Finite Group Databasebeta

← #20247512

Subgroups — #20247512

Order 6016.

786 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic, complemented
2C2×#13094004C211yesmaximal, characteristic, complemented
3C2×#13093994C211yesmaximal, characteristic
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic, complemented
8#15689036C211yesmaximal, characteristic, complemented
9#15689025C211yesmaximal, characteristic, complemented
10#15689015C211yesmaximal, characteristic, complemented
11#15689001C211yesmaximal, characteristic, complemented
12#15689001C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×Dic94C2211yescharacteristic, complemented
18C22×D188C2211yescharacteristic
19C22×D188C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23#13094010—24no—
24#13094004—24no—
25#13093994—24no—
26C2×C4⋊Dic47C2211yescharacteristic, complemented
27C2×C4⋊Dic47C2211yescharacteristic, complemented
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C22⋊C4×D47—24no—
43C2×C4×Dic47C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C47C2211yescharacteristic, complemented
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic, complemented
53#95×C47C2211yescharacteristic, complemented
54#95×C47C2211yescharacteristic, complemented
55C24×C47C2311yescharacteristic
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—41no—
62C23×D47—41no—
63C23×D47C2311yescharacteristic
64C23×D47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
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—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C2×D188—22no—
81C2×D188—22no—
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—22no—
85C2×D188—41no—
86C2×C4×D47—22no—
87C2×C4×D47—22no—
88C2×C4×D47—22no—
89C2×C4×D47—22no—
90C2×C4×D47—41no—
91C2×C4×D47—41no—
92C2×Dic94—22no—
93C2×Dic94—22no—
94C2×Dic94—41no—
95C4⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47D414yescomplemented
99C42×C47—41no—
100C22⋊Dic47—22no—
101C22⋊Dic47—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—41no—
111(C2×D47)⋊C4—41no—
112(C2×D47)⋊C4—41no—
113(C2×D47)⋊C4D414yes—
114C4⋊Dic47—22no—
115C4⋊Dic47—22no—
116C4×Dic47—22no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47C2×D412yes—
124C23×C47C2411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—28no—
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—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—44no—
144C22×D47—44no—
145C22×D47—44no—
146C22×D47—44no—
147C22×D47—44no—
148C22×D47—44no—
149C22×D47C2×D412yes—
150C22×D47#4112yes—
151C22×D47#4112yes—
152C22×D47#4112yes—
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—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47C2×D412yes—
169C2×C4×C47C2×D412yes—
170C2×C4×C47C2×D412yes—
171C22⋊D47—44no—
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—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47C2×D412yes—
187D188—44no—
188D188—44no—
189C4×D47—44no—
190C4×D47—44no—
191Dic94—44no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47C22×D411yescharacteristic
200C22×C47C22×D411yescharacteristic
201C22×C47C2×#4111yescharacteristic
202C22×C47C2×#4111yescharacteristic
203C22×C47C2×#4111yescharacteristic
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—22no—
213C2×D47—22no—
214C2×D47—22no—
215C2×D47—416no—
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47#12414yescomplemented
228C4×C47—22no—
229C4×C47—22no—
230C4×C47—22no—
231C4×C47—41no—
232C4×C47—41no—
233C4×C47—41no—
234Dic47—22no—
235Dic47—41no—
236Dic47—41no—
237Dic47—41no—
238Dic47—41no—
239#2472—471nomaximal, Sylow
240C2×C47—42no—
241C2×C47#52511yescharacteristic
242C2×C47C2×#12411yescharacteristic
243C2×C47#53811yescharacteristic
244C2×C47D4211yescharacteristic
245C2×C47#54611yescharacteristic
246C2×C47#54611yescharacteristic
247C2×C47#55111yescharacteristic
248D47—24no—
249D47—42no—
250D47—81no—
251C2×#124—471no—
252C2×C22⋊Q8—471no—
253C2×#120—471no—
254C22×C22⋊C4—471no—
255#397—471no—
256#394—471no—
257#394—471no—
258#393—471no—
259#390—471no—
260#388—471no—
261#388D4711yescharacteristic, complemented
262#386—471no—
263#386—471no—
264#379—471no—
265C4×C22⋊C4—471no—
266C47#247211yescharacteristic, complemented, Sylow
267C25—471no—
268C22×Q8—471no—
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—471no—
272C23×C4—471no—
273C23×C4—471no—
274#124—944no—
275C22⋊Q8—944no—
276#120—944no—
277C2×C4⋊C4—471no—
278C2×C4⋊C4—471no—
279C2×C4⋊C4C2×D4711yescharacteristic, complemented
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4—471no—
286C2×C22⋊C4—471no—
287C2×C22⋊C4—471no—
288C2×C22⋊C4—471no—
289C2×C22⋊C4—471no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—471no—
294C2×C22⋊C4—944no—
295C2×C22⋊C4C2×D4711yescharacteristic
296C2×C22⋊C4C2×D4711yescharacteristic
297C2×C22⋊C4C2×D4711yescharacteristic
298C2×C42—471no—
299C2×C42C2×D4711yescharacteristic, complemented
300#95—471no—
301#95—471no—
302#95—471no—
303#95—471no—
304#95C2×D4711yescharacteristic, complemented
305#95C2×D4711yescharacteristic, complemented
306C24—471no—
307C24—471no—
308C24—471no—
309C24—942no—
310C24—942no—
311C24—942no—
312C24—942no—
313C24—942no—
314C24—1881no—
315C24—1881no—
316C24C22×D4711yescharacteristic
317C2×Q8—942no—
318C2×Q8—942no—
319C2×Q8—1881no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—942no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—1881no—
328C2×D4—1881no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—471no—
332C22×C4—471no—
333C22×C4—471no—
334C22×C4—942no—
335C22×C4—942no—
336C22×C4—942no—
337C22×C4—942no—
338C22×C4—1881no—
339C22×C4—1881no—
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C22×C4C22×D4711yescharacteristic
343C22×C4C22×D4711yescharacteristic
344C22×C4C22×D4711yescharacteristic
345C22×C4C22×D4711yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—942no—
348C4⋊C4—942no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—474no—
352C22⋊C4—942no—
353C22⋊C4—942no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4—942no—
360C22⋊C4—942no—
361C22⋊C4—942no—
362C22⋊C4—1881no—
363C22⋊C4—1881no—
364C22⋊C4—1881no—
365C22⋊C4D18814yescomplemented
366C42—41no—
367C42—942no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—472no—
375C23—472no—
376C23—472no—
377C23—472no—
378C23—948no—
379C23—941no—
380C23—941no—
381C23—941no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23—941no—
386C23—941no—
387C23—941no—
388C23—941no—
389C23—941no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—1884no—
397C23—1884no—
398C23—1884no—
399C23—1884no—
400C23—1884no—
401C23—1884no—
402C23C2×D18812yes—
403C23C23×D4711yescharacteristic
404Q8—1884no—
405D4—1884no—
406D4—1884no—
407D4—1884no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—472no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—1884no—
439C2×C4—1884no—
440C2×C4C2×D18812yes—
441C2×C4C2×D18812yes—
442C2×C4D4×D4712yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—474no—
451C22—942no—
452C22—942no—
453C22—942no—
454C22—942no—
455C22—942no—
456C22—942no—
457C22—942no—
458C22—942no—
459C22—942no—
460C22—18816no—
461C22—1881no—
462C22—1881no—
463C22—1881no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22C2×D4×D4711yescharacteristic
473C22C22×D18811yescharacteristic
474C22#41×D4711yescharacteristic
475C22#41×D4711yescharacteristic
476C22#41×D4711yescharacteristic
477C22#1309406911yescharacteristic
478C22#1309407011yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—942no—
486C4—1881no—
487C4—1881no—
488C4—1881no—
489C4—1881no—
490C2—42no—
491C2—944no—
492C2—3761no—
493C2—1882no—
494C2#1568963511yescharacteristic
495C2#124×D4711yescharacteristic
496C2#1568970911yescharacteristic
497C2D4×D18811yescharacteristic
498C2#1568976211yescharacteristic
499C2#1568976811yescharacteristic
500C2#1568979811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2472
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. C2×#13094004C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689048C2semidirect
6. #15689040C2semidirect
7. #15689039C2semidirect
8. #15689036C2semidirect
9. #15689025C2semidirect
10. #15689015C2semidirect
11. #15689001C2semidirect
12. #15689001C2semidirect
13. #15688978C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C47×#388C2semidirect
17. C22×Dic94C22semidirect
26. C2×C4⋊Dic47C22semidirect
27. C2×C4⋊Dic47C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
43. C2×C4×Dic47C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C2×C4⋊C4×C47C22semidirect
52. C2×C42×C47C22semidirect
53. #95×C47C22semidirect
54. #95×C47C22semidirect
98. C22⋊C4×C47D4semidirect
227. C2×D47#124semidirect
261. #388D47semidirect
266. C47#2472semidirect
279. C2×C4⋊C4C2×D47semidirect
299. C2×C42C2×D47semidirect
304. #95C2×D47semidirect
305. #95C2×D47semidirect
365. C22⋊C4D188semidirect