Finite Group Databasebeta

← #20246710

Subgroups — #20246710

Order 6016.

1116 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D47C211yesmaximal, characteristic
2C2×#13094009C211yesmaximal, characteristic, complemented
3C2×#13094006C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic, complemented
6#15689038C211yesmaximal, characteristic, complemented
7#15689037C211yesmaximal, characteristic, complemented
8#15689001C211yesmaximal, characteristic, complemented
9#15688999C211yesmaximal, characteristic, complemented
10#15688997C211yesmaximal, characteristic, complemented
11#15688994C211yesmaximal, characteristic, complemented
12#15688978C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688978C211yesmaximal, characteristic, complemented
15C47×#394C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C24×D47C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C2×D4×D47—24no—
22C2×D4×D47—24no—
23C2×D4×D47—24no—
24C22×C4×D47C2211yescharacteristic
25C22×C4×D47C2211yescharacteristic, complemented
26C22×C4×D47C2211yescharacteristic, complemented
27#13094009—24no—
28#13094006—24no—
29C2×C4⋊Dic47C2211yescharacteristic, complemented
30C2×Dic47⋊C4C2211yescharacteristic, complemented
31C2×Dic47⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic47C2211yescharacteristic, complemented
33C2×C22⋊Dic47C2211yescharacteristic, complemented
34C2×C22⋊Dic47C2211yescharacteristic, complemented
35C2×C22⋊Dic47C2211yescharacteristic, complemented
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D47—24no—
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C47⋊#95C2211yescharacteristic, complemented
50C22×D4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic, complemented
52C2×C22⋊C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic, complemented
54C2×C22⋊C4×C47C2211yescharacteristic, complemented
55C2×C22⋊C4×C47C2211yescharacteristic, complemented
56#95×C47C2211yescharacteristic, complemented
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—22no—
62C23×D47—22no—
63C23×D47—22no—
64C23×D47—22no—
65C23×D47—22no—
66C23×D47—22no—
67C23×D47—22no—
68C23×D47—41no—
69C23×D47—41no—
70C23×D47—41no—
71C23×D47—41no—
72C23×D47D414yes—
73C23×D47C2311yescharacteristic
74C23×D47C2311yescharacteristic
75C23×D47C2311yescharacteristic
76C2×D4×C47—22no—
77C2×D4×C47—22no—
78C2×D4×C47—22no—
79C22×C4×C47C2311yescharacteristic
80C22×C4×C47C2311yescharacteristic
81C22×C4×C47C2311yescharacteristic
82C22×C4×C47C2311yescharacteristic
83C22×C4×C47C2311yescharacteristic
84C2×C22⋊D47—22no—
85C2×C22⋊D47—22no—
86C2×C22⋊D47—22no—
87C2×C22⋊D47—22no—
88C2×C22⋊D47—22no—
89C2×C22⋊D47D414yes—
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95D4×D47—232no—
96C2×D188—22no—
97C2×D188—22no—
98C2×D188D414yes—
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47—22no—
102C2×C4×D47—22no—
103C2×C4×D47—22no—
104C2×C4×D47—22no—
105C2×C4×D47—22no—
106C2×C4×D47—41no—
107C2×C4×D47—41no—
108C4⋊C4×C47—22no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—22no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—41no—
113C22⋊Dic47—22no—
114C22⋊Dic47—22no—
115C22⋊Dic47—41no—
116C22⋊Dic47—41no—
117(C2×D47)⋊C4—22no—
118(C2×D47)⋊C4—22no—
119(C2×D47)⋊C4—22no—
120(C2×D47)⋊C4—22no—
121(C2×D47)⋊C4—22no—
122(C2×D47)⋊C4—22no—
123(C2×D47)⋊C4—22no—
124(C2×D47)⋊C4—22no—
125(C2×D47)⋊C4—41no—
126(C2×D47)⋊C4—41no—
127C4⋊Dic47—22no—
128Dic47⋊C4—22no—
129Dic47⋊C4—22no—
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×C47C2×D412yes—
143C23×C47C2×D412yes—
144C23×C47C2411yescharacteristic
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—28no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47—21no—
158C22×D47—21no—
159C22×D47—21no—
160C22×D47—28no—
161C22×D47—28no—
162C22×D47—44no—
163C22×D47—44no—
164C22×D47—44no—
165C22×D47—44no—
166C22×D47—44no—
167C22×D47—44no—
168C22×D47—44no—
169C22×D47—44no—
170C22×D47—44no—
171C22×D47—44no—
172C22×D47—44no—
173C22×D47C2×D412yes—
174C22×D47C2×D412yes—
175C22×D47C2×D412yes—
176C22×D47C2×D412yes—
177C22×D47C2×D412yes—
178C22×D47#4112yes—
179C22×D47#4112yes—
180D4×C47—28no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47—21no—
184C2×C4×C47—21no—
185C2×C4×C47—21no—
186C2×C4×C47—21no—
187C2×C4×C47—21no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—21no—
193C2×C4×C47—21no—
194C2×C4×C47—21no—
195C2×C4×C47C2×D412yes—
196C22⋊D47—28no—
197C22⋊D47—28no—
198C2×Dic47—21no—
199C2×Dic47—21no—
200C2×Dic47—21no—
201C2×Dic47—21no—
202C2×Dic47—21no—
203C2×Dic47—21no—
204C2×Dic47—21no—
205C2×Dic47—21no—
206C2×Dic47—21no—
207C2×Dic47—21no—
208C2×Dic47—21no—
209C2×Dic47—21no—
210C2×Dic47—21no—
211C2×Dic47—21no—
212C2×Dic47C2×D412yes—
213D188—28no—
214C4×D47—28no—
215C4×D47—44no—
216C4×D47—44no—
217C22×C47—22no—
218C22×C47—22no—
219C22×C47—22no—
220C22×C47—22no—
221C22×C47—22no—
222C22×C47—22no—
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×C47C22×D411yescharacteristic
232C22×C47C22×D411yescharacteristic
233C22×C47C22×D411yescharacteristic
234C22×C47C2×#4111yescharacteristic
235C22×C47C2×#4111yescharacteristic
236C22×C47H(5,𝔽2)11yescharacteristic
237C22×C47H(5,𝔽2)11yescharacteristic
238C2×D47—22no—
239C2×D47—22no—
240C2×D47—22no—
241C2×D47—22no—
242C2×D47—22no—
243C2×D47—22no—
244C2×D47—22no—
245C2×D47—22no—
246C2×D47—22no—
247C2×D47—22no—
248C2×D47—22no—
249C2×D47—22no—
250C2×D47—22no—
251C2×D47—22no—
252C2×D47—22no—
253C2×D47—416no—
254C2×D47—416no—
255C2×D47—41no—
256C2×D47—41no—
257C2×D47—41no—
258C2×D47—41no—
259C2×D47#12014yes—
260C2×D47#12314yescomplemented
261C4×C47—22no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266Dic47—22no—
267Dic47—41no—
268Dic47—41no—
269Dic47—41no—
270Dic47—41no—
271#2405—471nomaximal, Sylow
272C2×C47—42no—
273C2×C47—42no—
274C2×C47C2×#12011yescharacteristic
275C2×C47C2×#12311yescharacteristic
276C2×C47#53411yescharacteristic
277C2×C47#54611yescharacteristic
278C2×C47#54611yescharacteristic
279C2×C47#54611yescharacteristic
280C2×C47#54611yescharacteristic
281D47—24no—
282D47—24no—
283D47—42no—
284C23×D4—471no—
285C2×#123—471no—
286C2×#123—471no—
287C22×C22⋊C4—471no—
288#394—471no—
289#394—471no—
290#394—471no—
291#394D4711yescharacteristic, complemented
292#386—471no—
293#386—471no—
294#385—471no—
295#385—471no—
296#379—471no—
297#379—471no—
298#379—471no—
299C47#240511yescharacteristic, complemented, Sylow
300C25—471no—
301C25—471no—
302C22×D4—471no—
303C22×D4—471no—
304C22×D4—471no—
305C22×D4—944no—
306C22×D4—944no—
307C22×D4—944no—
308C22×D4C2×D4711yescharacteristic
309C23×C4—471no—
310C23×C4—471no—
311C23×C4—471no—
312#123—944no—
313#123—944no—
314C2×C4⋊C4—471no—
315C2×C4⋊C4—471no—
316C2×C4⋊C4—471no—
317C2×C4⋊C4C2×D4711yescharacteristic, complemented
318C2×C22⋊C4—471no—
319C2×C22⋊C4—471no—
320C2×C22⋊C4—471no—
321C2×C22⋊C4—471no—
322C2×C22⋊C4—471no—
323C2×C22⋊C4—471no—
324C2×C22⋊C4—471no—
325C2×C22⋊C4—471no—
326C2×C22⋊C4—471no—
327C2×C22⋊C4—471no—
328C2×C22⋊C4—471no—
329C2×C22⋊C4—471no—
330C2×C22⋊C4—471no—
331C2×C22⋊C4—471no—
332C2×C22⋊C4—944no—
333C2×C22⋊C4C2×D4711yescharacteristic, complemented
334C2×C22⋊C4C2×D4711yescharacteristic, complemented
335C2×C22⋊C4C2×D4711yescharacteristic, complemented
336C2×C22⋊C4C2×D4711yescharacteristic, complemented
337#95—471no—
338#95—471no—
339#95—471no—
340#95C2×D4711yescharacteristic, complemented
341C24—471no—
342C24—471no—
343C24—471no—
344C24—474no—
345C24—942no—
346C24—942no—
347C24—942no—
348C24—942no—
349C24—942no—
350C24—942no—
351C24—942no—
352C24—942no—
353C24—942no—
354C24—1881no—
355C24—1881no—
356C24—1881no—
357C24—1881no—
358C24C22×D4711yescharacteristic
359C24C22×D4711yescharacteristic
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—474no—
364C2×D4—474no—
365C2×D4—942no—
366C2×D4—942no—
367C2×D4—942no—
368C2×D4—9432no—
369C2×D4—942no—
370C2×D4—942no—
371C2×D4—942no—
372C2×D4—942no—
373C22×C4—471no—
374C22×C4—471no—
375C22×C4—471no—
376C22×C4—471no—
377C22×C4—471no—
378C22×C4—942no—
379C22×C4—942no—
380C22×C4—942no—
381C22×C4—942no—
382C22×C4—942no—
383C22×C4—942no—
384C22×C4—942no—
385C22×C4—1881no—
386C22×C4—1881no—
387C22×C4C22×D4711yescharacteristic
388C22×C4C22×D4711yescharacteristic
389C22×C4C22×D4711yescharacteristic
390C22×C4C22×D4711yescharacteristic
391C22×C4C22×D4711yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—942no—
394C4⋊C4—942no—
395C4⋊C4—942no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—942no—
401C22⋊C4—942no—
402C22⋊C4—942no—
403C22⋊C4—942no—
404C22⋊C4—942no—
405C22⋊C4—942no—
406C22⋊C4—942no—
407C22⋊C4—942no—
408C22⋊C4—942no—
409C22⋊C4—942no—
410C22⋊C4—1881no—
411C22⋊C4—1881no—
412C22⋊C4—1881no—
413C22⋊C4—1881no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—472no—
427C23—472no—
428C23—472no—
429C23—472no—
430C23—472no—
431C23—472no—
432C23—472no—
433C23—948no—
434C23—948no—
435C23—948no—
436C23—941no—
437C23—941no—
438C23—941no—
439C23—941no—
440C23—941no—
441C23—941no—
442C23—941no—
443C23—941no—
444C23—941no—
445C23—941no—
446C23—941no—
447C23—941no—
448C23—941no—
449C23—941no—
450C23—1884no—
451C23—1884no—
452C23—1884no—
453C23—1884no—
454C23—1884no—
455C23—1884no—
456C23—1884no—
457C23—1884no—
458C23—1884no—
459C23—1884no—
460C23—1884no—
461C23D4×D4712yes—
462C23D4×D4712yes—
463C23C23×D4711yescharacteristic
464D4—28no—
465D4—948no—
466D4—948no—
467D4—948no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—472no—
483C2×C4—948no—
484C2×C4—941no—
485C2×C4—941no—
486C2×C4—941no—
487C2×C4—941no—
488C2×C4—941no—
489C2×C4—941no—
490C2×C4—941no—
491C2×C4—941no—
492C2×C4—941no—
493C2×C4—941no—
494C2×C4—941no—
495C2×C4—941no—
496C2×C4—941no—
497C2×C4—941no—
498C2×C4—1884no—
499C2×C4—1884no—
500C2×C4D4×D4712yes—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—474no—
516C22—474no—
517C22—942no—
518C22—942no—
519C22—942no—
520C22—942no—
521C22—942no—
522C22—942no—
523C22—942no—
524C22—942no—
525C22—942no—
526C22—942no—
527C22—942no—
528C22—942no—
529C22—942no—
530C22—942no—
531C22—942no—
532C22—18816no—
533C22—18816no—
534C22—1881no—
535C22—1881no—
536C22—1881no—
537C22—1881no—
538C22C2×D4×D4711yescharacteristic
539C22C2×D4×D4711yescharacteristic
540C22C2×D4×D4711yescharacteristic
541C22#41×D4711yescharacteristic
542C22#41×D4711yescharacteristic
543C22#1309406911yescharacteristic
544C22#1309407011yescharacteristic
545C4—22no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—942no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4—1881no—
555C2—42no—
556C2—42no—
557C2—944no—
558C2—944no—
559C2—1882no—
560C2#120×D4711yescharacteristic
561C2#123×D4711yescharacteristic
562C2#1568968111yescharacteristic
563C2#1568976211yescharacteristic
564C2#1568976511yescharacteristic
565C2#1568976611yescharacteristic
566C2#1568977011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2405
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13094009C2semidirect
3. C2×#13094006C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. #15689039C2semidirect
6. #15689038C2semidirect
7. #15689037C2semidirect
8. #15689001C2semidirect
9. #15688999C2semidirect
10. #15688997C2semidirect
11. #15688994C2semidirect
12. #15688978C2semidirect
13. #15688978C2semidirect
14. #15688978C2semidirect
15. C47×#394C2semidirect
25. C22×C4×D47C22semidirect
26. C22×C4×D47C22semidirect
29. C2×C4⋊Dic47C22semidirect
30. C2×Dic47⋊C4C22semidirect
31. C2×Dic47⋊C4C22semidirect
32. C2×C22⋊Dic47C22semidirect
33. C2×C22⋊Dic47C22semidirect
34. C2×C22⋊Dic47C22semidirect
35. C2×C22⋊Dic47C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
41. C2×(C2×D47)⋊C4C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
43. C2×(C2×D47)⋊C4C22semidirect
44. C2×(C2×D47)⋊C4C22semidirect
45. C2×(C2×D47)⋊C4C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
49. C47⋊#95C22semidirect
51. C2×C4⋊C4×C47C22semidirect
52. C2×C22⋊C4×C47C22semidirect
53. C2×C22⋊C4×C47C22semidirect
54. C2×C22⋊C4×C47C22semidirect
55. C2×C22⋊C4×C47C22semidirect
56. #95×C47C22semidirect
260. C2×D47#123semidirect
291. #394D47semidirect
299. C47#2405semidirect
317. C2×C4⋊C4C2×D47semidirect
333. C2×C22⋊C4C2×D47semidirect
334. C2×C22⋊C4C2×D47semidirect
335. C2×C22⋊C4C2×D47semidirect
336. C2×C22⋊C4C2×D47semidirect
340. #95C2×D47semidirect