Finite Group Databasebeta

← C47×#33553 #26073251

Subgroups — C47×#33553 #26073251

Order 12032.

1252 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×#3537C211yesmaximal, characteristic, complemented
2C47×#3027C211yesmaximal, characteristic, complemented
3C47×#3025C211yesmaximal, characteristic, complemented
4C47×#3021C211yesmaximal, characteristic, complemented
5C47×#2200C214yesmaximal, complemented
6C47×#2196C214yesmaximal, complemented
7C47×#2128C211yesmaximal, characteristic, complemented
8C47×#2122C211yesmaximal, characteristic, complemented
9C47×#2120C211yesmaximal, characteristic, complemented
10C47×#585C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C47—21no—
12C47×#560—21no—
13C47×#560C2212yescomplemented
14C47×#553—21no—
15C47×#553—21no—
16D42×C47—21no—
17D42×C47—21no—
18D42×C47—21no—
19D42×C47C2212yescomplemented
20C47×#540—21no—
21C47×#538—22no—
22C47×#535—21no—
23C47×#535C2211yescharacteristic
24C47×#535C2211yescharacteristic
25C47×#534—22no—
26C47×#525—21no—
27C47×#525C2211yescharacteristic
28C2×#121×C47—21no—
29C47×#458—21no—
30C47×#458C2212yescomplemented
31C47×B(4,𝔽2)—21no—
32C47×B(4,𝔽2)—22no—
33C47×B(4,𝔽2)C2212yescomplemented
34C47×B(4,𝔽2)C2214yescomplemented
35C47×#454—22no—
36C47×#453C2214yescomplemented
37C47×#421—21no—
38C47×#413C2211yescharacteristic, complemented
39C47×#410—21no—
40C47×#410—21no—
41C47×#410C2211yescharacteristic, complemented
42C47×#410C2211yescharacteristic, complemented
43C47×#353C2214yescomplemented
44C47×#352C2212yescomplemented
45C47×AΣL(1,𝔽16)C2212yescomplemented
46C47×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C47—21no—
482−1+4×C47—41no—
49H(5,𝔽2)×C47—21no—
50H(5,𝔽2)×C47—21no—
51H(5,𝔽2)×C47—41no—
52H(5,𝔽2)×C47C2312yes—
53C2×#41×C47—21no—
54C2×#41×C47—21no—
55C2×#41×C47—21no—
56C2×#41×C47—42no—
57C2×#41×C47C2311yescharacteristic
58C22×D4×C47—21no—
59C22×D4×C47—22no—
60C22×D4×C47—22no—
61C22×D4×C47—22no—
62C22×D4×C47D411yescharacteristic, complemented
63C22×D4×C47D411yescharacteristic, complemented
64C23×C4×C47D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C47—24no—
66AGL(1,ℤ/8)×C47—42no—
67C2×SD16×C47—41no—
68C2×D8×C47—41no—
69C2×M16×C47—21no—
70#127×C47—21no—
71#127×C47—21no—
72#127×C47—41no—
73#127×C47C2312yes—
74#126×C47—22no—
75#126×C47—22no—
76#125×C47—21no—
77#124×C47—21no—
78#124×C47—41no—
79#124×C47D412yescomplemented
80#123×C47—22no—
81#123×C47—22no—
82#123×C47—22no—
83#123×C47—22no—
84#123×C47—22no—
85#123×C47D411yescharacteristic, complemented
86#123×C47C2311yescharacteristic
87C22⋊Q8×C47—21no—
88C22⋊Q8×C47—41no—
89#121×C47—22no—
90#121×C47—21no—
91#121×C47—21no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—21no—
95#121×C47—22no—
96#121×C47—21no—
97#121×C47—21no—
98#121×C47—22no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—42no—
105#121×C47—41no—
106#120×C47—22no—
107#120×C47—22no—
108#120×C47—22no—
109#120×C47—21no—
110#120×C47—21no—
111#120×C47—22no—
112#120×C47—22no—
113#120×C47—24no—
114#120×C47D411yescharacteristic, complemented
115#120×C47D412yescomplemented
116#120×C47C2311yescharacteristic
117#120×C47C2312yes—
118C4×D4×C47—22no—
119C4×D4×C47—21no—
120C4×D4×C47—21no—
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47—22no—
124C4×D4×C47—42no—
125#117×C47—21no—
126#117×C47—21no—
127#117×C47D411yescharacteristic, complemented
128#117×C47D411yescharacteristic, complemented
129#117×C47D411yescharacteristic, complemented
130C2×C4⋊C4×C47—21no—
131C2×C22⋊C4×C47—22no—
132#104×C47—24no—
133#101×C47—21no—
134#100×C47C2312yes—
135#99×C47—21no—
136#99×C47—21no—
137#99×C47—24no—
138#99×C47—22no—
139#99×C47—22no—
140#99×C47C2312yes—
141#99×C47C2312yes—
142C24×C47—22no—
143C24×C47—21no—
144C24×C47C2×D411yescharacteristic
145C24×C47C2×D412yes—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—42no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156#41×C47—42no—
157#41×C47—42no—
158#41×C47—42no—
159#41×C47—41no—
160#41×C47—41no—
161#41×C47—41no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—42no—
166C2×Q8×C47C2×D411yescharacteristic
167C2×D4×C47—21no—
168C2×D4×C47—22no—
169C2×D4×C47—22no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—22no—
175C2×D4×C47—22no—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—22no—
179C2×D4×C47—22no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—22no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—41no—
187C2×D4×C47—41no—
188C2×D4×C47—41no—
189C2×D4×C47—41no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47—41no—
194C2×D4×C47—42no—
195C2×D4×C47—44no—
196C2×D4×C47—81no—
197C2×D4×C47—81no—
198C2×D4×C47—84no—
199C2×D4×C47—84no—
200C2×D4×C47—84no—
201C2×D4×C47C2×D411yescharacteristic
202C2×D4×C47C2×D411yescharacteristic
203C2×D4×C47C2×D412yes—
204C2×D4×C47C2411yescharacteristic
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—41no—
213C22×C4×C47—41no—
214C22×C4×C47—41no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219SD16×C47—44no—
220D8×C47—44no—
221M16×C47—22no—
222M16×C47—41no—
223C2×C8×C47—41no—
224C4⋊C4×C47—22no—
225C4⋊C4×C47—22no—
226C4⋊C4×C47—22no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—41no—
233C4⋊C4×C47—41no—
234C4⋊C4×C47—42no—
235C22⋊C4×C47—22no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—22no—
239C22⋊C4×C47—21no—
240C22⋊C4×C47—21no—
241C22⋊C4×C47—21no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—21no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—21no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—44no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47C2×D412yes—
254C22⋊C4×C47C2×D411yescharacteristic
255C22⋊C4×C47C2×D411yescharacteristic
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—41no—
259C42×C47—41no—
260C42×C47C2×D412yes—
261C23×C47—21no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—41no—
267C23×C47—42no—
268C23×C47—41no—
269C23×C47—44no—
270C23×C47—42no—
271C23×C47—81no—
272C23×C47—82no—
273C23×C47—82no—
274C23×C47—82no—
275C23×C47—82no—
276C23×C47#12011yescharacteristic
277C23×C47C22×D411yescharacteristic
278C23×C47C22×D411yescharacteristic
279Q8×C47—22no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—41no—
283Q8×C47—41no—
284D4×C47—22no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47—42no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—42no—
292D4×C47—42no—
293D4×C47—42no—
294D4×C47—42no—
295D4×C47—44no—
296D4×C47—44no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—81no—
305D4×C47—82no—
306D4×C47—82no—
307D4×C47—82no—
308D4×C47—82no—
309D4×C47—82no—
310D4×C47—82no—
311D4×C47—82no—
312D4×C47—84no—
313D4×C47—164no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
327C2×C4×C47—42no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—41no—
331C2×C4×C47—42no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—81no—
338C2×C4×C47—82no—
339C2×C4×C47—82no—
340C2×C4×C47—82no—
341C2×C4×C47#12011yescharacteristic
342C2×C4×C47#12011yescharacteristic
343C2×C4×C47#12011yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C8×C47—42no—
346#33553C4711yesmaximal, characteristic, direct product factor, Sylow
347C22×C47—22no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—81no—
365C22×C47—82no—
366C22×C47—82no—
367C22×C47—84no—
368C22×C47—161no—
369C22×C47—164no—
370C22×C47—162no—
371C22×C47C2×#12011yescharacteristic
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—21no—
375C4×C47—42no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—41no—
381C4×C47—82no—
382C4×C47—82no—
383C4×C47B(4,𝔽2)11yescharacteristic
384C4×C47B(4,𝔽2)11yescharacteristic
385#3537C2×C4711yescharacteristic, complemented
386#3027C2×C4711yescharacteristic, complemented
387#3025C2×C4711yescharacteristic, complemented
388#3021C2×C4711yescharacteristic, complemented
389#2200C2×C4714yescomplemented
390#2196C2×C4714yescomplemented
391#2128C2×C4711yescharacteristic, complemented
392#2122C2×C4711yescharacteristic, complemented
393#2120C2×C4711yescharacteristic, complemented
394C2×C47—21no—
395C2×C47—41no—
396C2×C47—41no—
397C2×C47—42no—
398C2×C47—41no—
399C2×C47—82no—
400C2×C47—82no—
401C2×C47—82no—
402C2×C47C2×B(4,𝔽2)11yescharacteristic
403#585C22×C4711yescharacteristic, complemented
404C2×AGL(1,ℤ/8)—21no—
405#560—21no—
406#560C22×C4712yescomplemented
407#553—21no—
408#553—21no—
409D42—21no—
410D42—21no—
411D42—21no—
412D42C22×C4712yescomplemented
413#540—21no—
414#538—22no—
415#535—21no—
416#535C22×C4711yescharacteristic
417#535C22×C4711yescharacteristic
418#534—22no—
419#525—21no—
420#525C22×C4711yescharacteristic
421C2×#121—21no—
422#458—21no—
423#458C22×C4712yescomplemented
424B(4,𝔽2)—21no—
425B(4,𝔽2)—22no—
426B(4,𝔽2)C22×C4712yescomplemented
427B(4,𝔽2)C22×C4714yescomplemented
428#454—22no—
429#453C22×C4714yescomplemented
430#421—21no—
431#413C22×C4711yescharacteristic, complemented
432#410—21no—
433#410—21no—
434#410C22×C4711yescharacteristic, complemented
435#410C22×C4711yescharacteristic, complemented
436#353C22×C4714yescomplemented
437#352C22×C4712yescomplemented
438AΣL(1,𝔽16)C22×C4712yescomplemented
439AΣL(1,𝔽16)C22×C4714yescomplemented
440C47#3355311yescharacteristic, direct product factor, Sylow
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C4712yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C4711yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C4711yescharacteristic, complemented
457C22×D4D4×C4711yescharacteristic, complemented
458C23×C4D4×C4711yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C4712yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C4712yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C4711yescharacteristic, complemented
480#123C23×C4711yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C4711yescharacteristic, complemented
509#120D4×C4712yescomplemented
510#120C23×C4711yescharacteristic
511#120C23×C4712yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C4711yescharacteristic, complemented
522#117D4×C4711yescharacteristic, complemented
523#117D4×C4711yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C4712yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C4712yes—
535#99C23×C4712yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C4711yescharacteristic
539C24C2×D4×C4712yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C4711yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C4711yescharacteristic
596C2×D4C2×D4×C4711yescharacteristic
597C2×D4C2×D4×C4712yes—
598C2×D4C24×C4711yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C4711yescharacteristic
610C22×C4C2×D4×C4711yescharacteristic
611C22×C4C2×D4×C4711yescharacteristic
612C22×C4C2×D4×C4711yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C4712yes—
648C22⋊C4C2×D4×C4711yescharacteristic
649C22⋊C4C2×D4×C4711yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C4712yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C4711yescharacteristic
671C23C22×D4×C4711yescharacteristic
672C23C22×D4×C4711yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C4711yescharacteristic
736C2×C4#120×C4711yescharacteristic
737C2×C4#120×C4711yescharacteristic
738C2×C4C22×D4×C4711yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C4711yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C47×B(4,𝔽2)11yescharacteristic
777C4C47×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C47C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C47
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C2×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3537C2semidirect
2. C47×#3027C2semidirect
3. C47×#3025C2semidirect
4. C47×#3021C2semidirect
5. C47×#2200C2semidirect
6. C47×#2196C2semidirect
7. C47×#2128C2semidirect
8. C47×#2122C2semidirect
9. C47×#2120C2semidirect
10. C47×#585C22semidirect
13. C47×#560C22semidirect
19. D42×C47C22semidirect
30. C47×#458C22semidirect
33. C47×B(4,𝔽2)C22semidirect
34. C47×B(4,𝔽2)C22semidirect
36. C47×#453C22semidirect
38. C47×#413C22semidirect
41. C47×#410C22semidirect
42. C47×#410C22semidirect
43. C47×#353C22semidirect
44. C47×#352C22semidirect
45. C47×AΣL(1,𝔽16)C22semidirect
46. C47×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C47D4semidirect
63. C22×D4×C47D4semidirect
64. C23×C4×C47D4semidirect
79. #124×C47D4semidirect
85. #123×C47D4semidirect
114. #120×C47D4semidirect
115. #120×C47D4semidirect
127. #117×C47D4semidirect
128. #117×C47D4semidirect
129. #117×C47D4semidirect
346. #33553C47direct (N × H)
385. #3537C2×C47semidirect
386. #3027C2×C47semidirect
387. #3025C2×C47semidirect
388. #3021C2×C47semidirect
389. #2200C2×C47semidirect
390. #2196C2×C47semidirect
391. #2128C2×C47semidirect
392. #2122C2×C47semidirect
393. #2120C2×C47semidirect
403. #585C22×C47semidirect
406. #560C22×C47semidirect
412. D42C22×C47semidirect
423. #458C22×C47semidirect
426. B(4,𝔽2)C22×C47semidirect
427. B(4,𝔽2)C22×C47semidirect
429. #453C22×C47semidirect
431. #413C22×C47semidirect
434. #410C22×C47semidirect
435. #410C22×C47semidirect
436. #353C22×C47semidirect
437. #352C22×C47semidirect
438. AΣL(1,𝔽16)C22×C47semidirect
439. AΣL(1,𝔽16)C22×C47semidirect
440. C47#33553direct (N × H)
456. C22×D4D4×C47semidirect
457. C22×D4D4×C47semidirect
458. C23×C4D4×C47semidirect
473. #124D4×C47semidirect
479. #123D4×C47semidirect
508. #120D4×C47semidirect
509. #120D4×C47semidirect
521. #117D4×C47semidirect
522. #117D4×C47semidirect
523. #117D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35372
C47×#30272
C47×#30252
C47×#30212
C47×#22002
C47×#21962
C47×#21282
C47×#21222
C47×#21202
#3355347