Finite Group Databasebeta

← #468×Dic47 #26222908

Subgroups — #468×Dic47 #26222908

Order 12032.

1086 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×M16×Dic47C211yesmaximal, characteristic, complemented
3C22⋊Q8×Dic47C211yesmaximal, characteristic, complemented
4#121×Dic47C211yesmaximal, characteristic
5#20244271C211yesmaximal, characteristic, complemented
6#20244127C211yesmaximal, characteristic, complemented
7#20244087C211yesmaximal, characteristic, complemented
8#20244080C211yesmaximal, characteristic, complemented
9#20243827C211yesmaximal, characteristic
10#20243822C211yesmaximal, characteristic, complemented
11#20243421C211yesmaximal, characteristic, complemented
12#107×Dic47C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#102×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#468C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×Q8×Dic47C2211yescharacteristic
18C2×D4×Dic47—21no—
19C2×D4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21SD16×Dic47—24no—
22C2×#13093958C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28M16×Dic47—24no—
29C2×#13093934C2211yescharacteristic
30C2×#13093934C2211yescharacteristic
31C2×C8×Dic47C2211yescharacteristic
32C2×C8×Dic47C2211yescharacteristic
33#15689030C2211yescharacteristic
34#15689026C2211yescharacteristic
35#15689022C2211yescharacteristic
36#15689022C2211yescharacteristic
37#15689016—21no—
38#15689009—21no—
39#15689003—21no—
40#15688998—21no—
41#15688983C2211yescharacteristic
42#15688983C2211yescharacteristic
43C4⋊C4×Dic47—21no—
44C4⋊C4×Dic47C2211yescharacteristic
45C4⋊C4×Dic47C2211yescharacteristic
46C22⋊C4×Dic47—21no—
47C22⋊C4×Dic47—21no—
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54C22×SD16×C47C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C2×C22⋊Q8×C47C2211yescharacteristic
57C2×#121×C47C2211yescharacteristic
58C47×#468C418yescomplemented
59C2×#107×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C2×#102×C47C2211yescharacteristic
62C23×Dic47—21no—
63C23×Dic47D411yescharacteristic
64C23×Dic47D411yescharacteristic
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—22no—
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72D4×Dic47—22no—
73D4×Dic47—22no—
74D4×Dic47—44no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47D411yescharacteristic
93C2×C4×Dic47D411yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95C2×C4×Dic47C2311yescharacteristic
96#13093958—22no—
97#13093956—22no—
98#13093948—22no—
99#13093948—22no—
100#13093945—22no—
101#13093945—22no—
102#13093934—22no—
103#13093934—22no—
104C8×Dic47—22no—
105C8×Dic47D414yescomplemented
106C47⋊#95—21no—
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×C47—21no—
116C22×D4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C2×SD16×C47—22no—
119C2×SD16×C47—22no—
120C2×SD16×C47C2×C414yescomplemented
121C2×M16×C47—22no—
122C2×M16×C47—22no—
123C2×M16×C47C2×C414yescomplemented
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126C22⋊Q8×C47—22no—
127C22⋊Q8×C47C2×C414yescomplemented
128#121×C47—22no—
129#121×C47C2×C414yes—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135#107×C47C2×C414yescomplemented
136#103×C47C2×C414yescomplemented
137#102×C47C2×C414yescomplemented
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
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—24no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—42no—
153C2×D4×C47—42no—
154C2×D4×C47C22×C412yes—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47#4112yes—
165C22×C4×C47C2411yescharacteristic
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—41no—
175C22×Dic47—41no—
176C22×Dic47—42no—
177C22×Dic47—42no—
178C22×Dic47—42no—
179C22×Dic47C2×D411yescharacteristic
180C22×Dic47C2×D411yescharacteristic
181C22×Dic47C2×D411yescharacteristic
182C22×Dic47C2×D411yescharacteristic
183SD16×C47—28no—
184M16×C47—28no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47C22×C412yes—
188C2×C8×C47C22×C412yes—
189C2×C8×C47C2×D412yes—
190C2×C8×C47#4112yes—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47C22×C412yes—
195C4⋊C4×C47C22×C412yes—
196C22⋊C4×C47—24no—
197C22⋊C4×C47—24no—
198C22⋊Dic47—42no—
199C22⋊Dic47—42no—
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—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—42no—
212C4⋊Dic47—42no—
213C4⋊Dic47—42no—
214C4×Dic47—21no—
215C4×Dic47—21no—
216C4×Dic47—22no—
217C4×Dic47—22no—
218C4×Dic47—42no—
219C4×Dic47—42no—
220C4×Dic47—42no—
221C4×Dic47C2×D412yes—
222C4×Dic47#4112yes—
223#10625329—28no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8C2×D412yes—
229C2×C47⋊C8#4112yes—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—22no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47C4×D412yes—
244C23×C47C22×D411yescharacteristic
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47—48no—
252D4×C47—41no—
253D4×C47—41no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
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—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—44no—
285C2×Dic47—44no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—84no—
299C2×Dic47#12112yes—
300C2×Dic47#12112yes—
301C2×Dic47AGL(1,ℤ/8)12yes—
302C2×Dic47#13712yes—
303C8×C47—22no—
304C8×C47C4×D414yescomplemented
305C47⋊C8—22no—
306C47⋊C8—22no—
307C4×#468—471nomaximal, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
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#53211yescharacteristic
325C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C47C2×#13711yescharacteristic
327C22×C47#57511yescharacteristic
328C22×C47#57511yescharacteristic
329C4×C47—22no—
330C4×C47—42no—
331C4×C47—42no—
332C4×C47—42no—
333C4×C47C2×C4×D411yescharacteristic
334C4×C47C4×#4111yescharacteristic
335C4×C47#52511yescharacteristic
336C4×C47#52911yescharacteristic
337Dic47—22no—
338Dic47—41no—
339Dic47—41no—
340Dic47—81no—
341Dic47—81no—
342Dic47—81no—
343Dic47—81no—
344Dic47#46814yesdirect product factor
345C2×#468D4711yescharacteristic
346C2×C4×SD16—471no—
347C2×C4×M16—471no—
348C4×C22⋊Q8—471no—
349C4×#121—471no—
350#1973—471no—
351#1943—471no—
352#1936—471no—
353#1935—471no—
354#1895—471no—
355#1894—471no—
356#1809—471no—
357C4×#107—471no—
358C4×#103—471no—
359C4×#102—471no—
360C2×C47—42no—
361C2×C47—82no—
362C2×C47C4×#12111yescharacteristic
363C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
364C2×C47C4×#13711yescharacteristic
365C2×C47C2×#46811yescharacteristic
366C2×C47#305411yescharacteristic
367C2×C47#317111yescharacteristic
368C2×C47#317211yescharacteristic
369C22×SD16C2×D4711yescharacteristic
370C22×M16—471no—
371C22×M16C2×D4711yescharacteristic
372C2×C22⋊Q8C2×D4711yescharacteristic
373C2×#121C2×D4711yescharacteristic
374C2×C4×Q8—471no—
375C2×C4×D4—471no—
376C2×C4×D4—941no—
377C22×C42—471no—
378#468Dic4718yesdirect product factor
379C4×SD16—944no—
380C2×#107—471no—
381C2×#107C2×D4711yescharacteristic
382C2×#106—471no—
383C2×#103—471no—
384C2×#103—471no—
385C2×#103C2×D4711yescharacteristic
386C2×#102—471no—
387C2×#102—471no—
388C2×#102C2×D4711yescharacteristic
389C4×M16—944no—
390C2×#97—471no—
391C2×#97—471no—
392C2×C4×C8—471no—
393C2×C4×C8—471no—
394#391—471no—
395#390—471no—
396#389—471no—
397#389—471no—
398#388—941no—
399#387—941no—
400#386—941no—
401#385—941no—
402#380—471no—
403#380—471no—
404C4×C4⋊C4—471no—
405C4×C4⋊C4—471no—
406C4×C4⋊C4—941no—
407C4×C22⋊C4—941no—
408C4×C22⋊C4—941no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415C47C4×#46811yescharacteristic, complemented, Sylow
416C22×Q8C22×D4711yescharacteristic
417C22×D4—21no—
418C22×D4C22×D4711yescharacteristic
419C23×C4—471no—
420C23×C4—471no—
421C23×C4—941no—
422C23×C4C22×D4711yescharacteristic
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×Dic4714yescomplemented
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—942no—
429C2×M16—942no—
430C2×M16—942no—
431C2×M16C2×Dic4714yescomplemented
432C22×C8—471no—
433C22×C8—471no—
434C22×C8C22×D4711yescharacteristic
435C22×C8C22×D4711yescharacteristic
436C22⋊Q8—22no—
437C22⋊Q8C2×Dic4714yescomplemented
438#121—22no—
439#121C2×Dic4714yes—
440C4×Q8—942no—
441C4×Q8—942no—
442C4×D4—942no—
443C4×D4—942no—
444C4×D4—1884no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—471no—
450C2×C4⋊C4—941no—
451C2×C4⋊C4—941no—
452C2×C4⋊C4—941no—
453C2×C4⋊C4C22×D4711yescharacteristic
454C2×C4⋊C4C22×D4711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—941no—
458C2×C22⋊C4—941no—
459C2×C22⋊C4—941no—
460C2×C22⋊C4—941no—
461C2×C22⋊C4—941no—
462C2×C42—471no—
463C2×C42—471no—
464C2×C42—471no—
465C2×C42—471no—
466C2×C42—942no—
467C2×C42—942no—
468C2×C42—941no—
469C2×C42—941no—
470C2×C42—941no—
471#107—942no—
472#107C2×Dic4714yescomplemented
473#106—942no—
474#103—942no—
475#103—942no—
476#103C2×Dic4714yescomplemented
477#102—942no—
478#102—942no—
479#102C2×Dic4714yescomplemented
480#97—942no—
481#97—942no—
482C4×C8—474no—
483C4×C8—942no—
484#95—941no—
485#95—941no—
486#95—941no—
487#95—941no—
488#95—941no—
489#95—941no—
490#95—941no—
491#95—941no—
492C24—21no—
493C24D4×D4711yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×Dic4712yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4C22×Dic4712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—471no—
517C22×C4—471no—
518C22×C4—471no—
519C22×C4—471no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—1882no—
529C22×C4—1882no—
530C22×C4—1882no—
531C22×C4—1881no—
532C22×C4—1881no—
533C22×C4D4×D4711yescharacteristic
534C22×C4#1062535212yes—
535C22×C4C22×Dic4712yes—
536C22×C4C23×D4711yescharacteristic
537SD16—28no—
538M16—28no—
539M16—948no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—472no—
543C2×C8—472no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8D4×D4712yes—
549C2×C8#1062535212yes—
550C2×C8C22×Dic4712yes—
551C2×C8C22×Dic4712yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—941no—
556C4⋊C4—941no—
557C4⋊C4—941no—
558C4⋊C4—941no—
559C4⋊C4—941no—
560C4⋊C4—941no—
561C4⋊C4—941no—
562C4⋊C4—941no—
563C4⋊C4—1882no—
564C4⋊C4—1882no—
565C4⋊C4—1882no—
566C4⋊C4C22×Dic4712yes—
567C4⋊C4C22×Dic4712yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—1882no—
571C22⋊C4—1882no—
572C22⋊C4—1882no—
573C22⋊C4—1882no—
574C22⋊C4—1882no—
575C42—472no—
576C42—472no—
577C42—942no—
578C42—942no—
579C42—941no—
580C42—941no—
581C42—1882no—
582C42—1882no—
583C42—1882no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23D4×Dic4712yes—
598C23C2×D4×D4711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
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—941no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—3764no—
636C2×C4—1884no—
637C2×C4—1884no—
638C2×C4—1881no—
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×C4—1881no—
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—942no—
659C8—942no—
660C8D4×Dic4714yescomplemented
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×D4×Dic4711yescharacteristic
676C22#121×D4711yescharacteristic
677C22#1568966811yescharacteristic
678C22AGL(1,ℤ/8)×D4711yescharacteristic
679C22#137×D4711yescharacteristic
680C22#1568991911yescharacteristic
681C22#1568992211yescharacteristic
682C4—22no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—474no—
687C4—942no—
688C4—3761no—
689C4—3761no—
690C4—3761no—
691C4—3761no—
692C4—1881no—
693C4—1881no—
694C4C2×D4×Dic4711yescharacteristic
695C4#41×Dic4711yescharacteristic
696C4#1568963311yescharacteristic
697C4#1568965411yescharacteristic
698C2—42no—
699C2—82no—
700C2#121×Dic4711yescharacteristic
701C2AGL(1,ℤ/8)×Dic4711yescharacteristic
702C2#137×Dic4711yescharacteristic
703C2#468×D4711yescharacteristic
704C2#2025299211yescharacteristic
705C2#2025397611yescharacteristic
706C2#2025398711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#468D47
hypocenterC47C4×#468
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic47C2semidirect
2. C2×M16×Dic47C2semidirect
3. C22⋊Q8×Dic47C2semidirect
5. #20244271C2semidirect
6. #20244127C2semidirect
7. #20244087C2semidirect
8. #20244080C2semidirect
10. #20243822C2semidirect
11. #20243421C2semidirect
12. #107×Dic47C2semidirect
13. #103×Dic47C2semidirect
14. #102×Dic47C2semidirect
58. C47×#468C4semidirect
105. C8×Dic47D4semidirect
120. C2×SD16×C47C2×C4semidirect
123. C2×M16×C47C2×C4semidirect
127. C22⋊Q8×C47C2×C4semidirect
135. #107×C47C2×C4semidirect
136. #103×C47C2×C4semidirect
137. #102×C47C2×C4semidirect
304. C8×C47C4×D4semidirect
344. Dic47#468direct (N × H)
378. #468Dic47direct (N × H)
415. C47C4×#468semidirect
425. C2×SD16C2×Dic47semidirect
431. C2×M16C2×Dic47semidirect
437. C22⋊Q8C2×Dic47semidirect
472. #107C2×Dic47semidirect
476. #103C2×Dic47semidirect
479. #102C2×Dic47semidirect
660. C8D4×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×M16×Dic472
C22⋊Q8×Dic472
#121×Dic472
#202442712
#202441272
#202440872
#202440802
#202438272
#202438222
#202434212
#107×Dic472
#103×Dic472
#102×Dic472
C2×C47×#4682
C4×#46847