Finite Group Databasebeta

← C47×#18224 #26057922

Subgroups — C47×#18224 #26057922

Order 12032.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3534C211yesmaximal, characteristic, complemented
2C47×#3003C211yesmaximal, characteristic, complemented
3C2×C47×#447C211yesmaximal, characteristic, complemented
4C47×#2613C211yesmaximal, characteristic, complemented
5C47×#1600C212yesmaximal, complemented
6C47×#1598C212yesmaximal, complemented
7C47×#1597C212yesmaximal, complemented
8C47×#1595C212yesmaximal, complemented
9C47×#1516C211yesmaximal, characteristic, complemented
10C47×#1510C211yesmaximal, characteristic, complemented
11C47×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C47—21no—
14C22×D8×C47—21no—
15C47×#562—21no—
16C47×#560—21no—
17C47×#553—21no—
18C47×#551—21no—
19C47×#546—21no—
20C47×#546—21no—
21C47×#546—21no—
22D42×C47—21no—
23C47×#540—21no—
24C47×#539—21no—
25C47×#539C2211yescharacteristic, complemented
26C47×#538—21no—
27C47×#538C2211yescharacteristic, complemented
28C47×#537C2211yescharacteristic, complemented
29C47×#534—21no—
30C47×#534C2211yescharacteristic, complemented
31C47×#525C2211yescharacteristic
32C2×#123×C47C2211yescharacteristic
33C2×#121×C47C2211yescharacteristic
34C2×#120×C47—21no—
35C47×#450—21no—
36C47×#450C2212yescomplemented
37C47×#447—21no—
38C47×#447—21no—
39C47×#447—21no—
40C47×#447C2212yes—
41C47×#447C2212yescomplemented
42C47×#447C2212yescomplemented
43C47×#418—21no—
44C2×#102×C47—21no—
45C47×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C47C2211yescharacteristic, complemented
47C47×#394—21no—
48C47×#394C2212yescomplemented
49C47×#392—21no—
50C47×#392C2212yescomplemented
51C47×#381C2211yescharacteristic, complemented
52C47×#379—21no—
53C47×#328C2212yescomplemented
54C47×#327C2212yescomplemented
55C47×#327C2212yescomplemented
56C47×#327C2212yescomplemented
57C47×#324C2212yescomplemented
58C47×#323C2212yescomplemented
59C25×C47—21no—
60C2×#41×C47—21no—
61C2×#41×C47D411yescharacteristic, complemented
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—44no—
72C22×D4×C47D411yescharacteristic
73C22×D4×C47D411yescharacteristic, complemented
74C22×D4×C47C2312yes—
75C23×C4×C47C2311yescharacteristic
76AGL(1,ℤ/8)×C47—44no—
77C2×SD16×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—44no—
82C2×M16×C47—21no—
83C22×C8×C47—21no—
84#127×C47—21no—
85#126×C47—21no—
86#126×C47—21no—
87#126×C47—21no—
88#126×C47—21no—
89#125×C47—21no—
90#125×C47—21no—
91#124×C47—21no—
92#124×C47—21no—
93#124×C47—21no—
94#123×C47—21no—
95#123×C47—21no—
96#123×C47—21no—
97#123×C47—21no—
98#123×C47—21no—
99#123×C47—21no—
100#123×C47—21no—
101#123×C47—21no—
102#123×C47—21no—
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47D411yescharacteristic, complemented
114C22⋊Q8×C47C2311yescharacteristic
115#121×C47—21no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47—21no—
130#121×C47D411yescharacteristic, complemented
131#121×C47D411yescharacteristic, complemented
132#121×C47D411yescharacteristic, complemented
133#121×C47C2311yescharacteristic
134#121×C47C2311yescharacteristic
135#121×C47C2311yescharacteristic
136#120×C47—21no—
137#120×C47—21no—
138#120×C47—21no—
139#120×C47—21no—
140#120×C47—21no—
141#120×C47—21no—
142#120×C47—21no—
143#120×C47—21no—
144#120×C47—44no—
145C4×D4×C47—21no—
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47—21no—
149C4×D4×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—21no—
153#117×C47—21no—
154#117×C47D411yescharacteristic, complemented
155C2×C4⋊C4×C47D411yescharacteristic
156C2×C4⋊C4×C47D411yescharacteristic, complemented
157C2×C4⋊C4×C47C2311yescharacteristic
158C2×C22⋊C4×C47—21no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—21no—
161C2×C22⋊C4×C47—21no—
162C2×C22⋊C4×C47—22no—
163C2×C22⋊C4×C47—22no—
164C2×C22⋊C4×C47—22no—
165C2×C22⋊C4×C47D411yescharacteristic
166C2×C22⋊C4×C47D411yescharacteristic
167C2×C22⋊C4×C47C2311yescharacteristic
168#102×C47—22no—
169#102×C47—22no—
170#102×C47—22no—
171#102×C47—22no—
172C22⋊C8×C47—21no—
173C22⋊C8×C47—21no—
174C22⋊C8×C47C2312yes—
175C22⋊C8×C47C2312yes—
176#95×C47—21no—
177#95×C47C2312yes—
178C24×C47—24no—
179C24×C47—21no—
180C24×C47—22no—
181C24×C47—21no—
182C24×C47—42no—
183C24×C47—41no—
184C24×C47—41no—
185C24×C47—82no—
186C24×C47—82no—
187C24×C47C2×D411yescharacteristic
188C24×C47C2×D411yescharacteristic
189#41×C47—42no—
190#41×C47—82no—
191C2×Q8×C47—21no—
192C2×Q8×C47C2×D411yescharacteristic
193C2×D4×C47—24no—
194C2×D4×C47—24no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
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—21no—
212C2×D4×C47—22no—
213C2×D4×C47—22no—
214C2×D4×C47—42no—
215C2×D4×C47—42no—
216C2×D4×C47—42no—
217C2×D4×C47—44no—
218C2×D4×C47—44no—
219C2×D4×C47—44no—
220C2×D4×C47—44no—
221C2×D4×C47—42no—
222C2×D4×C47—44no—
223C2×D4×C47—41no—
224C2×D4×C47—41no—
225C2×D4×C47—82no—
226C2×D4×C47—82no—
227C2×D4×C47—82no—
228C2×D4×C47—82no—
229C2×D4×C47—82no—
230C2×D4×C47C2×D411yescharacteristic
231C2×D4×C47C2×D411yescharacteristic
232C2×D4×C47C2×D411yescharacteristic
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—22no—
241C22×C4×C47—42no—
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2411yescharacteristic
251SD16×C47—44no—
252D8×C47—44no—
253D8×C47—44no—
254D8×C47—44no—
255M16×C47—42no—
256C2×C8×C47—22no—
257C2×C8×C47—22no—
258C2×C8×C47—42no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47C2×D411yescharacteristic
273C4⋊C4×C47C2×D411yescharacteristic
274C4⋊C4×C47C2×D411yescharacteristic
275C4⋊C4×C47C2×D411yescharacteristic
276C22⋊C4×C47—21no—
277C22⋊C4×C47—21no—
278C22⋊C4×C47—21no—
279C22⋊C4×C47—21no—
280C22⋊C4×C47—21no—
281C22⋊C4×C47—21no—
282C22⋊C4×C47—21no—
283C22⋊C4×C47—21no—
284C22⋊C4×C47—21no—
285C22⋊C4×C47—21no—
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—21no—
292C22⋊C4×C47—21no—
293C22⋊C4×C47—21no—
294C22⋊C4×C47—21no—
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—44no—
302C22⋊C4×C47—42no—
303C22⋊C4×C47—82no—
304C22⋊C4×C47—82no—
305C42×C47—21no—
306C42×C47—21no—
307C42×C47—21no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—24no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—21no—
314C23×C47—21no—
315C23×C47—22no—
316C23×C47—41no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—44no—
320C23×C47—42no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47—42no—
324C23×C47—42no—
325C23×C47—42no—
326C23×C47—44no—
327C23×C47—42no—
328C23×C47—81no—
329C23×C47—81no—
330C23×C47—82no—
331C23×C47—82no—
332C23×C47—82no—
333C23×C47—82no—
334C23×C47—88no—
335C23×C47—81no—
336C23×C47—81no—
337C23×C47—81no—
338C23×C47—88no—
339C23×C47#12011yescharacteristic
340C23×C47#12011yescharacteristic
341C23×C47C22×D411yescharacteristic
342Q8×C47—41no—
343Q8×C47—81no—
344D4×C47—24no—
345D4×C47—24no—
346D4×C47—41no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—42no—
350D4×C47—42no—
351D4×C47—44no—
352D4×C47—44no—
353D4×C47—42no—
354D4×C47—42no—
355D4×C47—42no—
356D4×C47—42no—
357D4×C47—42no—
358D4×C47—81no—
359D4×C47—81no—
360D4×C47—81no—
361D4×C47—81no—
362D4×C47—81no—
363D4×C47—81no—
364D4×C47—81no—
365D4×C47—81no—
366D4×C47—81no—
367D4×C47—81no—
368D4×C47—81no—
369D4×C47—81no—
370D4×C47—88no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—21no—
374C2×C4×C47—21no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—21no—
380C2×C4×C47—21no—
381C2×C4×C47—22no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—42no—
389C2×C4×C47—42no—
390C2×C4×C47—42no—
391C2×C4×C47—81no—
392C2×C4×C47—81no—
393C2×C4×C47—81no—
394C2×C4×C47—81no—
395C2×C4×C47—81no—
396C2×C4×C47—81no—
397C2×C4×C47—81no—
398C2×C4×C47#12011yescharacteristic
399C2×C4×C47#12011yescharacteristic
400C2×C4×C47C22×D411yescharacteristic
401C2×C4×C47C22×D411yescharacteristic
402C8×C47—42no—
403C8×C47—42no—
404#18224C4711yesmaximal, characteristic, direct product factor, Sylow
405C22×C47—21no—
406C22×C47—21no—
407C22×C47—21no—
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—21no—
411C22×C47—21no—
412C22×C47—44no—
413C22×C47—44no—
414C22×C47—44no—
415C22×C47—41no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—41no—
422C22×C47—41no—
423C22×C47—41no—
424C22×C47—41no—
425C22×C47—44no—
426C22×C47—41no—
427C22×C47—41no—
428C22×C47—82no—
429C22×C47—82no—
430C22×C47—82no—
431C22×C47—88no—
432C22×C47—88no—
433C22×C47—82no—
434C22×C47—82no—
435C22×C47—162no—
436C22×C47—162no—
437C22×C47B(4,𝔽2)12yes—
438C22×C47C2×#12011yescharacteristic
439C22×C47#57612yes—
440C4×C47—21no—
441C4×C47—21no—
442C4×C47—21no—
443C4×C47—21no—
444C4×C47—41no—
445C4×C47—41no—
446C4×C47—41no—
447C4×C47—41no—
448C4×C47—41no—
449C4×C47—41no—
450C4×C47—41no—
451C4×C47—41no—
452C4×C47—82no—
453#3534C2×C4711yescharacteristic, complemented
454#3003C2×C4711yescharacteristic, complemented
455C2×#447C2×C4711yescharacteristic, complemented
456#2613C2×C4711yescharacteristic, complemented
457#1600C2×C4712yescomplemented
458#1598C2×C4712yescomplemented
459#1597C2×C4712yescomplemented
460#1595C2×C4712yescomplemented
461#1516C2×C4711yescharacteristic, complemented
462#1510C2×C4711yescharacteristic, complemented
463#1468C2×C4711yescharacteristic, complemented
464C2×C47—22no—
465C2×C47—22no—
466C2×C47—41no—
467C2×C47—84no—
468C2×C47—81no—
469C2×C47—81no—
470C2×C47—81no—
471C2×C47—81no—
472C2×C47#300811yescharacteristic
473C2×C47#302111yescharacteristic
474C2×C47C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C4711yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C4711yescharacteristic, complemented
489#538—21no—
490#538C22×C4711yescharacteristic, complemented
491#537C22×C4711yescharacteristic, complemented
492#534—21no—
493#534C22×C4711yescharacteristic, complemented
494#525C22×C4711yescharacteristic
495C2×#123C22×C4711yescharacteristic
496C2×#121C22×C4711yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C4712yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C4712yes—
504#447C22×C4712yescomplemented
505#447C22×C4712yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C4711yescharacteristic, complemented
509C2×C22⋊C8C22×C4711yescharacteristic, complemented
510#394—21no—
511#394C22×C4712yescomplemented
512#392—21no—
513#392C22×C4712yescomplemented
514#381C22×C4711yescharacteristic, complemented
515#379—21no—
516#328C22×C4712yescomplemented
517#327C22×C4712yescomplemented
518#327C22×C4712yescomplemented
519#327C22×C4712yescomplemented
520#324C22×C4712yescomplemented
521#323C22×C4712yescomplemented
522C47#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C4711yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C4711yescharacteristic
537C22×D4D4×C4711yescharacteristic, complemented
538C22×D4C23×C4712yes—
539C23×C4C23×C4711yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C4711yescharacteristic, complemented
578C22⋊Q8C23×C4711yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C4711yescharacteristic, complemented
595#121D4×C4711yescharacteristic, complemented
596#121D4×C4711yescharacteristic, complemented
597#121C23×C4711yescharacteristic
598#121C23×C4711yescharacteristic
599#121C23×C4711yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C4711yescharacteristic, complemented
619C2×C4⋊C4D4×C4711yescharacteristic
620C2×C4⋊C4D4×C4711yescharacteristic, complemented
621C2×C4⋊C4C23×C4711yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C4711yescharacteristic
630C2×C22⋊C4D4×C4711yescharacteristic
631C2×C22⋊C4C23×C4711yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C4712yes—
639C22⋊C8C23×C4712yes—
640#95—21no—
641#95C23×C4712yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C4711yescharacteristic
652C24C2×D4×C4711yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C4711yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C4711yescharacteristic
695C2×D4C2×D4×C4711yescharacteristic
696C2×D4C2×D4×C4711yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C4711yescharacteristic
707C22×C4C2×D4×C4711yescharacteristic
708C22×C4C2×D4×C4711yescharacteristic
709C22×C4C2×D4×C4711yescharacteristic
710C22×C4C2×D4×C4711yescharacteristic
711C22×C4C2×D4×C4711yescharacteristic
712C22×C4C2×D4×C4711yescharacteristic
713C22×C4C2×D4×C4711yescharacteristic
714C22×C4C24×C4711yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C4711yescharacteristic
737C4⋊C4C2×D4×C4711yescharacteristic
738C4⋊C4C2×D4×C4711yescharacteristic
739C4⋊C4C2×D4×C4711yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C4711yescharacteristic
804C23#120×C4711yescharacteristic
805C23C22×D4×C4711yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C4711yescharacteristic
863C2×C4#120×C4711yescharacteristic
864C2×C4C22×D4×C4711yescharacteristic
865C2×C4C22×D4×C4711yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C47×B(4,𝔽2)12yes—
901C22C2×#120×C4711yescharacteristic
902C22C47×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C47×#300811yescharacteristic
925C2C47×#302111yescharacteristic
926C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×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×#3534C2semidirect
2. C47×#3003C2semidirect
3. C2×C47×#447C2semidirect
4. C47×#2613C2semidirect
5. C47×#1600C2semidirect
6. C47×#1598C2semidirect
7. C47×#1597C2semidirect
8. C47×#1595C2semidirect
9. C47×#1516C2semidirect
10. C47×#1510C2semidirect
11. C47×#1468C2semidirect
12. C23×D4×C47C22semidirect
25. C47×#539C22semidirect
27. C47×#538C22semidirect
28. C47×#537C22semidirect
30. C47×#534C22semidirect
36. C47×#450C22semidirect
41. C47×#447C22semidirect
42. C47×#447C22semidirect
45. C47×#407C22semidirect
46. C2×C22⋊C8×C47C22semidirect
48. C47×#394C22semidirect
50. C47×#392C22semidirect
51. C47×#381C22semidirect
53. C47×#328C22semidirect
54. C47×#327C22semidirect
55. C47×#327C22semidirect
56. C47×#327C22semidirect
57. C47×#324C22semidirect
58. C47×#323C22semidirect
61. C2×#41×C47D4semidirect
73. C22×D4×C47D4semidirect
113. C22⋊Q8×C47D4semidirect
130. #121×C47D4semidirect
131. #121×C47D4semidirect
132. #121×C47D4semidirect
154. #117×C47D4semidirect
156. C2×C4⋊C4×C47D4semidirect
404. #18224C47direct (N × H)
453. #3534C2×C47semidirect
454. #3003C2×C47semidirect
455. C2×#447C2×C47semidirect
456. #2613C2×C47semidirect
457. #1600C2×C47semidirect
458. #1598C2×C47semidirect
459. #1597C2×C47semidirect
460. #1595C2×C47semidirect
461. #1516C2×C47semidirect
462. #1510C2×C47semidirect
463. #1468C2×C47semidirect
475. C23×D4C22×C47semidirect
488. #539C22×C47semidirect
490. #538C22×C47semidirect
491. #537C22×C47semidirect
493. #534C22×C47semidirect
499. #450C22×C47semidirect
504. #447C22×C47semidirect
505. #447C22×C47semidirect
508. #407C22×C47semidirect
509. C2×C22⋊C8C22×C47semidirect
511. #394C22×C47semidirect
513. #392C22×C47semidirect
514. #381C22×C47semidirect
516. #328C22×C47semidirect
517. #327C22×C47semidirect
518. #327C22×C47semidirect
519. #327C22×C47semidirect
520. #324C22×C47semidirect
521. #323C22×C47semidirect
522. C47#18224direct (N × H)
525. C2×#41D4×C47semidirect
537. C22×D4D4×C47semidirect
577. C22⋊Q8D4×C47semidirect
594. #121D4×C47semidirect
595. #121D4×C47semidirect
596. #121D4×C47semidirect
618. #117D4×C47semidirect
620. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35342
C47×#30032
C2×C47×#4472
C47×#26132
C47×#16002
C47×#15982
C47×#15972
C47×#15952
C47×#15162
C47×#15102
C47×#14682
#1822447