Finite Group Databasebeta

← #20246772

Subgroups — #20246772

Order 6016.

786 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094009C211yesmaximal, characteristic, complemented
2C2×#13093994C211yesmaximal, characteristic
3C2×#13093981C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689047C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689041C211yesmaximal, characteristic, complemented
8#15689038C211yesmaximal, characteristic, complemented
9#15689025C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689013C211yesmaximal, characteristic, complemented
12#15689001C211yesmaximal, characteristic, complemented
13#15688997C211yesmaximal, characteristic, complemented
14#15688978C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22#13094009—24no—
23#13093994—24no—
24#13093981—24no—
25C2×C4⋊Dic47C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×Dic47⋊C4C2211yescharacteristic, complemented
29C2×Dic47⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
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
43C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C22⋊C4×D47—24no—
45C2×C4×Dic47C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C47C2211yescharacteristic, complemented
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic, complemented
53#95×C47C2211yescharacteristic, complemented
54#95×C47C2211yescharacteristic, complemented
55C24×C47C2311yescharacteristic
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—41no—
62C23×D47—41no—
63C23×D47C2311yescharacteristic
64C23×D47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—41no—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C2×D188—22no—
81C2×D188—22no—
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—22no—
85C2×D188—41no—
86C2×C4×D47—22no—
87C2×C4×D47—22no—
88C2×C4×D47—22no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×C4×D47D414yescomplemented
92C4⋊C4×C47—22no—
93C22⋊C4×C47—22no—
94C22⋊C4×C47—22no—
95C22⋊C4×C47—22no—
96C42×C47—22no—
97C22⋊Dic47—22no—
98C22⋊Dic47—41no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109(C2×D47)⋊C4—41no—
110(C2×D47)⋊C4D414yes—
111C4⋊Dic47—41no—
112Dic47⋊C4—22no—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115Dic47⋊C4—41no—
116C4×Dic47—22no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47#4112yes—
124C23×C47C2411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—28no—
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
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—44no—
144C22×D47—44no—
145C22×D47—44no—
146C22×D47—44no—
147C22×D47—44no—
148C22×D47—44no—
149C22×D47C2×D412yes—
150C22×D47C2×D412yes—
151C22×D47#4112yes—
152C22×D47#4112yes—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
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×C47C2×D412yes—
170C2×C4×C47C2×D412yes—
171C22⋊D47—44no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
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×Dic47C2×D412yes—
186C2×Dic47C2×D412yes—
187D188—44no—
188D188—44no—
189C4×D47—28no—
190C4×D47—44no—
191C22×C47—22no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47C22×D411yescharacteristic
199C22×C47C22×D411yescharacteristic
200C22×C47C2×#4111yescharacteristic
201C22×C47C2×#4111yescharacteristic
202C22×C47C2×#4111yescharacteristic
203C22×C47H(5,𝔽2)11yescharacteristic
204C22×C47H(5,𝔽2)11yescharacteristic
205C2×D47—22no—
206C2×D47—22no—
207C2×D47—22no—
208C2×D47—22no—
209C2×D47—22no—
210C2×D47—22no—
211C2×D47—22no—
212C2×D47—22no—
213C2×D47—22no—
214C2×D47—416no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47#12114yes—
227C4×C47—22no—
228C4×C47—22no—
229C4×C47—41no—
230C4×C47—41no—
231C4×C47—41no—
232C4×C47—41no—
233Dic47—22no—
234Dic47—22no—
235Dic47—41no—
236Dic47—41no—
237Dic47—41no—
238#2411—471nomaximal, Sylow
239C2×C47—42no—
240C2×C47C2×#12111yescharacteristic
241C2×C47#52511yescharacteristic
242C2×C47#53511yescharacteristic
243C2×C47#54611yescharacteristic
244C2×C47#54611yescharacteristic
245C2×C47#55111yescharacteristic
246C2×C47#55111yescharacteristic
247D47—24no—
248D47—42no—
249D47—81no—
250C2×#123—471no—
251C2×#120—471no—
252C2×#117—471no—
253C22×C22⋊C4—471no—
254#396—471no—
255#396—471no—
256#394—471no—
257#394—471no—
258#390—471no—
259#390—471no—
260#388—471no—
261#388D4711yescharacteristic, complemented
262#386—471no—
263#385—471no—
264#379—471no—
265C47#241111yescharacteristic, complemented, Sylow
266C25—471no—
267C22×D4—471no—
268C22×D4—471no—
269C22×D4—471no—
270C23×C4—471no—
271C23×C4—471no—
272#123—944no—
273#120—944no—
274#117—944no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4—471no—
278C2×C4⋊C4—471no—
279C2×C4⋊C4—471no—
280C2×C4⋊C4C2×D4711yescharacteristic, complemented
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4—471no—
286C2×C22⋊C4—471no—
287C2×C22⋊C4—471no—
288C2×C22⋊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—944no—
296C2×C22⋊C4C2×D4711yescharacteristic
297C2×C22⋊C4C2×D4711yescharacteristic
298C2×C22⋊C4C2×D4711yescharacteristic
299C2×C42—471no—
300C2×C42C2×D4711yescharacteristic, complemented
301#95—471no—
302#95—471no—
303#95C2×D4711yescharacteristic, complemented
304#95C2×D4711yescharacteristic, complemented
305C24—471no—
306C24—471no—
307C24—471no—
308C24—942no—
309C24—942no—
310C24—942no—
311C24—942no—
312C24—942no—
313C24—1881no—
314C24—1881no—
315C24C22×D4711yescharacteristic
316C2×D4—942no—
317C2×D4—942no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—1881no—
324C2×D4—1881no—
325C22×C4—471no—
326C22×C4—471no—
327C22×C4—474no—
328C22×C4—471no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—942no—
332C22×C4—942no—
333C22×C4—942no—
334C22×C4—1881no—
335C22×C4—1881no—
336C22×C4C22×D4711yescharacteristic
337C22×C4C22×D4711yescharacteristic
338C22×C4C22×D4711yescharacteristic
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—942no—
344C4⋊C4—942no—
345C4⋊C4—942no—
346C4⋊C4—1881no—
347C4⋊C4—1881no—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—474no—
352C22⋊C4—942no—
353C22⋊C4—942no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4—942no—
360C22⋊C4—942no—
361C22⋊C4—1881no—
362C22⋊C4—1881no—
363C22⋊C4—1881no—
364C22⋊C4—1881no—
365C42—22no—
366C42—942no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—472no—
374C23—472no—
375C23—472no—
376C23—472no—
377C23—948no—
378C23—941no—
379C23—941no—
380C23—941no—
381C23—941no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23—941no—
386C23—941no—
387C23—941no—
388C23—941no—
389C23—941no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—1884no—
396C23—1884no—
397C23—1884no—
398C23—1884no—
399C23—1884no—
400C23—1884no—
401C23#1062535012yes—
402C23C23×D4711yescharacteristic
403D4—1884no—
404D4—1884no—
405D4—1884no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—472no—
423C2×C4—472no—
424C2×C4—948no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—1884no—
439C2×C4D4×D4712yes—
440C2×C4D4×D4712yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—474no—
449C22—942no—
450C22—942no—
451C22—942no—
452C22—942no—
453C22—942no—
454C22—942no—
455C22—942no—
456C22—942no—
457C22—942no—
458C22—18816no—
459C22—1881no—
460C22—1881no—
461C22—1881no—
462C22—1881no—
463C22—1881no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22C2×D4×D4711yescharacteristic
471C22C2×D4×D4711yescharacteristic
472C22#41×D4711yescharacteristic
473C22#41×D4711yescharacteristic
474C22C2×#1062535011yescharacteristic
475C22#1309407011yescharacteristic
476C22#1309407011yescharacteristic
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—942no—
484C4—942no—
485C4—1881no—
486C4—1881no—
487C4—1881no—
488C2—42no—
489C2—944no—
490C2—3761no—
491C2—1882no—
492C2#121×D4711yescharacteristic
493C2#1568963211yescharacteristic
494C2#1568969111yescharacteristic
495C2#1568976511yescharacteristic
496C2#1568976911yescharacteristic
497C2#1568979711yescharacteristic
498C2#1568979811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2411
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13094009C2semidirect
3. C2×#13093981C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689047C2semidirect
6. #15689046C2semidirect
7. #15689041C2semidirect
8. #15689038C2semidirect
9. #15689025C2semidirect
10. #15689023C2semidirect
11. #15689013C2semidirect
12. #15689001C2semidirect
13. #15688997C2semidirect
14. #15688978C2semidirect
15. C47×#388C2semidirect
25. C2×C4⋊Dic47C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
28. C2×Dic47⋊C4C22semidirect
29. C2×Dic47⋊C4C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
43. C2×(C2×D47)⋊C4C22semidirect
45. C2×C4×Dic47C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C2×C4⋊C4×C47C22semidirect
52. C2×C42×C47C22semidirect
53. #95×C47C22semidirect
54. #95×C47C22semidirect
91. C2×C4×D47D4semidirect
261. #388D47semidirect
265. C47#2411semidirect
280. C2×C4⋊C4C2×D47semidirect
300. C2×C42C2×D47semidirect
303. #95C2×D47semidirect
304. #95C2×D47semidirect