Finite Group Databasebeta

← C47×#25147 #26064845

Subgroups — C47×#25147 #26064845

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#471C211yesmaximal, characteristic, complemented
2C47×#3055C211yesmaximal, characteristic, complemented
3C47×#3005C211yesmaximal, characteristic, complemented
4C2×C47×#449C211yesmaximal, characteristic, complemented
5C47×#2933C211yesmaximal, characteristic, complemented
6C2×C47×#413C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2052C211yesmaximal, characteristic, complemented
9C47×#2046C211yesmaximal, characteristic, complemented
10C47×#2018C211yesmaximal, characteristic, complemented
11C47×#1978C211yesmaximal, characteristic, complemented
12C47×#1930C211yesmaximal, characteristic, complemented
13C47×#1907C211yesmaximal, characteristic, complemented
14C47×#1900C211yesmaximal, characteristic, complemented
15C47×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C22×M16×C47C2211yescharacteristic
24C22×M16×C47C2211yescharacteristic
25C47×#525C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C47×#471—24no—
28C47×#469—21no—
29C47×#468—21no—
30C47×#466—21no—
31C47×#465—21no—
32C47×#452—21no—
33C47×#452—21no—
34C47×#449—21no—
35C47×#449—21no—
36C47×#449—21no—
37C47×#449—21no—
38C47×#449—21no—
39C47×#449—21no—
40C47×#436—21no—
41C47×#435—21no—
42C47×#435—21no—
43C8×D4×C47—21no—
44C2×#108×C47C2211yescharacteristic
45C2×#108×C47C2211yescharacteristic
46C47×#428C2211yescharacteristic
47C47×#424C2211yescharacteristic
48C47×#419C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#418C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C2×#103×C47C2211yescharacteristic
53C2×#102×C47C2211yescharacteristic
54C47×#413—24no—
55C2×#101×C47C2211yescharacteristic
56C2×#101×C47C2211yescharacteristic
57C2×#100×C47C2211yescharacteristic
58C2×#100×C47C2211yescharacteristic
59C2×#100×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic
61C47×#408C2211yescharacteristic
62C47×#407C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#341C2211yescharacteristic
68C47×#341C2211yescharacteristic
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—41no—
76C2×#41×C47—41no—
77C2×#41×C47C2311yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47C2311yescharacteristic
82C22×D4×C47C2311yescharacteristic
83C23×C4×C47—21no—
84C23×C4×C47C2311yescharacteristic
85#137×C47—22no—
86#137×C47—41no—
87AGL(1,ℤ/8)×C47—22no—
88AGL(1,ℤ/8)×C47—22no—
89AGL(1,ℤ/8)×C47—41no—
90AGL(1,ℤ/8)×C47—41no—
91C2×Q16×C47—21no—
92C2×SD16×C47—21no—
93C2×SD16×C47—21no—
94C2×SD16×C47—22no—
95C2×SD16×C47—21no—
96C2×SD16×C47—21no—
97C2×SD16×C47—21no—
98C2×SD16×C47—41no—
99C2×D8×C47—21no—
100C2×D8×C47—21no—
101C2×D8×C47—22no—
102C2×D8×C47—21no—
103C2×D8×C47—21no—
104C2×D8×C47—41no—
105#131×C47—22no—
106#131×C47—41no—
107C2×M16×C47—21no—
108C2×M16×C47—21no—
109C2×M16×C47—21no—
110C2×M16×C47—22no—
111C2×M16×C47—22no—
112C2×M16×C47—41no—
113C2×M16×C47—41no—
114C2×M16×C47C2311yescharacteristic
115C2×M16×C47C2311yescharacteristic
116C2×M16×C47C2311yescharacteristic
117C2×M16×C47C2311yescharacteristic
118C2×M16×C47C2311yescharacteristic
119C2×M16×C47C2311yescharacteristic
120C22×C8×C47—21no—
121C22×C8×C47—21no—
122C22×C8×C47—21no—
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125#123×C47—21no—
126C22⋊Q8×C47D411yescharacteristic
127C22⋊Q8×C47D411yescharacteristic
128#121×C47—21no—
129#121×C47—21no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47D411yescharacteristic
133#121×C47D411yescharacteristic
134#120×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137#117×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—21no—
140#108×C47—22no—
141#108×C47—41no—
142#107×C47—21no—
143#106×C47—21no—
144C4⋊C8×C47—21no—
145C4⋊C8×C47—21no—
146#103×C47—21no—
147#103×C47—21no—
148#103×C47—21no—
149#103×C47—21no—
150#103×C47—21no—
151#102×C47—21no—
152#102×C47—21no—
153#102×C47—21no—
154#102×C47—21no—
155#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#101×C47—22no—
159#101×C47D414yescomplemented
160#100×C47—22no—
161#100×C47—22no—
162#100×C47—22no—
163#100×C47—41no—
164C22⋊C8×C47—21no—
165C22⋊C8×C47—21no—
166C22⋊C8×C47—21no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170C22⋊C8×C47D411yescharacteristic
171C22⋊C8×C47D411yescharacteristic
172#97×C47—21no—
173C4×C8×C47—21no—
174C24×C47—21no—
175C24×C47—21no—
176C24×C47#4111yescharacteristic
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—42no—
182#41×C47—42no—
183#41×C47—42no—
184#41×C47—42no—
185#41×C47—42no—
186#41×C47—42no—
187#41×C47—42no—
188#41×C47—42no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—21no—
194C2×Q8×C47C2×D411yescharacteristic
195C2×Q8×C47C2×D412yes—
196C2×D4×C47—24no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—42no—
212C2×D4×C47—41no—
213C2×D4×C47—41no—
214C2×D4×C47—41no—
215C2×D4×C47—41no—
216C2×D4×C47—82no—
217C2×D4×C47C2×D411yescharacteristic
218C2×D4×C47#4112yes—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—24no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—42no—
228C22×C4×C47—41no—
229C22×C4×C47—41no—
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47#4111yescharacteristic
235C22×C4×C47C2411yescharacteristic
236Q16×C47—42no—
237SD16×C47—42no—
238SD16×C47—42no—
239SD16×C47—42no—
240SD16×C47—42no—
241SD16×C47—42no—
242D8×C47—42no—
243D8×C47—42no—
244D8×C47—42no—
245D8×C47—42no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—21no—
252M16×C47—21no—
253M16×C47—21no—
254M16×C47—21no—
255M16×C47—21no—
256M16×C47—42no—
257M16×C47—42no—
258M16×C47—42no—
259M16×C47C2×D412yes—
260M16×C47C2×D412yes—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—42no—
272C2×C8×C47—42no—
273C2×C8×C47—42no—
274C2×C8×C47C2×D411yescharacteristic
275C2×C8×C47C2×D411yescharacteristic
276C2×C8×C47C2×D411yescharacteristic
277C2×C8×C47C2×D411yescharacteristic
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47C2×D411yescharacteristic
283C4⋊C4×C47C2×D411yescharacteristic
284C22⋊C4×C47—21no—
285C22⋊C4×C47—21no—
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—41no—
290C22⋊C4×C47—41no—
291C42×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—22no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—81no—
304C23×C47—81no—
305C23×C47—81no—
306C23×C47—81no—
307C23×C47#12111yescharacteristic
308C23×C47#12111yescharacteristic
309C23×C47C2×#4111yescharacteristic
310Q8×C47—21no—
311Q8×C47—22no—
312Q8×C47—22no—
313Q8×C47—21no—
314Q8×C47—41no—
315Q8×C47—41no—
316D4×C47—21no—
317D4×C47—22no—
318D4×C47—21no—
319D4×C47—22no—
320D4×C47—42no—
321D4×C47—44no—
322D4×C47—44no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47—41no—
328D4×C47—41no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—81no—
332D4×C47—82no—
333D4×C47—82no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—22no—
348C2×C4×C47—44no—
349C2×C4×C47—44no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—81no—
356C2×C4×C47#12111yescharacteristic
357C2×C4×C47#12111yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C2×#4111yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×C4×C47H(5,𝔽2)11yescharacteristic
364C8×C47—21no—
365C8×C47—21no—
366C8×C47—22no—
367C8×C47—22no—
368C8×C47—21no—
369C8×C47—21no—
370C8×C47—41no—
371C8×C47—41no—
372C8×C47—41no—
373C8×C47—41no—
374#25147C4711yesmaximal, characteristic, direct product factor, Sylow
375C22×C47—21no—
376C22×C47—21no—
377C22×C47—21no—
378C22×C47—21no—
379C22×C47—21no—
380C22×C47—21no—
381C22×C47—21no—
382C22×C47—21no—
383C22×C47—42no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—82no—
390C22×C47—82no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47—81no—
396C22×C47—161no—
397C22×C47—161no—
398C22×C47C2×#12111yescharacteristic
399C22×C47#52511yescharacteristic
400C22×C47#53811yescharacteristic
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—42no—
404C4×C47—41no—
405C4×C47—41no—
406C4×C47—41no—
407C4×C47—81no—
408C4×C47D4211yescharacteristic
409C4×C47D4211yescharacteristic
410C4×C47#54611yescharacteristic
411C4×C47#54611yescharacteristic
412C2×#471C2×C4711yescharacteristic, complemented
413#3055C2×C4711yescharacteristic, complemented
414#3005C2×C4711yescharacteristic, complemented
415C2×#449C2×C4711yescharacteristic, complemented
416#2933C2×C4711yescharacteristic, complemented
417C2×#413C2×C4711yescharacteristic, complemented
418#2063C2×C4711yescharacteristic, complemented
419#2052C2×C4711yescharacteristic, complemented
420#2046C2×C4711yescharacteristic, complemented
421#2018C2×C4711yescharacteristic, complemented
422#1978C2×C4711yescharacteristic, complemented
423#1930C2×C4711yescharacteristic, complemented
424#1907C2×C4711yescharacteristic, complemented
425#1900C2×C4711yescharacteristic, complemented
426#1855C2×C4711yescharacteristic, complemented
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—41no—
430C2×C47—41no—
431C2×C47—81no—
432C2×C47—82no—
433C2×C47—161no—
434C2×C47#242411yescharacteristic
435C2×C47#306711yescharacteristic
436C2×C47#306811yescharacteristic
437C22×#41C22×C4711yescharacteristic
438C2×#137C22×C4711yescharacteristic
439C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
440C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
441C22×SD16C22×C4711yescharacteristic
442C22×D8C22×C4711yescharacteristic
443C2×#131C22×C4711yescharacteristic
444C22×M16C22×C4711yescharacteristic
445C22×M16C22×C4711yescharacteristic
446#525C22×C4711yescharacteristic
447C2×#121C22×C4711yescharacteristic
448#471—24no—
449#469—21no—
450#468—21no—
451#466—21no—
452#465—21no—
453#452—21no—
454#452—21no—
455#449—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#436—21no—
462#435—21no—
463#435—21no—
464C8×D4—21no—
465C2×#108C22×C4711yescharacteristic
466C2×#108C22×C4711yescharacteristic
467#428C22×C4711yescharacteristic
468#424C22×C4711yescharacteristic
469#419C22×C4711yescharacteristic
470#418C22×C4711yescharacteristic
471#418C22×C4711yescharacteristic
472#417C22×C4711yescharacteristic
473C2×#103C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475#413—24no—
476C2×#101C22×C4711yescharacteristic
477C2×#101C22×C4711yescharacteristic
478C2×#100C22×C4711yescharacteristic
479C2×#100C22×C4711yescharacteristic
480C2×#100C22×C4711yescharacteristic
481C2×#100C22×C4711yescharacteristic
482#408C22×C4711yescharacteristic
483#407C22×C4711yescharacteristic
484C2×C22⋊C8C22×C4711yescharacteristic
485#405C22×C4711yescharacteristic
486#343C22×C4711yescharacteristic
487#343C22×C4711yescharacteristic
488#341C22×C4711yescharacteristic
489#341C22×C4711yescharacteristic
490C47#2514711yescharacteristic, direct product factor, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C4711yescharacteristic
500C22×Q8C23×C4711yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C4711yescharacteristic
504C22×D4C23×C4711yescharacteristic
505C23×C4—21no—
506C23×C4C23×C4711yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C4711yescharacteristic
537C2×M16C23×C4711yescharacteristic
538C2×M16C23×C4711yescharacteristic
539C2×M16C23×C4711yescharacteristic
540C2×M16C23×C4711yescharacteristic
541C2×M16C23×C4711yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C4711yescharacteristic
546C22×C8C23×C4711yescharacteristic
547#123—21no—
548C22⋊Q8D4×C4711yescharacteristic
549C22⋊Q8D4×C4711yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C4711yescharacteristic
555#121D4×C4711yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C4711yescharacteristic
560C2×C4⋊C4C23×C4711yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C4714yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C4711yescharacteristic
591C22⋊C8D4×C4711yescharacteristic
592C22⋊C8D4×C4711yescharacteristic
593C22⋊C8D4×C4711yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C4711yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C4712yes—
617C2×Q8C2×D4×C4711yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C4711yescharacteristic
640C2×D4#41×C4712yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C4711yescharacteristic
653C22×C4C2×D4×C4711yescharacteristic
654C22×C4C2×D4×C4711yescharacteristic
655C22×C4C2×D4×C4711yescharacteristic
656C22×C4#41×C4711yescharacteristic
657C22×C4C24×C4711yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C4712yes—
682M16C2×D4×C4712yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C4711yescharacteristic
697C2×C8C2×D4×C4711yescharacteristic
698C2×C8C2×D4×C4711yescharacteristic
699C2×C8C2×D4×C4711yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C4711yescharacteristic
705C4⋊C4C2×D4×C4711yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C4711yescharacteristic
730C23#121×C4711yescharacteristic
731C23C2×#41×C4711yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—42no—
743D4—44no—
744D4—44no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C4711yescharacteristic
779C2×C4#121×C4711yescharacteristic
780C2×C4C22×D4×C4711yescharacteristic
781C2×C4C22×D4×C4711yescharacteristic
782C2×C4C22×D4×C4711yescharacteristic
783C2×C4C2×#41×C4711yescharacteristic
784C2×C4H(5,𝔽2)×C4711yescharacteristic
785C2×C4H(5,𝔽2)×C4711yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C4711yescharacteristic
820C22C47×#52511yescharacteristic
821C22C47×#53811yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C4711yescharacteristic
830C4D42×C4711yescharacteristic
831C4C47×#54611yescharacteristic
832C4C47×#54611yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C47×#242411yescharacteristic
841C2C47×#306711yescharacteristic
842C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#471C2semidirect
2. C47×#3055C2semidirect
3. C47×#3005C2semidirect
4. C2×C47×#449C2semidirect
5. C47×#2933C2semidirect
6. C2×C47×#413C2semidirect
7. C47×#2063C2semidirect
8. C47×#2052C2semidirect
9. C47×#2046C2semidirect
10. C47×#2018C2semidirect
11. C47×#1978C2semidirect
12. C47×#1930C2semidirect
13. C47×#1907C2semidirect
14. C47×#1900C2semidirect
15. C47×#1855C2semidirect
159. #101×C47D4semidirect
374. #25147C47direct (N × H)
412. C2×#471C2×C47semidirect
413. #3055C2×C47semidirect
414. #3005C2×C47semidirect
415. C2×#449C2×C47semidirect
416. #2933C2×C47semidirect
417. C2×#413C2×C47semidirect
418. #2063C2×C47semidirect
419. #2052C2×C47semidirect
420. #2046C2×C47semidirect
421. #2018C2×C47semidirect
422. #1978C2×C47semidirect
423. #1930C2×C47semidirect
424. #1907C2×C47semidirect
425. #1900C2×C47semidirect
426. #1855C2×C47semidirect
490. C47#25147direct (N × H)
581. #101D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4712
C47×#30552
C47×#30052
C2×C47×#4492
C47×#29332
C2×C47×#4132
C47×#20632
C47×#20522
C47×#20462
C47×#20182
C47×#19782
C47×#19302
C47×#19072
C47×#19002
C47×#18552
#2514747