Finite Group Databasebeta

← #463×Dic47 #26222499

Subgroups — #463×Dic47 #26222499

Order 12032.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic47C211yesmaximal, characteristic, complemented
2C2×D8×Dic47C211yesmaximal, characteristic
3#124×Dic47C211yesmaximal, characteristic, complemented
4C4×D4×Dic47C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244158C211yesmaximal, characteristic, complemented
7#20244031C211yesmaximal, characteristic, complemented
8#20244017C211yesmaximal, characteristic, complemented
9#20243738C211yesmaximal, characteristic
10#20243724C211yesmaximal, characteristic, complemented
11#20243398C211yesmaximal, characteristic, complemented
12C4⋊C8×Dic47C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#102×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#463C211yesmaximal, characteristic
16C2×Q8×Dic47C2211yescharacteristic
17C2×D4×Dic47C2211yescharacteristic
18C2×D4×Dic47C2211yescharacteristic
19C2×D4×Dic47C2211yescharacteristic
20C22×C4×Dic47—21no—
21SD16×Dic47—24no—
22D8×Dic47—24no—
23C2×#13093958C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×C8×Dic47C2211yescharacteristic
33C2×C8×Dic47C2211yescharacteristic
34#15689030C2211yescharacteristic
35#15689026C2211yescharacteristic
36#15689016—21no—
37#15689016—21no—
38#15688989C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4⋊C4×Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C22⋊C4×Dic47—21no—
43C22⋊C4×Dic47—21no—
44C22⋊C4×Dic47—21no—
45C22⋊C4×Dic47—21no—
46C4×C22⋊Dic47—21no—
47C42×Dic47C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C22×SD16×C47C2211yescharacteristic
55C22×D8×C47C2211yescharacteristic
56C2×#124×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C47×#463C418yescomplemented
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C2×#102×C47C2211yescharacteristic
62C23×Dic47—21no—
63C23×Dic47—21no—
64C23×Dic47—21no—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67Q8×Dic47—22no—
68Q8×Dic47—22no—
69D4×Dic47—22no—
70D4×Dic47—22no—
71D4×Dic47—22no—
72D4×Dic47—22no—
73D4×Dic47—22no—
74D4×Dic47D414yes—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C22⋊Dic47—21no—
81C2×C22⋊Dic47—21no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—44no—
90C2×C4×Dic47D411yescharacteristic
91C2×C4×Dic47D411yescharacteristic
92C2×C4×Dic47D411yescharacteristic
93C2×C4×Dic47D411yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95C2×C4×Dic47C2311yescharacteristic
96#13093958—22no—
97#13093956—22no—
98C4⋊(C47⋊C8)—22no—
99#13093948—22no—
100#13093948—22no—
101#13093945—22no—
102#13093945—22no—
103#13093945—22no—
104#13093945—22no—
105C8×Dic47—22no—
106C8×Dic47—22no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C47⋊#95—21no—
114C22×Q8×C47C2311yescharacteristic
115C22×D4×C47C2311yescharacteristic
116C22×D4×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C2×SD16×C47—22no—
119C2×SD16×C47—22no—
120C2×SD16×C47C2×C414yescomplemented
121C2×D8×C47—22no—
122C2×D8×C47—22no—
123C2×D8×C47C2×C414yes—
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126#124×C47—22no—
127#124×C47C2×C414yescomplemented
128C4×D4×C47—22no—
129C4×D4×C47C2×C414yescomplemented
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C42×C47C2311yescharacteristic
135C4⋊C8×C47C2×C414yescomplemented
136#103×C47C2×C414yescomplemented
137#102×C47C2×C414yescomplemented
138C24×C47—21no—
139C24×C47—21no—
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C412yes—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47C22×C412yes—
155C2×D4×C47C22×C412yes—
156C2×D4×C47C2×D412yes—
157C2×D4×C47#4112yes—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—24no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2411yescharacteristic
166C22×Dic47—24no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—24no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—42no—
173C22×Dic47—42no—
174C22×Dic47—42no—
175C22×Dic47—42no—
176C22×Dic47—42no—
177C22×Dic47—42no—
178C22×Dic47—42no—
179C22×Dic47C2×D411yescharacteristic
180C22×Dic47C2×D411yescharacteristic
181C22×Dic47C2×D411yescharacteristic
182C22×Dic47C2×D411yescharacteristic
183SD16×C47—28no—
184D8×C47—28no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47C22×C412yes—
190C2×C8×C47C22×C412yes—
191C4⋊C4×C47—21no—
192C4⋊C4×C47C22×C412yes—
193C22⋊C4×C47—24no—
194C22⋊C4×C47—24no—
195C22⋊C4×C47—24no—
196C42×C47C22×C412yes—
197C42×C47#4112yes—
198C22⋊Dic47—24no—
199C22⋊Dic47—24no—
200C22⋊Dic47—42no—
201C22⋊Dic47—42no—
202C22⋊Dic47—42no—
203C4⋊Dic47—21no—
204C4⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47—21no—
209C4⋊Dic47—42no—
210C4⋊Dic47C2×D412yes—
211C4⋊Dic47#4112yes—
212C4×Dic47—21no—
213C4×Dic47—21no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C4×Dic47—41no—
218C4×Dic47—42no—
219C4×Dic47—42no—
220C4×Dic47—42no—
221C4×Dic47—42no—
222C4×Dic47C2×D412yes—
223C4×Dic47#4112yes—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—22no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47C22×D411yescharacteristic
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47—22no—
252D4×C47—22no—
253D4×C47—22no—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47C4×D414yes—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—48no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47C4×D412yes—
269C2×C4×C47C4×D412yes—
270C2×C4×C47C23×C411yescharacteristic
271C2×C4×C47C22×D411yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—22no—
281C2×Dic47—21no—
282C2×Dic47—22no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—48no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—48no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—84no—
298C2×Dic47#12112yes—
299C2×Dic47#12112yes—
300C2×Dic47#13512yes—
301C2×Dic47#13512yes—
302C2×Dic47AGL(1,ℤ/8)12yes—
303C8×C47—22no—
304C8×C47—22no—
305C47⋊C8—41no—
306C47⋊C8—41no—
307C4×#463—471nomaximal, Sylow
308C22×C47—24no—
309C22×C47—42no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—42no—
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47C2×C4×D411yescharacteristic
323C22×C47C2×#12111yescharacteristic
324C22×C47#52511yescharacteristic
325C22×C47C2×#13511yescharacteristic
326C22×C47C2×#13511yescharacteristic
327C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C47#57511yescharacteristic
329C4×C47—22no—
330C4×C47—22no—
331C4×C47—42no—
332C4×C47—42no—
333C4×C47C2×C4×D411yescharacteristic
334C4×C47C4×#4111yescharacteristic
335C4×C47#52911yescharacteristic
336C4×C47#53211yescharacteristic
337Dic47—22no—
338Dic47—22no—
339Dic47—41no—
340Dic47—42no—
341Dic47—42no—
342Dic47—81no—
343Dic47—81no—
344Dic47#46314yesdirect product factor
345C2×#463D4711yescharacteristic
346C2×C4×SD16—471no—
347C2×C4×D8—471no—
348C4×#124—471no—
349C42×D4—471no—
350#1983—471no—
351#1949—471no—
352#1928—471no—
353#1926—471no—
354#1879—471no—
355#1877—471no—
356#1804—471no—
357C4×C4⋊C8—471no—
358C4×#103—471no—
359C4×#102—471no—
360C2×C47—44no—
361C2×C47—82no—
362C2×C47C4×#12111yescharacteristic
363C2×C47C4×#13511yescharacteristic
364C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
365C2×C47C2×#46311yescharacteristic
366C2×C47#303511yescharacteristic
367C2×C47#310211yescharacteristic
368C2×C47#310511yescharacteristic
369C22×SD16C2×D4711yescharacteristic
370C22×D8C2×D4711yescharacteristic
371C2×#124C2×D4711yescharacteristic
372C2×C4×Q8—471no—
373C2×C4×D4—471no—
374C2×C4×D4—471no—
375C2×C4×D4—471no—
376C2×C4×D4C2×D4711yescharacteristic
377C22×C42—941no—
378#463Dic4718yesdirect product factor
379C4×SD16—944no—
380C4×D8—944no—
381C2×#107—471no—
382C2×#106—471no—
383C2×C4⋊C8—471no—
384C2×C4⋊C8C2×D4711yescharacteristic
385C2×#103—471no—
386C2×#103—471no—
387C2×#103C2×D4711yescharacteristic
388C2×#102—471no—
389C2×#102—471no—
390C2×#102—471no—
391C2×#102—471no—
392C2×#102C2×D4711yescharacteristic
393C2×C4×C8—471no—
394C2×C4×C8—471no—
395#391—471no—
396#390—471no—
397#388—941no—
398#388—941no—
399#382—471no—
400C4×C4⋊C4—471no—
401C4×C4⋊C4—471no—
402C4×C4⋊C4—471no—
403C4×C22⋊C4—941no—
404C4×C22⋊C4—941no—
405C4×C22⋊C4—941no—
406C4×C22⋊C4—941no—
407C4×C22⋊C4—941no—
408C43—471no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#336—471no—
414#336—471no—
415C47C4×#46311yescharacteristic, complemented, Sylow
416C22×Q8C22×D4711yescharacteristic
417C22×D4C22×D4711yescharacteristic
418C22×D4C22×D4711yescharacteristic
419C23×C4—21no—
420C23×C4—941no—
421C23×C4—941no—
422C23×C4—941no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×Dic4714yescomplemented
426C2×D8—22no—
427C2×D8—22no—
428C2×D8C2×Dic4714yes—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8C22×D4711yescharacteristic
432C22×C8C22×D4711yescharacteristic
433#124—22no—
434#124C2×Dic4714yescomplemented
435C4×Q8—942no—
436C4×Q8—942no—
437C4×D4—22no—
438C4×D4—474no—
439C4×D4—942no—
440C4×D4—942no—
441C4×D4—942no—
442C4×D4—942no—
443C4×D4—942no—
444C4×D4C2×Dic4714yescomplemented
445C2×C4⋊C4—471no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—941no—
450C2×C4⋊C4C22×D4711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—941no—
455C2×C22⋊C4—941no—
456C2×C22⋊C4—941no—
457C2×C22⋊C4—941no—
458C2×C22⋊C4—941no—
459C2×C42—471no—
460C2×C42—471no—
461C2×C42—471no—
462C2×C42—471no—
463C2×C42—471no—
464C2×C42—471no—
465C2×C42—941no—
466C2×C42—941no—
467C2×C42—941no—
468C2×C42—941no—
469C2×C42—1884no—
470C2×C42C22×D4711yescharacteristic
471#107—942no—
472#106—942no—
473C4⋊C8—942no—
474C4⋊C8C2×Dic4714yescomplemented
475#103—942no—
476#103—942no—
477#103C2×Dic4714yescomplemented
478#102—942no—
479#102—942no—
480#102—942no—
481#102—942no—
482#102C2×Dic4714yescomplemented
483C4×C8—942no—
484C4×C8—942no—
485#95—941no—
486#95—941no—
487#95—941no—
488#95—941no—
489#95—941no—
490#95—941no—
491#95—941no—
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×Dic4712yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4D4×D4712yes—
509C2×D4#1062535212yes—
510C2×D4C22×Dic4712yes—
511C2×D4C22×Dic4712yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—471no—
518C22×C4—471no—
519C22×C4—471no—
520C22×C4—471no—
521C22×C4—944no—
522C22×C4—944no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—1882no—
528C22×C4—1882no—
529C22×C4—1882no—
530C22×C4—1882no—
531C22×C4—1882no—
532C22×C4—1882no—
533C22×C4—1882no—
534C22×C4D4×D4711yescharacteristic
535C22×C4D4×D4711yescharacteristic
536C22×C4C23×D4711yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—941no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8C22×Dic4712yes—
550C2×C8C22×Dic4712yes—
551C4⋊C4—21no—
552C4⋊C4—472no—
553C4⋊C4—472no—
554C4⋊C4—941no—
555C4⋊C4—941no—
556C4⋊C4—941no—
557C4⋊C4—941no—
558C4⋊C4—941no—
559C4⋊C4—941no—
560C4⋊C4—1882no—
561C4⋊C4C22×Dic4712yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—944no—
566C22⋊C4—944no—
567C22⋊C4—1882no—
568C22⋊C4—1882no—
569C22⋊C4—1882no—
570C42—472no—
571C42—472no—
572C42—942no—
573C42—942no—
574C42—942no—
575C42—941no—
576C42—941no—
577C42—1881no—
578C42—1882no—
579C42—1882no—
580C42—1882no—
581C42—1882no—
582C42#1062535212yes—
583C42C22×Dic4712yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C2×D4×D4711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4D4×Dic4714yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—48no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—472no—
623C2×C4—472no—
624C2×C4—472no—
625C2×C4—472no—
626C2×C4—472no—
627C2×C4—941no—
628C2×C4—941no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—942no—
632C2×C4—941no—
633C2×C4—942no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—3764no—
637C2×C4—1888no—
638C2×C4—1888no—
639C2×C4—1881no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4D4×Dic4712yes—
650C2×C4D4×Dic4712yes—
651C2×C4C23×Dic4711yescharacteristic
652C2×C4C2×D4×D4711yescharacteristic
653C2×C4#41×D4711yescharacteristic
654C2×C4#41×D4711yescharacteristic
655C2×C4C2×#1062535211yescharacteristic
656C2×C4C2×#1062535211yescharacteristic
657C8—22no—
658C8—22no—
659C8—1881no—
660C8—1881no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×D4×Dic4711yescharacteristic
676C22#121×D4711yescharacteristic
677C22#1568963311yescharacteristic
678C22#135×D4711yescharacteristic
679C22#135×D4711yescharacteristic
680C22AGL(1,ℤ/8)×D4711yescharacteristic
681C22#1568991911yescharacteristic
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—474no—
687C4—942no—
688C4—942no—
689C4—3761no—
690C4—3761no—
691C4—1882no—
692C4—1881no—
693C4—1882no—
694C4C2×D4×Dic4711yescharacteristic
695C4#41×Dic4711yescharacteristic
696C4#1568965411yescharacteristic
697C4#1568966811yescharacteristic
698C2—44no—
699C2—82no—
700C2#121×Dic4711yescharacteristic
701C2#135×Dic4711yescharacteristic
702C2AGL(1,ℤ/8)×Dic4711yescharacteristic
703C2#463×D4711yescharacteristic
704C2#2025284011yescharacteristic
705C2#2025340311yescharacteristic
706C2#2025343411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#463C2
socleC23×C47C22×D4
prime radicalC22×D8×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#463D47
hypocenterC47C4×#463
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic47C2semidirect
3. #124×Dic47C2semidirect
4. C4×D4×Dic47C2semidirect
5. #20244321C2semidirect
6. #20244158C2semidirect
7. #20244031C2semidirect
8. #20244017C2semidirect
10. #20243724C2semidirect
11. #20243398C2semidirect
12. C4⋊C8×Dic47C2semidirect
13. #103×Dic47C2semidirect
14. #102×Dic47C2semidirect
58. C47×#463C4semidirect
120. C2×SD16×C47C2×C4semidirect
127. #124×C47C2×C4semidirect
129. C4×D4×C47C2×C4semidirect
135. C4⋊C8×C47C2×C4semidirect
136. #103×C47C2×C4semidirect
137. #102×C47C2×C4semidirect
344. Dic47#463direct (N × H)
378. #463Dic47direct (N × H)
415. C47C4×#463semidirect
425. C2×SD16C2×Dic47semidirect
434. #124C2×Dic47semidirect
444. C4×D4C2×Dic47semidirect
474. C4⋊C8C2×Dic47semidirect
477. #103C2×Dic47semidirect
482. #102C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic472
C2×D8×Dic472
#124×Dic472
C4×D4×Dic472
#202443212
#202441582
#202440312
#202440172
#202437382
#202437242
#202433982
C4⋊C8×Dic472
#103×Dic472
#102×Dic472
C2×C47×#4632
C4×#46347