Finite Group Databasebeta

← C47×#9938 #26049636

Subgroups — C47×#9938 #26049636

Order 12032.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C47×#3006C211yesmaximal, characteristic, complemented
2C47×#2539C211yesmaximal, characteristic, complemented
3C47×#2404C211yesmaximal, characteristic, complemented
4C47×#1789C211yesmaximal, characteristic, complemented
5C47×#1510C211yesmaximal, characteristic, complemented
6C47×#1462C211yesmaximal, characteristic, complemented
7C47×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C47C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C47—21no—
10C2×#123×C47—21no—
11C2×#121×C47C2211yescharacteristic
12C2×#120×C47—21no—
13C2×#120×C47—21no—
14C22×C22⋊C4×C47C2211yescharacteristic
15C47×#449—22no—
16C47×#448—21no—
17C47×#447—21no—
18C2×#104×C47—22no—
19C47×#417—21no—
20C47×#407C2211yescharacteristic
21C47×#407C2211yescharacteristic
22C47×#399—21no—
23C47×#393—21no—
24C47×#392—21no—
25C47×#392—21no—
26C47×#390—22no—
27C47×#386—22no—
28C47×#386—21no—
29C47×#381C2211yescharacteristic
30C4×C22⋊C4×C47C2211yescharacteristic
31C47×#327—22no—
32C47×#323—22no—
33C25×C47D411yescharacteristic
34C2×#41×C47—21no—
35C2×#41×C47—21no—
36C2×#41×C47—21no—
37C2×#41×C47—21no—
38C2×#41×C47—44no—
39C22×Q8×C47D411yescharacteristic, complemented
40C22×D4×C47—21no—
41C22×D4×C47—21no—
42C22×D4×C47—22no—
43C22×D4×C47—22no—
44C22×D4×C47D411yescharacteristic, complemented
45C22×D4×C47D411yescharacteristic, complemented
46C23×C4×C47—21no—
47C23×C4×C47D411yescharacteristic
48C23×C4×C47C2311yescharacteristic
49AGL(1,ℤ/8)×C47—44no—
50C2×SD16×C47—22no—
51C2×D8×C47—22no—
52C2×M16×C47—21no—
53C2×M16×C47—21no—
54#123×C47—44no—
55#121×C47—21no—
56#121×C47—21no—
57#121×C47—21no—
58#121×C47—21no—
59#120×C47—44no—
60#120×C47—44no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47D411yescharacteristic, complemented
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—22no—
65C2×C22⋊C4×C47—22no—
66C2×C22⋊C4×C47—22no—
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—22no—
76C2×C42×C47D412yescomplemented
77#104×C47—44no—
78#103×C47—22no—
79#102×C47—22no—
80C22⋊C8×C47—21no—
81C22⋊C8×C47—21no—
82C22⋊C8×C47—21no—
83C22⋊C8×C47D412yescomplemented
84#95×C47—22no—
85#95×C47—21no—
86#95×C47—21no—
87#95×C47D412yescomplemented
88C24×C47—21no—
89C24×C47—21no—
90C24×C47—21no—
91C24×C47—21no—
92C24×C47—21no—
93C24×C47—42no—
94C24×C47—42no—
95C24×C47—42no—
96C24×C47C2×D411yescharacteristic
97#41×C47—24no—
98#41×C47—24no—
99#41×C47—42no—
100#41×C47—42no—
101#41×C47—42no—
102#41×C47—42no—
103#41×C47—42no—
104#41×C47—42no—
105C2×Q8×C47—21no—
106C2×Q8×C47—21no—
107C2×Q8×C47—42no—
108C2×D4×C47—24no—
109C2×D4×C47—21no—
110C2×D4×C47—21no—
111C2×D4×C47—21no—
112C2×D4×C47—21no—
113C2×D4×C47—42no—
114C2×D4×C47—44no—
115C2×D4×C47—42no—
116C2×D4×C47—42no—
117C2×D4×C47—41no—
118C2×D4×C47—41no—
119C2×D4×C47—42no—
120C2×D4×C47—44no—
121C2×D4×C47—42no—
122C2×D4×C47—44no—
123C2×D4×C47—44no—
124C2×D4×C47—41no—
125C2×D4×C47—41no—
126C2×D4×C47—82no—
127C2×D4×C47—82no—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—22no—
134C22×C4×C47—21no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—42no—
138C22×C4×C47—41no—
139C22×C4×C47—41no—
140C22×C4×C47—42no—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147SD16×C47—44no—
148D8×C47—44no—
149M16×C47—42no—
150M16×C47—42no—
151C2×C8×C47—22no—
152C2×C8×C47—41no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—44no—
156C22⋊C4×C47—24no—
157C22⋊C4×C47—44no—
158C22⋊C4×C47—44no—
159C22⋊C4×C47—44no—
160C22⋊C4×C47—42no—
161C22⋊C4×C47—41no—
162C22⋊C4×C47—41no—
163C22⋊C4×C47—41no—
164C22⋊C4×C47—41no—
165C22⋊C4×C47—41no—
166C22⋊C4×C47—41no—
167C22⋊C4×C47—82no—
168C42×C47—42no—
169C23×C47—22no—
170C23×C47—22no—
171C23×C47—22no—
172C23×C47—22no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—41no—
176C23×C47—42no—
177C23×C47—42no—
178C23×C47—41no—
179C23×C47—42no—
180C23×C47—41no—
181C23×C47—41no—
182C23×C47—41no—
183C23×C47—41no—
184C23×C47—41no—
185C23×C47—42no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47—42no—
189C23×C47—42no—
190C23×C47—42no—
191C23×C47—41no—
192C23×C47—42no—
193C23×C47—81no—
194C23×C47—81no—
195C23×C47—88no—
196C23×C47#12011yescharacteristic
197C23×C47#12011yescharacteristic
198C23×C47#12111yescharacteristic
199Q8×C47—22no—
200Q8×C47—22no—
201Q8×C47—41no—
202Q8×C47—41no—
203D4×C47—22no—
204D4×C47—22no—
205D4×C47—41no—
206D4×C47—41no—
207D4×C47—42no—
208D4×C47—44no—
209D4×C47—44no—
210D4×C47—81no—
211D4×C47—88no—
212D4×C47—82no—
213D4×C47—88no—
214D4×C47—82no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—44no—
224C2×C4×C47—44no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—42no—
232C2×C4×C47—41no—
233C2×C4×C47—42no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—81no—
239C2×C4×C47#12011yescharacteristic
240C2×C4×C47#12111yescharacteristic
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47#12711yescharacteristic
243C8×C47—42no—
244C8×C47—81no—
245#9938C4711yesmaximal, characteristic, direct product factor, Sylow
246C22×C47—21no—
247C22×C47—21no—
248C22×C47—21no—
249C22×C47—21no—
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—44no—
254C22×C47—44no—
255C22×C47—44no—
256C22×C47—44no—
257C22×C47—42no—
258C22×C47—42no—
259C22×C47—82no—
260C22×C47—82no—
261C22×C47—82no—
262C22×C47—82no—
263C22×C47—82no—
264C22×C47—82no—
265C22×C47—82no—
266C22×C47—81no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47#39211yescharacteristic
274C22×C47#45312yes—
275C22×C47B(4,𝔽2)12yes—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—21no—
279C4×C47—21no—
280C4×C47—44no—
281C4×C47—42no—
282C4×C47—82no—
283C4×C47—81no—
284C4×C47—81no—
285#3006C2×C4711yescharacteristic, complemented
286#2539C2×C4711yescharacteristic, complemented
287#2404C2×C4711yescharacteristic, complemented
288#1789C2×C4711yescharacteristic, complemented
289#1510C2×C4711yescharacteristic, complemented
290#1462C2×C4711yescharacteristic, complemented
291#1284C2×C4711yescharacteristic, complemented
292C2×C47—22no—
293C2×C47—22no—
294C2×C47—41no—
295C2×C47—82no—
296C2×C47—82no—
297C2×C47—161no—
298C2×C47#200211yescharacteristic
299C2×C47#201011yescharacteristic
300C2×C47#202111yescharacteristic
301C22×#41C22×C4711yescharacteristic
302C2×AGL(1,ℤ/8)—21no—
303C2×#123—21no—
304C2×#121C22×C4711yescharacteristic
305C2×#120—21no—
306C2×#120—21no—
307C22×C22⋊C4C22×C4711yescharacteristic
308#449—22no—
309#448—21no—
310#447—21no—
311C2×#104—22no—
312#417—21no—
313#407C22×C4711yescharacteristic
314#407C22×C4711yescharacteristic
315#399—21no—
316#393—21no—
317#392—21no—
318#392—21no—
319#390—22no—
320#386—21no—
321#386—22no—
322#381C22×C4711yescharacteristic
323C4×C22⋊C4C22×C4711yescharacteristic
324#327—22no—
325#323—22no—
326C47#993811yescharacteristic, direct product factor, Sylow
327C25D4×C4711yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C4711yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C4711yescharacteristic, complemented
339C22×D4D4×C4711yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C4711yescharacteristic
342C23×C4C23×C4711yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C4711yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C4712yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C4712yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C4712yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C4711yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C4711yescharacteristic
436C22×C4C2×D4×C4711yescharacteristic
437C22×C4C2×D4×C4711yescharacteristic
438C22×C4C2×D4×C4711yescharacteristic
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4#41×C4711yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C4711yescharacteristic
491C23#120×C4711yescharacteristic
492C23#121×C4711yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—81no—
533C2×C4#120×C4711yescharacteristic
534C2×C4#121×C4711yescharacteristic
535C2×C4#121×C4711yescharacteristic
536C2×C4#127×C4711yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C47×#39211yescharacteristic
567C22C47×#45312yes—
568C22C47×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C47×#200211yescharacteristic
585C2C47×#201011yescharacteristic
586C2C47×#202111yescharacteristic
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC23×C4C23×C47
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3006C2semidirect
2. C47×#2539C2semidirect
3. C47×#2404C2semidirect
4. C47×#1789C2semidirect
5. C47×#1510C2semidirect
6. C47×#1462C2semidirect
7. C47×#1284C2semidirect
39. C22×Q8×C47D4semidirect
44. C22×D4×C47D4semidirect
45. C22×D4×C47D4semidirect
62. C2×C4⋊C4×C47D4semidirect
76. C2×C42×C47D4semidirect
83. C22⋊C8×C47D4semidirect
87. #95×C47D4semidirect
245. #9938C47direct (N × H)
285. #3006C2×C47semidirect
286. #2539C2×C47semidirect
287. #2404C2×C47semidirect
288. #1789C2×C47semidirect
289. #1510C2×C47semidirect
290. #1462C2×C47semidirect
291. #1284C2×C47semidirect
326. C47#9938direct (N × H)
333. C22×Q8D4×C47semidirect
338. C22×D4D4×C47semidirect
339. C22×D4D4×C47semidirect
356. C2×C4⋊C4D4×C47semidirect
370. C2×C42D4×C47semidirect
377. C22⋊C8D4×C47semidirect
381. #95D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30062
C47×#25392
C47×#24042
C47×#17892
C47×#15102
C47×#14622
C47×#12842
#993847