Finite Group Databasebeta

← #20247049

Subgroups — #20247049

Order 6016.

780 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094003C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic47C211yesmaximal, characteristic
4#15689059C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15688998C211yesmaximal, characteristic, complemented
9#15688996C211yesmaximal, characteristic, complemented
10#15688996C211yesmaximal, characteristic, complemented
11#15688995C211yesmaximal, characteristic, complemented
12#15688983C211yesmaximal, characteristic, complemented
13#15688981C211yesmaximal, characteristic, complemented
14#15688979C211yesmaximal, characteristic
15C22×C22⋊C4×C47C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic, complemented
17C23×Dic47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19#13094003—24no—
20#13094001—24no—
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×C4⋊Dic47C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
28C2×Dic47⋊C4C2211yescharacteristic, complemented
29C2×Dic47⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic47—24no—
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C22⋊Dic47C2211yescharacteristic
40C2×C22⋊Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C25×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47—24no—
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—41no—
60C24×C47—41no—
61C24×C47Q814yescomplemented
62C24×C47C2311yescharacteristic
63C24×C47C2311yescharacteristic
64C24×C47C2311yescharacteristic
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×Dic47—22no—
76C22×Dic47—22no—
77C22×Dic47—22no—
78C22×Dic47—22no—
79C22×Dic47—41no—
80C22×Dic47—41no—
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C2×Dic94—22no—
90C2×Dic94—22no—
91C2×Dic94—41no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—22no—
94C22⋊C4×C47—22no—
95C22⋊C4×C47D414yes—
96C22⋊Dic47—22no—
97C22⋊Dic47—22no—
98C22⋊Dic47—22no—
99C22⋊Dic47—22no—
100C22⋊Dic47—22no—
101C22⋊Dic47—22no—
102C22⋊Dic47—22no—
103C22⋊Dic47—41no—
104C22⋊Dic47—41no—
105C22⋊Dic47D414yes—
106C4⋊Dic47—22no—
107C4⋊Dic47—22no—
108C4⋊Dic47—41no—
109Dic47⋊C4—22no—
110Dic47⋊C4—22no—
111Dic47⋊C4—22no—
112Dic47⋊C4—22no—
113Dic47⋊C4—41no—
114Dic47⋊C4—41no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—28no—
124C23×C47—28no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—44no—
132C23×C47—44no—
133C23×C47—44no—
134C23×C47—44no—
135C23×C47—44no—
136C23×C47C2×D412yes—
137C23×C47C2×D412yes—
138C23×C47C2×Q812yes—
139C23×C47C2×Q812yes—
140C23×C47C2×Q812yes—
141C23×C47#4112yes—
142C23×C47#4112yes—
143C23×C47C2411yescharacteristic
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×C47—44no—
156C2×C4×C47C2×D412yes—
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—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—44no—
181C2×Dic47—44no—
182C2×Dic47C2×D412yes—
183C2×Dic47C2×D412yes—
184Dic94—44no—
185C22×C47—22no—
186C22×C47—22no—
187C22×C47—22no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—22no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—416no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47C22⋊Q814yescomplemented
206C22×C47C22⋊Q814yescomplemented
207C22×C47C22×D411yescharacteristic
208C22×C47C22×D411yescharacteristic
209C22×C47C22×Q811yescharacteristic
210C22×C47C2×#4111yescharacteristic
211C22×C47C2×#4111yescharacteristic
212C22×C47H(5,𝔽2)11yescharacteristic
213C22×C47H(5,𝔽2)11yescharacteristic
214C4×C47—22no—
215C4×C47—22no—
216C4×C47—41no—
217C4×C47—41no—
218Dic47—22no—
219Dic47—22no—
220Dic47—41no—
221Dic47—41no—
222Dic47—41no—
223Dic47—41no—
224Dic47—41no—
225Dic47—41no—
226#2437—471nomaximal, Sylow
227C2×C47—24no—
228C2×C47—24no—
229C2×C47—42no—
230C2×C47C2×C22⋊Q811yescharacteristic
231C2×C47C2×C22⋊Q811yescharacteristic
232C2×C47#54311yescharacteristic
233C2×C47D4211yescharacteristic
234C2×C47#54611yescharacteristic
235C2×C47#54611yescharacteristic
236C2×C47#55111yescharacteristic
237C2×C22⋊Q8—471no—
238C2×C22⋊Q8—471no—
239C22×C22⋊C4—471no—
240C22×C22⋊C4D4711yescharacteristic
241#399—471no—
242#396—471no—
243#396—471no—
244#393—471no—
245#385—471no—
246#385—471no—
247#385—471no—
248#385—471no—
249#380—471no—
250#380—471no—
251#379—471no—
252C47#243711yescharacteristic, complemented, Sylow
253C25C2×D4711yescharacteristic
254C22×Q8—471no—
255C23×C4—471no—
256C23×C4—471no—
257C23×C4C2×D4711yescharacteristic
258C23×C4C2×D4711yescharacteristic
259C22⋊Q8—944no—
260C22⋊Q8—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—471no—
268C2×C4⋊C4—471no—
269C2×C4⋊C4—471no—
270C2×C22⋊C4—24no—
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⋊C4—471no—
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—944no—
282C2×C22⋊C4C2×D4711yescharacteristic
283C2×C22⋊C4C2×D4711yescharacteristic
284C2×C22⋊C4C2×D4711yescharacteristic
285C2×C22⋊C4C2×D4711yescharacteristic
286#95—471no—
287#95—471no—
288#95—471no—
289#95—471no—
290#95—471no—
291#95—471no—
292C24—22no—
293C24—22no—
294C24—22no—
295C24—22no—
296C24—41no—
297C24—41no—
298C24Dic9414yescomplemented
299C24C22×D4711yescharacteristic
300C24C22×D4711yescharacteristic
301C24C22×D4711yescharacteristic
302C2×Q8—942no—
303C2×Q8—942no—
304C2×Q8—1881no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—471no—
312C22×C4—471no—
313C22×C4—471no—
314C22×C4—471no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—942no—
320C22×C4—942no—
321C22×C4—942no—
322C22×C4—942no—
323C22×C4—1881no—
324C22×C4—1881no—
325C22×C4C22×D4711yescharacteristic
326C22×C4C22×D4711yescharacteristic
327C22×C4C22×D4711yescharacteristic
328C22×C4C22×D4711yescharacteristic
329C4⋊C4—942no—
330C4⋊C4—942no—
331C4⋊C4—942no—
332C4⋊C4—942no—
333C4⋊C4—942no—
334C4⋊C4—942no—
335C4⋊C4—1881no—
336C4⋊C4—1881no—
337C4⋊C4—1881no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—474no—
342C22⋊C4—942no—
343C22⋊C4—942no—
344C22⋊C4—942no—
345C22⋊C4—942no—
346C22⋊C4—942no—
347C22⋊C4—942no—
348C22⋊C4—942no—
349C22⋊C4—1881no—
350C22⋊C4—1881no—
351C22⋊C4C22⋊D4714yes—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—28no—
361C23—28no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23—44no—
372C23—44no—
373C23C2×Dic9412yes—
374C23C2×Dic9412yes—
375C23C2×Dic9412yes—
376C23#1062535012yes—
377C23D4×D4712yes—
378C23#1062535212yes—
379C23C2×C22⋊D4712yes—
380C23C23×D4711yescharacteristic
381Q8—1884no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—472no—
395C2×C4—472no—
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—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—941no—
418C2×C4—1884no—
419C2×C4—1884no—
420C2×C4C2×C22⋊D4712yes—
421C2×C4C2×C22⋊D4712yes—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—416no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22#1309400114yescomplemented
443C22#1309400314yescomplemented
444C22C2×D4×D4711yescharacteristic
445C22C22×C22⋊D4711yescharacteristic
446C22C22×Dic9411yescharacteristic
447C22C2×#1062535211yescharacteristic
448C22C2×#1062535011yescharacteristic
449C22#1309406911yescharacteristic
450C22#1309406911yescharacteristic
451C4—22no—
452C4—22no—
453C4—41no—
454C4—41no—
455C4—942no—
456C4—942no—
457C4—1881no—
458C4—1881no—
459C4—1881no—
460C4—1881no—
461C4—1881no—
462C4—1881no—
463C2—24no—
464C2—24no—
465C2—42no—
466C2C2×#1309400111yescharacteristic
467C2C2×#1309400311yescharacteristic
468C2#1568974911yescharacteristic
469C2D4×C22⋊D4711yescharacteristic
470C2#1568976311yescharacteristic
471C2#1568976711yescharacteristic
472C2#1568979911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C22⋊C4×C47C2
hypercenterC22×C22⋊C4D47
hypocenterC47#2437
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094003C2semidirect
2. C2×#13094001C2semidirect
4. #15689059C2semidirect
5. #15689046C2semidirect
6. #15689046C2semidirect
7. #15689035C2semidirect
8. #15688998C2semidirect
9. #15688996C2semidirect
10. #15688996C2semidirect
11. #15688995C2semidirect
12. #15688983C2semidirect
13. #15688981C2semidirect
16. C22×Dic94C22semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×C4⋊Dic47C22semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
28. C2×Dic47⋊C4C22semidirect
29. C2×Dic47⋊C4C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
61. C24×C47Q8semidirect
205. C22×C47C22⋊Q8semidirect
206. C22×C47C22⋊Q8semidirect
252. C47#2437semidirect
298. C24Dic94semidirect
442. C22#13094001semidirect
443. C22#13094003semidirect