Finite Group Databasebeta

← C47×#24402 #26064100

Subgroups — C47×#24402 #26064100

Order 12032.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#575C211yesmaximal, characteristic, complemented
2C2×C47×#472C211yesmaximal, characteristic, complemented
3C2×C47×#471C211yesmaximal, characteristic, complemented
4C47×#3006C211yesmaximal, characteristic, complemented
5C2×C47×#449C211yesmaximal, characteristic, complemented
6C47×#2880C211yesmaximal, characteristic, complemented
7C47×#2052C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2019C211yesmaximal, characteristic, complemented
10C47×#2018C211yesmaximal, characteristic, complemented
11C47×#1908C211yesmaximal, characteristic, complemented
12C47×#1907C211yesmaximal, characteristic, complemented
13C47×#1900C211yesmaximal, characteristic, complemented
14C47×#1855C211yesmaximal, characteristic, complemented
15C47×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C47×#575—24no—
19C47×#575—24no—
20C2×#137×C47—21no—
21C2×#137×C47C2211yescharacteristic
22C2×#137×C47C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C47—21no—
24C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
28C2×#135×C47—21no—
29C2×#135×C47—21no—
30C22×SD16×C47C2211yescharacteristic, complemented
31C22×D8×C47C2211yescharacteristic, complemented
32C2×#131×C47C2211yescharacteristic
33C2×#131×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C2×#121×C47C2211yescharacteristic
36C47×#472—24no—
37C47×#471—24no—
38C47×#449—21no—
39C47×#449—21no—
40C47×#449—21no—
41C47×#449—21no—
42C47×#449—21no—
43C47×#449—21no—
44C47×#448—21no—
45C47×#447—21no—
46C2×#108×C47C2211yescharacteristic, complemented
47C2×#108×C47C2211yescharacteristic, complemented
48C47×#417C2211yescharacteristic
49C47×#417C2211yescharacteristic
50C2×#103×C47C2211yescharacteristic, complemented
51C2×#102×C47C2211yescharacteristic, complemented
52C2×#101×C47C2211yescharacteristic, complemented
53C2×#101×C47C2211yescharacteristic, complemented
54C2×#100×C47C2211yescharacteristic, complemented
55C2×#100×C47C2211yescharacteristic, complemented
56C2×#100×C47C2211yescharacteristic, complemented
57C2×#100×C47C2211yescharacteristic, complemented
58C47×#408—21no—
59C47×#408—21no—
60C47×#408C2211yescharacteristic
61C47×#408C2211yescharacteristic
62C47×#407—21no—
63C47×#407C2211yescharacteristic
64C47×#407C2211yescharacteristic
65C2×C22⋊C8×C47—21no—
66C2×C22⋊C8×C47C2211yescharacteristic
67C47×#343C2211yescharacteristic, complemented
68C47×#343C2211yescharacteristic, complemented
69C47×#341C2211yescharacteristic, complemented
70C47×#341C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—22no—
74C2×#41×C47—22no—
75C2×#41×C47—22no—
76C2×#41×C47—22no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—41no—
82C2×#41×C47—41no—
83C2×#41×C47—41no—
84C2×#41×C47—41no—
85C2×#41×C47D411yescharacteristic
86C2×#41×C47D411yescharacteristic
87C2×#41×C47C2311yescharacteristic
88C2×#41×C47C2311yescharacteristic
89C22×Q8×C47D411yescharacteristic
90C22×Q8×C47C2311yescharacteristic
91C22×D4×C47—21no—
92C22×D4×C47—21no—
93C22×D4×C47—21no—
94C22×D4×C47D411yescharacteristic
95C22×D4×C47C2311yescharacteristic
96C22×D4×C47C2311yescharacteristic
97C23×C4×C47—21no—
98C23×C4×C47—21no—
99C23×C4×C47C2311yescharacteristic
100#137×C47—28no—
101#137×C47—22no—
102#137×C47—22no—
103#137×C47—22no—
104#137×C47D414yescomplemented
105AGL(1,ℤ/8)×C47—28no—
106AGL(1,ℤ/8)×C47—22no—
107AGL(1,ℤ/8)×C47—22no—
108AGL(1,ℤ/8)×C47—22no—
109AGL(1,ℤ/8)×C47—22no—
110AGL(1,ℤ/8)×C47—22no—
111AGL(1,ℤ/8)×C47—41no—
112AGL(1,ℤ/8)×C47—41no—
113AGL(1,ℤ/8)×C47D414yescomplemented
114#135×C47—28no—
115#135×C47—28no—
116C2×Q16×C47—21no—
117C2×Q16×C47—21no—
118C2×SD16×C47—21no—
119C2×SD16×C47—21no—
120C2×SD16×C47—21no—
121C2×SD16×C47—21no—
122C2×SD16×C47—21no—
123C2×SD16×C47—21no—
124C2×SD16×C47—22no—
125C2×SD16×C47—21no—
126C2×SD16×C47—21no—
127C2×SD16×C47—41no—
128C2×D8×C47—21no—
129C2×D8×C47—21no—
130C2×D8×C47—21no—
131C2×D8×C47—21no—
132C2×D8×C47—22no—
133C2×D8×C47—21no—
134C2×D8×C47—21no—
135C2×D8×C47—41no—
136#131×C47—22no—
137#131×C47—22no—
138#131×C47—41no—
139#131×C47—41no—
140C2×M16×C47—21no—
141C2×M16×C47—22no—
142C2×M16×C47—22no—
143C2×M16×C47—21no—
144C2×M16×C47—21no—
145C2×M16×C47C2311yescharacteristic
146C2×M16×C47C2311yescharacteristic
147C2×M16×C47C2311yescharacteristic
148C2×M16×C47C2311yescharacteristic
149C2×M16×C47C2311yescharacteristic
150C2×M16×C47C2311yescharacteristic
151C22×C8×C47—21no—
152C22×C8×C47—21no—
153C22×C8×C47—21no—
154C22×C8×C47C2311yescharacteristic
155C22×C8×C47C2311yescharacteristic
156#121×C47—21no—
157#121×C47—21no—
158#121×C47—21no—
159#121×C47—21no—
160C2×C4⋊C4×C47C2311yescharacteristic
161C2×C22⋊C4×C47—21no—
162#108×C47—22no—
163#108×C47—22no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—21no—
172#101×C47—22no—
173#101×C47—41no—
174#100×C47—22no—
175#100×C47—22no—
176#100×C47—22no—
177#100×C47—41no—
178C22⋊C8×C47—21no—
179C22⋊C8×C47—21no—
180C22⋊C8×C47—21no—
181C22⋊C8×C47—21no—
182C22⋊C8×C47—21no—
183C22⋊C8×C47—21no—
184C22⋊C8×C47—21no—
185C22⋊C8×C47—21no—
186C22⋊C8×C47D411yescharacteristic
187C22⋊C8×C47D411yescharacteristic
188C22⋊C8×C47D411yescharacteristic
189C22⋊C8×C47D411yescharacteristic
190C24×C47—21no—
191C24×C47—21no—
192C24×C47—21no—
193C24×C47#4111yescharacteristic
194#41×C47—21no—
195#41×C47—21no—
196#41×C47—24no—
197#41×C47—24no—
198#41×C47—22no—
199#41×C47—22no—
200#41×C47—21no—
201#41×C47—21no—
202#41×C47—21no—
203#41×C47—21no—
204#41×C47—42no—
205#41×C47—42no—
206#41×C47—41no—
207#41×C47—41no—
208#41×C47—42no—
209#41×C47—42no—
210#41×C47—42no—
211#41×C47—42no—
212#41×C47—42no—
213#41×C47—42no—
214#41×C47—42no—
215#41×C47—42no—
216#41×C47C2×D412yes—
217#41×C47C2×D412yes—
218C2×Q8×C47—21no—
219C2×Q8×C47—21no—
220C2×Q8×C47—22no—
221C2×Q8×C47—21no—
222C2×Q8×C47—21no—
223C2×Q8×C47—21no—
224C2×Q8×C47—21no—
225C2×Q8×C47—41no—
226C2×Q8×C47C2×D411yescharacteristic
227C2×Q8×C47C2×D412yes—
228C2×Q8×C47C2×D411yescharacteristic
229C2×D4×C47—21no—
230C2×D4×C47—22no—
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—21no—
238C2×D4×C47—21no—
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—41no—
247C2×D4×C47—42no—
248C2×D4×C47—42no—
249C2×D4×C47—42no—
250C2×D4×C47—42no—
251C2×D4×C47—41no—
252C2×D4×C47—41no—
253C2×D4×C47—41no—
254C2×D4×C47—41no—
255C2×D4×C47—82no—
256C2×D4×C47C2×D411yescharacteristic
257C2×D4×C47C2×D412yes—
258C2×D4×C47C2×D411yescharacteristic
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—21no—
267C22×C4×C47—21no—
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—42no—
271C22×C4×C47—42no—
272C22×C4×C47—42no—
273C22×C4×C47—42no—
274C22×C4×C47—41no—
275C22×C4×C47—41no—
276C22×C4×C47C2×D411yescharacteristic
277C22×C4×C47C2×D411yescharacteristic
278C22×C4×C47C2×D411yescharacteristic
279C22×C4×C47C2×D411yescharacteristic
280C22×C4×C47#4111yescharacteristic
281C22×C4×C47C2411yescharacteristic
282Q16×C47—24no—
283Q16×C47—24no—
284SD16×C47—24no—
285SD16×C47—24no—
286SD16×C47—24no—
287SD16×C47—24no—
288SD16×C47—42no—
289SD16×C47—42no—
290SD16×C47—42no—
291SD16×C47—42no—
292D8×C47—24no—
293D8×C47—24no—
294D8×C47—42no—
295D8×C47—42no—
296D8×C47—42no—
297D8×C47—42no—
298M16×C47—24no—
299M16×C47—21no—
300M16×C47—21no—
301M16×C47—21no—
302M16×C47—21no—
303M16×C47—21no—
304M16×C47—21no—
305M16×C47—21no—
306M16×C47—21no—
307M16×C47—21no—
308M16×C47—21no—
309M16×C47—42no—
310M16×C47—42no—
311M16×C47C2×D412yes—
312M16×C47C2×D412yes—
313C2×C8×C47—24no—
314C2×C8×C47—21no—
315C2×C8×C47—21no—
316C2×C8×C47—21no—
317C2×C8×C47—21no—
318C2×C8×C47—21no—
319C2×C8×C47—21no—
320C2×C8×C47—21no—
321C2×C8×C47—21no—
322C2×C8×C47—21no—
323C2×C8×C47—21no—
324C2×C8×C47—42no—
325C2×C8×C47—42no—
326C2×C8×C47C2×D411yescharacteristic
327C2×C8×C47C2×D411yescharacteristic
328C2×C8×C47C2×D411yescharacteristic
329C2×C8×C47C2×D411yescharacteristic
330C4⋊C4×C47—21no—
331C4⋊C4×C47—21no—
332C22⋊C4×C47—41no—
333C22⋊C4×C47—41no—
334C23×C47—21no—
335C23×C47—21no—
336C23×C47—21no—
337C23×C47—21no—
338C23×C47—22no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—42no—
342C23×C47—42no—
343C23×C47—41no—
344C23×C47—41no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47—81no—
349C23×C47—81no—
350C23×C47—81no—
351C23×C47—81no—
352C23×C47—81no—
353C23×C47#12111yescharacteristic
354C23×C47#12111yescharacteristic
355C23×C47C2×#4111yescharacteristic
356Q8×C47—21no—
357Q8×C47—21no—
358Q8×C47—22no—
359Q8×C47—21no—
360Q8×C47—22no—
361Q8×C47—42no—
362Q8×C47—41no—
363Q8×C47—41no—
364Q8×C47#12012yes—
365D4×C47—22no—
366D4×C47—22no—
367D4×C47—21no—
368D4×C47—22no—
369D4×C47—21no—
370D4×C47—21no—
371D4×C47—22no—
372D4×C47—42no—
373D4×C47—42no—
374D4×C47—42no—
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—82no—
386D4×C47—82no—
387D4×C47#12012yes—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—21no—
398C2×C4×C47—21no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—21no—
402C2×C4×C47—22no—
403C2×C4×C47—42no—
404C2×C4×C47—42no—
405C2×C4×C47—42no—
406C2×C4×C47—44no—
407C2×C4×C47—44no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—81no—
414C2×C4×C47#12111yescharacteristic
415C2×C4×C47#12111yescharacteristic
416C2×C4×C47C22×D411yescharacteristic
417C2×C4×C47C22×D411yescharacteristic
418C2×C4×C47C22×D411yescharacteristic
419C2×C4×C47C22×D411yescharacteristic
420C2×C4×C47H(5,𝔽2)11yescharacteristic
421C2×C4×C47H(5,𝔽2)11yescharacteristic
422C8×C47—22no—
423C8×C47—22no—
424C8×C47—21no—
425C8×C47—21no—
426C8×C47—21no—
427C8×C47—21no—
428C8×C47—41no—
429C8×C47—41no—
430C8×C47—41no—
431C8×C47—41no—
432#24402C4711yesmaximal, characteristic, direct product factor, Sylow
433C22×C47—21no—
434C22×C47—21no—
435C22×C47—21no—
436C22×C47—21no—
437C22×C47—22no—
438C22×C47—21no—
439C22×C47—21no—
440C22×C47—21no—
441C22×C47—21no—
442C22×C47—41no—
443C22×C47—41no—
444C22×C47—41no—
445C22×C47—42no—
446C22×C47—41no—
447C22×C47—41no—
448C22×C47—81no—
449C22×C47—81no—
450C22×C47—82no—
451C22×C47—82no—
452C22×C47—84no—
453C22×C47—81no—
454C22×C47—81no—
455C22×C47—81no—
456C22×C47—81no—
457C22×C47—81no—
458C22×C47—161no—
459C22×C47—161no—
460C22×C47C2×#12111yescharacteristic
461C22×C47#54611yescharacteristic
462C22×C47#54611yescharacteristic
463C4×C47—21no—
464C4×C47—21no—
465C4×C47—22no—
466C4×C47—41no—
467C4×C47—42no—
468C4×C47—81no—
469C4×C47C2×#12011yescharacteristic
470C4×C47#53411yescharacteristic
471C4×C47D4211yescharacteristic
472C4×C47D4211yescharacteristic
473C2×#575C2×C4711yescharacteristic, complemented
474C2×#472C2×C4711yescharacteristic, complemented
475C2×#471C2×C4711yescharacteristic, complemented
476#3006C2×C4711yescharacteristic, complemented
477C2×#449C2×C4711yescharacteristic, complemented
478#2880C2×C4711yescharacteristic, complemented
479#2052C2×C4711yescharacteristic, complemented
480#2051C2×C4711yescharacteristic, complemented
481#2019C2×C4711yescharacteristic, complemented
482#2018C2×C4711yescharacteristic, complemented
483#1908C2×C4711yescharacteristic, complemented
484#1907C2×C4711yescharacteristic, complemented
485#1900C2×C4711yescharacteristic, complemented
486#1855C2×C4711yescharacteristic, complemented
487#1785C2×C4711yescharacteristic, complemented
488C2×C47—21no—
489C2×C47—21no—
490C2×C47—41no—
491C2×C47—41no—
492C2×C47—42no—
493C2×C47—81no—
494C2×C47—82no—
495C2×C47—161no—
496C2×C47#241011yescharacteristic
497C2×C47#306711yescharacteristic
498C2×C47#306811yescharacteristic
499C22×#41C22×C4711yescharacteristic
500C22×#41C22×C4711yescharacteristic
501#575—24no—
502#575—24no—
503C2×#137—21no—
504C2×#137C22×C4711yescharacteristic
505C2×#137C22×C4711yescharacteristic
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
508C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
509C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
510C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
511C2×#135—21no—
512C2×#135—21no—
513C22×SD16C22×C4711yescharacteristic, complemented
514C22×D8C22×C4711yescharacteristic, complemented
515C2×#131C22×C4711yescharacteristic
516C2×#131C22×C4711yescharacteristic
517C22×M16C22×C4711yescharacteristic
518C2×#121C22×C4711yescharacteristic
519#472—24no—
520#471—24no—
521#449—21no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#448—21no—
528#447—21no—
529C2×#108C22×C4711yescharacteristic, complemented
530C2×#108C22×C4711yescharacteristic, complemented
531#417C22×C4711yescharacteristic
532#417C22×C4711yescharacteristic
533C2×#103C22×C4711yescharacteristic, complemented
534C2×#102C22×C4711yescharacteristic, complemented
535C2×#101C22×C4711yescharacteristic, complemented
536C2×#101C22×C4711yescharacteristic, complemented
537C2×#100C22×C4711yescharacteristic, complemented
538C2×#100C22×C4711yescharacteristic, complemented
539C2×#100C22×C4711yescharacteristic, complemented
540C2×#100C22×C4711yescharacteristic, complemented
541#408—21no—
542#408—21no—
543#408C22×C4711yescharacteristic
544#408C22×C4711yescharacteristic
545#407—21no—
546#407C22×C4711yescharacteristic
547#407C22×C4711yescharacteristic
548C2×C22⋊C8—21no—
549C2×C22⋊C8C22×C4711yescharacteristic
550#343C22×C4711yescharacteristic, complemented
551#343C22×C4711yescharacteristic, complemented
552#341C22×C4711yescharacteristic, complemented
553#341C22×C4711yescharacteristic, complemented
554C47#2440211yescharacteristic, direct product factor, Sylow
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C4711yescharacteristic
570C2×#41D4×C4711yescharacteristic
571C2×#41C23×C4711yescharacteristic
572C2×#41C23×C4711yescharacteristic
573C22×Q8D4×C4711yescharacteristic
574C22×Q8C23×C4711yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C4711yescharacteristic
579C22×D4C23×C4711yescharacteristic
580C22×D4C23×C4711yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C4711yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C4714yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C4714yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C4711yescharacteristic
630C2×M16C23×C4711yescharacteristic
631C2×M16C23×C4711yescharacteristic
632C2×M16C23×C4711yescharacteristic
633C2×M16C23×C4711yescharacteristic
634C2×M16C23×C4711yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C4711yescharacteristic
639C22×C8C23×C4711yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C4711yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C4711yescharacteristic
671C22⋊C8D4×C4711yescharacteristic
672C22⋊C8D4×C4711yescharacteristic
673C22⋊C8D4×C4711yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C4711yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C4712yes—
701#41C2×D4×C4712yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C4712yes—
711C2×Q8C2×D4×C4711yescharacteristic
712C2×Q8C2×D4×C4711yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C4712yes—
741C2×D4C2×D4×C4711yescharacteristic
742C2×D4C2×D4×C4711yescharacteristic
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C4711yescharacteristic
761C22×C4C2×D4×C4711yescharacteristic
762C22×C4C2×D4×C4711yescharacteristic
763C22×C4C2×D4×C4711yescharacteristic
764C22×C4#41×C4711yescharacteristic
765C22×C4C24×C4711yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C4712yes—
796M16C2×D4×C4712yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C4711yescharacteristic
811C2×C8C2×D4×C4711yescharacteristic
812C2×C8C2×D4×C4711yescharacteristic
813C2×C8C2×D4×C4711yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C4711yescharacteristic
838C23#121×C4711yescharacteristic
839C23C2×#41×C4711yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C4712yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—22no—
853D4—21no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C4712yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C4711yescharacteristic
899C2×C4#121×C4711yescharacteristic
900C2×C4C22×D4×C4711yescharacteristic
901C2×C4C22×D4×C4711yescharacteristic
902C2×C4C22×D4×C4711yescharacteristic
903C2×C4C22×D4×C4711yescharacteristic
904C2×C4H(5,𝔽2)×C4711yescharacteristic
905C2×C4H(5,𝔽2)×C4711yescharacteristic
906C8—22no—
907C8—22no—
908C8—21no—
909C8—21no—
910C8—21no—
911C8—21no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C4711yescharacteristic
944C22C47×#54611yescharacteristic
945C22C47×#54611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—41no—
950C4—42no—
951C4—81no—
952C4C2×#120×C4711yescharacteristic
953C4C47×#53411yescharacteristic
954C4D42×C4711yescharacteristic
955C4D42×C4711yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C47×#241011yescharacteristic
965C2C47×#306711yescharacteristic
966C2C47×#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×#575C2semidirect
2. C2×C47×#472C2semidirect
3. C2×C47×#471C2semidirect
4. C47×#3006C2semidirect
5. C2×C47×#449C2semidirect
6. C47×#2880C2semidirect
7. C47×#2052C2semidirect
8. C47×#2051C2semidirect
9. C47×#2019C2semidirect
10. C47×#2018C2semidirect
11. C47×#1908C2semidirect
12. C47×#1907C2semidirect
13. C47×#1900C2semidirect
14. C47×#1855C2semidirect
15. C47×#1785C2semidirect
30. C22×SD16×C47C22semidirect
31. C22×D8×C47C22semidirect
46. C2×#108×C47C22semidirect
47. C2×#108×C47C22semidirect
50. C2×#103×C47C22semidirect
51. C2×#102×C47C22semidirect
52. C2×#101×C47C22semidirect
53. C2×#101×C47C22semidirect
54. C2×#100×C47C22semidirect
55. C2×#100×C47C22semidirect
56. C2×#100×C47C22semidirect
57. C2×#100×C47C22semidirect
67. C47×#343C22semidirect
68. C47×#343C22semidirect
69. C47×#341C22semidirect
70. C47×#341C22semidirect
104. #137×C47D4semidirect
113. AGL(1,ℤ/8)×C47D4semidirect
432. #24402C47direct (N × H)
473. C2×#575C2×C47semidirect
474. C2×#472C2×C47semidirect
475. C2×#471C2×C47semidirect
476. #3006C2×C47semidirect
477. C2×#449C2×C47semidirect
478. #2880C2×C47semidirect
479. #2052C2×C47semidirect
480. #2051C2×C47semidirect
481. #2019C2×C47semidirect
482. #2018C2×C47semidirect
483. #1908C2×C47semidirect
484. #1907C2×C47semidirect
485. #1900C2×C47semidirect
486. #1855C2×C47semidirect
487. #1785C2×C47semidirect
513. C22×SD16C22×C47semidirect
514. C22×D8C22×C47semidirect
529. C2×#108C22×C47semidirect
530. C2×#108C22×C47semidirect
533. C2×#103C22×C47semidirect
534. C2×#102C22×C47semidirect
535. C2×#101C22×C47semidirect
536. C2×#101C22×C47semidirect
537. C2×#100C22×C47semidirect
538. C2×#100C22×C47semidirect
539. C2×#100C22×C47semidirect
540. C2×#100C22×C47semidirect
550. #343C22×C47semidirect
551. #343C22×C47semidirect
552. #341C22×C47semidirect
553. #341C22×C47semidirect
554. C47#24402direct (N × H)
588. #137D4×C47semidirect
597. AGL(1,ℤ/8)D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5752
C2×C47×#4722
C2×C47×#4712
C47×#30062
C2×C47×#4492
C47×#28802
C47×#20522
C47×#20512
C47×#20192
C47×#20182
C47×#19082
C47×#19072
C47×#19002
C47×#18552
C47×#17852
#2440247