Finite Group Databasebeta

← #20246050

Subgroups — #20246050

Order 6016.

808 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×#13093994C211yesmaximal, characteristic
2C2×C4×D188C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
4#15689024C211yesmaximal, characteristic, complemented
5#15689023C211yesmaximal, characteristic, complemented
6#15689016C211yesmaximal, characteristic, complemented
7#15689015C211yesmaximal, characteristic, complemented
8#15689014C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15688999C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic, complemented
23#13093994C418yescomplemented
24C4×D188—24no—
25C2×C4⋊Dic47C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
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, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C22⋊C4×D47—24no—
41C2×C4×Dic47C2211yescharacteristic, complemented
42C2×C4×Dic47C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53#95×C47C2211yescharacteristic, complemented
54C24×C47C2311yescharacteristic
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—41no—
58C23×D47—41no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47C2×C414yescomplemented
62C23×D47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C23×D47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C2×C22⋊D47—41no—
72C2×C22⋊D47—41no—
73C2×C22⋊D47C2×C414yescomplemented
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C2×D188—22no—
80C2×D188—22no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188C2×C414yes—
84C2×D188C2×C414yescomplemented
85C2×C4×D47—22no—
86C2×C4×D47—22no—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×C4×D47—41no—
92C2×C4×D47—41no—
93C2×C4×D47D414yescomplemented
94C4⋊C4×C47—41no—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47C2×C414yescomplemented
98C42×C47—22no—
99C22⋊Dic47—22no—
100C22⋊Dic47—41no—
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—41no—
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109(C2×D47)⋊C4—41no—
110(C2×D47)⋊C4C2×C414yescomplemented
111(C2×D47)⋊C4C2×C414yescomplemented
112C4⋊Dic47—22no—
113Dic47⋊C4—41no—
114C4×Dic47—41no—
115C4×Dic47—41no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47C22×C412yes—
123C23×C47C2411yescharacteristic
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
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—28no—
141C22×D47—44no—
142C22×D47—44no—
143C22×D47—44no—
144C22×D47—44no—
145C22×D47—44no—
146C22×D47—44no—
147C22×D47C22×C412yes—
148C22×D47C22×C412yes—
149C22×D47C22×C412yes—
150C22×D47C2×D412yes—
151C22×D47#4112yes—
152C2×C4×C47—21no—
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×C47C22×C412yes—
168C2×C4×C47C22×C412yes—
169C2×C4×C47C2×D412yes—
170C22⋊D47—44no—
171C2×Dic47—21no—
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×Dic47C22×C412yes—
185C2×Dic47C2×D412yes—
186D188—28no—
187D188—44no—
188C4×D47—44no—
189C4×D47—44no—
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×C47C23×C411yescharacteristic
199C22×C47C22×D411yescharacteristic
200C22×C47C2×#4111yescharacteristic
201C22×C47H(5,𝔽2)11yescharacteristic
202C22×C47H(5,𝔽2)11yescharacteristic
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—22no—
215C2×D47—22no—
216C2×D47—22no—
217C2×D47—416no—
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×D47C4×D414yes—
227C4×C47—22no—
228C4×C47—22no—
229C4×C47—22no—
230C4×C47—41no—
231C4×C47—41no—
232C4×C47—41no—
233Dic47—22no—
234Dic47—22no—
235Dic47—41no—
236Dic47—41no—
237Dic47—41no—
238#2321—471nomaximal, Sylow
239C2×C47—42no—
240C2×C47C2×C4×D411yescharacteristic
241C2×C47#51811yescharacteristic
242C2×C47#51811yescharacteristic
243C2×C47#53411yescharacteristic
244C2×C47#53511yescharacteristic
245C2×C47#53811yescharacteristic
246C2×C47#53811yescharacteristic
247D47—24no—
248D47—42no—
249D47—42no—
250C2×#120—471no—
251C2×C4×D4—471no—
252C22×C22⋊C4—471no—
253#390—471no—
254#390—471no—
255#388—471no—
256#388—471no—
257#388—471no—
258#388D4711yescharacteristic, complemented
259#386—471no—
260#386—471no—
261#386—471no—
262#385—471no—
263#379—471no—
264C4×C22⋊C4—471no—
265C47#232111yescharacteristic, complemented, Sylow
266C25—471no—
267C22×D4—471no—
268C22×D4—471no—
269C22×D4—471no—
270C23×C4—471no—
271C23×C4—471no—
272C23×C4—471no—
273#120—478no—
274C4×D4—944no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4C2×D4711yescharacteristic, complemented
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
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—944no—
292C2×C22⋊C4C2×D4711yescharacteristic
293C2×C22⋊C4C2×D4711yescharacteristic
294C2×C22⋊C4C2×D4711yescharacteristic
295C2×C42—471no—
296C2×C42—471no—
297C2×C42C2×D4711yescharacteristic, complemented
298#95—471no—
299#95—471no—
300#95—471no—
301#95—471no—
302#95C2×D4711yescharacteristic, complemented
303#95C2×D4711yescharacteristic, complemented
304C24—471no—
305C24—471no—
306C24—471no—
307C24—474no—
308C24—942no—
309C24—942no—
310C24—1881no—
311C24—1881no—
312C24—1881no—
313C24—1881no—
314C24C22×D4711yescharacteristic
315C2×D4—474no—
316C2×D4—474no—
317C2×D4—474no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—1881no—
321C2×D4—1881no—
322C2×D4—1881no—
323C2×D4—1881no—
324C22×C4—471no—
325C22×C4—471no—
326C22×C4—474no—
327C22×C4—471no—
328C22×C4—471no—
329C22×C4—471no—
330C22×C4—942no—
331C22×C4—942no—
332C22×C4—1881no—
333C22×C4—1881no—
334C22×C4—1881no—
335C22×C4—1881no—
336C22×C4—1881no—
337C22×C4—1881no—
338C22×C4C22×D4711yescharacteristic
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C22×C4C22×D4711yescharacteristic
343C22×C4C22×D4711yescharacteristic
344C4⋊C4—41no—
345C4⋊C4—942no—
346C4⋊C4—1881no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—474no—
350C22⋊C4—474no—
351C22⋊C4—942no—
352C22⋊C4—942no—
353C22⋊C4—942no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—1881no—
358C22⋊C4—1881no—
359C22⋊C4—1881no—
360C22⋊C4—1881no—
361C22⋊C4—1881no—
362C22⋊C4C4×D4714yescomplemented
363C42—22no—
364C42—1881no—
365C42—1881no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—472no—
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—1884no—
395C23—1884no—
396C23—1884no—
397C23—1884no—
398C23—1884no—
399C23—1884no—
400C23C2×C4×D4712yes—
401C23C23×D4711yescharacteristic
402D4—948no—
403D4—1884no—
404D4—1884no—
405C2×C4—21no—
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—472no—
421C2×C4—472no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
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—1884no—
436C2×C4—1884no—
437C2×C4—1884no—
438C2×C4C2×C4×D4712yes—
439C2×C4C2×C4×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—942no—
459C22—942no—
460C22—942no—
461C22—18816no—
462C22—1881no—
463C22—1881no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22C22×C4×D4711yescharacteristic
471C22C2×D4×D4711yescharacteristic
472C22#41×D4711yescharacteristic
473C22#1309406911yescharacteristic
474C22#1309407011yescharacteristic
475C22#1309407011yescharacteristic
476C22#1309407011yescharacteristic
477C4—22no—
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—942no—
484C4—942no—
485C4—1881no—
486C4—1881no—
487C4—1881no—
488C2—42no—
489C2—944no—
490C2—1882no—
491C2—1882no—
492C2C4×D4×D4711yescharacteristic
493C2#1568959511yescharacteristic
494C2#1568959711yescharacteristic
495C2#1568968411yescharacteristic
496C2#1568968911yescharacteristic
497C2#1568970711yescharacteristic
498C2#1568971211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#388C2
socleC23×C47C24
hypercenter#388D47
hypocenterC47#2321
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D188C2semidirect
3. C2×C22⋊C4×D47C2semidirect
4. #15689024C2semidirect
5. #15689023C2semidirect
6. #15689016C2semidirect
7. #15689015C2semidirect
8. #15689014C2semidirect
9. #15689001C2semidirect
10. #15689001C2semidirect
11. #15688999C2semidirect
12. #15688994C2semidirect
13. #15688978C2semidirect
14. #15688970C2semidirect
15. C47×#388C2semidirect
22. C22×C4×D47C22semidirect
23. #13093994C4semidirect
25. C2×C4⋊Dic47C22semidirect
26. C2×Dic47⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
41. C2×C4×Dic47C22semidirect
42. C2×C4×Dic47C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C2×C4⋊C4×C47C22semidirect
51. C2×C42×C47C22semidirect
52. #95×C47C22semidirect
53. #95×C47C22semidirect
61. C23×D47C2×C4semidirect
73. C2×C22⋊D47C2×C4semidirect
84. C2×D188C2×C4semidirect
93. C2×C4×D47D4semidirect
97. C22⋊C4×C47C2×C4semidirect
110. (C2×D47)⋊C4C2×C4semidirect
111. (C2×D47)⋊C4C2×C4semidirect
258. #388D47semidirect
265. C47#2321semidirect
277. C2×C4⋊C4C2×D47semidirect
297. C2×C42C2×D47semidirect
302. #95C2×D47semidirect
303. #95C2×D47semidirect
362. C22⋊C4C4×D47semidirect