Finite Group Databasebeta

← C47×#18415 #26058113

Subgroups — C47×#18415 #26058113

Order 12032.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3534C211yesmaximal, characteristic
2C47×#3196C211yesmaximal, characteristic, complemented
3C47×#3187C211yesmaximal, characteristic, complemented
4C47×#2663C211yesmaximal, characteristic, complemented
5C47×#1618C211yesmaximal, characteristic, complemented
6C47×#1616C211yesmaximal, characteristic, complemented
7C47×#1615C211yesmaximal, characteristic, complemented
8C47×#1613C211yesmaximal, characteristic, complemented
9C47×#1606C211yesmaximal, characteristic, complemented
10C47×#1604C211yesmaximal, characteristic, complemented
11C47×#1603C211yesmaximal, characteristic, complemented
12C47×#1601C211yesmaximal, characteristic, complemented
13C47×#1507C211yesmaximal, characteristic, complemented
14C47×#1501C211yesmaximal, 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×C22⋊Q8×C47C2211yescharacteristic, complemented
35C2×#121×C47C2211yescharacteristic
36C47×#485—21no—
37C47×#484C2211yescharacteristic, complemented
38C47×#483—21no—
39C47×#481C2211yescharacteristic
40C47×#481C2211yescharacteristic, complemented
41C47×#481C2211yescharacteristic, complemented
42C47×#470—21no—
43C47×#468—21no—
44C47×#465—21no—
45C47×#465—21no—
46C47×#452—21no—
47C47×#451C2211yescharacteristic, complemented
48C47×#450—21no—
49C47×#448C2211yescharacteristic
50C47×#448C2211yescharacteristic, complemented
51C47×#448C2211yescharacteristic, complemented
52C47×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#400C2211yescharacteristic, complemented
55C47×#399C2211yescharacteristic, complemented
56C47×#397—21no—
57C47×#395C2211yescharacteristic, complemented
58C47×#394—21no—
59C47×#393C2211yescharacteristic, complemented
60C47×#389—21no—
61C47×#388—21no—
62C4×C22⋊C4×C47C2211yescharacteristic, 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
77C22×Q8×C47C2311yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47D411yescharacteristic
82C22×D4×C47D411yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C2×Q16×C47—21no—
85C2×SD16×C47—21no—
86C2×SD16×C47—21no—
87C2×SD16×C47—21no—
88C2×M16×C47—21no—
89C22×C8×C47—21no—
90#127×C47—21no—
91#126×C47—21no—
92#126×C47—21no—
93#126×C47—21no—
94#126×C47—21no—
95#125×C47—21no—
96#125×C47—21no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47—21no—
100#123×C47—21no—
101#123×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—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47—21no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47—21no—
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47—21no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47—21no—
122C22⋊Q8×C47—21no—
123C22⋊Q8×C47D411yescharacteristic
124C22⋊Q8×C47C2311yescharacteristic
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×C47D411yescharacteristic
141#121×C47D411yescharacteristic
142#121×C47D411yescharacteristic
143#121×C47C2311yescharacteristic
144#121×C47C2311yescharacteristic
145#121×C47C2311yescharacteristic
146#120×C47—21no—
147#120×C47—21no—
148#120×C47—21no—
149#120×C47—21no—
150#120×C47—21no—
151#120×C47—21no—
152#120×C47—21no—
153#120×C47—21no—
154C4×D4×C47—21no—
155C4×D4×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—
162#117×C47—21no—
163#117×C47D411yescharacteristic
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
179C2×C22⋊C4×C47D411yescharacteristic
180C2×C22⋊C4×C47C2311yescharacteristic
181C2×C42×C47—21no—
182#107×C47—21no—
183#106×C47—21no—
184#106×C47—21no—
185#106×C47—21no—
186#103×C47—21no—
187#103×C47—21no—
188#103×C47—21no—
189#103×C47—21no—
190#103×C47—21no—
191#102×C47—21no—
192#102×C47—21no—
193#102×C47—21no—
194C22⋊C8×C47—21no—
195C22⋊C8×C47—21no—
196C22⋊C8×C47C2311yescharacteristic
197C22⋊C8×C47C2311yescharacteristic
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200#95×C47—21no—
201#95×C47—21no—
202#95×C47—21no—
203#95×C47—21no—
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47—21no—
207C24×C47—21no—
208C24×C47C2×D411yescharacteristic
209C24×C47C2×D411yescharacteristic
210#41×C47—81no—
211#41×C47—81no—
212#41×C47—81no—
213C2×Q8×C47—21no—
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—81no—
217C2×Q8×C47C2×D411yescharacteristic
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—81no—
236C2×D4×C47—81no—
237C2×D4×C47—81no—
238C2×D4×C47—81no—
239C2×D4×C47—81no—
240C2×D4×C47—81no—
241C2×D4×C47—82no—
242C2×D4×C47C2×D411yescharacteristic
243C2×D4×C47C2×D411yescharacteristic
244C2×D4×C47C2×D411yescharacteristic
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—81no—
257C22×C4×C47C2×D411yescharacteristic
258C22×C4×C47C2×D411yescharacteristic
259C22×C4×C47C2×D411yescharacteristic
260C22×C4×C47C2×D411yescharacteristic
261C22×C4×C47C2×D411yescharacteristic
262C22×C4×C47C2×D411yescharacteristic
263C22×C4×C47C2×D411yescharacteristic
264C22×C4×C47C2×D411yescharacteristic
265C22×C4×C47C2411yescharacteristic
266Q16×C47—81no—
267SD16×C47—81no—
268SD16×C47—81no—
269SD16×C47—81no—
270M16×C47—81no—
271C2×C8×C47—21no—
272C2×C8×C47—21no—
273C2×C8×C47—21no—
274C2×C8×C47—21no—
275C2×C8×C47—81no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—42no—
292C4⋊C4×C47—41no—
293C4⋊C4×C47—41no—
294C4⋊C4×C47—81no—
295C4⋊C4×C47C2×D411yescharacteristic
296C4⋊C4×C47C2×D411yescharacteristic
297C4⋊C4×C47C2×D411yescharacteristic
298C4⋊C4×C47C2×D411yescharacteristic
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—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—42no—
325C22⋊C4×C47—42no—
326C22⋊C4×C47—41no—
327C22⋊C4×C47—41no—
328C22⋊C4×C47—81no—
329C42×C47—21no—
330C42×C47—21no—
331C42×C47—21no—
332C42×C47—81no—
333C23×C47—21no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—21no—
339C23×C47—21no—
340C23×C47—21no—
341C23×C47—41no—
342C23×C47—41no—
343C23×C47—42no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—81no—
347C23×C47—81no—
348C23×C47—81no—
349C23×C47—81no—
350C23×C47—81no—
351C23×C47#12011yescharacteristic
352C23×C47#12011yescharacteristic
353C23×C47C22×D411yescharacteristic
354Q8×C47—41no—
355Q8×C47—41no—
356Q8×C47—41no—
357Q8×C47—41no—
358Q8×C47—41no—
359Q8×C47—81no—
360D4×C47—41no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—42no—
364D4×C47—42no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47—41no—
368D4×C47—41no—
369D4×C47—41no—
370D4×C47—41no—
371D4×C47—81no—
372D4×C47—81no—
373D4×C47—81no—
374D4×C47—81no—
375D4×C47—81no—
376D4×C47—81no—
377D4×C47—81no—
378D4×C47—81no—
379D4×C47—81no—
380D4×C47—81no—
381D4×C47—81no—
382D4×C47—81no—
383C2×C4×C47—22no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—21no—
387C2×C4×C47—21no—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—41no—
395C2×C4×C47—41no—
396C2×C4×C47—41no—
397C2×C4×C47—41no—
398C2×C4×C47—41no—
399C2×C4×C47—41no—
400C2×C4×C47—41no—
401C2×C4×C47—41no—
402C2×C4×C47—41no—
403C2×C4×C47—41no—
404C2×C4×C47—41no—
405C2×C4×C47—41no—
406C2×C4×C47—41no—
407C2×C4×C47—41no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—81no—
414C2×C4×C47—81no—
415C2×C4×C47—81no—
416C2×C4×C47—81no—
417C2×C4×C47—81no—
418C2×C4×C47—81no—
419C2×C4×C47—81no—
420C2×C4×C47#12011yescharacteristic
421C2×C4×C47#12011yescharacteristic
422C2×C4×C47C22×D411yescharacteristic
423C2×C4×C47C22×D411yescharacteristic
424C8×C47—41no—
425C8×C47—41no—
426C8×C47—41no—
427C8×C47—41no—
428#18415C4711yesmaximal, characteristic, direct product factor, Sylow
429C22×C47—21no—
430C22×C47—21no—
431C22×C47—21no—
432C22×C47—21no—
433C22×C47—21no—
434C22×C47—21no—
435C22×C47—21no—
436C22×C47—21no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—41no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—41no—
443C22×C47—41no—
444C22×C47—41no—
445C22×C47—41no—
446C22×C47—41no—
447C22×C47—41no—
448C22×C47—41no—
449C22×C47—81no—
450C22×C47—81no—
451C22×C47—81no—
452C22×C47—81no—
453C22×C47—162no—
454C22×C47—162no—
455C22×C47C2×#12011yescharacteristic
456C22×C47#57711yescharacteristic
457C22×C47#57711yescharacteristic
458C4×C47—21no—
459C4×C47—21no—
460C4×C47—21no—
461C4×C47—21no—
462C4×C47—42no—
463C4×C47—41no—
464C4×C47—41no—
465C4×C47—41no—
466C4×C47—41no—
467C4×C47—41no—
468C4×C47—41no—
469C4×C47—41no—
470C4×C47—41no—
471C4×C47—81no—
472C4×C47—81no—
473C4×C47—81no—
474#3534C2×C4711yescharacteristic
475#3196C2×C4711yescharacteristic, complemented
476#3187C2×C4711yescharacteristic, complemented
477#2663C2×C4711yescharacteristic, complemented
478#1618C2×C4711yescharacteristic, complemented
479#1616C2×C4711yescharacteristic, complemented
480#1615C2×C4711yescharacteristic, complemented
481#1613C2×C4711yescharacteristic, complemented
482#1606C2×C4711yescharacteristic, complemented
483#1604C2×C4711yescharacteristic, complemented
484#1603C2×C4711yescharacteristic, complemented
485#1601C2×C4711yescharacteristic, complemented
486#1507C2×C4711yescharacteristic, complemented
487#1501C2×C4711yescharacteristic, complemented
488#1468C2×C4711yescharacteristic, complemented
489C2×C47—21no—
490C2×C47—21no—
491C2×C47—41no—
492C2×C47—41no—
493C2×C47—81no—
494C2×C47—81no—
495C2×C47—81no—
496C2×C47—81no—
497C2×C47#300911yescharacteristic
498C2×C47#301811yescharacteristic
499C2×C47#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C4711yescharacteristic
511#538—21no—
512#538C22×C4711yescharacteristic
513#537C22×C4711yescharacteristic
514#534—21no—
515#534C22×C4711yescharacteristic
516#525C22×C4711yescharacteristic
517C2×#123C22×C4711yescharacteristic
518C2×C22⋊Q8C22×C4711yescharacteristic, complemented
519C2×#121C22×C4711yescharacteristic
520#485—21no—
521#484C22×C4711yescharacteristic, complemented
522#483—21no—
523#481C22×C4711yescharacteristic
524#481C22×C4711yescharacteristic, complemented
525#481C22×C4711yescharacteristic, complemented
526#470—21no—
527#468—21no—
528#465—21no—
529#465—21no—
530#452—21no—
531#451C22×C4711yescharacteristic, complemented
532#450—21no—
533#448C22×C4711yescharacteristic
534#448C22×C4711yescharacteristic, complemented
535#448C22×C4711yescharacteristic, complemented
536#407C22×C4711yescharacteristic, complemented
537C2×C22⋊C8C22×C4711yescharacteristic, complemented
538#400C22×C4711yescharacteristic, complemented
539#399C22×C4711yescharacteristic, complemented
540#397—21no—
541#395C22×C4711yescharacteristic, complemented
542#394—21no—
543#393C22×C4711yescharacteristic, complemented
544#389—21no—
545#388—21no—
546C4×C22⋊C4C22×C4711yescharacteristic, complemented
547#328C22×C4711yescharacteristic, complemented
548#328C22×C4711yescharacteristic, complemented
549#327C22×C4711yescharacteristic
550#327C22×C4711yescharacteristic
551#327C22×C4711yescharacteristic, complemented
552#327C22×C4711yescharacteristic, complemented
553#327C22×C4711yescharacteristic, complemented
554#327C22×C4711yescharacteristic, complemented
555#324C22×C4711yescharacteristic, complemented
556#324C22×C4711yescharacteristic, complemented
557#323C22×C4711yescharacteristic, complemented
558#323C22×C4711yescharacteristic, complemented
559C47#1841511yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C4711yescharacteristic
562C22×Q8C23×C4711yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C4711yescharacteristic
567C22×D4D4×C4711yescharacteristic
568C23×C4C23×C4711yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C4711yescharacteristic
609C22⋊Q8C23×C4711yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C4711yescharacteristic
626#121D4×C4711yescharacteristic
627#121D4×C4711yescharacteristic
628#121C23×C4711yescharacteristic
629#121C23×C4711yescharacteristic
630#121C23×C4711yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C4711yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C4711yescharacteristic
653C2×C4⋊C4D4×C4711yescharacteristic
654C2×C4⋊C4C23×C4711yescharacteristic
655C2×C4⋊C4C23×C4711yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C4711yescharacteristic
664C2×C22⋊C4D4×C4711yescharacteristic
665C2×C22⋊C4C23×C4711yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C4711yescharacteristic
682C22⋊C8C23×C4711yescharacteristic
683C22⋊C8C23×C4711yescharacteristic
684C22⋊C8C23×C4711yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C4711yescharacteristic
690#95C23×C4711yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C4711yescharacteristic
694C24C2×D4×C4711yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C4711yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C4711yescharacteristic
728C2×D4C2×D4×C4711yescharacteristic
729C2×D4C2×D4×C4711yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C4711yescharacteristic
743C22×C4C2×D4×C4711yescharacteristic
744C22×C4C2×D4×C4711yescharacteristic
745C22×C4C2×D4×C4711yescharacteristic
746C22×C4C2×D4×C4711yescharacteristic
747C22×C4C2×D4×C4711yescharacteristic
748C22×C4C2×D4×C4711yescharacteristic
749C22×C4C2×D4×C4711yescharacteristic
750C22×C4C24×C4711yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C4711yescharacteristic
781C4⋊C4C2×D4×C4711yescharacteristic
782C4⋊C4C2×D4×C4711yescharacteristic
783C4⋊C4C2×D4×C4711yescharacteristic
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C4711yescharacteristic
837C23#120×C4711yescharacteristic
838C23C22×D4×C4711yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C4711yescharacteristic
906C2×C4#120×C4711yescharacteristic
907C2×C4C22×D4×C4711yescharacteristic
908C2×C4C22×D4×C4711yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C4711yescharacteristic
940C22C47×#57711yescharacteristic
941C22C47×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C47×#300911yescharacteristic
967C2C47×#301811yescharacteristic
968C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3534C2
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
2. C47×#3196C2semidirect
3. C47×#3187C2semidirect
4. C47×#2663C2semidirect
5. C47×#1618C2semidirect
6. C47×#1616C2semidirect
7. C47×#1615C2semidirect
8. C47×#1613C2semidirect
9. C47×#1606C2semidirect
10. C47×#1604C2semidirect
11. C47×#1603C2semidirect
12. C47×#1601C2semidirect
13. C47×#1507C2semidirect
14. C47×#1501C2semidirect
15. C47×#1468C2semidirect
34. C2×C22⋊Q8×C47C22semidirect
37. C47×#484C22semidirect
40. C47×#481C22semidirect
41. C47×#481C22semidirect
47. C47×#451C22semidirect
50. C47×#448C22semidirect
51. C47×#448C22semidirect
52. C47×#407C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C47×#400C22semidirect
55. C47×#399C22semidirect
57. C47×#395C22semidirect
59. C47×#393C22semidirect
62. C4×C22⋊C4×C47C22semidirect
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
428. #18415C47direct (N × H)
475. #3196C2×C47semidirect
476. #3187C2×C47semidirect
477. #2663C2×C47semidirect
478. #1618C2×C47semidirect
479. #1616C2×C47semidirect
480. #1615C2×C47semidirect
481. #1613C2×C47semidirect
482. #1606C2×C47semidirect
483. #1604C2×C47semidirect
484. #1603C2×C47semidirect
485. #1601C2×C47semidirect
486. #1507C2×C47semidirect
487. #1501C2×C47semidirect
488. #1468C2×C47semidirect
518. C2×C22⋊Q8C22×C47semidirect
521. #484C22×C47semidirect
524. #481C22×C47semidirect
525. #481C22×C47semidirect
531. #451C22×C47semidirect
534. #448C22×C47semidirect
535. #448C22×C47semidirect
536. #407C22×C47semidirect
537. C2×C22⋊C8C22×C47semidirect
538. #400C22×C47semidirect
539. #399C22×C47semidirect
541. #395C22×C47semidirect
543. #393C22×C47semidirect
546. C4×C22⋊C4C22×C47semidirect
547. #328C22×C47semidirect
548. #328C22×C47semidirect
551. #327C22×C47semidirect
552. #327C22×C47semidirect
553. #327C22×C47semidirect
554. #327C22×C47semidirect
555. #324C22×C47semidirect
556. #324C22×C47semidirect
557. #323C22×C47semidirect
558. #323C22×C47semidirect
559. C47#18415direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35342
C47×#31962
C47×#31872
C47×#26632
C47×#16182
C47×#16162
C47×#16152
C47×#16132
C47×#16062
C47×#16042
C47×#16032
C47×#16012
C47×#15072
C47×#15012
C47×#14682
#1841547