Finite Group Databasebeta

← C47×#11043 #26050741

Subgroups — C47×#11043 #26050741

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C47C212yesmaximal
2C2×C47×#386C211yesmaximal, characteristic
3C2×C47×#380C211yesmaximal, characteristic, complemented
4C2×C47×#342C212yesmaximal, complemented
5C47×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C47C2211yescharacteristic
7C24×C4×C47C2211yescharacteristic
8C22×C4⋊C4×C47—21no—
9C22×C22⋊C4×C47C412yescomplemented
10C22×C22⋊C4×C47C2211yescharacteristic
11C22×C22⋊C4×C47C2212yes—
12C22×C22⋊C4×C47C2212yes—
13C2×#99×C47—24no—
14C2×#99×C47—24no—
15C2×#99×C47—24no—
16C47×#386—21no—
17C47×#386—22no—
18C47×#386—21no—
19C47×#380—24no—
20C2×#95×C47—21no—
21C2×#95×C47—22no—
22C2×#95×C47C412yescomplemented
23C47×#342—24no—
24C25×C47C2×C411yescharacteristic
25C25×C47C2311yescharacteristic
26C22×D4×C47—21no—
27C22×D4×C47—21no—
28C22×D4×C47—22no—
29C22×D4×C47—22no—
30C22×D4×C47—21no—
31C22×D4×C47—21no—
32C22×D4×C47—22no—
33C22×D4×C47—22no—
34C22×D4×C47D412yes—
35C22×D4×C47Q812yes—
36C23×C4×C47—22no—
37C23×C4×C47—22no—
38C23×C4×C47—22no—
39C23×C4×C47—22no—
40C23×C4×C47—44no—
41C23×C4×C47C2×C411yescharacteristic
42C23×C4×C47C2×C412yes—
43C23×C4×C47C2×C412yes—
44C23×C4×C47D411yescharacteristic
45C23×C4×C47D412yes—
46C23×C4×C47D411yescharacteristic
47C2×C4⋊C4×C47—24no—
48C2×C4⋊C4×C47—44no—
49C2×C22⋊C4×C47—22no—
50C2×C22⋊C4×C47—22no—
51C2×C22⋊C4×C47—22no—
52C2×C22⋊C4×C47—22no—
53C2×C22⋊C4×C47—22no—
54C2×C22⋊C4×C47—22no—
55C2×C22⋊C4×C47—22no—
56C2×C22⋊C4×C47—22no—
57C2×C22⋊C4×C47—22no—
58C2×C22⋊C4×C47—22no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—22no—
62C2×C22⋊C4×C47—22no—
63C2×C22⋊C4×C47—22no—
64C2×C22⋊C4×C47—22no—
65C2×C22⋊C4×C47—44no—
66C2×C22⋊C4×C47D414yes—
67C2×C22⋊C4×C47D414yes—
68#99×C47—216no—
69#95×C47—24no—
70#95×C47—22no—
71#95×C47—22no—
72#95×C47—44no—
73C24×C47—21no—
74C24×C47—21no—
75C24×C47—22no—
76C24×C47—22no—
77C24×C47—42no—
78C24×C47—42no—
79C24×C47—42no—
80C24×C47—42no—
81C24×C47C4⋊C412yescomplemented
82C24×C47C22×C411yescharacteristic
83C24×C47C2×D411yescharacteristic
84C24×C47C2×D411yescharacteristic
85C24×C47C2×D411yescharacteristic
86C24×C47C2×D412yes—
87C24×C47C2×D412yes—
88C24×C47C2×Q811yescharacteristic
89C24×C47#4111yescharacteristic
90C24×C47#4111yescharacteristic
91C24×C47#4112yes—
92C24×C47#4112yes—
93C2×D4×C47—24no—
94C2×D4×C47—22no—
95C2×D4×C47—22no—
96C2×D4×C47—22no—
97C2×D4×C47—22no—
98C2×D4×C47—24no—
99C2×D4×C47—24no—
100C2×D4×C47—24no—
101C2×D4×C47—41no—
102C2×D4×C47—42no—
103C2×D4×C47—42no—
104C2×D4×C47—42no—
105C2×D4×C47—41no—
106C2×D4×C47—42no—
107C2×D4×C47—42no—
108C2×D4×C47—41no—
109C2×D4×C47—42no—
110C2×D4×C47—41no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—24no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—24no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—24no—
121C22×C4×C47—21no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—22no—
125C22×C4×C47—24no—
126C22×C4×C47—24no—
127C22×C4×C47—24no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47—48no—
132C22×C4×C47—48no—
133C22×C4×C47—44no—
134C22×C4×C47—44no—
135C22×C4×C47—44no—
136C22×C4×C47—44no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47C22⋊C412yes—
144C22×C4×C47C22⋊C412yes—
145C22×C4×C47C4⋊C412yescomplemented
146C4⋊C4×C47—48no—
147C22⋊C4×C47—24no—
148C22⋊C4×C47—24no—
149C22⋊C4×C47—24no—
150C22⋊C4×C47—24no—
151C22⋊C4×C47—44no—
152C22⋊C4×C47—42no—
153C22⋊C4×C47—42no—
154C22⋊C4×C47—42no—
155C22⋊C4×C47—42no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—42no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47—44no—
160C23×C47—22no—
161C23×C47—22no—
162C23×C47—22no—
163C23×C47—22no—
164C23×C47—22no—
165C23×C47—22no—
166C23×C47—22no—
167C23×C47—24no—
168C23×C47—42no—
169C23×C47—42no—
170C23×C47—42no—
171C23×C47—42no—
172C23×C47—44no—
173C23×C47—42no—
174C23×C47—42no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47—44no—
178C23×C47—44no—
179C23×C47—44no—
180C23×C47—41no—
181C23×C47—42no—
182C23×C47—41no—
183C23×C47—42no—
184C23×C47—42no—
185C23×C47—82no—
186C23×C47—82no—
187C23×C47—84no—
188C23×C47C2×C22⋊C411yescharacteristic
189C23×C47C2×C4⋊C411yescharacteristic
190C23×C47#11711yescharacteristic
191C23×C47C4×D412yes—
192C23×C47C4×D412yes—
193C23×C47#12011yescharacteristic
194C23×C47#12012yes—
195C23×C47#12111yescharacteristic
196C23×C47#12111yescharacteristic
197C23×C47#12112yes—
198C23×C47#12112yes—
199C23×C47#12112yes—
200C23×C47C22⋊Q811yescharacteristic
201C23×C47C22⋊Q811yescharacteristic
202C23×C47C22⋊Q812yes—
203C23×C47C22⋊Q812yes—
204C23×C47#12311yescharacteristic
205C23×C47#12312yes—
206C23×C47#12312yes—
207C23×C47#12411yescharacteristic
208C23×C47#12412yes—
209C23×C47#12612yes—
210C23×C47#12711yescharacteristic
211D4×C47—42no—
212D4×C47—42no—
213D4×C47—44no—
214D4×C47—44no—
215D4×C47—42no—
216D4×C47—42no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—24no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—48no—
227C2×C4×C47—48no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—42no—
232C2×C4×C47—41no—
233C2×C4×C47—44no—
234C2×C4×C47—44no—
235C2×C4×C47—48no—
236C2×C4×C47—42no—
237C2×C4×C47—44no—
238C2×C4×C47—44no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—84no—
242C2×C4×C47—84no—
243C2×C4×C47—82no—
244C2×C4×C47—82no—
245C2×C4×C47—84no—
246C2×C4×C47—84no—
247C2×C4×C47#9914yescomplemented
248#11043C4711yesmaximal, characteristic, direct product factor, Sylow
249C22×C47—22no—
250C22×C47—22no—
251C22×C47—22no—
252C22×C47—22no—
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—22no—
258C22×C47—22no—
259C22×C47—21no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—21no—
263C22×C47—24no—
264C22×C47—22no—
265C22×C47—24no—
266C22×C47—22no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—44no—
276C22×C47—42no—
277C22×C47—84no—
278C22×C47—84no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—82no—
282C22×C47#38011yescharacteristic
283C22×C47#38512yes—
284C22×C47#38611yescharacteristic
285C22×C47#38812yes—
286C22×C47#39011yescharacteristic
287C22×C47#39211yescharacteristic
288C22×C47#39311yescharacteristic
289C22×C47#39412yes—
290C22×C47#39612yes—
291C22×C47#39711yescharacteristic
292C22×C47#39911yescharacteristic
293C22×C47C2×#9912yes—
294C22×C47#41012yes—
295C4×C47—24no—
296C4×C47—42no—
297C4×C47—42no—
298C4×C47—84no—
299C4×C47—84no—
300C4×C47—82no—
301C22×#99C2×C4712yes—
302C2×#386C2×C4711yescharacteristic
303C2×#380C2×C4711yescharacteristic, complemented
304C2×#342C2×C4712yescomplemented
305C22⋊#95C2×C4711yescharacteristic, complemented
306C2×C47—21no—
307C2×C47—22no—
308C2×C47—22no—
309C2×C47—22no—
310C2×C47—21no—
311C2×C47—22no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—82no—
315C2×C47#143911yescharacteristic
316C2×C47#179912yes—
317C2×C47#189811yescharacteristic
318C2×C47#189911yescharacteristic
319C2×C47#196412yes—
320C23×D4C22×C4711yescharacteristic
321C24×C4C22×C4711yescharacteristic
322C22×C4⋊C4—21no—
323C22×C22⋊C4C4×C4712yescomplemented
324C22×C22⋊C4C22×C4711yescharacteristic
325C22×C22⋊C4C22×C4712yes—
326C22×C22⋊C4C22×C4712yes—
327C2×#99—24no—
328C2×#99—24no—
329C2×#99—24no—
330#386—21no—
331#386—22no—
332#386—21no—
333#380—24no—
334C2×#95—21no—
335C2×#95—22no—
336C2×#95C4×C4712yescomplemented
337#342—24no—
338C47#1104311yescharacteristic, direct product factor, Sylow
339C25C2×C4×C4711yescharacteristic
340C25C23×C4711yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4D4×C4712yes—
350C22×D4Q8×C4712yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—44no—
356C23×C4C2×C4×C4711yescharacteristic
357C23×C4C2×C4×C4712yes—
358C23×C4C2×C4×C4712yes—
359C23×C4D4×C4711yescharacteristic
360C23×C4D4×C4712yes—
361C23×C4D4×C4711yescharacteristic
362C2×C4⋊C4—24no—
363C2×C4⋊C4—44no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4D4×C4714yes—
382C2×C22⋊C4D4×C4714yes—
383#99—216no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—44no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C4⋊C4×C4712yescomplemented
397C24C22×C4×C4711yescharacteristic
398C24C2×D4×C4711yescharacteristic
399C24C2×D4×C4711yescharacteristic
400C24C2×D4×C4711yescharacteristic
401C24C2×D4×C4712yes—
402C24C2×D4×C4712yes—
403C24C2×Q8×C4711yescharacteristic
404C24#41×C4711yescharacteristic
405C24#41×C4711yescharacteristic
406C24#41×C4712yes—
407C24#41×C4712yes—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C22⋊C4×C4712yes—
459C22×C4C22⋊C4×C4712yes—
460C22×C4C4⋊C4×C4712yescomplemented
461C4⋊C4—48no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—44no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—41no—
474C22⋊C4—44no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—41no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—42no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23C2×C22⋊C4×C4711yescharacteristic
504C23C2×C4⋊C4×C4711yescharacteristic
505C23#117×C4711yescharacteristic
506C23C4×D4×C4712yes—
507C23C4×D4×C4712yes—
508C23#120×C4711yescharacteristic
509C23#120×C4712yes—
510C23#121×C4711yescharacteristic
511C23#121×C4711yescharacteristic
512C23#121×C4712yes—
513C23#121×C4712yes—
514C23#121×C4712yes—
515C23C22⋊Q8×C4711yescharacteristic
516C23C22⋊Q8×C4711yescharacteristic
517C23C22⋊Q8×C4712yes—
518C23C22⋊Q8×C4712yes—
519C23#123×C4711yescharacteristic
520C23#123×C4712yes—
521C23#123×C4712yes—
522C23#124×C4711yescharacteristic
523C23#124×C4712yes—
524C23#126×C4712yes—
525C23#127×C4711yescharacteristic
526D4—42no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—48no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—84no—
561C2×C4—84no—
562C2×C4#99×C4714yescomplemented
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—21no—
577C22—24no—
578C22—22no—
579C22—24no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—84no—
592C22—84no—
593C22—81no—
594C22—81no—
595C22—82no—
596C22C47×#38011yescharacteristic
597C22C47×#38512yes—
598C22C47×#38611yescharacteristic
599C22C47×#38812yes—
600C22C47×#39011yescharacteristic
601C22C47×#39211yescharacteristic
602C22C47×#39311yescharacteristic
603C22C47×#39412yes—
604C22C47×#39612yes—
605C22C47×#39711yescharacteristic
606C22C47×#39911yescharacteristic
607C22C2×#99×C4712yes—
608C22C47×#41012yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—84no—
613C4—84no—
614C4—82no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2C47×#143911yescharacteristic
625C2C47×#179912yes—
626C2C47×#189811yescharacteristic
627C2C47×#189911yescharacteristic
628C2C47×#196412yes—
subgroupG/H
center, socleC23×C47C2×C22⋊C4
commutatorC24C22×C4×C47
Frattini, cosocleC25C23×C47
prime radicalC23×D4×C47C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C47×#380C2semidirect
4. C2×C47×#342C2semidirect
5. C47×C22⋊#95C2semidirect
9. C22×C22⋊C4×C47C4semidirect
22. C2×#95×C47C4semidirect
81. C24×C47C4⋊C4semidirect
145. C22×C4×C47C4⋊C4semidirect
247. C2×C4×C47#99semidirect
248. #11043C47direct (N × H)
303. C2×#380C2×C47semidirect
304. C2×#342C2×C47semidirect
305. C22⋊#95C2×C47semidirect
323. C22×C22⋊C4C4×C47semidirect
336. C2×#95C4×C47semidirect
338. C47#11043direct (N × H)
396. C24C4⋊C4×C47semidirect
460. C22×C4C4⋊C4×C47semidirect
562. C2×C4#99×C47semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C472
C2×C47×#3862
C2×C47×#3802
C2×C47×#3422
C47×C22⋊#952
#1104347