Finite Group Databasebeta

← #20249783

Subgroups — #20249783

Order 6016.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094017C211yesmaximal, characteristic, complemented
2C2×#13093993C211yesmaximal, characteristic
3#15689059C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689038C211yesmaximal, characteristic, complemented
8#15689038C211yesmaximal, characteristic, complemented
9#15689023C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689017C211yesmaximal, characteristic, complemented
12#15689016C211yesmaximal, characteristic, complemented
13#15689011C211yesmaximal, characteristic, complemented
14#15688979C211yesmaximal, characteristic, complemented
15C47×#379C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19#13094017—24no—
20#13093993—24no—
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C2×C4×Dic47C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C25×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C24×C47—22no—
54C24×C47—22no—
55C24×C47—22no—
56C24×C47—41no—
57C24×C47—41no—
58C24×C47—41no—
59C24×C47—41no—
60C24×C47C2311yescharacteristic
61C24×C47C2311yescharacteristic
62C24×C47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—22no—
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—41no—
74C2×C22⋊D47—41no—
75C2×C22⋊D47—41no—
76C2×C22⋊D47—41no—
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22⋊C4×C47—22no—
85C22⋊C4×C47—22no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊C4×C47—41no—
90C22⋊Dic47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—22no—
94C22⋊Dic47—41no—
95C22⋊Dic47—41no—
96C22⋊Dic47—41no—
97C22⋊Dic47—41no—
98C22⋊Dic47D414yes—
99(C2×D47)⋊C4—41no—
100(C2×D47)⋊C4—41no—
101(C2×D47)⋊C4—41no—
102(C2×D47)⋊C4—41no—
103C4⋊Dic47—22no—
104C4⋊Dic47—41no—
105Dic47⋊C4—22no—
106Dic47⋊C4—22no—
107Dic47⋊C4—41no—
108Dic47⋊C4—41no—
109C4×Dic47—22no—
110C4×Dic47—41no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
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—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—44no—
130C23×C47—44no—
131C23×C47—44no—
132C23×C47—44no—
133C23×C47—44no—
134C23×C47—44no—
135C23×C47—44no—
136C23×C47C2×D412yes—
137C23×C47#4112yes—
138C23×C47#4112yes—
139C23×C47C2411yescharacteristic
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—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—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C22⋊D47—44no—
160C22⋊D47—44no—
161C22⋊D47—44no—
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—21no—
181C2×Dic47C2×D412yes—
182C2×Dic47C2×D412yes—
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—22no—
192C22×C47—416no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47C22×D411yescharacteristic
206C22×C47C2×#4111yescharacteristic
207C22×C47C2×#4111yescharacteristic
208C22×C47H(5,𝔽2)11yescharacteristic
209C22×C47H(5,𝔽2)11yescharacteristic
210C22×C47H(5,𝔽2)11yescharacteristic
211C22×C47H(5,𝔽2)11yescharacteristic
212C2×D47—41no—
213C2×D47—41no—
214C2×D47—41no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C4×C47—41no—
220C4×C47—41no—
221C4×C47—41no—
222C4×C47—41no—
223Dic47—22no—
224Dic47—22no—
225Dic47—41no—
226Dic47—41no—
227Dic47—41no—
228Dic47—41no—
229Dic47—41no—
230#2685—471nomaximal, Sylow
231C2×C47—42no—
232C2×C47—42no—
233C2×C47—42no—
234C2×C47#53511yescharacteristic
235C2×C47#53811yescharacteristic
236C2×C47#53811yescharacteristic
237C2×C47#54611yescharacteristic
238C2×C47#54611yescharacteristic
239C2×C47#55111yescharacteristic
240C2×C47#56011yescharacteristic
241D47—81no—
242C2×#126—471no—
243C2×#120—471no—
244#399—471no—
245#396—471no—
246#394—471no—
247#394—471no—
248#394—471no—
249#394—471no—
250#390—471no—
251#390—471no—
252#388—471no—
253#388—471no—
254#388—471no—
255#379—471no—
256#379D4711yescharacteristic, complemented
257C47#268511yescharacteristic, complemented, Sylow
258C25C2×D4711yescharacteristic
259C22×D4—471no—
260C22×D4—471no—
261C22×D4—471no—
262#126—944no—
263#120—944no—
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—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⋊C4—471no—
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4C2×D4711yescharacteristic
284C2×C22⋊C4C2×D4711yescharacteristic
285C2×C22⋊C4C2×D4711yescharacteristic
286C2×C22⋊C4C2×D4711yescharacteristic
287C2×C22⋊C4C2×D4711yescharacteristic
288C2×C22⋊C4C2×D4711yescharacteristic
289C2×C42—471no—
290C2×C42—471no—
291#95—471no—
292#95—471no—
293#95—471no—
294#95—471no—
295C24—22no—
296C24—22no—
297C24—22no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—471no—
303C24C22×D4711yescharacteristic
304C24C22×D4711yescharacteristic
305C24C22×D4711yescharacteristic
306C2×D4—942no—
307C2×D4—942no—
308C2×D4—942no—
309C2×D4—942no—
310C2×D4—942no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4—1881no—
314C2×D4—1881no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4C22×D4711yescharacteristic
323C22×C4C22×D4711yescharacteristic
324C22×C4C22×D4711yescharacteristic
325C22×C4C22×D4711yescharacteristic
326C4⋊C4—942no—
327C4⋊C4—942no—
328C4⋊C4—942no—
329C4⋊C4—1881no—
330C4⋊C4—1881no—
331C4⋊C4—1881no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—474no—
339C22⋊C4—942no—
340C22⋊C4—942no—
341C22⋊C4—942no—
342C22⋊C4—942no—
343C22⋊C4—1881no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C22⋊C4—1881no—
349C22⋊C4—1881no—
350C22⋊C4—1881no—
351C42—942no—
352C42—1881no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—44no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—941no—
379C23—941no—
380C23—941no—
381C23—941no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23#1062535012yes—
386C23D4×D4712yes—
387C23#1062535212yes—
388C23C23×D4711yescharacteristic
389D4—1884no—
390D4—1884no—
391D4—1884no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—472no—
405C2×C4—472no—
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—941no—
419C2×C4—941no—
420C2×C4—941no—
421C2×C4—941no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—1881no—
448C22—1881no—
449C22—1881no—
450C22—1881no—
451C22—1881no—
452C22—1881no—
453C22—1881no—
454C22C2×D4×D4711yescharacteristic
455C22C2×#1062535211yescharacteristic
456C22C2×#1062535011yescharacteristic
457C22#1309406911yescharacteristic
458C22#1309406911yescharacteristic
459C22#1309406911yescharacteristic
460C22#1309406911yescharacteristic
461C4—41no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—942no—
466C4—942no—
467C4—1881no—
468C4—1881no—
469C4—1881no—
470C4—1881no—
471C4—1881no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—3761no—
476C2#1568968811yescharacteristic
477C2#1568970811yescharacteristic
478C2#1568971111yescharacteristic
479C2#1568976011yescharacteristic
480C2#1568976311yescharacteristic
481C2#1568979911yescharacteristic
482C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2685
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13094017C2semidirect
3. #15689059C2semidirect
4. #15689046C2semidirect
5. #15689039C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689038C2semidirect
9. #15689023C2semidirect
10. #15689023C2semidirect
11. #15689017C2semidirect
12. #15689016C2semidirect
13. #15689011C2semidirect
14. #15688979C2semidirect
15. C47×#379C2semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×Dic47⋊C4C22semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×Dic47⋊C4C22semidirect
36. C2×(C2×D47)⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×C4×Dic47C22semidirect
41. C2×C4×Dic47C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
256. #379D47semidirect
257. C47#2685semidirect