Finite Group Databasebeta

← C47×#24405 #26064103

Subgroups — C47×#24405 #26064103

Order 12032.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3484C211yesmaximal, characteristic
2C2×C47×#458C211yesmaximal, characteristic, complemented
3C22×#99×C47C211yesmaximal, characteristic, complemented
4C47×#2412C212yesmaximal, complemented
5C47×#2405C211yesmaximal, characteristic, complemented
6C47×#2044C212yesmaximal, complemented
7C47×#2022C212yesmaximal, complemented
8C47×#1898C212yesmaximal, complemented
9C47×#1890C211yesmaximal, characteristic, complemented
10C47×#1867C211yesmaximal, characteristic, complemented
11C47×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C47C2211yescharacteristic
13C23×D4×C47C2211yescharacteristic
14C47×#546—22no—
15C47×#546—22no—
16D42×C47—22no—
17D42×C47—22no—
18C47×#535—21no—
19C47×#534—21no—
20C47×#534C2212yes—
21C47×#525—21no—
22C2×#123×C47C2211yescharacteristic
23C2×#123×C47C2212yescomplemented
24C2×#123×C47C2211yescharacteristic, complemented
25C2×#120×C47—21no—
26C2×#120×C47C2212yes—
27C47×#518C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic, complemented
29C22×C22⋊C4×C47C2212yescomplemented
30C47×#458—24no—
31C2×#99×C47—24no—
32C2×#99×C47C2211yescharacteristic
33C2×#99×C47C2211yescharacteristic
34C2×#99×C47C2212yescomplemented
35C2×#99×C47C2212yescomplemented
36C2×#99×C47C2212yescomplemented
37C47×#397—22no—
38C47×#394—21no—
39C47×#394—21no—
40C47×#394—22no—
41C47×#386—22no—
42C47×#386C2211yescharacteristic
43C47×#386C2211yescharacteristic, complemented
44C47×#386C2212yescomplemented
45C47×#385—21no—
46C47×#385C2212yescomplemented
47C47×#381C2212yescomplemented
48C47×#380—22no—
49C47×#379—21no—
50C47×#379C2211yescharacteristic, complemented
51C47×#342C2212yescomplemented
52C47×#342C2212yescomplemented
53C25×C47D411yescharacteristic
54C25×C47C2311yescharacteristic
55H(5,𝔽2)×C47—22no—
56H(5,𝔽2)×C47—22no—
57H(5,𝔽2)×C47—42no—
58C2×#41×C47—21no—
59C2×#41×C47—22no—
60C22×D4×C47—21no—
61C22×D4×C47—22no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—22no—
67C22×D4×C47—22no—
68C22×D4×C47—42no—
69C22×D4×C47D411yescharacteristic
70C22×D4×C47D411yescharacteristic
71C22×D4×C47D412yes—
72C22×D4×C47D412yes—
73C22×D4×C47C2312yes—
74C22×D4×C47C2311yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C23×C4×C47—22no—
77C23×C4×C47D411yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80#127×C47—22no—
81#124×C47—22no—
82#123×C47—22no—
83#123×C47—22no—
84#123×C47—22no—
85#123×C47—22no—
86#123×C47—22no—
87#123×C47—24no—
88#123×C47—42no—
89#123×C47—42no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92#121×C47—21no—
93#121×C47—21no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47—22no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#120×C47—22no—
101#120×C47—22no—
102#120×C47—22no—
103#120×C47—22no—
104#120×C47—22no—
105#120×C47—22no—
106#120×C47—22no—
107#120×C47—22no—
108#120×C47—22no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113#117×C47—21no—
114C2×C4⋊C4×C47—21no—
115C2×C4⋊C4×C47—22no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—22no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—24no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—22no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—22no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—22no—
135C2×C22⋊C4×C47—42no—
136C2×C22⋊C4×C47D412yes—
137C2×C22⋊C4×C47D412yes—
138C2×C22⋊C4×C47C2312yes—
139C2×C22⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47C2311yescharacteristic
141C2×C22⋊C4×C47C2312yes—
142C2×C22⋊C4×C47C2312yes—
143#99×C47—22no—
144#99×C47—24no—
145#99×C47—24no—
146#99×C47—42no—
147#99×C47D414yescomplemented
148#95×C47—22no—
149#95×C47—22no—
150#95×C47—22no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—22no—
154C24×C47—21no—
155C24×C47—21no—
156C24×C47—22no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—22no—
161C24×C47—41no—
162C24×C47—42no—
163C24×C47—42no—
164C24×C47—81no—
165C24×C47—81no—
166C24×C47C2×D411yescharacteristic
167C24×C47C2×D412yes—
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D412yes—
170C24×C47C2×D412yes—
171C24×C47C2×D411yescharacteristic
172C24×C47C2×D411yescharacteristic
173C24×C47C2411yescharacteristic
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—42no—
177#41×C47—42no—
178C2×Q8×C47—21no—
179C2×D4×C47—22no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—21no—
183C2×D4×C47—22no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—22no—
203C2×D4×C47—41no—
204C2×D4×C47—41no—
205C2×D4×C47—44no—
206C2×D4×C47—44no—
207C2×D4×C47—44no—
208C2×D4×C47—44no—
209C2×D4×C47—44no—
210C2×D4×C47—44no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—44no—
214C2×D4×C47—82no—
215C2×D4×C47—82no—
216C2×D4×C47—82no—
217C2×D4×C47C2×D412yes—
218C2×D4×C47#4112yes—
219C22×C4×C47—21no—
220C22×C4×C47—22no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—22no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—22no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—22no—
237C22×C4×C47—41no—
238C22×C4×C47—44no—
239C22×C4×C47—44no—
240C22×C4×C47—81no—
241C22×C4×C47—82no—
242C22×C4×C47C2×D412yes—
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2×D412yes—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—22no—
250C4⋊C4×C47—22no—
251C4⋊C4×C47—44no—
252C4⋊C4×C47—42no—
253C4⋊C4×C47—42no—
254C4⋊C4×C47—82no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—22no—
264C22⋊C4×C47—22no—
265C22⋊C4×C47—22no—
266C22⋊C4×C47—22no—
267C22⋊C4×C47—22no—
268C22⋊C4×C47—21no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—22no—
272C22⋊C4×C47—44no—
273C22⋊C4×C47—44no—
274C22⋊C4×C47—42no—
275C22⋊C4×C47—42no—
276C22⋊C4×C47—41no—
277C22⋊C4×C47—42no—
278C22⋊C4×C47—41no—
279C22⋊C4×C47—42no—
280C22⋊C4×C47—81no—
281C22⋊C4×C47—81no—
282C22⋊C4×C47—81no—
283C22⋊C4×C47—82no—
284C22⋊C4×C47C2×D414yescomplemented
285C42×C47—22no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—24no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—21no—
299C23×C47—22no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—42no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—42no—
310C23×C47—42no—
311C23×C47—41no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47—42no—
321C23×C47—42no—
322C23×C47—42no—
323C23×C47—81no—
324C23×C47—81no—
325C23×C47—82no—
326C23×C47—82no—
327C23×C47—84no—
328C23×C47—81no—
329C23×C47—81no—
330C23×C47—84no—
331C23×C47—84no—
332C23×C47#12011yescharacteristic
333C23×C47#12012yes—
334C23×C47#12011yescharacteristic
335C23×C47#12112yes—
336C23×C47C22×D411yescharacteristic
337C23×C47C22×D412yes—
338C23×C47C22×D411yescharacteristic
339C23×C47C2×#4111yescharacteristic
340C23×C47H(5,𝔽2)12yes—
341Q8×C47—42no—
342D4×C47—24no—
343D4×C47—24no—
344D4×C47—44no—
345D4×C47—42no—
346D4×C47—44no—
347D4×C47—44no—
348D4×C47—44no—
349D4×C47—42no—
350D4×C47—42no—
351D4×C47—42no—
352D4×C47—42no—
353D4×C47—42no—
354D4×C47—42no—
355D4×C47—44no—
356D4×C47—82no—
357D4×C47—82no—
358D4×C47—82no—
359D4×C47—82no—
360C2×C4×C47—21no—
361C2×C4×C47—21no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—24no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—42no—
372C2×C4×C47—42no—
373C2×C4×C47—44no—
374C2×C4×C47—42no—
375C2×C4×C47—42no—
376C2×C4×C47—42no—
377C2×C4×C47—42no—
378C2×C4×C47—42no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—42no—
384C2×C4×C47—42no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—42no—
388C2×C4×C47—42no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—41no—
393C2×C4×C47—41no—
394C2×C4×C47—41no—
395C2×C4×C47—42no—
396C2×C4×C47—42no—
397C2×C4×C47—42no—
398C2×C4×C47—81no—
399C2×C4×C47—81no—
400C2×C4×C47—88no—
401C2×C4×C47#12112yes—
402#24405C4711yesmaximal, characteristic, direct product factor, Sylow
403C22×C47—21no—
404C22×C47—22no—
405C22×C47—21no—
406C22×C47—22no—
407C22×C47—21no—
408C22×C47—21no—
409C22×C47—21no—
410C22×C47—22no—
411C22×C47—22no—
412C22×C47—22no—
413C22×C47—21no—
414C22×C47—21no—
415C22×C47—22no—
416C22×C47—41no—
417C22×C47—41no—
418C22×C47—42no—
419C22×C47—44no—
420C22×C47—44no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—41no—
426C22×C47—41no—
427C22×C47—42no—
428C22×C47—41no—
429C22×C47—42no—
430C22×C47—41no—
431C22×C47—42no—
432C22×C47—41no—
433C22×C47—82no—
434C22×C47—81no—
435C22×C47—81no—
436C22×C47—81no—
437C22×C47—82no—
438C22×C47—84no—
439C22×C47—82no—
440C22×C47—82no—
441C22×C47—81no—
442C22×C47—84no—
443C22×C47—162no—
444C22×C47#45812yescomplemented
445C22×C47C2×#12011yescharacteristic
446C22×C47C2×#12111yescharacteristic
447C22×C47#53411yescharacteristic
448C22×C47D4212yes—
449C22×C47#54612yes—
450C4×C47—22no—
451C4×C47—44no—
452C4×C47—41no—
453C4×C47—42no—
454C4×C47—42no—
455C4×C47—42no—
456C4×C47—81no—
457C4×C47—81no—
458C4×C47—82no—
459C4×C47—81no—
460C4×C47—81no—
461#3484C2×C4711yescharacteristic
462C2×#458C2×C4711yescharacteristic, complemented
463C22×#99C2×C4711yescharacteristic, complemented
464#2412C2×C4712yescomplemented
465#2405C2×C4711yescharacteristic, complemented
466#2044C2×C4712yescomplemented
467#2022C2×C4712yescomplemented
468#1898C2×C4712yescomplemented
469#1890C2×C4711yescharacteristic, complemented
470#1867C2×C4711yescharacteristic, complemented
471#1790C2×C4711yescharacteristic, complemented
472C2×C47—22no—
473C2×C47—21no—
474C2×C47—21no—
475C2×C47—22no—
476C2×C47—22no—
477C2×C47—42no—
478C2×C47—41no—
479C2×C47—42no—
480C2×C47—81no—
481C2×C47—82no—
482C2×C47#241011yescharacteristic
483C2×C47C2×#45811yescharacteristic
484C2×C47#302611yescharacteristic
485C2×H(5,𝔽2)C22×C4711yescharacteristic
486C23×D4C22×C4711yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C4712yes—
494#525—21no—
495C2×#123C22×C4711yescharacteristic
496C2×#123C22×C4712yescomplemented
497C2×#123C22×C4711yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C4712yes—
500#518C22×C4711yescharacteristic
501C22×C22⋊C4C22×C4711yescharacteristic, complemented
502C22×C22⋊C4C22×C4712yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C4711yescharacteristic
506C2×#99C22×C4711yescharacteristic
507C2×#99C22×C4712yescomplemented
508C2×#99C22×C4712yescomplemented
509C2×#99C22×C4712yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C4711yescharacteristic
516#386C22×C4711yescharacteristic, complemented
517#386C22×C4712yescomplemented
518#385—21no—
519#385C22×C4712yescomplemented
520#381C22×C4712yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C4711yescharacteristic, complemented
524#342C22×C4712yescomplemented
525#342C22×C4712yescomplemented
526C47#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C4711yescharacteristic
528C25C23×C4711yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C4711yescharacteristic
544C22×D4D4×C4711yescharacteristic
545C22×D4D4×C4712yes—
546C22×D4D4×C4712yes—
547C22×D4C23×C4712yes—
548C22×D4C23×C4711yescharacteristic
549C22×D4C23×C4711yescharacteristic
550C23×C4—22no—
551C23×C4D4×C4711yescharacteristic
552C23×C4C23×C4711yescharacteristic
553C23×C4C23×C4711yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C4712yes—
611C2×C22⋊C4D4×C4712yes—
612C2×C22⋊C4C23×C4712yes—
613C2×C22⋊C4C23×C4711yescharacteristic
614C2×C22⋊C4C23×C4711yescharacteristic
615C2×C22⋊C4C23×C4712yes—
616C2×C22⋊C4C23×C4712yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C4714yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C4711yescharacteristic
641C24C2×D4×C4712yes—
642C24C2×D4×C4711yescharacteristic
643C24C2×D4×C4712yes—
644C24C2×D4×C4712yes—
645C24C2×D4×C4711yescharacteristic
646C24C2×D4×C4711yescharacteristic
647C24C24×C4711yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C4712yes—
692C2×D4#41×C4712yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C4712yes—
717C22×C4C2×D4×C4711yescharacteristic
718C22×C4C2×D4×C4711yescharacteristic
719C22×C4C2×D4×C4712yes—
720C22×C4C2×D4×C4712yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C4714yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C4711yescharacteristic
807C23#120×C4712yes—
808C23#120×C4711yescharacteristic
809C23#121×C4712yes—
810C23C22×D4×C4711yescharacteristic
811C23C22×D4×C4712yes—
812C23C22×D4×C4711yescharacteristic
813C23C2×#41×C4711yescharacteristic
814C23H(5,𝔽2)×C4712yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C4712yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C47×#45812yescomplemented
918C22C2×#120×C4711yescharacteristic
919C22C2×#121×C4711yescharacteristic
920C22C47×#53411yescharacteristic
921C22D42×C4712yes—
922C22C47×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C47×#241011yescharacteristic
945C2C2×C47×#45811yescharacteristic
946C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
prime radicalC47×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#458C2semidirect
3. C22×#99×C47C2semidirect
4. C47×#2412C2semidirect
5. C47×#2405C2semidirect
6. C47×#2044C2semidirect
7. C47×#2022C2semidirect
8. C47×#1898C2semidirect
9. C47×#1890C2semidirect
10. C47×#1867C2semidirect
11. C47×#1790C2semidirect
23. C2×#123×C47C22semidirect
24. C2×#123×C47C22semidirect
28. C22×C22⋊C4×C47C22semidirect
29. C22×C22⋊C4×C47C22semidirect
34. C2×#99×C47C22semidirect
35. C2×#99×C47C22semidirect
36. C2×#99×C47C22semidirect
43. C47×#386C22semidirect
44. C47×#386C22semidirect
46. C47×#385C22semidirect
47. C47×#381C22semidirect
50. C47×#379C22semidirect
51. C47×#342C22semidirect
52. C47×#342C22semidirect
147. #99×C47D4semidirect
284. C22⋊C4×C47C2×D4semidirect
402. #24405C47direct (N × H)
444. C22×C47#458semidirect
462. C2×#458C2×C47semidirect
463. C22×#99C2×C47semidirect
464. #2412C2×C47semidirect
465. #2405C2×C47semidirect
466. #2044C2×C47semidirect
467. #2022C2×C47semidirect
468. #1898C2×C47semidirect
469. #1890C2×C47semidirect
470. #1867C2×C47semidirect
471. #1790C2×C47semidirect
496. C2×#123C22×C47semidirect
497. C2×#123C22×C47semidirect
501. C22×C22⋊C4C22×C47semidirect
502. C22×C22⋊C4C22×C47semidirect
507. C2×#99C22×C47semidirect
508. C2×#99C22×C47semidirect
509. C2×#99C22×C47semidirect
516. #386C22×C47semidirect
517. #386C22×C47semidirect
519. #385C22×C47semidirect
520. #381C22×C47semidirect
523. #379C22×C47semidirect
524. #342C22×C47semidirect
525. #342C22×C47semidirect
526. C47#24405direct (N × H)
621. #99D4×C47semidirect
758. C22⋊C4C2×D4×C47semidirect
917. C22C47×#458semidirect

Maximal subgroups

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

subgroupindex
C47×#34842
C2×C47×#4582
C22×#99×C472
C47×#24122
C47×#24052
C47×#20442
C47×#20222
C47×#18982
C47×#18902
C47×#18672
C47×#17902
#2440547