Finite Group Databasebeta

← C2×#20255523 #27092830

Subgroups — C2×#20255523 #27092830

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D188C211yesmaximal, characteristic, complemented
2#20255523C2116yesmaximal, direct product factor
3C2×#15689489C211yesmaximal, characteristic, complemented
4C2×#15689441C211yesmaximal, characteristic, complemented
5C2×#15689447C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689357C211yesmaximal, characteristic, complemented
9C2×#15689318C211yesmaximal, characteristic, complemented
10C2×#15689256C211yesmaximal, characteristic, complemented
11C2×#15689256C211yesmaximal, characteristic, complemented
12C2×#15689233C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689127C211yesmaximal, characteristic, complemented
15C22×#13093944C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×D4×D47—21no—
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic, complemented
22C22×#10625334C2211yescharacteristic, complemented
23C22×#10625329C2211yescharacteristic, complemented
24C23×C47⋊C8C2211yescharacteristic, complemented
25D4×D188—24no—
26D4×D188C2218yescomplemented
27C2×#13094021C2211yescharacteristic
28C2×#13093999—21no—
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093994—21no—
32C2×#13093994—21no—
33C2×C4×D188C2211yescharacteristic
34#15689489C2218yescomplemented
35#15689447C2218yescomplemented
36#15689441C2218yescomplemented
37#15689420C2218yescomplemented
38#15689374C2218yescomplemented
39#15689357C2218yescomplemented
40#15689318C2218yescomplemented
41#15689256C2218yescomplemented
42#15689256C2218yescomplemented
43#15689233C2218yescomplemented
44#15689195C2218yescomplemented
45C2×#13093957C2211yescharacteristic, complemented
46C2×#13093955C2211yescharacteristic, complemented
47C2×#13093955C2211yescharacteristic, complemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49#15689127C2218yescomplemented
50C2×#13093945C2211yescharacteristic, complemented
51C2×#13093944C2211yescharacteristic
52C2×#13093944C2211yescharacteristic
53C2×#13093944C2211yescharacteristic
54C2×#13093944C2211yescharacteristic, complemented
55C2×#13093944C2211yescharacteristic, complemented
56C2×#13093944C2211yescharacteristic, complemented
57C2×#13093944C2211yescharacteristic, complemented
58C2×#13093944C2211yescharacteristic, complemented
59C2×#13093944C2211yescharacteristic, complemented
60C2×#13093944C2218yescomplemented
61C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
62C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×#13093935C2211yescharacteristic, complemented
64C47×#553—24no—
65C47×#553C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic, complemented
68C2×#123×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47C2211yescharacteristic, complemented
71C2×#121×C47C2211yescharacteristic, complemented
72C2×C4×D4×C47—21no—
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic, complemented
75C2×#117×C47C2211yescharacteristic, complemented
76C22×C4⋊C4×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C24×D47—21no—
79C22×D188—24no—
80C22×D188—24no—
81C22×D188—22no—
82C22×D188—22no—
83C22×D188—21no—
84C22×D188—21no—
85C22×D188—21no—
86C22×D188—21no—
87C22×D188—42no—
88C22×D188—42no—
89C22×D188C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×D188C2314yes—
92C22×D188C2314yes—
93C22×D188C2311yescharacteristic
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C2×D4×D47—28no—
97C2×D4×D47—48no—
98C22×C4×D47—21no—
99C2×#10625334—24no—
100C2×#10625334—42no—
101C2×#10625334—42no—
102C2×#10625334C2314yes—
103C2×#10625334C2314yescomplemented
104C2×#10625334C2314yescomplemented
105C2×#10625329—42no—
106C2×#10625329C2314yescomplemented
107C22×C47⋊C8—42no—
108C22×C47⋊C8C2311yescharacteristic
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2314yescomplemented
113#13094021—22no—
114#13094021C2314yes—
115#13093999—28no—
116#13093998—22no—
117#13093998—22no—
118#13093998C2314yes—
119#13093998C2314yes—
120#13093994—28no—
121#13093994—28no—
122C4×D188—22no—
123C4×D188C2314yes—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×(C2×D47)⋊C4—21no—
126C2×(C2×D47)⋊C4—21no—
127C2×(C2×D47)⋊C4—21no—
128#13093957C2314yescomplemented
129#13093955C2314yescomplemented
130#13093955C2314yescomplemented
131C4⋊(C47⋊C8)C2314yescomplemented
132#13093945C2314yescomplemented
133#13093944C2314yes—
134#13093944C2314yes—
135#13093944C2314yes—
136#13093944C2314yescomplemented
137#13093944C2314yescomplemented
138#13093944C2314yescomplemented
139#13093944C2314yescomplemented
140#13093944C2314yescomplemented
141#13093944C2314yescomplemented
142C22⋊(C47⋊C8)C2314yescomplemented
143C22⋊(C47⋊C8)C2314yescomplemented
144#13093935C2314yescomplemented
145C22×D4×C47—21no—
146C22×D4×C47—21no—
147C22×D4×C47D411yescharacteristic
148C22×D4×C47C2311yescharacteristic
149C23×C4×C47—21no—
150C23×C4×C47—21no—
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153#126×C47—28no—
154#125×C47—22no—
155#125×C47C2314yescomplemented
156#123×C47—28no—
157#121×C47—28no—
158#121×C47—22no—
159#121×C47—22no—
160#121×C47C2314yescomplemented
161#121×C47C2314yescomplemented
162C4×D4×C47—28no—
163C4×D4×C47—22no—
164C4×D4×C47D414yes—
165C4×D4×C47C2314yes—
166C4×D4×C47C2314yescomplemented
167#117×C47—22no—
168#117×C47C2314yescomplemented
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—22no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2314yescomplemented
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C42×C47—21no—
185C2×C42×C47C2311yescharacteristic
186C24×C47—21no—
187C24×C47C2×D411yescharacteristic
188C24×C47C2×D411yescharacteristic
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—24no—
194C23×D47—44no—
195C23×D47—44no—
196C23×D47—44no—
197C23×D47—44no—
198C23×D47—82no—
199C23×D47—82no—
200C2×D4×C47—24no—
201C2×D4×C47—24no—
202C2×D4×C47—24no—
203C2×D4×C47—21no—
204C2×D4×C47—22no—
205C2×D4×C47—22no—
206C2×D4×C47—44no—
207C2×D4×C47—82no—
208C2×D4×C47C2×D414yes—
209C2×D4×C47C2412yes—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—24no—
218C22×C4×C47—24no—
219C22×C4×C47—82no—
220C22×C4×C47—82no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D412yes—
226C22×C4×C47C2×D412yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—24no—
231C2×C22⋊D47—24no—
232C2×C22⋊D47—44no—
233C2×C22⋊D47—44no—
234C22×Dic47—21no—
235D4×D47—432no—
236C2×D188—21no—
237C2×D188—22no—
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—28no—
243C2×D188—28no—
244C2×D188—24no—
245C2×D188—24no—
246C2×D188—21no—
247C2×D188—21no—
248C2×D188—24no—
249C2×D188—24no—
250C2×D188—44no—
251C2×D188—44no—
252C2×D188—48no—
253C2×D188—48no—
254C2×D188—44no—
255C2×D188—44no—
256C2×D188—44no—
257C2×D188—82no—
258C2×D188#4114yes—
259C2×D188C2412yes—
260C2×D188C2412yes—
261C2×D188C2412yes—
262C2×C4×D47—24no—
263C2×C4×D47—44no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—24no—
267C4⋊C4×C47—24no—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47C2×D414yes—
271C4⋊C4×C47C2412yes—
272C4⋊C4×C47C2412yes—
273C4⋊C4×C47C2412yes—
274C22⋊C4×C47—24no—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—24no—
277C22⋊C4×C47—24no—
278C22⋊C4×C47C2×D414yes—
279C22⋊C4×C47C2×D414yes—
280C42×C47—24no—
281C42×C47C2×D412yes—
282C42×C47C2412yes—
283#10625334—28no—
284#10625334—44no—
285#10625334—44no—
286(C2×D47)⋊C4—24no—
287(C2×D47)⋊C4—24no—
288(C2×D47)⋊C4—24no—
289C4⋊Dic47—21no—
290C4⋊Dic47C2412yes—
291#10625329—44no—
292C2×C47⋊C8—22no—
293C2×C47⋊C8—22no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—44no—
297C2×C47⋊C8C2412yes—
298C2×C47⋊C8C2412yes—
299C2×C47⋊C8C2412yes—
300C2×C47⋊C8C2412yes—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—42no—
308C23×C47—42no—
309C23×C47—42no—
310C23×C47AGL(1,ℤ/8)14yes—
311C23×C47C22×D412yes—
312C23×C47C22×D412yes—
313C23×C47C22×D411yescharacteristic
314C22×D47—24no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—48no—
319C22×D47—48no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—48no—
323C22×D47—42no—
324C22×D47—42no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—48no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—84no—
331C22×D47—84no—
332C22×D47—816no—
333C22×D47—816no—
334D4×C47—28no—
335D4×C47—22no—
336D4×C47—22no—
337D4×C47—48no—
338D4×C47—42no—
339D4×C47—84no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—24no—
345C2×C4×C47—24no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—42no—
356C2×C4×C47—84no—
357C2×C4×C47—84no—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D412yes—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D412yes—
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4112yes—
364C2×C4×C47H(5,𝔽2)12yes—
365C2×C4×C47C2511yescharacteristic
366C22⋊D47—48no—
367C22⋊D47—48no—
368C2×Dic47—22no—
369C2×Dic47—42no—
370D188—24no—
371D188—22no—
372D188—22no—
373D188—22no—
374D188—22no—
375D188—22no—
376D188—48no—
377D188—48no—
378D188—48no—
379D188—42no—
380D188—42no—
381D188—84no—
382D188C2×#4114yes—
383C4×D47—48no—
384C47⋊C8—22no—
385C47⋊C8—22no—
386C47⋊C8—22no—
387C47⋊C8—22no—
388C2×#3318—471nomaximal, Sylow
389C22×C47—22no—
390C22×C47—28no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—22no—
395C22×C47—44no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—84no—
400C22×C47#54612yes—
401C22×C47C2×AGL(1,ℤ/8)14yes—
402C22×C47C2×AGL(1,ℤ/8)12yes—
403C22×C47#57612yes—
404C22×C47C23×D411yescharacteristic
405C2×D47—24no—
406C2×D47—48no—
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—42no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—816no—
416C2×D47—816no—
417C2×D47—84no—
418C2×D47—84no—
419C4×C47—22no—
420C4×C47—22no—
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—42no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47#54612yes—
427C4×C47C22×#4111yescharacteristic
428C4×C47C2×H(5,𝔽2)11yescharacteristic
429Dic47—42no—
430C2×#553D4711yescharacteristic, complemented
431C2×D42—471no—
432#3318—4716no—
433C2×#490—471no—
434C2×#481—471no—
435C2×#482—471no—
436C2×#478—471no—
437C2×#469—471no—
438C2×#466—471no—
439C2×#459—471no—
440C2×#447—471no—
441C2×#447—471no—
442C2×#442—471no—
443C2×#435—471no—
444C2×#418—471no—
445C22×#102—471no—
446C2×C47—24no—
447C2×C47—42no—
448C2×C47—82no—
449C2×C47#331814yescomplemented
450C2×C47C2×#54611yescharacteristic
451C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C47C2×#57611yescharacteristic
453D47—44no—
454D47—82no—
455D47—82no—
456C23×D4—471no—
457C23×D4—471no—
458C23×D4—941no—
459C22×D8—471no—
460C22×D8—471no—
461C22×D8—471no—
462C22×M16—471no—
463C23×C8—471no—
464#553—24no—
465#553C2×D4718yescomplemented
466D42—478no—
467D42—944no—
468C2×#127—471no—
469C2×#126—21no—
470C2×#125C2×D4711yescharacteristic, complemented
471C2×#123—21no—
472C2×#121—21no—
473C2×#121—471no—
474C2×#121—471no—
475C2×#121—941no—
476C2×#121C2×D4711yescharacteristic, complemented
477C2×#121C2×D4711yescharacteristic, complemented
478C2×#120—941no—
479C2×#120—941no—
480C2×C4×D4—21no—
481C2×C4×D4—471no—
482C2×C4×D4C2×D4711yescharacteristic
483C2×C4×D4C2×D4711yescharacteristic, complemented
484C2×#117C2×D4711yescharacteristic, complemented
485C22×C4⋊C4C2×D4711yescharacteristic, complemented
486#490—478no—
487#482—478no—
488#481—478no—
489#478—478no—
490#469—478no—
491#466—478no—
492#459—478no—
493#447—478no—
494#447—478no—
495#442—478no—
496#435—478no—
497C2×#107—471no—
498C2×#106—471no—
499C2×#106—471no—
500C2×C4⋊C8—471no—
501#418—478no—
502C2×#102—471no—
503C2×#102—471no—
504C2×#102—471no—
505C2×#102—471no—
506C2×#102—471no—
507C2×#102—471no—
508C2×#102—471no—
509C2×#102—471no—
510C2×#102—471no—
511C2×#102—471no—
512C2×#102—478no—
513C2×C22⋊C8—471no—
514C2×C22⋊C8—471no—
515C2×#97—471no—
516C47C2×#331811yescharacteristic, complemented, Sylow
517C25—941no—
518C25—941no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—471no—
522C22×D4—471no—
523C22×D4—471no—
524C22×D4—474no—
525C22×D4—474no—
526C22×D4—944no—
527C22×D4—944no—
528C22×D4—941no—
529C22×D4—941no—
530C22×D4—948no—
531C22×D4—941no—
532C22×D4—941no—
533C22×D4—941no—
534C22×D4—941no—
535C22×D4—942no—
536C22×D4—942no—
537C22×D4—1882no—
538C22×D4—1882no—
539C22×D4—1888no—
540C22×D4C22⋊D4711yescharacteristic
541C22×D4C22×D4711yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—941no—
545C23×C4C22×D4711yescharacteristic
546C23×C4C22×D4711yescharacteristic
547C2×D8—474no—
548C2×D8—474no—
549C2×D8—474no—
550C2×D8—944no—
551C2×D8—1882no—
552C2×D8—1882no—
553C2×M16—474no—
554C2×M16—1882no—
555C22×C8—471no—
556C22×C8—471no—
557C22×C8—471no—
558C22×C8—471no—
559C22×C8—474no—
560C22×C8—1882no—
561#127—474no—
562#127—942no—
563#126—28no—
564#125—22no—
565#125C22×D4714yescomplemented
566#123—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—474no—
571#121—474no—
572#121—942no—
573#121—942no—
574#121—948no—
575#121C22×D4714yescomplemented
576#121C22×D4714yescomplemented
577#120—948no—
578#120—948no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—474no—
582C4×D4—942no—
583C4×D4C22⋊D4714yes—
584C4×D4C22×D4714yes—
585C4×D4C22×D4714yescomplemented
586#117—22no—
587#117C22×D4714yescomplemented
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—471no—
593C2×C4⋊C4C22⋊D4711yescharacteristic
594C2×C4⋊C4C22×D4711yescharacteristic
595C2×C4⋊C4C22×D4711yescharacteristic
596C2×C4⋊C4C22×D4711yescharacteristic
597C2×C4⋊C4C22×D4714yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604C2×C22⋊C4—941no—
605C2×C22⋊C4C22⋊D4711yescharacteristic
606C2×C22⋊C4C22⋊D4711yescharacteristic
607C2×C42—21no—
608C2×C42C22×D4711yescharacteristic
609#107—474no—
610#106—474no—
611#106—474no—
612C4⋊C8—474no—
613#102—474no—
614#102—474no—
615#102—474no—
616#102—474no—
617#102—474no—
618#102—474no—
619#102—474no—
620#102—474no—
621#102—474no—
622#102—474no—
623C22⋊C8—474no—
624C22⋊C8—474no—
625#97—474no—
626C24—21no—
627C24—941no—
628C24—944no—
629C24—944no—
630C24—941no—
631C24—941no—
632C24—3762no—
633C24—3762no—
634C24—1884no—
635C24—1884no—
636C24—1884no—
637C24—1884no—
638C24C2×C22⋊D4711yescharacteristic
639C24C2×C22⋊D4711yescharacteristic
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—474no—
649C2×D4—472no—
650C2×D4—472no—
651C2×D4—472no—
652C2×D4—948no—
653C2×D4—948no—
654C2×D4—944no—
655C2×D4—944no—
656C2×D4—941no—
657C2×D4—944no—
658C2×D4—944no—
659C2×D4—944no—
660C2×D4—944no—
661C2×D4—941no—
662C2×D4—941no—
663C2×D4—942no—
664C2×D4—942no—
665C2×D4—942no—
666C2×D4—942no—
667C2×D4—942no—
668C2×D4—3762no—
669C2×D4—1884no—
670C2×D4—1884no—
671C2×D4—1888no—
672C2×D4—1888no—
673C2×D4—1884no—
674C2×D4—1884no—
675C2×D4—1884no—
676C2×D4—18832no—
677C2×D4—1884no—
678C2×D4—1884no—
679C2×D4C2×C22⋊D4714yes—
680C2×D4C23×D4712yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—82no—
691C22×C4—82no—
692C22×C4—941no—
693C22×C4—944no—
694C22×C4—1884no—
695C22×C4C2×C22⋊D4712yes—
696C22×C4C2×C22⋊D4712yes—
697C22×C4C2×C22⋊D4711yescharacteristic
698C22×C4C2×C22⋊D4711yescharacteristic
699C22×C4C2×C22⋊D4711yescharacteristic
700C22×C4C2×C22⋊D4711yescharacteristic
701C22×C4C23×D4712yes—
702C22×C4C23×D4712yes—
703C22×C4C23×D4711yescharacteristic
704D8—948no—
705D8—1884no—
706D8—1884no—
707M16—1884no—
708C2×C8—472no—
709C2×C8—472no—
710C2×C8—472no—
711C2×C8—472no—
712C2×C8—942no—
713C2×C8—942no—
714C2×C8—942no—
715C2×C8—942no—
716C2×C8—1884no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—472no—
724C4⋊C4—941no—
725C4⋊C4C2×C22⋊D4714yes—
726C4⋊C4C23×D4712yes—
727C4⋊C4C23×D4712yes—
728C4⋊C4C23×D4712yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C22⋊C4C2×C22⋊D4714yes—
737C22⋊C4C2×C22⋊D4714yes—
738C42—24no—
739C42C2×C22⋊D4712yes—
740C42C23×D4712yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—944no—
751C23—942no—
752C23—942no—
753C23—942no—
754C23—37616no—
755C23—3764no—
756C23—3764no—
757C23—37616no—
758C23—1888no—
759C23—1888no—
760C23—1888no—
761C23—1882no—
762C23—1882no—
763C23—1888no—
764C23—1882no—
765C23—1882no—
766C23—1882no—
767C23—1882no—
768C23—1882no—
769C23—1882no—
770C23#1309404914yes—
771C23C22×C22⋊D4712yes—
772C23C22×C22⋊D4712yes—
773C23C22×C22⋊D4711yescharacteristic
774D4—28no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—84no—
780D4—474no—
781D4—944no—
782D4—942no—
783D4—942no—
784D4—942no—
785D4—942no—
786D4—942no—
787D4—3764no—
788D4—1888no—
789D4—1888no—
790D4—1888no—
791D4—1888no—
792D4—1888no—
793D4—1882no—
794D4—1882no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—942no—
814C2×C4—1888no—
815C2×C4—1882no—
816C2×C4C22×C22⋊D4712yes—
817C2×C4C22×C22⋊D4712yes—
818C2×C4C22×C22⋊D4712yes—
819C2×C4C22×C22⋊D4712yes—
820C2×C4C22×C22⋊D4711yescharacteristic
821C2×C4#41×D4712yes—
822C2×C4#1309407012yes—
823C2×C4C24×D4711yescharacteristic
824C8—942no—
825C8—942no—
826C8—942no—
827C8—942no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22—944no—
840C22—37616no—
841C22—37616no—
842C22—3764no—
843C22—3764no—
844C22—1882no—
845C22—1882no—
846C22—1882no—
847C22—1882no—
848C22—1882no—
849C22—1882no—
850C22—1888no—
851C22—1882no—
852C22—1882no—
853C22#1568976112yes—
854C22C2×#1309404914yes—
855C22C2×#1309404912yes—
856C22#1568992612yes—
857C22C23×C22⋊D4711yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—1882no—
866C4#1568976112yes—
867C4C2×#41×D4711yescharacteristic
868C4C2×#1309407011yescharacteristic
869C2—24no—
870C2—42no—
871C2—82no—
872C2—3762no—
873C2—3762no—
874C2—1884no—
875C2#2025552314yesdirect product factor
876C2C2×#1568976111yescharacteristic
877C2C22×#1309404911yescharacteristic
878C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3318
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×D188C2semidirect
2. #20255523C2direct (N × H)
3. C2×#15689489C2semidirect
4. C2×#15689441C2semidirect
5. C2×#15689447C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689357C2semidirect
9. C2×#15689318C2semidirect
10. C2×#15689256C2semidirect
11. C2×#15689256C2semidirect
12. C2×#15689233C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689127C2semidirect
15. C22×#13093944C2semidirect
16. C2×C47×#553C2semidirect
21. C22×#10625334C22semidirect
22. C22×#10625334C22semidirect
23. C22×#10625329C22semidirect
24. C23×C47⋊C8C22semidirect
26. D4×D188C22semidirect
34. #15689489C22semidirect
35. #15689447C22semidirect
36. #15689441C22semidirect
37. #15689420C22semidirect
38. #15689374C22semidirect
39. #15689357C22semidirect
40. #15689318C22semidirect
41. #15689256C22semidirect
42. #15689256C22semidirect
43. #15689233C22semidirect
44. #15689195C22semidirect
45. C2×#13093957C22semidirect
46. C2×#13093955C22semidirect
47. C2×#13093955C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. #15689127C22semidirect
50. C2×#13093945C22semidirect
54. C2×#13093944C22semidirect
55. C2×#13093944C22semidirect
56. C2×#13093944C22semidirect
57. C2×#13093944C22semidirect
58. C2×#13093944C22semidirect
59. C2×#13093944C22semidirect
60. C2×#13093944C22semidirect
61. C2×C22⋊(C47⋊C8)C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×#13093935C22semidirect
65. C47×#553C22semidirect
67. C2×#125×C47C22semidirect
70. C2×#121×C47C22semidirect
71. C2×#121×C47C22semidirect
74. C2×C4×D4×C47C22semidirect
75. C2×#117×C47C22semidirect
76. C22×C4⋊C4×C47C22semidirect
103. C2×#10625334C23semidirect
104. C2×#10625334C23semidirect
106. C2×#10625329C23semidirect
112. C22×C47⋊C8C23semidirect
128. #13093957C23semidirect
129. #13093955C23semidirect
130. #13093955C23semidirect
131. C4⋊(C47⋊C8)C23semidirect
132. #13093945C23semidirect
136. #13093944C23semidirect
137. #13093944C23semidirect
138. #13093944C23semidirect
139. #13093944C23semidirect
140. #13093944C23semidirect
141. #13093944C23semidirect
142. C22⋊(C47⋊C8)C23semidirect
143. C22⋊(C47⋊C8)C23semidirect
144. #13093935C23semidirect
155. #125×C47C23semidirect
160. #121×C47C23semidirect
161. #121×C47C23semidirect
166. C4×D4×C47C23semidirect
168. #117×C47C23semidirect
177. C2×C4⋊C4×C47C23semidirect
430. C2×#553D47semidirect
449. C2×C47#3318semidirect
465. #553C2×D47semidirect
470. C2×#125C2×D47semidirect
476. C2×#121C2×D47semidirect
477. C2×#121C2×D47semidirect
483. C2×C4×D4C2×D47semidirect
484. C2×#117C2×D47semidirect
485. C22×C4⋊C4C2×D47semidirect
516. C47C2×#3318semidirect
565. #125C22×D47semidirect
575. #121C22×D47semidirect
576. #121C22×D47semidirect
585. C4×D4C22×D47semidirect
587. #117C22×D47semidirect
597. C2×C4⋊C4C22×D47semidirect
875. C2#20255523direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D4×D1882
#202555232
C2×#156894892
C2×#156894412
C2×#156894472
C2×#156894202
C2×#156893742
C2×#156893572
C2×#156893182
C2×#156892562
C2×#156892332
C2×#156891952
C2×#156891272
C22×#130939442
C2×C47×#5532
C2×#331847