Finite Group Databasebeta

← C47×#25192 #26064890

Subgroups — C47×#25192 #26064890

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3062C211yesmaximal, characteristic, complemented
2C47×#3045C211yesmaximal, characteristic, complemented
3C2×C47×#453C211yesmaximal, characteristic, complemented
4C47×#3012C211yesmaximal, characteristic, complemented
5C2×C47×#444C211yesmaximal, characteristic, complemented
6C47×#2897C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2040C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1961C211yesmaximal, characteristic, complemented
12C47×#1938C211yesmaximal, characteristic, complemented
13C47×#1907C211yesmaximal, characteristic, complemented
14C47×#1907C211yesmaximal, characteristic, complemented
15C47×#1860C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C2×#135×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic, complemented
23C47×#537C2211yescharacteristic
24C47×#535C2211yescharacteristic, complemented
25C2×#127×C47C2211yescharacteristic
26C47×#520C2211yescharacteristic
27C47×#469—21no—
28C47×#468—21no—
29C47×#466—21no—
30C47×#465—21no—
31C47×#464—21no—
32C47×#463—21no—
33C47×#460—21no—
34C47×#459—21no—
35C47×#453—24no—
36C47×#452—21no—
37C47×#450—21no—
38C47×#449—21no—
39C47×#447—21no—
40C47×#444—24no—
41C2×#108×C47C2211yescharacteristic, complemented
42C47×#428C2211yescharacteristic, complemented
43C47×#424C2211yescharacteristic, complemented
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic, complemented
47C47×#418—21no—
48C47×#418C2211yescharacteristic
49C47×#417—21no—
50C47×#417C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C47×#417C2211yescharacteristic, complemented
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C2×#102×C47—21no—
56C2×#102×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic, complemented
59C2×#102×C47C2211yescharacteristic, complemented
60C2×#100×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic, complemented
62C47×#408C2211yescharacteristic
63C2×#97×C47C2211yescharacteristic, complemented
64C47×#382C2211yescharacteristic, complemented
65C47×#343C2211yescharacteristic, complemented
66C47×#343C2211yescharacteristic, complemented
67C47×#341C2211yescharacteristic, complemented
68C47×#339C2211yescharacteristic, complemented
69H(5,𝔽2)×C47—22no—
70H(5,𝔽2)×C47—22no—
71H(5,𝔽2)×C47—22no—
72H(5,𝔽2)×C47—41no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47C2311yescharacteristic
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—41no—
81C22×D4×C47—41no—
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84AGL(1,ℤ/8)×C47—22no—
85AGL(1,ℤ/8)×C47—22no—
86AGL(1,ℤ/8)×C47—22no—
87AGL(1,ℤ/8)×C47—22no—
88AGL(1,ℤ/8)×C47—41no—
89AGL(1,ℤ/8)×C47—41no—
90#135×C47—22no—
91#135×C47—22no—
92C2×Q16×C47D411yescharacteristic, complemented
93C2×SD16×C47—21no—
94C2×SD16×C47—21no—
95C2×SD16×C47—21no—
96C2×SD16×C47D411yescharacteristic, complemented
97C2×SD16×C47D411yescharacteristic, complemented
98C2×D8×C47—21no—
99C2×D8×C47—21no—
100C2×D8×C47—21no—
101C2×D8×C47D411yescharacteristic, complemented
102#131×C47—22no—
103#131×C47—22no—
104#131×C47—41no—
105#131×C47—41no—
106C2×M16×C47—21no—
107C2×M16×C47—21no—
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C22×C8×C47—21no—
113C22×C8×C47—21no—
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116#127×C47—21no—
117#127×C47—22no—
118#127×C47—22no—
119#124×C47—21no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—41no—
127#120×C47—41no—
128C4×Q8×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—41no—
131#117×C47—21no—
132#117×C47C2311yescharacteristic
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137#108×C47—22no—
138#107×C47—21no—
139#106×C47—21no—
140C4⋊C8×C47—21no—
141C4⋊C8×C47—21no—
142#104×C47—22no—
143#104×C47—22no—
144#104×C47D414yescomplemented
145#103×C47—21no—
146#103×C47—21no—
147#103×C47—21no—
148#103×C47D411yescharacteristic, complemented
149#103×C47D411yescharacteristic, complemented
150#102×C47—21no—
151#102×C47—21no—
152#102×C47—21no—
153#102×C47—21no—
154#102×C47—21no—
155#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#102×C47—21no—
161#102×C47—21no—
162#102×C47—21no—
163#102×C47D411yescharacteristic, complemented
164#102×C47D411yescharacteristic, complemented
165#100×C47—22no—
166#100×C47—41no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47—21no—
169#97×C47—22no—
170#95×C47—41no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—41no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—24no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—42no—
186#41×C47—42no—
187#41×C47—42no—
188#41×C47C2×D412yes—
189#41×C47#4112yes—
190C2×Q8×C47C2×D411yescharacteristic
191C2×Q8×C47C2×D411yescharacteristic
192C2×Q8×C47C2×D411yescharacteristic
193C2×D4×C47—21no—
194C2×D4×C47—24no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—42no—
209C2×D4×C47—41no—
210C2×D4×C47—41no—
211C2×D4×C47—44no—
212C2×D4×C47—41no—
213C2×D4×C47—41no—
214C2×D4×C47—42no—
215C2×D4×C47—44no—
216C2×D4×C47—44no—
217C2×D4×C47—42no—
218C2×D4×C47—41no—
219C2×D4×C47—82no—
220C2×D4×C47—82no—
221C2×D4×C47C2×D411yescharacteristic
222C2×D4×C47C2×D411yescharacteristic
223C2×D4×C47C2×D411yescharacteristic
224C2×D4×C47#4112yes—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—41no—
232C22×C4×C47—41no—
233C22×C4×C47C2411yescharacteristic
234Q16×C47—22no—
235SD16×C47—22no—
236SD16×C47—22no—
237SD16×C47—42no—
238SD16×C47—42no—
239SD16×C47—42no—
240D8×C47—22no—
241D8×C47—42no—
242D8×C47—42no—
243D8×C47—42no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—42no—
252M16×C47—42no—
253M16×C47C2×D412yes—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—42no—
263C2×C8×C47—42no—
264C2×C8×C47C2×D411yescharacteristic
265C2×C8×C47C2×D411yescharacteristic
266C2×C8×C47C2×D411yescharacteristic
267C2×C8×C47C2×D411yescharacteristic
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—41no—
273C4⋊C4×C47—41no—
274C4⋊C4×C47C2×D411yescharacteristic
275C4⋊C4×C47C2×D411yescharacteristic
276C22⋊C4×C47—21no—
277C22⋊C4×C47—41no—
278C22⋊C4×C47—41no—
279C22⋊C4×C47—41no—
280C22⋊C4×C47—41no—
281C22⋊C4×C47—41no—
282C42×C47—21no—
283C42×C47—21no—
284C42×C47—41no—
285C42×C47C2×D412yes—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—22no—
290C23×C47—44no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—81no—
297C23×C47—81no—
298C23×C47—81no—
299C23×C47—81no—
300C23×C47—161no—
301C23×C47—161no—
302C23×C47H(5,𝔽2)11yescharacteristic
303Q8×C47—21no—
304Q8×C47—21no—
305Q8×C47—21no—
306Q8×C47—21no—
307Q8×C47—21no—
308Q8×C47#12112yes—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—21no—
312D4×C47—21no—
313D4×C47—22no—
314D4×C47—21no—
315D4×C47—21no—
316D4×C47—21no—
317D4×C47—22no—
318D4×C47—44no—
319D4×C47—44no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47—41no—
328D4×C47—41no—
329D4×C47—41no—
330D4×C47—88no—
331D4×C47—161no—
332D4×C47—161no—
333D4×C47—161no—
334D4×C47#12112yes—
335C2×C4×C47—21no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—44no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—81no—
353C2×C4×C47—81no—
354C2×C4×C47—161no—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C2×#4111yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47H(5,𝔽2)11yescharacteristic
361C8×C47—21no—
362C8×C47—21no—
363C8×C47—21no—
364C8×C47—21no—
365C8×C47—22no—
366C8×C47—41no—
367C8×C47—41no—
368C8×C47—41no—
369#25192C4711yesmaximal, characteristic, direct product factor, Sylow
370C22×C47—21no—
371C22×C47—21no—
372C22×C47—22no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—82no—
383C22×C47—82no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—161no—
390C22×C47—161no—
391C22×C47—164no—
392C22×C47#53811yescharacteristic
393C22×C47D4211yescharacteristic
394C22×C47#54611yescharacteristic
395C4×C47—22no—
396C4×C47—42no—
397C4×C47—41no—
398C4×C47—41no—
399C4×C47—41no—
400C4×C47—41no—
401C4×C47—81no—
402C4×C47—81no—
403C4×C47C2×#12111yescharacteristic
404C4×C47#52511yescharacteristic
405C4×C47D4211yescharacteristic
406C4×C47#54611yescharacteristic
407#3062C2×C4711yescharacteristic, complemented
408#3045C2×C4711yescharacteristic, complemented
409C2×#453C2×C4711yescharacteristic, complemented
410#3012C2×C4711yescharacteristic, complemented
411C2×#444C2×C4711yescharacteristic, complemented
412#2897C2×C4711yescharacteristic, complemented
413#2063C2×C4711yescharacteristic, complemented
414#2051C2×C4711yescharacteristic, complemented
415#2040C2×C4711yescharacteristic, complemented
416#2002C2×C4711yescharacteristic, complemented
417#1961C2×C4711yescharacteristic, complemented
418#1938C2×C4711yescharacteristic, complemented
419#1907C2×C4711yescharacteristic, complemented
420#1907C2×C4711yescharacteristic, complemented
421#1860C2×C4711yescharacteristic, complemented
422C2×C47—21no—
423C2×C47—21no—
424C2×C47—42no—
425C2×C47—81no—
426C2×C47—81no—
427C2×C47—82no—
428C2×C47—161no—
429C2×C47#242411yescharacteristic
430C2×C47#328811yescharacteristic
431C2×C47#328811yescharacteristic
432C2×H(5,𝔽2)C22×C4711yescharacteristic
433C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
436C2×#135C22×C4711yescharacteristic
437C2×#131C22×C4711yescharacteristic
438C2×#131C22×C4711yescharacteristic, complemented
439#537C22×C4711yescharacteristic
440#535C22×C4711yescharacteristic, complemented
441C2×#127C22×C4711yescharacteristic
442#520C22×C4711yescharacteristic
443#469—21no—
444#468—21no—
445#466—21no—
446#465—21no—
447#464—21no—
448#463—21no—
449#460—21no—
450#459—21no—
451#453—24no—
452#452—21no—
453#450—21no—
454#449—21no—
455#447—21no—
456#444—24no—
457C2×#108C22×C4711yescharacteristic, complemented
458#428C22×C4711yescharacteristic, complemented
459#424C22×C4711yescharacteristic, complemented
460C2×#104C22×C4711yescharacteristic
461C2×#104C22×C4711yescharacteristic
462C2×#104C22×C4711yescharacteristic, complemented
463#418—21no—
464#418C22×C4711yescharacteristic
465#417—21no—
466#417C22×C4711yescharacteristic
467#417C22×C4711yescharacteristic
468#417C22×C4711yescharacteristic, complemented
469#416—21no—
470#416C22×C4711yescharacteristic
471C2×#102—21no—
472C2×#102C22×C4711yescharacteristic
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic, complemented
475C2×#102C22×C4711yescharacteristic, complemented
476C2×#100C22×C4711yescharacteristic
477C2×#100C22×C4711yescharacteristic, complemented
478#408C22×C4711yescharacteristic
479C2×#97C22×C4711yescharacteristic, complemented
480#382C22×C4711yescharacteristic, complemented
481#343C22×C4711yescharacteristic, complemented
482#343C22×C4711yescharacteristic, complemented
483#341C22×C4711yescharacteristic, complemented
484#339C22×C4711yescharacteristic, complemented
485C47#2519211yescharacteristic, direct product factor, Sylow
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C4711yescharacteristic
493C2×#41C23×C4711yescharacteristic
494C2×#41C23×C4711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C4711yescharacteristic
500C22×D4C23×C4711yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C4711yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C4711yescharacteristic, complemented
514C2×SD16D4×C4711yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C4711yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C4711yescharacteristic
526C2×M16C23×C4711yescharacteristic
527C2×M16C23×C4711yescharacteristic
528C2×M16C23×C4711yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C4711yescharacteristic
532C22×C8C23×C4711yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C4711yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C4711yescharacteristic
552C2×C4⋊C4C23×C4711yescharacteristic
553C2×C42C23×C4711yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C4714yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C4711yescharacteristic, complemented
566#103D4×C4711yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C4711yescharacteristic, complemented
581#102D4×C4711yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C4712yes—
606#41#41×C4712yes—
607C2×Q8C2×D4×C4711yescharacteristic
608C2×Q8C2×D4×C4711yescharacteristic
609C2×Q8C2×D4×C4711yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C4711yescharacteristic
639C2×D4C2×D4×C4711yescharacteristic
640C2×D4C2×D4×C4711yescharacteristic
641C2×D4#41×C4712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C4711yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C4712yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C4711yescharacteristic
682C2×C8C2×D4×C4711yescharacteristic
683C2×C8C2×D4×C4711yescharacteristic
684C2×C8C2×D4×C4711yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C4711yescharacteristic
692C4⋊C4C2×D4×C4711yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C4712yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C4711yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C4712yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C4712yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C4711yescharacteristic
773C2×C4C22×D4×C4711yescharacteristic
774C2×C4C22×D4×C4711yescharacteristic
775C2×C4C2×#41×C4711yescharacteristic
776C2×C4C2×#41×C4711yescharacteristic
777C2×C4H(5,𝔽2)×C4711yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22C47×#53811yescharacteristic
809C22D42×C4711yescharacteristic
810C22C47×#54611yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C4711yescharacteristic
820C4C47×#52511yescharacteristic
821C4D42×C4711yescharacteristic
822C4C47×#54611yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C47×#242411yescharacteristic
831C2C47×#328811yescharacteristic
832C2C47×#328811yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3062C2semidirect
2. C47×#3045C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3012C2semidirect
5. C2×C47×#444C2semidirect
6. C47×#2897C2semidirect
7. C47×#2063C2semidirect
8. C47×#2051C2semidirect
9. C47×#2040C2semidirect
10. C47×#2002C2semidirect
11. C47×#1961C2semidirect
12. C47×#1938C2semidirect
13. C47×#1907C2semidirect
14. C47×#1907C2semidirect
15. C47×#1860C2semidirect
22. C2×#131×C47C22semidirect
24. C47×#535C22semidirect
41. C2×#108×C47C22semidirect
42. C47×#428C22semidirect
43. C47×#424C22semidirect
46. C2×#104×C47C22semidirect
52. C47×#417C22semidirect
58. C2×#102×C47C22semidirect
59. C2×#102×C47C22semidirect
61. C2×#100×C47C22semidirect
63. C2×#97×C47C22semidirect
64. C47×#382C22semidirect
65. C47×#343C22semidirect
66. C47×#343C22semidirect
67. C47×#341C22semidirect
68. C47×#339C22semidirect
92. C2×Q16×C47D4semidirect
96. C2×SD16×C47D4semidirect
97. C2×SD16×C47D4semidirect
101. C2×D8×C47D4semidirect
144. #104×C47D4semidirect
148. #103×C47D4semidirect
149. #103×C47D4semidirect
163. #102×C47D4semidirect
164. #102×C47D4semidirect
369. #25192C47direct (N × H)
407. #3062C2×C47semidirect
408. #3045C2×C47semidirect
409. C2×#453C2×C47semidirect
410. #3012C2×C47semidirect
411. C2×#444C2×C47semidirect
412. #2897C2×C47semidirect
413. #2063C2×C47semidirect
414. #2051C2×C47semidirect
415. #2040C2×C47semidirect
416. #2002C2×C47semidirect
417. #1961C2×C47semidirect
418. #1938C2×C47semidirect
419. #1907C2×C47semidirect
420. #1907C2×C47semidirect
421. #1860C2×C47semidirect
438. C2×#131C22×C47semidirect
440. #535C22×C47semidirect
457. C2×#108C22×C47semidirect
458. #428C22×C47semidirect
459. #424C22×C47semidirect
462. C2×#104C22×C47semidirect
468. #417C22×C47semidirect
474. C2×#102C22×C47semidirect
475. C2×#102C22×C47semidirect
477. C2×#100C22×C47semidirect
479. C2×#97C22×C47semidirect
480. #382C22×C47semidirect
481. #343C22×C47semidirect
482. #343C22×C47semidirect
483. #341C22×C47semidirect
484. #339C22×C47semidirect
485. C47#25192direct (N × H)
509. C2×Q16D4×C47semidirect
513. C2×SD16D4×C47semidirect
514. C2×SD16D4×C47semidirect
518. C2×D8D4×C47semidirect
561. #104D4×C47semidirect
565. #103D4×C47semidirect
566. #103D4×C47semidirect
580. #102D4×C47semidirect
581. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30622
C47×#30452
C2×C47×#4532
C47×#30122
C2×C47×#4442
C47×#28972
C47×#20632
C47×#20512
C47×#20402
C47×#20022
C47×#19612
C47×#19382
C47×#19072
C47×#18602
#2519247