Finite Group Databasebeta

← C47×#25181 #26064879

Subgroups — C47×#25181 #26064879

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#471C211yesmaximal, characteristic, complemented
2C47×#3043C211yesmaximal, characteristic, complemented
3C2×C47×#456C211yesmaximal, characteristic, complemented
4C47×#3010C211yesmaximal, characteristic
5C47×#2947C211yesmaximal, characteristic, complemented
6C47×#2898C211yesmaximal, characteristic, complemented
7C47×#2064C211yesmaximal, characteristic, complemented
8C47×#2052C211yesmaximal, characteristic, complemented
9C47×#2037C211yesmaximal, characteristic, complemented
10C47×#2013C211yesmaximal, characteristic, complemented
11C47×#1977C211yesmaximal, characteristic, complemented
12C47×#1929C211yesmaximal, characteristic, complemented
13C47×#1886C211yesmaximal, characteristic, complemented
14C47×#1883C211yesmaximal, characteristic, complemented
15C47×#1866C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C22×SD16×C47C2211yescharacteristic
21C22×SD16×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C47×#535C2211yescharacteristic
24C2×C4⋊Q8×C47C2211yescharacteristic
25C47×#520C2211yescharacteristic
26C47×#519C2211yescharacteristic
27C47×#471—24no—
28C47×#464—21no—
29C47×#464—21no—
30C47×#460—21no—
31C47×#460—21no—
32C47×#456—24no—
33C47×#449—21no—
34C47×#449—21no—
35C47×#448—21no—
36C47×#448—21no—
37C47×#441—21no—
38C47×#440—21no—
39C4×Q16×C47—21no—
40C4×SD16×C47—21no—
41C2×#108×C47C2211yescharacteristic
42C2×#108×C47C2211yescharacteristic
43C47×#428C2211yescharacteristic
44C47×#424C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic
47C47×#419—21no—
48C47×#419C2211yescharacteristic
49C47×#419C2211yescharacteristic
50C47×#418C2211yescharacteristic
51C47×#417—21no—
52C47×#417C2211yescharacteristic
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C47×#416C2211yescharacteristic
56C2×#103×C47—21no—
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×#101×C47C2211yescharacteristic
60C2×#101×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C47×#405C2211yescharacteristic
64C47×#390C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C47×#339C2211yescharacteristic
68C47×#336C2211yescharacteristic
692−1+4×C47—22no—
702−1+4×C47—22no—
712−1+4×C47—22no—
722−1+4×C47—41no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—41no—
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C22×Q8×C47—21no—
79C22×Q8×C47—21no—
80C22×Q8×C47C2311yescharacteristic
81C22×Q8×C47C2311yescharacteristic
82C22×D4×C47C2311yescharacteristic
83#137×C47—22no—
84#137×C47—22no—
85#137×C47—41no—
86#137×C47D414yescomplemented
87AGL(1,ℤ/8)×C47—22no—
88AGL(1,ℤ/8)×C47—22no—
89C2×Q16×C47—21no—
90C2×Q16×C47—21no—
91C2×SD16×C47—21no—
92C2×SD16×C47—22no—
93C2×SD16×C47—21no—
94C2×SD16×C47—22no—
95C2×SD16×C47—21no—
96C2×SD16×C47—21no—
97C2×SD16×C47—21no—
98C2×SD16×C47—21no—
99C2×SD16×C47—21no—
100C2×SD16×C47—41no—
101C2×SD16×C47—41no—
102C2×D8×C47—21no—
103#131×C47—22no—
104#131×C47—41no—
105C2×M16×C47—21no—
106C2×M16×C47C2311yescharacteristic
107C2×M16×C47C2311yescharacteristic
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C22×C8×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C4⋊Q8×C47—22no—
114C4⋊Q8×C47—22no—
115#127×C47—21no—
116#124×C47—21no—
117#121×C47—21no—
118#121×C47—21no—
119#120×C47—41no—
120C4×Q8×C47—21no—
121C4×Q8×C47—21no—
122C4×Q8×C47—21no—
123C4×Q8×C47—21no—
124C4×Q8×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—41no—
127#117×C47—21no—
128#117×C47—41no—
129#117×C47C2311yescharacteristic
130#117×C47C2311yescharacteristic
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—41no—
133C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
146#103×C47—21no—
147#103×C47—21no—
148#103×C47—21no—
149#103×C47—21no—
150#103×C47—21no—
151#103×C47—21no—
152#103×C47—21no—
153#103×C47D411yescharacteristic
154#103×C47D411yescharacteristic
155#103×C47D411yescharacteristic
156#103×C47D411yescharacteristic
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#102×C47D411yescharacteristic
161#102×C47D411yescharacteristic
162#102×C47D411yescharacteristic
163#102×C47D411yescharacteristic
164#101×C47—22no—
165#101×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—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—24no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—42no—
180#41×C47—44no—
181#41×C47—42no—
182#41×C47—44no—
183#41×C47—42no—
184#41×C47C2×D412yes—
185#41×C47#4112yes—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—24no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—21no—
194C2×Q8×C47—21no—
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—41no—
198C2×Q8×C47—42no—
199C2×Q8×C47—42no—
200C2×Q8×C47—42no—
201C2×Q8×C47C2×D411yescharacteristic
202C2×Q8×C47C2×D412yes—
203C2×Q8×C47C2×D411yescharacteristic
204C2×Q8×C47#4112yes—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—21no—
212C2×D4×C47—21no—
213C2×D4×C47—41no—
214C2×D4×C47—41no—
215C2×D4×C47—41no—
216C2×D4×C47C2×D411yescharacteristic
217C2×D4×C47C2×D411yescharacteristic
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—41no—
225C22×C4×C47—41no—
226C22×C4×C47—41no—
227C22×C4×C47C2411yescharacteristic
228Q16×C47—24no—
229Q16×C47—42no—
230SD16×C47—24no—
231SD16×C47—42no—
232SD16×C47—42no—
233SD16×C47—42no—
234SD16×C47—42no—
235SD16×C47—42no—
236SD16×C47—42no—
237D8×C47—42no—
238M16×C47—21no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47—21no—
245M16×C47—42no—
246M16×C47C2×D412yes—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—42no—
256C2×C8×C47C2×D411yescharacteristic
257C2×C8×C47C2×D411yescharacteristic
258C2×C8×C47C2×D411yescharacteristic
259C2×C8×C47C2×D411yescharacteristic
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—41no—
263C4⋊C4×C47—44no—
264C4⋊C4×C47—41no—
265C4⋊C4×C47—41no—
266C4⋊C4×C47C2×D411yescharacteristic
267C4⋊C4×C47C2×D411yescharacteristic
268C4⋊C4×C47C2×D411yescharacteristic
269C4⋊C4×C47C2×D411yescharacteristic
270C22⋊C4×C47—21no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—41no—
273C22⋊C4×C47—41no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—82no—
276C42×C47—21no—
277C42×C47—21no—
278C42×C47—21no—
279C42×C47—21no—
280C42×C47—41no—
281C42×C47—41no—
282C42×C47—41no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—81no—
289C23×C47—81no—
290C23×C47H(5,𝔽2)11yescharacteristic
291Q8×C47—21no—
292Q8×C47—22no—
293Q8×C47—21no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—21no—
297Q8×C47—22no—
298Q8×C47—44no—
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47—41no—
302Q8×C47—41no—
303Q8×C47#12112yes—
304D4×C47—22no—
305D4×C47—22no—
306D4×C47—21no—
307D4×C47—21no—
308D4×C47—21no—
309D4×C47—44no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—161no—
317D4×C47—161no—
318D4×C47#12112yes—
319C2×C4×C47—21no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—44no—
331C2×C4×C47—41no—
332C2×C4×C47—44no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—81no—
342C2×C4×C47—161no—
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C2×#4111yescharacteristic
347C2×C4×C47C2×#4111yescharacteristic
348C2×C4×C47H(5,𝔽2)11yescharacteristic
349C8×C47—22no—
350C8×C47—21no—
351C8×C47—21no—
352C8×C47—21no—
353C8×C47—21no—
354C8×C47—41no—
355C8×C47—41no—
356C8×C47—41no—
357#25181C4711yesmaximal, characteristic, direct product factor, Sylow
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—22no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—82no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47—161no—
371C22×C47#53811yescharacteristic
372C22×C47D4211yescharacteristic
373C22×C47#54611yescharacteristic
374C4×C47—22no—
375C4×C47—42no—
376C4×C47—41no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—81no—
384C4×C47C2×#12111yescharacteristic
385C4×C47#52511yescharacteristic
386C4×C47D4211yescharacteristic
387C4×C47#54611yescharacteristic
388C2×#471C2×C4711yescharacteristic, complemented
389#3043C2×C4711yescharacteristic, complemented
390C2×#456C2×C4711yescharacteristic, complemented
391#3010C2×C4711yescharacteristic
392#2947C2×C4711yescharacteristic, complemented
393#2898C2×C4711yescharacteristic, complemented
394#2064C2×C4711yescharacteristic, complemented
395#2052C2×C4711yescharacteristic, complemented
396#2037C2×C4711yescharacteristic, complemented
397#2013C2×C4711yescharacteristic, complemented
398#1977C2×C4711yescharacteristic, complemented
399#1929C2×C4711yescharacteristic, complemented
400#1886C2×C4711yescharacteristic, complemented
401#1883C2×C4711yescharacteristic, complemented
402#1866C2×C4711yescharacteristic, complemented
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—42no—
406C2×C47—81no—
407C2×C47—161no—
408C2×C47#242411yescharacteristic
409C2×C47#328911yescharacteristic
410C2×C47#329111yescharacteristic
411C2×2−1+4C22×C4711yescharacteristic
412C2×#137C22×C4711yescharacteristic
413C2×#137C22×C4711yescharacteristic
414C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
415C22×SD16C22×C4711yescharacteristic
416C22×SD16C22×C4711yescharacteristic
417C2×#131C22×C4711yescharacteristic
418#535C22×C4711yescharacteristic
419C2×C4⋊Q8C22×C4711yescharacteristic
420#520C22×C4711yescharacteristic
421#519C22×C4711yescharacteristic
422#471—24no—
423#464—21no—
424#464—21no—
425#460—21no—
426#460—21no—
427#456—24no—
428#449—21no—
429#449—21no—
430#448—21no—
431#448—21no—
432#441—21no—
433#440—21no—
434C4×Q16—21no—
435C4×SD16—21no—
436C2×#108C22×C4711yescharacteristic
437C2×#108C22×C4711yescharacteristic
438#428C22×C4711yescharacteristic
439#424C22×C4711yescharacteristic
440C2×#104C22×C4711yescharacteristic
441C2×#104C22×C4711yescharacteristic
442#419—21no—
443#419C22×C4711yescharacteristic
444#419C22×C4711yescharacteristic
445#418C22×C4711yescharacteristic
446#417—21no—
447#417C22×C4711yescharacteristic
448#416—21no—
449#416C22×C4711yescharacteristic
450#416C22×C4711yescharacteristic
451C2×#103—21no—
452C2×#103C22×C4711yescharacteristic
453C2×#103C22×C4711yescharacteristic
454C2×#101C22×C4711yescharacteristic
455C2×#101C22×C4711yescharacteristic
456C2×#100C22×C4711yescharacteristic
457#408C22×C4711yescharacteristic
458#405C22×C4711yescharacteristic
459#390C22×C4711yescharacteristic
460#343C22×C4711yescharacteristic
461#339C22×C4711yescharacteristic
462#339C22×C4711yescharacteristic
463#336C22×C4711yescharacteristic
464C47#2518111yescharacteristic, direct product factor, Sylow
4652−1+4—22no—
4662−1+4—22no—
4672−1+4—22no—
4682−1+4—41no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—41no—
472C2×#41C23×C4711yescharacteristic
473C2×#41C23×C4711yescharacteristic
474C22×Q8—21no—
475C22×Q8—21no—
476C22×Q8C23×C4711yescharacteristic
477C22×Q8C23×C4711yescharacteristic
478C22×D4C23×C4711yescharacteristic
479#137—22no—
480#137—22no—
481#137—41no—
482#137D4×C4714yescomplemented
483AGL(1,ℤ/8)—22no—
484AGL(1,ℤ/8)—22no—
485C2×Q16—21no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—22no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—41no—
497C2×SD16—41no—
498C2×D8—21no—
499#131—22no—
500#131—41no—
501C2×M16—21no—
502C2×M16C23×C4711yescharacteristic
503C2×M16C23×C4711yescharacteristic
504C2×M16C23×C4711yescharacteristic
505C2×M16C23×C4711yescharacteristic
506C22×C8—21no—
507C22×C8C23×C4711yescharacteristic
508C22×C8C23×C4711yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511#127—21no—
512#124—21no—
513#121—21no—
514#121—21no—
515#120—41no—
516C4×Q8—21no—
517C4×Q8—21no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×D4—21no—
522C4×D4—41no—
523#117—21no—
524#117—41no—
525#117C23×C4711yescharacteristic
526#117C23×C4711yescharacteristic
527C2×C4⋊C4—21no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C23×C4711yescharacteristic
530C2×C22⋊C4—41no—
531C2×C42C23×C4711yescharacteristic
532#108—22no—
533#108—41no—
534#107—21no—
535#106—21no—
536C4⋊C8—21no—
537C4⋊C8—21no—
538#104—22no—
539#104—22no—
540#103—21no—
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#103—21no—
546#103—21no—
547#103—21no—
548#103—21no—
549#103D4×C4711yescharacteristic
550#103D4×C4711yescharacteristic
551#103D4×C4711yescharacteristic
552#103D4×C4711yescharacteristic
553#102—21no—
554#102—21no—
555#102—21no—
556#102D4×C4711yescharacteristic
557#102D4×C4711yescharacteristic
558#102D4×C4711yescharacteristic
559#102D4×C4711yescharacteristic
560#101—22no—
561#101—22no—
562#100—22no—
563C22⋊C8—21no—
564C22⋊C8—21no—
565#97—21no—
566C4×C8—21no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—24no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—42no—
576#41—44no—
577#41—42no—
578#41—44no—
579#41—42no—
580#41C2×D4×C4712yes—
581#41#41×C4712yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—24no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—41no—
594C2×Q8—42no—
595C2×Q8—42no—
596C2×Q8—42no—
597C2×Q8C2×D4×C4712yes—
598C2×Q8C2×D4×C4711yescharacteristic
599C2×Q8C2×D4×C4711yescharacteristic
600C2×Q8#41×C4712yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4C2×D4×C4711yescharacteristic
613C2×D4C2×D4×C4711yescharacteristic
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4C24×C4711yescharacteristic
624Q16—24no—
625Q16—42no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631SD16—42no—
632SD16—42no—
633D8—42no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—42no—
642M16C2×D4×C4712yes—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—42no—
652C2×C8C2×D4×C4711yescharacteristic
653C2×C8C2×D4×C4711yescharacteristic
654C2×C8C2×D4×C4711yescharacteristic
655C2×C8C2×D4×C4711yescharacteristic
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—41no—
659C4⋊C4—44no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4C2×D4×C4711yescharacteristic
663C4⋊C4C2×D4×C4711yescharacteristic
664C4⋊C4C2×D4×C4711yescharacteristic
665C4⋊C4C2×D4×C4711yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—82no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—41no—
677C42—41no—
678C42—41no—
679C23—21no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—81no—
686C23H(5,𝔽2)×C4711yescharacteristic
687Q8—21no—
688Q8—22no—
689Q8—21no—
690Q8—22no—
691Q8—22no—
692Q8—21no—
693Q8—22no—
694Q8—44no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699Q8#121×C4712yes—
700D4—22no—
701D4—22no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—161no—
713D4—161no—
714D4#121×C4712yes—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—81no—
738C2×C4—161no—
739C2×C4C22×D4×C4711yescharacteristic
740C2×C4C22×D4×C4711yescharacteristic
741C2×C4C22×D4×C4711yescharacteristic
742C2×C4C2×#41×C4711yescharacteristic
743C2×C4C2×#41×C4711yescharacteristic
744C2×C4H(5,𝔽2)×C4711yescharacteristic
745C8—22no—
746C8—21no—
747C8—21no—
748C8—21no—
749C8—21no—
750C8—41no—
751C8—41no—
752C8—41no—
753C22—21no—
754C22—21no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22C47×#53811yescharacteristic
767C22D42×C4711yescharacteristic
768C22C47×#54611yescharacteristic
769C4—22no—
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—81no—
779C4C2×#121×C4711yescharacteristic
780C4C47×#52511yescharacteristic
781C4D42×C4711yescharacteristic
782C4C47×#54611yescharacteristic
783C2—21no—
784C2—21no—
785C2—42no—
786C2—81no—
787C2—161no—
788C2C47×#242411yescharacteristic
789C2C47×#328911yescharacteristic
790C2C47×#329111yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3010C2
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×#471C2semidirect
2. C47×#3043C2semidirect
3. C2×C47×#456C2semidirect
5. C47×#2947C2semidirect
6. C47×#2898C2semidirect
7. C47×#2064C2semidirect
8. C47×#2052C2semidirect
9. C47×#2037C2semidirect
10. C47×#2013C2semidirect
11. C47×#1977C2semidirect
12. C47×#1929C2semidirect
13. C47×#1886C2semidirect
14. C47×#1883C2semidirect
15. C47×#1866C2semidirect
86. #137×C47D4semidirect
357. #25181C47direct (N × H)
388. C2×#471C2×C47semidirect
389. #3043C2×C47semidirect
390. C2×#456C2×C47semidirect
392. #2947C2×C47semidirect
393. #2898C2×C47semidirect
394. #2064C2×C47semidirect
395. #2052C2×C47semidirect
396. #2037C2×C47semidirect
397. #2013C2×C47semidirect
398. #1977C2×C47semidirect
399. #1929C2×C47semidirect
400. #1886C2×C47semidirect
401. #1883C2×C47semidirect
402. #1866C2×C47semidirect
464. C47#25181direct (N × H)
482. #137D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4712
C47×#30432
C2×C47×#4562
C47×#30102
C47×#29472
C47×#28982
C47×#20642
C47×#20522
C47×#20372
C47×#20132
C47×#19772
C47×#19292
C47×#18862
C47×#18832
C47×#18662
#2518147