Finite Group Databasebeta

← C47×#19010 #26058708

Subgroups — C47×#19010 #26058708

Order 12032.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3529C211yesmaximal, characteristic, complemented
2C47×#3219C211yesmaximal, characteristic, complemented
3C47×#3214C211yesmaximal, characteristic, complemented
4C47×#3180C211yesmaximal, characteristic, complemented
5C47×#1664C211yesmaximal, characteristic, complemented
6C47×#1662C211yesmaximal, characteristic, complemented
7C47×#1661C211yesmaximal, characteristic, complemented
8C47×#1659C211yesmaximal, characteristic, complemented
9C47×#1657C211yesmaximal, characteristic, complemented
10C47×#1656C211yesmaximal, characteristic, complemented
11C47×#1656C211yesmaximal, characteristic, complemented
12C47×#1655C211yesmaximal, characteristic, complemented
13C47×#1535C211yesmaximal, characteristic, complemented
14C47×#1532C211yesmaximal, characteristic, complemented
15C47×#1530C211yesmaximal, characteristic, complemented
16C47×#563—21no—
17C47×#563C2211yescharacteristic
18C47×#562—21no—
19C47×#562—21no—
20C47×#562C2211yescharacteristic
21C47×#562C2211yescharacteristic
22C47×H(3,𝔽4)C2211yescharacteristic
23C47×#560—21no—
24C47×#560—21no—
25C47×#560—21no—
26C47×#532—21no—
27C47×#532C2211yescharacteristic
28C47×#532C2211yescharacteristic, complemented
29C47×#529—21no—
30C47×#529—21no—
31C47×#529C2211yescharacteristic
32C47×#529C2211yescharacteristic
33C47×#525—21no—
34C47×#525—21no—
35C47×#525—21no—
36C47×#501C2211yescharacteristic, complemented
37C47×#497C2211yescharacteristic
38C47×#496C2211yescharacteristic
39C47×#496C2211yescharacteristic
40C47×#496C2211yescharacteristic
41C47×#496C2211yescharacteristic, complemented
42C47×#491C2211yescharacteristic, complemented
43C47×#490C2211yescharacteristic, complemented
44C47×#490C2211yescharacteristic, complemented
45C47×#489C2211yescharacteristic
46C47×#489C2211yescharacteristic
47C47×#489C2211yescharacteristic, complemented
48C47×#466—21no—
49C47×#465—21no—
50C47×#464—21no—
51C47×#463—21no—
52C47×#461—21no—
53C47×#459—21no—
54C47×#452—21no—
55C47×#449—21no—
56C47×#449—21no—
57C47×#449—21no—
58C47×#442—21no—
59C47×#440—21no—
60C47×#432C2211yescharacteristic, complemented
61C47×#432C2211yescharacteristic, complemented
62C2×#97×C47C2211yescharacteristic, complemented
63C47×#330C2211yescharacteristic, complemented
64C47×#330C2211yescharacteristic, complemented
65C47×#330C2211yescharacteristic, complemented
66C47×#330C2211yescharacteristic, complemented
67C47×#329C2211yescharacteristic
68C47×#329C2211yescharacteristic
69C47×#329C2211yescharacteristic
70C47×#329C2211yescharacteristic
71C47×#329C2211yescharacteristic
72C47×#329C2211yescharacteristic
73C47×#329C2211yescharacteristic, complemented
74C47×#329C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47D411yescharacteristic
78C2×#41×C47D411yescharacteristic
79C23×C4×C47—21no—
80C2×Q16×C47—21no—
81C2×SD16×C47—21no—
82C2×SD16×C47—21no—
83C2×SD16×C47—21no—
84C2×SD16×C47—21no—
85C2×SD16×C47—21no—
86C2×D8×C47—21no—
87C2×D8×C47—21no—
88C2×D8×C47—21no—
89C2×D8×C47—21no—
90C22×C8×C47—21no—
91C4⋊Q8×C47—21no—
92C4⋊Q8×C47D411yescharacteristic
93C4⋊Q8×C47C2311yescharacteristic
94#127×C47—21no—
95#127×C47D411yescharacteristic
96#127×C47C2311yescharacteristic
97#126×C47—21no—
98#126×C47—21no—
99#126×C47—21no—
100#126×C47—21no—
101#126×C47—21no—
102#126×C47—21no—
103#125×C47—21no—
104#125×C47—21no—
105#125×C47C2311yescharacteristic
106#125×C47C2311yescharacteristic
107#124×C47—21no—
108#124×C47—21no—
109#124×C47—21no—
110#124×C47—21no—
111#124×C47—21no—
112#124×C47C2311yescharacteristic
113#124×C47C2311yescharacteristic
114#124×C47C2311yescharacteristic
115#124×C47C2311yescharacteristic
116#123×C47—21no—
117#123×C47—21no—
118#123×C47—21no—
119#123×C47—21no—
120#123×C47—21no—
121#123×C47—21no—
122#123×C47—21no—
123#123×C47—21no—
124#123×C47—21no—
125#123×C47—21no—
126#123×C47—21no—
127#123×C47—21no—
128C22⋊Q8×C47—21no—
129C22⋊Q8×C47—21no—
130C22⋊Q8×C47—21no—
131C22⋊Q8×C47—21no—
132C22⋊Q8×C47—21no—
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47—21no—
136C22⋊Q8×C47D411yescharacteristic
137C22⋊Q8×C47D411yescharacteristic
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47—21no—
142#121×C47—21no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47—21no—
150#121×C47—21no—
151#121×C47—21no—
152#121×C47—21no—
153#121×C47—21no—
154#121×C47D411yescharacteristic
155#121×C47D411yescharacteristic
156#120×C47—21no—
157#120×C47—21no—
158#120×C47—21no—
159#120×C47—21no—
160#120×C47—21no—
161#120×C47—21no—
162C4×Q8×C47D411yescharacteristic
163C4×Q8×C47D411yescharacteristic
164C4×D4×C47—21no—
165C4×D4×C47—21no—
166C4×D4×C47—21no—
167C4×D4×C47—21no—
168C4×D4×C47—21no—
169C4×D4×C47—21no—
170C4×D4×C47—21no—
171C4×D4×C47—21no—
172C4×D4×C47—21no—
173C4×D4×C47—21no—
174C4×D4×C47D411yescharacteristic
175C4×D4×C47D411yescharacteristic
176#117×C47—21no—
177#117×C47—21no—
178#117×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#107×C47—21no—
182#106×C47—21no—
183C4⋊C8×C47—21no—
184C4⋊C8×C47—21no—
185#103×C47—21no—
186#103×C47—21no—
187#103×C47—21no—
188#103×C47—21no—
189#103×C47—21no—
190#102×C47—21no—
191#102×C47—21no—
192#102×C47—21no—
193#102×C47—21no—
194#102×C47—21no—
195#102×C47—21no—
196#102×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47—21no—
199#97×C47—21no—
200#97×C47C2311yescharacteristic
201#97×C47C2311yescharacteristic
202#97×C47C2311yescharacteristic
203#97×C47C2311yescharacteristic
204#97×C47C2311yescharacteristic
205#97×C47C2311yescharacteristic
206C24×C47—21no—
207#41×C47—81no—
208#41×C47—81no—
209#41×C47—82no—
210#41×C47—81no—
211#41×C47—81no—
212C2×Q8×C47—21no—
213C2×Q8×C47—21no—
214C2×Q8×C47C2×D411yescharacteristic
215C2×Q8×C47C2×D411yescharacteristic
216C2×Q8×C47C2×D411yescharacteristic
217C2×Q8×C47C2×D411yescharacteristic
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—41no—
235C2×D4×C47C2×D411yescharacteristic
236C2×D4×C47C2×D411yescharacteristic
237C2×D4×C47C2×D411yescharacteristic
238C2×D4×C47C2×D411yescharacteristic
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—41no—
249C22×C4×C47—82no—
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253Q16×C47—81no—
254SD16×C47—42no—
255SD16×C47—81no—
256SD16×C47—81no—
257SD16×C47—81no—
258SD16×C47—81no—
259D8×C47—42no—
260D8×C47—81no—
261D8×C47—81no—
262D8×C47—81no—
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—42no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47C2×D411yescharacteristic
289C4⋊C4×C47C2×D411yescharacteristic
290C4⋊C4×C47C2×D411yescharacteristic
291C4⋊C4×C47C2×D411yescharacteristic
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—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—41no—
317C22⋊C4×C47—41no—
318C42×C47—21no—
319C42×C47—21no—
320C42×C47—21no—
321C42×C47—21no—
322C42×C47C2×D411yescharacteristic
323C42×C47C2×D411yescharacteristic
324C42×C47C2×D411yescharacteristic
325C42×C47C2411yescharacteristic
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—21no—
329C23×C47—21no—
330C23×C47—41no—
331C23×C47—81no—
332C23×C47—81no—
333C23×C47—81no—
334C23×C47#12011yescharacteristic
335Q8×C47—41no—
336Q8×C47—41no—
337Q8×C47—41no—
338Q8×C47—41no—
339Q8×C47—41no—
340Q8×C47—41no—
341Q8×C47—81no—
342D4×C47—41no—
343D4×C47—41no—
344D4×C47—41no—
345D4×C47—41no—
346D4×C47—41no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—41no—
352D4×C47—81no—
353D4×C47—81no—
354D4×C47—81no—
355D4×C47—81no—
356D4×C47—81no—
357D4×C47—81no—
358D4×C47—81no—
359D4×C47—81no—
360D4×C47—81no—
361D4×C47—81no—
362D4×C47—81no—
363D4×C47—81no—
364D4×C47—81no—
365D4×C47—82no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—21no—
372C2×C4×C47—21no—
373C2×C4×C47—21no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—42no—
378C2×C4×C47—42no—
379C2×C4×C47—42no—
380C2×C4×C47—42no—
381C2×C4×C47—41no—
382C2×C4×C47—82no—
383C2×C4×C47—81no—
384C2×C4×C47—81no—
385C2×C4×C47—81no—
386C2×C4×C47—81no—
387C2×C4×C47—81no—
388C2×C4×C47#12011yescharacteristic
389C2×C4×C47#12011yescharacteristic
390C2×C4×C47#12011yescharacteristic
391C2×C4×C47C22×D411yescharacteristic
392C2×C4×C47C22×D411yescharacteristic
393C2×C4×C47C22×D411yescharacteristic
394C8×C47—22no—
395C8×C47—41no—
396C8×C47—41no—
397C8×C47—41no—
398C8×C47—41no—
399C8×C47—41no—
400#19010C4711yesmaximal, characteristic, direct product factor, Sylow
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—41no—
405C22×C47—41no—
406C22×C47—41no—
407C22×C47—41no—
408C22×C47—41no—
409C22×C47—41no—
410C22×C47—41no—
411C22×C47—41no—
412C22×C47—41no—
413C22×C47—41no—
414C22×C47—41no—
415C22×C47—41no—
416C22×C47—84no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47—81no—
420C22×C47C2×#12011yescharacteristic
421C4×C47—21no—
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—41no—
428C4×C47—41no—
429C4×C47—41no—
430C4×C47—41no—
431C4×C47—41no—
432C4×C47—41no—
433C4×C47—41no—
434C4×C47—41no—
435C4×C47—81no—
436#3529C2×C4711yescharacteristic, complemented
437#3219C2×C4711yescharacteristic, complemented
438#3214C2×C4711yescharacteristic, complemented
439#3180C2×C4711yescharacteristic, complemented
440#1664C2×C4711yescharacteristic, complemented
441#1662C2×C4711yescharacteristic, complemented
442#1661C2×C4711yescharacteristic, complemented
443#1659C2×C4711yescharacteristic, complemented
444#1657C2×C4711yescharacteristic, complemented
445#1656C2×C4711yescharacteristic, complemented
446#1656C2×C4711yescharacteristic, complemented
447#1655C2×C4711yescharacteristic, complemented
448#1535C2×C4711yescharacteristic, complemented
449#1532C2×C4711yescharacteristic, complemented
450#1530C2×C4711yescharacteristic, complemented
451C2×C47—41no—
452C2×C47—81no—
453C2×C47—81no—
454C2×C47—81no—
455C2×C47—81no—
456C2×C47—161no—
457C2×C47#301811yescharacteristic
458C2×C47#301911yescharacteristic
459C2×C47#302111yescharacteristic
460#563—21no—
461#563C22×C4711yescharacteristic
462#562—21no—
463#562—21no—
464#562C22×C4711yescharacteristic
465#562C22×C4711yescharacteristic
466H(3,𝔽4)C22×C4711yescharacteristic
467#560—21no—
468#560—21no—
469#560—21no—
470#532—21no—
471#532C22×C4711yescharacteristic
472#532C22×C4711yescharacteristic, complemented
473#529—21no—
474#529—21no—
475#529C22×C4711yescharacteristic
476#529C22×C4711yescharacteristic
477#525—21no—
478#525—21no—
479#525—21no—
480#501C22×C4711yescharacteristic, complemented
481#497C22×C4711yescharacteristic
482#496C22×C4711yescharacteristic
483#496C22×C4711yescharacteristic
484#496C22×C4711yescharacteristic
485#496C22×C4711yescharacteristic, complemented
486#491C22×C4711yescharacteristic, complemented
487#490C22×C4711yescharacteristic, complemented
488#490C22×C4711yescharacteristic, complemented
489#489C22×C4711yescharacteristic
490#489C22×C4711yescharacteristic
491#489C22×C4711yescharacteristic, complemented
492#466—21no—
493#465—21no—
494#464—21no—
495#463—21no—
496#461—21no—
497#459—21no—
498#452—21no—
499#449—21no—
500#449—21no—
501#449—21no—
502#442—21no—
503#440—21no—
504#432C22×C4711yescharacteristic, complemented
505#432C22×C4711yescharacteristic, complemented
506C2×#97C22×C4711yescharacteristic, complemented
507#330C22×C4711yescharacteristic, complemented
508#330C22×C4711yescharacteristic, complemented
509#330C22×C4711yescharacteristic, complemented
510#330C22×C4711yescharacteristic, complemented
511#329C22×C4711yescharacteristic
512#329C22×C4711yescharacteristic
513#329C22×C4711yescharacteristic
514#329C22×C4711yescharacteristic
515#329C22×C4711yescharacteristic
516#329C22×C4711yescharacteristic
517#329C22×C4711yescharacteristic, complemented
518#329C22×C4711yescharacteristic, complemented
519C47#1901011yescharacteristic, direct product factor, Sylow
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C4711yescharacteristic
523C2×#41D4×C4711yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C4711yescharacteristic
538C4⋊Q8C23×C4711yescharacteristic
539#127—21no—
540#127D4×C4711yescharacteristic
541#127C23×C4711yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C4711yescharacteristic
551#125C23×C4711yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C4711yescharacteristic
558#124C23×C4711yescharacteristic
559#124C23×C4711yescharacteristic
560#124C23×C4711yescharacteristic
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—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C4711yescharacteristic
582C22⋊Q8D4×C4711yescharacteristic
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#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C4711yescharacteristic
600#121D4×C4711yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C4711yescharacteristic
608C4×Q8D4×C4711yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C4711yescharacteristic
620C4×D4D4×C4711yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C4711yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C4711yescharacteristic
646#97C23×C4711yescharacteristic
647#97C23×C4711yescharacteristic
648#97C23×C4711yescharacteristic
649#97C23×C4711yescharacteristic
650#97C23×C4711yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C4711yescharacteristic
660C2×Q8C2×D4×C4711yescharacteristic
661C2×Q8C2×D4×C4711yescharacteristic
662C2×Q8C2×D4×C4711yescharacteristic
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—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C4711yescharacteristic
681C2×D4C2×D4×C4711yescharacteristic
682C2×D4C2×D4×C4711yescharacteristic
683C2×D4C2×D4×C4711yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C4711yescharacteristic
696C22×C4C2×D4×C4711yescharacteristic
697C22×C4C2×D4×C4711yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
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⋊C4C2×D4×C4711yescharacteristic
734C4⋊C4C2×D4×C4711yescharacteristic
735C4⋊C4C2×D4×C4711yescharacteristic
736C4⋊C4C2×D4×C4711yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
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—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C4711yescharacteristic
768C42C2×D4×C4711yescharacteristic
769C42C2×D4×C4711yescharacteristic
770C42C24×C4711yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C4711yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C4711yescharacteristic
834C2×C4#120×C4711yescharacteristic
835C2×C4#120×C4711yescharacteristic
836C2×C4C22×D4×C4711yescharacteristic
837C2×C4C22×D4×C4711yescharacteristic
838C2×C4C22×D4×C4711yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C4711yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C47×#301811yescharacteristic
887C2C47×#301911yescharacteristic
888C2C47×#302111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3529C2semidirect
2. C47×#3219C2semidirect
3. C47×#3214C2semidirect
4. C47×#3180C2semidirect
5. C47×#1664C2semidirect
6. C47×#1662C2semidirect
7. C47×#1661C2semidirect
8. C47×#1659C2semidirect
9. C47×#1657C2semidirect
10. C47×#1656C2semidirect
11. C47×#1656C2semidirect
12. C47×#1655C2semidirect
13. C47×#1535C2semidirect
14. C47×#1532C2semidirect
15. C47×#1530C2semidirect
28. C47×#532C22semidirect
36. C47×#501C22semidirect
41. C47×#496C22semidirect
42. C47×#491C22semidirect
43. C47×#490C22semidirect
44. C47×#490C22semidirect
47. C47×#489C22semidirect
60. C47×#432C22semidirect
61. C47×#432C22semidirect
62. C2×#97×C47C22semidirect
63. C47×#330C22semidirect
64. C47×#330C22semidirect
65. C47×#330C22semidirect
66. C47×#330C22semidirect
73. C47×#329C22semidirect
74. C47×#329C22semidirect
400. #19010C47direct (N × H)
436. #3529C2×C47semidirect
437. #3219C2×C47semidirect
438. #3214C2×C47semidirect
439. #3180C2×C47semidirect
440. #1664C2×C47semidirect
441. #1662C2×C47semidirect
442. #1661C2×C47semidirect
443. #1659C2×C47semidirect
444. #1657C2×C47semidirect
445. #1656C2×C47semidirect
446. #1656C2×C47semidirect
447. #1655C2×C47semidirect
448. #1535C2×C47semidirect
449. #1532C2×C47semidirect
450. #1530C2×C47semidirect
472. #532C22×C47semidirect
480. #501C22×C47semidirect
485. #496C22×C47semidirect
486. #491C22×C47semidirect
487. #490C22×C47semidirect
488. #490C22×C47semidirect
491. #489C22×C47semidirect
504. #432C22×C47semidirect
505. #432C22×C47semidirect
506. C2×#97C22×C47semidirect
507. #330C22×C47semidirect
508. #330C22×C47semidirect
509. #330C22×C47semidirect
510. #330C22×C47semidirect
517. #329C22×C47semidirect
518. #329C22×C47semidirect
519. C47#19010direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35292
C47×#32192
C47×#32142
C47×#31802
C47×#16642
C47×#16622
C47×#16612
C47×#16592
C47×#16572
C47×#16562
C47×#16552
C47×#15352
C47×#15322
C47×#15302
#1901047