Finite Group Databasebeta

← C47×#23894 #26063592

Subgroups — C47×#23894 #26063592

Order 12032.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3586C211yesmaximal, characteristic, complemented
2C47×#3585C211yesmaximal, characteristic, complemented
3C47×#3020C211yesmaximal, characteristic, complemented
4C47×#3019C211yesmaximal, characteristic, complemented
5C47×#3010C211yesmaximal, characteristic, complemented
6C47×#3009C211yesmaximal, characteristic, complemented
7C47×#2019C211yesmaximal, characteristic, complemented
8C47×#2017C211yesmaximal, characteristic, complemented
9C47×#2009C211yesmaximal, characteristic, complemented
10C47×#2008C211yesmaximal, characteristic, complemented
11C47×#1903C211yesmaximal, characteristic, complemented
12C47×#1902C211yesmaximal, characteristic, complemented
13C47×#1881C211yesmaximal, characteristic, complemented
14C47×#1881C211yesmaximal, characteristic, complemented
15C47×#1794C211yesmaximal, characteristic, complemented
16C47×#585C2211yescharacteristic
17C2×2−1+4×C47C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C47C2211yescharacteristic
19C47×#578—22no—
20C47×#578—22no—
21C47×#577—22no—
22C47×#577—22no—
23C47×#577—22no—
24C47×#577—22no—
25C47×#576—22no—
26C47×#576—22no—
27C47×#575—22no—
28C47×#575—22no—
29C47×#575C2211yescharacteristic
30C47×#575C2211yescharacteristic
31C47×#575C2211yescharacteristic
32C47×#575C2211yescharacteristic, complemented
33C47×#575C2211yescharacteristic, complemented
34C2×#137×C47—22no—
35C2×#137×C47C2211yescharacteristic
36C2×#137×C47C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C47—22no—
38C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
40C22×SD16×C47C2211yescharacteristic, complemented
41C47×#568C2211yescharacteristic
42C47×#568C2211yescharacteristic, complemented
43C47×#536C2211yescharacteristic, complemented
44C47×#535C2211yescharacteristic, complemented
45C47×#456—22no—
46C47×#455—22no—
47C47×#454—22no—
48C47×#453—22no—
49C47×#452—22no—
50C47×#450—22no—
51C47×#449—22no—
52C47×#448—22no—
53C47×#421C2211yescharacteristic
54C47×#421C2211yescharacteristic, complemented
55C47×#421C2211yescharacteristic, complemented
56C47×#421C2211yescharacteristic, complemented
57C47×#419C2211yescharacteristic, complemented
58C47×#418C2211yescharacteristic, complemented
59C47×#416C2211yescharacteristic
60C47×#416C2211yescharacteristic, complemented
61C2×#101×C47C2211yescharacteristic, complemented
62C2×#100×C47C2211yescharacteristic, complemented
63C47×#410C2211yescharacteristic, complemented
64C47×#408C2211yescharacteristic, complemented
65C47×#408C2211yescharacteristic, complemented
66C47×#408C2211yescharacteristic, complemented
67C47×#344C2211yescharacteristic, complemented
68C47×#344C2211yescharacteristic, complemented
69C47×#341C2211yescharacteristic, complemented
70C47×#338C2211yescharacteristic, complemented
712−1+4×C47—22no—
722−1+4×C47—21no—
732−1+4×C47—22no—
742−1+4×C47—21no—
752−1+4×C47—22no—
762−1+4×C47—41no—
772−1+4×C47D412yescomplemented
78H(5,𝔽2)×C47—22no—
79H(5,𝔽2)×C47—21no—
80H(5,𝔽2)×C47—22no—
81H(5,𝔽2)×C47—21no—
82H(5,𝔽2)×C47—22no—
83H(5,𝔽2)×C47—41no—
84H(5,𝔽2)×C47—41no—
85H(5,𝔽2)×C47D412yescomplemented
86C2×#41×C47—22no—
87C2×#41×C47—22no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—21no—
92C2×#41×C47—41no—
93C2×#41×C47—41no—
94C2×#41×C47C2311yescharacteristic
95C2×#41×C47C2311yescharacteristic
96C2×#41×C47C2311yescharacteristic
97C2×#41×C47C2311yescharacteristic
98C2×#41×C47C2311yescharacteristic
99C22×Q8×C47—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47C2311yescharacteristic
102C22×D4×C47—21no—
103C22×D4×C47—21no—
104C22×D4×C47—41no—
105C22×D4×C47C2311yescharacteristic
106#137×C47—24no—
107#137×C47—24no—
108#137×C47—24no—
109#137×C47—24no—
110#137×C47—22no—
111#137×C47—22no—
112#137×C47—21no—
113#137×C47—22no—
114#137×C47—21no—
115#137×C47—21no—
116#137×C47—21no—
117#137×C47—21no—
118#137×C47—21no—
119#137×C47—21no—
120#137×C47—21no—
121#137×C47—22no—
122#137×C47D412yes—
123#137×C47D412yescomplemented
124AGL(1,ℤ/8)×C47—24no—
125AGL(1,ℤ/8)×C47—24no—
126AGL(1,ℤ/8)×C47—24no—
127AGL(1,ℤ/8)×C47—24no—
128AGL(1,ℤ/8)×C47—22no—
129AGL(1,ℤ/8)×C47—22no—
130AGL(1,ℤ/8)×C47—21no—
131AGL(1,ℤ/8)×C47—22no—
132AGL(1,ℤ/8)×C47—21no—
133AGL(1,ℤ/8)×C47—21no—
134AGL(1,ℤ/8)×C47—21no—
135AGL(1,ℤ/8)×C47—21no—
136AGL(1,ℤ/8)×C47—21no—
137AGL(1,ℤ/8)×C47—21no—
138AGL(1,ℤ/8)×C47—21no—
139AGL(1,ℤ/8)×C47—22no—
140AGL(1,ℤ/8)×C47D412yes—
141AGL(1,ℤ/8)×C47D412yescomplemented
142#135×C47—24no—
143#135×C47—24no—
144#135×C47—24no—
145#135×C47—24no—
146#135×C47—22no—
147#135×C47—22no—
148#135×C47—22no—
149#135×C47—22no—
150#135×C47—41no—
151C2×Q16×C47—24no—
152C2×Q16×C47—21no—
153C2×Q16×C47D412yescomplemented
154C2×SD16×C47—24no—
155C2×SD16×C47—24no—
156C2×SD16×C47—21no—
157C2×SD16×C47—21no—
158C2×SD16×C47—22no—
159C2×SD16×C47—22no—
160C2×SD16×C47—41no—
161C2×SD16×C47D412yes—
162C2×SD16×C47D412yescomplemented
163C2×D8×C47—24no—
164C2×D8×C47—21no—
165C2×D8×C47D412yes—
166#131×C47—22no—
167#131×C47—22no—
168#131×C47—22no—
169#131×C47—22no—
170C2×M16×C47—22no—
171C2×M16×C47—22no—
172C2×M16×C47C2311yescharacteristic
173C2×M16×C47C2311yescharacteristic
174C2×M16×C47C2311yescharacteristic
175C2×M16×C47C2311yescharacteristic
176C2×M16×C47C2311yescharacteristic
177C22×C8×C47C2311yescharacteristic
178C4⋊Q8×C47—21no—
179#127×C47—21no—
180#124×C47—21no—
181#124×C47—21no—
182#123×C47—41no—
183C22⋊Q8×C47—22no—
184#121×C47—22no—
185#120×C47—41no—
186#117×C47C2311yescharacteristic
187#117×C47C2311yescharacteristic
188#104×C47—22no—
189#104×C47—22no—
190#104×C47—22no—
191#104×C47—22no—
192#103×C47—21no—
193#103×C47—21no—
194#103×C47—22no—
195#102×C47—21no—
196#102×C47—21no—
197#102×C47—22no—
198#101×C47—22no—
199#100×C47—22no—
200#99×C47—41no—
201C22⋊C8×C47—22no—
202C22⋊C8×C47—22no—
203C22⋊C8×C47—41no—
204C24×C47—21no—
205C24×C47—41no—
206#41×C47—21no—
207#41×C47—21no—
208#41×C47—21no—
209#41×C47—21no—
210#41×C47—24no—
211#41×C47—24no—
212#41×C47—22no—
213#41×C47—22no—
214#41×C47—22no—
215#41×C47—22no—
216#41×C47—21no—
217#41×C47—21no—
218#41×C47—21no—
219#41×C47—21no—
220#41×C47—21no—
221#41×C47—21no—
222#41×C47—21no—
223#41×C47—21no—
224#41×C47—21no—
225#41×C47—21no—
226#41×C47—21no—
227#41×C47—21no—
228#41×C47—42no—
229#41×C47—42no—
230#41×C47—42no—
231#41×C47—42no—
232#41×C47—42no—
233#41×C47—44no—
234#41×C47—42no—
235#41×C47—42no—
236#41×C47—42no—
237#41×C47—41no—
238#41×C47—41no—
239#41×C47—44no—
240#41×C47—42no—
241#41×C47—42no—
242#41×C47C2×D412yes—
243#41×C47C2×D412yes—
244#41×C47C2×D412yes—
245#41×C47C2×D412yes—
246C2×Q8×C47—21no—
247C2×Q8×C47—24no—
248C2×Q8×C47—22no—
249C2×Q8×C47—22no—
250C2×Q8×C47—21no—
251C2×Q8×C47—21no—
252C2×Q8×C47—21no—
253C2×Q8×C47—21no—
254C2×Q8×C47—41no—
255C2×Q8×C47—42no—
256C2×Q8×C47—42no—
257C2×Q8×C47—41no—
258C2×Q8×C47—42no—
259C2×Q8×C47C2×D412yes—
260C2×Q8×C47C2×D411yescharacteristic
261C2×Q8×C47C2×D411yescharacteristic
262C2×Q8×C47C2×D411yescharacteristic
263C2×Q8×C47C2×D411yescharacteristic
264C2×Q8×C47C2×D411yescharacteristic
265C2×D4×C47—21no—
266C2×D4×C47—21no—
267C2×D4×C47—24no—
268C2×D4×C47—22no—
269C2×D4×C47—22no—
270C2×D4×C47—21no—
271C2×D4×C47—21no—
272C2×D4×C47—21no—
273C2×D4×C47—21no—
274C2×D4×C47—21no—
275C2×D4×C47—21no—
276C2×D4×C47—21no—
277C2×D4×C47—21no—
278C2×D4×C47—42no—
279C2×D4×C47—41no—
280C2×D4×C47—41no—
281C2×D4×C47—42no—
282C2×D4×C47—42no—
283C2×D4×C47—41no—
284C2×D4×C47—44no—
285C2×D4×C47—42no—
286C2×D4×C47—42no—
287C2×D4×C47—44no—
288C2×D4×C47—41no—
289C2×D4×C47—42no—
290C2×D4×C47—42no—
291C2×D4×C47C2×D412yes—
292C2×D4×C47C2×D411yescharacteristic
293C2×D4×C47C2×D411yescharacteristic
294C2×D4×C47C2×D411yescharacteristic
295C2×D4×C47C2×D411yescharacteristic
296C2×D4×C47C2×D411yescharacteristic
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—41no—
304C22×C4×C47—42no—
305C22×C4×C47—41no—
306C22×C4×C47—41no—
307C22×C4×C47C2411yescharacteristic
308Q16×C47—24no—
309Q16×C47—22no—
310Q16×C47—22no—
311Q16×C47—22no—
312Q16×C47—24no—
313Q16×C47—22no—
314Q16×C47—41no—
315SD16×C47—24no—
316SD16×C47—22no—
317SD16×C47—24no—
318SD16×C47—22no—
319SD16×C47—22no—
320SD16×C47—22no—
321SD16×C47—22no—
322SD16×C47—24no—
323SD16×C47—22no—
324SD16×C47—22no—
325SD16×C47—24no—
326SD16×C47—22no—
327SD16×C47—44no—
328SD16×C47—41no—
329SD16×C47—41no—
330D8×C47—24no—
331D8×C47—22no—
332D8×C47—22no—
333D8×C47—22no—
334D8×C47—24no—
335D8×C47—22no—
336D8×C47—41no—
337M16×C47—24no—
338M16×C47—24no—
339M16×C47—21no—
340M16×C47—21no—
341M16×C47—21no—
342M16×C47—21no—
343M16×C47—21no—
344M16×C47—21no—
345M16×C47—21no—
346M16×C47—21no—
347M16×C47C2×D412yes—
348M16×C47C2×D412yes—
349C2×C8×C47—24no—
350C2×C8×C47—24no—
351C2×C8×C47—21no—
352C2×C8×C47—21no—
353C2×C8×C47—21no—
354C2×C8×C47—21no—
355C2×C8×C47—21no—
356C2×C8×C47—21no—
357C2×C8×C47C2×D412yes—
358C2×C8×C47C2×D412yes—
359C4⋊C4×C47—21no—
360C4⋊C4×C47—21no—
361C4⋊C4×C47—42no—
362C22⋊C4×C47—21no—
363C22⋊C4×C47—21no—
364C22⋊C4×C47—42no—
365C22⋊C4×C47—42no—
366C42×C47—21no—
367C42×C47—21no—
368C23×C47—21no—
369C23×C47—21no—
370C23×C47—21no—
371C23×C47—21no—
372C23×C47—21no—
373C23×C47—22no—
374C23×C47—42no—
375C23×C47—44no—
376C23×C47—41no—
377C23×C47—41no—
378C23×C47—161no—
379C23×C47—162no—
380C23×C47H(5,𝔽2)11yescharacteristic
381Q8×C47—21no—
382Q8×C47—21no—
383Q8×C47—21no—
384Q8×C47—21no—
385Q8×C47—22no—
386Q8×C47—21no—
387Q8×C47—21no—
388Q8×C47—22no—
389Q8×C47—21no—
390Q8×C47—21no—
391Q8×C47—42no—
392Q8×C47—44no—
393Q8×C47—41no—
394Q8×C47—41no—
395Q8×C47#12012yes—
396Q8×C47#12012yes—
397D4×C47—22no—
398D4×C47—22no—
399D4×C47—22no—
400D4×C47—22no—
401D4×C47—21no—
402D4×C47—21no—
403D4×C47—22no—
404D4×C47—21no—
405D4×C47—21no—
406D4×C47—21no—
407D4×C47—21no—
408D4×C47—21no—
409D4×C47—21no—
410D4×C47—22no—
411D4×C47—42no—
412D4×C47—42no—
413D4×C47—44no—
414D4×C47—42no—
415D4×C47—44no—
416D4×C47—44no—
417D4×C47—41no—
418D4×C47—41no—
419D4×C47—41no—
420D4×C47—41no—
421D4×C47—41no—
422D4×C47—41no—
423D4×C47—41no—
424D4×C47—41no—
425D4×C47—162no—
426D4×C47#12012yes—
427D4×C47#12012yes—
428C2×C4×C47—21no—
429C2×C4×C47—21no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—22no—
437C2×C4×C47—21no—
438C2×C4×C47—42no—
439C2×C4×C47—42no—
440C2×C4×C47—42no—
441C2×C4×C47—44no—
442C2×C4×C47—44no—
443C2×C4×C47—44no—
444C2×C4×C47—41no—
445C2×C4×C47—41no—
446C2×C4×C47—41no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—41no—
453C2×C4×C47—41no—
454C2×C4×C47C22×D411yescharacteristic
455C2×C4×C47C22×D411yescharacteristic
456C2×C4×C47C22×D411yescharacteristic
457C2×C4×C47C22×D411yescharacteristic
458C2×C4×C47C22×D411yescharacteristic
459C2×C4×C47H(5,𝔽2)11yescharacteristic
460C8×C47—22no—
461C8×C47—22no—
462C8×C47—22no—
463C8×C47—22no—
464C8×C47—41no—
465C8×C47—41no—
466#23894C4711yesmaximal, characteristic, direct product factor, Sylow
467C22×C47—22no—
468C22×C47—22no—
469C22×C47—41no—
470C22×C47—42no—
471C22×C47—42no—
472C22×C47—41no—
473C22×C47—41no—
474C22×C47—41no—
475C22×C47—42no—
476C22×C47—81no—
477C22×C47—81no—
478C22×C47—82no—
479C22×C47—81no—
480C22×C47—82no—
481C22×C47—161no—
482C22×C47—162no—
483C22×C47—164no—
484C22×C47#53411yescharacteristic
485C22×C47D4211yescharacteristic
486C22×C47D4211yescharacteristic
487C4×C47—22no—
488C4×C47—22no—
489C4×C47—41no—
490C4×C47—41no—
491C4×C47—41no—
492C4×C47—42no—
493C4×C47—81no—
494C4×C47—81no—
495C4×C47C2×#12011yescharacteristic
496C4×C47C2×#12011yescharacteristic
497C4×C47D4211yescharacteristic
498C4×C47D4211yescharacteristic
499#3586C2×C4711yescharacteristic, complemented
500#3585C2×C4711yescharacteristic, complemented
501#3020C2×C4711yescharacteristic, complemented
502#3019C2×C4711yescharacteristic, complemented
503#3010C2×C4711yescharacteristic, complemented
504#3009C2×C4711yescharacteristic, complemented
505#2019C2×C4711yescharacteristic, complemented
506#2017C2×C4711yescharacteristic, complemented
507#2009C2×C4711yescharacteristic, complemented
508#2008C2×C4711yescharacteristic, complemented
509#1903C2×C4711yescharacteristic, complemented
510#1902C2×C4711yescharacteristic, complemented
511#1881C2×C4711yescharacteristic, complemented
512#1881C2×C4711yescharacteristic, complemented
513#1794C2×C4711yescharacteristic, complemented
514C2×C47—21no—
515C2×C47—21no—
516C2×C47—21no—
517C2×C47—42no—
518C2×C47—42no—
519C2×C47—81no—
520C2×C47—81no—
521C2×C47—82no—
522C2×C47—81no—
523C2×C47#240311yescharacteristic
524#585C22×C4711yescharacteristic
525C2×2−1+4C22×C4711yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C4711yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C4711yescharacteristic
538#575C22×C4711yescharacteristic
539#575C22×C4711yescharacteristic
540#575C22×C4711yescharacteristic, complemented
541#575C22×C4711yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C4711yescharacteristic
544C2×#137C22×C4711yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
547C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
548C22×SD16C22×C4711yescharacteristic, complemented
549#568C22×C4711yescharacteristic
550#568C22×C4711yescharacteristic, complemented
551#536C22×C4711yescharacteristic, complemented
552#535C22×C4711yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C4711yescharacteristic
562#421C22×C4711yescharacteristic, complemented
563#421C22×C4711yescharacteristic, complemented
564#421C22×C4711yescharacteristic, complemented
565#419C22×C4711yescharacteristic, complemented
566#418C22×C4711yescharacteristic, complemented
567#416C22×C4711yescharacteristic
568#416C22×C4711yescharacteristic, complemented
569C2×#101C22×C4711yescharacteristic, complemented
570C2×#100C22×C4711yescharacteristic, complemented
571#410C22×C4711yescharacteristic, complemented
572#408C22×C4711yescharacteristic, complemented
573#408C22×C4711yescharacteristic, complemented
574#408C22×C4711yescharacteristic, complemented
575#344C22×C4711yescharacteristic, complemented
576#344C22×C4711yescharacteristic, complemented
577#341C22×C4711yescharacteristic, complemented
578#338C22×C4711yescharacteristic, complemented
579C47#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C4712yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C4712yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C4711yescharacteristic
604C2×#41C23×C4711yescharacteristic
605C2×#41C23×C4711yescharacteristic
606C2×#41C23×C4711yescharacteristic
607C2×#41C23×C4711yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C4711yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C4711yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C4712yes—
632#137D4×C4712yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C4712yes—
650AGL(1,ℤ/8)D4×C4712yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C4712yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C4712yes—
671C2×SD16D4×C4712yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C4712yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C4711yescharacteristic
682C2×M16C23×C4711yescharacteristic
683C2×M16C23×C4711yescharacteristic
684C2×M16C23×C4711yescharacteristic
685C2×M16C23×C4711yescharacteristic
686C22×C8C23×C4711yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C4711yescharacteristic
696#117C23×C4711yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C4712yes—
752#41C2×D4×C4712yes—
753#41C2×D4×C4712yes—
754#41C2×D4×C4712yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C4712yes—
769C2×Q8C2×D4×C4711yescharacteristic
770C2×Q8C2×D4×C4711yescharacteristic
771C2×Q8C2×D4×C4711yescharacteristic
772C2×Q8C2×D4×C4711yescharacteristic
773C2×Q8C2×D4×C4711yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C4712yes—
801C2×D4C2×D4×C4711yescharacteristic
802C2×D4C2×D4×C4711yescharacteristic
803C2×D4C2×D4×C4711yescharacteristic
804C2×D4C2×D4×C4711yescharacteristic
805C2×D4C2×D4×C4711yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C4711yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C4712yes—
857M16C2×D4×C4712yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C4712yes—
867C2×C8C2×D4×C4712yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C4711yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C4712yes—
905Q8#120×C4712yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C4712yes—
936D4#120×C4712yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C4711yescharacteristic
964C2×C4C22×D4×C4711yescharacteristic
965C2×C4C22×D4×C4711yescharacteristic
966C2×C4C22×D4×C4711yescharacteristic
967C2×C4C22×D4×C4711yescharacteristic
968C2×C4H(5,𝔽2)×C4711yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C47×#53411yescharacteristic
993C22D42×C4711yescharacteristic
994C22D42×C4711yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C4711yescharacteristic
1004C4C2×#120×C4711yescharacteristic
1005C4D42×C4711yescharacteristic
1006C4D42×C4711yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C47×#240311yescharacteristic
subgroupG/H
center, socleC2×C47#2403
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3586C2semidirect
2. C47×#3585C2semidirect
3. C47×#3020C2semidirect
4. C47×#3019C2semidirect
5. C47×#3010C2semidirect
6. C47×#3009C2semidirect
7. C47×#2019C2semidirect
8. C47×#2017C2semidirect
9. C47×#2009C2semidirect
10. C47×#2008C2semidirect
11. C47×#1903C2semidirect
12. C47×#1902C2semidirect
13. C47×#1881C2semidirect
14. C47×#1881C2semidirect
15. C47×#1794C2semidirect
17. C2×2−1+4×C47C22semidirect
32. C47×#575C22semidirect
33. C47×#575C22semidirect
36. C2×#137×C47C22semidirect
40. C22×SD16×C47C22semidirect
42. C47×#568C22semidirect
43. C47×#536C22semidirect
44. C47×#535C22semidirect
54. C47×#421C22semidirect
55. C47×#421C22semidirect
56. C47×#421C22semidirect
57. C47×#419C22semidirect
58. C47×#418C22semidirect
60. C47×#416C22semidirect
61. C2×#101×C47C22semidirect
62. C2×#100×C47C22semidirect
63. C47×#410C22semidirect
64. C47×#408C22semidirect
65. C47×#408C22semidirect
66. C47×#408C22semidirect
67. C47×#344C22semidirect
68. C47×#344C22semidirect
69. C47×#341C22semidirect
70. C47×#338C22semidirect
77. 2−1+4×C47D4semidirect
85. H(5,𝔽2)×C47D4semidirect
123. #137×C47D4semidirect
141. AGL(1,ℤ/8)×C47D4semidirect
153. C2×Q16×C47D4semidirect
162. C2×SD16×C47D4semidirect
466. #23894C47direct (N × H)
499. #3586C2×C47semidirect
500. #3585C2×C47semidirect
501. #3020C2×C47semidirect
502. #3019C2×C47semidirect
503. #3010C2×C47semidirect
504. #3009C2×C47semidirect
505. #2019C2×C47semidirect
506. #2017C2×C47semidirect
507. #2009C2×C47semidirect
508. #2008C2×C47semidirect
509. #1903C2×C47semidirect
510. #1902C2×C47semidirect
511. #1881C2×C47semidirect
512. #1881C2×C47semidirect
513. #1794C2×C47semidirect
525. C2×2−1+4C22×C47semidirect
540. #575C22×C47semidirect
541. #575C22×C47semidirect
544. C2×#137C22×C47semidirect
548. C22×SD16C22×C47semidirect
550. #568C22×C47semidirect
551. #536C22×C47semidirect
552. #535C22×C47semidirect
562. #421C22×C47semidirect
563. #421C22×C47semidirect
564. #421C22×C47semidirect
565. #419C22×C47semidirect
566. #418C22×C47semidirect
568. #416C22×C47semidirect
569. C2×#101C22×C47semidirect
570. C2×#100C22×C47semidirect
571. #410C22×C47semidirect
572. #408C22×C47semidirect
573. #408C22×C47semidirect
574. #408C22×C47semidirect
575. #344C22×C47semidirect
576. #344C22×C47semidirect
577. #341C22×C47semidirect
578. #338C22×C47semidirect
579. C47#23894direct (N × H)
586. 2−1+4D4×C47semidirect
594. H(5,𝔽2)D4×C47semidirect
632. #137D4×C47semidirect
650. AGL(1,ℤ/8)D4×C47semidirect
662. C2×Q16D4×C47semidirect
671. C2×SD16D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35862
C47×#35852
C47×#30202
C47×#30192
C47×#30102
C47×#30092
C47×#20192
C47×#20172
C47×#20092
C47×#20082
C47×#19032
C47×#19022
C47×#18812
C47×#17942
#2389447