Finite Group Databasebeta

← C47×#18262 #26057960

Subgroups — C47×#18262 #26057960

Order 12032.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3534C211yesmaximal, characteristic
2C47×#3094C211yesmaximal, characteristic, complemented
3C47×#3091C211yesmaximal, characteristic, complemented
4C47×#2498C211yesmaximal, characteristic, complemented
5C47×#1618C211yesmaximal, characteristic, complemented
6C47×#1616C211yesmaximal, characteristic, complemented
7C47×#1615C211yesmaximal, characteristic, complemented
8C47×#1613C211yesmaximal, characteristic, complemented
9C47×#1612C211yesmaximal, characteristic, complemented
10C47×#1610C211yesmaximal, characteristic, complemented
11C47×#1609C211yesmaximal, characteristic, complemented
12C47×#1607C211yesmaximal, characteristic, complemented
13C47×#1504C211yesmaximal, characteristic, complemented
14C2×C47×#327C211yesmaximal, 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×#117×C47C2211yescharacteristic, complemented
36C47×#485—21no—
37C47×#484C2211yescharacteristic, complemented
38C47×#483C2211yescharacteristic, complemented
39C47×#482—21no—
40C47×#482—21no—
41C47×#482—21no—
42C47×#481C2211yescharacteristic
43C47×#481C2211yescharacteristic, complemented
44C47×#481C2211yescharacteristic, complemented
45C47×#480C2211yescharacteristic
46C47×#480C2211yescharacteristic, complemented
47C47×#480C2211yescharacteristic, complemented
48C47×#428—21no—
49C47×#427—21no—
50C47×#418—21no—
51C47×#416—21no—
52C47×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C47×#400C2211yescharacteristic, complemented
55C47×#399C2211yescharacteristic, complemented
56C47×#398C2211yescharacteristic, complemented
57C47×#397C2211yescharacteristic, complemented
58C47×#388—21no—
59C47×#387—21no—
60C47×#386—21no—
61C47×#380—21no—
62C2×#95×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×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47D411yescharacteristic
81C22×D4×C47D411yescharacteristic
82C23×C4×C47—21no—
83C23×C4×C47C2311yescharacteristic
84C2×M16×C47—21no—
85C22×C8×C47—21no—
86#127×C47—21no—
87#126×C47—21no—
88#126×C47—21no—
89#126×C47—21no—
90#126×C47—21no—
91#125×C47—21no—
92#125×C47—21no—
93#124×C47—21no—
94#124×C47—21no—
95#124×C47—21no—
96#123×C47—21no—
97#123×C47—21no—
98#123×C47—21no—
99#123×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—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47D411yescharacteristic
116C22⋊Q8×C47C2311yescharacteristic
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
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×C47D411yescharacteristic
133#121×C47D411yescharacteristic
134#121×C47D411yescharacteristic
135#121×C47C2311yescharacteristic
136#121×C47C2311yescharacteristic
137#121×C47C2311yescharacteristic
138#120×C47—21no—
139#120×C47—21no—
140#120×C47—21no—
141#120×C47—21no—
142#120×C47—21no—
143#120×C47—21no—
144#120×C47—21no—
145#120×C47—21no—
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47—21no—
149C4×D4×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—21no—
152C4×D4×C47—21no—
153C4×D4×C47—21no—
154#117×C47—21no—
155#117×C47—21no—
156#117×C47—21no—
157#117×C47—21no—
158#117×C47—21no—
159#117×C47D411yescharacteristic
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47D411yescharacteristic
163C2×C4⋊C4×C47D411yescharacteristic
164C2×C4⋊C4×C47C2311yescharacteristic
165C2×C4⋊C4×C47C2311yescharacteristic
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C22⋊C4×C47—21no—
168C2×C22⋊C4×C47—21no—
169C2×C22⋊C4×C47—21no—
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C22⋊C4×C47D411yescharacteristic
175C2×C22⋊C4×C47C2311yescharacteristic
176C2×C42×C47—21no—
177#107×C47—21no—
178#107×C47—21no—
179#107×C47—21no—
180#107×C47—21no—
181#106×C47—21no—
182#106×C47—21no—
183#106×C47—21no—
184#106×C47—21no—
185#103×C47—21no—
186#103×C47—21no—
187#102×C47—21no—
188#102×C47—21no—
189#102×C47—21no—
190#102×C47—21no—
191#102×C47—21no—
192#102×C47—21no—
193C22⋊C8×C47—21no—
194C22⋊C8×C47—21no—
195C22⋊C8×C47C2311yescharacteristic
196C22⋊C8×C47C2311yescharacteristic
197C22⋊C8×C47C2311yescharacteristic
198C22⋊C8×C47C2311yescharacteristic
199#95×C47—21no—
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—42no—
211#41×C47—81no—
212#41×C47—81no—
213C2×Q8×C47—21no—
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×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—42no—
233C2×D4×C47—42no—
234C2×D4×C47—81no—
235C2×D4×C47—81no—
236C2×D4×C47—81no—
237C2×D4×C47—81no—
238C2×D4×C47—82no—
239C2×D4×C47C2×D411yescharacteristic
240C2×D4×C47C2×D411yescharacteristic
241C2×D4×C47C2×D411yescharacteristic
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
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—42no—
254C22×C4×C47—42no—
255C22×C4×C47—42no—
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
266M16×C47—42no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—42no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47—21no—
285C4⋊C4×C47—21no—
286C4⋊C4×C47—21no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47—21no—
289C4⋊C4×C47—42no—
290C4⋊C4×C47—81no—
291C4⋊C4×C47C2×D411yescharacteristic
292C4⋊C4×C47C2×D411yescharacteristic
293C4⋊C4×C47C2×D411yescharacteristic
294C4⋊C4×C47C2×D411yescharacteristic
295C22⋊C4×C47—21no—
296C22⋊C4×C47—21no—
297C22⋊C4×C47—21no—
298C22⋊C4×C47—21no—
299C22⋊C4×C47—21no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—21no—
317C22⋊C4×C47—21no—
318C22⋊C4×C47—21no—
319C22⋊C4×C47—21no—
320C22⋊C4×C47—42no—
321C22⋊C4×C47—41no—
322C22⋊C4×C47—41no—
323C22⋊C4×C47—81no—
324C42×C47—21no—
325C42×C47—21no—
326C42×C47—21no—
327C42×C47—41no—
328C42×C47—41no—
329C23×C47—21no—
330C23×C47—21no—
331C23×C47—22no—
332C23×C47—21no—
333C23×C47—21no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—41no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—42no—
342C23×C47—81no—
343C23×C47—81no—
344C23×C47—81no—
345C23×C47—81no—
346C23×C47—81no—
347C23×C47#12011yescharacteristic
348C23×C47#12011yescharacteristic
349C23×C47C22×D411yescharacteristic
350Q8×C47—41no—
351Q8×C47—81no—
352D4×C47—41no—
353D4×C47—41no—
354D4×C47—41no—
355D4×C47—41no—
356D4×C47—41no—
357D4×C47—41no—
358D4×C47—41no—
359D4×C47—41no—
360D4×C47—41no—
361D4×C47—42no—
362D4×C47—42no—
363D4×C47—81no—
364D4×C47—81no—
365D4×C47—81no—
366D4×C47—81no—
367D4×C47—81no—
368D4×C47—81no—
369D4×C47—81no—
370D4×C47—81no—
371D4×C47—81no—
372D4×C47—81no—
373D4×C47—81no—
374D4×C47—81no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—21no—
379C2×C4×C47—21no—
380C2×C4×C47—21no—
381C2×C4×C47—21no—
382C2×C4×C47—21no—
383C2×C4×C47—21no—
384C2×C4×C47—21no—
385C2×C4×C47—21no—
386C2×C4×C47—21no—
387C2×C4×C47—21no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
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—81no—
406C2×C4×C47—81no—
407C2×C4×C47—81no—
408C2×C4×C47—81no—
409C2×C4×C47—81no—
410C2×C4×C47—81no—
411C2×C4×C47—81no—
412C2×C4×C47—84no—
413C2×C4×C47#12011yescharacteristic
414C2×C4×C47#12011yescharacteristic
415C2×C4×C47C22×D411yescharacteristic
416C2×C4×C47C22×D411yescharacteristic
417C8×C47—41no—
418C8×C47—41no—
419C8×C47—41no—
420C8×C47—41no—
421#18262C4711yesmaximal, characteristic, direct product factor, Sylow
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—21no—
427C22×C47—21no—
428C22×C47—21no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47—41no—
432C22×C47—41no—
433C22×C47—41no—
434C22×C47—41no—
435C22×C47—41no—
436C22×C47—41no—
437C22×C47—41no—
438C22×C47—41no—
439C22×C47—41no—
440C22×C47—41no—
441C22×C47—41no—
442C22×C47—41no—
443C22×C47—81no—
444C22×C47—81no—
445C22×C47—162no—
446C22×C47—162no—
447C22×C47#45812yes—
448C22×C47C2×#12011yescharacteristic
449C22×C47#57611yescharacteristic
450C22×C47#57711yescharacteristic
451C4×C47—21no—
452C4×C47—21no—
453C4×C47—21no—
454C4×C47—21no—
455C4×C47—42no—
456C4×C47—41no—
457C4×C47—41no—
458C4×C47—41no—
459C4×C47—41no—
460C4×C47—41no—
461C4×C47—41no—
462C4×C47—41no—
463C4×C47—41no—
464C4×C47—81no—
465C4×C47—81no—
466C4×C47—81no—
467#3534C2×C4711yescharacteristic
468#3094C2×C4711yescharacteristic, complemented
469#3091C2×C4711yescharacteristic, complemented
470#2498C2×C4711yescharacteristic, complemented
471#1618C2×C4711yescharacteristic, complemented
472#1616C2×C4711yescharacteristic, complemented
473#1615C2×C4711yescharacteristic, complemented
474#1613C2×C4711yescharacteristic, complemented
475#1612C2×C4711yescharacteristic, complemented
476#1610C2×C4711yescharacteristic, complemented
477#1609C2×C4711yescharacteristic, complemented
478#1607C2×C4711yescharacteristic, complemented
479#1504C2×C4711yescharacteristic, complemented
480C2×#327C2×C4711yescharacteristic, complemented
481#1468C2×C4711yescharacteristic, complemented
482C2×C47—21no—
483C2×C47—21no—
484C2×C47—22no—
485C2×C47—41no—
486C2×C47—81no—
487C2×C47—81no—
488C2×C47—81no—
489C2×C47—81no—
490C2×C47#301211yescharacteristic
491C2×C47#301811yescharacteristic
492C2×C47C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C4711yescharacteristic
504#538—21no—
505#538C22×C4711yescharacteristic
506#537C22×C4711yescharacteristic
507#534—21no—
508#534C22×C4711yescharacteristic
509#525C22×C4711yescharacteristic
510C2×#123C22×C4711yescharacteristic
511C2×#121C22×C4711yescharacteristic
512C2×#117C22×C4711yescharacteristic, complemented
513#485—21no—
514#484C22×C4711yescharacteristic, complemented
515#483C22×C4711yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C4711yescharacteristic
520#481C22×C4711yescharacteristic, complemented
521#481C22×C4711yescharacteristic, complemented
522#480C22×C4711yescharacteristic
523#480C22×C4711yescharacteristic, complemented
524#480C22×C4711yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C4711yescharacteristic, complemented
530C2×C22⋊C8C22×C4711yescharacteristic, complemented
531#400C22×C4711yescharacteristic, complemented
532#399C22×C4711yescharacteristic, complemented
533#398C22×C4711yescharacteristic, complemented
534#397C22×C4711yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C4711yescharacteristic, complemented
540#328C22×C4711yescharacteristic, complemented
541#328C22×C4711yescharacteristic, complemented
542#327C22×C4711yescharacteristic
543#327C22×C4711yescharacteristic
544#327C22×C4711yescharacteristic, complemented
545#327C22×C4711yescharacteristic, complemented
546#327C22×C4711yescharacteristic, complemented
547#327C22×C4711yescharacteristic, complemented
548#324C22×C4711yescharacteristic, complemented
549#324C22×C4711yescharacteristic, complemented
550#323C22×C4711yescharacteristic, complemented
551#323C22×C4711yescharacteristic, complemented
552C47#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C4711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C4711yescharacteristic
559C22×D4D4×C4711yescharacteristic
560C23×C4—21no—
561C23×C4C23×C4711yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C4711yescharacteristic
594C22⋊Q8C23×C4711yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C4711yescharacteristic
611#121D4×C4711yescharacteristic
612#121D4×C4711yescharacteristic
613#121C23×C4711yescharacteristic
614#121C23×C4711yescharacteristic
615#121C23×C4711yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C4711yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C4711yescharacteristic
641C2×C4⋊C4D4×C4711yescharacteristic
642C2×C4⋊C4C23×C4711yescharacteristic
643C2×C4⋊C4C23×C4711yescharacteristic
644C2×C4⋊C4C23×C4711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C4711yescharacteristic
652C2×C22⋊C4D4×C4711yescharacteristic
653C2×C22⋊C4C23×C4711yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C4711yescharacteristic
674C22⋊C8C23×C4711yescharacteristic
675C22⋊C8C23×C4711yescharacteristic
676C22⋊C8C23×C4711yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C4711yescharacteristic
683#95C23×C4711yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C4711yescharacteristic
687C24C2×D4×C4711yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C4711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C4711yescharacteristic
718C2×D4C2×D4×C4711yescharacteristic
719C2×D4C2×D4×C4711yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C4711yescharacteristic
736C22×C4C2×D4×C4711yescharacteristic
737C22×C4C2×D4×C4711yescharacteristic
738C22×C4C2×D4×C4711yescharacteristic
739C22×C4C2×D4×C4711yescharacteristic
740C22×C4C2×D4×C4711yescharacteristic
741C22×C4C2×D4×C4711yescharacteristic
742C22×C4C2×D4×C4711yescharacteristic
743C22×C4C24×C4711yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C4711yescharacteristic
770C4⋊C4C2×D4×C4711yescharacteristic
771C4⋊C4C2×D4×C4711yescharacteristic
772C4⋊C4C2×D4×C4711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
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—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C4711yescharacteristic
826C23#120×C4711yescharacteristic
827C23C22×D4×C4711yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C4711yescharacteristic
892C2×C4#120×C4711yescharacteristic
893C2×C4C22×D4×C4711yescharacteristic
894C2×C4C22×D4×C4711yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C47×#45812yes—
925C22C2×#120×C4711yescharacteristic
926C22C47×#57611yescharacteristic
927C22C47×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C47×#301211yescharacteristic
953C2C47×#301811yescharacteristic
954C2C2×C47×#45811yescharacteristic
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×#3094C2semidirect
3. C47×#3091C2semidirect
4. C47×#2498C2semidirect
5. C47×#1618C2semidirect
6. C47×#1616C2semidirect
7. C47×#1615C2semidirect
8. C47×#1613C2semidirect
9. C47×#1612C2semidirect
10. C47×#1610C2semidirect
11. C47×#1609C2semidirect
12. C47×#1607C2semidirect
13. C47×#1504C2semidirect
14. C2×C47×#327C2semidirect
15. C47×#1468C2semidirect
35. C2×#117×C47C22semidirect
37. C47×#484C22semidirect
38. C47×#483C22semidirect
43. C47×#481C22semidirect
44. C47×#481C22semidirect
46. C47×#480C22semidirect
47. C47×#480C22semidirect
52. C47×#407C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C47×#400C22semidirect
55. C47×#399C22semidirect
56. C47×#398C22semidirect
57. C47×#397C22semidirect
62. C2×#95×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
421. #18262C47direct (N × H)
468. #3094C2×C47semidirect
469. #3091C2×C47semidirect
470. #2498C2×C47semidirect
471. #1618C2×C47semidirect
472. #1616C2×C47semidirect
473. #1615C2×C47semidirect
474. #1613C2×C47semidirect
475. #1612C2×C47semidirect
476. #1610C2×C47semidirect
477. #1609C2×C47semidirect
478. #1607C2×C47semidirect
479. #1504C2×C47semidirect
480. C2×#327C2×C47semidirect
481. #1468C2×C47semidirect
512. C2×#117C22×C47semidirect
514. #484C22×C47semidirect
515. #483C22×C47semidirect
520. #481C22×C47semidirect
521. #481C22×C47semidirect
523. #480C22×C47semidirect
524. #480C22×C47semidirect
529. #407C22×C47semidirect
530. C2×C22⋊C8C22×C47semidirect
531. #400C22×C47semidirect
532. #399C22×C47semidirect
533. #398C22×C47semidirect
534. #397C22×C47semidirect
539. C2×#95C22×C47semidirect
540. #328C22×C47semidirect
541. #328C22×C47semidirect
544. #327C22×C47semidirect
545. #327C22×C47semidirect
546. #327C22×C47semidirect
547. #327C22×C47semidirect
548. #324C22×C47semidirect
549. #324C22×C47semidirect
550. #323C22×C47semidirect
551. #323C22×C47semidirect
552. C47#18262direct (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×#30942
C47×#30912
C47×#24982
C47×#16182
C47×#16162
C47×#16152
C47×#16132
C47×#16122
C47×#16102
C47×#16092
C47×#16072
C47×#15042
C2×C47×#3272
C47×#14682
#1826247