Finite Group Databasebeta

← C47×#25180 #26064878

Subgroups — C47×#25180 #26064878

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#472C211yesmaximal, characteristic, complemented
2C47×#3041C211yesmaximal, characteristic, complemented
3C2×C47×#453C211yesmaximal, characteristic, complemented
4C47×#3008C211yesmaximal, characteristic, complemented
5C47×#2946C211yesmaximal, characteristic, complemented
6C47×#2897C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2037C211yesmaximal, characteristic, complemented
10C47×#2011C211yesmaximal, characteristic, complemented
11C47×#1978C211yesmaximal, characteristic, complemented
12C47×#1929C211yesmaximal, characteristic, complemented
13C47×#1887C211yesmaximal, characteristic, complemented
14C47×#1883C211yesmaximal, characteristic, complemented
15C47×#1866C211yesmaximal, 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
20C22×D8×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic, complemented
22C2×#131×C47C2211yescharacteristic
23C47×#535C2211yescharacteristic
24C2×#127×C47C2211yescharacteristic
25C47×#520C2211yescharacteristic
26C47×#518C2211yescharacteristic, complemented
27C47×#472—24no—
28C47×#463—21no—
29C47×#463—21no—
30C47×#459—21no—
31C47×#459—21no—
32C47×#453—24no—
33C47×#449—21no—
34C47×#449—21no—
35C47×#447—21no—
36C47×#447—21no—
37C47×#442—21no—
38C47×#440—21no—
39C4×SD16×C47—21no—
40C4×D8×C47—21no—
41C2×#108×C47C2211yescharacteristic, complemented
42C2×#108×C47C2211yescharacteristic, complemented
43C47×#428C2211yescharacteristic, complemented
44C47×#424C2211yescharacteristic, complemented
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic
47C47×#418—21no—
48C47×#418C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#418C2211yescharacteristic, complemented
51C47×#417—21no—
52C47×#417C2211yescharacteristic
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C47×#416C2211yescharacteristic
56C2×#102×C47—21no—
57C2×#102×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic, complemented
59C2×#100×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic, complemented
61C2×#100×C47C2211yescharacteristic, complemented
62C47×#408C2211yescharacteristic
63C47×#405C2211yescharacteristic, complemented
64C47×#390C2211yescharacteristic, complemented
65C47×#343C2211yescharacteristic, complemented
66C47×#339C2211yescharacteristic, complemented
67C47×#339C2211yescharacteristic, complemented
68C47×#336C2211yescharacteristic, 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
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—41no—
80C22×D4×C47—41no—
81C22×D4×C47C2311yescharacteristic
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)×C47D414yescomplemented
90C2×SD16×C47—21no—
91C2×SD16×C47—21no—
92C2×SD16×C47—21no—
93C2×D8×C47—21no—
94C2×D8×C47—21no—
95C2×D8×C47—22no—
96C2×D8×C47—21no—
97C2×D8×C47—22no—
98C2×D8×C47—21no—
99C2×D8×C47—21no—
100C2×D8×C47—21no—
101C2×D8×C47—21no—
102C2×D8×C47—41no—
103C2×D8×C47—41no—
104#131×C47—22no—
105#131×C47—41no—
106C2×M16×C47—21no—
107C2×M16×C47C2311yescharacteristic
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C22×C8×C47—21no—
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114#127×C47—22no—
115#127×C47—21no—
116#127×C47—22no—
117#124×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#120×C47—41no—
121C4×Q8×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47—21no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—21no—
127C4×D4×C47—41no—
128#117×C47—21no—
129#117×C47C2311yescharacteristic
130#117×C47C2311yescharacteristic
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47—41no—
134C2×C22⋊C4×C47—41no—
135C2×C42×C47C2311yescharacteristic
136#108×C47—22no—
137#108×C47—41no—
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#103×C47—21no—
145#103×C47D411yescharacteristic, complemented
146#103×C47D411yescharacteristic, complemented
147#103×C47D411yescharacteristic, complemented
148#103×C47D411yescharacteristic, complemented
149#102×C47—21no—
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×C47D411yescharacteristic, complemented
161#102×C47D411yescharacteristic, complemented
162#102×C47D411yescharacteristic, complemented
163#102×C47D411yescharacteristic, complemented
164#100×C47—22no—
165#100×C47—22no—
166#100×C47—22no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47—21no—
169#97×C47—21no—
170C4×C8×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—21no—
174C24×C47—41no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—24no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—42no—
183#41×C47—42no—
184#41×C47—42no—
185#41×C47C2×D412yes—
186#41×C47#4112yes—
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×D4×C47—21no—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
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—41no—
212C2×D4×C47—41no—
213C2×D4×C47—42no—
214C2×D4×C47—44no—
215C2×D4×C47—44no—
216C2×D4×C47—42no—
217C2×D4×C47—44no—
218C2×D4×C47—82no—
219C2×D4×C47—82no—
220C2×D4×C47C2×D412yes—
221C2×D4×C47C2×D411yescharacteristic
222C2×D4×C47C2×D411yescharacteristic
223C2×D4×C47#4112yes—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—41no—
229C22×C4×C47—41no—
230C22×C4×C47—41no—
231C22×C4×C47—41no—
232C22×C4×C47C2411yescharacteristic
233SD16×C47—24no—
234SD16×C47—42no—
235SD16×C47—42no—
236D8×C47—24no—
237D8×C47—42no—
238D8×C47—42no—
239D8×C47—42no—
240D8×C47—42no—
241D8×C47—42no—
242D8×C47—42no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—42no—
251M16×C47C2×D412yes—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
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—42no—
261C2×C8×C47C2×D411yescharacteristic
262C2×C8×C47C2×D411yescharacteristic
263C2×C8×C47C2×D411yescharacteristic
264C2×C8×C47C2×D411yescharacteristic
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—41no—
268C4⋊C4×C47C2×D411yescharacteristic
269C4⋊C4×C47C2×D411yescharacteristic
270C4⋊C4×C47C2×D411yescharacteristic
271C4⋊C4×C47C2×D411yescharacteristic
272C22⋊C4×C47—21no—
273C22⋊C4×C47—21no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—41no—
276C22⋊C4×C47—41no—
277C22⋊C4×C47—41no—
278C22⋊C4×C47—41no—
279C22⋊C4×C47—82no—
280C42×C47—21no—
281C42×C47—21no—
282C42×C47—21no—
283C42×C47—21no—
284C42×C47—41no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—44no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—81no—
298C23×C47—81no—
299C23×C47—81no—
300C23×C47—81no—
301C23×C47—81no—
302C23×C47—81no—
303C23×C47—161no—
304C23×C47—161no—
305C23×C47H(5,𝔽2)11yescharacteristic
306Q8×C47—21no—
307Q8×C47—21no—
308Q8×C47—21no—
309Q8×C47#12112yes—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—21no—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—21no—
317D4×C47—21no—
318D4×C47—22no—
319D4×C47—44no—
320D4×C47—44no—
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—41no—
331D4×C47—88no—
332D4×C47—161no—
333D4×C47—161no—
334D4×C47#12112yes—
335C2×C4×C47—21no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—44no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—81no—
351C2×C4×C47—161no—
352C2×C4×C47—161no—
353C2×C4×C47—161no—
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C2×#4111yescharacteristic
358C2×C4×C47C2×#4111yescharacteristic
359C2×C4×C47H(5,𝔽2)11yescharacteristic
360C8×C47—22no—
361C8×C47—21no—
362C8×C47—21no—
363C8×C47—21no—
364C8×C47—21no—
365C8×C47—41no—
366C8×C47—41no—
367C8×C47—41no—
368#25180C4711yesmaximal, characteristic, direct product factor, Sylow
369C22×C47—21no—
370C22×C47—21no—
371C22×C47—22no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—82no—
380C22×C47—82no—
381C22×C47—82no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—161no—
390C22×C47—161no—
391C22×C47—161no—
392C22×C47—164no—
393C22×C47#53811yescharacteristic
394C22×C47D4211yescharacteristic
395C22×C47#54611yescharacteristic
396C4×C47—22no—
397C4×C47—42no—
398C4×C47—41no—
399C4×C47—41no—
400C4×C47—41no—
401C4×C47—41no—
402C4×C47—41no—
403C4×C47—81no—
404C4×C47C2×#12111yescharacteristic
405C4×C47#52511yescharacteristic
406C4×C47D4211yescharacteristic
407C4×C47#54611yescharacteristic
408C2×#472C2×C4711yescharacteristic, complemented
409#3041C2×C4711yescharacteristic, complemented
410C2×#453C2×C4711yescharacteristic, complemented
411#3008C2×C4711yescharacteristic, complemented
412#2946C2×C4711yescharacteristic, complemented
413#2897C2×C4711yescharacteristic, complemented
414#2063C2×C4711yescharacteristic, complemented
415#2051C2×C4711yescharacteristic, complemented
416#2037C2×C4711yescharacteristic, complemented
417#2011C2×C4711yescharacteristic, complemented
418#1978C2×C4711yescharacteristic, complemented
419#1929C2×C4711yescharacteristic, complemented
420#1887C2×C4711yescharacteristic, complemented
421#1883C2×C4711yescharacteristic, complemented
422#1866C2×C4711yescharacteristic, complemented
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—42no—
426C2×C47—81no—
427C2×C47—82no—
428C2×C47—82no—
429C2×C47—161no—
430C2×C47#242411yescharacteristic
431C2×C47#328811yescharacteristic
432C2×C47#329211yescharacteristic
433C2×H(5,𝔽2)C22×C4711yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
436C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
437C22×D8C22×C4711yescharacteristic
438C22×D8C22×C4711yescharacteristic, complemented
439C2×#131C22×C4711yescharacteristic
440#535C22×C4711yescharacteristic
441C2×#127C22×C4711yescharacteristic
442#520C22×C4711yescharacteristic
443#518C22×C4711yescharacteristic, complemented
444#472—24no—
445#463—21no—
446#463—21no—
447#459—21no—
448#459—21no—
449#453—24no—
450#449—21no—
451#449—21no—
452#447—21no—
453#447—21no—
454#442—21no—
455#440—21no—
456C4×SD16—21no—
457C4×D8—21no—
458C2×#108C22×C4711yescharacteristic, complemented
459C2×#108C22×C4711yescharacteristic, complemented
460#428C22×C4711yescharacteristic, complemented
461#424C22×C4711yescharacteristic, complemented
462C2×#104C22×C4711yescharacteristic
463C2×#104C22×C4711yescharacteristic
464#418—21no—
465#418C22×C4711yescharacteristic
466#418C22×C4711yescharacteristic
467#418C22×C4711yescharacteristic, complemented
468#417—21no—
469#417C22×C4711yescharacteristic
470#416—21no—
471#416C22×C4711yescharacteristic
472#416C22×C4711yescharacteristic
473C2×#102—21no—
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic, complemented
476C2×#100C22×C4711yescharacteristic
477C2×#100C22×C4711yescharacteristic, complemented
478C2×#100C22×C4711yescharacteristic, complemented
479#408C22×C4711yescharacteristic
480#405C22×C4711yescharacteristic, complemented
481#390C22×C4711yescharacteristic, complemented
482#343C22×C4711yescharacteristic, complemented
483#339C22×C4711yescharacteristic, complemented
484#339C22×C4711yescharacteristic, complemented
485#336C22×C4711yescharacteristic, complemented
486C47#2518011yescharacteristic, direct product factor, Sylow
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C4711yescharacteristic
494C2×#41C23×C4711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C4711yescharacteristic
500C22×D4C23×C4711yescharacteristic
501C22×D4C23×C4711yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C4714yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C4711yescharacteristic
526C2×M16C23×C4711yescharacteristic
527C2×M16C23×C4711yescharacteristic
528C2×M16C23×C4711yescharacteristic
529C22×C8—21no—
530C22×C8C23×C4711yescharacteristic
531C22×C8C23×C4711yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C4711yescharacteristic
548#117C23×C4711yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C4711yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C4711yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C4711yescharacteristic, complemented
564#103D4×C4711yescharacteristic, complemented
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#102D4×C4711yescharacteristic, complemented
579#102D4×C4711yescharacteristic, complemented
580#102D4×C4711yescharacteristic, complemented
581#102D4×C4711yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C4712yes—
604#41#41×C4712yes—
605C2×Q8C2×D4×C4711yescharacteristic
606C2×Q8C2×D4×C4711yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
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—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C4712yes—
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—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C4711yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C4712yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C4711yescharacteristic
680C2×C8C2×D4×C4711yescharacteristic
681C2×C8C2×D4×C4711yescharacteristic
682C2×C8C2×D4×C4711yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C4711yescharacteristic
687C4⋊C4C2×D4×C4711yescharacteristic
688C4⋊C4C2×D4×C4711yescharacteristic
689C4⋊C4C2×D4×C4711yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C4711yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C4712yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C4712yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
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—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22C47×#53811yescharacteristic
811C22D42×C4711yescharacteristic
812C22C47×#54611yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C4711yescharacteristic
822C4C47×#52511yescharacteristic
823C4D42×C4711yescharacteristic
824C4C47×#54611yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C47×#242411yescharacteristic
833C2C47×#328811yescharacteristic
834C2C47×#329211yescharacteristic
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. C2×C47×#472C2semidirect
2. C47×#3041C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3008C2semidirect
5. C47×#2946C2semidirect
6. C47×#2897C2semidirect
7. C47×#2063C2semidirect
8. C47×#2051C2semidirect
9. C47×#2037C2semidirect
10. C47×#2011C2semidirect
11. C47×#1978C2semidirect
12. C47×#1929C2semidirect
13. C47×#1887C2semidirect
14. C47×#1883C2semidirect
15. C47×#1866C2semidirect
21. C22×D8×C47C22semidirect
26. C47×#518C22semidirect
41. C2×#108×C47C22semidirect
42. C2×#108×C47C22semidirect
43. C47×#428C22semidirect
44. C47×#424C22semidirect
50. C47×#418C22semidirect
58. C2×#102×C47C22semidirect
60. C2×#100×C47C22semidirect
61. C2×#100×C47C22semidirect
63. C47×#405C22semidirect
64. C47×#390C22semidirect
65. C47×#343C22semidirect
66. C47×#339C22semidirect
67. C47×#339C22semidirect
68. C47×#336C22semidirect
89. AGL(1,ℤ/8)×C47D4semidirect
145. #103×C47D4semidirect
146. #103×C47D4semidirect
147. #103×C47D4semidirect
148. #103×C47D4semidirect
160. #102×C47D4semidirect
161. #102×C47D4semidirect
162. #102×C47D4semidirect
163. #102×C47D4semidirect
368. #25180C47direct (N × H)
408. C2×#472C2×C47semidirect
409. #3041C2×C47semidirect
410. C2×#453C2×C47semidirect
411. #3008C2×C47semidirect
412. #2946C2×C47semidirect
413. #2897C2×C47semidirect
414. #2063C2×C47semidirect
415. #2051C2×C47semidirect
416. #2037C2×C47semidirect
417. #2011C2×C47semidirect
418. #1978C2×C47semidirect
419. #1929C2×C47semidirect
420. #1887C2×C47semidirect
421. #1883C2×C47semidirect
422. #1866C2×C47semidirect
438. C22×D8C22×C47semidirect
443. #518C22×C47semidirect
458. C2×#108C22×C47semidirect
459. C2×#108C22×C47semidirect
460. #428C22×C47semidirect
461. #424C22×C47semidirect
467. #418C22×C47semidirect
475. C2×#102C22×C47semidirect
477. C2×#100C22×C47semidirect
478. C2×#100C22×C47semidirect
480. #405C22×C47semidirect
481. #390C22×C47semidirect
482. #343C22×C47semidirect
483. #339C22×C47semidirect
484. #339C22×C47semidirect
485. #336C22×C47semidirect
486. C47#25180direct (N × H)
507. AGL(1,ℤ/8)D4×C47semidirect
563. #103D4×C47semidirect
564. #103D4×C47semidirect
565. #103D4×C47semidirect
566. #103D4×C47semidirect
578. #102D4×C47semidirect
579. #102D4×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
C2×C47×#4722
C47×#30412
C2×C47×#4532
C47×#30082
C47×#29462
C47×#28972
C47×#20632
C47×#20512
C47×#20372
C47×#20112
C47×#19782
C47×#19292
C47×#18872
C47×#18832
C47×#18662
#2518047