Finite Group Databasebeta

← C47×#19039 #26058737

Subgroups — C47×#19039 #26058737

Order 12032.

842 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3568C211yesmaximal, characteristic
2C47×#3240C211yesmaximal, characteristic, complemented
3C47×#3181C211yesmaximal, characteristic, complemented
4C47×#3172C211yesmaximal, characteristic, complemented
5C47×#1664C211yesmaximal, characteristic, complemented
6C47×#1664C211yesmaximal, characteristic, complemented
7C47×#1664C211yesmaximal, characteristic, complemented
8C47×#1664C211yesmaximal, characteristic, complemented
9C47×#1660C211yesmaximal, characteristic, complemented
10C47×#1660C211yesmaximal, characteristic, complemented
11C47×#1659C211yesmaximal, characteristic, complemented
12C47×#1659C211yesmaximal, characteristic, complemented
13C47×#1532C211yesmaximal, characteristic, complemented
14C47×#1529C211yesmaximal, characteristic, complemented
15C47×#1524C211yesmaximal, characteristic, complemented
16C47×#563C2211yescharacteristic
17C47×#563C2211yescharacteristic
18C47×#563C2211yescharacteristic
19C47×H(3,𝔽4)C2211yescharacteristic
20C47×#556—21no—
21C47×#556—21no—
22C47×#556—21no—
23C47×#551—21no—
24C47×#551—21no—
25C47×#551—21no—
26C47×#542—21no—
27C47×#542—21no—
28C47×#542—21no—
29C47×#538—21no—
30C47×#538—21no—
31C47×#538—21no—
32C47×#533C2211yescharacteristic, complemented
33C47×#529C2211yescharacteristic
34C47×#529C2211yescharacteristic
35C47×#529C2211yescharacteristic
36C47×#501C2211yescharacteristic, complemented
37C47×#501C2211yescharacteristic, complemented
38C47×#501C2211yescharacteristic, complemented
39C47×#501C2211yescharacteristic, complemented
40C47×#497C2211yescharacteristic
41C47×#497C2211yescharacteristic
42C47×#491C2211yescharacteristic, complemented
43C47×#491C2211yescharacteristic, complemented
44C47×#489C2211yescharacteristic
45C47×#489C2211yescharacteristic
46C47×#489C2211yescharacteristic
47C47×#489C2211yescharacteristic
48C47×#485—21no—
49C47×#482—21no—
50C47×#479—21no—
51C47×#478—21no—
52C47×#470—21no—
53C47×#468—21no—
54C47×#467—21no—
55C47×#465—21no—
56C47×#441—21no—
57C47×#440—21no—
58C4×Q16×C47—21no—
59C4×SD16×C47—21no—
60C47×#432C2211yescharacteristic, complemented
61C4×M16×C47C2211yescharacteristic, complemented
62C2×#97×C47C2211yescharacteristic, complemented
63C47×#330C2211yescharacteristic, complemented
64C47×#330C2211yescharacteristic, complemented
65C47×#330C2211yescharacteristic, complemented
66C47×#330C2211yescharacteristic, complemented
67C47×#330C2211yescharacteristic, complemented
68C47×#330C2211yescharacteristic, complemented
69C47×#329C2211yescharacteristic
70C47×#329C2211yescharacteristic
71C47×#329C2211yescharacteristic
72C47×#329C2211yescharacteristic
73C47×#329C2211yescharacteristic
74C47×#329C2211yescharacteristic
75C2×Q16×C47—21no—
76C2×Q16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×M16×C47—21no—
80C22×C8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#126×C47—21no—
87#126×C47—21no—
88#126×C47—21no—
89#126×C47—21no—
90#126×C47—21no—
91#126×C47—21no—
92#126×C47—21no—
93#126×C47—21no—
94#126×C47—21no—
95#126×C47—21no—
96#126×C47—21no—
97#126×C47—21no—
98#126×C47—21no—
99#125×C47—21no—
100#125×C47C2311yescharacteristic
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×C47C2311yescharacteristic
113#124×C47C2311yescharacteristic
114#124×C47C2311yescharacteristic
115#123×C47—21no—
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—
124C22⋊Q8×C47—21no—
125C22⋊Q8×C47—21no—
126C22⋊Q8×C47—21no—
127C22⋊Q8×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×C47D411yescharacteristic
136C22⋊Q8×C47D411yescharacteristic
137C22⋊Q8×C47D411yescharacteristic
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47D411yescharacteristic
142#121×C47D411yescharacteristic
143#121×C47D411yescharacteristic
144#120×C47—21no—
145#120×C47—21no—
146#120×C47—21no—
147#120×C47—21no—
148C4×Q8×C47—21no—
149C4×Q8×C47—21no—
150C4×Q8×C47—21no—
151C4×Q8×C47—21no—
152C4×Q8×C47—21no—
153C4×Q8×C47D411yescharacteristic
154C4×Q8×C47D411yescharacteristic
155C4×Q8×C47D411yescharacteristic
156C4×D4×C47—21no—
157C4×D4×C47—21no—
158C4×D4×C47—21no—
159C4×D4×C47—21no—
160C4×D4×C47—21no—
161C4×D4×C47—21no—
162C4×D4×C47D411yescharacteristic
163C4×D4×C47D411yescharacteristic
164C4×D4×C47D411yescharacteristic
165#117×C47—21no—
166#117×C47—21no—
167#117×C47—21no—
168#117×C47—21no—
169#117×C47—21no—
170#117×C47—21no—
171#117×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C42×C47C2311yescharacteristic
176#107×C47—21no—
177#107×C47—21no—
178#107×C47—21no—
179#107×C47—21no—
180#106×C47—21no—
181#106×C47—21no—
182#106×C47—21no—
183#106×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#103×C47—21no—
191#103×C47—21no—
192#103×C47—21no—
193#102×C47—21no—
194#102×C47—21no—
195#102×C47—21no—
196#102×C47—21no—
197C22⋊C8×C47—21no—
198#97×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—
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47—21no—
211C2×Q8×C47—21no—
212C2×Q8×C47C2×D411yescharacteristic
213C2×Q8×C47C2×D411yescharacteristic
214C2×Q8×C47C2×D411yescharacteristic
215C2×D4×C47—21no—
216C2×D4×C47—21no—
217C2×D4×C47—21no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47C2×D411yescharacteristic
222C2×D4×C47C2×D411yescharacteristic
223C2×D4×C47C2×D411yescharacteristic
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233Q16×C47—42no—
234Q16×C47—42no—
235SD16×C47—42no—
236SD16×C47—42no—
237M16×C47—42no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—42no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
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—41no—
268C4⋊C4×C47—41no—
269C4⋊C4×C47C2×D411yescharacteristic
270C4⋊C4×C47C2×D411yescharacteristic
271C4⋊C4×C47C2×D411yescharacteristic
272C4⋊C4×C47C2×D411yescharacteristic
273C4⋊C4×C47C2×D411yescharacteristic
274C4⋊C4×C47C2×D411yescharacteristic
275C22⋊C4×C47—21no—
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—21no—
302C22⋊C4×C47—41no—
303C42×C47—21no—
304C42×C47—21no—
305C42×C47—21no—
306C42×C47—21no—
307C42×C47—21no—
308C42×C47—21no—
309C42×C47—21no—
310C42×C47—41no—
311C42×C47C2×D411yescharacteristic
312C42×C47C2×D411yescharacteristic
313C42×C47C2×D411yescharacteristic
314C42×C47C2411yescharacteristic
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—21no—
318C23×C47—81no—
319C23×C47—81no—
320C23×C47—81no—
321C23×C47#12011yescharacteristic
322Q8×C47—41no—
323Q8×C47—41no—
324Q8×C47—41no—
325Q8×C47—41no—
326Q8×C47—41no—
327Q8×C47—41no—
328Q8×C47—41no—
329Q8×C47—81no—
330Q8×C47—81no—
331Q8×C47—81no—
332D4×C47—41no—
333D4×C47—41no—
334D4×C47—41no—
335D4×C47—81no—
336D4×C47—81no—
337D4×C47—81no—
338D4×C47—81no—
339D4×C47—81no—
340D4×C47—81no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—81no—
356C2×C4×C47—81no—
357C2×C4×C47—81no—
358C2×C4×C47—81no—
359C2×C4×C47—81no—
360C2×C4×C47—81no—
361C2×C4×C47#12011yescharacteristic
362C2×C4×C47#12011yescharacteristic
363C2×C4×C47#12011yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C22×D411yescharacteristic
367C8×C47—22no—
368C8×C47—22no—
369C8×C47—41no—
370C8×C47—41no—
371C8×C47—41no—
372C8×C47—41no—
373#19039C4711yesmaximal, characteristic, direct product factor, Sylow
374C22×C47—21no—
375C22×C47—21no—
376C22×C47—21no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—162no—
387C22×C47C2×#12011yescharacteristic
388C4×C47—21no—
389C4×C47—21no—
390C4×C47—21no—
391C4×C47—21no—
392C4×C47—21no—
393C4×C47—21no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—41no—
397C4×C47—41no—
398C4×C47—41no—
399C4×C47—41no—
400C4×C47—41no—
401C4×C47—41no—
402C4×C47—41no—
403C4×C47—81no—
404C4×C47—81no—
405#3568C2×C4711yescharacteristic
406#3240C2×C4711yescharacteristic, complemented
407#3181C2×C4711yescharacteristic, complemented
408#3172C2×C4711yescharacteristic, complemented
409#1664C2×C4711yescharacteristic, complemented
410#1664C2×C4711yescharacteristic, complemented
411#1664C2×C4711yescharacteristic, complemented
412#1664C2×C4711yescharacteristic, complemented
413#1660C2×C4711yescharacteristic, complemented
414#1660C2×C4711yescharacteristic, complemented
415#1659C2×C4711yescharacteristic, complemented
416#1659C2×C4711yescharacteristic, complemented
417#1532C2×C4711yescharacteristic, complemented
418#1529C2×C4711yescharacteristic, complemented
419#1524C2×C4711yescharacteristic, complemented
420C2×C47—41no—
421C2×C47—81no—
422C2×C47—81no—
423C2×C47—81no—
424C2×C47#301811yescharacteristic
425C2×C47#301811yescharacteristic
426C2×C47#302211yescharacteristic
427#563C22×C4711yescharacteristic
428#563C22×C4711yescharacteristic
429#563C22×C4711yescharacteristic
430H(3,𝔽4)C22×C4711yescharacteristic
431#556—21no—
432#556—21no—
433#556—21no—
434#551—21no—
435#551—21no—
436#551—21no—
437#542—21no—
438#542—21no—
439#542—21no—
440#538—21no—
441#538—21no—
442#538—21no—
443#533C22×C4711yescharacteristic, complemented
444#529C22×C4711yescharacteristic
445#529C22×C4711yescharacteristic
446#529C22×C4711yescharacteristic
447#501C22×C4711yescharacteristic, complemented
448#501C22×C4711yescharacteristic, complemented
449#501C22×C4711yescharacteristic, complemented
450#501C22×C4711yescharacteristic, complemented
451#497C22×C4711yescharacteristic
452#497C22×C4711yescharacteristic
453#491C22×C4711yescharacteristic, complemented
454#491C22×C4711yescharacteristic, complemented
455#489C22×C4711yescharacteristic
456#489C22×C4711yescharacteristic
457#489C22×C4711yescharacteristic
458#489C22×C4711yescharacteristic
459#485—21no—
460#482—21no—
461#479—21no—
462#478—21no—
463#470—21no—
464#468—21no—
465#467—21no—
466#465—21no—
467#441—21no—
468#440—21no—
469C4×Q16—21no—
470C4×SD16—21no—
471#432C22×C4711yescharacteristic, complemented
472C4×M16C22×C4711yescharacteristic, complemented
473C2×#97C22×C4711yescharacteristic, complemented
474#330C22×C4711yescharacteristic, complemented
475#330C22×C4711yescharacteristic, complemented
476#330C22×C4711yescharacteristic, complemented
477#330C22×C4711yescharacteristic, complemented
478#330C22×C4711yescharacteristic, complemented
479#330C22×C4711yescharacteristic, complemented
480#329C22×C4711yescharacteristic
481#329C22×C4711yescharacteristic
482#329C22×C4711yescharacteristic
483#329C22×C4711yescharacteristic
484#329C22×C4711yescharacteristic
485#329C22×C4711yescharacteristic
486C47#1903911yescharacteristic, direct product factor, Sylow
487C2×Q16—21no—
488C2×Q16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×M16—21no—
492C22×C8—21no—
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496C4⋊Q8C23×C4711yescharacteristic
497C4⋊Q8C23×C4711yescharacteristic
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#125—21no—
512#125C23×C4711yescharacteristic
513#125C23×C4711yescharacteristic
514#125C23×C4711yescharacteristic
515#124—21no—
516#124—21no—
517#124—21no—
518#124—21no—
519#124—21no—
520#124—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124C23×C4711yescharacteristic
525#124C23×C4711yescharacteristic
526#124C23×C4711yescharacteristic
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8D4×C4711yescharacteristic
548C22⋊Q8D4×C4711yescharacteristic
549C22⋊Q8D4×C4711yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121D4×C4711yescharacteristic
554#121D4×C4711yescharacteristic
555#121D4×C4711yescharacteristic
556#120—21no—
557#120—21no—
558#120—21no—
559#120—21no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8D4×C4711yescharacteristic
566C4×Q8D4×C4711yescharacteristic
567C4×Q8D4×C4711yescharacteristic
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4D4×C4711yescharacteristic
575C4×D4D4×C4711yescharacteristic
576C4×D4D4×C4711yescharacteristic
577#117—21no—
578#117—21no—
579#117—21no—
580#117—21no—
581#117—21no—
582#117—21no—
583#117—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C42C23×C4711yescharacteristic
588#107—21no—
589#107—21no—
590#107—21no—
591#107—21no—
592#106—21no—
593#106—21no—
594#106—21no—
595#106—21no—
596C4⋊C8—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#103—21no—
603#103—21no—
604#103—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608#102—21no—
609C22⋊C8—21no—
610#97—21no—
611#97C23×C4711yescharacteristic
612#97C23×C4711yescharacteristic
613#97C23×C4711yescharacteristic
614#97C23×C4711yescharacteristic
615#97C23×C4711yescharacteristic
616#97C23×C4711yescharacteristic
617C4×C8—21no—
618C24—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×D4×C4711yescharacteristic
625C2×Q8C2×D4×C4711yescharacteristic
626C2×Q8C2×D4×C4711yescharacteristic
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C2×D4×C4711yescharacteristic
634C2×D4C2×D4×C4711yescharacteristic
635C2×D4C2×D4×C4711yescharacteristic
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4C2×D4×C4711yescharacteristic
643C22×C4C2×D4×C4711yescharacteristic
644C22×C4C2×D4×C4711yescharacteristic
645Q16—42no—
646Q16—42no—
647SD16—42no—
648SD16—42no—
649M16—42no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—42no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4C2×D4×C4711yescharacteristic
682C4⋊C4C2×D4×C4711yescharacteristic
683C4⋊C4C2×D4×C4711yescharacteristic
684C4⋊C4C2×D4×C4711yescharacteristic
685C4⋊C4C2×D4×C4711yescharacteristic
686C4⋊C4C2×D4×C4711yescharacteristic
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—41no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42C2×D4×C4711yescharacteristic
724C42C2×D4×C4711yescharacteristic
725C42C2×D4×C4711yescharacteristic
726C42C24×C4711yescharacteristic
727C23—21no—
728C23—21no—
729C23—21no—
730C23—81no—
731C23—81no—
732C23—81no—
733C23#120×C4711yescharacteristic
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—81no—
742Q8—81no—
743Q8—81no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4#120×C4711yescharacteristic
774C2×C4#120×C4711yescharacteristic
775C2×C4#120×C4711yescharacteristic
776C2×C4C22×D4×C4711yescharacteristic
777C2×C4C22×D4×C4711yescharacteristic
778C2×C4C22×D4×C4711yescharacteristic
779C8—22no—
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—162no—
798C22C2×#120×C4711yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—81no—
815C4—81no—
816C2—41no—
817C2—81no—
818C2—81no—
819C2—81no—
820C2C47×#301811yescharacteristic
821C2C47×#301811yescharacteristic
822C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3568C2
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
2. C47×#3240C2semidirect
3. C47×#3181C2semidirect
4. C47×#3172C2semidirect
5. C47×#1664C2semidirect
6. C47×#1664C2semidirect
7. C47×#1664C2semidirect
8. C47×#1664C2semidirect
9. C47×#1660C2semidirect
10. C47×#1660C2semidirect
11. C47×#1659C2semidirect
12. C47×#1659C2semidirect
13. C47×#1532C2semidirect
14. C47×#1529C2semidirect
15. C47×#1524C2semidirect
32. C47×#533C22semidirect
36. C47×#501C22semidirect
37. C47×#501C22semidirect
38. C47×#501C22semidirect
39. C47×#501C22semidirect
42. C47×#491C22semidirect
43. C47×#491C22semidirect
60. C47×#432C22semidirect
61. C4×M16×C47C22semidirect
62. C2×#97×C47C22semidirect
63. C47×#330C22semidirect
64. C47×#330C22semidirect
65. C47×#330C22semidirect
66. C47×#330C22semidirect
67. C47×#330C22semidirect
68. C47×#330C22semidirect
373. #19039C47direct (N × H)
406. #3240C2×C47semidirect
407. #3181C2×C47semidirect
408. #3172C2×C47semidirect
409. #1664C2×C47semidirect
410. #1664C2×C47semidirect
411. #1664C2×C47semidirect
412. #1664C2×C47semidirect
413. #1660C2×C47semidirect
414. #1660C2×C47semidirect
415. #1659C2×C47semidirect
416. #1659C2×C47semidirect
417. #1532C2×C47semidirect
418. #1529C2×C47semidirect
419. #1524C2×C47semidirect
443. #533C22×C47semidirect
447. #501C22×C47semidirect
448. #501C22×C47semidirect
449. #501C22×C47semidirect
450. #501C22×C47semidirect
453. #491C22×C47semidirect
454. #491C22×C47semidirect
471. #432C22×C47semidirect
472. C4×M16C22×C47semidirect
473. C2×#97C22×C47semidirect
474. #330C22×C47semidirect
475. #330C22×C47semidirect
476. #330C22×C47semidirect
477. #330C22×C47semidirect
478. #330C22×C47semidirect
479. #330C22×C47semidirect
486. C47#19039direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35682
C47×#32402
C47×#31812
C47×#31722
C47×#16642
C47×#16602
C47×#16592
C47×#15322
C47×#15292
C47×#15242
#1903947