Finite Group Databasebeta

← #20246206

Subgroups — #20246206

Order 6016.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D47C211yesmaximal, characteristic
2C2×C4×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#15689023C211yesmaximal, characteristic, complemented
7#15689023C211yesmaximal, characteristic, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15688982C211yesmaximal, characteristic, complemented
12#15688978C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C24×D47C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C2×D4×D47—24no—
22C2×D4×D47—24no—
23C2×D4×D47C418yescomplemented
24C23×Dic47C2211yescharacteristic, complemented
25C22×C4×D47C2211yescharacteristic
26C22×C4×D47C2211yescharacteristic, complemented
27C22×C4×D47C2211yescharacteristic, complemented
28C4×C22⋊D47—24no—
29(C22⋊D47)⋊C4—24no—
30C2×Dic47⋊C4C2211yescharacteristic, complemented
31C2×Dic47⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic47C2211yescharacteristic, complemented
33C2×C22⋊Dic47C2211yescharacteristic, complemented
34C2×C22⋊Dic47C2211yescharacteristic, complemented
35C2×(C2×D47)⋊C4—24no—
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—
47C2×C4×Dic47C2211yescharacteristic, complemented
48C2×C4×Dic47C2211yescharacteristic, complemented
49C47⋊#95C2211yescharacteristic, complemented
50C47⋊#95C2211yescharacteristic, complemented
51C22×D4×C47C2211yescharacteristic
52C23×C4×C47C2211yescharacteristic, complemented
53C2×C22⋊C4×C47C2211yescharacteristic, complemented
54C2×C22⋊C4×C47C2211yescharacteristic, complemented
55C2×C22⋊C4×C47C2211yescharacteristic, complemented
56#95×C47C2211yescharacteristic, complemented
57#95×C47C2211yescharacteristic, complemented
58C24×C47C2311yescharacteristic
59C24×C47C2311yescharacteristic
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×D47C2×C414yescomplemented
73C23×D47C2×C414yescomplemented
74C23×D47C2311yescharacteristic
75C23×D47C2311yescharacteristic
76C23×D47C2311yescharacteristic
77C2×D4×C47—22no—
78C2×D4×C47—22no—
79C2×D4×C47C2×C414yescomplemented
80C22×C4×C47—22no—
81C22×C4×C47—22no—
82C22×C4×C47—41no—
83C22×C4×C47C2311yescharacteristic
84C22×C4×C47C2311yescharacteristic
85C22×C4×C47C2311yescharacteristic
86C22×C4×C47C2311yescharacteristic
87C22×C4×C47C2311yescharacteristic
88C2×C22⋊D47—22no—
89C2×C22⋊D47—22no—
90C2×C22⋊D47C2×C414yes—
91C2×C22⋊D47C2×C414yescomplemented
92C2×C22⋊D47D414yes—
93C2×C22⋊D47D414yes—
94C22×Dic47—22no—
95C22×Dic47—22no—
96C22×Dic47—41no—
97C22×Dic47C2311yescharacteristic
98C22×Dic47C2311yescharacteristic
99C22×Dic47C2311yescharacteristic
100C22×Dic47C2311yescharacteristic
101C22×Dic47C2311yescharacteristic
102D4×D47—232no—
103C2×D188—22no—
104C2×D188—22no—
105C2×D188C2×C414yescomplemented
106C2×C4×D47—22no—
107C2×C4×D47—22no—
108C2×C4×D47—22no—
109C2×C4×D47—22no—
110C2×C4×D47—22no—
111C2×C4×D47—22no—
112C2×C4×D47—41no—
113C2×C4×D47—41no—
114C2×C4×D47C2×C414yescomplemented
115C22⋊C4×C47—22no—
116C22⋊C4×C47—22no—
117C22⋊C4×C47—41no—
118C22⋊Dic47—22no—
119C22⋊Dic47—22no—
120C22⋊Dic47—41no—
121(C2×D47)⋊C4—22no—
122(C2×D47)⋊C4—22no—
123(C2×D47)⋊C4—22no—
124(C2×D47)⋊C4—22no—
125(C2×D47)⋊C4—22no—
126(C2×D47)⋊C4—22no—
127(C2×D47)⋊C4—22no—
128(C2×D47)⋊C4—41no—
129(C2×D47)⋊C4—41no—
130(C2×D47)⋊C4D414yescomplemented
131Dic47⋊C4—22no—
132Dic47⋊C4—22no—
133C4×Dic47—22no—
134C4×Dic47—22no—
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×C47C22×C412yes—
146C23×C47C22×C412yes—
147C23×C47C2×D412yes—
148C23×C47C2×D412yes—
149C23×C47C2411yescharacteristic
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—28no—
159C22×D47—21no—
160C22×D47—21no—
161C22×D47—21no—
162C22×D47—21no—
163C22×D47—21no—
164C22×D47—21no—
165C22×D47—28no—
166C22×D47—28no—
167C22×D47—28no—
168C22×D47—44no—
169C22×D47—44no—
170C22×D47—44no—
171C22×D47—44no—
172C22×D47—44no—
173C22×D47—44no—
174C22×D47—44no—
175C22×D47—44no—
176C22×D47—44no—
177C22×D47—44no—
178C22×D47C22×C412yes—
179C22×D47C22×C412yes—
180C22×D47C22×C412yes—
181C22×D47C2×D412yes—
182C22×D47C2×D412yes—
183C22×D47C2×D412yes—
184C22×D47#4112yes—
185D4×C47—28no—
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×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—44no—
200C2×C4×C47C22×C412yes—
201C2×C4×C47C2×D412yescomplemented
202C22⋊D47—28no—
203C22⋊D47C22⋊C4116yescomplemented
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×Dic47—21no—
213C2×Dic47—21no—
214C2×Dic47—21no—
215C2×Dic47—44no—
216C2×Dic47C22×C412yes—
217C2×Dic47C2×D412yes—
218C2×Dic47C2×D412yes—
219C2×Dic47C2×D412yescomplemented
220D188—28no—
221C4×D47—28no—
222C4×D47—44no—
223C4×D47—44no—
224C22×C47—22no—
225C22×C47—22no—
226C22×C47—22no—
227C22×C47—22no—
228C22×C47—22no—
229C22×C47—22no—
230C22×C47—22no—
231C22×C47—22no—
232C22×C47—22no—
233C22×C47—41no—
234C22×C47—41no—
235C22×C47—41no—
236C22×C47—41no—
237C22×C47C2×C22⋊C414yescomplemented
238C22×C47C23×C411yescharacteristic
239C22×C47C22×D411yescharacteristic
240C22×C47C22×D411yescharacteristic
241C22×C47C22×D411yescharacteristic
242C22×C47C2×#4111yescharacteristic
243C22×C47H(5,𝔽2)11yescharacteristic
244C22×C47H(5,𝔽2)11yescharacteristic
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—22no—
254C2×D47—22no—
255C2×D47—22no—
256C2×D47—22no—
257C2×D47—22no—
258C2×D47—22no—
259C2×D47—22no—
260C2×D47—416no—
261C2×D47—416no—
262C2×D47—41no—
263C2×D47—41no—
264C2×D47—41no—
265C2×D47—41no—
266C2×D47C2×C22⋊C414yescomplemented
267C2×D47C4×D414yescomplemented
268C4×C47—22no—
269C4×C47—22no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273Dic47—22no—
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277Dic47C2×C22⋊C414yescomplemented
278D4×C22⋊C4—471nomaximal, Sylow
279C2×C47—24no—
280C2×C47—42no—
281C2×C47C22×C22⋊C411yescharacteristic
282C2×C47C2×C4×D411yescharacteristic
283C2×C47#51811yescharacteristic
284C2×C47D4211yescharacteristic
285C2×C47D4211yescharacteristic
286C2×C47#54611yescharacteristic
287C2×C47#54611yescharacteristic
288D47—24no—
289D47—24no—
290D47—42no—
291C23×D4—471no—
292C2×C4×D4—471no—
293C2×C4×D4—471no—
294C22×C22⋊C4—471no—
295C22×C22⋊C4—471no—
296#390—471no—
297#390—471no—
298#386—471no—
299#386—471no—
300#386—471no—
301#386D4711yescharacteristic, complemented
302#380—471no—
303#379—471no—
304#379—471no—
305C4×C22⋊C4—471no—
306C47D4×C22⋊C411yescharacteristic, complemented, Sylow
307C25—471no—
308C25—471no—
309C22×D4—471no—
310C22×D4—471no—
311C22×D4—478no—
312C22×D4—471no—
313C22×D4—944no—
314C22×D4—944no—
315C22×D4C2×D4711yescharacteristic
316C23×C4—471no—
317C23×C4—471no—
318C23×C4—471no—
319C23×C4—471no—
320C23×C4C2×D4711yescharacteristic, complemented
321C4×D4—944no—
322C4×D4—944no—
323C2×C4⋊C4—471no—
324C2×C4⋊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—471no—
333C2×C22⋊C4—471no—
334C2×C22⋊C4—471no—
335C2×C22⋊C4—471no—
336C2×C22⋊C4—471no—
337C2×C22⋊C4—471no—
338C2×C22⋊C4—944no—
339C2×C22⋊C4—944no—
340C2×C22⋊C4C2×D4711yescharacteristic, complemented
341C2×C22⋊C4C2×D4711yescharacteristic, complemented
342C2×C22⋊C4C2×D4711yescharacteristic, complemented
343C2×C42—471no—
344C2×C42—471no—
345#95—471no—
346#95—471no—
347#95C2×D4711yescharacteristic, complemented
348#95C2×D4711yescharacteristic, complemented
349C24—471no—
350C24—471no—
351C24—471no—
352C24—474no—
353C24—474no—
354C24—942no—
355C24—942no—
356C24—942no—
357C24—942no—
358C24—942no—
359C24—942no—
360C24—942no—
361C24—942no—
362C24—1881no—
363C24—1881no—
364C24—1881no—
365C24—1881no—
366C24C22×D4711yescharacteristic
367C24C22×D4711yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—474no—
371C2×D4—474no—
372C2×D4—474no—
373C2×D4—474no—
374C2×D4—474no—
375C2×D4—942no—
376C2×D4—942no—
377C2×D4—942no—
378C2×D4—942no—
379C2×D4—9432no—
380C2×D4C4×D4714yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—471no—
385C22×C4—471no—
386C22×C4—474no—
387C22×C4—471no—
388C22×C4—471no—
389C22×C4—471no—
390C22×C4—942no—
391C22×C4—942no—
392C22×C4—942no—
393C22×C4—942no—
394C22×C4—942no—
395C22×C4—942no—
396C22×C4—942no—
397C22×C4—942no—
398C22×C4—1881no—
399C22×C4—1881no—
400C22×C4—1881no—
401C22×C4C22×D4711yescharacteristic
402C22×C4C22×D4711yescharacteristic
403C22×C4C22×D4711yescharacteristic
404C22×C4C22×D4711yescharacteristic
405C22×C4C22×D4711yescharacteristic
406C4⋊C4—942no—
407C4⋊C4—942no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—474no—
412C22⋊C4—942no—
413C22⋊C4—942no—
414C22⋊C4—942no—
415C22⋊C4—942no—
416C22⋊C4—942no—
417C22⋊C4—942no—
418C22⋊C4—942no—
419C22⋊C4—942no—
420C22⋊C4—942no—
421C22⋊C4—1881no—
422C22⋊C4—1881no—
423C22⋊C4—1881no—
424C42—942no—
425C42—942no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—472no—
437C23—472no—
438C23—472no—
439C23—472no—
440C23—472no—
441C23—472no—
442C23—472no—
443C23—948no—
444C23—948no—
445C23—948no—
446C23—941no—
447C23—941no—
448C23—941no—
449C23—941no—
450C23—941no—
451C23—941no—
452C23—941no—
453C23—941no—
454C23—948no—
455C23—941no—
456C23—941no—
457C23—941no—
458C23—941no—
459C23—941no—
460C23—941no—
461C23—1884no—
462C23—1884no—
463C23—1884no—
464C23—1884no—
465C23—1884no—
466C23—1884no—
467C23—1884no—
468C23—1884no—
469C23—1884no—
470C23—1884no—
471C23C2×C4×D4712yes—
472C23C2×C4×D4712yes—
473C23D4×D4712yes—
474C23D4×D4712yes—
475C23C23×D4711yescharacteristic
476D4—28no—
477D4—4716no—
478D4—948no—
479D4—948no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—472no—
495C2×C4—472no—
496C2×C4—472no—
497C2×C4—472no—
498C2×C4—948no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—941no—
502C2×C4—941no—
503C2×C4—941no—
504C2×C4—941no—
505C2×C4—941no—
506C2×C4—941no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—1884no—
511C2×C4—1884no—
512C2×C4—1884no—
513C2×C4C2×C4×D4712yes—
514C2×C4D4×D4712yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—474no—
529C22—474no—
530C22—942no—
531C22—942no—
532C22—942no—
533C22—942no—
534C22—942no—
535C22—942no—
536C22—942no—
537C22—942no—
538C22—942no—
539C22—942no—
540C22—942no—
541C22—942no—
542C22—942no—
543C22—942no—
544C22—942no—
545C22—18816no—
546C22—18816no—
547C22—1881no—
548C22—1881no—
549C22—1881no—
550C22—1881no—
551C22C22⋊C4×D4714yescomplemented
552C22C22×C4×D4711yescharacteristic
553C22C2×D4×D4711yescharacteristic
554C22C2×D4×D4711yescharacteristic
555C22C2×D4×D4711yescharacteristic
556C22#41×D4711yescharacteristic
557C22#1309406911yescharacteristic
558C22#1309407011yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—474no—
565C4—942no—
566C4—1881no—
567C4—1881no—
568C4—1881no—
569C2—24no—
570C2—42no—
571C2—944no—
572C2—944no—
573C2—1882no—
574C2C2×C22⋊C4×D4711yescharacteristic
575C2C4×D4×D4711yescharacteristic
576C2#1568959511yescharacteristic
577C2#1568975511yescharacteristic
578C2#1568975711yescharacteristic
579C2#1568976211yescharacteristic
580C2#1568976511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#386C2
socleC23×C47C24
hypercenter#386D47
hypocenterC47D4×C22⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. C22×(C2×D47)⋊C4C2semidirect
5. C2×C22⋊C4×D47C2semidirect
6. #15689023C2semidirect
7. #15689023C2semidirect
8. #15689003C2semidirect
9. #15689001C2semidirect
10. #15689001C2semidirect
11. #15688982C2semidirect
12. #15688978C2semidirect
13. #15688978C2semidirect
14. #15688970C2semidirect
15. C47×#386C2semidirect
23. C2×D4×D47C4semidirect
24. C23×Dic47C22semidirect
26. C22×C4×D47C22semidirect
27. C22×C4×D47C22semidirect
30. C2×Dic47⋊C4C22semidirect
31. C2×Dic47⋊C4C22semidirect
32. C2×C22⋊Dic47C22semidirect
33. C2×C22⋊Dic47C22semidirect
34. 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. C2×C4×Dic47C22semidirect
48. C2×C4×Dic47C22semidirect
49. C47⋊#95C22semidirect
50. C47⋊#95C22semidirect
52. C23×C4×C47C22semidirect
53. C2×C22⋊C4×C47C22semidirect
54. C2×C22⋊C4×C47C22semidirect
55. C2×C22⋊C4×C47C22semidirect
56. #95×C47C22semidirect
57. #95×C47C22semidirect
72. C23×D47C2×C4semidirect
73. C23×D47C2×C4semidirect
79. C2×D4×C47C2×C4semidirect
91. C2×C22⋊D47C2×C4semidirect
105. C2×D188C2×C4semidirect
114. C2×C4×D47C2×C4semidirect
130. (C2×D47)⋊C4D4semidirect
201. C2×C4×C47C2×D4semidirect
203. C22⋊D47C22⋊C4semidirect
219. C2×Dic47C2×D4semidirect
237. C22×C47C2×C22⋊C4semidirect
266. C2×D47C2×C22⋊C4semidirect
267. C2×D47C4×D4semidirect
277. Dic47C2×C22⋊C4semidirect
301. #386D47semidirect
306. C47D4×C22⋊C4semidirect
320. C23×C4C2×D47semidirect
340. C2×C22⋊C4C2×D47semidirect
341. C2×C22⋊C4C2×D47semidirect
342. C2×C22⋊C4C2×D47semidirect
347. #95C2×D47semidirect
348. #95C2×D47semidirect
380. C2×D4C4×D47semidirect
514. C2×C4D4×D47semidirect
551. C22C22⋊C4×D47semidirect