Finite Group Databasebeta

← C47×#25140 #26064838

Subgroups — C47×#25140 #26064838

Order 12032.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#472C211yesmaximal, characteristic, complemented
2C47×#3055C211yesmaximal, characteristic, complemented
3C47×#3003C211yesmaximal, characteristic, complemented
4C2×C47×#447C211yesmaximal, characteristic, complemented
5C47×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C47C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2045C211yesmaximal, characteristic, complemented
10C47×#2018C211yesmaximal, characteristic, complemented
11C47×#1978C211yesmaximal, characteristic, complemented
12C47×#1931C211yesmaximal, characteristic, complemented
13C47×#1907C211yesmaximal, characteristic, complemented
14C47×#1900C211yesmaximal, characteristic, complemented
15C47×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
20C22×D8×C47C2211yescharacteristic
21C22×D8×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic, complemented
23C22×M16×C47C2211yescharacteristic
24C22×M16×C47C2211yescharacteristic
25C47×#525C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C47×#472—24no—
28C47×#469—21no—
29C47×#468—21no—
30C47×#466—21no—
31C47×#465—21no—
32C47×#450—21no—
33C47×#450—21no—
34C47×#447—21no—
35C47×#447—21no—
36C47×#447—21no—
37C47×#447—21no—
38C47×#447—21no—
39C47×#447—21no—
40C47×#436—21no—
41C47×#435—21no—
42C47×#435—21no—
43C8×D4×C47—21no—
44C2×#108×C47C2211yescharacteristic, complemented
45C2×#108×C47C2211yescharacteristic, complemented
46C47×#428C2211yescharacteristic, complemented
47C47×#424C2211yescharacteristic, complemented
48C47×#418C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C47×#418C2211yescharacteristic, complemented
51C47×#417C2211yescharacteristic, complemented
52C2×#102×C47C2211yescharacteristic
53C2×#102×C47C2211yescharacteristic
54C2×#100×C47—24no—
55C2×#100×C47C2211yescharacteristic
56C2×#100×C47C2211yescharacteristic
57C2×#100×C47C2211yescharacteristic
58C2×#100×C47C2211yescharacteristic
59C2×#100×C47C2211yescharacteristic, complemented
60C2×#100×C47C2211yescharacteristic, complemented
61C47×#408C2211yescharacteristic, complemented
62C47×#407C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C47×#405C2211yescharacteristic, complemented
65C47×#343C2211yescharacteristic, complemented
66C47×#343C2211yescharacteristic, complemented
67C47×#341C2211yescharacteristic, complemented
68C47×#341C2211yescharacteristic, complemented
69C25×C47—21no—
70C2×#41×C47C2311yescharacteristic
71C22×D4×C47—22no—
72C22×D4×C47—22no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
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
84C23×C4×C47C2311yescharacteristic
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—
90AGL(1,ℤ/8)×C47—41no—
91C2×SD16×C47—21no—
92C2×SD16×C47—21no—
93C2×SD16×C47—21no—
94C2×D8×C47—21no—
95C2×D8×C47—22no—
96C2×D8×C47—21no—
97C2×D8×C47—21no—
98C2×D8×C47—22no—
99C2×D8×C47—21no—
100C2×D8×C47—21no—
101C2×D8×C47—21no—
102C2×D8×C47—21no—
103C2×D8×C47—41no—
104C2×D8×C47—41no—
105#131×C47—22no—
106#131×C47—41no—
107C2×M16×C47—21no—
108C2×M16×C47—21no—
109C2×M16×C47—21no—
110C2×M16×C47—22no—
111C2×M16×C47—22no—
112C2×M16×C47—41no—
113C2×M16×C47—41no—
114C2×M16×C47C2311yescharacteristic
115C2×M16×C47C2311yescharacteristic
116C2×M16×C47C2311yescharacteristic
117C2×M16×C47C2311yescharacteristic
118C2×M16×C47C2311yescharacteristic
119C2×M16×C47C2311yescharacteristic
120C22×C8×C47—21no—
121C22×C8×C47—21no—
122C22×C8×C47—21no—
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125#123×C47—21no—
126C22⋊Q8×C47D411yescharacteristic
127C22⋊Q8×C47D411yescharacteristic
128#121×C47—21no—
129#121×C47—21no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47D411yescharacteristic
133#121×C47D411yescharacteristic
134#120×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137#117×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—21no—
140#108×C47—22no—
141#108×C47—41no—
142#107×C47—21no—
143#106×C47—21no—
144C4⋊C8×C47—21no—
145C4⋊C8×C47—21no—
146#103×C47—21no—
147#102×C47—21no—
148#102×C47—21no—
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#100×C47—22no—
159#100×C47—22no—
160#100×C47—22no—
161#100×C47—22no—
162#100×C47—41no—
163#100×C47D414yescomplemented
164C22⋊C8×C47—21no—
165C22⋊C8×C47—21no—
166C22⋊C8×C47—21no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170C22⋊C8×C47D411yescharacteristic
171C22⋊C8×C47D411yescharacteristic
172#97×C47—21no—
173C4×C8×C47—21no—
174C24×C47—24no—
175C24×C47—21no—
176C24×C47—21no—
177C24×C47—21no—
178C24×C47—42no—
179C24×C47—41no—
180C24×C47—41no—
181C24×C47—82no—
182C24×C47—82no—
183C24×C47#4111yescharacteristic
184#41×C47—21no—
185#41×C47—21no—
186#41×C47—21no—
187#41×C47—21no—
188C2×Q8×C47C2×D411yescharacteristic
189C2×D4×C47—24no—
190C2×D4×C47—21no—
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—21no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—42no—
215C2×D4×C47—42no—
216C2×D4×C47—42no—
217C2×D4×C47—42no—
218C2×D4×C47—41no—
219C2×D4×C47—41no—
220C2×D4×C47—41no—
221C2×D4×C47—41no—
222C2×D4×C47—82no—
223C2×D4×C47C2×D411yescharacteristic
224C2×D4×C47C2×D412yes—
225C2×D4×C47#4112yes—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47#4111yescharacteristic
237C22×C4×C47C2411yescharacteristic
238SD16×C47—42no—
239SD16×C47—42no—
240SD16×C47—42no—
241D8×C47—42no—
242D8×C47—42no—
243D8×C47—42no—
244D8×C47—42no—
245D8×C47—42no—
246D8×C47—42no—
247D8×C47—42no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—21no—
252M16×C47—21no—
253M16×C47—21no—
254M16×C47—21no—
255M16×C47—21no—
256M16×C47—21no—
257M16×C47—21no—
258M16×C47—42no—
259M16×C47—42no—
260M16×C47—42no—
261M16×C47C2×D412yes—
262M16×C47C2×D412yes—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—21no—
266C2×C8×C47—21no—
267C2×C8×C47—21no—
268C2×C8×C47—21no—
269C2×C8×C47—21no—
270C2×C8×C47—21no—
271C2×C8×C47—21no—
272C2×C8×C47—21no—
273C2×C8×C47—42no—
274C2×C8×C47—42no—
275C2×C8×C47—42no—
276C2×C8×C47C2×D411yescharacteristic
277C2×C8×C47C2×D411yescharacteristic
278C2×C8×C47C2×D411yescharacteristic
279C2×C8×C47C2×D411yescharacteristic
280C4⋊C4×C47—21no—
281C4⋊C4×C47—21no—
282C4⋊C4×C47—21no—
283C4⋊C4×C47—21no—
284C4⋊C4×C47C2×D411yescharacteristic
285C4⋊C4×C47C2×D411yescharacteristic
286C22⋊C4×C47—21no—
287C22⋊C4×C47—21no—
288C22⋊C4×C47—21no—
289C22⋊C4×C47—21no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—41no—
292C22⋊C4×C47—41no—
293C42×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—22no—
297C23×C47—21no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—41no—
301C23×C47—44no—
302C23×C47—44no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—81no—
311C23×C47—81no—
312C23×C47—81no—
313C23×C47—81no—
314C23×C47—82no—
315C23×C47—82no—
316C23×C47—82no—
317C23×C47—81no—
318C23×C47—81no—
319C23×C47—88no—
320C23×C47—88no—
321C23×C47—82no—
322C23×C47#12111yescharacteristic
323C23×C47#12111yescharacteristic
324C23×C47C2×#4111yescharacteristic
325Q8×C47—21no—
326Q8×C47—21no—
327D4×C47—21no—
328D4×C47—22no—
329D4×C47—22no—
330D4×C47—22no—
331D4×C47—21no—
332D4×C47—22no—
333D4×C47—44no—
334D4×C47—44no—
335D4×C47—41no—
336D4×C47—41no—
337D4×C47—42no—
338D4×C47—41no—
339D4×C47—41no—
340D4×C47—41no—
341D4×C47—41no—
342D4×C47—41no—
343D4×C47—41no—
344D4×C47—41no—
345D4×C47—41no—
346D4×C47—81no—
347D4×C47—82no—
348D4×C47—82no—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—21no—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—81no—
366C2×C4×C47#12111yescharacteristic
367C2×C4×C47#12111yescharacteristic
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C22×D411yescharacteristic
371C2×C4×C47C2×#4111yescharacteristic
372C2×C4×C47H(5,𝔽2)11yescharacteristic
373C2×C4×C47H(5,𝔽2)11yescharacteristic
374C8×C47—21no—
375C8×C47—21no—
376C8×C47—22no—
377C8×C47—22no—
378C8×C47—21no—
379C8×C47—21no—
380C8×C47—41no—
381C8×C47—41no—
382C8×C47—41no—
383C8×C47—41no—
384#25140C4711yesmaximal, characteristic, direct product factor, Sylow
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—41no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—82no—
400C22×C47—82no—
401C22×C47—88no—
402C22×C47—82no—
403C22×C47—82no—
404C22×C47—88no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—161no—
413C22×C47—161no—
414C22×C47#47212yescomplemented
415C22×C47C2×#12111yescharacteristic
416C22×C47#52511yescharacteristic
417C22×C47#53811yescharacteristic
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—41no—
421C4×C47—41no—
422C4×C47—41no—
423C4×C47—81no—
424C4×C47D4211yescharacteristic
425C4×C47D4211yescharacteristic
426C4×C47#54611yescharacteristic
427C4×C47#54611yescharacteristic
428C2×#472C2×C4711yescharacteristic, complemented
429#3055C2×C4711yescharacteristic, complemented
430#3003C2×C4711yescharacteristic, complemented
431C2×#447C2×C4711yescharacteristic, complemented
432#2933C2×C4711yescharacteristic, complemented
433C22×#100C2×C4711yescharacteristic, complemented
434#2063C2×C4711yescharacteristic, complemented
435#2051C2×C4711yescharacteristic, complemented
436#2045C2×C4711yescharacteristic, complemented
437#2018C2×C4711yescharacteristic, complemented
438#1978C2×C4711yescharacteristic, complemented
439#1931C2×C4711yescharacteristic, complemented
440#1907C2×C4711yescharacteristic, complemented
441#1900C2×C4711yescharacteristic, complemented
442#1855C2×C4711yescharacteristic, complemented
443C2×C47—21no—
444C2×C47—21no—
445C2×C47—22no—
446C2×C47—41no—
447C2×C47—81no—
448C2×C47—82no—
449C2×C47—82no—
450C2×C47—161no—
451C2×C47#242411yescharacteristic
452C2×C47C2×#47211yescharacteristic
453C2×C47#306811yescharacteristic
454C23×D4C22×C4711yescharacteristic
455C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
456C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
457C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
458C22×D8C22×C4711yescharacteristic
459C22×D8C22×C4711yescharacteristic
460C2×#131C22×C4711yescharacteristic, complemented
461C22×M16C22×C4711yescharacteristic
462C22×M16C22×C4711yescharacteristic
463#525C22×C4711yescharacteristic
464C2×#121C22×C4711yescharacteristic
465#472—24no—
466#469—21no—
467#468—21no—
468#466—21no—
469#465—21no—
470#450—21no—
471#450—21no—
472#447—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#436—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482C2×#108C22×C4711yescharacteristic, complemented
483C2×#108C22×C4711yescharacteristic, complemented
484#428C22×C4711yescharacteristic, complemented
485#424C22×C4711yescharacteristic, complemented
486#418C22×C4711yescharacteristic
487#418C22×C4711yescharacteristic
488#418C22×C4711yescharacteristic, complemented
489#417C22×C4711yescharacteristic, complemented
490C2×#102C22×C4711yescharacteristic
491C2×#102C22×C4711yescharacteristic
492C2×#100—24no—
493C2×#100C22×C4711yescharacteristic
494C2×#100C22×C4711yescharacteristic
495C2×#100C22×C4711yescharacteristic
496C2×#100C22×C4711yescharacteristic
497C2×#100C22×C4711yescharacteristic, complemented
498C2×#100C22×C4711yescharacteristic, complemented
499#408C22×C4711yescharacteristic, complemented
500#407C22×C4711yescharacteristic
501C2×C22⋊C8C22×C4711yescharacteristic
502#405C22×C4711yescharacteristic, complemented
503#343C22×C4711yescharacteristic, complemented
504#343C22×C4711yescharacteristic, complemented
505#341C22×C4711yescharacteristic, complemented
506#341C22×C4711yescharacteristic, complemented
507C47#2514011yescharacteristic, direct product factor, Sylow
508C25—21no—
509C2×#41C23×C4711yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C4711yescharacteristic
521C22×D4C23×C4711yescharacteristic
522C22×D4C23×C4711yescharacteristic
523C23×C4C23×C4711yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C4711yescharacteristic
554C2×M16C23×C4711yescharacteristic
555C2×M16C23×C4711yescharacteristic
556C2×M16C23×C4711yescharacteristic
557C2×M16C23×C4711yescharacteristic
558C2×M16C23×C4711yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C4711yescharacteristic
563C22×C8C23×C4711yescharacteristic
564#123—21no—
565C22⋊Q8D4×C4711yescharacteristic
566C22⋊Q8D4×C4711yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C4711yescharacteristic
572#121D4×C4711yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C4711yescharacteristic
577C2×C4⋊C4C23×C4711yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C4714yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C4711yescharacteristic
608C22⋊C8D4×C4711yescharacteristic
609C22⋊C8D4×C4711yescharacteristic
610C22⋊C8D4×C4711yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C4711yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C4711yescharacteristic
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C4712yes—
663C2×D4C2×D4×C4711yescharacteristic
664C2×D4#41×C4712yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C4711yescharacteristic
672C22×C4C2×D4×C4711yescharacteristic
673C22×C4C2×D4×C4711yescharacteristic
674C22×C4C2×D4×C4711yescharacteristic
675C22×C4#41×C4711yescharacteristic
676C22×C4C24×C4711yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C4712yes—
701M16C2×D4×C4712yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C4711yescharacteristic
716C2×C8C2×D4×C4711yescharacteristic
717C2×C8C2×D4×C4711yescharacteristic
718C2×C8C2×D4×C4711yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C4711yescharacteristic
724C4⋊C4C2×D4×C4711yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C4711yescharacteristic
762C23#121×C4711yescharacteristic
763C23C2×#41×C4711yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—42no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C4711yescharacteristic
806C2×C4#121×C4711yescharacteristic
807C2×C4C22×D4×C4711yescharacteristic
808C2×C4C22×D4×C4711yescharacteristic
809C2×C4C22×D4×C4711yescharacteristic
810C2×C4C2×#41×C4711yescharacteristic
811C2×C4H(5,𝔽2)×C4711yescharacteristic
812C2×C4H(5,𝔽2)×C4711yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22C47×#47212yescomplemented
853C22C2×#121×C4711yescharacteristic
854C22C47×#52511yescharacteristic
855C22C47×#53811yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C4711yescharacteristic
863C4D42×C4711yescharacteristic
864C4C47×#54611yescharacteristic
865C4C47×#54611yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2C47×#242411yescharacteristic
875C2C2×C47×#47211yescharacteristic
876C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#472C2semidirect
2. C47×#3055C2semidirect
3. C47×#3003C2semidirect
4. C2×C47×#447C2semidirect
5. C47×#2933C2semidirect
6. C22×#100×C47C2semidirect
7. C47×#2063C2semidirect
8. C47×#2051C2semidirect
9. C47×#2045C2semidirect
10. C47×#2018C2semidirect
11. C47×#1978C2semidirect
12. C47×#1931C2semidirect
13. C47×#1907C2semidirect
14. C47×#1900C2semidirect
15. C47×#1855C2semidirect
19. C2×AGL(1,ℤ/8)×C47C22semidirect
22. C2×#131×C47C22semidirect
44. C2×#108×C47C22semidirect
45. C2×#108×C47C22semidirect
46. C47×#428C22semidirect
47. C47×#424C22semidirect
50. C47×#418C22semidirect
51. C47×#417C22semidirect
59. C2×#100×C47C22semidirect
60. C2×#100×C47C22semidirect
61. C47×#408C22semidirect
64. C47×#405C22semidirect
65. C47×#343C22semidirect
66. C47×#343C22semidirect
67. C47×#341C22semidirect
68. C47×#341C22semidirect
163. #100×C47D4semidirect
384. #25140C47direct (N × H)
414. C22×C47#472semidirect
428. C2×#472C2×C47semidirect
429. #3055C2×C47semidirect
430. #3003C2×C47semidirect
431. C2×#447C2×C47semidirect
432. #2933C2×C47semidirect
433. C22×#100C2×C47semidirect
434. #2063C2×C47semidirect
435. #2051C2×C47semidirect
436. #2045C2×C47semidirect
437. #2018C2×C47semidirect
438. #1978C2×C47semidirect
439. #1931C2×C47semidirect
440. #1907C2×C47semidirect
441. #1900C2×C47semidirect
442. #1855C2×C47semidirect
457. C2×AGL(1,ℤ/8)C22×C47semidirect
460. C2×#131C22×C47semidirect
482. C2×#108C22×C47semidirect
483. C2×#108C22×C47semidirect
484. #428C22×C47semidirect
485. #424C22×C47semidirect
488. #418C22×C47semidirect
489. #417C22×C47semidirect
497. C2×#100C22×C47semidirect
498. C2×#100C22×C47semidirect
499. #408C22×C47semidirect
502. #405C22×C47semidirect
503. #343C22×C47semidirect
504. #343C22×C47semidirect
505. #341C22×C47semidirect
506. #341C22×C47semidirect
507. C47#25140direct (N × H)
602. #100D4×C47semidirect
852. C22C47×#472semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4722
C47×#30552
C47×#30032
C2×C47×#4472
C47×#29332
C22×#100×C472
C47×#20632
C47×#20512
C47×#20452
C47×#20182
C47×#19782
C47×#19312
C47×#19072
C47×#19002
C47×#18552
#2514047