Finite Group Databasebeta

← C47×#18446 #26058144

Subgroups — C47×#18446 #26058144

Order 12032.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3534C211yesmaximal, characteristic, complemented
2C47×#3192C211yesmaximal, characteristic, complemented
3C47×#3188C211yesmaximal, characteristic, complemented
4C47×#2813C211yesmaximal, characteristic, complemented
5C47×#1618C211yesmaximal, characteristic, complemented
6C47×#1616C211yesmaximal, characteristic, complemented
7C47×#1615C211yesmaximal, characteristic, complemented
8C47×#1613C211yesmaximal, characteristic, complemented
9C47×#1600C211yesmaximal, characteristic, complemented
10C47×#1598C211yesmaximal, characteristic, complemented
11C47×#1597C211yesmaximal, characteristic, complemented
12C47×#1595C211yesmaximal, characteristic, complemented
13C47×#1519C211yesmaximal, characteristic, complemented
14C47×#1513C211yesmaximal, characteristic, complemented
15C47×#1468C211yesmaximal, characteristic, complemented
16C47×#562—21no—
17C47×#560—21no—
18C47×#553—21no—
19C47×#551—21no—
20C47×#546—21no—
21C47×#546—21no—
22C47×#546—21no—
23D42×C47—21no—
24C47×#540—21no—
25C47×#539—21no—
26C47×#539C2211yescharacteristic
27C47×#538—21no—
28C47×#538C2211yescharacteristic
29C47×#537C2211yescharacteristic
30C47×#534—21no—
31C47×#534C2211yescharacteristic
32C47×#525C2211yescharacteristic
33C2×#123×C47C2211yescharacteristic
34C2×#121×C47C2211yescharacteristic
35C2×#121×C47C2211yescharacteristic, complemented
36C47×#484C2211yescharacteristic, complemented
37C47×#482—21no—
38C47×#481—21no—
39C47×#481C2211yescharacteristic
40C47×#481C2211yescharacteristic, complemented
41C47×#481C2211yescharacteristic, complemented
42C47×#469—21no—
43C47×#469—21no—
44C47×#466—21no—
45C47×#465—21no—
46C47×#450C2211yescharacteristic, complemented
47C47×#449—21no—
48C47×#447—21no—
49C47×#447C2211yescharacteristic
50C47×#447C2211yescharacteristic, complemented
51C47×#447C2211yescharacteristic, complemented
52C47×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#400C2211yescharacteristic, complemented
55C47×#399C2211yescharacteristic, complemented
56C47×#396—21no—
57C47×#394—21no—
58C47×#394—21no—
59C47×#394C2211yescharacteristic, complemented
60C47×#392—21no—
61C47×#392C2211yescharacteristic, complemented
62C47×#380C2211yescharacteristic, complemented
63C47×#328C2211yescharacteristic, complemented
64C47×#328C2211yescharacteristic, complemented
65C47×#327C2211yescharacteristic
66C47×#327C2211yescharacteristic
67C47×#327C2211yescharacteristic, complemented
68C47×#327C2211yescharacteristic, complemented
69C47×#327C2211yescharacteristic, complemented
70C47×#327C2211yescharacteristic, complemented
71C47×#324C2211yescharacteristic, complemented
72C47×#324C2211yescharacteristic, complemented
73C47×#323C2211yescharacteristic, complemented
74C47×#323C2211yescharacteristic, complemented
75C2×#41×C47—21no—
76C2×#41×C47D411yescharacteristic, complemented
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47D411yescharacteristic
83C22×D4×C47D411yescharacteristic, complemented
84C22×D4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C2×SD16×C47—21no—
87C2×D8×C47—21no—
88C2×D8×C47—21no—
89C2×D8×C47—21no—
90C2×M16×C47—21no—
91C22×C8×C47—21no—
92#127×C47—21no—
93#126×C47—21no—
94#126×C47—21no—
95#126×C47—21no—
96#126×C47—21no—
97#125×C47—21no—
98#125×C47—21no—
99#124×C47—21no—
100#124×C47—21no—
101#124×C47—21no—
102#123×C47—21no—
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108#123×C47—21no—
109#123×C47—21no—
110#123×C47—21no—
111#123×C47—21no—
112#123×C47—21no—
113#123×C47—21no—
114#123×C47—21no—
115#123×C47—21no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47—21no—
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47—21no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47D411yescharacteristic, complemented
122C22⋊Q8×C47C2311yescharacteristic
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47—21no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47—21no—
133#121×C47—21no—
134#121×C47—21no—
135#121×C47—21no—
136#121×C47—21no—
137#121×C47—21no—
138#121×C47—21no—
139#121×C47—21no—
140#121×C47—21no—
141#121×C47—21no—
142#121×C47D411yescharacteristic, complemented
143#121×C47D411yescharacteristic, complemented
144#121×C47D411yescharacteristic, complemented
145#121×C47C2311yescharacteristic
146#121×C47C2311yescharacteristic
147#121×C47C2311yescharacteristic
148#120×C47—21no—
149#120×C47—21no—
150#120×C47—21no—
151#120×C47—21no—
152#120×C47—21no—
153#120×C47—21no—
154#120×C47—21no—
155#120×C47—21no—
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×C47—21no—
163C4×D4×C47—21no—
164#117×C47—21no—
165#117×C47D411yescharacteristic, complemented
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic, complemented
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×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×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47C2311yescharacteristic
184#107×C47—21no—
185#106×C47—21no—
186#106×C47—21no—
187#106×C47—21no—
188#103×C47—21no—
189#102×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—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200C22⋊C8×C47C2311yescharacteristic
201C22⋊C8×C47C2311yescharacteristic
202#95×C47—21no—
203#95×C47—21no—
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47—21no—
208C24×C47—21no—
209C24×C47C2×D411yescharacteristic
210C24×C47C2×D411yescharacteristic
211#41×C47—81no—
212#41×C47—81no—
213#41×C47—81no—
214C2×Q8×C47—21no—
215C2×Q8×C47C2×D411yescharacteristic
216C2×D4×C47—21no—
217C2×D4×C47—21no—
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—21no—
235C2×D4×C47—41no—
236C2×D4×C47—41no—
237C2×D4×C47—81no—
238C2×D4×C47—81no—
239C2×D4×C47—81no—
240C2×D4×C47—81no—
241C2×D4×C47—81no—
242C2×D4×C47—81no—
243C2×D4×C47—81no—
244C2×D4×C47—81no—
245C2×D4×C47—81no—
246C2×D4×C47—81no—
247C2×D4×C47—81no—
248C2×D4×C47—81no—
249C2×D4×C47—82no—
250C2×D4×C47C2×D411yescharacteristic
251C2×D4×C47C2×D411yescharacteristic
252C2×D4×C47C2×D411yescharacteristic
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—81no—
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2×D411yescharacteristic
266C22×C4×C47C2×D411yescharacteristic
267C22×C4×C47C2×D411yescharacteristic
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2411yescharacteristic
273SD16×C47—81no—
274D8×C47—81no—
275D8×C47—81no—
276D8×C47—81no—
277M16×C47—81no—
278C2×C8×C47—21no—
279C2×C8×C47—21no—
280C2×C8×C47—21no—
281C2×C8×C47—21no—
282C2×C8×C47—81no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—21no—
293C4⋊C4×C47—21no—
294C4⋊C4×C47—21no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47—21no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47—81no—
299C4⋊C4×C47—81no—
300C4⋊C4×C47C2×D411yescharacteristic
301C4⋊C4×C47C2×D411yescharacteristic
302C4⋊C4×C47C2×D411yescharacteristic
303C4⋊C4×C47C2×D411yescharacteristic
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—21no—
317C22⋊C4×C47—21no—
318C22⋊C4×C47—21no—
319C22⋊C4×C47—21no—
320C22⋊C4×C47—21no—
321C22⋊C4×C47—21no—
322C22⋊C4×C47—21no—
323C22⋊C4×C47—21no—
324C22⋊C4×C47—21no—
325C22⋊C4×C47—21no—
326C22⋊C4×C47—21no—
327C22⋊C4×C47—21no—
328C22⋊C4×C47—21no—
329C22⋊C4×C47—41no—
330C22⋊C4×C47—41no—
331C22⋊C4×C47—81no—
332C22⋊C4×C47—81no—
333C22⋊C4×C47—81no—
334C22⋊C4×C47—81no—
335C22⋊C4×C47—81no—
336C42×C47—21no—
337C42×C47—21no—
338C42×C47—21no—
339C23×C47—21no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—21no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—41no—
348C23×C47—41no—
349C23×C47—42no—
350C23×C47—41no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—41no—
354C23×C47—41no—
355C23×C47—41no—
356C23×C47—41no—
357C23×C47—41no—
358C23×C47—41no—
359C23×C47—81no—
360C23×C47—81no—
361C23×C47—81no—
362C23×C47—81no—
363C23×C47—81no—
364C23×C47#12011yescharacteristic
365C23×C47#12011yescharacteristic
366C23×C47C22×D411yescharacteristic
367Q8×C47—41no—
368Q8×C47—81no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—41no—
372D4×C47—41no—
373D4×C47—41no—
374D4×C47—41no—
375D4×C47—41no—
376D4×C47—42no—
377D4×C47—42no—
378D4×C47—41no—
379D4×C47—41no—
380D4×C47—41no—
381D4×C47—41no—
382D4×C47—41no—
383D4×C47—41no—
384D4×C47—81no—
385D4×C47—81no—
386D4×C47—81no—
387D4×C47—81no—
388D4×C47—81no—
389D4×C47—81no—
390D4×C47—81no—
391D4×C47—81no—
392D4×C47—81no—
393D4×C47—81no—
394D4×C47—81no—
395D4×C47—81no—
396D4×C47—82no—
397D4×C47—82no—
398D4×C47—84no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—21no—
402C2×C4×C47—21no—
403C2×C4×C47—21no—
404C2×C4×C47—21no—
405C2×C4×C47—21no—
406C2×C4×C47—21no—
407C2×C4×C47—21no—
408C2×C4×C47—21no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—41no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47—41no—
422C2×C4×C47—41no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—81no—
427C2×C4×C47—81no—
428C2×C4×C47—81no—
429C2×C4×C47—81no—
430C2×C4×C47—81no—
431C2×C4×C47—81no—
432C2×C4×C47—81no—
433C2×C4×C47#12011yescharacteristic
434C2×C4×C47#12011yescharacteristic
435C2×C4×C47C22×D411yescharacteristic
436C2×C4×C47C22×D411yescharacteristic
437C8×C47—41no—
438C8×C47—41no—
439C8×C47—41no—
440C8×C47—41no—
441#18446C4711yesmaximal, characteristic, direct product factor, Sylow
442C22×C47—21no—
443C22×C47—21no—
444C22×C47—21no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47—21no—
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—41no—
451C22×C47—41no—
452C22×C47—41no—
453C22×C47—41no—
454C22×C47—41no—
455C22×C47—41no—
456C22×C47—41no—
457C22×C47—41no—
458C22×C47—41no—
459C22×C47—41no—
460C22×C47—41no—
461C22×C47—41no—
462C22×C47—81no—
463C22×C47—81no—
464C22×C47—81no—
465C22×C47—81no—
466C22×C47—81no—
467C22×C47—81no—
468C22×C47—81no—
469C22×C47—81no—
470C22×C47—81no—
471C22×C47—81no—
472C22×C47—81no—
473C22×C47—162no—
474C22×C47—162no—
475C22×C47C2×#12011yescharacteristic
476C22×C47#57611yescharacteristic
477C22×C47#57711yescharacteristic
478C4×C47—21no—
479C4×C47—21no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—41no—
483C4×C47—41no—
484C4×C47—41no—
485C4×C47—41no—
486C4×C47—41no—
487C4×C47—41no—
488C4×C47—41no—
489C4×C47—41no—
490C4×C47—81no—
491C4×C47—81no—
492C4×C47—81no—
493#3534C2×C4711yescharacteristic, complemented
494#3192C2×C4711yescharacteristic, complemented
495#3188C2×C4711yescharacteristic, complemented
496#2813C2×C4711yescharacteristic, complemented
497#1618C2×C4711yescharacteristic, complemented
498#1616C2×C4711yescharacteristic, complemented
499#1615C2×C4711yescharacteristic, complemented
500#1613C2×C4711yescharacteristic, complemented
501#1600C2×C4711yescharacteristic, complemented
502#1598C2×C4711yescharacteristic, complemented
503#1597C2×C4711yescharacteristic, complemented
504#1595C2×C4711yescharacteristic, complemented
505#1519C2×C4711yescharacteristic, complemented
506#1513C2×C4711yescharacteristic, complemented
507#1468C2×C4711yescharacteristic, complemented
508C2×C47—21no—
509C2×C47—21no—
510C2×C47—41no—
511C2×C47—41no—
512C2×C47—81no—
513C2×C47—81no—
514C2×C47—81no—
515C2×C47—81no—
516C2×C47—161no—
517C2×C47#301211yescharacteristic
518C2×C47#302111yescharacteristic
519C2×C47#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C4711yescharacteristic
531#538—21no—
532#538C22×C4711yescharacteristic
533#537C22×C4711yescharacteristic
534#534—21no—
535#534C22×C4711yescharacteristic
536#525C22×C4711yescharacteristic
537C2×#123C22×C4711yescharacteristic
538C2×#121C22×C4711yescharacteristic
539C2×#121C22×C4711yescharacteristic, complemented
540#484C22×C4711yescharacteristic, complemented
541#482—21no—
542#481—21no—
543#481C22×C4711yescharacteristic
544#481C22×C4711yescharacteristic, complemented
545#481C22×C4711yescharacteristic, complemented
546#469—21no—
547#469—21no—
548#466—21no—
549#465—21no—
550#450C22×C4711yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C4711yescharacteristic
554#447C22×C4711yescharacteristic, complemented
555#447C22×C4711yescharacteristic, complemented
556#407C22×C4711yescharacteristic, complemented
557C2×C22⋊C8C22×C4711yescharacteristic, complemented
558#400C22×C4711yescharacteristic, complemented
559#399C22×C4711yescharacteristic, complemented
560#396—21no—
561#394—21no—
562#394—21no—
563#394C22×C4711yescharacteristic, complemented
564#392—21no—
565#392C22×C4711yescharacteristic, complemented
566#380C22×C4711yescharacteristic, complemented
567#328C22×C4711yescharacteristic, complemented
568#328C22×C4711yescharacteristic, complemented
569#327C22×C4711yescharacteristic
570#327C22×C4711yescharacteristic
571#327C22×C4711yescharacteristic, complemented
572#327C22×C4711yescharacteristic, complemented
573#327C22×C4711yescharacteristic, complemented
574#327C22×C4711yescharacteristic, complemented
575#324C22×C4711yescharacteristic, complemented
576#324C22×C4711yescharacteristic, complemented
577#323C22×C4711yescharacteristic, complemented
578#323C22×C4711yescharacteristic, complemented
579C47#1844611yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C4711yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C4711yescharacteristic
588C22×D4D4×C4711yescharacteristic, complemented
589C22×D4C23×C4711yescharacteristic
590C23×C4C23×C4711yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C4711yescharacteristic, complemented
627C22⋊Q8C23×C4711yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C4711yescharacteristic, complemented
648#121D4×C4711yescharacteristic, complemented
649#121D4×C4711yescharacteristic, complemented
650#121C23×C4711yescharacteristic
651#121C23×C4711yescharacteristic
652#121C23×C4711yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C4711yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C4711yescharacteristic
674C2×C4⋊C4D4×C4711yescharacteristic, complemented
675C2×C4⋊C4C23×C4711yescharacteristic
676C2×C4⋊C4C23×C4711yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C4711yescharacteristic
687C2×C22⋊C4D4×C4711yescharacteristic
688C2×C22⋊C4C23×C4711yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C4711yescharacteristic
704C22⋊C8C23×C4711yescharacteristic
705C22⋊C8C23×C4711yescharacteristic
706C22⋊C8C23×C4711yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C4711yescharacteristic
710#95C23×C4711yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C4711yescharacteristic
715C24C2×D4×C4711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C4711yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C4711yescharacteristic
756C2×D4C2×D4×C4711yescharacteristic
757C2×D4C2×D4×C4711yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C4711yescharacteristic
770C22×C4C2×D4×C4711yescharacteristic
771C22×C4C2×D4×C4711yescharacteristic
772C22×C4C2×D4×C4711yescharacteristic
773C22×C4C2×D4×C4711yescharacteristic
774C22×C4C2×D4×C4711yescharacteristic
775C22×C4C2×D4×C4711yescharacteristic
776C22×C4C2×D4×C4711yescharacteristic
777C22×C4C24×C4711yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C4711yescharacteristic
806C4⋊C4C2×D4×C4711yescharacteristic
807C4⋊C4C2×D4×C4711yescharacteristic
808C4⋊C4C2×D4×C4711yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C4711yescharacteristic
870C23#120×C4711yescharacteristic
871C23C22×D4×C4711yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C4711yescharacteristic
939C2×C4#120×C4711yescharacteristic
940C2×C4C22×D4×C4711yescharacteristic
941C2×C4C22×D4×C4711yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C4711yescharacteristic
980C22C47×#57611yescharacteristic
981C22C47×#57711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C47×#301211yescharacteristic
1007C2C47×#302111yescharacteristic
1008C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3534C2semidirect
2. C47×#3192C2semidirect
3. C47×#3188C2semidirect
4. C47×#2813C2semidirect
5. C47×#1618C2semidirect
6. C47×#1616C2semidirect
7. C47×#1615C2semidirect
8. C47×#1613C2semidirect
9. C47×#1600C2semidirect
10. C47×#1598C2semidirect
11. C47×#1597C2semidirect
12. C47×#1595C2semidirect
13. C47×#1519C2semidirect
14. C47×#1513C2semidirect
15. C47×#1468C2semidirect
35. C2×#121×C47C22semidirect
36. C47×#484C22semidirect
40. C47×#481C22semidirect
41. C47×#481C22semidirect
46. C47×#450C22semidirect
50. C47×#447C22semidirect
51. C47×#447C22semidirect
52. C47×#407C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C47×#400C22semidirect
55. C47×#399C22semidirect
59. C47×#394C22semidirect
61. C47×#392C22semidirect
62. C47×#380C22semidirect
63. C47×#328C22semidirect
64. C47×#328C22semidirect
67. C47×#327C22semidirect
68. C47×#327C22semidirect
69. C47×#327C22semidirect
70. C47×#327C22semidirect
71. C47×#324C22semidirect
72. C47×#324C22semidirect
73. C47×#323C22semidirect
74. C47×#323C22semidirect
76. C2×#41×C47D4semidirect
83. C22×D4×C47D4semidirect
121. C22⋊Q8×C47D4semidirect
142. #121×C47D4semidirect
143. #121×C47D4semidirect
144. #121×C47D4semidirect
165. #117×C47D4semidirect
169. C2×C4⋊C4×C47D4semidirect
441. #18446C47direct (N × H)
493. #3534C2×C47semidirect
494. #3192C2×C47semidirect
495. #3188C2×C47semidirect
496. #2813C2×C47semidirect
497. #1618C2×C47semidirect
498. #1616C2×C47semidirect
499. #1615C2×C47semidirect
500. #1613C2×C47semidirect
501. #1600C2×C47semidirect
502. #1598C2×C47semidirect
503. #1597C2×C47semidirect
504. #1595C2×C47semidirect
505. #1519C2×C47semidirect
506. #1513C2×C47semidirect
507. #1468C2×C47semidirect
539. C2×#121C22×C47semidirect
540. #484C22×C47semidirect
544. #481C22×C47semidirect
545. #481C22×C47semidirect
550. #450C22×C47semidirect
554. #447C22×C47semidirect
555. #447C22×C47semidirect
556. #407C22×C47semidirect
557. C2×C22⋊C8C22×C47semidirect
558. #400C22×C47semidirect
559. #399C22×C47semidirect
563. #394C22×C47semidirect
565. #392C22×C47semidirect
566. #380C22×C47semidirect
567. #328C22×C47semidirect
568. #328C22×C47semidirect
571. #327C22×C47semidirect
572. #327C22×C47semidirect
573. #327C22×C47semidirect
574. #327C22×C47semidirect
575. #324C22×C47semidirect
576. #324C22×C47semidirect
577. #323C22×C47semidirect
578. #323C22×C47semidirect
579. C47#18446direct (N × H)
581. C2×#41D4×C47semidirect
588. C22×D4D4×C47semidirect
626. C22⋊Q8D4×C47semidirect
647. #121D4×C47semidirect
648. #121D4×C47semidirect
649. #121D4×C47semidirect
670. #117D4×C47semidirect
674. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35342
C47×#31922
C47×#31882
C47×#28132
C47×#16182
C47×#16162
C47×#16152
C47×#16132
C47×#16002
C47×#15982
C47×#15972
C47×#15952
C47×#15192
C47×#15132
C47×#14682
#1844647