Finite Group Databasebeta

← #26147608

Subgroups — #26147608

Order 12032.

2842 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic
2C22×C42×D47C211yesmaximal, characteristic, complemented
3C2×#15689001C212yesmaximal
4C2×#15688985C211yesmaximal, characteristic, complemented
5#20241626C211yesmaximal, characteristic, complemented
6#20241624C212yesmaximal, complemented
7#20241624C211yesmaximal, characteristic, complemented
8#20241620C211yesmaximal, characteristic, complemented
9#20241619C212yesmaximal, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C47×#1436C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C2×#13094009—24no—
16C2×#13094009—24no—
17C2×#13094009C418yescomplemented
18C22×Dic47⋊C4C2211yescharacteristic
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×C4×Dic47C2212yes—
26C22×C4×Dic47C2211yescharacteristic
27C2×C42×D47—28no—
28C2×C42×D47—24no—
29#15689001—28no—
30#15688985—24no—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C2×#95×C47C2212yes—
42C24×D47C2311yescharacteristic
43C24×D47C2311yescharacteristic
44C22×D188—24no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—24no—
48C22×D188C2×C414yes—
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C22×C4×D47—24no—
54C22×C4×D47—24no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—24no—
60C22×C4×D47—24no—
61C22×C4×D47C2×C414yes—
62C22×C4×D47D418yes—
63C22×C4×D47D414yes—
64C22×C4×D47D414yes—
65#13094009—232no—
66C2×Dic47⋊C4—22no—
67C2×Dic47⋊C4—22no—
68C2×Dic47⋊C4C2×C414yescomplemented
69C2×(C2×D47)⋊C4—22no—
70C2×(C2×D47)⋊C4—22no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4—22no—
73C2×(C2×D47)⋊C4—22no—
74C2×(C2×D47)⋊C4—22no—
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4C2×C414yes—
85C2×(C2×D47)⋊C4C2×C414yescomplemented
86C2×(C2×D47)⋊C4C2×C414yescomplemented
87C2×C4×Dic47—22no—
88C2×C4×Dic47—24no—
89C2×C4×Dic47—24no—
90C2×C4×Dic47—24no—
91C2×C4×Dic47—24no—
92C42×D47—232no—
93C47⋊#95—22no—
94C47⋊#95—24no—
95C47⋊#95—24no—
96C47⋊#95—24no—
97C47⋊#95—24no—
98C47⋊#95—24no—
99C23×C4×C47C2312yes—
100C23×C4×C47C2311yescharacteristic
101C23×C4×C47C2311yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2312yes—
104C2×C4⋊C4×C47—22no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47C2×C414yescomplemented
107C2×C42×C47—22no—
108C2×C42×C47—24no—
109#95×C47—22no—
110#95×C47—24no—
111#95×C47—24no—
112C24×C47C2411yescharacteristic
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47C22×C412yes—
126C23×D47C22×C412yes—
127C23×D47C2×D412yes—
128C23×D47C2×D412yes—
129C23×D47C2×D414yes—
130C23×D47#4114yes—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D414yes—
158C22×C4×C47#4114yes—
159C22×C4×C47#4114yes—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47C22×C412yes—
178C22×Dic47C22×C412yes—
179C22×Dic47C2×D412yes—
180C22×Dic47C2×D412yes—
181C22×Dic47C2×D414yes—
182C22×Dic47#4114yes—
183C22×Dic47#4114yes—
184C2×D188—28no—
185C2×D188—216no—
186C2×D188—44no—
187C2×D188—48no—
188C2×D188—44no—
189C2×C4×D47—216no—
190C2×C4×D47—216no—
191C2×C4×D47—216no—
192C2×C4×D47—216no—
193C2×C4×D47—216no—
194C2×C4×D47—216no—
195C2×C4×D47—28no—
196C2×C4×D47—216no—
197C2×C4×D47—28no—
198C2×C4×D47—216no—
199C2×C4×D47—216no—
200C2×C4×D47C22⋊C4116yescomplemented
201C4⋊C4×C47—28no—
202C42×C47—28no—
203(C2×D47)⋊C4—28no—
204(C2×D47)⋊C4—28no—
205(C2×D47)⋊C4—28no—
206(C2×D47)⋊C4—48no—
207(C2×D47)⋊C4—48no—
208(C2×D47)⋊C4—48no—
209Dic47⋊C4—28no—
210C4×Dic47—28no—
211C4×Dic47—216no—
212C23×C47C23×C411yescharacteristic
213C23×C47C22×D411yescharacteristic
214C23×C47C22×D411yescharacteristic
215C23×C47C22×D412yes—
216C23×C47C2×#4112yes—
217C23×C47C2×#4112yes—
218C23×C47C2×#4112yes—
219C23×C47C2×#4112yes—
220C23×C47C2×#4112yes—
221C22×D47—22no—
222C22×D47—22no—
223C22×D47—24no—
224C22×D47—24no—
225C22×D47—24no—
226C22×D47—24no—
227C22×D47—24no—
228C22×D47—24no—
229C22×D47—24no—
230C22×D47—24no—
231C22×D47—24no—
232C22×D47—24no—
233C22×D47—24no—
234C22×D47—24no—
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47—24no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—24no—
242C22×D47—41no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—41no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47C2×C22⋊C414yes—
259C22×D47C4×D418yes—
260C22×D47#12014yes—
261C22×D47#12118yes—
262C22×D47#12314yes—
263C2×C4×C47—24no—
264C2×C4×C47—24no—
265C2×C4×C47—22no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—22no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—24no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—41no—
279C2×C4×C47—42no—
280C2×C4×C47—41no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47C2×C22⋊C414yes—
291C2×C4×C47#12318yescomplemented
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—22no—
295C2×Dic47—24no—
296C2×Dic47—22no—
297C2×Dic47—24no—
298C2×Dic47—24no—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—24no—
302C2×Dic47—22no—
303C2×Dic47—24no—
304C2×Dic47—42no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47C2×C22⋊C414yes—
315C2×Dic47#12318yescomplemented
316D188—416no—
317C4×D47—264no—
318C4×D47—232no—
319#14706—471nomaximal, Sylow
320C22×C47C22×C22⋊C411yescharacteristic
321C22×C47C2×C4×D412yes—
322C22×C47C4×#4111yescharacteristic
323C22×C47C4×#4111yescharacteristic
324C22×C47C4×#4112yes—
325C22×C47C2×#12011yescharacteristic
326C22×C47C2×#12112yes—
327C22×C47C2×#12312yes—
328C22×C47C2×#12311yescharacteristic
329C22×C47C2×#12312yes—
330C22×C47#52512yes—
331C22×C47#52512yes—
332C22×C47#52512yes—
333C22×C47#52512yes—
334C22×C47#52912yes—
335C22×C47#52912yes—
336C22×C47#52912yes—
337C22×C47#52912yes—
338C22×C47#53212yes—
339C22×C47#53211yescharacteristic
340C22×C47#53211yescharacteristic
341C2×D47—28no—
342C2×D47—28no—
343C2×D47—28no—
344C2×D47—28no—
345C2×D47—24no—
346C2×D47—24no—
347C2×D47—28no—
348C2×D47—28no—
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—44no—
353C2×D47—44no—
354C2×D47—82no—
355C2×D47—82no—
356C2×D47—82no—
357C2×D47—82no—
358C2×D47#38618yes—
359C4×C47—28no—
360C4×C47—24no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47—82no—
364Dic47—28no—
365Dic47—24no—
366Dic47—42no—
367Dic47—82no—
368C22×#123—471no—
369C23×C42—471no—
370C2×#386—472no—
371C2×#381—471no—
372#1437—471no—
373#1437—471no—
374#1437—472no—
375#1436—472no—
376#1436—471no—
377#1436D4711yescharacteristic, complemented
378C22⋊#95—472no—
379C2×C47C2×#38611yescharacteristic
380C2×C47#229711yescharacteristic
381C2×C47#229711yescharacteristic
382C2×C47C4×#12312yes—
383C2×C47C4×#12312yes—
384C2×C47#284912yes—
385C2×C47#285312yes—
386C2×C47#285412yes—
387C2×C47#285412yes—
388D47—28no—
389D47—82no—
390C23×D4—471no—
391C24×C4—471no—
392C24×C4—472no—
393C2×#123—478no—
394C2×#123—944no—
395C2×#123—944no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4C2×D4711yescharacteristic
398C22×C22⋊C4—471no—
399C22×C22⋊C4—471no—
400C22×C22⋊C4—471no—
401C22×C22⋊C4—472no—
402C22×C22⋊C4—472no—
403C22×C22⋊C4—472no—
404C22×C42—472no—
405C22×C42—471no—
406C22×C42—944no—
407C22×C42—948no—
408C22×C42C2×D4711yescharacteristic
409#386—948no—
410#381—944no—
411C2×#95—472no—
412C2×#95—472no—
413C2×#95—472no—
414C2×#95—472no—
415C2×#95—472no—
416C2×#95—471no—
417C2×#95C2×D4712yes—
418C2×#95C2×D4712yes—
419C2×#95C2×D4711yescharacteristic
420C47#1470611yescharacteristic, complemented, Sylow
421C25—471no—
422C25—471no—
423C22×D4—474no—
424C22×D4—942no—
425C22×D4—942no—
426C22×D4—944no—
427C22×D4—944no—
428C23×C4—471no—
429C23×C4—472no—
430C23×C4—474no—
431C23×C4—474no—
432C23×C4—474no—
433C23×C4—471no—
434C23×C4—478no—
435C23×C4—472no—
436C23×C4—944no—
437C23×C4—944no—
438C23×C4—944no—
439C23×C4—944no—
440C23×C4—944no—
441C23×C4—944no—
442C23×C4—944no—
443C23×C4—944no—
444C23×C4C22×D4712yes—
445C23×C4C22×D4711yescharacteristic
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C23×C4C22×D4712yes—
449#123—9432no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—474no—
453C2×C4⋊C4—942no—
454C2×C4⋊C4—942no—
455C2×C4⋊C4C4×D4714yescomplemented
456C2×C22⋊C4—474no—
457C2×C22⋊C4—474no—
458C2×C22⋊C4—474no—
459C2×C22⋊C4—942no—
460C2×C22⋊C4—942no—
461C2×C22⋊C4—942no—
462C2×C22⋊C4—942no—
463C2×C22⋊C4—942no—
464C2×C22⋊C4—942no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—944no—
467C2×C22⋊C4—944no—
468C2×C22⋊C4—944no—
469C2×C22⋊C4—944no—
470C2×C22⋊C4—944no—
471C2×C22⋊C4—944no—
472C2×C22⋊C4—944no—
473C2×C22⋊C4—944no—
474C2×C42—22no—
475C2×C42—24no—
476C2×C42—9432no—
477C2×C42—944no—
478C2×C42—944no—
479C2×C42—944no—
480C2×C42—942no—
481C2×C42—944no—
482#95—24no—
483#95—22no—
484#95—24no—
485#95—944no—
486#95—944no—
487#95—944no—
488#95—944no—
489#95—942no—
490#95—944no—
491C24—472no—
492C24—472no—
493C24—472no—
494C24—474no—
495C24—474no—
496C24—472no—
497C24—942no—
498C24—942no—
499C24—942no—
500C24—942no—
501C24—941no—
502C24—941no—
503C24—942no—
504C24—942no—
505C24—942no—
506C24—942no—
507C24—942no—
508C24—942no—
509C24C23×D4711yescharacteristic
510C2×D4—948no—
511C2×D4—9416no—
512C2×D4—1884no—
513C2×D4—1888no—
514C2×D4—1884no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—472no—
537C22×C4—472no—
538C22×C4—474no—
539C22×C4—472no—
540C22×C4—474no—
541C22×C4—474no—
542C22×C4—4716no—
543C22×C4—472no—
544C22×C4—9416no—
545C22×C4—948no—
546C22×C4—9416no—
547C22×C4—9416no—
548C22×C4—9416no—
549C22×C4—948no—
550C22×C4—9416no—
551C22×C4—9416no—
552C22×C4—9416no—
553C22×C4—9416no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—9416no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4C2×C4×D4712yes—
573C22×C4C2×C4×D4712yes—
574C22×C4C2×C4×D4712yes—
575C22×C4#1062535014yes—
576C22×C4D4×D4712yes—
577C22×C4D4×D4712yes—
578C22×C4D4×D4714yes—
579C22×C4#1062535414yes—
580C4⋊C4—28no—
581C4⋊C4—948no—
582C22⋊C4—948no—
583C22⋊C4—948no—
584C22⋊C4—948no—
585C22⋊C4—1888no—
586C22⋊C4—1888no—
587C22⋊C4—1888no—
588C42—28no—
589C42—9416no—
590C42—948no—
591C23—474no—
592C23—478no—
593C23—474no—
594C23—478no—
595C23—474no—
596C23—942no—
597C23—942no—
598C23—944no—
599C23—944no—
600C23—944no—
601C23—944no—
602C23—944no—
603C23—944no—
604C23—944no—
605C23—944no—
606C23—944no—
607C23—944no—
608C23—944no—
609C23—944no—
610C23—942no—
611C23—942no—
612C23—942no—
613C23—944no—
614C23—942no—
615C23—942no—
616C23—944no—
617C23—1881no—
618C23—1882no—
619C23—1882no—
620C23—1881no—
621C23—1882no—
622C23—1882no—
623C23—1882no—
624C23—1882no—
625C23—1882no—
626C23—1882no—
627C23—1882no—
628C23—1882no—
629C23—1882no—
630C23—1882no—
631C23—1881no—
632C23—1881no—
633C23C22×C4×D4711yescharacteristic
634C23C2×D4×D4711yescharacteristic
635C23C2×D4×D4711yescharacteristic
636C23C2×D4×D4712yes—
637C23#41×D4712yes—
638C23#41×D4712yes—
639C23#41×D4712yes—
640C23C2×#1062535012yes—
641C23C2×#1062535412yes—
642D4—18816no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—474no—
671C2×C4—478no—
672C2×C4—9432no—
673C2×C4—9464no—
674C2×C4—944no—
675C2×C4—944no—
676C2×C4—942no—
677C2×C4—944no—
678C2×C4—942no—
679C2×C4—944no—
680C2×C4—944no—
681C2×C4—944no—
682C2×C4—944no—
683C2×C4—944no—
684C2×C4—942no—
685C2×C4—944no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4C22⋊C4×D4714yes—
697C2×C4#1309400918yescomplemented
698C22—478no—
699C22—948no—
700C22—948no—
701C22—948no—
702C22—948no—
703C22—944no—
704C22—944no—
705C22—948no—
706C22—948no—
707C22—3762no—
708C22—3762no—
709C22—3762no—
710C22—3762no—
711C22—1882no—
712C22—1882no—
713C22—1882no—
714C22—1884no—
715C22—1884no—
716C22C2×C22⋊C4×D4711yescharacteristic
717C22C4×D4×D4712yes—
718C22#1568959111yescharacteristic
719C22C4×#1062535011yescharacteristic
720C22C4×#1062535412yes—
721C22#120×D4711yescharacteristic
722C22#121×D4712yes—
723C22#123×D4712yes—
724C22#123×D4711yescharacteristic
725C22C2×#1309400912yes—
726C22#1568963212yes—
727C22#1568963212yes—
728C22#1568963612yes—
729C22#1568963612yes—
730C22#1568965112yes—
731C22#1568965612yes—
732C22#1568965812yes—
733C22#1568966012yes—
734C22#1568967012yes—
735C22#1568967211yescharacteristic
736C22#1568967411yescharacteristic
737C4—28no—
738C4—24no—
739C4—42no—
740C4—42no—
741C4—82no—
742C4—948no—
743C4—944no—
744C4—3762no—
745C4—1882no—
746C2—948no—
747C2—3762no—
748C2#386×D4711yescharacteristic
749C2#2024587411yescharacteristic
750C2#2024587711yescharacteristic
751C2#2024590912yes—
752C2C4×#1309400912yes—
753C2#2025168312yes—
754C2#2025171212yes—
755C2#2025171512yes—
756C2#2025172112yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenter#1436D47
hypocenterC47#14706
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C42×D47C2semidirect
4. C2×#15688985C2semidirect
5. #20241626C2semidirect
6. #20241624C2semidirect
7. #20241624C2semidirect
8. #20241620C2semidirect
9. #20241619C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C47×#1436C2semidirect
17. C2×#13094009C4semidirect
68. C2×Dic47⋊C4C2×C4semidirect
85. C2×(C2×D47)⋊C4C2×C4semidirect
86. C2×(C2×D47)⋊C4C2×C4semidirect
106. C2×C4⋊C4×C47C2×C4semidirect
200. C2×C4×D47C22⋊C4semidirect
291. C2×C4×C47#123semidirect
315. C2×Dic47#123semidirect
377. #1436D47semidirect
420. C47#14706semidirect
455. C2×C4⋊C4C4×D47semidirect
697. C2×C4#13094009semidirect

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×C42×D472
C2×#156890012
C2×#156889852
#202416262
#202416242
#202416202
#202416192
(C2×D47)⋊#952
C47×#14362
#1470647