Finite Group Databasebeta

← #20246231

Subgroups — #20246231

Order 6016.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093981C211yesmaximal, characteristic, complemented
2C22×(C2×D47)⋊C4C211yesmaximal, characteristic
3C2×C22⋊C4×D47C211yesmaximal, characteristic
4#15689014C211yesmaximal, characteristic, complemented
5#15689014C211yesmaximal, characteristic, complemented
6#15689012C211yesmaximal, characteristic, complemented
7#15689012C211yesmaximal, characteristic, complemented
8#15688996C211yesmaximal, characteristic, complemented
9#15688995C211yesmaximal, characteristic, complemented
10#15688985C211yesmaximal, characteristic, complemented
11#15688982C211yesmaximal, characteristic, complemented
12#15688978C211yesmaximal, characteristic
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13093981—24no—
21C2×Dic47⋊C4C2211yescharacteristic, complemented
22C2×Dic47⋊C4C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×(C2×D47)⋊C4—24no—
28C2×(C2×D47)⋊C4C2211yescharacteristic
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
38C22⋊C4×D47C418yescomplemented
39C2×C4×Dic47C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C23×C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C42×C47C2211yescharacteristic, complemented
51C2×C42×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53#95×C47C2211yescharacteristic, complemented
54C24×C47C2311yescharacteristic
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47C2×C414yes—
62C23×D47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C22×C4×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×Dic47—22no—
74C22×Dic47—22no—
75C22×Dic47—41no—
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C2×C4×D47—22no—
83C2×C4×D47—22no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47C2×C414yescomplemented
87C2×C4×D47C2×C414yescomplemented
88C22⋊C4×C47—22no—
89C22⋊C4×C47C2×C414yes—
90C42×C47—22no—
91C42×C47—41no—
92C22⋊Dic47—22no—
93C22⋊Dic47C2×C414yes—
94(C2×D47)⋊C4—22no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—41no—
100(C2×D47)⋊C4—41no—
101(C2×D47)⋊C4C2×C414yescomplemented
102(C2×D47)⋊C4C2×C414yescomplemented
103(C2×D47)⋊C4D414yes—
104Dic47⋊C4—22no—
105Dic47⋊C4—22no—
106Dic47⋊C4—41no—
107Dic47⋊C4—41no—
108C4×Dic47—22no—
109C4×Dic47—41no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47C22×C412yes—
115C23×C47#4112yes—
116C23×C47#4112yes—
117C23×C47C2411yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—28no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—28no—
130C22×D47—44no—
131C22×D47—44no—
132C22×D47—44no—
133C22×D47—44no—
134C22×D47—44no—
135C22×D47C22×C412yes—
136C22×D47C22×C412yes—
137C22×D47C2×D412yes—
138C22×D47#4112yes—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—44no—
155C2×C4×C47C22×C412yes—
156C2×C4×C47C22×C412yes—
157C2×C4×C47C2×D412yes—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—44no—
174C2×Dic47C22×C412yes—
175C2×Dic47C22×C412yes—
176C2×Dic47C2×D412yes—
177C4×D47—28no—
178C4×D47—44no—
179C22×C47—22no—
180C22×C47—22no—
181C22×C47—22no—
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47#11714yescomplemented
186C22×C47C23×C411yescharacteristic
187C22×C47C22×D411yescharacteristic
188C22×C47C2×#4111yescharacteristic
189C22×C47C2×#4111yescharacteristic
190C22×C47C2×#4111yescharacteristic
191C22×C47H(5,𝔽2)11yescharacteristic
192C22×C47H(5,𝔽2)11yescharacteristic
193C2×D47—22no—
194C2×D47—22no—
195C2×D47—22no—
196C2×D47—22no—
197C2×D47—22no—
198C2×D47—22no—
199C2×D47—22no—
200C2×D47—22no—
201C2×D47—22no—
202C2×D47—416no—
203C2×D47—41no—
204C2×D47—41no—
205C2×D47—41no—
206C2×D47—41no—
207C2×D47C4×D414yes—
208C4×C47—22no—
209C4×C47—22no—
210C4×C47—22no—
211C4×C47—41no—
212C4×C47—41no—
213C4×C47—41no—
214Dic47—22no—
215Dic47—22no—
216Dic47—22no—
217Dic47—41no—
218Dic47—41no—
219Dic47—41no—
220#2342—471nomaximal, Sylow
221C2×C47—24no—
222C2×C47C2×#11711yescharacteristic
223C2×C47C2×C4×D411yescharacteristic
224C2×C47#51811yescharacteristic
225C2×C47#54611yescharacteristic
226C2×C47#54611yescharacteristic
227C2×C47#55111yescharacteristic
228C2×C47#55111yescharacteristic
229D47—24no—
230D47—42no—
231C2×#117—471no—
232C22×C22⋊C4—471no—
233C22×C22⋊C4—471no—
234#388—471no—
235#388—471no—
236#388—471no—
237#388—471no—
238#385—471no—
239#385—471no—
240#381—471no—
241#380—471no—
242#379—471no—
243C4×C22⋊C4—471no—
244C4×C22⋊C4—471no—
245C4×C22⋊C4D4711yescharacteristic, complemented
246C47#234211yescharacteristic, complemented, Sylow
247C25—471no—
248C23×C4—471no—
249C23×C4—471no—
250C23×C4—471no—
251C23×C4C2×D4711yescharacteristic
252#117—944no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—478no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4—471no—
270C2×C22⋊C4—944no—
271C2×C22⋊C4C2×D4711yescharacteristic
272C2×C22⋊C4C2×D4711yescharacteristic
273C2×C42—471no—
274C2×C42—471no—
275C2×C42C2×D4711yescharacteristic, complemented
276C2×C42C2×D4711yescharacteristic, complemented
277#95—471no—
278#95—471no—
279#95—471no—
280#95—471no—
281#95—471no—
282#95—471no—
283#95C2×D4711yescharacteristic, complemented
284#95C2×D4711yescharacteristic, complemented
285C24—471no—
286C24—471no—
287C24—474no—
288C24—942no—
289C24—942no—
290C24—942no—
291C24—942no—
292C24—1881no—
293C24—1881no—
294C24C22×D4711yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—471no—
299C22×C4—471no—
300C22×C4—471no—
301C22×C4—474no—
302C22×C4—474no—
303C22×C4—471no—
304C22×C4—471no—
305C22×C4—471no—
306C22×C4—942no—
307C22×C4—942no—
308C22×C4—942no—
309C22×C4—942no—
310C22×C4—1881no—
311C22×C4—1881no—
312C22×C4—1881no—
313C22×C4C22×D4711yescharacteristic
314C22×C4C22×D4711yescharacteristic
315C22×C4C22×D4711yescharacteristic
316C22×C4C22×D4711yescharacteristic
317C22×C4C22×D4711yescharacteristic
318C22×C4C22×D4711yescharacteristic
319C4⋊C4—942no—
320C4⋊C4—942no—
321C4⋊C4—1881no—
322C4⋊C4—1881no—
323C22⋊C4—22no—
324C22⋊C4—474no—
325C22⋊C4—474no—
326C22⋊C4—474no—
327C22⋊C4—474no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—942no—
332C22⋊C4—942no—
333C22⋊C4—942no—
334C22⋊C4—1881no—
335C22⋊C4—1881no—
336C22⋊C4C4×D4714yes—
337C42—22no—
338C42—41no—
339C42—942no—
340C42—1881no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—472no—
346C23—472no—
347C23—472no—
348C23—472no—
349C23—948no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—948no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23—941no—
359C23—941no—
360C23—941no—
361C23—1884no—
362C23—1884no—
363C23—1884no—
364C23—1884no—
365C23—1884no—
366C23C2×C4×D4712yes—
367C23#1062535012yes—
368C23#1062535012yes—
369C23C23×D4711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—472no—
387C2×C4—472no—
388C2×C4—472no—
389C2×C4—948no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
403C2×C4—941no—
404C2×C4—941no—
405C2×C4—1884no—
406C2×C4—1884no—
407C2×C4C2×C4×D4712yes—
408C2×C4C2×C4×D4712yes—
409C2×C4D4×D4712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—474no—
417C22—942no—
418C22—942no—
419C22—942no—
420C22—942no—
421C22—942no—
422C22—942no—
423C22—942no—
424C22—942no—
425C22—942no—
426C22—18816no—
427C22—1881no—
428C22—1881no—
429C22—1881no—
430C22—1881no—
431C22#1309398114yescomplemented
432C22C22×C4×D4711yescharacteristic
433C22C2×D4×D4711yescharacteristic
434C22#41×D4711yescharacteristic
435C22C2×#1062535011yescharacteristic
436C22C2×#1062535011yescharacteristic
437C22#1309406911yescharacteristic
438C22#1309407011yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—942no—
446C4—942no—
447C4—942no—
448C4—1881no—
449C4—1881no—
450C4—1881no—
451C2—24no—
452C2—944no—
453C2—1882no—
454C2C2×#1309398111yescharacteristic
455C2C4×D4×D4711yescharacteristic
456C2#1568959511yescharacteristic
457C2#1568976311yescharacteristic
458C2#1568976911yescharacteristic
459C2#1568979711yescharacteristic
460C2#1568980211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC4×C22⋊C4×C47C2
socleC23×C47C24
hypercenterC4×C22⋊C4D47
hypocenterC47#2342
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13093981C2semidirect
4. #15689014C2semidirect
5. #15689014C2semidirect
6. #15689012C2semidirect
7. #15689012C2semidirect
8. #15688996C2semidirect
9. #15688995C2semidirect
10. #15688985C2semidirect
11. #15688982C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C4×C22⋊C4×C47C2semidirect
21. C2×Dic47⋊C4C22semidirect
22. C2×Dic47⋊C4C22semidirect
23. C2×Dic47⋊C4C22semidirect
24. C2×Dic47⋊C4C22semidirect
38. C22⋊C4×D47C4semidirect
39. C2×C4×Dic47C22semidirect
40. C2×C4×Dic47C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
50. C2×C42×C47C22semidirect
51. C2×C42×C47C22semidirect
52. #95×C47C22semidirect
53. #95×C47C22semidirect
86. C2×C4×D47C2×C4semidirect
87. C2×C4×D47C2×C4semidirect
101. (C2×D47)⋊C4C2×C4semidirect
102. (C2×D47)⋊C4C2×C4semidirect
185. C22×C47#117semidirect
245. C4×C22⋊C4D47semidirect
246. C47#2342semidirect
275. C2×C42C2×D47semidirect
276. C2×C42C2×D47semidirect
283. #95C2×D47semidirect
284. #95C2×D47semidirect
431. C22#13093981semidirect