Finite Group Databasebeta

← C47×#14135 #26053833

Subgroups — C47×#14135 #26053833

Order 12032.

2634 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C47C211yesmaximal, characteristic
2C22×#117×C47C211yesmaximal, characteristic, complemented
3C2×C47×#386C212yesmaximal
4C22×#95×C47C211yesmaximal, characteristic, complemented
5C47×#1441C212yesmaximal, complemented
6C47×#1439C212yesmaximal, complemented
7C47×#1437C212yesmaximal, complemented
8C47×#1436C212yesmaximal, complemented
9C47×C22⋊#95C212yesmaximal, complemented
10C23×D4×C47C2211yescharacteristic
11C24×C4×C47C2212yes—
12C24×C4×C47C2211yescharacteristic
13C2×#123×C47—24no—
14C2×#123×C47—24no—
15C2×#123×C47C418yescomplemented
16C2×#117×C47—24no—
17C2×#117×C47—28no—
18C22×C4⋊C4×C47C2212yes—
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2214yes—
22C22×C22⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2212yes—
26C22×C42×C47C2212yes—
27C47×#386—28no—
28C2×#95×C47—24no—
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2214yes—
32C2×#95×C47C2214yes—
33C2×#95×C47C2214yes—
34C25×C47C2311yescharacteristic
35C25×C47C2311yescharacteristic
36C22×D4×C47—22no—
37C22×D4×C47—22no—
38C22×D4×C47—24no—
39C22×D4×C47—24no—
40C22×D4×C47C2×C414yes—
41C23×C4×C47—24no—
42C23×C4×C47—24no—
43C23×C4×C47—24no—
44C23×C4×C47—28no—
45C23×C4×C47—24no—
46C23×C4×C47—24no—
47C23×C4×C47—44no—
48C23×C4×C47C2×C414yes—
49C23×C4×C47D414yes—
50C23×C4×C47D414yes—
51C23×C4×C47C2311yescharacteristic
52C23×C4×C47C2311yescharacteristic
53C23×C4×C47C2311yescharacteristic
54C23×C4×C47C2314yes—
55C23×C4×C47C2314yes—
56C23×C4×C47C2311yescharacteristic
57C23×C4×C47C2311yescharacteristic
58#123×C47—232no—
59#117×C47—232no—
60C2×C4⋊C4×C47—28no—
61C2×C4⋊C4×C47—24no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47—22no—
65C2×C4⋊C4×C47—22no—
66C2×C4⋊C4×C47C2×C414yescomplemented
67C2×C4⋊C4×C47C2×C414yescomplemented
68C2×C22⋊C4×C47—24no—
69C2×C22⋊C4×C47—24no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—22no—
74C2×C22⋊C4×C47—22no—
75C2×C22⋊C4×C47—22no—
76C2×C22⋊C4×C47—28no—
77C2×C22⋊C4×C47—28no—
78C2×C22⋊C4×C47—44no—
79C2×C22⋊C4×C47C2×C414yes—
80C2×C22⋊C4×C47C2×C414yescomplemented
81C2×C22⋊C4×C47C2×C414yescomplemented
82C2×C22⋊C4×C47D418yes—
83C2×C42×C47—28no—
84C2×C42×C47—24no—
85#95×C47—24no—
86#95×C47—24no—
87#95×C47—28no—
88#95×C47—28no—
89#95×C47—44no—
90C24×C47—24no—
91C24×C47—22no—
92C24×C47—22no—
93C24×C47—21no—
94C24×C47—21no—
95C24×C47—22no—
96C24×C47—24no—
97C24×C47—22no—
98C24×C47—22no—
99C24×C47—22no—
100C24×C47C22×C412yes—
101C24×C47C22×C412yes—
102C24×C47C2×D412yes—
103C24×C47C2×D412yes—
104C24×C47C2×D414yes—
105C24×C47#4114yes—
106C24×C47C2411yescharacteristic
107C2×D4×C47—28no—
108C2×D4×C47—216no—
109C2×D4×C47—44no—
110C2×D4×C47—48no—
111C2×D4×C47—44no—
112C22×C4×C47—216no—
113C22×C4×C47—28no—
114C22×C4×C47—216no—
115C22×C4×C47—28no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—216no—
121C22×C4×C47—24no—
122C22×C4×C47—24no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—24no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—24no—
131C22×C4×C47—22no—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—22no—
136C22×C4×C47—24no—
137C22×C4×C47—24no—
138C22×C4×C47—24no—
139C22×C4×C47—24no—
140C22×C4×C47—24no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—24no—
144C22×C4×C47—416no—
145C22×C4×C47—416no—
146C22×C4×C47—48no—
147C22×C4×C47—48no—
148C22×C4×C47C22⋊C4116yescomplemented
149C22×C4×C47C22×C412yes—
150C22×C4×C47C22×C412yes—
151C22×C4×C47C22×C412yes—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C2×D418yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47#4118yes—
160C4⋊C4×C47—216no—
161C4⋊C4×C47—28no—
162C4⋊C4×C47—28no—
163C22⋊C4×C47—28no—
164C22⋊C4×C47—216no—
165C22⋊C4×C47—28no—
166C22⋊C4×C47—28no—
167C22⋊C4×C47—416no—
168C42×C47—216no—
169C23×C47—24no—
170C23×C47—24no—
171C23×C47—24no—
172C23×C47—24no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—24no—
176C23×C47—28no—
177C23×C47—28no—
178C23×C47—28no—
179C23×C47—28no—
180C23×C47—22no—
181C23×C47—24no—
182C23×C47—24no—
183C23×C47—24no—
184C23×C47—41no—
185C23×C47—42no—
186C23×C47—41no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—42no—
192C23×C47—44no—
193C23×C47—44no—
194C23×C47—44no—
195C23×C47—44no—
196C23×C47C2×C22⋊C414yes—
197C23×C47C4×D418yes—
198C23×C47#12014yes—
199C23×C47#12118yes—
200C23×C47#12314yes—
201C23×C47C23×C411yescharacteristic
202C23×C47C22×D411yescharacteristic
203C23×C47C22×D411yescharacteristic
204C23×C47C22×D412yes—
205C23×C47C2×#4112yes—
206C23×C47C2×#4114yes—
207C23×C47H(5,𝔽2)12yes—
208C23×C472−1+412yes—
209D4×C47—416no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—232no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—28no—
226C2×C4×C47—28no—
227C2×C4×C47—28no—
228C2×C4×C47—28no—
229C2×C4×C47—28no—
230C2×C4×C47—28no—
231C2×C4×C47—432no—
232C2×C4×C47—41no—
233C2×C4×C47—44no—
234C2×C4×C47—42no—
235C2×C4×C47—41no—
236C2×C4×C47—42no—
237C2×C4×C47—44no—
238C2×C4×C47—42no—
239C2×C4×C47—41no—
240C2×C4×C47—44no—
241C2×C4×C47—41no—
242C2×C4×C47—42no—
243C2×C4×C47—44no—
244C2×C4×C47—44no—
245C2×C4×C47—44no—
246C2×C4×C47—44no—
247C2×C4×C47—44no—
248C2×C4×C47C2×C22⋊C414yes—
249C2×C4×C47C2×C22⋊C414yes—
250#14135C4711yesmaximal, characteristic, direct product factor, Sylow
251C22×C47—24no—
252C22×C47—216no—
253C22×C47—28no—
254C22×C47—28no—
255C22×C47—28no—
256C22×C47—28no—
257C22×C47—24no—
258C22×C47—42no—
259C22×C47—48no—
260C22×C47—42no—
261C22×C47—42no—
262C22×C47—82no—
263C22×C47—82no—
264C22×C47—82no—
265C22×C47—82no—
266C22×C47#38618yes—
267C22×C47C22×C22⋊C411yescharacteristic
268C22×C47C2×C4×D412yes—
269C22×C47C4×#4112yes—
270C22×C47#52012yes—
271C22×C47C2×#12011yescharacteristic
272C22×C47C2×#12112yes—
273C22×C47C2×#12311yescharacteristic
274C22×C47#52512yes—
275C22×C47#53212yes—
276C22×C47#53511yescharacteristic
277C22×C47#53611yescharacteristic
278C22×C47#53712yes—
279C22×C47#54614yes—
280C22×C47#54714yes—
281C22×C47#55114yes—
282C22×C47#55214yes—
283C4×C47—24no—
284C4×C47—24no—
285C4×C47—42no—
286C4×C47—48no—
287C4×C47—48no—
288C4×C47—42no—
289C4×C47—42no—
290C22×#123C2×C4711yescharacteristic
291C22×#117C2×C4711yescharacteristic, complemented
292C2×#386C2×C4712yes—
293C22×#95C2×C4711yescharacteristic, complemented
294#1441C2×C4712yescomplemented
295#1439C2×C4712yescomplemented
296#1437C2×C4712yescomplemented
297#1436C2×C4712yescomplemented
298C22⋊#95C2×C4712yescomplemented
299C2×C47—28no—
300C2×C47—82no—
301C2×C47C2×#38611yescharacteristic
302C2×C47#229711yescharacteristic
303C2×C47#231111yescharacteristic
304C2×C47#235914yes—
305C2×C47#241112yes—
306C2×C47#241312yes—
307C2×C47#243012yes—
308C2×C47#249812yes—
309C23×D4C22×C4711yescharacteristic
310C24×C4C22×C4712yes—
311C24×C4C22×C4711yescharacteristic
312C2×#123—24no—
313C2×#123—24no—
314C2×#123C4×C4718yescomplemented
315C2×#117—24no—
316C2×#117—28no—
317C22×C4⋊C4C22×C4712yes—
318C22×C4⋊C4C22×C4711yescharacteristic
319C22×C4⋊C4C22×C4711yescharacteristic
320C22×C22⋊C4C22×C4714yes—
321C22×C22⋊C4C22×C4711yescharacteristic
322C22×C22⋊C4C22×C4711yescharacteristic
323C22×C22⋊C4C22×C4711yescharacteristic
324C22×C22⋊C4C22×C4712yes—
325C22×C42C22×C4712yes—
326#386—28no—
327C2×#95—24no—
328C2×#95C22×C4714yes—
329C2×#95C22×C4712yes—
330C2×#95C22×C4714yes—
331C2×#95C22×C4712yes—
332C2×#95C22×C4714yes—
333C47#1413511yescharacteristic, direct product factor, Sylow
334C25C23×C4711yescharacteristic
335C25C23×C4711yescharacteristic
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4C2×C4×C4714yes—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—28no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—44no—
348C23×C4C2×C4×C4714yes—
349C23×C4D4×C4714yes—
350C23×C4D4×C4714yes—
351C23×C4C23×C4711yescharacteristic
352C23×C4C23×C4711yescharacteristic
353C23×C4C23×C4711yescharacteristic
354C23×C4C23×C4714yes—
355C23×C4C23×C4714yes—
356C23×C4C23×C4711yescharacteristic
357C23×C4C23×C4711yescharacteristic
358#123—232no—
359#117—232no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4C2×C4×C4714yescomplemented
367C2×C4⋊C4C2×C4×C4714yescomplemented
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4C2×C4×C4714yes—
380C2×C22⋊C4C2×C4×C4714yescomplemented
381C2×C22⋊C4C2×C4×C4714yescomplemented
382C2×C22⋊C4D4×C4718yes—
383C2×C42—28no—
384C2×C42—24no—
385#95—24no—
386#95—24no—
387#95—28no—
388#95—28no—
389#95—44no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24C22×C4×C4712yes—
401C24C22×C4×C4712yes—
402C24C2×D4×C4712yes—
403C24C2×D4×C4712yes—
404C24C2×D4×C4714yes—
405C24#41×C4714yes—
406C24C24×C4711yescharacteristic
407C2×D4—28no—
408C2×D4—216no—
409C2×D4—44no—
410C2×D4—48no—
411C2×D4—44no—
412C22×C4—216no—
413C22×C4—28no—
414C22×C4—216no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—216no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—416no—
445C22×C4—416no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4C22⋊C4×C47116yescomplemented
449C22×C4C22×C4×C4712yes—
450C22×C4C22×C4×C4712yes—
451C22×C4C22×C4×C4712yes—
452C22×C4C22×C4×C4712yes—
453C22×C4C22×C4×C4712yes—
454C22×C4C2×D4×C4718yes—
455C22×C4C2×D4×C4712yes—
456C22×C4C2×D4×C4712yes—
457C22×C4C2×D4×C4712yes—
458C22×C4C2×D4×C4712yes—
459C22×C4#41×C4718yes—
460C4⋊C4—216no—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—216no—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—416no—
468C42—216no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—22no—
474C23—22no—
475C23—24no—
476C23—28no—
477C23—28no—
478C23—28no—
479C23—28no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23C2×C22⋊C4×C4714yes—
497C23C4×D4×C4718yes—
498C23#120×C4714yes—
499C23#121×C4718yes—
500C23#123×C4714yes—
501C23C23×C4×C4711yescharacteristic
502C23C22×D4×C4711yescharacteristic
503C23C22×D4×C4711yescharacteristic
504C23C22×D4×C4712yes—
505C23C2×#41×C4712yes—
506C23C2×#41×C4714yes—
507C23H(5,𝔽2)×C4712yes—
508C232−1+4×C4712yes—
509D4—416no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—232no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—28no—
526C2×C4—28no—
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—432no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4C2×C22⋊C4×C4714yes—
549C2×C4C2×C22⋊C4×C4714yes—
550C22—24no—
551C22—24no—
552C22—216no—
553C22—28no—
554C22—28no—
555C22—28no—
556C22—28no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—48no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22C47×#38618yes—
566C22C22×C22⋊C4×C4711yescharacteristic
567C22C2×C4×D4×C4712yes—
568C22C4×#41×C4712yes—
569C22C47×#52012yes—
570C22C2×#120×C4711yescharacteristic
571C22C2×#121×C4712yes—
572C22C2×#123×C4711yescharacteristic
573C22C47×#52512yes—
574C22C47×#53212yes—
575C22C47×#53511yescharacteristic
576C22C47×#53611yescharacteristic
577C22C47×#53712yes—
578C22C47×#54614yes—
579C22C47×#54714yes—
580C22C47×#55114yes—
581C22C47×#55214yes—
582C4—24no—
583C4—24no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—48no—
588C4—48no—
589C2—28no—
590C2—82no—
591C2C2×C47×#38611yescharacteristic
592C2C47×#229711yescharacteristic
593C2C47×#231111yescharacteristic
594C2C47×#235914yes—
595C2C47×#241112yes—
596C2C47×#241312yes—
597C2C47×#243012yes—
598C2C47×#249812yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#117×C47C2semidirect
4. C22×#95×C47C2semidirect
5. C47×#1441C2semidirect
6. C47×#1439C2semidirect
7. C47×#1437C2semidirect
8. C47×#1436C2semidirect
9. C47×C22⋊#95C2semidirect
15. C2×#123×C47C4semidirect
66. C2×C4⋊C4×C47C2×C4semidirect
67. C2×C4⋊C4×C47C2×C4semidirect
80. C2×C22⋊C4×C47C2×C4semidirect
81. C2×C22⋊C4×C47C2×C4semidirect
148. C22×C4×C47C22⋊C4semidirect
250. #14135C47direct (N × H)
291. C22×#117C2×C47semidirect
293. C22×#95C2×C47semidirect
294. #1441C2×C47semidirect
295. #1439C2×C47semidirect
296. #1437C2×C47semidirect
297. #1436C2×C47semidirect
298. C22⋊#95C2×C47semidirect
314. C2×#123C4×C47semidirect
333. C47#14135direct (N × H)
366. C2×C4⋊C4C2×C4×C47semidirect
367. C2×C4⋊C4C2×C4×C47semidirect
380. C2×C22⋊C4C2×C4×C47semidirect
381. C2×C22⋊C4C2×C4×C47semidirect
448. C22×C4C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C472
C22×#117×C472
C2×C47×#3862
C22×#95×C472
C47×#14412
C47×#14392
C47×#14372
C47×#14362
C47×C22⋊#952
#1413547