Finite Group Databasebeta

← #20249709

Subgroups — #20249709

Order 6016.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094006C211yesmaximal, characteristic, complemented
2C2×#13093995C211yesmaximal, characteristic, complemented
3C2×#13093993C211yesmaximal, characteristic, complemented
4#15689048C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689037C211yesmaximal, characteristic, complemented
8#15689031C211yesmaximal, characteristic, complemented
9#15689031C211yesmaximal, characteristic, complemented
10#15689026C211yesmaximal, characteristic, complemented
11#15689023C211yesmaximal, characteristic, complemented
12#15689016C211yesmaximal, characteristic, complemented
13#15688999C211yesmaximal, characteristic, complemented
14#15688979C211yesmaximal, characteristic, complemented
15C2×#120×C47C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic, complemented
20C22×C4×D47C2211yescharacteristic, complemented
21#13094006—24no—
22#13093995—24no—
23#13093993—24no—
24C2×C4⋊Dic47C2211yescharacteristic, complemented
25C2×C4⋊Dic47C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×Dic47⋊C4C2211yescharacteristic, complemented
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×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic, complemented
38C2×C22⋊Dic47C2211yescharacteristic, complemented
39C2×C22⋊Dic47C2211yescharacteristic, complemented
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C2×C4×Dic47C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C25×C47C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51#120×C47—24no—
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—41no—
59C24×C47—41no—
60C24×C47—41no—
61C24×C47—41no—
62C24×C47C2311yescharacteristic
63C24×C47C2311yescharacteristic
64C24×C47C2311yescharacteristic
65C24×C47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47—22no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C2×D4×C47—41no—
75C2×D4×C47—41no—
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C22×C4×C47C2311yescharacteristic
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—22no—
83C2×C22⋊D47—22no—
84C2×C22⋊D47—41no—
85C2×C22⋊D47—41no—
86C2×C22⋊D47—41no—
87C2×C22⋊D47—41no—
88C2×C22⋊D47—41no—
89C2×C22⋊D47—41no—
90C2×C22⋊D47D414yescomplemented
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95C22×Dic47C2311yescharacteristic
96C22×Dic47C2311yescharacteristic
97C22×Dic47C2311yescharacteristic
98C2×C4×D47—22no—
99C2×C4×D47—22no—
100C2×C4×D47—41no—
101C22⋊C4×C47—22no—
102C22⋊C4×C47—22no—
103C22⋊C4×C47D414yescomplemented
104C22⋊Dic47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47—22no—
107C22⋊Dic47—22no—
108C22⋊Dic47—22no—
109C22⋊Dic47—22no—
110C22⋊Dic47—41no—
111C22⋊Dic47—41no—
112C22⋊Dic47—41no—
113C22⋊Dic47—41no—
114C22⋊Dic47—41no—
115C22⋊Dic47—41no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—41no—
118C4⋊Dic47—22no—
119C4⋊Dic47—22no—
120Dic47⋊C4—22no—
121Dic47⋊C4—41no—
122C4×Dic47—41no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—21no—
140C23×C47—21no—
141C23×C47—21no—
142C23×C47—21no—
143C23×C47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—21no—
147C23×C47—21no—
148C23×C47—44no—
149C23×C47—44no—
150C23×C47—44no—
151C23×C47—44no—
152C23×C47—44no—
153C23×C47—44no—
154C23×C47—44no—
155C23×C47C2×D412yes—
156C23×C47C2×D412yes—
157C23×C47#4112yes—
158C23×C47C2411yescharacteristic
159C22×D47—21no—
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—21no—
164C22×D47—21no—
165C22×D47C2×D412yes—
166D4×C47—44no—
167D4×C47—44no—
168D4×C47—44no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
175C2×C4×C47—21no—
176C2×C4×C47C2×D412yes—
177C2×C4×C47C2×D412yes—
178C22⋊D47—44no—
179C22⋊D47—44no—
180C22⋊D47—44no—
181C22⋊D47—44no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—21no—
193C2×Dic47—21no—
194C2×Dic47—21no—
195C2×Dic47—21no—
196C2×Dic47—21no—
197C2×Dic47—21no—
198C2×Dic47—21no—
199C2×Dic47—21no—
200C2×Dic47—21no—
201C2×Dic47—21no—
202C2×Dic47C2×D412yes—
203C4×D47—44no—
204C22×C47—22no—
205C22×C47—22no—
206C22×C47—22no—
207C22×C47—22no—
208C22×C47—22no—
209C22×C47—22no—
210C22×C47—22no—
211C22×C47—22no—
212C22×C47—22no—
213C22×C47—416no—
214C22×C47—41no—
215C22×C47—41no—
216C22×C47—41no—
217C22×C47—41no—
218C22×C47—41no—
219C22×C47—41no—
220C22×C47—41no—
221C22×C47—41no—
222C22×C47—41no—
223C22×C47—41no—
224C22×C47—41no—
225C22×C47—41no—
226C22×C47—41no—
227C22×C47—41no—
228C22×C47—41no—
229C22×C47—41no—
230C22×C47—41no—
231C22×C47—41no—
232C22×C47—41no—
233C22×C47C22×D411yescharacteristic
234C22×C47C22×D411yescharacteristic
235C22×C47C2×#4111yescharacteristic
236C22×C47H(5,𝔽2)11yescharacteristic
237C22×C47H(5,𝔽2)11yescharacteristic
238C22×C47H(5,𝔽2)11yescharacteristic
239C22×C47H(5,𝔽2)11yescharacteristic
240C2×D47—22no—
241C2×D47—22no—
242C2×D47—22no—
243C2×D47—41no—
244C2×D47—41no—
245C2×D47—41no—
246C2×D47—41no—
247C4×C47—22no—
248C4×C47—22no—
249C4×C47—41no—
250Dic47—22no—
251Dic47—41no—
252Dic47—41no—
253Dic47—41no—
254Dic47—41no—
255Dic47—41no—
256Dic47—41no—
257#2678—471nomaximal, Sylow
258C2×C47—42no—
259C2×C47—42no—
260C2×C47—42no—
261C2×C47—81no—
262C2×C47#53411yescharacteristic
263C2×C47#53511yescharacteristic
264C2×C47#53811yescharacteristic
265C2×C47D4211yescharacteristic
266C2×C47#54611yescharacteristic
267C2×C47#54611yescharacteristic
268C2×C47#56011yescharacteristic
269D47—42no—
270C2×#123—471no—
271C2×#121—471no—
272C2×#120—471no—
273C2×#120D4711yescharacteristic, complemented
274#397—471no—
275#396—471no—
276#394—471no—
277#394—471no—
278#392—471no—
279#392—471no—
280#390—471no—
281#390—471no—
282#388—471no—
283#386—471no—
284#379—471no—
285C47#267811yescharacteristic, complemented, Sylow
286C25C2×D4711yescharacteristic
287C22×D4—471no—
288C22×D4—471no—
289C22×D4—471no—
290C22×D4—471no—
291C22×D4C2×D4711yescharacteristic
292C22×D4C2×D4711yescharacteristic
293C22×D4C2×D4711yescharacteristic
294C23×C4—471no—
295#123—944no—
296#121—944no—
297#120—24no—
298#120—944no—
299C2×C4⋊C4—471no—
300C2×C4⋊C4—471no—
301C2×C4⋊C4—471no—
302C2×C4⋊C4—471no—
303C2×C22⋊C4—471no—
304C2×C22⋊C4—471no—
305C2×C22⋊C4—471no—
306C2×C22⋊C4—471no—
307C2×C22⋊C4—471no—
308C2×C22⋊C4—471no—
309C2×C22⋊C4—471no—
310C2×C22⋊C4—471no—
311C2×C22⋊C4—471no—
312C2×C22⋊C4—471no—
313C2×C22⋊C4—471no—
314C2×C22⋊C4—471no—
315C2×C22⋊C4—471no—
316C2×C22⋊C4—471no—
317C2×C22⋊C4C2×D4711yescharacteristic
318C2×C22⋊C4C2×D4711yescharacteristic
319C2×C22⋊C4C2×D4711yescharacteristic
320C2×C42—471no—
321#95—471no—
322#95—471no—
323#95—471no—
324#95—471no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—471no—
333C24C22×D4711yescharacteristic
334C24C22×D4711yescharacteristic
335C24C22×D4711yescharacteristic
336C24C22×D4711yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—474no—
347C2×D4—942no—
348C2×D4—942no—
349C2×D4—942no—
350C2×D4—942no—
351C2×D4—942no—
352C2×D4—1881no—
353C2×D4—1881no—
354C2×D4—1881no—
355C2×D4—1881no—
356C2×D4—1881no—
357C2×D4—1881no—
358C22×C4—471no—
359C22×C4—471no—
360C22×C4—471no—
361C22×C4—471no—
362C22×C4—471no—
363C22×C4—471no—
364C22×C4—471no—
365C22×C4—942no—
366C22×C4—942no—
367C22×C4—1881no—
368C22×C4C22×D4711yescharacteristic
369C22×C4C22×D4711yescharacteristic
370C22×C4C22×D4711yescharacteristic
371C4⋊C4—942no—
372C4⋊C4—942no—
373C4⋊C4—942no—
374C4⋊C4—1881no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—942no—
378C22⋊C4—942no—
379C22⋊C4—942no—
380C22⋊C4—942no—
381C22⋊C4—942no—
382C22⋊C4—942no—
383C22⋊C4—942no—
384C22⋊C4—1881no—
385C22⋊C4—1881no—
386C22⋊C4—1881no—
387C22⋊C4—1881no—
388C22⋊C4—1881no—
389C22⋊C4—1881no—
390C22⋊C4—1881no—
391C22⋊C4C22⋊D4714yescomplemented
392C42—1881no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—44no—
424C23—44no—
425C23—472no—
426C23—941no—
427C23—941no—
428C23—941no—
429C23—941no—
430C23—941no—
431C23—941no—
432C23D4×D4712yes—
433C23#1062535212yes—
434C23C2×C22⋊D4712yes—
435C23C23×D4711yescharacteristic
436D4—44no—
437D4—44no—
438D4—44no—
439D4—1884no—
440D4—1884no—
441D4—1884no—
442D4—1884no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—472no—
451C2×C4—941no—
452C2×C4—941no—
453C2×C4—941no—
454C2×C4—941no—
455C2×C4—941no—
456C2×C4—941no—
457C2×C4—941no—
458C2×C4—941no—
459C2×C4—941no—
460C2×C4—941no—
461C2×C4—941no—
462C2×C4—941no—
463C2×C4—941no—
464C2×C4—941no—
465C2×C4—941no—
466C2×C4—941no—
467C2×C4—941no—
468C2×C4—941no—
469C2×C4—941no—
470C2×C4—941no—
471C2×C4—1884no—
472C2×C4C2×C22⋊D4712yes—
473C2×C4C2×C22⋊D4712yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—416no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—942no—
504C22—942no—
505C22—942no—
506C22—1881no—
507C22—1881no—
508C22—1881no—
509C22—1881no—
510C22C2×D4×D4711yescharacteristic
511C22C22×C22⋊D4711yescharacteristic
512C22C2×#1062535211yescharacteristic
513C22#1309406911yescharacteristic
514C22#1309406911yescharacteristic
515C22#1309406911yescharacteristic
516C22#1309406911yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—942no—
521C4—1881no—
522C4—1881no—
523C4—1881no—
524C4—1881no—
525C4—1881no—
526C4—1881no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—1882no—
532C2#1568968311yescharacteristic
533C2#1568969011yescharacteristic
534C2#1568970811yescharacteristic
535C2D4×C22⋊D4711yescharacteristic
536C2#1568976011yescharacteristic
537C2#1568976711yescharacteristic
538C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#120×C47C2
hypercenterC2×#120D47
hypocenterC47#2678
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13094006C2semidirect
2. C2×#13093995C2semidirect
3. C2×#13093993C2semidirect
4. #15689048C2semidirect
5. #15689046C2semidirect
6. #15689037C2semidirect
7. #15689037C2semidirect
8. #15689031C2semidirect
9. #15689031C2semidirect
10. #15689026C2semidirect
11. #15689023C2semidirect
12. #15689016C2semidirect
13. #15688999C2semidirect
14. #15688979C2semidirect
15. C2×#120×C47C2semidirect
19. C22×C22⋊D47C22semidirect
20. C22×C4×D47C22semidirect
24. C2×C4⋊Dic47C22semidirect
25. C2×C4⋊Dic47C22semidirect
26. C2×Dic47⋊C4C22semidirect
27. C2×Dic47⋊C4C22semidirect
37. C2×C22⋊Dic47C22semidirect
38. C2×C22⋊Dic47C22semidirect
39. C2×C22⋊Dic47C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
42. C2×C4×Dic47C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
90. C2×C22⋊D47D4semidirect
103. C22⋊C4×C47D4semidirect
273. C2×#120D47semidirect
285. C47#2678semidirect
391. C22⋊C4C22⋊D47semidirect