Finite Group Databasebeta

← C47×#25587 #26065285

Subgroups — C47×#25587 #26065285

Order 12032.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3505C211yesmaximal, characteristic, complemented
2C47×#2561C211yesmaximal, characteristic, complemented
3C47×#2539C211yesmaximal, characteristic, complemented
4C47×#2534C211yesmaximal, characteristic, complemented
5C47×#2022C212yesmaximal, complemented
6C47×#2021C212yesmaximal, complemented
7C47×#1996C211yesmaximal, characteristic, complemented
8C47×#1964C211yesmaximal, characteristic, complemented
9C47×#1890C212yesmaximal, complemented
10C47×#1889C212yesmaximal, complemented
11C4×#99×C47C211yesmaximal, characteristic, complemented
12C47×#553—22no—
13C47×#553—21no—
14C47×#552—21no—
15C47×#551—22no—
16C47×#548—21no—
17C47×#546—21no—
18C47×#539—21no—
19C47×#538—21no—
20C47×#534C2212yes—
21C47×#529—21no—
22C47×#525—21no—
23C2×#123×C47C2212yes—
24C2×#123×C47C2211yescharacteristic
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#120×C47C2212yes—
28C2×#120×C47C2211yescharacteristic
29C47×#518C2212yes—
30C2×C4×D4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C2×#99×C47C2212yes—
33C2×#99×C47C2212yes—
34C2×#99×C47C2212yes—
35C47×#399—21no—
36C47×#397—21no—
37C47×#396—21no—
38C47×#394—21no—
39C47×#393—21no—
40C47×#392—21no—
41C47×#390—22no—
42C47×#388—22no—
43C47×#388—21no—
44C47×#386—21no—
45C47×#381C2212yes—
46C47×#381C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C47×#379C2212yes—
49C47×#379C2211yescharacteristic
50C4×C22⋊C4×C47C2211yescharacteristic
51C4×C22⋊C4×C47C2211yescharacteristic
52C47×#342C2212yes—
53C47×#342C2212yes—
54C47×#342C2212yes—
55C25×C47C2311yescharacteristic
56C2×#41×C47—21no—
57C22×Q8×C47D411yescharacteristic, complemented
58C22×D4×C47—21no—
59C22×D4×C47—22no—
60C22×D4×C47D411yescharacteristic, complemented
61C22×D4×C47C2311yescharacteristic
62C22×D4×C47C2312yes—
63C23×C4×C47D411yescharacteristic, complemented
64C23×C4×C47C2311yescharacteristic
65C23×C4×C47C2311yescharacteristic
66#126×C47—22no—
67#126×C47—22no—
68#126×C47—22no—
69#125×C47—21no—
70#125×C47—22no—
71#124×C47—21no—
72#124×C47—22no—
73#123×C47—22no—
74#123×C47—22no—
75#123×C47—22no—
76#123×C47—22no—
77#123×C47—22no—
78#123×C47—24no—
79#123×C47—42no—
80#123×C47—42no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—22no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47—21no—
87#121×C47—21no—
88#121×C47—22no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—21no—
93#121×C47—22no—
94#121×C47—22no—
95#120×C47—22no—
96#120×C47—22no—
97#120×C47—24no—
98#120×C47—42no—
99#120×C47—42no—
100C4×Q8×C47—21no—
101C4×D4×C47—22no—
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106C4×D4×C47—21no—
107C4×D4×C47—22no—
108C4×D4×C47—22no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111#117×C47—21no—
112#117×C47—22no—
113#117×C47—22no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—22no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47D411yescharacteristic, complemented
118C2×C4⋊C4×C47D411yescharacteristic, complemented
119C2×C4⋊C4×C47D412yescomplemented
120C2×C4⋊C4×C47D411yescharacteristic, complemented
121C2×C22⋊C4×C47—22no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—22no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—22no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—22no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—22no—
136C2×C22⋊C4×C47D411yescharacteristic, complemented
137C2×C22⋊C4×C47D412yescomplemented
138C2×C22⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47C2312yes—
141C2×C22⋊C4×C47C2311yescharacteristic
142C2×C22⋊C4×C47C2312yes—
143C2×C22⋊C4×C47C2312yes—
144C2×C42×C47—21no—
145C2×C42×C47—21no—
146C2×C42×C47D411yescharacteristic, complemented
147#99×C47—24no—
148#99×C47—42no—
149#99×C47—42no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154#95×C47—22no—
155#95×C47—21no—
156#95×C47—22no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—42no—
163C24×C47—81no—
164C24×C47C2×D412yes—
165C24×C47C2×D411yescharacteristic
166C24×C47C2411yescharacteristic
167#41×C47—82no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—81no—
171C2×D4×C47—21no—
172C2×D4×C47—22no—
173C2×D4×C47—21no—
174C2×D4×C47—22no—
175C2×D4×C47—22no—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—22no—
179C2×D4×C47—22no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—44no—
186C2×D4×C47—42no—
187C2×D4×C47—44no—
188C2×D4×C47—42no—
189C2×D4×C47—81no—
190C2×D4×C47—82no—
191C2×D4×C47—81no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—81no—
206C22×C4×C47—81no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D412yes—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C4⋊C4×C47—22no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—22no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—44no—
232C4⋊C4×C47—42no—
233C4⋊C4×C47—81no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—22no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—22no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—21no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—21no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—21no—
247C22⋊C4×C47—21no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—44no—
254C22⋊C4×C47—44no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—44no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—41no—
260C22⋊C4×C47—41no—
261C22⋊C4×C47—41no—
262C22⋊C4×C47—41no—
263C22⋊C4×C47—81no—
264C22⋊C4×C47—82no—
265C22⋊C4×C47#4114yescomplemented
266C42×C47—22no—
267C42×C47—22no—
268C42×C47—21no—
269C42×C47—21no—
270C42×C47—81no—
271C42×C47—81no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—42no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—42no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—84no—
300C23×C47—84no—
301C23×C47C22×D411yescharacteristic
302C23×C47C22×D411yescharacteristic
303C23×C47C22×D411yescharacteristic
304C23×C47C2×#4112yes—
305C23×C47H(5,𝔽2)12yes—
306Q8×C47—42no—
307Q8×C47—81no—
308D4×C47—42no—
309D4×C47—42no—
310D4×C47—42no—
311D4×C47—42no—
312D4×C47—42no—
313D4×C47—42no—
314D4×C47—42no—
315D4×C47—81no—
316D4×C47—82no—
317D4×C47—82no—
318D4×C47—88no—
319D4×C47—84no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—24no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47—42no—
340C2×C4×C47—41no—
341C2×C4×C47—42no—
342C2×C4×C47—41no—
343C2×C4×C47—42no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—42no—
356C2×C4×C47—42no—
357C2×C4×C47—42no—
358C2×C4×C47—81no—
359C2×C4×C47—82no—
360C2×C4×C47—82no—
361C2×C4×C47#12011yescharacteristic
362C2×C4×C47#12011yescharacteristic
363C2×C4×C47#12011yescharacteristic
364C2×C4×C47#12011yescharacteristic
365#25587C4711yesmaximal, characteristic, direct product factor, Sylow
366C22×C47—21no—
367C22×C47—21no—
368C22×C47—21no—
369C22×C47—21no—
370C22×C47—21no—
371C22×C47—21no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—44no—
376C22×C47—42no—
377C22×C47—44no—
378C22×C47—42no—
379C22×C47—41no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—42no—
384C22×C47—41no—
385C22×C47—42no—
386C22×C47—82no—
387C22×C47—82no—
388C22×C47—81no—
389C22×C47—82no—
390C22×C47—81no—
391C22×C47—82no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47C2×#12011yescharacteristic
396C22×C47#53211yescharacteristic
397C22×C47#53511yescharacteristic
398C22×C47#54612yes—
399C22×C47#55012yes—
400C4×C47—21no—
401C4×C47—21no—
402C4×C47—21no—
403C4×C47—21no—
404C4×C47—44no—
405C4×C47—41no—
406C4×C47—42no—
407C4×C47—41no—
408C4×C47—42no—
409C4×C47—41no—
410C4×C47—42no—
411C4×C47—81no—
412C4×C47—82no—
413C4×C47—81no—
414C4×C47—81no—
415#3505C2×C4711yescharacteristic, complemented
416#2561C2×C4711yescharacteristic, complemented
417#2539C2×C4711yescharacteristic, complemented
418#2534C2×C4711yescharacteristic, complemented
419#2022C2×C4712yescomplemented
420#2021C2×C4712yescomplemented
421#1996C2×C4711yescharacteristic, complemented
422#1964C2×C4711yescharacteristic, complemented
423#1890C2×C4712yescomplemented
424#1889C2×C4712yescomplemented
425C4×#99C2×C4711yescharacteristic, complemented
426C2×C47—22no—
427C2×C47—21no—
428C2×C47—22no—
429C2×C47—21no—
430C2×C47—82no—
431C2×C47—81no—
432C2×C47—82no—
433C2×C47#243111yescharacteristic
434C2×C47#302511yescharacteristic
435C2×C47#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C4712yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C4712yes—
448C2×#123C22×C4711yescharacteristic
449C2×C22⋊Q8C22×C4711yescharacteristic
450C2×#121C22×C4711yescharacteristic
451C2×#120C22×C4712yes—
452C2×#120C22×C4711yescharacteristic
453#518C22×C4712yes—
454C2×C4×D4C22×C4711yescharacteristic
455C22×C22⋊C4C22×C4711yescharacteristic
456C2×#99C22×C4712yes—
457C2×#99C22×C4712yes—
458C2×#99C22×C4712yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C4712yes—
470#381C22×C4711yescharacteristic
471#380C22×C4711yescharacteristic
472#379C22×C4712yes—
473#379C22×C4711yescharacteristic
474C4×C22⋊C4C22×C4711yescharacteristic
475C4×C22⋊C4C22×C4711yescharacteristic
476#342C22×C4712yes—
477#342C22×C4712yes—
478#342C22×C4712yes—
479C47#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C4711yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C4711yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C4711yescharacteristic, complemented
486C22×D4C23×C4711yescharacteristic
487C22×D4C23×C4712yes—
488C23×C4D4×C4711yescharacteristic, complemented
489C23×C4C23×C4711yescharacteristic
490C23×C4C23×C4711yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4711yescharacteristic, complemented
543C2×C4⋊C4D4×C4711yescharacteristic, complemented
544C2×C4⋊C4D4×C4712yescomplemented
545C2×C4⋊C4D4×C4711yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C4711yescharacteristic, complemented
562C2×C22⋊C4D4×C4712yescomplemented
563C2×C22⋊C4C23×C4711yescharacteristic
564C2×C22⋊C4C23×C4711yescharacteristic
565C2×C22⋊C4C23×C4712yes—
566C2×C22⋊C4C23×C4711yescharacteristic
567C2×C22⋊C4C23×C4712yes—
568C2×C22⋊C4C23×C4712yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C4711yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C4712yes—
590C24C2×D4×C4711yescharacteristic
591C24C24×C4711yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C2×D4×C4712yes—
634C22×C4C2×D4×C4711yescharacteristic
635C22×C4C2×D4×C4712yes—
636C22×C4C2×D4×C4711yescharacteristic
637C22×C4C2×D4×C4712yes—
638C22×C4C2×D4×C4711yescharacteristic
639C22×C4C2×D4×C4711yescharacteristic
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C2×D4×C4711yescharacteristic
642C22×C4C2×D4×C4711yescharacteristic
643C22×C4C2×D4×C4711yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C4714yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C4711yescharacteristic
727C23C22×D4×C4711yescharacteristic
728C23C22×D4×C4711yescharacteristic
729C23C2×#41×C4712yes—
730C23H(5,𝔽2)×C4712yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C4711yescharacteristic
787C2×C4#120×C4711yescharacteristic
788C2×C4#120×C4711yescharacteristic
789C2×C4#120×C4711yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C4711yescharacteristic
820C22C47×#53211yescharacteristic
821C22C47×#53511yescharacteristic
822C22C47×#54612yes—
823C22C47×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C47×#243111yescharacteristic
847C2C47×#302511yescharacteristic
848C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3505C2semidirect
2. C47×#2561C2semidirect
3. C47×#2539C2semidirect
4. C47×#2534C2semidirect
5. C47×#2022C2semidirect
6. C47×#2021C2semidirect
7. C47×#1996C2semidirect
8. C47×#1964C2semidirect
9. C47×#1890C2semidirect
10. C47×#1889C2semidirect
11. C4×#99×C47C2semidirect
57. C22×Q8×C47D4semidirect
60. C22×D4×C47D4semidirect
63. C23×C4×C47D4semidirect
117. C2×C4⋊C4×C47D4semidirect
118. C2×C4⋊C4×C47D4semidirect
119. C2×C4⋊C4×C47D4semidirect
120. C2×C4⋊C4×C47D4semidirect
136. C2×C22⋊C4×C47D4semidirect
137. C2×C22⋊C4×C47D4semidirect
146. C2×C42×C47D4semidirect
265. C22⋊C4×C47#41semidirect
365. #25587C47direct (N × H)
415. #3505C2×C47semidirect
416. #2561C2×C47semidirect
417. #2539C2×C47semidirect
418. #2534C2×C47semidirect
419. #2022C2×C47semidirect
420. #2021C2×C47semidirect
421. #1996C2×C47semidirect
422. #1964C2×C47semidirect
423. #1890C2×C47semidirect
424. #1889C2×C47semidirect
425. C4×#99C2×C47semidirect
479. C47#25587direct (N × H)
482. C22×Q8D4×C47semidirect
485. C22×D4D4×C47semidirect
488. C23×C4D4×C47semidirect
542. C2×C4⋊C4D4×C47semidirect
543. C2×C4⋊C4D4×C47semidirect
544. C2×C4⋊C4D4×C47semidirect
545. C2×C4⋊C4D4×C47semidirect
561. C2×C22⋊C4D4×C47semidirect
562. C2×C22⋊C4D4×C47semidirect
571. C2×C42D4×C47semidirect
690. C22⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35052
C47×#25612
C47×#25392
C47×#25342
C47×#20222
C47×#20212
C47×#19962
C47×#19642
C47×#18902
C47×#18892
C4×#99×C472
#2558747