Finite Group Databasebeta

← #20246368

Subgroups — #20246368

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×D4×Dic47C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#15689023C211yesmaximal, characteristic, complemented
7#15689015C211yesmaximal, characteristic, complemented
8#15689012C211yesmaximal, characteristic, complemented
9#15689000C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11#15688997C211yesmaximal, characteristic, complemented
12#15688995C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic, complemented
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23#13093992C418yescomplemented
24D4×Dic47—24no—
25(C22⋊D47)⋊C4—24no—
26C2×C4⋊Dic47C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×Dic47⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic, complemented
32C2×(C2×D47)⋊C4—24no—
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
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
49C22×D4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic, complemented
54#95×C47C2211yescharacteristic, complemented
55#95×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—41no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—41no—
81C2×C22⋊D47—41no—
82C2×C22⋊D47C2×C414yescomplemented
83C2×C22⋊D47C2×C414yescomplemented
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—41no—
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—
102C22⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—41no—
105C22⋊Dic47—22no—
106C22⋊Dic47C2×C414yescomplemented
107C22⋊Dic47D414yescomplemented
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)⋊C4C2×C414yescomplemented
114(C2×D47)⋊C4C2×C414yescomplemented
115(C2×D47)⋊C4D414yescomplemented
116C4⋊Dic47—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—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—21no—
171C2×C4×C47—21no—
172C2×C4×C47—44no—
173C2×C4×C47C22×C412yes—
174C2×C4×C47C2×D412yes—
175C22⋊D47—28no—
176C22⋊D47—44no—
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—44no—
191C2×Dic47—44no—
192C2×Dic47C22×C412yes—
193C2×Dic47C22×C412yes—
194C2×Dic47C2×D412yes—
195C2×Dic47C2×D412yes—
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—41no—
238C4×C47—41no—
239C4×C47—41no—
240Dic47—22no—
241Dic47—22no—
242Dic47—22no—
243Dic47—22no—
244Dic47—22no—
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×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#386D4711yescharacteristic, complemented
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×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—944no—
301C2×C22⋊C4—944no—
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic, complemented
304C2×C22⋊C4C2×D4711yescharacteristic, complemented
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—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—41no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—942no—
351C22×C4—1881no—
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—942no—
361C4⋊C4—942no—
362C4⋊C4—1881no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—474no—
367C22⋊C4—474no—
368C22⋊C4—474no—
369C22⋊C4—474no—
370C22⋊C4—474no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—942no—
376C22⋊C4—942no—
377C42—942no—
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—
413C23D4×D4712yes—
414C23#1062535212yes—
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—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—472no—
436C2×C4—472no—
437C2×C4—472no—
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—1884no—
452C2×C4—1884no—
453C2×C4—1884no—
454C2×C4—1884no—
455C2×C4C2×C4×D4712yes—
456C2×C4D4×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—
485C22(C22⋊D47)⋊C414yescomplemented
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C2×D4×D4711yescharacteristic
489C22#41×D4711yescharacteristic
490C22C2×#1062535211yescharacteristic
491C22#1309406911yescharacteristic
492C22#1309407011yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—942no—
499C4—942no—
500C4—942no—
501C4—942no—
502C4—942no—
503C4—1881no—
504C2—24no—
505C2—42no—
506C2—944no—
507C2—1882no—
508C2C4×D4×D4711yescharacteristic
509C2C2×(C22⋊D47)⋊C411yescharacteristic
510C2#1568959511yescharacteristic
511C2#1568975711yescharacteristic
512C2#1568976011yescharacteristic
513C2#1568976211yescharacteristic
514C2#1568979611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#386C2
socleC23×C47C24
hypercenter#386D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. C22×(C2×D47)⋊C4C2semidirect
5. C2×C22⋊C4×D47C2semidirect
6. #15689023C2semidirect
7. #15689015C2semidirect
8. #15689012C2semidirect
9. #15689000C2semidirect
10. #15688999C2semidirect
11. #15688997C2semidirect
12. #15688995C2semidirect
13. C4×C22⋊Dic47C2semidirect
14. #15688970C2semidirect
15. C47×#386C2semidirect
20. C23×Dic47C22semidirect
23. #13093992C4semidirect
26. C2×C4⋊Dic47C22semidirect
27. C2×Dic47⋊C4C22semidirect
28. C2×Dic47⋊C4C22semidirect
31. C2×C22⋊Dic47C22semidirect
42. C2×C4×Dic47C22semidirect
43. C2×C4×Dic47C22semidirect
44. C2×C4×Dic47C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
52. C2×C22⋊C4×C47C22semidirect
53. C2×C22⋊C4×C47C22semidirect
54. #95×C47C22semidirect
55. #95×C47C22semidirect
64. C23×D47C2×C4semidirect
69. C2×D4×C47C2×C4semidirect
82. C2×C22⋊D47C2×C4semidirect
83. C2×C22⋊D47C2×C4semidirect
106. C22⋊Dic47C2×C4semidirect
107. C22⋊Dic47D4semidirect
113. (C2×D47)⋊C4C2×C4semidirect
114. (C2×D47)⋊C4C2×C4semidirect
115. (C2×D47)⋊C4D4semidirect
212. C22×C47C4×D4semidirect
234. C2×D47C4×D4semidirect
268. #386D47semidirect
273. C47#2358semidirect
303. C2×C22⋊C4C2×D47semidirect
304. C2×C22⋊C4C2×D47semidirect
312. #95C2×D47semidirect
313. #95C2×D47semidirect
333. C2×D4C4×D47semidirect
485. C22(C22⋊D47)⋊C4semidirect