Finite Group Databasebeta

← C47×#24295 #26063993

Subgroups — C47×#24295 #26063993

Order 12032.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#577C211yesmaximal, characteristic, complemented
2C47×#3067C211yesmaximal, characteristic, complemented
3C47×#3057C211yesmaximal, characteristic, complemented
4C47×#3020C211yesmaximal, characteristic, complemented
5C47×#3019C211yesmaximal, characteristic, complemented
6C47×#2955C211yesmaximal, characteristic, complemented
7C47×#2049C211yesmaximal, characteristic, complemented
8C47×#2048C211yesmaximal, characteristic, complemented
9C47×#2009C211yesmaximal, characteristic, complemented
10C47×#2008C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1976C211yesmaximal, characteristic, complemented
13C47×#1814C211yesmaximal, characteristic, complemented
14C47×#1796C211yesmaximal, characteristic, complemented
15C47×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×H(5,𝔽2)×C47C2211yescharacteristic
18C47×#577—22no—
19C47×#577—22no—
20C47×#577—22no—
21C47×#577—22no—
22C47×#575C2211yescharacteristic
23C47×#575C2211yescharacteristic
24C47×#575C2211yescharacteristic, complemented
25C2×#137×C47—21no—
26C2×#137×C47C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C47—21no—
28C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
29C2×#135×C47—21no—
30C2×#135×C47C2211yescharacteristic
31C22×SD16×C47—21no—
32C22×SD16×C47C2211yescharacteristic
33C2×#131×C47C2211yescharacteristic
34C2×#131×C47C2211yescharacteristic, complemented
35C47×#536C2211yescharacteristic, complemented
36C47×#535C2211yescharacteristic
37C47×#473—21no—
38C47×#472—21no—
39C47×#471—21no—
40C47×#471—21no—
41C47×#468—22no—
42C47×#465—22no—
43C47×#456—22no—
44C47×#455—22no—
45C47×#454—22no—
46C47×#453—22no—
47C47×#444—22no—
48C47×#443—22no—
49C47×#430C2211yescharacteristic, complemented
50C2×#108×C47C2211yescharacteristic, complemented
51C47×#427C2211yescharacteristic, complemented
52C47×#421C2211yescharacteristic
53C47×#421C2211yescharacteristic
54C47×#421C2211yescharacteristic
55C47×#421C2211yescharacteristic
56C47×#421C2211yescharacteristic, complemented
57C47×#421C2211yescharacteristic, complemented
58C47×#419C2211yescharacteristic, complemented
59C47×#419C2211yescharacteristic, complemented
60C47×#418C2211yescharacteristic
61C47×#418C2211yescharacteristic
62C47×#413C2211yescharacteristic
63C47×#413C2211yescharacteristic, complemented
64C2×#101×C47C2211yescharacteristic, complemented
65C2×#100×C47C2211yescharacteristic
66C47×#410C2211yescharacteristic
67C47×#410C2211yescharacteristic, complemented
68C47×#405C2211yescharacteristic, complemented
69C47×#344C2211yescharacteristic, complemented
70C47×#344C2211yescharacteristic, complemented
712−1+4×C47—22no—
722−1+4×C47—22no—
732−1+4×C47—22no—
742−1+4×C47—41no—
75H(5,𝔽2)×C47—22no—
76H(5,𝔽2)×C47—22no—
77H(5,𝔽2)×C47—22no—
78H(5,𝔽2)×C47—41no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—41no—
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47C2311yescharacteristic
91C22×D4×C47—21no—
92C22×D4×C47—21no—
93C22×D4×C47—41no—
94C22×D4×C47C2311yescharacteristic
95#137×C47—24no—
96#137×C47—24no—
97#137×C47—22no—
98#137×C47—21no—
99#137×C47—21no—
100#137×C47—21no—
101#137×C47—21no—
102#137×C47—21no—
103#137×C47—22no—
104#137×C47D412yes—
105AGL(1,ℤ/8)×C47—24no—
106AGL(1,ℤ/8)×C47—24no—
107AGL(1,ℤ/8)×C47—22no—
108AGL(1,ℤ/8)×C47—21no—
109AGL(1,ℤ/8)×C47—21no—
110AGL(1,ℤ/8)×C47—21no—
111AGL(1,ℤ/8)×C47—21no—
112AGL(1,ℤ/8)×C47—21no—
113AGL(1,ℤ/8)×C47—22no—
114AGL(1,ℤ/8)×C47D412yes—
115#135×C47—24no—
116#135×C47—24no—
117#135×C47—22no—
118#135×C47—21no—
119#135×C47—21no—
120#135×C47—21no—
121#135×C47—21no—
122#135×C47—41no—
123#135×C47—41no—
124C2×Q16×C47—21no—
125C2×Q16×C47D411yescharacteristic, complemented
126C2×SD16×C47—24no—
127C2×SD16×C47—24no—
128C2×SD16×C47—21no—
129C2×SD16×C47—21no—
130C2×SD16×C47—21no—
131C2×SD16×C47—21no—
132C2×SD16×C47—21no—
133C2×SD16×C47—21no—
134C2×SD16×C47D412yes—
135C2×SD16×C47D412yes—
136C2×SD16×C47D411yescharacteristic, complemented
137C2×SD16×C47D411yescharacteristic, complemented
138C2×D8×C47—21no—
139C2×D8×C47D411yescharacteristic, complemented
140#131×C47—21no—
141#131×C47—21no—
142#131×C47—21no—
143#131×C47—21no—
144#131×C47—21no—
145#131×C47—21no—
146#131×C47D412yescomplemented
147#131×C47D412yescomplemented
148C2×M16×C47—21no—
149C2×M16×C47—21no—
150C2×M16×C47C2311yescharacteristic
151C2×M16×C47C2311yescharacteristic
152C2×M16×C47C2311yescharacteristic
153C2×M16×C47C2311yescharacteristic
154C2×M16×C47C2311yescharacteristic
155C22×C8×C47—21no—
156C22×C8×C47—21no—
157C22×C8×C47C2311yescharacteristic
158C4⋊Q8×C47—21no—
159#127×C47—21no—
160#124×C47—21no—
161#124×C47—21no—
162#123×C47—41no—
163C22⋊Q8×C47—22no—
164#121×C47—22no—
165#120×C47—41no—
166#117×C47C2311yescharacteristic
167#117×C47C2311yescharacteristic
168#117×C47C2311yescharacteristic
169#108×C47—22no—
170#108×C47—21no—
171#108×C47—21no—
172#107×C47—21no—
173#106×C47—21no—
174#104×C47—22no—
175#104×C47—22no—
176#104×C47—22no—
177#104×C47—22no—
178#104×C47—22no—
179#104×C47—22no—
180#103×C47—22no—
181#103×C47—41no—
182#102×C47—22no—
183#102×C47—41no—
184#101×C47—21no—
185#101×C47—21no—
186#101×C47—22no—
187#100×C47—21no—
188#100×C47—21no—
189#100×C47—22no—
190#99×C47—41no—
191#99×C47—41no—
192#97×C47—21no—
193C4×C8×C47—21no—
194C24×C47—21no—
195C24×C47—41no—
196#41×C47—21no—
197#41×C47—21no—
198#41×C47—24no—
199#41×C47—24no—
200#41×C47—21no—
201#41×C47—21no—
202#41×C47—21no—
203#41×C47—21no—
204#41×C47—21no—
205#41×C47—21no—
206#41×C47—21no—
207#41×C47—21no—
208#41×C47—21no—
209#41×C47—21no—
210#41×C47—21no—
211#41×C47—21no—
212#41×C47—42no—
213#41×C47—44no—
214#41×C47—42no—
215#41×C47—42no—
216#41×C47—42no—
217#41×C47—44no—
218#41×C47—42no—
219#41×C47—42no—
220#41×C47C2×D412yes—
221#41×C47C2×D412yes—
222C2×Q8×C47—21no—
223C2×Q8×C47—24no—
224C2×Q8×C47—21no—
225C2×Q8×C47—21no—
226C2×Q8×C47—21no—
227C2×Q8×C47—21no—
228C2×Q8×C47—41no—
229C2×Q8×C47—42no—
230C2×Q8×C47—42no—
231C2×Q8×C47—42no—
232C2×Q8×C47C2×D412yes—
233C2×Q8×C47C2×D411yescharacteristic
234C2×Q8×C47C2×D411yescharacteristic
235C2×Q8×C47C2×D411yescharacteristic
236C2×Q8×C47#4111yescharacteristic
237C2×D4×C47—21no—
238C2×D4×C47—24no—
239C2×D4×C47—21no—
240C2×D4×C47—21no—
241C2×D4×C47—21no—
242C2×D4×C47—21no—
243C2×D4×C47—21no—
244C2×D4×C47—21no—
245C2×D4×C47—21no—
246C2×D4×C47—21no—
247C2×D4×C47—42no—
248C2×D4×C47—41no—
249C2×D4×C47—41no—
250C2×D4×C47—42no—
251C2×D4×C47—44no—
252C2×D4×C47—44no—
253C2×D4×C47—41no—
254C2×D4×C47—42no—
255C2×D4×C47—42no—
256C2×D4×C47C2×D412yes—
257C2×D4×C47C2×D411yescharacteristic
258C2×D4×C47C2×D411yescharacteristic
259C2×D4×C47C2×D411yescharacteristic
260C2×D4×C47#4111yescharacteristic
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—41no—
267C22×C4×C47—41no—
268C22×C4×C47—41no—
269C22×C4×C47C2411yescharacteristic
270Q16×C47—24no—
271Q16×C47—22no—
272Q16×C47—21no—
273Q16×C47—21no—
274Q16×C47—41no—
275Q16×C47—41no—
276SD16×C47—24no—
277SD16×C47—24no—
278SD16×C47—22no—
279SD16×C47—22no—
280SD16×C47—22no—
281SD16×C47—22no—
282SD16×C47—21no—
283SD16×C47—21no—
284SD16×C47—22no—
285SD16×C47—22no—
286SD16×C47—21no—
287SD16×C47—21no—
288SD16×C47—41no—
289SD16×C47—41no—
290SD16×C47—41no—
291SD16×C47—41no—
292D8×C47—24no—
293D8×C47—22no—
294D8×C47—21no—
295D8×C47—21no—
296D8×C47—41no—
297D8×C47—41no—
298M16×C47—21no—
299M16×C47—21no—
300M16×C47—22no—
301M16×C47—22no—
302M16×C47—21no—
303M16×C47—21no—
304M16×C47—21no—
305M16×C47—21no—
306M16×C47—21no—
307M16×C47—21no—
308M16×C47—41no—
309M16×C47—41no—
310M16×C47C2×D412yes—
311M16×C47C2×D412yes—
312C2×C8×C47—21no—
313C2×C8×C47—21no—
314C2×C8×C47—22no—
315C2×C8×C47—22no—
316C2×C8×C47—21no—
317C2×C8×C47—21no—
318C2×C8×C47—21no—
319C2×C8×C47—41no—
320C2×C8×C47—41no—
321C2×C8×C47C2×D411yescharacteristic
322C2×C8×C47C2×D411yescharacteristic
323C2×C8×C47C2×D411yescharacteristic
324C2×C8×C47C2×D411yescharacteristic
325C2×C8×C47C2×D411yescharacteristic
326C2×C8×C47C2×D411yescharacteristic
327C4⋊C4×C47—21no—
328C4⋊C4×C47—21no—
329C4⋊C4×C47—21no—
330C4⋊C4×C47—42no—
331C22⋊C4×C47—21no—
332C22⋊C4×C47—21no—
333C22⋊C4×C47—21no—
334C22⋊C4×C47—42no—
335C22⋊C4×C47—42no—
336C42×C47—21no—
337C42×C47—21no—
338C42×C47—21no—
339C23×C47—21no—
340C23×C47—21no—
341C23×C47—22no—
342C23×C47—21no—
343C23×C47—21no—
344C23×C47—44no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—161no—
348C23×C47—162no—
349C23×C47H(5,𝔽2)11yescharacteristic
350Q8×C47—21no—
351Q8×C47—21no—
352Q8×C47—22no—
353Q8×C47—21no—
354Q8×C47—21no—
355Q8×C47—21no—
356Q8×C47—21no—
357Q8×C47—21no—
358Q8×C47—22no—
359Q8×C47—44no—
360Q8×C47—41no—
361Q8×C47—41no—
362Q8×C47#12112yes—
363D4×C47—22no—
364D4×C47—22no—
365D4×C47—21no—
366D4×C47—22no—
367D4×C47—21no—
368D4×C47—21no—
369D4×C47—21no—
370D4×C47—21no—
371D4×C47—21no—
372D4×C47—21no—
373D4×C47—22no—
374D4×C47—44no—
375D4×C47—44no—
376D4×C47—44no—
377D4×C47—41no—
378D4×C47—41no—
379D4×C47—41no—
380D4×C47—41no—
381D4×C47—41no—
382D4×C47—41no—
383D4×C47—41no—
384D4×C47—41no—
385D4×C47—162no—
386D4×C47#12112yes—
387C2×C4×C47—21no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—21no—
391C2×C4×C47—22no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—44no—
395C2×C4×C47—44no—
396C2×C4×C47—44no—
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×C47C22×D411yescharacteristic
409C2×C4×C47C22×D411yescharacteristic
410C2×C4×C47C22×D411yescharacteristic
411C2×C4×C47C22×D411yescharacteristic
412C2×C4×C47C2×#4111yescharacteristic
413C2×C4×C47H(5,𝔽2)11yescharacteristic
414C8×C47—22no—
415C8×C47—22no—
416C8×C47—41no—
417C8×C47—41no—
418C8×C47—41no—
419C8×C47#12011yescharacteristic
420C8×C47#12011yescharacteristic
421C8×C47#12011yescharacteristic
422C8×C47#12011yescharacteristic
423#24295C4711yesmaximal, characteristic, direct product factor, Sylow
424C22×C47—22no—
425C22×C47—41no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—41no—
429C22×C47—42no—
430C22×C47—41no—
431C22×C47—41no—
432C22×C47—82no—
433C22×C47—81no—
434C22×C47—81no—
435C22×C47—82no—
436C22×C47—161no—
437C22×C47—164no—
438C22×C47#53511yescharacteristic
439C22×C47D4211yescharacteristic
440C22×C47#54611yescharacteristic
441C4×C47—22no—
442C4×C47—41no—
443C4×C47—42no—
444C4×C47—41no—
445C4×C47—41no—
446C4×C47—81no—
447C4×C47—81no—
448C4×C47—81no—
449C4×C47C2×#12011yescharacteristic
450C4×C47C2×#12111yescharacteristic
451C4×C47D4211yescharacteristic
452C4×C47#54611yescharacteristic
453C2×#577C2×C4711yescharacteristic, complemented
454#3067C2×C4711yescharacteristic, complemented
455#3057C2×C4711yescharacteristic, complemented
456#3020C2×C4711yescharacteristic, complemented
457#3019C2×C4711yescharacteristic, complemented
458#2955C2×C4711yescharacteristic, complemented
459#2049C2×C4711yescharacteristic, complemented
460#2048C2×C4711yescharacteristic, complemented
461#2009C2×C4711yescharacteristic, complemented
462#2008C2×C4711yescharacteristic, complemented
463#1977C2×C4711yescharacteristic, complemented
464#1976C2×C4711yescharacteristic, complemented
465#1814C2×C4711yescharacteristic, complemented
466#1796C2×C4711yescharacteristic, complemented
467#1795C2×C4711yescharacteristic, complemented
468C2×C47—21no—
469C2×C47—21no—
470C2×C47—21no—
471C2×C47—42no—
472C2×C47—81no—
473C2×C47—81no—
474C2×C47—82no—
475C2×C47—81no—
476C2×C47#240811yescharacteristic
477C2×2−1+4C22×C4711yescharacteristic
478C2×H(5,𝔽2)C22×C4711yescharacteristic
479#577—22no—
480#577—22no—
481#577—22no—
482#577—22no—
483#575C22×C4711yescharacteristic
484#575C22×C4711yescharacteristic
485#575C22×C4711yescharacteristic, complemented
486C2×#137—21no—
487C2×#137C22×C4711yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
490C2×#135—21no—
491C2×#135C22×C4711yescharacteristic
492C22×SD16—21no—
493C22×SD16C22×C4711yescharacteristic
494C2×#131C22×C4711yescharacteristic
495C2×#131C22×C4711yescharacteristic, complemented
496#536C22×C4711yescharacteristic, complemented
497#535C22×C4711yescharacteristic
498#473—21no—
499#472—21no—
500#471—21no—
501#471—21no—
502#468—22no—
503#465—22no—
504#456—22no—
505#455—22no—
506#454—22no—
507#453—22no—
508#444—22no—
509#443—22no—
510#430C22×C4711yescharacteristic, complemented
511C2×#108C22×C4711yescharacteristic, complemented
512#427C22×C4711yescharacteristic, complemented
513#421C22×C4711yescharacteristic
514#421C22×C4711yescharacteristic
515#421C22×C4711yescharacteristic
516#421C22×C4711yescharacteristic
517#421C22×C4711yescharacteristic, complemented
518#421C22×C4711yescharacteristic, complemented
519#419C22×C4711yescharacteristic, complemented
520#419C22×C4711yescharacteristic, complemented
521#418C22×C4711yescharacteristic
522#418C22×C4711yescharacteristic
523#413C22×C4711yescharacteristic
524#413C22×C4711yescharacteristic, complemented
525C2×#101C22×C4711yescharacteristic, complemented
526C2×#100C22×C4711yescharacteristic
527#410C22×C4711yescharacteristic
528#410C22×C4711yescharacteristic, complemented
529#405C22×C4711yescharacteristic, complemented
530#344C22×C4711yescharacteristic, complemented
531#344C22×C4711yescharacteristic, complemented
532C47#2429511yescharacteristic, direct product factor, Sylow
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C4711yescharacteristic
547C2×#41C23×C4711yescharacteristic
548C2×#41C23×C4711yescharacteristic
549C2×#41C23×C4711yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C4711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C4711yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C4712yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C4712yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C4711yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C4712yes—
597C2×SD16D4×C4712yes—
598C2×SD16D4×C4711yescharacteristic, complemented
599C2×SD16D4×C4711yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C4711yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C4712yescomplemented
609#131D4×C4712yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C4711yescharacteristic
613C2×M16C23×C4711yescharacteristic
614C2×M16C23×C4711yescharacteristic
615C2×M16C23×C4711yescharacteristic
616C2×M16C23×C4711yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C4711yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C4711yescharacteristic
629#117C23×C4711yescharacteristic
630#117C23×C4711yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C4712yes—
683#41C2×D4×C4712yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C4711yescharacteristic
695C2×Q8C2×D4×C4711yescharacteristic
696C2×Q8C2×D4×C4712yes—
697C2×Q8C2×D4×C4711yescharacteristic
698C2×Q8#41×C4711yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
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—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C4711yescharacteristic
719C2×D4C2×D4×C4711yescharacteristic
720C2×D4C2×D4×C4712yes—
721C2×D4C2×D4×C4711yescharacteristic
722C2×D4#41×C4711yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C4711yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C4712yes—
773M16C2×D4×C4712yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C4711yescharacteristic
784C2×C8C2×D4×C4711yescharacteristic
785C2×C8C2×D4×C4711yescharacteristic
786C2×C8C2×D4×C4711yescharacteristic
787C2×C8C2×D4×C4711yescharacteristic
788C2×C8C2×D4×C4711yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C4711yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C4712yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C4712yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C4711yescharacteristic
871C2×C4C22×D4×C4711yescharacteristic
872C2×C4C22×D4×C4711yescharacteristic
873C2×C4C22×D4×C4711yescharacteristic
874C2×C4C2×#41×C4711yescharacteristic
875C2×C4H(5,𝔽2)×C4711yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C4711yescharacteristic
882C8#120×C4711yescharacteristic
883C8#120×C4711yescharacteristic
884C8#120×C4711yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22C47×#53511yescharacteristic
900C22D42×C4711yescharacteristic
901C22C47×#54611yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C4711yescharacteristic
911C4C2×#121×C4711yescharacteristic
912C4D42×C4711yescharacteristic
913C4C47×#54611yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C47×#240811yescharacteristic
subgroupG/H
center, socleC2×C47#2408
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#577C2semidirect
2. C47×#3067C2semidirect
3. C47×#3057C2semidirect
4. C47×#3020C2semidirect
5. C47×#3019C2semidirect
6. C47×#2955C2semidirect
7. C47×#2049C2semidirect
8. C47×#2048C2semidirect
9. C47×#2009C2semidirect
10. C47×#2008C2semidirect
11. C47×#1977C2semidirect
12. C47×#1976C2semidirect
13. C47×#1814C2semidirect
14. C47×#1796C2semidirect
15. C47×#1795C2semidirect
24. C47×#575C22semidirect
34. C2×#131×C47C22semidirect
35. C47×#536C22semidirect
49. C47×#430C22semidirect
50. C2×#108×C47C22semidirect
51. C47×#427C22semidirect
56. C47×#421C22semidirect
57. C47×#421C22semidirect
58. C47×#419C22semidirect
59. C47×#419C22semidirect
63. C47×#413C22semidirect
64. C2×#101×C47C22semidirect
67. C47×#410C22semidirect
68. C47×#405C22semidirect
69. C47×#344C22semidirect
70. C47×#344C22semidirect
125. C2×Q16×C47D4semidirect
136. C2×SD16×C47D4semidirect
137. C2×SD16×C47D4semidirect
139. C2×D8×C47D4semidirect
146. #131×C47D4semidirect
147. #131×C47D4semidirect
423. #24295C47direct (N × H)
453. C2×#577C2×C47semidirect
454. #3067C2×C47semidirect
455. #3057C2×C47semidirect
456. #3020C2×C47semidirect
457. #3019C2×C47semidirect
458. #2955C2×C47semidirect
459. #2049C2×C47semidirect
460. #2048C2×C47semidirect
461. #2009C2×C47semidirect
462. #2008C2×C47semidirect
463. #1977C2×C47semidirect
464. #1976C2×C47semidirect
465. #1814C2×C47semidirect
466. #1796C2×C47semidirect
467. #1795C2×C47semidirect
485. #575C22×C47semidirect
495. C2×#131C22×C47semidirect
496. #536C22×C47semidirect
510. #430C22×C47semidirect
511. C2×#108C22×C47semidirect
512. #427C22×C47semidirect
517. #421C22×C47semidirect
518. #421C22×C47semidirect
519. #419C22×C47semidirect
520. #419C22×C47semidirect
524. #413C22×C47semidirect
525. C2×#101C22×C47semidirect
528. #410C22×C47semidirect
529. #405C22×C47semidirect
530. #344C22×C47semidirect
531. #344C22×C47semidirect
532. C47#24295direct (N × H)
587. C2×Q16D4×C47semidirect
598. C2×SD16D4×C47semidirect
599. C2×SD16D4×C47semidirect
601. C2×D8D4×C47semidirect
608. #131D4×C47semidirect
609. #131D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5772
C47×#30672
C47×#30572
C47×#30202
C47×#30192
C47×#29552
C47×#20492
C47×#20482
C47×#20092
C47×#20082
C47×#19772
C47×#19762
C47×#18142
C47×#17962
C47×#17952
#2429547