Finite Group Databasebeta

← C47×#18931 #26058629

Subgroups — C47×#18931 #26058629

Order 12032.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3543C211yesmaximal, characteristic
2C47×#3252C211yesmaximal, characteristic, complemented
3C47×#3233C211yesmaximal, characteristic, complemented
4C47×#3208C211yesmaximal, characteristic, complemented
5C47×#1642C211yesmaximal, characteristic, complemented
6C47×#1641C211yesmaximal, characteristic, complemented
7C47×#1640C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1631C211yesmaximal, characteristic, complemented
10C47×#1631C211yesmaximal, characteristic, complemented
11C47×#1630C211yesmaximal, characteristic, complemented
12C47×#1629C211yesmaximal, characteristic, complemented
13C47×#1545C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1482C211yesmaximal, characteristic, complemented
16C47×#560—22no—
17C47×#559C2211yescharacteristic
18C47×#550C2211yescharacteristic
19C47×#550C2211yescharacteristic
20C47×#546—21no—
21C47×#546—21no—
22D42×C47—21no—
23D42×C47—21no—
24D42×C47C2211yescharacteristic
25C47×#540—21no—
26C47×#540—21no—
27C47×#535—21no—
28C47×#535—21no—
29C47×#534—22no—
30C47×#533C2211yescharacteristic, complemented
31C2×#127×C47C2211yescharacteristic
32C47×#529C2211yescharacteristic
33C47×#529C2211yescharacteristic
34C47×#499—21no—
35C47×#492C2211yescharacteristic
36C47×#492C2211yescharacteristic, complemented
37C47×#488—21no—
38C47×#486C2211yescharacteristic
39C47×#486C2211yescharacteristic, complemented
40C47×#485—21no—
41C47×#482—21no—
42C47×#479—21no—
43C47×#477C2211yescharacteristic, complemented
44C47×#477C2211yescharacteristic, complemented
45C47×#476C2211yescharacteristic, complemented
46C47×#476C2211yescharacteristic, complemented
47C47×#475C2211yescharacteristic, complemented
48C47×#474C2211yescharacteristic, complemented
49C47×#470—21no—
50C47×#468—21no—
51C47×#464—21no—
52C47×#462C2211yescharacteristic, complemented
53C47×#461C2211yescharacteristic, complemented
54C47×#460—22no—
55C47×#450—22no—
56C47×#431C2211yescharacteristic, complemented
57C47×#431C2211yescharacteristic, complemented
58C47×#423C2211yescharacteristic, complemented
59C47×#331C2211yescharacteristic
60C47×#331C2211yescharacteristic
61C47×#331C2211yescharacteristic, complemented
62C47×#331C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×Q8⋊C8C2211yescharacteristic, complemented
66C47×Q8⋊C8C2211yescharacteristic, complemented
67C47×D4⋊C8C2211yescharacteristic, complemented
68C47×D4⋊C8C2211yescharacteristic, complemented
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C22×D4×C47—22no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47D412yes—
79C2×Q16×C47—21no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—21no—
83C2×M16×C47—21no—
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86#127×C47—21no—
87#127×C47—21no—
88#127×C47—21no—
89#127×C47—21no—
90#127×C47D412yes—
91#127×C47C2311yescharacteristic
92#127×C47C2311yescharacteristic
93#126×C47—21no—
94#126×C47—21no—
95#125×C47—21no—
96#125×C47D411yescharacteristic
97#125×C47D411yescharacteristic
98#124×C47—21no—
99#124×C47—21no—
100#124×C47D411yescharacteristic
101#124×C47D411yescharacteristic
102#123×C47—22no—
103#123×C47—22no—
104#123×C47—22no—
105#123×C47—22no—
106#123×C47—21no—
107#123×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47D411yescharacteristic
111C22⋊Q8×C47D411yescharacteristic
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47D411yescharacteristic
125#121×C47D411yescharacteristic
126#120×C47—22no—
127#120×C47—22no—
128#120×C47—22no—
129#120×C47—22no—
130#120×C47—22no—
131#120×C47—22no—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
134C4×Q8×C47C2311yescharacteristic
135C4×Q8×C47C2311yescharacteristic
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47C2311yescharacteristic
143C4×D4×C47C2311yescharacteristic
144#117×C47—21no—
145#117×C47—21no—
146#117×C47—21no—
147C2×C22⋊C4×C47—22no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—21no—
150#107×C47—21no—
151#107×C47—21no—
152#106×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155C4⋊C8×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—21no—
162#103×C47—21no—
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#102×C47—22no—
167#102×C47—22no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172C22⋊C8×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C24×C47—22no—
177C24×C47—22no—
178#41×C47—81no—
179#41×C47—81no—
180#41×C47—81no—
181#41×C47—81no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47C2×D411yescharacteristic
185C2×Q8×C47C2×D411yescharacteristic
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47—81no—
208C2×D4×C47—81no—
209C2×D4×C47—82no—
210C2×D4×C47—84no—
211C2×D4×C47C2×D411yescharacteristic
212C2×D4×C47C2×D411yescharacteristic
213C2×D4×C47C2×D412yes—
214C2×D4×C47C2×D412yes—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223Q16×C47—81no—
224SD16×C47—81no—
225SD16×C47—82no—
226SD16×C47—82no—
227M16×C47—81no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—41no—
247C4⋊C4×C47—41no—
248C4⋊C4×C47C2×D411yescharacteristic
249C4⋊C4×C47C2×D411yescharacteristic
250C4⋊C4×C47C2×D411yescharacteristic
251C4⋊C4×C47C2×D411yescharacteristic
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—21no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—21no—
267C22⋊C4×C47—21no—
268C22⋊C4×C47—41no—
269C42×C47—21no—
270C42×C47—21no—
271C42×C47—41no—
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C42×C47C2×D411yescharacteristic
275C42×C47C2411yescharacteristic
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—44no—
281C23×C47—82no—
282C23×C47—82no—
283C23×C47—82no—
284C23×C47—82no—
285C23×C47—82no—
286C23×C47#12011yescharacteristic
287Q8×C47—21no—
288Q8×C47—21no—
289Q8×C47—21no—
290Q8×C47—21no—
291Q8×C47—42no—
292Q8×C47—41no—
293Q8×C47—41no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—21no—
298D4×C47—42no—
299D4×C47—42no—
300D4×C47—42no—
301D4×C47—42no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—82no—
311D4×C47—82no—
312D4×C47—82no—
313D4×C47—82no—
314D4×C47—82no—
315D4×C47—82no—
316D4×C47—82no—
317D4×C47—82no—
318D4×C47—82no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—82no—
337C2×C4×C47—82no—
338C2×C4×C47—82no—
339C2×C4×C47#12011yescharacteristic
340C2×C4×C47#12011yescharacteristic
341C2×C4×C47#12011yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C8×C47—41no—
346C8×C47—41no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350C8×C47—41no—
351#18931C4711yesmaximal, characteristic, direct product factor, Sylow
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—41no—
356C22×C47—42no—
357C22×C47—41no—
358C22×C47—42no—
359C22×C47—41no—
360C22×C47—42no—
361C22×C47—41no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—42no—
367C22×C47—164no—
368C22×C47—164no—
369C22×C47C2×#12011yescharacteristic
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47#57611yescharacteristic
383C4×C47#57711yescharacteristic
384C4×C47#57711yescharacteristic
385C4×C47#57711yescharacteristic
386#3543C2×C4711yescharacteristic
387#3252C2×C4711yescharacteristic, complemented
388#3233C2×C4711yescharacteristic, complemented
389#3208C2×C4711yescharacteristic, complemented
390#1642C2×C4711yescharacteristic, complemented
391#1641C2×C4711yescharacteristic, complemented
392#1640C2×C4711yescharacteristic, complemented
393#1639C2×C4711yescharacteristic, complemented
394#1631C2×C4711yescharacteristic, complemented
395#1631C2×C4711yescharacteristic, complemented
396#1630C2×C4711yescharacteristic, complemented
397#1629C2×C4711yescharacteristic, complemented
398#1545C2×C4711yescharacteristic, complemented
399#1495C2×C4711yescharacteristic, complemented
400#1482C2×C4711yescharacteristic, complemented
401C2×C47—41no—
402C2×C47—82no—
403C2×C47—81no—
404C2×C47—81no—
405C2×C47—82no—
406C2×C47#300911yescharacteristic
407C2×C47#301211yescharacteristic
408C2×C47#301911yescharacteristic
409#560—22no—
410#559C22×C4711yescharacteristic
411#550C22×C4711yescharacteristic
412#550C22×C4711yescharacteristic
413#546—21no—
414#546—21no—
415D42—21no—
416D42—21no—
417D42C22×C4711yescharacteristic
418#540—21no—
419#540—21no—
420#535—21no—
421#535—21no—
422#534—22no—
423#533C22×C4711yescharacteristic, complemented
424C2×#127C22×C4711yescharacteristic
425#529C22×C4711yescharacteristic
426#529C22×C4711yescharacteristic
427#499—21no—
428#492C22×C4711yescharacteristic
429#492C22×C4711yescharacteristic, complemented
430#488—21no—
431#486C22×C4711yescharacteristic
432#486C22×C4711yescharacteristic, complemented
433#485—21no—
434#482—21no—
435#479—21no—
436#477C22×C4711yescharacteristic, complemented
437#477C22×C4711yescharacteristic, complemented
438#476C22×C4711yescharacteristic, complemented
439#476C22×C4711yescharacteristic, complemented
440#475C22×C4711yescharacteristic, complemented
441#474C22×C4711yescharacteristic, complemented
442#470—21no—
443#468—21no—
444#464—21no—
445#462C22×C4711yescharacteristic, complemented
446#461C22×C4711yescharacteristic, complemented
447#460—22no—
448#450—22no—
449#431C22×C4711yescharacteristic, complemented
450#431C22×C4711yescharacteristic, complemented
451#423C22×C4711yescharacteristic, complemented
452#331C22×C4711yescharacteristic
453#331C22×C4711yescharacteristic
454#331C22×C4711yescharacteristic, complemented
455#331C22×C4711yescharacteristic, complemented
456Q8⋊C8C22×C4711yescharacteristic, complemented
457Q8⋊C8C22×C4711yescharacteristic, complemented
458Q8⋊C8C22×C4711yescharacteristic, complemented
459Q8⋊C8C22×C4711yescharacteristic, complemented
460D4⋊C8C22×C4711yescharacteristic, complemented
461D4⋊C8C22×C4711yescharacteristic, complemented
462D4⋊C8C22×C4711yescharacteristic, complemented
463D4⋊C8C22×C4711yescharacteristic, complemented
464C47#1893111yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C4712yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C4711yescharacteristic
479C4⋊Q8C23×C4711yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C4712yes—
485#127C23×C4711yescharacteristic
486#127C23×C4711yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C4711yescharacteristic
491#125D4×C4711yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C4711yescharacteristic
495#124D4×C4711yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C4711yescharacteristic
505C22⋊Q8D4×C4711yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C4711yescharacteristic
519#121D4×C4711yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C4711yescharacteristic
529C4×Q8C23×C4711yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C4711yescharacteristic
537C4×D4C23×C4711yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C4711yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C4711yescharacteristic
552C4⋊C8C23×C4711yescharacteristic
553C4⋊C8C23×C4711yescharacteristic
554C4⋊C8C23×C4711yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C4711yescharacteristic
569C4×C8C23×C4711yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C4711yescharacteristic
579C2×Q8C2×D4×C4711yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C4711yescharacteristic
606C2×D4C2×D4×C4711yescharacteristic
607C2×D4C2×D4×C4712yes—
608C2×D4C2×D4×C4712yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C4711yescharacteristic
615C22×C4C2×D4×C4711yescharacteristic
616C22×C4C2×D4×C4711yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C4711yescharacteristic
643C4⋊C4C2×D4×C4711yescharacteristic
644C4⋊C4C2×D4×C4711yescharacteristic
645C4⋊C4C2×D4×C4711yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C4711yescharacteristic
667C42C2×D4×C4711yescharacteristic
668C42C2×D4×C4711yescharacteristic
669C42C24×C4711yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C4711yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C4711yescharacteristic
734C2×C4#120×C4711yescharacteristic
735C2×C4#120×C4711yescharacteristic
736C2×C4C22×D4×C4711yescharacteristic
737C2×C4C22×D4×C4711yescharacteristic
738C2×C4C22×D4×C4711yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C4711yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4C47×#57611yescharacteristic
776C4C47×#57711yescharacteristic
777C4C47×#57711yescharacteristic
778C4C47×#57711yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C47×#300911yescharacteristic
785C2C47×#301211yescharacteristic
786C2C47×#301911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3543C2
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×#3252C2semidirect
3. C47×#3233C2semidirect
4. C47×#3208C2semidirect
5. C47×#1642C2semidirect
6. C47×#1641C2semidirect
7. C47×#1640C2semidirect
8. C47×#1639C2semidirect
9. C47×#1631C2semidirect
10. C47×#1631C2semidirect
11. C47×#1630C2semidirect
12. C47×#1629C2semidirect
13. C47×#1545C2semidirect
14. C47×#1495C2semidirect
15. C47×#1482C2semidirect
30. C47×#533C22semidirect
36. C47×#492C22semidirect
39. C47×#486C22semidirect
43. C47×#477C22semidirect
44. C47×#477C22semidirect
45. C47×#476C22semidirect
46. C47×#476C22semidirect
47. C47×#475C22semidirect
48. C47×#474C22semidirect
52. C47×#462C22semidirect
53. C47×#461C22semidirect
56. C47×#431C22semidirect
57. C47×#431C22semidirect
58. C47×#423C22semidirect
61. C47×#331C22semidirect
62. C47×#331C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
65. C47×Q8⋊C8C22semidirect
66. C47×Q8⋊C8C22semidirect
67. C47×D4⋊C8C22semidirect
68. C47×D4⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
351. #18931C47direct (N × H)
387. #3252C2×C47semidirect
388. #3233C2×C47semidirect
389. #3208C2×C47semidirect
390. #1642C2×C47semidirect
391. #1641C2×C47semidirect
392. #1640C2×C47semidirect
393. #1639C2×C47semidirect
394. #1631C2×C47semidirect
395. #1631C2×C47semidirect
396. #1630C2×C47semidirect
397. #1629C2×C47semidirect
398. #1545C2×C47semidirect
399. #1495C2×C47semidirect
400. #1482C2×C47semidirect
423. #533C22×C47semidirect
429. #492C22×C47semidirect
432. #486C22×C47semidirect
436. #477C22×C47semidirect
437. #477C22×C47semidirect
438. #476C22×C47semidirect
439. #476C22×C47semidirect
440. #475C22×C47semidirect
441. #474C22×C47semidirect
445. #462C22×C47semidirect
446. #461C22×C47semidirect
449. #431C22×C47semidirect
450. #431C22×C47semidirect
451. #423C22×C47semidirect
454. #331C22×C47semidirect
455. #331C22×C47semidirect
456. Q8⋊C8C22×C47semidirect
457. Q8⋊C8C22×C47semidirect
458. Q8⋊C8C22×C47semidirect
459. Q8⋊C8C22×C47semidirect
460. D4⋊C8C22×C47semidirect
461. D4⋊C8C22×C47semidirect
462. D4⋊C8C22×C47semidirect
463. D4⋊C8C22×C47semidirect
464. C47#18931direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35432
C47×#32522
C47×#32332
C47×#32082
C47×#16422
C47×#16412
C47×#16402
C47×#16392
C47×#16312
C47×#16302
C47×#16292
C47×#15452
C47×#14952
C47×#14822
#1893147