Finite Group Databasebeta

← C47×#10394 #26050092

Subgroups — C47×#10394 #26050092

Order 12032.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2617C211yesmaximal, characteristic
2C47×#1874C211yesmaximal, characteristic, complemented
3C47×#1852C211yesmaximal, characteristic, complemented
4C2×C47×#327C211yesmaximal, characteristic, complemented
5C2×C47×#323C211yesmaximal, characteristic, complemented
6C47×#1439C211yesmaximal, characteristic, complemented
7C47×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C47C2211yescharacteristic
9C2×#120×C47—21no—
10C22×C4⋊C4×C47C2211yescharacteristic
11C22×C22⋊C4×C47—21no—
12C22×C22⋊C4×C47C2211yescharacteristic
13C2×#107×C47—21no—
14C2×#102×C47—21no—
15C2×C22⋊C8×C47C2211yescharacteristic
16C2×C22⋊C8×C47C2211yescharacteristic
17C47×#397—21no—
18C47×#394—21no—
19C47×#394—21no—
20C47×#392—21no—
21C47×#386—21no—
22C47×#380C2211yescharacteristic
23C2×#95×C47—21no—
24C2×#95×C47C2211yescharacteristic
25C47×#340—21no—
26C47×#340—21no—
27C47×#327—22no—
28C47×#323—22no—
29C25×C47D411yescharacteristic
30C22×D4×C47—21no—
31C22×D4×C47—21no—
32C22×D4×C47—21no—
33C22×D4×C47D411yescharacteristic
34C23×C4×C47—21no—
35C23×C4×C47—21no—
36C23×C4×C47D411yescharacteristic
37C23×C4×C47C2311yescharacteristic
38C22×C8×C47—21no—
39C22×C8×C47—21no—
40#121×C47—21no—
41#121×C47—21no—
42#121×C47—21no—
43#121×C47—21no—
44#120×C47—42no—
45#120×C47—42no—
46C2×C4⋊C4×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—42no—
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C4⋊C4×C47D411yescharacteristic
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47—21no—
55C2×C22⋊C4×C47—21no—
56C2×C22⋊C4×C47—21no—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—21no—
62C2×C22⋊C4×C47—21no—
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—42no—
65C2×C22⋊C4×C47—42no—
66C2×C22⋊C4×C47—42no—
67#107×C47—42no—
68#102×C47—42no—
69C22⋊C8×C47—21no—
70C22⋊C8×C47—21no—
71C22⋊C8×C47—21no—
72C22⋊C8×C47D412yescomplemented
73#95×C47—21no—
74#95×C47—21no—
75#95×C47—21no—
76#95×C47—21no—
77#95×C47—21no—
78#95×C47—42no—
79C24×C47—21no—
80C24×C47—21no—
81C24×C47—21no—
82C24×C47—21no—
83C24×C47—21no—
84C24×C47—21no—
85C24×C47—21no—
86C24×C47—41no—
87C24×C47—41no—
88C24×C47—41no—
89C24×C47—41no—
90C24×C47D812yes—
91C24×C47C2×D411yescharacteristic
92C2×D4×C47—21no—
93C2×D4×C47—21no—
94C2×D4×C47—41no—
95C2×D4×C47—41no—
96C2×D4×C47—42no—
97C2×D4×C47—42no—
98C2×D4×C47—41no—
99C2×D4×C47—41no—
100C2×D4×C47—41no—
101C2×D4×C47—41no—
102C2×D4×C47—41no—
103C2×D4×C47—41no—
104C2×D4×C47—81no—
105C2×D4×C47—81no—
106C2×D4×C47—81no—
107C2×D4×C47—81no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—41no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47—41no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×C4×C47#4111yescharacteristic
137C22×C4×C47#4111yescharacteristic
138C2×C8×C47—22no—
139C2×C8×C47—41no—
140C2×C8×C47—41no—
141C2×C8×C47—41no—
142C2×C8×C47—41no—
143C2×C8×C47—41no—
144C4⋊C4×C47—22no—
145C4⋊C4×C47—22no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—41no—
149C4⋊C4×C47—41no—
150C4⋊C4×C47—41no—
151C4⋊C4×C47—41no—
152C22⋊C4×C47—42no—
153C22⋊C4×C47—42no—
154C22⋊C4×C47—48no—
155C22⋊C4×C47—41no—
156C22⋊C4×C47—41no—
157C22⋊C4×C47—41no—
158C22⋊C4×C47—41no—
159C22⋊C4×C47—41no—
160C22⋊C4×C47—41no—
161C22⋊C4×C47—41no—
162C22⋊C4×C47—41no—
163C22⋊C4×C47—81no—
164C22⋊C4×C47—81no—
165C23×C47—21no—
166C23×C47—21no—
167C23×C47—21no—
168C23×C47—21no—
169C23×C47—22no—
170C23×C47—22no—
171C23×C47—22no—
172C23×C47—42no—
173C23×C47—42no—
174C23×C47—42no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47—42no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47—41no—
181C23×C47—41no—
182C23×C47—41no—
183C23×C47—41no—
184C23×C47—41no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—41no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—81no—
194C23×C47—81no—
195C23×C47—81no—
196C23×C47—81no—
197C23×C47—81no—
198C23×C47—81no—
199C23×C47#12011yescharacteristic
200C23×C47#12111yescharacteristic
201C23×C47#12311yescharacteristic
202C23×C47C2×D811yescharacteristic
203C23×C47#13511yescharacteristic
204C23×C47AGL(1,ℤ/8)11yescharacteristic
205C23×C47#13711yescharacteristic
206D4×C47—42no—
207D4×C47—81no—
208D4×C47—84no—
209D4×C47—84no—
210D4×C47—81no—
211D4×C47—81no—
212D4×C47—81no—
213D4×C47—81no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—42no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—81no—
242C2×C4×C47—81no—
243C2×C4×C47—81no—
244C2×C4×C47—81no—
245C2×C4×C47—81no—
246C2×C4×C47—81no—
247C2×C4×C47—81no—
248C2×C4×C47—81no—
249C2×C4×C47—81no—
250C2×C4×C47#12111yescharacteristic
251C2×C4×C47#12111yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12411yescharacteristic
254C8×C47—42no—
255C8×C47—81no—
256#10394C4711yesmaximal, characteristic, direct product factor, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—21no—
269C22×C47—44no—
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—82no—
274C22×C47—82no—
275C22×C47—82no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47—81no—
287C22×C47#39411yescharacteristic
288C22×C47#44711yescharacteristic
289C22×C47#45211yescharacteristic
290C22×C47#45311yescharacteristic
291C22×C47#45511yescharacteristic
292C22×C47B(4,𝔽2)11yescharacteristic
293C22×C47#45811yescharacteristic
294C22×C47#46611yescharacteristic
295C22×C47#46811yescharacteristic
296C22×C47#48011yescharacteristic
297C22×C47#48211yescharacteristic
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—21no—
301C4×C47—21no—
302C4×C47—82no—
303C4×C47—82no—
304C4×C47—81no—
305C4×C47—81no—
306C4×C47—81no—
307C4×C47—81no—
308#2617C2×C4711yescharacteristic
309#1874C2×C4711yescharacteristic, complemented
310#1852C2×C4711yescharacteristic, complemented
311C2×#327C2×C4711yescharacteristic, complemented
312C2×#323C2×C4711yescharacteristic, complemented
313#1439C2×C4711yescharacteristic, complemented
314#1294C2×C4711yescharacteristic, complemented
315C2×C47—21no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—82no—
320C2×C47—161no—
321C2×C47#159511yescharacteristic
322C2×C47#160611yescharacteristic
323C2×C47#160711yescharacteristic
324C2×C47#161811yescharacteristic
325C2×C47#203311yescharacteristic
326C2×C47#203711yescharacteristic
327C2×C47#204411yescharacteristic
328C2×#121C22×C4711yescharacteristic
329C2×#120—21no—
330C22×C4⋊C4C22×C4711yescharacteristic
331C22×C22⋊C4—21no—
332C22×C22⋊C4C22×C4711yescharacteristic
333C2×#107—21no—
334C2×#102—21no—
335C2×C22⋊C8C22×C4711yescharacteristic
336C2×C22⋊C8C22×C4711yescharacteristic
337#397—21no—
338#394—21no—
339#394—21no—
340#392—21no—
341#386—21no—
342#380C22×C4711yescharacteristic
343C2×#95—21no—
344C2×#95C22×C4711yescharacteristic
345#340—21no—
346#340—21no—
347#327—22no—
348#323—22no—
349C47#1039411yescharacteristic, direct product factor, Sylow
350C25D4×C4711yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C4711yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C4711yescharacteristic
358C23×C4C23×C4711yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C4711yescharacteristic
371C2×C4⋊C4D4×C4711yescharacteristic
372C2×C4⋊C4D4×C4711yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C4712yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C4712yes—
412C24C2×D4×C4711yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C4711yescharacteristic
454C22×C4C2×D4×C4711yescharacteristic
455C22×C4C2×D4×C4711yescharacteristic
456C22×C4#41×C4711yescharacteristic
457C22×C4#41×C4711yescharacteristic
458C22×C4#41×C4711yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C4711yescharacteristic
521C23#121×C4711yescharacteristic
522C23#123×C4711yescharacteristic
523C23C2×D8×C4711yescharacteristic
524C23#135×C4711yescharacteristic
525C23AGL(1,ℤ/8)×C4711yescharacteristic
526C23#137×C4711yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C4711yescharacteristic
572C2×C4#121×C4711yescharacteristic
573C2×C4#123×C4711yescharacteristic
574C2×C4#124×C4711yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22C47×#39411yescharacteristic
608C22C47×#44711yescharacteristic
609C22C47×#45211yescharacteristic
610C22C47×#45311yescharacteristic
611C22C47×#45511yescharacteristic
612C22C47×B(4,𝔽2)11yescharacteristic
613C22C47×#45811yescharacteristic
614C22C47×#46611yescharacteristic
615C22C47×#46811yescharacteristic
616C22C47×#48011yescharacteristic
617C22C47×#48211yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2C47×#159511yescharacteristic
635C2C47×#160611yescharacteristic
636C2C47×#160711yescharacteristic
637C2C47×#161811yescharacteristic
638C2C47×#203311yescharacteristic
639C2C47×#203711yescharacteristic
640C2C47×#204411yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutator, Frattini, cosocleC23×C4C23×C47
prime radicalC47×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1874C2semidirect
3. C47×#1852C2semidirect
4. C2×C47×#327C2semidirect
5. C2×C47×#323C2semidirect
6. C47×#1439C2semidirect
7. C47×#1294C2semidirect
72. C22⋊C8×C47D4semidirect
256. #10394C47direct (N × H)
309. #1874C2×C47semidirect
310. #1852C2×C47semidirect
311. C2×#327C2×C47semidirect
312. C2×#323C2×C47semidirect
313. #1439C2×C47semidirect
314. #1294C2×C47semidirect
349. C47#10394direct (N × H)
393. C22⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#26172
C47×#18742
C47×#18522
C2×C47×#3272
C2×C47×#3232
C47×#14392
C47×#12942
#1039447