Finite Group Databasebeta

← #20249763

Subgroups — #20249763

Order 6016.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic, complemented
2C2×#13093992C211yesmaximal, characteristic
3#15689050C211yesmaximal, characteristic, complemented
4#15689049C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic, complemented
6#15689036C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15689016C211yesmaximal, characteristic, complemented
9#15689013C211yesmaximal, characteristic, complemented
10#15689003C211yesmaximal, characteristic, complemented
11#15689000C211yesmaximal, characteristic, complemented
12#15689000C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688978C211yesmaximal, characteristic, complemented
15C47×#394C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×Dic94C2211yescharacteristic, complemented
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic, complemented
21#13094010—24no—
22#13093992—24no—
23C2×C4⋊Dic47C2211yescharacteristic, complemented
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic, complemented
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
38C2×C4×Dic47C2211yescharacteristic, complemented
39C47⋊#95C2211yescharacteristic, complemented
40C47⋊#95C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C22×D4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic, complemented
51C2×C22⋊C4×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—41no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47—41no—
62C23×D47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C2×D4×C47—22no—
65C2×D4×C47—22no—
66C2×D4×C47—41no—
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—41no—
75C2×C22⋊D47—41no—
76C2×C22⋊D47—41no—
77C2×C22⋊D47D414yes—
78C22×Dic47—41no—
79C22×Dic47—41no—
80C22×Dic47—41no—
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C22×Dic47C2311yescharacteristic
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C2×Dic94—22no—
88C2×Dic94—41no—
89C2×Dic94—41no—
90C4⋊C4×C47—41no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—41no—
94C22⋊C4×C47—41no—
95C22⋊Dic47—22no—
96C22⋊Dic47—22no—
97C22⋊Dic47—41no—
98C22⋊Dic47—41no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—41no—
105(C2×D47)⋊C4—41no—
106(C2×D47)⋊C4—41no—
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109C4⋊Dic47—41no—
110C4×Dic47—22no—
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×C47C2×D412yes—
124C23×C47#4112yes—
125C23×C47C2411yescharacteristic
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—44no—
139C22×D47—44no—
140C22×D47—44no—
141C22×D47—44no—
142C22×D47—44no—
143C22×D47—44no—
144C22×D47—44no—
145C22×D47C2×D412yes—
146C22×D47#4112yes—
147D4×C47—44no—
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—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C22⋊D47—44no—
164C22⋊D47—44no—
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×Dic47—21no—
182C2×Dic47—44no—
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—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47C22×D411yescharacteristic
200C22×C47C2×#4111yescharacteristic
201C22×C47C2×#4111yescharacteristic
202C22×C47H(5,𝔽2)11yescharacteristic
203C22×C47H(5,𝔽2)11yescharacteristic
204C22×C47H(5,𝔽2)11yescharacteristic
205C22×C47H(5,𝔽2)11yescharacteristic
206C2×D47—22no—
207C2×D47—22no—
208C2×D47—22no—
209C2×D47—22no—
210C2×D47—22no—
211C2×D47—22no—
212C2×D47—416no—
213C2×D47—41no—
214C2×D47—41no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C4×C47—41no—
222C4×C47—41no—
223C4×C47—41no—
224C4×C47—41no—
225C4×C47—41no—
226Dic47—22no—
227Dic47—41no—
228Dic47—41no—
229Dic47—41no—
230Dic47—41no—
231Dic47—41no—
232#2684—471nomaximal, Sylow
233C2×C47—42no—
234C2×C47—42no—
235C2×C47#53411yescharacteristic
236C2×C47#53811yescharacteristic
237C2×C47#53811yescharacteristic
238C2×C47#54611yescharacteristic
239C2×C47#54611yescharacteristic
240C2×C47#55111yescharacteristic
241C2×C47H(3,𝔽4)11yescharacteristic
242D47—42no—
243D47—42no—
244C2×#124—471no—
245C2×#120—471no—
246#397—471no—
247#397—471no—
248#394—471no—
249#394D4711yescharacteristic, complemented
250#393—471no—
251#393—471no—
252#388—471no—
253#388—471no—
254#386—471no—
255#386—471no—
256#386—471no—
257#379—471no—
258#379—471no—
259C47#268411yescharacteristic, complemented, Sylow
260C25—471no—
261C22×Q8—471no—
262C22×D4—471no—
263C22×D4—471no—
264C22×D4C2×D4711yescharacteristic
265C23×C4—471no—
266#124—944no—
267#120—944no—
268C2×C4⋊C4—471no—
269C2×C4⋊C4C2×D4711yescharacteristic, complemented
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⋊C4—471no—
284C2×C22⋊C4C2×D4711yescharacteristic
285C2×C22⋊C4C2×D4711yescharacteristic
286C2×C22⋊C4C2×D4711yescharacteristic, complemented
287C2×C22⋊C4C2×D4711yescharacteristic, complemented
288C2×C42—471no—
289#95—471no—
290#95—471no—
291#95—471no—
292#95—471no—
293#95—471no—
294#95—471no—
295#95—471no—
296#95C2×D4711yescharacteristic, complemented
297C24—471no—
298C24—471no—
299C24—942no—
300C24—942no—
301C24—942no—
302C24—1881no—
303C24—1881no—
304C24—1881no—
305C24—1881no—
306C24C22×D4711yescharacteristic
307C24C22×D4711yescharacteristic
308C2×Q8—942no—
309C2×Q8—1881no—
310C2×Q8—1881no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—474no—
315C2×D4—942no—
316C2×D4—942no—
317C2×D4—1881no—
318C2×D4—1881no—
319C2×D4—1881no—
320C22×C4—471no—
321C22×C4—471no—
322C22×C4—471no—
323C22×C4—471no—
324C22×C4—471no—
325C22×C4—471no—
326C22×C4—1881no—
327C22×C4—1881no—
328C22×C4—1881no—
329C22×C4C22×D4711yescharacteristic
330C22×C4C22×D4711yescharacteristic
331C22×C4C22×D4711yescharacteristic
332C22×C4C22×D4711yescharacteristic
333C22×C4C22×D4711yescharacteristic
334C4⋊C4—41no—
335C4⋊C4—1881no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—942no—
341C22⋊C4—942no—
342C22⋊C4—942no—
343C22⋊C4—942no—
344C22⋊C4—942no—
345C22⋊C4—942no—
346C22⋊C4—942no—
347C22⋊C4—1881no—
348C22⋊C4—1881no—
349C22⋊C4—1881no—
350C22⋊C4—1881no—
351C22⋊C4—1881no—
352C22⋊C4—1881no—
353C22⋊C4—1881no—
354C42—942no—
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—472no—
368C23—472no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23—941no—
373C23—941no—
374C23—941no—
375C23—941no—
376C23—941no—
377C23—941no—
378C23—941no—
379C23—941no—
380C23—941no—
381C23—1884no—
382C23—1884no—
383C23—1884no—
384C23—1884no—
385C23—1884no—
386C23—1884no—
387C23—1884no—
388C23D4×D4712yes—
389C23#1062535212yes—
390C23C23×D4711yescharacteristic
391Q8—1884no—
392D4—44no—
393D4—1884no—
394D4—1884no—
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—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—472no—
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—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—1884no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—942no—
444C22—942no—
445C22—942no—
446C22—942no—
447C22—942no—
448C22—942no—
449C22—18816no—
450C22—1881no—
451C22—1881no—
452C22—1881no—
453C22—1881no—
454C22—1881no—
455C22—1881no—
456C22—1881no—
457C22—1881no—
458C22C2×D4×D4711yescharacteristic
459C22#41×D4711yescharacteristic
460C22C2×#1062535211yescharacteristic
461C22#1309406911yescharacteristic
462C22#1309406911yescharacteristic
463C22#1309407011yescharacteristic
464C22#1309407011yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—942no—
471C4—1881no—
472C4—1881no—
473C4—1881no—
474C4—1881no—
475C4—1881no—
476C2—42no—
477C2—42no—
478C2—1882no—
479C2—1882no—
480C2#1568968111yescharacteristic
481C2#1568970511yescharacteristic
482C2#1568971011yescharacteristic
483C2#1568976011yescharacteristic
484C2#1568976511yescharacteristic
485C2#1568979611yescharacteristic
486C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2684
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
3. #15689050C2semidirect
4. #15689049C2semidirect
5. #15689039C2semidirect
6. #15689036C2semidirect
7. #15689035C2semidirect
8. #15689016C2semidirect
9. #15689013C2semidirect
10. #15689003C2semidirect
11. #15689000C2semidirect
12. #15689000C2semidirect
13. #15688978C2semidirect
14. #15688978C2semidirect
15. C47×#394C2semidirect
17. C22×Dic94C22semidirect
20. C23×Dic47C22semidirect
23. C2×C4⋊Dic47C22semidirect
27. C2×C22⋊Dic47C22semidirect
38. C2×C4×Dic47C22semidirect
39. C47⋊#95C22semidirect
40. C47⋊#95C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
47. C2×C4⋊C4×C47C22semidirect
50. C2×C22⋊C4×C47C22semidirect
51. C2×C22⋊C4×C47C22semidirect
52. #95×C47C22semidirect
249. #394D47semidirect
259. C47#2684semidirect
269. C2×C4⋊C4C2×D47semidirect
286. C2×C22⋊C4C2×D47semidirect
287. C2×C22⋊C4C2×D47semidirect
296. #95C2×D47semidirect