Finite Group Databasebeta

← #20246364

Subgroups — #20246364

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×#13093986C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic, complemented
7#15689013C211yesmaximal, characteristic, complemented
8#15689012C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15689000C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#385C211yesmaximal, 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
25#13093986—24no—
26C4×C22⋊D47—24no—
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic47C2211yescharacteristic
29C2×(C2×D47)⋊C4—24no—
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×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D47—24no—
42C2×C4×Dic47C2211yescharacteristic, complemented
43C2×C4×Dic47C2211yescharacteristic, complemented
44C2×C4×Dic47C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C23×C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic, complemented
51C2×C4⋊C4×C47C2211yescharacteristic, complemented
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
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—
102C4⋊C4×C47—22no—
103C4⋊C4×C47—41no—
104C22⋊C4×C47—22no—
105C22⋊C4×C47C2×C414yescomplemented
106C22⋊Dic47D414yescomplemented
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
118Dic47⋊C4—22no—
119C4×Dic47—22no—
120C4×Dic47—22no—
121C4×Dic47—41no—
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—21no—
172C2×C4×C47—21no—
173C2×C4×C47—44no—
174C2×C4×C47C22×C412yes—
175C2×C4×C47C22×C412yes—
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—44no—
190C2×Dic47C22×C412yes—
191C2×Dic47C2×D412yes—
192C2×Dic47C2×D412yes—
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—41no—
239C4×C47—41no—
240C4×C47—41no—
241Dic47—22no—
242Dic47—22no—
243Dic47—22no—
244Dic47—22no—
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#385D4711yescharacteristic, complemented
271C4×C22⋊C4—471no—
272C4×C22⋊C4—471no—
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⋊C4C2×D4711yescharacteristic, complemented
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
305C2×C42—471no—
306C2×C42—471no—
307C2×C42—471no—
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—22no—
361C4⋊C4—41no—
362C4⋊C4—942no—
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⋊C4C4×D4714yescomplemented
377C42—942no—
378C42—942no—
379C42—1881no—
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—
413C23D4×D4712yes—
414C23#1062535412yes—
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—21no—
433C2×C4—21no—
434C2×C4—44no—
435C2×C4—472no—
436C2×C4—472no—
437C2×C4—472no—
438C2×C4—472no—
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×C4—1884no—
454C2×C4C2×C4×D4712yes—
455C2×C4C2×C4×D4712yes—
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—
485C22#1309398614yescomplemented
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C2×D4×D4711yescharacteristic
489C22#41×D4711yescharacteristic
490C22C2×#1062535411yescharacteristic
491C22#1309406911yescharacteristic
492C22#1309407011yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—942no—
500C4—942no—
501C4—942no—
502C4—942no—
503C4—1881no—
504C2—24no—
505C2—944no—
506C2—1882no—
507C2—1882no—
508C2C4×D4×D4711yescharacteristic
509C2C2×#1309398611yescharacteristic
510C2#1568959511yescharacteristic
511C2#1568975511yescharacteristic
512C2#1568976411yescharacteristic
513C2#1568976511yescharacteristic
514C2#1568980011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#385C2
socleC23×C47C24
hypercenter#385D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#13093986C2semidirect
3. C2×C4×C22⋊D47C2semidirect
4. C22×(C2×D47)⋊C4C2semidirect
5. C2×C22⋊C4×D47C2semidirect
6. #15689024C2semidirect
7. #15689013C2semidirect
8. #15689012C2semidirect
9. #15689001C2semidirect
10. #15689001C2semidirect
11. #15689000C2semidirect
12. #15688994C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. #15688970C2semidirect
15. C47×#385C2semidirect
23. C22×C4×D47C22semidirect
24. #13093994C4semidirect
27. C2×Dic47⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
42. C2×C4×Dic47C22semidirect
43. C2×C4×Dic47C22semidirect
44. C2×C4×Dic47C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
50. C2×C4⋊C4×C47C22semidirect
51. C2×C4⋊C4×C47C22semidirect
54. #95×C47C22semidirect
55. #95×C47C22semidirect
63. C23×D47C2×C4semidirect
78. C2×C22⋊D47C2×C4semidirect
91. C2×D188C2×C4semidirect
92. C2×D188C2×C4semidirect
105. C22⋊C4×C47C2×C4semidirect
106. C22⋊Dic47D4semidirect
115. (C2×D47)⋊C4C2×C4semidirect
116. (C2×D47)⋊C4C2×C4semidirect
117. (C2×D47)⋊C4D4semidirect
205. C22×C47C4×D4semidirect
234. C2×D47C4×D4semidirect
270. #385D47semidirect
273. C47#2358semidirect
287. C2×C4⋊C4C2×D47semidirect
288. C2×C4⋊C4C2×D47semidirect
312. #95C2×D47semidirect
313. #95C2×D47semidirect
376. C22⋊C4C4×D47semidirect
485. C22#13093986semidirect