Finite Group Databasebeta

← C47×#25440 #26065138

Subgroups — C47×#25440 #26065138

Order 12032.

914 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
1C47×#3154C211yesmaximal, characteristic, complemented
2C2×C47×#471C211yesmaximal, characteristic, complemented
3C47×#3063C211yesmaximal, characteristic, complemented
4C47×#3062C211yesmaximal, characteristic, complemented
5C47×#3060C211yesmaximal, characteristic, complemented
6C2×C47×#443C211yesmaximal, characteristic, complemented
7C47×#2038C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#2007C211yesmaximal, characteristic, complemented
10C47×#2006C211yesmaximal, characteristic, complemented
11C47×#1968C211yesmaximal, characteristic, complemented
12C47×#1951C211yesmaximal, characteristic, complemented
13C47×#1908C211yesmaximal, characteristic, complemented
14C47×#1907C211yesmaximal, characteristic, complemented
15C47×#1764C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C2×#135×C47C2211yescharacteristic
21C22×SD16×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic
23C2×#131×C47C2211yescharacteristic
24C2×#131×C47C2211yescharacteristic
25C47×#537C2211yescharacteristic
26C47×#537C2211yescharacteristic
27C47×#536C2211yescharacteristic
28C47×#535C2211yescharacteristic
29C47×#497—21no—
30C47×#496—21no—
31C47×#495—21no—
32C47×#492—21no—
33C47×#471—24no—
34C47×#470—21no—
35C47×#470—21no—
36C47×#469—21no—
37C47×#469—21no—
38C47×#468—21no—
39C47×#468—21no—
40C47×#467—21no—
41C47×#466—21no—
42C47×#465—21no—
43C47×#465—21no—
44C47×#465—21no—
45C47×#465—21no—
46C47×#443—24no—
47C2×#108×C47C2211yescharacteristic
48C47×#428C2211yescharacteristic
49C47×#428C2211yescharacteristic
50C2×#106×C47C2211yescharacteristic
51C2×#104×C47C2211yescharacteristic
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C47×#417C2211yescharacteristic
55C47×#417C2211yescharacteristic
56C47×#416C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic
59C2×#101×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic
61C47×#405C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×#391C2211yescharacteristic
64C47×#390C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#341C2211yescharacteristic
68C47×#339C2211yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C2×#41×C47C2311yescharacteristic
71C2×#41×C47C2311yescharacteristic
72C22×Q8×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74#137×C47—22no—
75#137×C47—22no—
76#137×C47—41no—
77#137×C47—41no—
78AGL(1,ℤ/8)×C47—22no—
79AGL(1,ℤ/8)×C47—22no—
80AGL(1,ℤ/8)×C47—41no—
81AGL(1,ℤ/8)×C47—41no—
82#135×C47—22no—
83#135×C47—22no—
84C2×Q16×C47—21no—
85C2×Q16×C47—21no—
86C2×Q16×C47D411yescharacteristic
87C2×SD16×C47—21no—
88C2×SD16×C47—21no—
89C2×SD16×C47—21no—
90C2×SD16×C47—21no—
91C2×SD16×C47—22no—
92C2×SD16×C47—21no—
93C2×SD16×C47—21no—
94C2×SD16×C47—22no—
95C2×SD16×C47D411yescharacteristic
96C2×SD16×C47D411yescharacteristic
97C2×D8×C47—21no—
98C2×D8×C47—21no—
99C2×D8×C47D411yescharacteristic
100#131×C47—22no—
101#131×C47—22no—
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×C47—21no—
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C2×M16×C47C2311yescharacteristic
113C22×C8×C47—21no—
114C22×C8×C47—21no—
115C22×C8×C47—21no—
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C4⋊Q8×C47—21no—
119#127×C47—21no—
120#124×C47—21no—
121#124×C47—21no—
122#123×C47—41no—
123C22⋊Q8×C47—21no—
124C22⋊Q8×C47—21no—
125C22⋊Q8×C47—21no—
126C22⋊Q8×C47—21no—
127C22⋊Q8×C47—21no—
128C22⋊Q8×C47—21no—
129#121×C47—21no—
130#121×C47—21no—
131#121×C47—21no—
132#121×C47—21no—
133#121×C47—21no—
134#121×C47—21no—
135#121×C47—41no—
136#121×C47—41no—
137#120×C47—41no—
138#117×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C22⋊C4×C47—41no—
142C2×C42×C47C2311yescharacteristic
143#108×C47D414yescomplemented
144#107×C47—21no—
145#107×C47—21no—
146#106×C47—21no—
147#106×C47—21no—
148#106×C47—21no—
149#106×C47—21no—
150#104×C47—22no—
151#104×C47—22no—
152#104×C47—22no—
153#103×C47—21no—
154#103×C47—21no—
155#103×C47—21no—
156#103×C47—21no—
157#103×C47D411yescharacteristic
158#103×C47D411yescharacteristic
159#102×C47—21no—
160#102×C47—21no—
161#102×C47—21no—
162#102×C47—21no—
163#102×C47D411yescharacteristic
164#102×C47D411yescharacteristic
165#101×C47—22no—
166#100×C47—22no—
167#97×C47—21no—
168C4×C8×C47—21no—
169C4×C8×C47—22no—
170#95×C47—41no—
171C24×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
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—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47C2×D411yescharacteristic
191C2×Q8×C47C2×D411yescharacteristic
192C2×Q8×C47C2×D411yescharacteristic
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—41no—
203C2×D4×C47—41no—
204C2×D4×C47—41no—
205C2×D4×C47—41no—
206C2×D4×C47C2×D411yescharacteristic
207C2×D4×C47C2×D411yescharacteristic
208C2×D4×C47C2×D411yescharacteristic
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47C2411yescharacteristic
217Q16×C47—22no—
218Q16×C47—42no—
219Q16×C47—42no—
220SD16×C47—22no—
221SD16×C47—22no—
222SD16×C47—42no—
223SD16×C47—42no—
224SD16×C47—42no—
225SD16×C47—42no—
226SD16×C47—42no—
227SD16×C47—42no—
228D8×C47—22no—
229D8×C47—42no—
230D8×C47—42no—
231M16×C47—21no—
232M16×C47—21no—
233M16×C47—21no—
234M16×C47—21no—
235M16×C47—21no—
236M16×C47—42no—
237M16×C47—42no—
238M16×C47—42no—
239M16×C47C2×D412yes—
240M16×C47C2×D412yes—
241M16×C47#4112yes—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—42no—
249C2×C8×C47—42no—
250C2×C8×C47—42no—
251C2×C8×C47C2×D411yescharacteristic
252C2×C8×C47C2×D411yescharacteristic
253C2×C8×C47C2×D411yescharacteristic
254C2×C8×C47C2×D411yescharacteristic
255C2×C8×C47C2×D412yes—
256C2×C8×C47#4112yes—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—41no—
262C4⋊C4×C47—41no—
263C4⋊C4×C47—41no—
264C4⋊C4×C47—41no—
265C4⋊C4×C47C2×D411yescharacteristic
266C4⋊C4×C47C2×D411yescharacteristic
267C22⋊C4×C47—21no—
268C22⋊C4×C47—41no—
269C22⋊C4×C47—41no—
270C22⋊C4×C47—41no—
271C22⋊C4×C47—41no—
272C22⋊C4×C47—41no—
273C22⋊C4×C47—41no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—41no—
276C22⋊C4×C47—82no—
277C42×C47—21no—
278C42×C47—21no—
279C42×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—81no—
287C23×C47—81no—
288C23×C47H(5,𝔽2)11yescharacteristic
289Q8×C47—21no—
290Q8×C47—21no—
291Q8×C47—21no—
292Q8×C47—21no—
293Q8×C47—21no—
294Q8×C47—21no—
295Q8×C47—41no—
296Q8×C47—41no—
297Q8×C47—41no—
298Q8×C47—41no—
299D4×C47—21no—
300D4×C47—21no—
301D4×C47—21no—
302D4×C47—21no—
303D4×C47—21no—
304D4×C47—21no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—161no—
316D4×C47—161no—
317D4×C47—161no—
318D4×C47—161no—
319C2×C4×C47—22no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—81no—
339C2×C4×C47—81no—
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C2×C4×C47C2×#4111yescharacteristic
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C8×C47—21no—
347C8×C47—21no—
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—22no—
351C8×C47—41no—
352C8×C47#12112yes—
353C8×C47#12112yes—
354#25440C4711yesmaximal, characteristic, direct product factor, Sylow
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
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#54011yescharacteristic
372C22×C47D4211yescharacteristic
373C22×C47#55011yescharacteristic
374C4×C47—42no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—81no—
381C4×C47—81no—
382C4×C47—81no—
383C4×C47C2×#12111yescharacteristic
384C4×C47#53211yescharacteristic
385C4×C47D4211yescharacteristic
386C4×C47#54611yescharacteristic
387#3154C2×C4711yescharacteristic, complemented
388C2×#471C2×C4711yescharacteristic, complemented
389#3063C2×C4711yescharacteristic, complemented
390#3062C2×C4711yescharacteristic, complemented
391#3060C2×C4711yescharacteristic, complemented
392C2×#443C2×C4711yescharacteristic, complemented
393#2038C2×C4711yescharacteristic, complemented
394#2037C2×C4711yescharacteristic, complemented
395#2007C2×C4711yescharacteristic, complemented
396#2006C2×C4711yescharacteristic, complemented
397#1968C2×C4711yescharacteristic, complemented
398#1951C2×C4711yescharacteristic, complemented
399#1908C2×C4711yescharacteristic, complemented
400#1907C2×C4711yescharacteristic, complemented
401#1764C2×C4711yescharacteristic, complemented
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—81no—
405C2×C47—81no—
406C2×C47—81no—
407C2×C47—161no—
408C2×C47#242811yescharacteristic
409C2×C47#329011yescharacteristic
410C2×C47#329111yescharacteristic
411C2×#137C22×C4711yescharacteristic
412C2×#137C22×C4711yescharacteristic
413C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
414C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
415C2×#135C22×C4711yescharacteristic
416C22×SD16C22×C4711yescharacteristic
417C2×#131C22×C4711yescharacteristic
418C2×#131C22×C4711yescharacteristic
419C2×#131C22×C4711yescharacteristic
420#537C22×C4711yescharacteristic
421#537C22×C4711yescharacteristic
422#536C22×C4711yescharacteristic
423#535C22×C4711yescharacteristic
424#497—21no—
425#496—21no—
426#495—21no—
427#492—21no—
428#471—24no—
429#470—21no—
430#470—21no—
431#469—21no—
432#469—21no—
433#468—21no—
434#468—21no—
435#467—21no—
436#466—21no—
437#465—21no—
438#465—21no—
439#465—21no—
440#465—21no—
441#443—24no—
442C2×#108C22×C4711yescharacteristic
443#428C22×C4711yescharacteristic
444#428C22×C4711yescharacteristic
445C2×#106C22×C4711yescharacteristic
446C2×#104C22×C4711yescharacteristic
447C2×#104C22×C4711yescharacteristic
448C2×#104C22×C4711yescharacteristic
449#417C22×C4711yescharacteristic
450#417C22×C4711yescharacteristic
451#416C22×C4711yescharacteristic
452C2×#103C22×C4711yescharacteristic
453C2×#102C22×C4711yescharacteristic
454C2×#101C22×C4711yescharacteristic
455C2×#100C22×C4711yescharacteristic
456#405C22×C4711yescharacteristic
457C2×C4×C8C22×C4711yescharacteristic
458#391C22×C4711yescharacteristic
459#390C22×C4711yescharacteristic
460#343C22×C4711yescharacteristic
461#343C22×C4711yescharacteristic
462#341C22×C4711yescharacteristic
463#339C22×C4711yescharacteristic
464C47#2544011yescharacteristic, direct product factor, Sylow
465C2×#41C23×C4711yescharacteristic
466C2×#41C23×C4711yescharacteristic
467C2×#41C23×C4711yescharacteristic
468C22×Q8C23×C4711yescharacteristic
469C22×D4C23×C4711yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C4711yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C4711yescharacteristic
492C2×SD16D4×C4711yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C4711yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C4711yescharacteristic
506C2×M16C23×C4711yescharacteristic
507C2×M16C23×C4711yescharacteristic
508C2×M16C23×C4711yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C4711yescharacteristic
513C22×C8C23×C4711yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
536C2×C4⋊C4C23×C4711yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C4711yescharacteristic
539#108D4×C4714yescomplemented
540#107—21no—
541#107—21no—
542#106—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C4711yescharacteristic
554#103D4×C4711yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C4711yescharacteristic
560#102D4×C4711yescharacteristic
561#101—22no—
562#100—22no—
563#97—21no—
564C4×C8—22no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C4711yescharacteristic
587C2×Q8C2×D4×C4711yescharacteristic
588C2×Q8C2×D4×C4711yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C4711yescharacteristic
603C2×D4C2×D4×C4711yescharacteristic
604C2×D4C2×D4×C4711yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C4711yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C4712yes—
636M16C2×D4×C4712yes—
637M16#41×C4712yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C4711yescharacteristic
648C2×C8C2×D4×C4711yescharacteristic
649C2×C8C2×D4×C4711yescharacteristic
650C2×C8C2×D4×C4712yes—
651C2×C8C2×D4×C4711yescharacteristic
652C2×C8#41×C4712yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C4711yescharacteristic
662C4⋊C4C2×D4×C4711yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C4711yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C4711yescharacteristic
737C2×C4C22×D4×C4711yescharacteristic
738C2×C4C22×D4×C4711yescharacteristic
739C2×C4C2×#41×C4711yescharacteristic
740C2×C4C2×#41×C4711yescharacteristic
741C2×C4H(5,𝔽2)×C4711yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C4712yes—
749C8#121×C4712yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22C47×#54011yescharacteristic
767C22D42×C4711yescharacteristic
768C22C47×#55011yescharacteristic
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C4711yescharacteristic
779C4C47×#53211yescharacteristic
780C4D42×C4711yescharacteristic
781C4C47×#54611yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C47×#242811yescharacteristic
789C2C47×#329011yescharacteristic
790C2C47×#329111yescharacteristic
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×#3154C2semidirect
2. C2×C47×#471C2semidirect
3. C47×#3063C2semidirect
4. C47×#3062C2semidirect
5. C47×#3060C2semidirect
6. C2×C47×#443C2semidirect
7. C47×#2038C2semidirect
8. C47×#2037C2semidirect
9. C47×#2007C2semidirect
10. C47×#2006C2semidirect
11. C47×#1968C2semidirect
12. C47×#1951C2semidirect
13. C47×#1908C2semidirect
14. C47×#1907C2semidirect
15. C47×#1764C2semidirect
143. #108×C47D4semidirect
354. #25440C47direct (N × H)
387. #3154C2×C47semidirect
388. C2×#471C2×C47semidirect
389. #3063C2×C47semidirect
390. #3062C2×C47semidirect
391. #3060C2×C47semidirect
392. C2×#443C2×C47semidirect
393. #2038C2×C47semidirect
394. #2037C2×C47semidirect
395. #2007C2×C47semidirect
396. #2006C2×C47semidirect
397. #1968C2×C47semidirect
398. #1951C2×C47semidirect
399. #1908C2×C47semidirect
400. #1907C2×C47semidirect
401. #1764C2×C47semidirect
464. C47#25440direct (N × H)
539. #108D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31542
C2×C47×#4712
C47×#30632
C47×#30622
C47×#30602
C2×C47×#4432
C47×#20382
C47×#20372
C47×#20072
C47×#20062
C47×#19682
C47×#19512
C47×#19082
C47×#19072
C47×#17642
#2544047