Finite Group Databasebeta

← #26138187

Subgroups — #26138187

Order 12032.

2950 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic47C211yesmaximal, characteristic, complemented
2C2×#15689003C212yesmaximal
3C2×#15688983C212yesmaximal, complemented
4C2×#15688983C211yesmaximal, characteristic, complemented
5#20241641C212yesmaximal, complemented
6#20241633C212yesmaximal, complemented
7#20241618C212yesmaximal, complemented
8#20241610C212yesmaximal, complemented
9C22×C4×D4×C47C211yesmaximal, characteristic
10C24×Dic47C2212yes—
11C22×C4⋊Dic47—28no—
12C22×C4⋊Dic47—24no—
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2212yes—
15C22×C4⋊Dic47C2212yes—
16C22×C22⋊Dic47C2212yes—
17C22×C22⋊Dic47C2214yes—
18#15689003—28no—
19#15688983—28no—
20#15688983—24no—
21C2×C47⋊#95C2214yes—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2214yes—
24C2×C47⋊#95C2214yes—
25C23×D4×C47C2211yescharacteristic
26C24×C4×C47C2211yescharacteristic
27C24×C4×C47C2211yescharacteristic
28C2×C4×D4×C47—24no—
29C2×C4×D4×C47—24no—
30C2×C4×D4×C47C418yescomplemented
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C23×Dic47—24no—
36C23×Dic47—28no—
37C23×Dic47—24no—
38C23×Dic47—24no—
39C23×Dic47—44no—
40C23×Dic47C2314yes—
41C23×Dic47C2314yes—
42C2×C4⋊Dic47—232no—
43C2×C4⋊Dic47—24no—
44C2×C4⋊Dic47—24no—
45C2×C4⋊Dic47—24no—
46C2×C4⋊Dic47—28no—
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47—24no—
50C2×C4⋊Dic47D418yescomplemented
51C2×C22⋊Dic47—24no—
52C2×C22⋊Dic47—28no—
53C2×C22⋊Dic47—24no—
54C2×C22⋊Dic47—24no—
55C2×C22⋊Dic47—28no—
56C2×C22⋊Dic47—44no—
57C47⋊#95—24no—
58C47⋊#95—28no—
59C47⋊#95—28no—
60C47⋊#95—44no—
61C25×C47C2311yescharacteristic
62C25×C47C2311yescharacteristic
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47C2×C414yes—
68C22×D4×C47D414yes—
69C22×D4×C47Q814yes—
70C23×C4×C47—24no—
71C23×C4×C47—24no—
72C23×C4×C47—24no—
73C23×C4×C47—22no—
74C23×C4×C47—22no—
75C23×C4×C47—24no—
76C23×C4×C47C2×C414yes—
77C23×C4×C47C2×C414yescomplemented
78C23×C4×C47D414yes—
79C23×C4×C47D414yes—
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C4×D4×C47—232no—
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47C2×C414yescomplemented
89C2×C22⋊C4×C47—22no—
90C2×C22⋊C4×C47—22no—
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—22no—
93C2×C22⋊C4×C47C2×C414yes—
94C2×C22⋊C4×C47C2×C414yescomplemented
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47C2×C414yescomplemented
98C24×C47—22no—
99C24×C47—22no—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47—21no—
103C24×C47—21no—
104C24×C47—22no—
105C24×C47—22no—
106C24×C47—21no—
107C24×C47—21no—
108C24×C47—22no—
109C24×C47—22no—
110C24×C47C22×C412yes—
111C24×C47C22×C412yes—
112C24×C47C2×D412yes—
113C24×C47C2×D412yes—
114C24×C47C2×D412yes—
115C24×C47C2×D412yes—
116C24×C47C2×Q812yes—
117C24×C47C2×Q812yes—
118C24×C47#4112yes—
119C24×C47#4112yes—
120C24×C47C2411yescharacteristic
121C2×D4×C47—28no—
122C2×D4×C47—28no—
123C2×D4×C47—28no—
124C2×D4×C47—28no—
125C2×D4×C47—28no—
126C2×D4×C47—28no—
127C2×D4×C47C4⋊C4116yescomplemented
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—216no—
135C22×C4×C47—28no—
136C22×C4×C47—216no—
137C22×C4×C47—28no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—28no—
147C22×C4×C47—216no—
148C22×C4×C47—44no—
149C22×C4×C47—48no—
150C22×C4×C47—44no—
151C22×C4×C47C22⋊C4116yescomplemented
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C412yes—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D414yes—
163C22×C4×C47C2×Q812yes—
164C22×C4×C47#4114yes—
165C22×Dic47—216no—
166C22×Dic47—24no—
167C22×Dic47—24no—
168C22×Dic47—24no—
169C22×Dic47—24no—
170C22×Dic47—24no—
171C22×Dic47—24no—
172C22×Dic47—24no—
173C22×Dic47—24no—
174C22×Dic47—24no—
175C22×Dic47—24no—
176C22×Dic47—24no—
177C22×Dic47—24no—
178C22×Dic47—24no—
179C22×Dic47—416no—
180C22×Dic47—416no—
181C22×Dic47—48no—
182C22×Dic47—48no—
183C22×Dic47C2×D418yes—
184C4⋊C4×C47—28no—
185C22⋊C4×C47—28no—
186C22⋊C4×C47—28no—
187C42×C47—28no—
188C22⋊Dic47—416no—
189C22⋊Dic47—48no—
190C4⋊Dic47—216no—
191C4⋊Dic47—216no—
192C4⋊Dic47—48no—
193C23×C47—24no—
194C23×C47—24no—
195C23×C47—22no—
196C23×C47—24no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47—24no—
205C23×C47—24no—
206C23×C47—24no—
207C23×C47—24no—
208C23×C47—24no—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—24no—
212C23×C47—24no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—24no—
218C23×C47—24no—
219C23×C47—24no—
220C23×C47—24no—
221C23×C47—41no—
222C23×C47—42no—
223C23×C47—41no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47C2×C22⋊C414yes—
232C23×C47C2×C4⋊C414yes—
233C23×C47C2×C4⋊C414yescomplemented
234C23×C47#11714yes—
235C23×C47#12114yes—
236C23×C47#12114yes—
237C23×C47C22⋊Q814yes—
238C23×C47C22⋊Q814yes—
239C23×C47C23×C411yescharacteristic
240C23×C47C22×D412yes—
241C23×C47C22×D411yescharacteristic
242C23×C47C22×D411yescharacteristic
243C23×C47C22×D411yescharacteristic
244C23×C47C22×Q811yescharacteristic
245C23×C47C2×#4112yes—
246C23×C47C2×#4111yescharacteristic
247C23×C47C2×#4111yescharacteristic
248C23×C47H(5,𝔽2)12yes—
249C23×C472−1+412yes—
250D4×C47—232no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—24no—
254C2×C4×C47—22no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—232no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—24no—
265C2×C4×C47—24no—
266C2×C4×C47—41no—
267C2×C4×C47—42no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—42no—
272C2×C4×C47—416no—
273C2×C4×C47C2×C22⋊C414yes—
274C2×C4×C47C2×C22⋊C414yes—
275C2×C4×C47C2×C4⋊C414yescomplemented
276C2×C4×C47C4×D418yes—
277C2×C4×C47#12014yes—
278C2×C4×C47#12118yes—
279C2×C4×C47#12314yes—
280C2×Dic47—28no—
281C2×Dic47—28no—
282C2×Dic47—28no—
283C2×Dic47—432no—
284C2×Dic47—44no—
285C2×Dic47—44no—
286C2×Dic47—44no—
287C2×Dic47—44no—
288C2×Dic47—44no—
289C2×Dic47—44no—
290C2×Dic47—44no—
291C2×Dic47—44no—
292C2×Dic47—44no—
293C2×Dic47—44no—
294C2×Dic47—44no—
295#13872—471nomaximal, Sylow
296C22×C47—24no—
297C22×C47—28no—
298C22×C47—28no—
299C22×C47—24no—
300C22×C47—24no—
301C22×C47—28no—
302C22×C47—28no—
303C22×C47—24no—
304C22×C47—24no—
305C22×C47—24no—
306C22×C47—28no—
307C22×C47—24no—
308C22×C47—42no—
309C22×C47—44no—
310C22×C47—42no—
311C22×C47—42no—
312C22×C47—44no—
313C22×C47—44no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—42no—
317C22×C47#38018yescomplemented
318C22×C47C22×C22⋊C411yescharacteristic
319C22×C47C22×C4⋊C411yescharacteristic
320C22×C47C2×#11711yescharacteristic
321C22×C47C2×C4×D412yes—
322C22×C47#52012yes—
323C22×C47C2×#12011yescharacteristic
324C22×C47C2×#12112yes—
325C22×C47C2×#12111yescharacteristic
326C22×C47C2×#12111yescharacteristic
327C22×C47C2×C22⋊Q811yescharacteristic
328C22×C47C2×C22⋊Q811yescharacteristic
329C22×C47C2×#12311yescharacteristic
330C22×C47#53511yescharacteristic
331C22×C47#53611yescharacteristic
332C22×C47#53712yes—
333C22×C47D4212yes—
334C22×C47#54612yes—
335C22×C47#54712yes—
336C22×C47#54812yes—
337C22×C47D4×Q812yes—
338C22×C47#55212yes—
339C22×C47#55312yes—
340C22×C47#55412yes—
341C4×C47—24no—
342C4×C47—24no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47#38618yescomplemented
346Dic47—48no—
347Dic47—84no—
348C22×C4×D4D4711yescharacteristic
349C23×C4⋊C4—471no—
350C2×#386—472no—
351C2×#380—471no—
352C2×#380—472no—
353#1441—472no—
354#1439—472no—
355C4⋊#95—472no—
356C22⋊#95—472no—
357C2×C47—28no—
358C2×C47—44no—
359C2×C47C2×#38011yescharacteristic
360C2×C47C2×#38611yescharacteristic
361C2×C47#231111yescharacteristic
362C2×C47D4×C4⋊C412yes—
363C2×C47#235212yes—
364C2×C47#240811yescharacteristic
365C2×C47#240911yescharacteristic
366C2×C47#241612yes—
367C2×C47#241712yes—
368C2×C47#248611yescharacteristic
369C2×C47#248711yescharacteristic
370C23×D4C2×D4711yescharacteristic
371C24×C4—472no—
372C24×C4C2×D4711yescharacteristic
373C24×C4C2×D4711yescharacteristic
374C2×C4×D4—24no—
375C2×C4×D4—24no—
376C2×C4×D4Dic4718yescomplemented
377C22×C4⋊C4—472no—
378C22×C4⋊C4—472no—
379C22×C4⋊C4—472no—
380C22×C4⋊C4—948no—
381C22×C4⋊C4—944no—
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C22⋊C4—472no—
384C22×C22⋊C4—474no—
385C22×C22⋊C4C2×D4711yescharacteristic
386C22×C22⋊C4C2×D4711yescharacteristic
387C22×C42C2×D4711yescharacteristic
388#386—948no—
389#380—948no—
390#380—944no—
391C2×#95—474no—
392C2×#95—474no—
393C2×#95—472no—
394C2×#95—474no—
395C47#1387211yescharacteristic, complemented, Sylow
396C25C22×D4711yescharacteristic
397C25C22×D4711yescharacteristic
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4Dic9414yes—
403C22×D4D18814yes—
404C22×D4C2×Dic4714yes—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—474no—
412C23×C4—474no—
413C23×C4—948no—
414C23×C4—944no—
415C23×C4—944no—
416C23×C4—944no—
417C23×C4—1884no—
418C23×C4C2×Dic4714yes—
419C23×C4C2×Dic4714yescomplemented
420C23×C4C22⋊D4714yes—
421C23×C4C22⋊D4714yes—
422C23×C4C22×D4711yescharacteristic
423C23×C4C22×D4711yescharacteristic
424C23×C4C22×D4711yescharacteristic
425C23×C4C22×D4711yescharacteristic
426C23×C4C22×D4711yescharacteristic
427C4×D4—232no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—478no—
431C2×C4⋊C4—948no—
432C2×C4⋊C4—9432no—
433C2×C4⋊C4—944no—
434C2×C4⋊C4—944no—
435C2×C4⋊C4—944no—
436C2×C4⋊C4—944no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—944no—
439C2×C4⋊C4C2×Dic4714yescomplemented
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—948no—
445C2×C22⋊C4—948no—
446C2×C22⋊C4—944no—
447C2×C22⋊C4—944no—
448C2×C22⋊C4—944no—
449C2×C22⋊C4—1884no—
450C2×C22⋊C4C2×Dic4714yes—
451C2×C22⋊C4C2×Dic4714yescomplemented
452C2×C42—22no—
453C2×C42—22no—
454C2×C42C2×Dic4714yescomplemented
455#95—948no—
456#95—948no—
457#95—944no—
458#95—1884no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24C2×Dic9412yes—
472C24C2×Dic9412yes—
473C24C2×D18812yes—
474C24C2×D18812yes—
475C24#1062535012yes—
476C24#1062535012yes—
477C24C22×Dic4712yes—
478C24C22×Dic4712yes—
479C24C2×C22⋊D4712yes—
480C24C2×C22⋊D4712yes—
481C24C23×D4711yescharacteristic
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4C4⋊Dic47116yescomplemented
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—216no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—216no—
509C22×C4—44no—
510C22×C4—48no—
511C22×C4—44no—
512C22×C4—478no—
513C22×C4—9416no—
514C22×C4—944no—
515C22×C4—944no—
516C22×C4—944no—
517C22×C4—944no—
518C22×C4—944no—
519C22×C4—944no—
520C22×C4—944no—
521C22×C4—944no—
522C22×C4—944no—
523C22×C4—944no—
524C22×C4—944no—
525C22×C4—944no—
526C22×C4—944no—
527C22×C4—18816no—
528C22×C4—18816no—
529C22×C4—1888no—
530C22×C4—1888no—
531C22×C4C22⋊Dic47116yescomplemented
532C22×C4C2×Dic9412yes—
533C22×C4C2×D18812yes—
534C22×C4D4×D4714yes—
535C22×C4#1062535214yes—
536C22×C4C22×Dic4712yes—
537C22×C4C22×Dic4712yes—
538C22×C4C22×Dic4712yes—
539C22×C4C22×Dic4712yes—
540C22×C4C22×Dic4712yes—
541C22×C4C2×C22⋊D4712yes—
542C22×C4C2×C22⋊D4712yes—
543C22×C4C2×C22⋊D4712yes—
544C22×C4C2×C22⋊D4712yes—
545C4⋊C4—28no—
546C4⋊C4—9416no—
547C4⋊C4—9416no—
548C4⋊C4—1888no—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—18816no—
552C22⋊C4—1888no—
553C42—28no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—24no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—41no—
587C23—42no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—42no—
592C23C2×C22⋊Dic4714yes—
593C23C2×C4⋊Dic4714yes—
594C23C2×C4⋊Dic4714yescomplemented
595C23#1309398314yes—
596C23#1309399814yes—
597C23#1309399814yes—
598C23#1309400314yes—
599C23#1309400314yes—
600C23C23×Dic4711yescharacteristic
601C23C2×D4×D4712yes—
602C23C22×C22⋊D4711yescharacteristic
603C23C22×C22⋊D4711yescharacteristic
604C23C22×D18811yescharacteristic
605C23C22×Dic9411yescharacteristic
606C23C2×#1062535212yes—
607C23C2×#1062535011yescharacteristic
608C23C2×#1062535011yescharacteristic
609C23#1309407012yes—
610C23#1309407112yes—
611D4—232no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—232no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—416no—
634C2×C4—948no—
635C2×C4—948no—
636C2×C4—948no—
637C2×C4—1884no—
638C2×C4—1884no—
639C2×C4—1884no—
640C2×C4—1884no—
641C2×C4—1884no—
642C2×C4—1884no—
643C2×C4—1884no—
644C2×C4—18832no—
645C2×C4—1884no—
646C2×C4—1884no—
647C2×C4—1884no—
648C2×C4—1884no—
649C2×C4C2×C22⋊Dic4714yes—
650C2×C4C2×C22⋊Dic4714yes—
651C2×C4C2×C4⋊Dic4714yescomplemented
652C2×C4D4×Dic4718yes—
653C2×C4#1309399214yes—
654C2×C4#1309399618yes—
655C2×C4#1309400514yes—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—28no—
668C22—44no—
669C22—44no—
670C22—42no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22#1568898318yescomplemented
678C22C22×C22⋊Dic4711yescharacteristic
679C22C22×C4⋊Dic4711yescharacteristic
680C22C2×#1309398311yescharacteristic
681C22C2×D4×Dic4712yes—
682C22#1568960612yes—
683C22C2×#1309399211yescharacteristic
684C22C2×#1309399612yes—
685C22C2×#1309399811yescharacteristic
686C22C2×#1309399811yescharacteristic
687C22C2×#1309400311yescharacteristic
688C22C2×#1309400311yescharacteristic
689C22C2×#1309400511yescharacteristic
690C22#1568968711yescharacteristic
691C22#1568969411yescharacteristic
692C22#1568970112yes—
693C22D4×D18812yes—
694C22#1568976912yes—
695C22#1568977712yes—
696C22#1568978212yes—
697C22D4×Dic9412yes—
698C22#1568981312yes—
699C22#1568981912yes—
700C22#1568983012yes—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—3764no—
706C4—1888no—
707C4#1568900318yescomplemented
708C2—28no—
709C2—44no—
710C2C2×#1568898311yescharacteristic
711C2C2×#1568900311yescharacteristic
712C2#2024598011yescharacteristic
713C2D4×C4⋊Dic4712yes—
714C2#2024631712yes—
715C2#2024674411yescharacteristic
716C2#2024675311yescharacteristic
717C2#2024682812yes—
718C2#2024683912yes—
719C2#2024769611yescharacteristic
720C2#2024770511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×C4×D4×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC22×C4×D4D47
hypocenterC47#13872
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊Dic47C2semidirect
3. C2×#15688983C2semidirect
4. C2×#15688983C2semidirect
5. #20241641C2semidirect
6. #20241633C2semidirect
7. #20241618C2semidirect
8. #20241610C2semidirect
30. C2×C4×D4×C47C4semidirect
50. C2×C4⋊Dic47D4semidirect
77. C23×C4×C47C2×C4semidirect
88. C2×C4⋊C4×C47C2×C4semidirect
94. C2×C22⋊C4×C47C2×C4semidirect
97. C2×C42×C47C2×C4semidirect
127. C2×D4×C47C4⋊C4semidirect
151. C22×C4×C47C22⋊C4semidirect
233. C23×C47C2×C4⋊C4semidirect
275. C2×C4×C47C2×C4⋊C4semidirect
317. C22×C47#380semidirect
345. C4×C47#386semidirect
376. C2×C4×D4Dic47semidirect
395. C47#13872semidirect
419. C23×C4C2×Dic47semidirect
439. C2×C4⋊C4C2×Dic47semidirect
451. C2×C22⋊C4C2×Dic47semidirect
454. C2×C42C2×Dic47semidirect
488. C2×D4C4⋊Dic47semidirect
531. C22×C4C22⋊Dic47semidirect
594. C23C2×C4⋊Dic47semidirect
651. C2×C4C2×C4⋊Dic47semidirect
677. C22#15688983semidirect
707. C4#15689003semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic472
C2×#156890032
C2×#156889832
#202416412
#202416332
#202416182
#202416102
C22×C4×D4×C472
#1387247