Finite Group Databasebeta

← C47×#13344 #26053042

Subgroups — C47×#13344 #26053042

Order 12032.

892 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 892 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#458C211yesmaximal, characteristic, complemented
2C2×C47×B(4,𝔽2)C211yesmaximal, characteristic
3C47×#2697C211yesmaximal, characteristic, complemented
4C2×C47×#352C211yesmaximal, characteristic, complemented
5C2×C47×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
6C47×#1792C211yesmaximal, characteristic, complemented
7C47×#1393C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C47C2211yescharacteristic
9C2×#123×C47—21no—
10C2×#123×C47C2211yescharacteristic
11C2×#120×C47—21no—
12C2×#120×C47C2211yescharacteristic
13C47×#458—22no—
14C47×#458—22no—
15C47×B(4,𝔽2)—22no—
16C47×B(4,𝔽2)—22no—
17C2×#104×C47—21no—
18C47×#417—21no—
19C2×#100×C47C2211yescharacteristic
20C2×#99×C47—21no—
21C2×#99×C47—21no—
22C2×#99×C47C2211yescharacteristic
23C2×#99×C47C2211yescharacteristic
24C47×#397—21no—
25C47×#396—21no—
26C47×#394—21no—
27C47×#390C2211yescharacteristic
28C47×#388—21no—
29C47×#386—21no—
30C47×#379—21no—
31C47×#352—22no—
32C47×AΣL(1,𝔽16)—22no—
33C25×C47D411yescharacteristic
34H(5,𝔽2)×C47—21no—
35H(5,𝔽2)×C47—21no—
36H(5,𝔽2)×C47—21no—
37H(5,𝔽2)×C47—42no—
38H(5,𝔽2)×C47D412yes—
39C2×#41×C47—21no—
40C2×#41×C47—41no—
41C22×D4×C47—21no—
42C22×D4×C47—21no—
43C22×D4×C47—21no—
44C22×D4×C47—41no—
45C22×D4×C47—41no—
46C22×D4×C47C2311yescharacteristic
47C23×C4×C47D411yescharacteristic, complemented
48C2×M16×C47—21no—
49#123×C47—24no—
50#123×C47—21no—
51#123×C47—21no—
52#123×C47—21no—
53#123×C47—21no—
54#123×C47—42no—
55#120×C47—24no—
56#120×C47—21no—
57#120×C47—21no—
58#120×C47—21no—
59#120×C47—21no—
60#120×C47—42no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—41no—
64C2×C4⋊C4×C47D411yescharacteristic, complemented
65C2×C22⋊C4×C47—21no—
66C2×C22⋊C4×C47—21no—
67C2×C22⋊C4×C47—21no—
68C2×C22⋊C4×C47—21no—
69C2×C22⋊C4×C47—21no—
70C2×C22⋊C4×C47—21no—
71C2×C22⋊C4×C47—21no—
72C2×C22⋊C4×C47—21no—
73C2×C22⋊C4×C47—21no—
74C2×C22⋊C4×C47—21no—
75C2×C22⋊C4×C47—41no—
76C2×C22⋊C4×C47—41no—
77C2×C22⋊C4×C47D411yescharacteristic
78C2×C22⋊C4×C47D411yescharacteristic, complemented
79C2×C42×C47D411yescharacteristic, complemented
80#104×C47—42no—
81#103×C47—41no—
82#102×C47—41no—
83#100×C47—21no—
84#100×C47—21no—
85#99×C47—24no—
86#99×C47—24no—
87#99×C47—21no—
88#99×C47—21no—
89#99×C47D412yes—
90#99×C47D412yescomplemented
91#95×C47—21no—
92#95×C47—21no—
93#95×C47—21no—
94C24×C47—21no—
95C24×C47—21no—
96C24×C47—21no—
97C24×C47—21no—
98C24×C47—21no—
99C24×C47—41no—
100C24×C47—41no—
101C24×C47—42no—
102C24×C47—81no—
103C24×C47C2×D411yescharacteristic
104C24×C47C2×D411yescharacteristic
105#41×C47—22no—
106#41×C47—22no—
107#41×C47—42no—
108#41×C47—41no—
109#41×C47—42no—
110#41×C47—42no—
111#41×C47—42no—
112#41×C47—41no—
113C2×Q8×C47—21no—
114C2×D4×C47—21no—
115C2×D4×C47—22no—
116C2×D4×C47—22no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47—42no—
122C2×D4×C47—42no—
123C2×D4×C47—41no—
124C2×D4×C47—41no—
125C2×D4×C47—41no—
126C2×D4×C47—41no—
127C2×D4×C47—42no—
128C2×D4×C47—42no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—44no—
133C2×D4×C47—42no—
134C2×D4×C47—41no—
135C2×D4×C47—41no—
136C2×D4×C47—81no—
137C2×D4×C47—82no—
138C2×D4×C47—82no—
139C2×D4×C47C2×D411yescharacteristic
140C2×D4×C47C2×D411yescharacteristic
141C2×D4×C47C2×D411yescharacteristic
142C2×D4×C47#4111yescharacteristic
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—41no—
153C22×C4×C47—41no—
154C22×C4×C47—41no—
155C22×C4×C47—41no—
156C22×C4×C47—41no—
157C22×C4×C47C2×D411yescharacteristic
158M16×C47—41no—
159M16×C47—41no—
160C2×C8×C47—41no—
161C4⋊C4×C47—44no—
162C4⋊C4×C47—41no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47—81no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47—22no—
168C22⋊C4×C47—21no—
169C22⋊C4×C47—21no—
170C22⋊C4×C47—21no—
171C22⋊C4×C47—21no—
172C22⋊C4×C47—44no—
173C22⋊C4×C47—42no—
174C22⋊C4×C47—41no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47—44no—
177C22⋊C4×C47—41no—
178C22⋊C4×C47—41no—
179C22⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—81no—
182C22⋊C4×C47—81no—
183C22⋊C4×C47—81no—
184C22⋊C4×C47—81no—
185C22⋊C4×C47—81no—
186C42×C47—41no—
187C23×C47—21no—
188C23×C47—21no—
189C23×C47—21no—
190C23×C47—21no—
191C23×C47—22no—
192C23×C47—22no—
193C23×C47—22no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—42no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—42no—
205C23×C47—42no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—81no—
211C23×C47—82no—
212C23×C47—81no—
213C23×C47—82no—
214C23×C47—84no—
215C23×C47—81no—
216C23×C47—81no—
217C23×C47—81no—
218C23×C47—81no—
219C23×C47—81no—
220C23×C47#12011yescharacteristic
221C23×C47#12011yescharacteristic
222C23×C47#12011yescharacteristic
223C23×C47#12111yescharacteristic
224C23×C47#12111yescharacteristic
225Q8×C47—22no—
226Q8×C47—41no—
227D4×C47—22no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—41no—
233D4×C47—42no—
234D4×C47—42no—
235D4×C47—42no—
236D4×C47—42no—
237D4×C47—42no—
238D4×C47—42no—
239D4×C47—82no—
240D4×C47—82no—
241D4×C47—88no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—42no—
252C2×C4×C47—42no—
253C2×C4×C47—42no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—81no—
270C2×C4×C47—81no—
271C2×C4×C47—81no—
272C2×C4×C47—81no—
273C2×C4×C47—81no—
274C2×C4×C47#12111yescharacteristic
275C2×C4×C47#12711yescharacteristic
276C8×C47—81no—
277#13344C4711yesmaximal, characteristic, direct product factor, Sylow
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—42no—
289C22×C47—42no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—41no—
294C22×C47—44no—
295C22×C47—42no—
296C22×C47—42no—
297C22×C47—81no—
298C22×C47—81no—
299C22×C47—81no—
300C22×C47—81no—
301C22×C47—82no—
302C22×C47—82no—
303C22×C47—82no—
304C22×C47—82no—
305C22×C47—82no—
306C22×C47—81no—
307C22×C47—81no—
308C22×C47—81no—
309C22×C47—81no—
310C22×C47—161no—
311C22×C47—161no—
312C22×C47#39211yescharacteristic
313C22×C47B(4,𝔽2)11yescharacteristic
314C22×C47B(4,𝔽2)11yescharacteristic
315C4×C47—21no—
316C4×C47—21no—
317C4×C47—42no—
318C4×C47—81no—
319C4×C47—81no—
320C4×C47—81no—
321C4×C47—82no—
322C4×C47—82no—
323C4×C47—81no—
324C4×C47—81no—
325C2×#458C2×C4711yescharacteristic, complemented
326C2×B(4,𝔽2)C2×C4711yescharacteristic
327#2697C2×C4711yescharacteristic, complemented
328C2×#352C2×C4711yescharacteristic, complemented
329C2×AΣL(1,𝔽16)C2×C4711yescharacteristic, complemented
330#1792C2×C4711yescharacteristic, complemented
331#1393C2×C4711yescharacteristic, complemented
332C2×C47—21no—
333C2×C47—21no—
334C2×C47—41no—
335C2×C47—41no—
336C2×C47—41no—
337C2×C47—41no—
338C2×C47—82no—
339C2×C47—82no—
340C2×C47#202111yescharacteristic
341C2×C47#219711yescharacteristic
342C2×C47#220011yescharacteristic
343C2×H(5,𝔽2)C22×C4711yescharacteristic
344C2×#123—21no—
345C2×#123C22×C4711yescharacteristic
346C2×#120—21no—
347C2×#120C22×C4711yescharacteristic
348#458—22no—
349#458—22no—
350B(4,𝔽2)—22no—
351B(4,𝔽2)—22no—
352C2×#104—21no—
353#417—21no—
354C2×#100C22×C4711yescharacteristic
355C2×#99—21no—
356C2×#99—21no—
357C2×#99C22×C4711yescharacteristic
358C2×#99C22×C4711yescharacteristic
359#397—21no—
360#396—21no—
361#394—21no—
362#390C22×C4711yescharacteristic
363#388—21no—
364#386—21no—
365#379—21no—
366#352—22no—
367AΣL(1,𝔽16)—22no—
368C47#1334411yescharacteristic, direct product factor, Sylow
369C25D4×C4711yescharacteristic
370H(5,𝔽2)—21no—
371H(5,𝔽2)—21no—
372H(5,𝔽2)—21no—
373H(5,𝔽2)—42no—
374H(5,𝔽2)D4×C4712yes—
375C2×#41—21no—
376C2×#41—41no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—41no—
381C22×D4—41no—
382C22×D4C23×C4711yescharacteristic
383C23×C4D4×C4711yescharacteristic, complemented
384C2×M16—21no—
385#123—24no—
386#123—21no—
387#123—21no—
388#123—21no—
389#123—21no—
390#123—42no—
391#120—24no—
392#120—21no—
393#120—21no—
394#120—21no—
395#120—21no—
396#120—42no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4D4×C4711yescharacteristic, complemented
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4D4×C4711yescharacteristic
414C2×C22⋊C4D4×C4711yescharacteristic, complemented
415C2×C42D4×C4711yescharacteristic, complemented
416#104—42no—
417#103—41no—
418#102—41no—
419#100—21no—
420#100—21no—
421#99—24no—
422#99—24no—
423#99—21no—
424#99—21no—
425#99D4×C4712yes—
426#99D4×C4712yescomplemented
427#95—21no—
428#95—21no—
429#95—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—41no—
436C24—41no—
437C24—42no—
438C24—81no—
439C24C2×D4×C4711yescharacteristic
440C24C2×D4×C4711yescharacteristic
441#41—22no—
442#41—22no—
443#41—42no—
444#41—41no—
445#41—42no—
446#41—42no—
447#41—42no—
448#41—41no—
449C2×Q8—21no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—81no—
473C2×D4—82no—
474C2×D4—82no—
475C2×D4C2×D4×C4711yescharacteristic
476C2×D4C2×D4×C4711yescharacteristic
477C2×D4C2×D4×C4711yescharacteristic
478C2×D4#41×C4711yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4C2×D4×C4711yescharacteristic
494M16—41no—
495M16—41no—
496C2×C8—41no—
497C4⋊C4—41no—
498C4⋊C4—44no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—81no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—44no—
509C22⋊C4—42no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—44no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C42—41no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—81no—
547C23—82no—
548C23—81no—
549C23—82no—
550C23—84no—
551C23—81no—
552C23—81no—
553C23—81no—
554C23—81no—
555C23—81no—
556C23#120×C4711yescharacteristic
557C23#120×C4711yescharacteristic
558C23#120×C4711yescharacteristic
559C23#121×C4711yescharacteristic
560C23#121×C4711yescharacteristic
561Q8—22no—
562Q8—41no—
563D4—22no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—82no—
576D4—82no—
577D4—88no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4#121×C4711yescharacteristic
611C2×C4#127×C4711yescharacteristic
612C8—81no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—44no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22—82no—
640C22—82no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—161no—
646C22—161no—
647C22C47×#39211yescharacteristic
648C22C47×B(4,𝔽2)11yescharacteristic
649C22C47×B(4,𝔽2)11yescharacteristic
650C4—21no—
651C4—21no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—82no—
657C4—82no—
658C4—81no—
659C4—81no—
660C2—21no—
661C2—21no—
662C2—41no—
663C2—41no—
664C2—41no—
665C2—41no—
666C2—82no—
667C2—82no—
668C2C47×#202111yescharacteristic
669C2C47×#219711yescharacteristic
670C2C47×#220011yescharacteristic
subgroupG/H
center, socleC22×C47B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C47
prime radicalC2×C47×B(4,𝔽2)C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C22×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#458C2semidirect
3. C47×#2697C2semidirect
4. C2×C47×#352C2semidirect
5. C2×C47×AΣL(1,𝔽16)C2semidirect
6. C47×#1792C2semidirect
7. C47×#1393C2semidirect
47. C23×C4×C47D4semidirect
64. C2×C4⋊C4×C47D4semidirect
78. C2×C22⋊C4×C47D4semidirect
79. C2×C42×C47D4semidirect
90. #99×C47D4semidirect
277. #13344C47direct (N × H)
325. C2×#458C2×C47semidirect
327. #2697C2×C47semidirect
328. C2×#352C2×C47semidirect
329. C2×AΣL(1,𝔽16)C2×C47semidirect
330. #1792C2×C47semidirect
331. #1393C2×C47semidirect
368. C47#13344direct (N × H)
383. C23×C4D4×C47semidirect
400. C2×C4⋊C4D4×C47semidirect
414. C2×C22⋊C4D4×C47semidirect
415. C2×C42D4×C47semidirect
426. #99D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4582
C2×C47×B(4,𝔽2)2
C47×#26972
C2×C47×#3522
C2×C47×AΣL(1,𝔽16)2
C47×#17922
C47×#13932
#1334447