Finite Group Databasebeta

← #20246365

Subgroups — #20246365

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×#13093992C211yesmaximal, characteristic
2C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689023C211yesmaximal, characteristic, complemented
6#15689014C211yesmaximal, characteristic, complemented
7#15689013C211yesmaximal, characteristic, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15689002C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C47C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22#13093992C418yescomplemented
23C4×C22⋊D47—24no—
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic, complemented
29C2×C22⋊Dic47C2211yescharacteristic, complemented
30C2×(C2×D47)⋊C4—24no—
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×(C2×D47)⋊C4C2211yescharacteristic
39C22⋊C4×D47—24no—
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
48C22×D4×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic, complemented
51C4×D4×C47—24no—
52C2×C4⋊C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic, complemented
55C2×C42×C47C2211yescharacteristic, complemented
56C24×C47C2311yescharacteristic
57C24×C47C2311yescharacteristic
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—22no—
62C23×D47—41no—
63C23×D47—41no—
64C23×D47C2×C414yescomplemented
65C23×D47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47C2×C414yescomplemented
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C2×C22⋊D47—22no—
82C2×C22⋊D47—22no—
83C2×C22⋊D47—41no—
84C2×C22⋊D47—41no—
85C2×C22⋊D47C2×C414yescomplemented
86C2×C22⋊D47C2×C414yescomplemented
87C22×Dic47—22no—
88C22×Dic47—22no—
89C22×Dic47—41no—
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95C22×Dic47C2311yescharacteristic
96C2×C4×D47—22no—
97C2×C4×D47—22no—
98C2×C4×D47—22no—
99C2×C4×D47—22no—
100C2×C4×D47—41no—
101C2×C4×D47—41no—
102C4⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47D414yescomplemented
105C42×C47—22no—
106C22⋊Dic47—22no—
107C22⋊Dic47—22no—
108C22⋊Dic47—41no—
109C22⋊Dic47C2×C414yescomplemented
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4C2×C414yescomplemented
116(C2×D47)⋊C4C2×C414yescomplemented
117(C2×D47)⋊C4D414yescomplemented
118Dic47⋊C4—22no—
119Dic47⋊C4—41no—
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—21no—
131C23×C47—21no—
132C23×C47C22×C412yes—
133C23×C47C22×C412yes—
134C23×C47C2×D412yes—
135C23×C47#4112yes—
136C23×C47C2411yescharacteristic
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—28no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—28no—
149C22×D47—44no—
150C22×D47—44no—
151C22×D47—44no—
152C22×D47—44no—
153C22×D47—44no—
154C22×D47C22×C412yes—
155C22×D47C22×C412yes—
156C22×D47C2×D412yes—
157C22×D47#4112yes—
158D4×C47—28no—
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—21no—
169C2×C4×C47—21no—
170C2×C4×C47—44no—
171C2×C4×C47—44no—
172C2×C4×C47C22×C412yes—
173C2×C4×C47C2×D412yes—
174C2×C4×C47C2×D412yes—
175C2×C4×C47C2×D412yes—
176C22⋊D47—28no—
177C22⋊D47—44no—
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—21no—
192C2×Dic47—21no—
193C2×Dic47—44no—
194C2×Dic47C22×C412yes—
195C2×Dic47C22×C412yes—
196C2×Dic47C2×D412yes—
197C4×D47—44no—
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—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47—41no—
212C22×C47C4×D414yescomplemented
213C22×C47C23×C411yescharacteristic
214C22×C47C22×D411yescharacteristic
215C22×C47C22×D411yescharacteristic
216C22×C47C2×#4111yescharacteristic
217C22×C47C2×#4111yescharacteristic
218C22×C47H(5,𝔽2)11yescharacteristic
219C22×C47H(5,𝔽2)11yescharacteristic
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—22no—
225C2×D47—22no—
226C2×D47—22no—
227C2×D47—22no—
228C2×D47—22no—
229C2×D47—416no—
230C2×D47—41no—
231C2×D47—41no—
232C2×D47—41no—
233C2×D47—41no—
234C2×D47C4×D414yescomplemented
235C4×C47—22no—
236C4×C47—22no—
237C4×C47—22no—
238C4×C47—22no—
239C4×C47—41no—
240Dic47—22no—
241Dic47—22no—
242Dic47—22no—
243Dic47—41no—
244Dic47—41no—
245Dic47—41no—
246#2358—471nomaximal, Sylow
247C2×C47—24no—
248C2×C47—42no—
249C2×C47C2×C4×D411yescharacteristic
250C2×C47C2×C4×D411yescharacteristic
251C2×C47#51811yescharacteristic
252C2×C47D4211yescharacteristic
253C2×C47#54611yescharacteristic
254C2×C47#54611yescharacteristic
255C2×C47#55111yescharacteristic
256D47—24no—
257D47—42no—
258C2×#120—471no—
259C2×C4×D4—471no—
260C2×C4×D4D4711yescharacteristic, complemented
261C22×C22⋊C4—471no—
262C22×C22⋊C4—471no—
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
274C25—471no—
275C22×D4—471no—
276C22×D4—471no—
277C22×D4C2×D4711yescharacteristic
278C23×C4—471no—
279C23×C4—471no—
280C23×C4—471no—
281C23×C4C2×D4711yescharacteristic
282C23×C4C2×D4711yescharacteristic, complemented
283#120—478no—
284C4×D4—24no—
285C4×D4—944no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4C2×D4711yescharacteristic, complemented
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⋊C4—471no—
296C2×C22⋊C4—471no—
297C2×C22⋊C4—471no—
298C2×C22⋊C4—471no—
299C2×C22⋊C4—471no—
300C2×C22⋊C4—471no—
301C2×C22⋊C4—944no—
302C2×C22⋊C4—944no—
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic, complemented
305C2×C42—471no—
306C2×C42—471no—
307C2×C42C2×D4711yescharacteristic, complemented
308#95—471no—
309#95—471no—
310#95—471no—
311#95—471no—
312#95—471no—
313#95—471no—
314C24—471no—
315C24—471no—
316C24—474no—
317C24—942no—
318C24—942no—
319C24—942no—
320C24—942no—
321C24—1881no—
322C24—1881no—
323C24C22×D4711yescharacteristic
324C24C22×D4711yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—474no—
328C2×D4—474no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—1881no—
332C2×D4—1881no—
333C2×D4C4×D4714yescomplemented
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—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—942no—
351C22×C4—942no—
352C22×C4—1881no—
353C22×C4—1881no—
354C22×C4—1881no—
355C22×C4C22×D4711yescharacteristic
356C22×C4C22×D4711yescharacteristic
357C22×C4C22×D4711yescharacteristic
358C22×C4C22×D4711yescharacteristic
359C22×C4C22×D4711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—942no—
362C4⋊C4—1881no—
363C22⋊C4—22no—
364C22⋊C4—474no—
365C22⋊C4—474no—
366C22⋊C4—474no—
367C22⋊C4—474no—
368C22⋊C4—942no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—1881no—
376C22⋊C4C22⋊D4714yescomplemented
377C42—22no—
378C42—942no—
379C42—1881no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—472no—
391C23—472no—
392C23—472no—
393C23—472no—
394C23—948no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—948no—
400C23—941no—
401C23—941no—
402C23—941no—
403C23—941no—
404C23—941no—
405C23—941no—
406C23—1884no—
407C23—1884no—
408C23—1884no—
409C23—1884no—
410C23—1884no—
411C23C2×C4×D4712yes—
412C23C2×C4×D4712yes—
413C23#1062535012yes—
414C23C2×C22⋊D4712yes—
415C23C23×D4711yescharacteristic
416D4—28no—
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—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—472no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—941no—
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—1884no—
451C2×C4—1884no—
452C2×C4—1884no—
453C2×C4C2×C4×D4712yes—
454C2×C4D4×D4712yes—
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—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—474no—
471C22—942no—
472C22—942no—
473C22—942no—
474C22—942no—
475C22—942no—
476C22—942no—
477C22—942no—
478C22—942no—
479C22—942no—
480C22—18816no—
481C22—1881no—
482C22—1881no—
483C22—1881no—
484C22—1881no—
485C22C4×C22⋊D4714yescomplemented
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C22×C22⋊D4711yescharacteristic
489C22#41×D4711yescharacteristic
490C22C2×#1062535011yescharacteristic
491C22#1309406911yescharacteristic
492C22#1309407011yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—942no—
499C4—942no—
500C4—942no—
501C4—1881no—
502C4—1881no—
503C4—1881no—
504C2—24no—
505C2—42no—
506C2—944no—
507C2—1882no—
508C2C4×D4×D4711yescharacteristic
509C2C2×C4×C22⋊D4711yescharacteristic
510C2#1568959511yescharacteristic
511C2D4×C22⋊D4711yescharacteristic
512C2#1568976111yescharacteristic
513C2#1568976911yescharacteristic
514C2#1568980211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC2×C4×D4×C47C2
socleC23×C47C24
hypercenterC2×C4×D4D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D47C2semidirect
3. C22×(C2×D47)⋊C4C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689023C2semidirect
6. #15689014C2semidirect
7. #15689013C2semidirect
8. #15689003C2semidirect
9. #15689002C2semidirect
10. #15688999C2semidirect
11. #15688996C2semidirect
12. #15688994C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C2×C4×D4×C47C2semidirect
22. #13093992C4semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
28. C2×C22⋊Dic47C22semidirect
29. C2×C22⋊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
50. C23×C4×C47C22semidirect
52. C2×C4⋊C4×C47C22semidirect
54. C2×C22⋊C4×C47C22semidirect
55. C2×C42×C47C22semidirect
64. C23×D47C2×C4semidirect
69. C2×D4×C47C2×C4semidirect
85. C2×C22⋊D47C2×C4semidirect
86. C2×C22⋊D47C2×C4semidirect
104. C22⋊C4×C47D4semidirect
109. C22⋊Dic47C2×C4semidirect
115. (C2×D47)⋊C4C2×C4semidirect
116. (C2×D47)⋊C4C2×C4semidirect
117. (C2×D47)⋊C4D4semidirect
212. C22×C47C4×D4semidirect
234. C2×D47C4×D4semidirect
260. C2×C4×D4D47semidirect
273. C47#2358semidirect
282. C23×C4C2×D47semidirect
288. C2×C4⋊C4C2×D47semidirect
304. C2×C22⋊C4C2×D47semidirect
307. C2×C42C2×D47semidirect
333. C2×D4C4×D47semidirect
376. C22⋊C4C22⋊D47semidirect
485. C22C4×C22⋊D47semidirect