Finite Group Databasebeta

← C47×#10972 #26050670

Subgroups — C47×#10972 #26050670

Order 12032.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#534C211yesmaximal, characteristic
2C22×#99×C47C212yesmaximal, complemented
3C22×#99×C47C211yesmaximal, characteristic, complemented
4C47×#2308C211yesmaximal, characteristic, complemented
5C2×C47×#342C212yesmaximal, complemented
6C23×D4×C47C2211yescharacteristic
7C23×D4×C47C2211yescharacteristic
8C47×#534—24no—
9C47×#534—24no—
10C2×#123×C47—21no—
11C2×#123×C47C412yescomplemented
12C2×#121×C47—22no—
13C2×#120×C47—21no—
14C2×#120×C47C412yescomplemented
15C22×C22⋊C4×C47C2212yes—
16C22×C22⋊C4×C47C2212yes—
17C22×C22⋊C4×C47C2211yescharacteristic
18C2×#99×C47—22no—
19C2×#99×C47—24no—
20C2×#99×C47—24no—
21C2×#99×C47—24no—
22C2×#99×C47—24no—
23C47×#386—24no—
24C47×#381—21no—
25C47×#379—21no—
26C47×#342—24no—
27C25×C47C2×C411yescharacteristic
28C25×C47D411yescharacteristic
29C25×C47C2311yescharacteristic
30C22×D4×C47—21no—
31C22×D4×C47—21no—
32C22×D4×C47—22no—
33C22×D4×C47—22no—
34C22×D4×C47—22no—
35C22×D4×C47—22no—
36C22×D4×C47—22no—
37C22×D4×C47—22no—
38C22×D4×C47—22no—
39C22×D4×C47—22no—
40C22×D4×C47—22no—
41C22×D4×C47—22no—
42C22×D4×C47—22no—
43C22×D4×C47—22no—
44C22×D4×C47C2×C412yes—
45C22×D4×C47D412yes—
46C22×D4×C47D414yes—
47C23×C4×C47—21no—
48C23×C4×C47—22no—
49C23×C4×C47—22no—
50C23×C4×C47C2×C411yescharacteristic
51C23×C4×C47D411yescharacteristic
52#123×C47—28no—
53#123×C47—24no—
54#123×C47—24no—
55#121×C47—216no—
56#120×C47—28no—
57#120×C47—24no—
58#120×C47—24no—
59C2×C4⋊C4×C47—22no—
60C2×C22⋊C4×C47—22no—
61C2×C22⋊C4×C47—21no—
62C2×C22⋊C4×C47—22no—
63C2×C22⋊C4×C47—22no—
64C2×C22⋊C4×C47—22no—
65C2×C22⋊C4×C47—22no—
66C2×C22⋊C4×C47—22no—
67C2×C22⋊C4×C47—22no—
68C2×C22⋊C4×C47—22no—
69C2×C22⋊C4×C47—22no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—22no—
74C2×C22⋊C4×C47—24no—
75C2×C22⋊C4×C47C2×C412yes—
76C2×C22⋊C4×C47D414yes—
77C2×C22⋊C4×C47D414yescomplemented
78C2×C22⋊C4×C47D414yescomplemented
79#99×C47—216no—
80#99×C47—28no—
81#95×C47—24no—
82C24×C47—21no—
83C24×C47—21no—
84C24×C47—21no—
85C24×C47—22no—
86C24×C47—22no—
87C24×C47—22no—
88C24×C47—22no—
89C24×C47—21no—
90C24×C47—82no—
91C24×C47—82no—
92C24×C47—82no—
93C24×C47C22⋊C412yes—
94C24×C47C22⋊C412yescomplemented
95C24×C47C22×C411yescharacteristic
96C24×C47C2×D411yescharacteristic
97C24×C47C2×D411yescharacteristic
98C24×C47C2×D412yes—
99C24×C47C2×D412yes—
100C24×C47C2×D412yes—
101C24×C47C2×D412yes—
102C24×C47#4112yes—
103C24×C47#4112yes—
104C2×D4×C47—22no—
105C2×D4×C47—22no—
106C2×D4×C47—24no—
107C2×D4×C47—24no—
108C2×D4×C47—24no—
109C2×D4×C47—24no—
110C2×D4×C47—24no—
111C2×D4×C47—22no—
112C2×D4×C47—24no—
113C2×D4×C47—24no—
114C2×D4×C47—24no—
115C2×D4×C47—24no—
116C2×D4×C47—22no—
117C2×D4×C47—24no—
118C2×D4×C47—28no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47—42no—
122C2×D4×C47—42no—
123C2×D4×C47—42no—
124C2×D4×C47—42no—
125C2×D4×C47—42no—
126C2×D4×C47—42no—
127C2×D4×C47—42no—
128C2×D4×C47—42no—
129C2×D4×C47—42no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—42no—
133C2×D4×C47—42no—
134C2×D4×C47—42no—
135C2×D4×C47—42no—
136C2×D4×C47—42no—
137C2×D4×C47—84no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—21no—
147C22×C4×C47—24no—
148C22×C4×C47—24no—
149C22×C4×C47—24no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—82no—
155C22×C4×C47—84no—
156C22×C4×C47—84no—
157C22×C4×C47C22⋊C412yes—
158C22×C4×C47C22⋊C412yescomplemented
159C4⋊C4×C47—28no—
160C22⋊C4×C47—28no—
161C22⋊C4×C47—28no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—24no—
164C22⋊C4×C47—24no—
165C22⋊C4×C47—24no—
166C22⋊C4×C47—24no—
167C22⋊C4×C47—24no—
168C22⋊C4×C47—42no—
169C22⋊C4×C47—42no—
170C22⋊C4×C47—42no—
171C22⋊C4×C47—42no—
172C22⋊C4×C47—84no—
173C22⋊C4×C47C22⋊C414yescomplemented
174C23×C47—22no—
175C23×C47—22no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—24no—
179C23×C47—44no—
180C23×C47—42no—
181C23×C47—44no—
182C23×C47—42no—
183C23×C47—42no—
184C23×C47—44no—
185C23×C47—44no—
186C23×C47—44no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—42no—
190C23×C47—42no—
191C23×C47—42no—
192C23×C47—82no—
193C23×C47—84no—
194C23×C47—82no—
195C23×C47—82no—
196C23×C47—82no—
197C23×C47—82no—
198C23×C47—82no—
199C23×C47—82no—
200C23×C47—84no—
201C23×C47—84no—
202C23×C47—84no—
203C23×C47C2×C22⋊C411yescharacteristic
204C23×C47C2×C22⋊C411yescharacteristic
205C23×C47C2×C22⋊C411yescharacteristic
206C23×C47C4×D412yes—
207C23×C47C4×D412yes—
208C23×C47#12011yescharacteristic
209C23×C47#12012yes—
210C23×C47#12012yes—
211C23×C47#12011yescharacteristic
212C23×C47#12012yes—
213C23×C47#12112yes—
214C23×C47#12112yes—
215C23×C47#12112yes—
216C23×C47#12112yes—
217C23×C47#12112yes—
218C23×C47#12112yes—
219C23×C47#12311yescharacteristic
220C23×C47#12311yescharacteristic
221C23×C47#12312yes—
222C23×C47#12412yes—
223C23×C47#12712yes—
224D4×C47—44no—
225D4×C47—44no—
226D4×C47—44no—
227D4×C47—44no—
228D4×C47—44no—
229D4×C47—44no—
230D4×C47—44no—
231D4×C47—44no—
232D4×C47—88no—
233C2×C4×C47—24no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—24no—
238C2×C4×C47—22no—
239C2×C4×C47—44no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—48no—
246C2×C4×C47—44no—
247C2×C4×C47—44no—
248C2×C4×C47—84no—
249C2×C4×C47—84no—
250C2×C4×C47—84no—
251C2×C4×C47—84no—
252C2×C4×C47—84no—
253C2×C4×C47—84no—
254#10972C4711yesmaximal, characteristic, direct product factor, Sylow
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—24no—
258C22×C47—24no—
259C22×C47—22no—
260C22×C47—42no—
261C22×C47—42no—
262C22×C47—42no—
263C22×C47—42no—
264C22×C47—42no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—42no—
271C22×C47—41no—
272C22×C47—42no—
273C22×C47—41no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—44no—
277C22×C47—44no—
278C22×C47—44no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—82no—
282C22×C47—84no—
283C22×C47—84no—
284C22×C47—82no—
285C22×C47—84no—
286C22×C47—84no—
287C22×C47—82no—
288C22×C47#37911yescharacteristic
289C22×C47#38611yescharacteristic
290C22×C47#38612yes—
291C22×C47#38611yescharacteristic
292C22×C47#39012yes—
293C22×C47#39212yes—
294C22×C47#39212yes—
295C22×C47#39412yes—
296C22×C47#39412yes—
297C4×C47—44no—
298C4×C47—42no—
299C4×C47—42no—
300C4×C47—84no—
301C4×C47—84no—
302C2×#534C2×C4711yescharacteristic
303C22×#99C2×C4712yescomplemented
304C22×#99C2×C4711yescharacteristic, complemented
305#2308C2×C4711yescharacteristic, complemented
306C2×#342C2×C4712yescomplemented
307C2×C47—21no—
308C2×C47—22no—
309C2×C47—22no—
310C2×C47—21no—
311C2×C47—22no—
312C2×C47—22no—
313C2×C47—22no—
314C2×C47—22no—
315C2×C47—82no—
316C2×C47—82no—
317C2×C47#143811yescharacteristic
318C2×C47#191312yes—
319C23×D4C22×C4711yescharacteristic
320C23×D4C22×C4711yescharacteristic
321#534—24no—
322#534—24no—
323C2×#123—21no—
324C2×#123C4×C4712yescomplemented
325C2×#121—22no—
326C2×#120—21no—
327C2×#120C4×C4712yescomplemented
328C22×C22⋊C4C22×C4712yes—
329C22×C22⋊C4C22×C4712yes—
330C22×C22⋊C4C22×C4711yescharacteristic
331C2×#99—22no—
332C2×#99—24no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336#386—24no—
337#381—21no—
338#379—21no—
339#342—24no—
340C47#1097211yescharacteristic, direct product factor, Sylow
341C25C2×C4×C4711yescharacteristic
342C25D4×C4711yescharacteristic
343C25C23×C4711yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C4712yes—
359C22×D4D4×C4712yes—
360C22×D4D4×C4714yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C4711yescharacteristic
365C23×C4D4×C4711yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C4712yes—
390C2×C22⋊C4D4×C4714yes—
391C2×C22⋊C4D4×C4714yescomplemented
392C2×C22⋊C4D4×C4714yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C4712yes—
408C24C22⋊C4×C4712yescomplemented
409C24C22×C4×C4711yescharacteristic
410C24C2×D4×C4711yescharacteristic
411C24C2×D4×C4711yescharacteristic
412C24C2×D4×C4712yes—
413C24C2×D4×C4712yes—
414C24C2×D4×C4712yes—
415C24C2×D4×C4712yes—
416C24#41×C4712yes—
417C24#41×C4712yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C4712yes—
472C22×C4C22⋊C4×C4712yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C4714yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C4711yescharacteristic
518C23C2×C22⋊C4×C4711yescharacteristic
519C23C2×C22⋊C4×C4711yescharacteristic
520C23C4×D4×C4712yes—
521C23C4×D4×C4712yes—
522C23#120×C4711yescharacteristic
523C23#120×C4712yes—
524C23#120×C4712yes—
525C23#120×C4711yescharacteristic
526C23#120×C4712yes—
527C23#121×C4712yes—
528C23#121×C4712yes—
529C23#121×C4712yes—
530C23#121×C4712yes—
531C23#121×C4712yes—
532C23#121×C4712yes—
533C23#123×C4711yescharacteristic
534C23#123×C4711yescharacteristic
535C23#123×C4712yes—
536C23#124×C4712yes—
537C23#127×C4712yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22C47×#37911yescharacteristic
602C22C47×#38611yescharacteristic
603C22C47×#38612yes—
604C22C47×#38611yescharacteristic
605C22C47×#39012yes—
606C22C47×#39212yes—
607C22C47×#39212yes—
608C22C47×#39412yes—
609C22C47×#39412yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2C47×#143811yescharacteristic
626C2C47×#191312yes—
subgroupG/H
center, socleC22×C47#386
commutatorC24C22×C4×C47
Frattini, cosocleC25C23×C47
prime radicalC2×C47×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C47C2semidirect
3. C22×#99×C47C2semidirect
4. C47×#2308C2semidirect
5. C2×C47×#342C2semidirect
11. C2×#123×C47C4semidirect
14. C2×#120×C47C4semidirect
77. C2×C22⋊C4×C47D4semidirect
78. C2×C22⋊C4×C47D4semidirect
94. C24×C47C22⋊C4semidirect
158. C22×C4×C47C22⋊C4semidirect
173. C22⋊C4×C47C22⋊C4semidirect
254. #10972C47direct (N × H)
303. C22×#99C2×C47semidirect
304. C22×#99C2×C47semidirect
305. #2308C2×C47semidirect
306. C2×#342C2×C47semidirect
324. C2×#123C4×C47semidirect
327. C2×#120C4×C47semidirect
340. C47#10972direct (N × H)
391. C2×C22⋊C4D4×C47semidirect
392. C2×C22⋊C4D4×C47semidirect
408. C24C22⋊C4×C47semidirect
472. C22×C4C22⋊C4×C47semidirect
487. C22⋊C4C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5342
C22×#99×C472
C47×#23082
C2×C47×#3422
#1097247