Finite Group Databasebeta

← #20246370

Subgroups — #20246370

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×#13093994C211yesmaximal, characteristic
2C2×C4×D188C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#15689025C211yesmaximal, characteristic, complemented
7#15689015C211yesmaximal, characteristic, complemented
8#15689014C211yesmaximal, characteristic, complemented
9#15689002C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15689001C211yesmaximal, characteristic, complemented
12#15688998C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23C22×C4×D47C2211yescharacteristic, complemented
24#13093994C418yescomplemented
25C4×D188—24no—
26(C22⋊D47)⋊C4—24no—
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C2×C4⋊Dic47C2211yescharacteristic, complemented
29C2×Dic47⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic47C2211yescharacteristic
31C2×(C2×D47)⋊C4—24no—
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
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C22⋊C4×D47—24no—
44C2×C4×Dic47C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C23×C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic, complemented
53C2×C42×C47C2211yescharacteristic, complemented
54#95×C47C2211yescharacteristic, complemented
55#95×C47C2211yescharacteristic, complemented
56C24×C47C2311yescharacteristic
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—41no—
62C23×D47—41no—
63C23×D47C2×C414yescomplemented
64C23×D47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—41no—
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—22no—
77C2×C22⋊D47—22no—
78C2×C22⋊D47C2×C414yescomplemented
79C22×Dic47—22no—
80C22×Dic47—22no—
81C22×Dic47—41no—
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C2×D188—22no—
88C2×D188—22no—
89C2×D188—41no—
90C2×D188—41no—
91C2×D188C2×C414yescomplemented
92C2×D188C2×C414yescomplemented
93C2×C4×D47—22no—
94C2×C4×D47—22no—
95C2×C4×D47—22no—
96C2×C4×D47—22no—
97C2×C4×D47—22no—
98C2×C4×D47—22no—
99C2×C4×D47—41no—
100C2×C4×D47—41no—
101C2×C4×D47—41no—
102C22⋊C4×C47C2×C414yescomplemented
103C22⋊C4×C47D414yescomplemented
104C42×C47—22no—
105C42×C47—41no—
106C22⋊Dic47—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—41no—
115(C2×D47)⋊C4C2×C414yescomplemented
116(C2×D47)⋊C4C2×C414yescomplemented
117(C2×D47)⋊C4D414yescomplemented
118C4⋊Dic47—22no—
119C4⋊Dic47—41no—
120Dic47⋊C4—22no—
121C4×Dic47—22no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47C22×C412yes—
127C23×C47C2×D412yes—
128C23×C47#4112yes—
129C23×C47C2411yescharacteristic
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—28no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—28no—
148C22×D47—44no—
149C22×D47—44no—
150C22×D47—44no—
151C22×D47—44no—
152C22×D47—44no—
153C22×D47C22×C412yes—
154C22×D47C22×C412yes—
155C22×D47C22×C412yes—
156C22×D47C2×D412yes—
157C22×D47#4112yes—
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—21no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—44no—
172C2×C4×C47C22×C412yes—
173C2×C4×C47C22×C412yes—
174C2×C4×C47C2×D412yes—
175C2×C4×C47C2×D412yes—
176C2×C4×C47C2×D412yes—
177C22⋊D47—28no—
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×Dic47C22×C412yes—
193C2×Dic47C2×D412yes—
194D188—28no—
195D188—44no—
196C4×D47—44no—
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×C47C4×D414yescomplemented
206C22×C47C23×C411yescharacteristic
207C22×C47C22×D411yescharacteristic
208C22×C47C22×D411yescharacteristic
209C22×C47C2×#4111yescharacteristic
210C22×C47C2×#4111yescharacteristic
211C22×C47H(5,𝔽2)11yescharacteristic
212C22×C47H(5,𝔽2)11yescharacteristic
213C2×D47—22no—
214C2×D47—22no—
215C2×D47—22no—
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—22no—
219C2×D47—22no—
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—22no—
225C2×D47—416no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
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—22no—
240C4×C47—41no—
241Dic47—22no—
242Dic47—22no—
243Dic47—41no—
244Dic47—41no—
245Dic47—41no—
246#2358—471nomaximal, Sylow
247C2×C47—24no—
248C2×C47C2×C4×D411yescharacteristic
249C2×C47C2×C4×D411yescharacteristic
250C2×C47#51811yescharacteristic
251C2×C47D4211yescharacteristic
252C2×C47#54611yescharacteristic
253C2×C47#54611yescharacteristic
254C2×C47#55111yescharacteristic
255D47—24no—
256D47—42no—
257D47—42no—
258C2×#120—471no—
259C2×C4×D4—471no—
260C2×C4×D4—471no—
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⋊C4D4711yescharacteristic, complemented
273C47#235811yescharacteristic, complemented, Sylow
274C25—471no—
275C22×D4—471no—
276C22×D4—471no—
277C22×D4—471no—
278C23×C4—471no—
279C23×C4—471no—
280C23×C4—471no—
281C23×C4—471no—
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—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
305C2×C42—471no—
306C2×C42C2×D4711yescharacteristic, complemented
307C2×C42C2×D4711yescharacteristic, complemented
308#95—471no—
309#95—471no—
310#95—471no—
311#95—471no—
312#95C2×D4711yescharacteristic, complemented
313#95C2×D4711yescharacteristic, complemented
314C24—471no—
315C24—471no—
316C24—471no—
317C24—474no—
318C24—942no—
319C24—942no—
320C24—942no—
321C24—942no—
322C24—1881no—
323C24—1881no—
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—41no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—942no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—1881no—
351C22×C4—1881no—
352C22×C4—1881no—
353C22×C4—1881no—
354C22×C4C22×D4711yescharacteristic
355C22×C4C22×D4711yescharacteristic
356C22×C4C22×D4711yescharacteristic
357C22×C4C22×D4711yescharacteristic
358C22×C4C22×D4711yescharacteristic
359C22×C4C22×D4711yescharacteristic
360C4⋊C4—942no—
361C4⋊C4—942no—
362C4⋊C4—1881no—
363C22⋊C4—474no—
364C22⋊C4—474no—
365C22⋊C4—474no—
366C22⋊C4—942no—
367C22⋊C4—942no—
368C22⋊C4—942no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—1881no—
375C22⋊C4C4×D4714yescomplemented
376C22⋊C4D18814yescomplemented
377C42—22no—
378C42—41no—
379C42—942no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—472no—
385C23—472no—
386C23—472no—
387C23—472no—
388C23—472no—
389C23—948no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—948no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23—941no—
402C23—941no—
403C23—941no—
404C23—941no—
405C23—941no—
406C23—941no—
407C23—1884no—
408C23—1884no—
409C23—1884no—
410C23—1884no—
411C23—1884no—
412C23C2×C4×D4712yes—
413C23C2×D18812yes—
414C23#1062535012yes—
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—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—44no—
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—1884no—
449C2×C4—1884no—
450C2×C4—1884no—
451C2×C4—1884no—
452C2×C4C2×C4×D4712yes—
453C2×C4C2×C4×D4712yes—
454C2×C4C2×D18812yes—
455C2×C4C2×D18812yes—
456C2×C4D4×D4712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—474no—
464C22—942no—
465C22—942no—
466C22—942no—
467C22—942no—
468C22—942no—
469C22—942no—
470C22—942no—
471C22—942no—
472C22—942no—
473C22—942no—
474C22—942no—
475C22—942no—
476C22—18816no—
477C22—1881no—
478C22—1881no—
479C22—1881no—
480C22—1881no—
481C22—1881no—
482C22—1881no—
483C22—1881no—
484C22—1881no—
485C22C4×D18814yescomplemented
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C22×D18811yescharacteristic
489C22#41×D4711yescharacteristic
490C22C2×#1062535011yescharacteristic
491C22#1309406911yescharacteristic
492C22#1309407011yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—942no—
500C4—942no—
501C4—1881no—
502C4—1881no—
503C4—1881no—
504C2—24no—
505C2—944no—
506C2—1882no—
507C2—1882no—
508C2C4×D4×D4711yescharacteristic
509C2C2×C4×D18811yescharacteristic
510C2#1568959511yescharacteristic
511C2D4×D18811yescharacteristic
512C2#1568976311yescharacteristic
513C2#1568976811yescharacteristic
514C2#1568979711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC4×C22⋊C4×C47C2
socleC23×C47C24
hypercenterC4×C22⋊C4D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D188C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. C22×(C2×D47)⋊C4C2semidirect
5. C2×C22⋊C4×D47C2semidirect
6. #15689025C2semidirect
7. #15689015C2semidirect
8. #15689014C2semidirect
9. #15689002C2semidirect
10. #15689001C2semidirect
11. #15689001C2semidirect
12. #15688998C2semidirect
13. #15688997C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C4×C22⋊C4×C47C2semidirect
23. C22×C4×D47C22semidirect
24. #13093994C4semidirect
27. C2×C4⋊Dic47C22semidirect
28. C2×C4⋊Dic47C22semidirect
29. C2×Dic47⋊C4C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
44. C2×C4×Dic47C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
52. C2×C42×C47C22semidirect
53. C2×C42×C47C22semidirect
54. #95×C47C22semidirect
55. #95×C47C22semidirect
63. C23×D47C2×C4semidirect
78. C2×C22⋊D47C2×C4semidirect
91. C2×D188C2×C4semidirect
92. C2×D188C2×C4semidirect
102. C22⋊C4×C47C2×C4semidirect
103. C22⋊C4×C47D4semidirect
115. (C2×D47)⋊C4C2×C4semidirect
116. (C2×D47)⋊C4C2×C4semidirect
117. (C2×D47)⋊C4D4semidirect
205. C22×C47C4×D4semidirect
234. C2×D47C4×D4semidirect
272. C4×C22⋊C4D47semidirect
273. C47#2358semidirect
306. C2×C42C2×D47semidirect
307. C2×C42C2×D47semidirect
312. #95C2×D47semidirect
313. #95C2×D47semidirect
375. C22⋊C4C4×D47semidirect
376. C22⋊C4D188semidirect
485. C22C4×D188semidirect