C414yescomplemented
112C22⋊Dic47D414yescomplemented
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4—41no—
116Dic47⋊C4—22no—
117Dic47⋊C4—22no—
118Dic47⋊C4—41no—
119C4×Dic47—22no—
120C4×Dic47—22no—
121C4×Dic47—41no—
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—28no—
131C23×C47—28no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—44no—
139C23×C47—44no—
140C23×C47—44no—
141C23×C47—44no—
142C23×C47—44no—
143C23×C47C22×C412yes—
144C23×C47C22×C412yes—
145C23×C47C22×C412yes—
146C23×C47C2×D412yes—
147C23×C47C2×D412yes—
148C23×C47#4112yes—
149C23×C47#4112yes—
150C23×C47C2411yescharacteristic
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—21no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47C22×C412yes—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—44no—
169C2×C4×C47—44no—
170C2×C4×C47C2×D412yes—
171C2×C4×C47C2×D412yes—
172C22⋊D47—28no—
173C22⋊D47—28no—
174C22⋊D47—44no—
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×Dic47—21no—
191C2×Dic47—44no—
192C2×Dic47—44no—
193C2×Dic47C22×C412yes—
194C2×Dic47C22×C412yes—
195C2×Dic47C22×C412yes—
196C2×Dic47C2×D412yes—
197C2×Dic47C2×D412yes—
198C4×D47—44no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—22no—
204C22×C47—22no—
205C22×C47—22no—
206C22×C47—22no—
207C22×C47—22no—
208C22×C47—22no—
209C22×C47—22no—
210C22×C47—22no—
211C22×C47—22no—
212C22×C47—22no—
213C22×C47—22no—
214C22×C47—416no—
215C22×C47—41no—
216C22×C47—41no—
217C22×C47—41no—
218C22×C47—41no—
219C22×C47C4×D414yescomplemented
220C22×C47C4×D414yescomplemented
221C22×C47C23×C411yescharacteristic
222C22×C47C22×D411yescharacteristic
223C22×C47C22×D411yescharacteristic
224C22×C47C2×#4111yescharacteristic
225C22×C47C2×#4111yescharacteristic
226C22×C47H(5,𝔽2)11yescharacteristic
227C22×C47H(5,𝔽2)11yescharacteristic
228C2×D47—22no—
229C2×D47—22no—
230C2×D47—22no—
231C2×D47—41no—
232C2×D47—41no—
233C2×D47—41no—
234C2×D47—41no—
235C4×C47—22no—
236C4×C47—22no—
237C4×C47—41no—
238C4×C47—41no—
239Dic47—22no—
240Dic47—22no—
241Dic47—22no—
242Dic47—22no—
243Dic47—22no—
244Dic47—41no—
245Dic47—41no—
246#2358—471nomaximal, Sylow
247C2×C47—24no—
248C2×C47—24no—
249C2×C47—42no—
250C2×C47C2×C4×D411yescharacteristic
251C2×C47C2×C4×D411yescharacteristic
252C2×C47#51811yescharacteristic
253C2×C47D4211yescharacteristic
254C2×C47#54611yescharacteristic
255C2×C47#54611yescharacteristic
256C2×C47#55111yescharacteristic
257D47—42no—
258C2×#120—471no—
259C2×C4×D4—471no—
260C2×C4×D4—471no—
261C22×C22⋊C4—471no—
262C22×C22⋊C4D4711yescharacteristic, complemented
263#390—471no—
264#388—471no—
265#388—471no—
266#386—471no—
267#386—471no—
268#386—471no—
269#385—471no—
270#385—471no—
271C4×C22⋊C4—471no—
272C4×C22⋊C4—471no—
273C47#235811yescharacteristic, complemented, Sylow
274C25C2×D4711yescharacteristic
275C22×D4—471no—
276C22×D4—471no—
277C22×D4—471no—
278C23×C4—471no—
279C23×C4—471no—
280C23×C4—471no—
281C23×C4C2×D4711yescharacteristic
282C23×C4C2×D4711yescharacteristic
283#120—478no—
284C4×D4—944no—
285C4×D4—944no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4—471no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—471no—
294C2×C22⋊C4—471no—
295C2×C22⋊C4—471no—
296C2×C22⋊C4—471no—
297C2×C22⋊C4—471no—
298C2×C22⋊C4—471no—
299C2×C22⋊C4—471no—
300C2×C22⋊C4—944no—
301C2×C22⋊C4C2×D4711yescharacteristic
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305C2×C42—471no—
306C2×C42—471no—
307C2×C42—471no—
308#95—471no—
309#95—471no—
310#95—471no—
311#95—471no—
312#95—471no—
313#95—471no—
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—471no—
321C24C4×D4714yescomplemented
322C24C22×D4711yescharacteristic
323C24C22×D4711yescharacteristic
324C24C22×D4711yescharacteristic
325C2×D4—474no—
326C2×D4—474no—
327C2×D4—474no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—1881no—
333C2×D4—1881no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—471no—
344C22×C4—471no—
345C22×C4—471no—
346C22×C4—471no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—942no—
351C22×C4—942no—
352C22×C4—942no—
353C22×C4—1881no—
354C22×C4—1881no—
355C22×C4—1881no—
356C22×C4C22×D4711yescharacteristic
357C22×C4C22×D4711yescharacteristic
358C22×C4C22×D4711yescharacteristic
359C22×C4C22×D4711yescharacteristic
360C4⋊C4—942no—
361C4⋊C4—942no—
362C4⋊C4—1881no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—474no—
367C22⋊C4—474no—
368C22⋊C4—474no—
369C22⋊C4—474no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—1881no—
376C22⋊C4C22⋊D4714yescomplemented
377C42—942no—
378C42—942no—
379C42—1881no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—28no—
389C23—28no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—472no—
402C23—941no—
403C23—941no—
404C23—941no—
405C23—941no—
406C23—941no—
407C23—941no—
408C23C2×C4×D4712yes—
409C23C2×C4×D4712yes—
410C23C2×C4×D4712yes—
411C23#1062535012yes—
412C23D4×D4712yes—
413C23#1062535212yes—
414C23C2×C22⋊D4712yes—
415C23C23×D4711yescharacteristic
416D4—948no—
417D4—948no—
418D4—1884no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—472no—
432C2×C4—472no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—472no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—941no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—941no—
449C2×C4—941no—
450C2×C4—941no—
451C2×C4—941no—
452C2×C4—1884no—
453C2×C4—1884no—
454C2×C4—1884no—
455C2×C4C2×C22⋊D4712yes—
456C2×C4C2×C22⋊D4712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—942no—
478C22—942no—
479C22—942no—
480C22—1881no—
481C22—1881no—
482C22—1881no—
483C22—1881no—
484C22(C22⋊D47)⋊C414yescomplemented
485C22C4×C22⋊D4714yescomplemented
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C22×C22⋊D4711yescharacteristic
489C22C2×#1062535211yescharacteristic
490C22C2×#1062535011yescharacteristic
491C22#1309406911yescharacteristic
492C22#1309406911yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—942no—
498C4—942no—
499C4—942no—
500C4—942no—
501C4—942no—
502C4—1881no—
503C4—1881no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—1882no—
508C2C2×(C22⋊D47)⋊C411yescharacteristic
509C2C2×C4×C22⋊D4711yescharacteristic
510C2#1568959611yescharacteristic
511C2D4×C22⋊D4711yescharacteristic
512C2#1568976311yescharacteristic
513C2#1568976711yescharacteristic
514C2#1568979911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC22×C22⋊C4×C47C2
socleC23×C47C24
hypercenterC22×C22⋊C4D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. C22×C22⋊Dic47C2semidirect
5. #15689023C2semidirect
6. #15689017C2semidirect
7. #15689011C2semidirect
8. #15689002C2semidirect
9. #15689000C2semidirect
10. #15688999C2semidirect
11. #15688996C2semidirect
12. #15688995C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×C22⋊Dic47C2semidirect
15. C22×C22⋊C4×C47C2semidirect
21. C22×C4×D47C22semidirect
22. #13093993C4semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
36. C2×(C2×D47)⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×C4×Dic47C22semidirect
40. C2×C4×Dic47C22semidirect
41. C2×C4×Dic47C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
62. C24×C47C2×C4semidirect
83. C2×C22⋊D47C2×C4semidirect
84. C2×C22⋊D47C2×C4semidirect
85. C2×C22⋊D47C2×C4semidirect
105. C22⋊C4×C47D4semidirect
109. C22⋊Dic47C2×C4semidirect
110. C22⋊Dic47C2×C4semidirect
111. C22⋊Dic47C2×C4semidirect
112. C22⋊Dic47D4semidirect
219. C22×C47C4×D4semidirect
220. C22×C47C4×D4semidirect
262. C22×C22⋊C4D47semidirect
273. C47#2358semidirect
321. C24C4×D47semidirect
376. C22⋊C4C22⋊D47semidirect
484. C22(C22⋊D47)⋊C4semidirect
485. C22C4×C22⋊D47semidirect