Finite Group Databasebeta

← C47×#24475 #26064173

Subgroups — C47×#24475 #26064173

Order 12032.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3585C211yesmaximal, characteristic
2C47×#3069C211yesmaximal, characteristic, complemented
3C47×#3040C211yesmaximal, characteristic, complemented
4C47×#3022C211yesmaximal, characteristic, complemented
5C2×C47×#455C211yesmaximal, characteristic, complemented
6C47×#2901C211yesmaximal, characteristic, complemented
7C47×#2050C211yesmaximal, characteristic, complemented
8C47×#2048C211yesmaximal, characteristic, complemented
9C47×#2009C211yesmaximal, characteristic, complemented
10C47×#2003C211yesmaximal, characteristic, complemented
11C47×#1906C211yesmaximal, characteristic, complemented
12C47×#1903C211yesmaximal, characteristic, complemented
13C47×#1902C211yesmaximal, characteristic, complemented
14C47×#1861C211yesmaximal, characteristic, complemented
15C47×#1795C211yesmaximal, characteristic, complemented
16C47×#585C2211yescharacteristic
17C2×H(5,𝔽2)×C47C2211yescharacteristic
18C47×#577—22no—
19C47×#577—22no—
20C47×#576—22no—
21C47×#576—22no—
22C47×#575—22no—
23C47×#575C2211yescharacteristic
24C47×#575C2211yescharacteristic
25C2×#137×C47C2211yescharacteristic
26C2×#137×C47C2211yescharacteristic, complemented
27C2×#137×C47C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C47—22no—
29C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
31C47×#568C2211yescharacteristic
32C47×#568C2211yescharacteristic, complemented
33C47×#536C2211yescharacteristic, complemented
34C2×#124×C47C2211yescharacteristic, complemented
35C4×#41×C47C2211yescharacteristic, complemented
36C47×#473—22no—
37C47×#471—22no—
38C47×#464—22no—
39C47×#463—22no—
40C47×#456—22no—
41C47×#455—22no—
42C47×#455—22no—
43C47×#455—22no—
44C47×#430C2211yescharacteristic, complemented
45C47×#423C2211yescharacteristic, complemented
46C47×#421—22no—
47C47×#421C2211yescharacteristic
48C47×#421C2211yescharacteristic
49C47×#421C2211yescharacteristic, complemented
50C47×#421C2211yescharacteristic, complemented
51C2×#104×C47—22no—
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic, complemented
54C2×#104×C47C2211yescharacteristic, complemented
55C47×#419C2211yescharacteristic, complemented
56C47×#418C2211yescharacteristic, complemented
57C47×#418C2211yescharacteristic, complemented
58C47×#413C2211yescharacteristic, complemented
59C47×#413C2211yescharacteristic, complemented
60C2×#101×C47C2211yescharacteristic, complemented
61C2×#100×C47C2211yescharacteristic, complemented
62C47×#410C2211yescharacteristic, complemented
63C47×#344C2211yescharacteristic, complemented
64C47×#344C2211yescharacteristic, complemented
65C47×#339C2211yescharacteristic, complemented
66C47×#338C2211yescharacteristic, complemented
672−1+4×C47—21no—
682−1+4×C47—21no—
692−1+4×C47D412yes—
70H(5,𝔽2)×C47—22no—
71H(5,𝔽2)×C47—21no—
72H(5,𝔽2)×C47—22no—
73H(5,𝔽2)×C47—21no—
74H(5,𝔽2)×C47—22no—
75H(5,𝔽2)×C47—41no—
76H(5,𝔽2)×C47—41no—
77H(5,𝔽2)×C47D412yes—
78C2×#41×C47—22no—
79C2×#41×C47—22no—
80C2×#41×C47—21no—
81C2×#41×C47—21no—
82C2×#41×C47—41no—
83C2×#41×C47C2311yescharacteristic
84C2×#41×C47C2311yescharacteristic
85C2×#41×C47C2311yescharacteristic
86C2×#41×C47C2311yescharacteristic
87C22×Q8×C47C2311yescharacteristic
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—41no—
91C22×D4×C47C2311yescharacteristic
92#137×C47—24no—
93#137×C47—21no—
94#137×C47—21no—
95#137×C47—21no—
96#137×C47—22no—
97#137×C47—22no—
98#137×C47—22no—
99#137×C47—22no—
100#137×C47—22no—
101#137×C47—41no—
102#137×C47D412yes—
103AGL(1,ℤ/8)×C47—24no—
104AGL(1,ℤ/8)×C47—24no—
105AGL(1,ℤ/8)×C47—24no—
106AGL(1,ℤ/8)×C47—22no—
107AGL(1,ℤ/8)×C47—22no—
108AGL(1,ℤ/8)×C47—21no—
109AGL(1,ℤ/8)×C47—22no—
110AGL(1,ℤ/8)×C47—21no—
111AGL(1,ℤ/8)×C47—21no—
112AGL(1,ℤ/8)×C47—22no—
113AGL(1,ℤ/8)×C47D412yes—
114#135×C47—24no—
115#135×C47—24no—
116#135×C47—22no—
117#135×C47—22no—
118C2×Q16×C47—21no—
119C2×Q16×C47—21no—
120C2×Q16×C47—21no—
121C2×SD16×C47—24no—
122C2×SD16×C47—21no—
123C2×SD16×C47—21no—
124C2×SD16×C47—21no—
125C2×SD16×C47—21no—
126C2×SD16×C47D412yes—
127C2×D8×C47—24no—
128C2×D8×C47—21no—
129C2×D8×C47D412yes—
130#131×C47—22no—
131#131×C47—22no—
132#131×C47—22no—
133#131×C47—41no—
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47C2311yescharacteristic
137C2×M16×C47C2311yescharacteristic
138C2×M16×C47C2311yescharacteristic
139C2×M16×C47C2311yescharacteristic
140C2×M16×C47C2311yescharacteristic
141C2×M16×C47C2311yescharacteristic
142C4⋊Q8×C47—21no—
143#124×C47—21no—
144#124×C47—22no—
145#124×C47—21no—
146#124×C47—21no—
147#123×C47—41no—
148C22⋊Q8×C47—41no—
149C4×Q8×C47—21no—
150C4×D4×C47—21no—
151C4×D4×C47—41no—
152#117×C47—21no—
153#117×C47C2311yescharacteristic
154#117×C47C2311yescharacteristic
155C2×C22⋊C4×C47—41no—
156C2×C42×C47—21no—
157C2×C42×C47C2311yescharacteristic
158#108×C47—22no—
159C4⋊C8×C47—22no—
160#104×C47—22no—
161#104×C47—22no—
162#104×C47—22no—
163#104×C47—22no—
164#104×C47—21no—
165#104×C47—21no—
166#104×C47—21no—
167#104×C47—21no—
168#104×C47D412yes—
169#104×C47D412yes—
170#103×C47—22no—
171#102×C47—22no—
172#102×C47—41no—
173#101×C47—21no—
174#101×C47—21no—
175#101×C47—22no—
176#100×C47—21no—
177#100×C47—21no—
178#100×C47—22no—
179#99×C47—41no—
180C24×C47—21no—
181C24×C47—41no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—21no—
186#41×C47—24no—
187#41×C47—22no—
188#41×C47—22no—
189#41×C47—22no—
190#41×C47—22no—
191#41×C47—21no—
192#41×C47—21no—
193#41×C47—21no—
194#41×C47—21no—
195#41×C47—21no—
196#41×C47—21no—
197#41×C47—21no—
198#41×C47—21no—
199#41×C47—42no—
200#41×C47—42no—
201#41×C47—42no—
202#41×C47—42no—
203#41×C47—42no—
204#41×C47—42no—
205#41×C47—41no—
206#41×C47—41no—
207#41×C47—42no—
208#41×C47C2×D412yes—
209#41×C47C2×D412yes—
210#41×C47C2×D412yes—
211#41×C47C2×D412yes—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47—21no—
215C2×Q8×C47—21no—
216C2×Q8×C47—21no—
217C2×Q8×C47—21no—
218C2×Q8×C47—21no—
219C2×Q8×C47—21no—
220C2×Q8×C47—41no—
221C2×Q8×C47C2×D411yescharacteristic
222C2×Q8×C47C2×D411yescharacteristic
223C2×Q8×C47C2×D411yescharacteristic
224C2×Q8×C47#4111yescharacteristic
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—24no—
228C2×D4×C47—22no—
229C2×D4×C47—22no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—42no—
238C2×D4×C47—41no—
239C2×D4×C47—41no—
240C2×D4×C47—42no—
241C2×D4×C47—42no—
242C2×D4×C47—41no—
243C2×D4×C47—44no—
244C2×D4×C47—42no—
245C2×D4×C47—42no—
246C2×D4×C47—44no—
247C2×D4×C47—42no—
248C2×D4×C47C2×D411yescharacteristic
249C2×D4×C47C2×D412yes—
250C2×D4×C47C2×D411yescharacteristic
251C2×D4×C47C2×D411yescharacteristic
252C2×D4×C47#4111yescharacteristic
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—41no—
260C22×C4×C47—42no—
261C22×C4×C47—41no—
262C22×C4×C47C2411yescharacteristic
263Q16×C47—22no—
264Q16×C47—22no—
265Q16×C47—42no—
266Q16×C47—42no—
267Q16×C47—42no—
268SD16×C47—24no—
269SD16×C47—22no—
270SD16×C47—22no—
271SD16×C47—22no—
272SD16×C47—24no—
273SD16×C47—22no—
274SD16×C47—42no—
275SD16×C47—42no—
276SD16×C47—42no—
277D8×C47—24no—
278D8×C47—22no—
279D8×C47—22no—
280D8×C47—24no—
281M16×C47—24no—
282M16×C47—21no—
283M16×C47—21no—
284M16×C47—21no—
285M16×C47—21no—
286M16×C47—21no—
287M16×C47—21no—
288M16×C47—21no—
289M16×C47—21no—
290M16×C47—21no—
291M16×C47—21no—
292M16×C47—42no—
293M16×C47C2×D412yes—
294M16×C47C2×D412yes—
295C2×C8×C47—24no—
296C2×C8×C47—21no—
297C2×C8×C47—21no—
298C2×C8×C47—21no—
299C2×C8×C47—21no—
300C2×C8×C47—21no—
301C2×C8×C47—42no—
302C2×C8×C47C2×D412yes—
303C4⋊C4×C47—21no—
304C4⋊C4×C47—21no—
305C4⋊C4×C47—41no—
306C4⋊C4×C47—42no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—42no—
310C22⋊C4×C47—42no—
311C22⋊C4×C47—41no—
312C22⋊C4×C47—42no—
313C42×C47—21no—
314C42×C47—21no—
315C42×C47—21no—
316C42×C47—41no—
317C42×C47C2×D411yescharacteristic
318C42×C47C2×D411yescharacteristic
319C23×C47—21no—
320C23×C47—21no—
321C23×C47—21no—
322C23×C47—22no—
323C23×C47—21no—
324C23×C47—42no—
325C23×C47—44no—
326C23×C47—41no—
327C23×C47—41no—
328C23×C47—82no—
329C23×C47—162no—
330C23×C47H(5,𝔽2)11yescharacteristic
331Q8×C47—21no—
332Q8×C47—21no—
333Q8×C47—21no—
334Q8×C47—21no—
335Q8×C47—21no—
336Q8×C47—21no—
337Q8×C47—42no—
338Q8×C47—41no—
339Q8×C47—41no—
340Q8×C47—41no—
341Q8×C47—41no—
342Q8×C47#12012yes—
343Q8×C47#12112yes—
344D4×C47—22no—
345D4×C47—22no—
346D4×C47—22no—
347D4×C47—22no—
348D4×C47—21no—
349D4×C47—21no—
350D4×C47—22no—
351D4×C47—21no—
352D4×C47—21no—
353D4×C47—21no—
354D4×C47—21no—
355D4×C47—22no—
356D4×C47—42no—
357D4×C47—42no—
358D4×C47—44no—
359D4×C47—42no—
360D4×C47—44no—
361D4×C47—41no—
362D4×C47—41no—
363D4×C47—41no—
364D4×C47—41no—
365D4×C47—41no—
366D4×C47—41no—
367D4×C47#12012yes—
368D4×C47#12112yes—
369C2×C4×C47—21no—
370C2×C4×C47—21no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—21no—
376C2×C4×C47—21no—
377C2×C4×C47—21no—
378C2×C4×C47—21no—
379C2×C4×C47—42no—
380C2×C4×C47—42no—
381C2×C4×C47—42no—
382C2×C4×C47—44no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—81no—
393C2×C4×C47—82no—
394C2×C4×C47C22×D411yescharacteristic
395C2×C4×C47C22×D411yescharacteristic
396C2×C4×C47C22×D411yescharacteristic
397C2×C4×C47C22×D411yescharacteristic
398C2×C4×C47C2×#4111yescharacteristic
399C2×C4×C47H(5,𝔽2)11yescharacteristic
400C8×C47—22no—
401C8×C47—22no—
402C8×C47—22no—
403C8×C47—41no—
404C8×C47—41no—
405C8×C47—41no—
406#24475C4711yesmaximal, characteristic, direct product factor, Sylow
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—41no—
410C22×C47—41no—
411C22×C47—42no—
412C22×C47—41no—
413C22×C47—81no—
414C22×C47—81no—
415C22×C47—81no—
416C22×C47—82no—
417C22×C47—81no—
418C22×C47—82no—
419C22×C47—161no—
420C22×C47—162no—
421C22×C47—164no—
422C22×C47#53411yescharacteristic
423C22×C47D4211yescharacteristic
424C22×C47#54611yescharacteristic
425C4×C47—22no—
426C4×C47—22no—
427C4×C47—41no—
428C4×C47—41no—
429C4×C47—41no—
430C4×C47—41no—
431C4×C47—81no—
432C4×C47—81no—
433C4×C47—81no—
434C4×C47C2×#12011yescharacteristic
435C4×C47C2×#12111yescharacteristic
436C4×C47D4211yescharacteristic
437C4×C47#54611yescharacteristic
438#3585C2×C4711yescharacteristic
439#3069C2×C4711yescharacteristic, complemented
440#3040C2×C4711yescharacteristic, complemented
441#3022C2×C4711yescharacteristic, complemented
442C2×#455C2×C4711yescharacteristic, complemented
443#2901C2×C4711yescharacteristic, complemented
444#2050C2×C4711yescharacteristic, complemented
445#2048C2×C4711yescharacteristic, complemented
446#2009C2×C4711yescharacteristic, complemented
447#2003C2×C4711yescharacteristic, complemented
448#1906C2×C4711yescharacteristic, complemented
449#1903C2×C4711yescharacteristic, complemented
450#1902C2×C4711yescharacteristic, complemented
451#1861C2×C4711yescharacteristic, complemented
452#1795C2×C4711yescharacteristic, complemented
453C2×C47—21no—
454C2×C47—21no—
455C2×C47—21no—
456C2×C47—42no—
457C2×C47—42no—
458C2×C47—82no—
459C2×C47—81no—
460C2×C47—81no—
461C2×C47#241011yescharacteristic
462#585C22×C4711yescharacteristic
463C2×H(5,𝔽2)C22×C4711yescharacteristic
464#577—22no—
465#577—22no—
466#576—22no—
467#576—22no—
468#575—22no—
469#575C22×C4711yescharacteristic
470#575C22×C4711yescharacteristic
471C2×#137C22×C4711yescharacteristic
472C2×#137C22×C4711yescharacteristic, complemented
473C2×#137C22×C4711yescharacteristic, complemented
474C2×AGL(1,ℤ/8)—22no—
475C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
476C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
477#568C22×C4711yescharacteristic
478#568C22×C4711yescharacteristic, complemented
479#536C22×C4711yescharacteristic, complemented
480C2×#124C22×C4711yescharacteristic, complemented
481C4×#41C22×C4711yescharacteristic, complemented
482#473—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#456—22no—
487#455—22no—
488#455—22no—
489#455—22no—
490#430C22×C4711yescharacteristic, complemented
491#423C22×C4711yescharacteristic, complemented
492#421—22no—
493#421C22×C4711yescharacteristic
494#421C22×C4711yescharacteristic
495#421C22×C4711yescharacteristic, complemented
496#421C22×C4711yescharacteristic, complemented
497C2×#104—22no—
498C2×#104C22×C4711yescharacteristic
499C2×#104C22×C4711yescharacteristic, complemented
500C2×#104C22×C4711yescharacteristic, complemented
501#419C22×C4711yescharacteristic, complemented
502#418C22×C4711yescharacteristic, complemented
503#418C22×C4711yescharacteristic, complemented
504#413C22×C4711yescharacteristic, complemented
505#413C22×C4711yescharacteristic, complemented
506C2×#101C22×C4711yescharacteristic, complemented
507C2×#100C22×C4711yescharacteristic, complemented
508#410C22×C4711yescharacteristic, complemented
509#344C22×C4711yescharacteristic, complemented
510#344C22×C4711yescharacteristic, complemented
511#339C22×C4711yescharacteristic, complemented
512#338C22×C4711yescharacteristic, complemented
513C47#2447511yescharacteristic, direct product factor, Sylow
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C4712yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C4712yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C4711yescharacteristic
531C2×#41C23×C4711yescharacteristic
532C2×#41C23×C4711yescharacteristic
533C2×#41C23×C4711yescharacteristic
534C22×Q8C23×C4711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C4711yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C4712yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C4712yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C4712yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C4712yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C4711yescharacteristic
584C2×M16C23×C4711yescharacteristic
585C2×M16C23×C4711yescharacteristic
586C2×M16C23×C4711yescharacteristic
587C2×M16C23×C4711yescharacteristic
588C2×M16C23×C4711yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C4711yescharacteristic
601#117C23×C4711yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C4711yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C4712yes—
616#104D4×C4712yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C4712yes—
656#41C2×D4×C4712yes—
657#41C2×D4×C4712yes—
658#41C2×D4×C4712yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C4711yescharacteristic
669C2×Q8C2×D4×C4711yescharacteristic
670C2×Q8C2×D4×C4711yescharacteristic
671C2×Q8#41×C4711yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C4711yescharacteristic
696C2×D4C2×D4×C4711yescharacteristic
697C2×D4C2×D4×C4712yes—
698C2×D4C2×D4×C4711yescharacteristic
699C2×D4#41×C4711yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C4711yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C4712yes—
741M16C2×D4×C4712yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C4712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C4711yescharacteristic
765C42C2×D4×C4711yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C4711yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C4712yes—
790Q8#121×C4712yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C4712yes—
815D4#121×C4712yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C4711yescharacteristic
842C2×C4C22×D4×C4711yescharacteristic
843C2×C4C22×D4×C4711yescharacteristic
844C2×C4C22×D4×C4711yescharacteristic
845C2×C4C2×#41×C4711yescharacteristic
846C2×C4H(5,𝔽2)×C4711yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22C47×#53411yescharacteristic
869C22D42×C4711yescharacteristic
870C22C47×#54611yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C4711yescharacteristic
881C4C2×#121×C4711yescharacteristic
882C4D42×C4711yescharacteristic
883C4C47×#54611yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C47×#241011yescharacteristic
subgroupG/H
center, socleC2×C47#2410
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3585C2
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
2. C47×#3069C2semidirect
3. C47×#3040C2semidirect
4. C47×#3022C2semidirect
5. C2×C47×#455C2semidirect
6. C47×#2901C2semidirect
7. C47×#2050C2semidirect
8. C47×#2048C2semidirect
9. C47×#2009C2semidirect
10. C47×#2003C2semidirect
11. C47×#1906C2semidirect
12. C47×#1903C2semidirect
13. C47×#1902C2semidirect
14. C47×#1861C2semidirect
15. C47×#1795C2semidirect
26. C2×#137×C47C22semidirect
27. C2×#137×C47C22semidirect
32. C47×#568C22semidirect
33. C47×#536C22semidirect
34. C2×#124×C47C22semidirect
35. C4×#41×C47C22semidirect
44. C47×#430C22semidirect
45. C47×#423C22semidirect
49. C47×#421C22semidirect
50. C47×#421C22semidirect
53. C2×#104×C47C22semidirect
54. C2×#104×C47C22semidirect
55. C47×#419C22semidirect
56. C47×#418C22semidirect
57. C47×#418C22semidirect
58. C47×#413C22semidirect
59. C47×#413C22semidirect
60. C2×#101×C47C22semidirect
61. C2×#100×C47C22semidirect
62. C47×#410C22semidirect
63. C47×#344C22semidirect
64. C47×#344C22semidirect
65. C47×#339C22semidirect
66. C47×#338C22semidirect
406. #24475C47direct (N × H)
439. #3069C2×C47semidirect
440. #3040C2×C47semidirect
441. #3022C2×C47semidirect
442. C2×#455C2×C47semidirect
443. #2901C2×C47semidirect
444. #2050C2×C47semidirect
445. #2048C2×C47semidirect
446. #2009C2×C47semidirect
447. #2003C2×C47semidirect
448. #1906C2×C47semidirect
449. #1903C2×C47semidirect
450. #1902C2×C47semidirect
451. #1861C2×C47semidirect
452. #1795C2×C47semidirect
472. C2×#137C22×C47semidirect
473. C2×#137C22×C47semidirect
478. #568C22×C47semidirect
479. #536C22×C47semidirect
480. C2×#124C22×C47semidirect
481. C4×#41C22×C47semidirect
490. #430C22×C47semidirect
491. #423C22×C47semidirect
495. #421C22×C47semidirect
496. #421C22×C47semidirect
499. C2×#104C22×C47semidirect
500. C2×#104C22×C47semidirect
501. #419C22×C47semidirect
502. #418C22×C47semidirect
503. #418C22×C47semidirect
504. #413C22×C47semidirect
505. #413C22×C47semidirect
506. C2×#101C22×C47semidirect
507. C2×#100C22×C47semidirect
508. #410C22×C47semidirect
509. #344C22×C47semidirect
510. #344C22×C47semidirect
511. #339C22×C47semidirect
512. #338C22×C47semidirect
513. C47#24475direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35852
C47×#30692
C47×#30402
C47×#30222
C2×C47×#4552
C47×#29012
C47×#20502
C47×#20482
C47×#20092
C47×#20032
C47×#19062
C47×#19032
C47×#19022
C47×#18612
C47×#17952
#2447547