Finite Group Databasebeta

← #20246922

Subgroups — #20246922

Order 6016.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093999C211yesmaximal, characteristic, complemented
2C2×#13093998C211yesmaximal, characteristic, complemented
3C2×#13093994C211yesmaximal, characteristic, complemented
4C2×#13093994C211yesmaximal, characteristic, complemented
5C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
6C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
7#15689045C211yesmaximal, characteristic, complemented
8#15689041C211yesmaximal, characteristic, complemented
9#15689040C211yesmaximal, characteristic, complemented
10#15689033C211yesmaximal, characteristic, complemented
11#15689024C211yesmaximal, characteristic, complemented
12#15689015C211yesmaximal, characteristic, complemented
13#15689001C211yesmaximal, characteristic, complemented
14#15689000C211yesmaximal, characteristic, complemented
15C47×#385C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×D188C2211yescharacteristic
20C22×D188C2211yescharacteristic
21C22×D188C2211yescharacteristic, complemented
22C22×C22⋊D47C2211yescharacteristic
23C22×C22⋊D47C2211yescharacteristic
24C23×Dic47C2211yescharacteristic
25C22×C4×D47C2211yescharacteristic, complemented
26#13093999—24no—
27#13093998—24no—
28#13093994—24no—
29#13093994—24no—
30(C22⋊D47)⋊C4—24no—
31C2×C4⋊Dic47C2211yescharacteristic, complemented
32C2×Dic47⋊C4C2211yescharacteristic, complemented
33C2×(C2×D47)⋊C4—24no—
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic47C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C47⋊#95C2211yescharacteristic, complemented
50C23×C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic, complemented
52C2×C4⋊C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55#95×C47C2211yescharacteristic, complemented
56#95×C47C2211yescharacteristic, complemented
57C24×C47C2311yescharacteristic
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—22no—
62C23×D47—22no—
63C23×D47—41no—
64C23×D47—41no—
65C23×D47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C23×D47C2311yescharacteristic
68C23×D47C2311yescharacteristic
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—41no—
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C22×C4×C47C2311yescharacteristic
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—22no—
83C2×C22⋊D47D414yescomplemented
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—41no—
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C2×D188—22no—
92C2×D188—22no—
93C2×D188—22no—
94C2×D188—22no—
95C2×D188—22no—
96C2×D188—22no—
97C2×D188—22no—
98C2×D188—22no—
99C2×D188—22no—
100C2×D188—22no—
101C2×D188—41no—
102C2×D188—41no—
103C2×D188—41no—
104C2×D188—41no—
105C2×D188—41no—
106C2×C4×D47—22no—
107C2×C4×D47—22no—
108C2×C4×D47—41no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—41no—
111C22⋊C4×C47—22no—
112C22⋊C4×C47D414yescomplemented
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
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—41no—
125(C2×D47)⋊C4D414yescomplemented
126C4⋊Dic47—22no—
127Dic47⋊C4—22no—
128C4×Dic47—22no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47C2×D412yes—
134C23×C47C2×D412yes—
135C23×C47#4112yes—
136C23×C47C2411yescharacteristic
137C22×D47—28no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
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—21no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47—21no—
158C22×D47—21no—
159C22×D47—21no—
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—44no—
164C22×D47—44no—
165C22×D47—44no—
166C22×D47—44no—
167C22×D47—44no—
168C22×D47—44no—
169C22×D47C2×D412yes—
170C22×D47C2×D412yes—
171C22×D47#4112yes—
172C2×C4×C47—21no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
175C2×C4×C47—21no—
176C2×C4×C47—21no—
177C2×C4×C47—21no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—21no—
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—44no—
188C2×C4×C47C2×D412yes—
189C2×C4×C47C2×D412yes—
190C2×C4×C47C2×D412yes—
191C22⋊D47—28no—
192C22⋊D47—44no—
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×Dic47—21no—
203C2×Dic47—44no—
204C2×Dic47C2×D412yes—
205C2×Dic47C2×D412yes—
206D188—44no—
207D188—44no—
208D188—44no—
209D188—44no—
210D188—44no—
211C4×D47—44no—
212C22×C47—22no—
213C22×C47—22no—
214C22×C47—22no—
215C22×C47—22no—
216C22×C47—22no—
217C22×C47—22no—
218C22×C47#12114yescomplemented
219C22×C47C22×D411yescharacteristic
220C22×C47C22×D411yescharacteristic
221C22×C47C22×D411yescharacteristic
222C22×C47C2×#4111yescharacteristic
223C22×C47C2×#4111yescharacteristic
224C22×C47H(5,𝔽2)11yescharacteristic
225C22×C47H(5,𝔽2)11yescharacteristic
226C2×D47—22no—
227C2×D47—22no—
228C2×D47—22no—
229C2×D47—22no—
230C2×D47—22no—
231C2×D47—22no—
232C2×D47—22no—
233C2×D47—22no—
234C2×D47—22no—
235C2×D47—416no—
236C2×D47—41no—
237C2×D47—41no—
238C2×D47—41no—
239C2×D47—41no—
240C2×D47—41no—
241C2×D47—41no—
242C2×D47—41no—
243C2×D47—41no—
244C2×D47—41no—
245C2×D47—41no—
246C2×D47—41no—
247C2×D47—41no—
248C2×D47—41no—
249C2×D47—41no—
250C2×D47—41no—
251C2×D47—41no—
252C2×D47—41no—
253C2×D47—41no—
254C2×D47—41no—
255C4×C47—22no—
256C4×C47—22no—
257C4×C47—22no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261Dic47—22no—
262Dic47—22no—
263Dic47—41no—
264Dic47—41no—
265#2424—471nomaximal, Sylow
266C2×C47—24no—
267C2×C47C2×#12111yescharacteristic
268C2×C47#52511yescharacteristic
269C2×C47#53811yescharacteristic
270C2×C47D4211yescharacteristic
271C2×C47D4211yescharacteristic
272C2×C47#54611yescharacteristic
273C2×C47#54611yescharacteristic
274D47—42no—
275D47—42no—
276D47—42no—
277D47—81no—
278C2×#121—471no—
279C2×#121—471no—
280C2×#120—471no—
281C2×#120—471no—
282C2×C4×D4—471no—
283C22×C22⋊C4—471no—
284#396—471no—
285#394—471no—
286#394—471no—
287#392—471no—
288#390—471no—
289#388—471no—
290#386—471no—
291#386—471no—
292#385D4711yescharacteristic, complemented
293C47#242411yescharacteristic, complemented, Sylow
294C25—471no—
295C22×D4—471no—
296C22×D4—471no—
297C22×D4—471no—
298C22×D4—471no—
299C22×D4—471no—
300C22×D4—471no—
301C22×D4—471no—
302C23×C4—471no—
303C23×C4—471no—
304C23×C4C2×D4711yescharacteristic
305#121—944no—
306#121—944no—
307#120—944no—
308#120—944no—
309C4×D4—944no—
310C2×C4⋊C4—471no—
311C2×C4⋊C4—471no—
312C2×C4⋊C4C2×D4711yescharacteristic, complemented
313C2×C4⋊C4C2×D4711yescharacteristic, complemented
314C2×C22⋊C4—471no—
315C2×C22⋊C4—471no—
316C2×C22⋊C4—471no—
317C2×C22⋊C4—471no—
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—944no—
328C2×C22⋊C4C2×D4711yescharacteristic
329C2×C22⋊C4C2×D4711yescharacteristic
330C2×C42—471no—
331#95—471no—
332#95—471no—
333#95C2×D4711yescharacteristic, complemented
334#95C2×D4711yescharacteristic, complemented
335C24—471no—
336C24—471no—
337C24—471no—
338C24—471no—
339C24—942no—
340C24—942no—
341C24—942no—
342C24—942no—
343C24—942no—
344C24—1881no—
345C24—1881no—
346C24C22×D4711yescharacteristic
347C2×D4—474no—
348C2×D4—942no—
349C2×D4—942no—
350C2×D4—942no—
351C2×D4—942no—
352C2×D4—942no—
353C2×D4—942no—
354C2×D4—942no—
355C2×D4—942no—
356C2×D4—942no—
357C2×D4—942no—
358C2×D4—942no—
359C2×D4—942no—
360C2×D4—942no—
361C2×D4—942no—
362C2×D4—942no—
363C2×D4—1881no—
364C2×D4—1881no—
365C2×D4—1881no—
366C2×D4—1881no—
367C2×D4—1881no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—471no—
372C22×C4—471no—
373C22×C4—471no—
374C22×C4—471no—
375C22×C4—942no—
376C22×C4—942no—
377C22×C4—942no—
378C22×C4—942no—
379C22×C4—1881no—
380C22×C4—1881no—
381C22×C4C22×D4711yescharacteristic
382C22×C4C22×D4711yescharacteristic
383C22×C4C22×D4711yescharacteristic
384C22×C4C22×D4711yescharacteristic
385C22×C4C22×D4711yescharacteristic
386C22×C4C22×D4711yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—41no—
389C4⋊C4—942no—
390C4⋊C4—942no—
391C22⋊C4—22no—
392C22⋊C4—474no—
393C22⋊C4—942no—
394C22⋊C4—942no—
395C22⋊C4—942no—
396C22⋊C4—942no—
397C22⋊C4—942no—
398C22⋊C4—942no—
399C22⋊C4—942no—
400C22⋊C4—942no—
401C22⋊C4—942no—
402C22⋊C4—942no—
403C22⋊C4—942no—
404C22⋊C4—1881no—
405C22⋊C4D18814yescomplemented
406C42—942no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—472no—
412C23—472no—
413C23—472no—
414C23—948no—
415C23—941no—
416C23—941no—
417C23—941no—
418C23—941no—
419C23—941no—
420C23—941no—
421C23—941no—
422C23—941no—
423C23—941no—
424C23—941no—
425C23—941no—
426C23—941no—
427C23—941no—
428C23—941no—
429C23—941no—
430C23—941no—
431C23—941no—
432C23—941no—
433C23—941no—
434C23—941no—
435C23—941no—
436C23—941no—
437C23—941no—
438C23—941no—
439C23—941no—
440C23—1884no—
441C23—1884no—
442C23—1884no—
443C23—1884no—
444C23—1884no—
445C23—1884no—
446C23C2×D18812yes—
447C23D4×D4712yes—
448C23#1062535412yes—
449C23C23×D4711yescharacteristic
450D4—948no—
451D4—1884no—
452D4—1884no—
453D4—1884no—
454D4—1884no—
455D4—1884no—
456D4—1884no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—44no—
473C2×C4—472no—
474C2×C4—472no—
475C2×C4—941no—
476C2×C4—941no—
477C2×C4—941no—
478C2×C4—941no—
479C2×C4—941no—
480C2×C4—941no—
481C2×C4—941no—
482C2×C4—941no—
483C2×C4—941no—
484C2×C4—941no—
485C2×C4—1884no—
486C2×C4—1884no—
487C2×C4C2×D18812yes—
488C2×C4C2×D18812yes—
489C2×C4D4×D4712yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—942no—
497C22—942no—
498C22—942no—
499C22—942no—
500C22—942no—
501C22—942no—
502C22—942no—
503C22—942no—
504C22—942no—
505C22—18816no—
506C22—1881no—
507C22—1881no—
508C22—1881no—
509C22—1881no—
510C22—1881no—
511C22—1881no—
512C22—1881no—
513C22—1881no—
514C22—1881no—
515C22—1881no—
516C22—1881no—
517C22—1881no—
518C22—1881no—
519C22—1881no—
520C22—1881no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22#1309399914yescomplemented
526C22C2×D4×D4711yescharacteristic
527C22C2×D4×D4711yescharacteristic
528C22C22×D18811yescharacteristic
529C22#41×D4711yescharacteristic
530C22C2×#1062535411yescharacteristic
531C22#1309406911yescharacteristic
532C22#1309407011yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—942no—
540C4—942no—
541C4—1881no—
542C4—1881no—
543C2—24no—
544C2—3761no—
545C2—1882no—
546C2—1882no—
547C2—1882no—
548C2C2×#1309399911yescharacteristic
549C2#1568963611yescharacteristic
550C2#1568971311yescharacteristic
551C2#1568975511yescharacteristic
552C2D4×D18811yescharacteristic
553C2#1568976511yescharacteristic
554C2#1568976811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13093999C2semidirect
2. C2×#13093998C2semidirect
3. C2×#13093994C2semidirect
4. C2×#13093994C2semidirect
5. C2×(C22⋊D47)⋊C4C2semidirect
6. C22×(C2×D47)⋊C4C2semidirect
7. #15689045C2semidirect
8. #15689041C2semidirect
9. #15689040C2semidirect
10. #15689033C2semidirect
11. #15689024C2semidirect
12. #15689015C2semidirect
13. #15689001C2semidirect
14. #15689000C2semidirect
15. C47×#385C2semidirect
21. C22×D188C22semidirect
25. C22×C4×D47C22semidirect
31. C2×C4⋊Dic47C22semidirect
32. C2×Dic47⋊C4C22semidirect
42. C2×(C2×D47)⋊C4C22semidirect
43. C2×(C2×D47)⋊C4C22semidirect
44. C2×(C2×D47)⋊C4C22semidirect
45. C2×(C2×D47)⋊C4C22semidirect
46. C2×(C2×D47)⋊C4C22semidirect
47. C2×C4×Dic47C22semidirect
48. C47⋊#95C22semidirect
49. C47⋊#95C22semidirect
51. C2×C4⋊C4×C47C22semidirect
52. C2×C4⋊C4×C47C22semidirect
55. #95×C47C22semidirect
56. #95×C47C22semidirect
83. C2×C22⋊D47D4semidirect
112. C22⋊C4×C47D4semidirect
125. (C2×D47)⋊C4D4semidirect
218. C22×C47#121semidirect
292. #385D47semidirect
293. C47#2424semidirect
312. C2×C4⋊C4C2×D47semidirect
313. C2×C4⋊C4C2×D47semidirect
333. #95C2×D47semidirect
334. #95C2×D47semidirect
405. C22⋊C4D188semidirect
525. C22#13093999semidirect