Finite Group Databasebeta

← #20246405

Subgroups — #20246405

Order 6016.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093996C211yesmaximal, characteristic
2C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
5#15689023C211yesmaximal, characteristic, complemented
6#15689018C211yesmaximal, characteristic, complemented
7#15689014C211yesmaximal, characteristic, complemented
8#15689011C211yesmaximal, characteristic, complemented
9#15689003C211yesmaximal, characteristic, complemented
10#15689002C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×D4×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13093996C418yescomplemented
22C4×C22⋊D47—24no—
23(C22⋊D47)⋊C4—24no—
24C2×Dic47⋊C4—24no—
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C4×D4×C47—24no—
52C2×C4⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C42×C47C2211yescharacteristic
56C24×C47C2311yescharacteristic
57C24×C47C2311yescharacteristic
58C23×D47C2311yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47C2×C414yescomplemented
62C22×C4×C47—22no—
63C22×C4×C47—22no—
64C22×C4×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47C2×C414yescomplemented
78C2×C22⋊D47C2×C414yescomplemented
79C22×Dic47—22no—
80C22×Dic47—22no—
81C22×Dic47—22no—
82C22×Dic47—22no—
83C22×Dic47—41no—
84C22×Dic47C2×C414yescomplemented
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C2×C4×D47—22no—
93C2×C4×D47—22no—
94C2×C4×D47—41no—
95C4⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47D414yescomplemented
98C42×C47—22no—
99C22⋊Dic47—22no—
100C22⋊Dic47—22no—
101C22⋊Dic47—41no—
102C22⋊Dic47C2×C414yescomplemented
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—41no—
106(C2×D47)⋊C4C2×C414yescomplemented
107Dic47⋊C4—22no—
108Dic47⋊C4—22no—
109Dic47⋊C4—22no—
110Dic47⋊C4—22no—
111Dic47⋊C4C2×C414yescomplemented
112Dic47⋊C4D414yescomplemented
113C4×Dic47—22no—
114C4×Dic47—22no—
115C4×Dic47—22no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47C22×C412yes—
127C23×C47C22×C412yes—
128C23×C47C2×D412yes—
129C23×C47#4112yes—
130C23×C47C2411yescharacteristic
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47C22×C412yes—
138D4×C47—28no—
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—44no—
151C2×C4×C47—44no—
152C2×C4×C47C22×C412yes—
153C2×C4×C47C2×D412yes—
154C2×C4×C47C2×D412yes—
155C2×C4×C47C2×D412yes—
156C22⋊D47—28no—
157C22⋊D47—28no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—28no—
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—21no—
174C2×Dic47—44no—
175C2×Dic47C22×C412yes—
176C2×Dic47C22×C412yes—
177C2×Dic47C22×C412yes—
178C2×Dic47C2×D412yes—
179C2×Dic47C2×D412yes—
180C2×Dic47#4112yes—
181C4×D47—44no—
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47—22no—
187C22×C47—22no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47C4×D414yescomplemented
196C22×C47C23×C411yescharacteristic
197C22×C47C22×D411yescharacteristic
198C22×C47C22×D411yescharacteristic
199C22×C47C2×#4111yescharacteristic
200C22×C47C2×#4111yescharacteristic
201C22×C47H(5,𝔽2)11yescharacteristic
202C22×C472−1+411yescharacteristic
203C2×D47—22no—
204C2×D47—22no—
205C2×D47—22no—
206C2×D47—41no—
207C2×D47—41no—
208C2×D47—41no—
209C2×D47—41no—
210C4×C47—22no—
211C4×C47—22no—
212C4×C47—22no—
213C4×C47—22no—
214C4×C47—41no—
215Dic47—22no—
216Dic47—22no—
217Dic47—22no—
218Dic47—41no—
219Dic47—41no—
220Dic47—41no—
221Dic47C4×D414yescomplemented
222#2361—471nomaximal, Sylow
223C2×C47—24no—
224C2×C47—42no—
225C2×C47C2×C4×D411yescharacteristic
226C2×C47C2×C4×D411yescharacteristic
227C2×C47#52011yescharacteristic
228C2×C47D4211yescharacteristic
229C2×C47#54711yescharacteristic
230C2×C47#54811yescharacteristic
231C2×C47#55311yescharacteristic
232D47—42no—
233C2×#121—471no—
234C2×C4×D4—471no—
235C2×C4×D4—471no—
236C2×C4×D4D4711yescharacteristic, complemented
237C22×C4⋊C4—471no—
238#390—471no—
239#389—471no—
240#388—471no—
241#388—471no—
242#386—471no—
243#386—471no—
244#385—471no—
245#385—471no—
246C4×C4⋊C4—471no—
247C4×C22⋊C4—471no—
248C47#236111yescharacteristic, complemented, Sylow
249C22×D4—471no—
250C22×D4—471no—
251C22×D4C2×D4711yescharacteristic
252C23×C4—471no—
253C23×C4—471no—
254C23×C4—471no—
255C23×C4C2×D4711yescharacteristic
256C23×C4C2×D4711yescharacteristic
257#121—478no—
258C4×D4—24no—
259C4×D4—944no—
260C4×D4—944no—
261C2×C4⋊C4—471no—
262C2×C4⋊C4—471no—
263C2×C4⋊C4—471no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4—471no—
267C2×C4⋊C4—944no—
268C2×C4⋊C4C2×D4711yescharacteristic
269C2×C22⋊C4—471no—
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C22⋊C4—471no—
274C2×C22⋊C4—471no—
275C2×C22⋊C4—471no—
276C2×C22⋊C4—471no—
277C2×C22⋊C4C2×D4711yescharacteristic
278C2×C22⋊C4C2×D4711yescharacteristic
279C2×C42—471no—
280C2×C42—471no—
281C2×C42—471no—
282C2×C42C2×D4711yescharacteristic
283#95—471no—
284#95—471no—
285#95—471no—
286#95—471no—
287#95—471no—
288#95—471no—
289C24—471no—
290C24C22×D4711yescharacteristic
291C24C22×D4711yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—474no—
295C2×D4—474no—
296C2×D4—942no—
297C2×D4—942no—
298C2×D4—942no—
299C2×D4—942no—
300C2×D4C4×D4714yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—471no—
308C22×C4—474no—
309C22×C4—471no—
310C22×C4—471no—
311C22×C4—471no—
312C22×C4—471no—
313C22×C4—471no—
314C22×C4—471no—
315C22×C4—942no—
316C22×C4—942no—
317C22×C4—942no—
318C22×C4—942no—
319C22×C4—942no—
320C22×C4—942no—
321C22×C4—1881no—
322C22×C4—1881no—
323C22×C4C22×D4711yescharacteristic
324C22×C4C22×D4711yescharacteristic
325C22×C4C22×D4711yescharacteristic
326C22×C4C22×D4711yescharacteristic
327C22×C4C22×D4711yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—474no—
330C4⋊C4—474no—
331C4⋊C4—942no—
332C4⋊C4—942no—
333C4⋊C4—942no—
334C4⋊C4—942no—
335C22⋊C4—22no—
336C22⋊C4—474no—
337C22⋊C4—474no—
338C22⋊C4—942no—
339C22⋊C4—942no—
340C22⋊C4—942no—
341C22⋊C4—942no—
342C22⋊C4—1881no—
343C22⋊C4—1881no—
344C22⋊C4C22⋊D4714yescomplemented
345C42—22no—
346C42—942no—
347C42—942no—
348C42—942no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—472no—
360C23—941no—
361C23—941no—
362C23—941no—
363C23—941no—
364C23—941no—
365C23—941no—
366C23C2×C4×D4712yes—
367C23C2×C4×D4712yes—
368C23#1062535012yes—
369C23C2×C22⋊D4712yes—
370C23C23×D4711yescharacteristic
371D4—28no—
372D4—948no—
373D4—948no—
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—44no—
387C2×C4—472no—
388C2×C4—472no—
389C2×C4—472no—
390C2×C4—472no—
391C2×C4—472no—
392C2×C4—472no—
393C2×C4—948no—
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—941no—
406C2×C4—941no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—1884no—
410C2×C4—1884no—
411C2×C4C2×C4×D4712yes—
412C2×C4D4×D4712yes—
413C2×C4C2×C22⋊D4712yes—
414C2×C4C2×C22⋊D4712yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—942no—
429C22—942no—
430C22—942no—
431C22—1881no—
432C22—1881no—
433C22—1881no—
434C22—1881no—
435C22C4×C22⋊D4714yescomplemented
436C22C22×C4×D4711yescharacteristic
437C22C2×D4×D4711yescharacteristic
438C22C22×C22⋊D4711yescharacteristic
439C22#41×D4711yescharacteristic
440C22C2×#1062535011yescharacteristic
441C22#1309406911yescharacteristic
442C22#1309407111yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—474no—
449C4—942no—
450C4—942no—
451C4—942no—
452C4—1881no—
453C4—1881no—
454C4—1881no—
455C2—24no—
456C2—42no—
457C2—1882no—
458C2C4×D4×D4711yescharacteristic
459C2C2×C4×C22⋊D4711yescharacteristic
460C2#1568960211yescharacteristic
461C2D4×C22⋊D4711yescharacteristic
462C2#1568977211yescharacteristic
463C2#1568978211yescharacteristic
464C2#1568982211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC2×C4×D4×C47C2
socleC23×C47C24
hypercenterC2×C4×D4D47
hypocenterC47#2361
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. C22×Dic47⋊C4C2semidirect
5. #15689023C2semidirect
6. #15689018C2semidirect
7. #15689014C2semidirect
8. #15689011C2semidirect
9. #15689003C2semidirect
10. #15689002C2semidirect
11. #15688996C2semidirect
12. #15688994C2semidirect
13. C4×Dic47⋊C4C2semidirect
14. C22⋊C4×Dic47C2semidirect
15. C2×C4×D4×C47C2semidirect
21. #13093996C4semidirect
61. C2×D4×C47C2×C4semidirect
77. C2×C22⋊D47C2×C4semidirect
78. C2×C22⋊D47C2×C4semidirect
84. C22×Dic47C2×C4semidirect
97. C22⋊C4×C47D4semidirect
102. C22⋊Dic47C2×C4semidirect
106. (C2×D47)⋊C4C2×C4semidirect
111. Dic47⋊C4C2×C4semidirect
112. Dic47⋊C4D4semidirect
195. C22×C47C4×D4semidirect
221. Dic47C4×D4semidirect
236. C2×C4×D4D47semidirect
248. C47#2361semidirect
300. C2×D4C4×D47semidirect
344. C22⋊C4C22⋊D47semidirect
435. C22C4×C22⋊D47semidirect