Finite Group Databasebeta

← C47×#19068 #26058766

Subgroups — C47×#19068 #26058766

Order 12032.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3545C211yesmaximal, characteristic, complemented
2C47×#3219C211yesmaximal, characteristic, complemented
3C47×#3213C211yesmaximal, characteristic, complemented
4C47×#3171C211yesmaximal, 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×#1529C211yesmaximal, characteristic, complemented
15C47×#1527C211yesmaximal, characteristic, complemented
16C47×#563C2211yescharacteristic
17C47×#562C2211yescharacteristic
18C47×#562C2211yescharacteristic
19C47×H(3,𝔽4)C2211yescharacteristic
20C47×#555—21no—
21C47×#551—21no—
22C47×#551—21no—
23C47×#551—21no—
24C47×#546—21no—
25C47×#546—21no—
26C47×#542—21no—
27C47×#542—21no—
28C47×#538—21no—
29C47×#538—21no—
30C47×#536—21no—
31C47×#534—21no—
32C47×#532C2211yescharacteristic, complemented
33C47×#529C2211yescharacteristic
34C47×#529C2211yescharacteristic
35C2×#124×C47C2211yescharacteristic
36C47×#501C2211yescharacteristic, complemented
37C47×#497C2211yescharacteristic, complemented
38C47×#496C2211yescharacteristic
39C47×#496C2211yescharacteristic, complemented
40C47×#496C2211yescharacteristic, complemented
41C47×#496C2211yescharacteristic, complemented
42C47×#491C2211yescharacteristic, complemented
43C47×#490C2211yescharacteristic, complemented
44C47×#490C2211yescharacteristic, complemented
45C47×#489C2211yescharacteristic
46C47×#489C2211yescharacteristic, complemented
47C47×#489C2211yescharacteristic, complemented
48C47×#469—21no—
49C47×#468—21no—
50C47×#464—21no—
51C47×#463—21no—
52C47×#463—21no—
53C47×#463—21no—
54C47×#452—21no—
55C47×#449—21no—
56C47×#448—21no—
57C47×#447—21no—
58C4×SD16×C47—21no—
59C4×D8×C47—21no—
60C47×#432C2211yescharacteristic, complemented
61C47×#432C2211yescharacteristic, complemented
62C4×M16×C47C2211yescharacteristic, complemented
63C47×#330C2211yescharacteristic, complemented
64C47×#330C2211yescharacteristic, complemented
65C47×#330C2211yescharacteristic, complemented
66C47×#330C2211yescharacteristic, complemented
67C47×#329C2211yescharacteristic
68C47×#329C2211yescharacteristic
69C47×#329C2211yescharacteristic, complemented
70C47×#329C2211yescharacteristic, complemented
71C47×#329C2211yescharacteristic, complemented
72C47×#329C2211yescharacteristic, complemented
73C47×#329C2211yescharacteristic, complemented
74C47×#329C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C22×Q8×C47D411yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47D411yescharacteristic
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—
90C2×M16×C47—21no—
91C4⋊Q8×C47—21no—
92C4⋊Q8×C47—21no—
93C4⋊Q8×C47C2311yescharacteristic
94#127×C47C2311yescharacteristic
95#126×C47—21no—
96#126×C47—21no—
97#126×C47—21no—
98#126×C47—21no—
99#126×C47—21no—
100#126×C47—21no—
101#125×C47C2311yescharacteristic
102#125×C47C2311yescharacteristic
103#124×C47—21no—
104#124×C47—21no—
105#124×C47—21no—
106#124×C47—21no—
107#124×C47—21no—
108#124×C47—21no—
109#124×C47—21no—
110#124×C47—21no—
111#124×C47—21no—
112#124×C47D411yescharacteristic
113#124×C47D411yescharacteristic
114#124×C47C2311yescharacteristic
115#124×C47C2311yescharacteristic
116#124×C47C2311yescharacteristic
117#124×C47C2311yescharacteristic
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—
128#123×C47—21no—
129#123×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×C47—21no—
137C22⋊Q8×C47—21no—
138C22⋊Q8×C47D411yescharacteristic
139C22⋊Q8×C47D411yescharacteristic
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×C47D411yescharacteristic
151#121×C47D411yescharacteristic
152#120×C47—21no—
153#120×C47—21no—
154#120×C47—21no—
155#120×C47—21no—
156#120×C47—21no—
157#120×C47—21no—
158C4×Q8×C47D411yescharacteristic
159C4×Q8×C47D411yescharacteristic
160C4×D4×C47—21no—
161C4×D4×C47—21no—
162C4×D4×C47—21no—
163C4×D4×C47—21no—
164C4×D4×C47—21no—
165C4×D4×C47—21no—
166C4×D4×C47—21no—
167C4×D4×C47—21no—
168C4×D4×C47D411yescharacteristic
169C4×D4×C47D411yescharacteristic
170#117×C47—21no—
171#117×C47—21no—
172#117×C47—21no—
173#117×C47—21no—
174#117×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×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×C47C2311yescharacteristic
200#97×C47C2311yescharacteristic
201#97×C47C2311yescharacteristic
202#97×C47C2311yescharacteristic
203#97×C47C2311yescharacteristic
204#97×C47C2311yescharacteristic
205C4×C8×C47—21no—
206C24×C47—21no—
207C24×C47—21no—
208#41×C47—82no—
209#41×C47—81no—
210#41×C47—81no—
211C2×Q8×C47—21no—
212C2×Q8×C47—21no—
213C2×Q8×C47—21no—
214C2×Q8×C47—81no—
215C2×Q8×C47C2×D411yescharacteristic
216C2×Q8×C47C2×D411yescharacteristic
217C2×Q8×C47C2×D411yescharacteristic
218C2×Q8×C47C2×D411yescharacteristic
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—41no—
233C2×D4×C47—81no—
234C2×D4×C47—82no—
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—41no—
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251Q16×C47—81no—
252SD16×C47—42no—
253SD16×C47—81no—
254SD16×C47—81no—
255SD16×C47—81no—
256SD16×C47—81no—
257D8×C47—42no—
258D8×C47—81no—
259D8×C47—81no—
260D8×C47—81no—
261M16×C47—42no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
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×C47C2×D411yescharacteristic
285C4⋊C4×C47C2×D411yescharacteristic
286C4⋊C4×C47C2×D411yescharacteristic
287C4⋊C4×C47C2×D411yescharacteristic
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—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—42no—
331C23×C47—41no—
332C23×C47—81no—
333C23×C47—81no—
334C23×C47—81no—
335C23×C47—81no—
336C23×C47—81no—
337C23×C47#12011yescharacteristic
338Q8×C47—41no—
339Q8×C47—41no—
340Q8×C47—41no—
341Q8×C47—41no—
342Q8×C47—41no—
343Q8×C47—41no—
344Q8×C47—81no—
345Q8×C47—81no—
346D4×C47—41no—
347D4×C47—41no—
348D4×C47—41no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—41no—
352D4×C47—41no—
353D4×C47—41no—
354D4×C47—41no—
355D4×C47—41no—
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—82no—
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—21no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—42no—
379C2×C4×C47—41no—
380C2×C4×C47—81no—
381C2×C4×C47—81no—
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#19068C4711yesmaximal, 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—81no—
417C22×C47—81no—
418C22×C47—81no—
419C22×C47—162no—
420C22×C47—162no—
421C22×C47C2×#12011yescharacteristic
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—41no—
429C4×C47—41no—
430C4×C47—41no—
431C4×C47—41no—
432C4×C47—41no—
433C4×C47—41no—
434C4×C47—41no—
435C4×C47—41no—
436C4×C47—81no—
437#3545C2×C4711yescharacteristic, complemented
438#3219C2×C4711yescharacteristic, complemented
439#3213C2×C4711yescharacteristic, complemented
440#3171C2×C4711yescharacteristic, complemented
441#1664C2×C4711yescharacteristic, complemented
442#1662C2×C4711yescharacteristic, complemented
443#1661C2×C4711yescharacteristic, complemented
444#1659C2×C4711yescharacteristic, complemented
445#1657C2×C4711yescharacteristic, complemented
446#1656C2×C4711yescharacteristic, complemented
447#1656C2×C4711yescharacteristic, complemented
448#1655C2×C4711yescharacteristic, complemented
449#1535C2×C4711yescharacteristic, complemented
450#1529C2×C4711yescharacteristic, complemented
451#1527C2×C4711yescharacteristic, complemented
452C2×C47—41no—
453C2×C47—81no—
454C2×C47—81no—
455C2×C47—81no—
456C2×C47—81no—
457C2×C47—161no—
458C2×C47#301811yescharacteristic
459C2×C47#301911yescharacteristic
460C2×C47#302111yescharacteristic
461#563C22×C4711yescharacteristic
462#562C22×C4711yescharacteristic
463#562C22×C4711yescharacteristic
464H(3,𝔽4)C22×C4711yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468#551—21no—
469#546—21no—
470#546—21no—
471#542—21no—
472#542—21no—
473#538—21no—
474#538—21no—
475#536—21no—
476#534—21no—
477#532C22×C4711yescharacteristic, complemented
478#529C22×C4711yescharacteristic
479#529C22×C4711yescharacteristic
480C2×#124C22×C4711yescharacteristic
481#501C22×C4711yescharacteristic, complemented
482#497C22×C4711yescharacteristic, complemented
483#496C22×C4711yescharacteristic
484#496C22×C4711yescharacteristic, complemented
485#496C22×C4711yescharacteristic, complemented
486#496C22×C4711yescharacteristic, complemented
487#491C22×C4711yescharacteristic, complemented
488#490C22×C4711yescharacteristic, complemented
489#490C22×C4711yescharacteristic, complemented
490#489C22×C4711yescharacteristic
491#489C22×C4711yescharacteristic, complemented
492#489C22×C4711yescharacteristic, complemented
493#469—21no—
494#468—21no—
495#464—21no—
496#463—21no—
497#463—21no—
498#463—21no—
499#452—21no—
500#449—21no—
501#448—21no—
502#447—21no—
503C4×SD16—21no—
504C4×D8—21no—
505#432C22×C4711yescharacteristic, complemented
506#432C22×C4711yescharacteristic, complemented
507C4×M16C22×C4711yescharacteristic, complemented
508#330C22×C4711yescharacteristic, complemented
509#330C22×C4711yescharacteristic, complemented
510#330C22×C4711yescharacteristic, complemented
511#330C22×C4711yescharacteristic, complemented
512#329C22×C4711yescharacteristic
513#329C22×C4711yescharacteristic
514#329C22×C4711yescharacteristic, complemented
515#329C22×C4711yescharacteristic, complemented
516#329C22×C4711yescharacteristic, complemented
517#329C22×C4711yescharacteristic, complemented
518#329C22×C4711yescharacteristic, complemented
519#329C22×C4711yescharacteristic, complemented
520C47#1906811yescharacteristic, direct product factor, Sylow
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C4711yescharacteristic
524C22×D4—21no—
525C22×D4D4×C4711yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C4711yescharacteristic
540#127C23×C4711yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C4711yescharacteristic
548#125C23×C4711yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C4711yescharacteristic
559#124D4×C4711yescharacteristic
560#124C23×C4711yescharacteristic
561#124C23×C4711yescharacteristic
562#124C23×C4711yescharacteristic
563#124C23×C4711yescharacteristic
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—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C4711yescharacteristic
585C22⋊Q8D4×C4711yescharacteristic
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#121D4×C4711yescharacteristic
597#121D4×C4711yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C4711yescharacteristic
605C4×Q8D4×C4711yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C4711yescharacteristic
615C4×D4D4×C4711yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C4711yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C4711yescharacteristic
646#97C23×C4711yescharacteristic
647#97C23×C4711yescharacteristic
648#97C23×C4711yescharacteristic
649#97C23×C4711yescharacteristic
650#97C23×C4711yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C4711yescharacteristic
662C2×Q8C2×D4×C4711yescharacteristic
663C2×Q8C2×D4×C4711yescharacteristic
664C2×Q8C2×D4×C4711yescharacteristic
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—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C4711yescharacteristic
682C2×D4C2×D4×C4711yescharacteristic
683C2×D4C2×D4×C4711yescharacteristic
684C2×D4C2×D4×C4711yescharacteristic
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×C4C2×D4×C4711yescharacteristic
695C22×C4C2×D4×C4711yescharacteristic
696C22×C4C2×D4×C4711yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
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⋊C4C2×D4×C4711yescharacteristic
731C4⋊C4C2×D4×C4711yescharacteristic
732C4⋊C4C2×D4×C4711yescharacteristic
733C4⋊C4C2×D4×C4711yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
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—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C4711yescharacteristic
769C42C2×D4×C4711yescharacteristic
770C42C2×D4×C4711yescharacteristic
771C42C24×C4711yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C4711yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C4711yescharacteristic
835C2×C4#120×C4711yescharacteristic
836C2×C4#120×C4711yescharacteristic
837C2×C4C22×D4×C4711yescharacteristic
838C2×C4C22×D4×C4711yescharacteristic
839C2×C4C22×D4×C4711yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C4711yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C47×#301811yescharacteristic
889C2C47×#301911yescharacteristic
890C2C47×#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×#3545C2semidirect
2. C47×#3219C2semidirect
3. C47×#3213C2semidirect
4. C47×#3171C2semidirect
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×#1529C2semidirect
15. C47×#1527C2semidirect
32. C47×#532C22semidirect
36. C47×#501C22semidirect
37. C47×#497C22semidirect
39. C47×#496C22semidirect
40. C47×#496C22semidirect
41. C47×#496C22semidirect
42. C47×#491C22semidirect
43. C47×#490C22semidirect
44. C47×#490C22semidirect
46. C47×#489C22semidirect
47. C47×#489C22semidirect
60. C47×#432C22semidirect
61. C47×#432C22semidirect
62. C4×M16×C47C22semidirect
63. C47×#330C22semidirect
64. C47×#330C22semidirect
65. C47×#330C22semidirect
66. C47×#330C22semidirect
69. C47×#329C22semidirect
70. C47×#329C22semidirect
71. C47×#329C22semidirect
72. C47×#329C22semidirect
73. C47×#329C22semidirect
74. C47×#329C22semidirect
400. #19068C47direct (N × H)
437. #3545C2×C47semidirect
438. #3219C2×C47semidirect
439. #3213C2×C47semidirect
440. #3171C2×C47semidirect
441. #1664C2×C47semidirect
442. #1662C2×C47semidirect
443. #1661C2×C47semidirect
444. #1659C2×C47semidirect
445. #1657C2×C47semidirect
446. #1656C2×C47semidirect
447. #1656C2×C47semidirect
448. #1655C2×C47semidirect
449. #1535C2×C47semidirect
450. #1529C2×C47semidirect
451. #1527C2×C47semidirect
477. #532C22×C47semidirect
481. #501C22×C47semidirect
482. #497C22×C47semidirect
484. #496C22×C47semidirect
485. #496C22×C47semidirect
486. #496C22×C47semidirect
487. #491C22×C47semidirect
488. #490C22×C47semidirect
489. #490C22×C47semidirect
491. #489C22×C47semidirect
492. #489C22×C47semidirect
505. #432C22×C47semidirect
506. #432C22×C47semidirect
507. C4×M16C22×C47semidirect
508. #330C22×C47semidirect
509. #330C22×C47semidirect
510. #330C22×C47semidirect
511. #330C22×C47semidirect
514. #329C22×C47semidirect
515. #329C22×C47semidirect
516. #329C22×C47semidirect
517. #329C22×C47semidirect
518. #329C22×C47semidirect
519. #329C22×C47semidirect
520. C47#19068direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35452
C47×#32192
C47×#32132
C47×#31712
C47×#16642
C47×#16622
C47×#16612
C47×#16592
C47×#16572
C47×#16562
C47×#16552
C47×#15352
C47×#15292
C47×#15272
#1906847