Finite Group Databasebeta

← #26139708

Subgroups — #26139708

Order 12032.

1506 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689029C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic
3C2×#15689029C211yesmaximal, characteristic
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic
5#20241649C212yesmaximal
6#20241647C212yesmaximal
7#20241620C212yesmaximal
8#20241618C211yesmaximal, characteristic
9#20241618C211yesmaximal, characteristic
10#20241614C212yesmaximal
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4×Dic47C2212yes—
17#15689029—24no—
18#15689029—24no—
19#15689029C418yescomplemented
20C4×C4⋊Dic47—24no—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C4×C4⋊C4×C47—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C22×Dic94—22no—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94C2×C414yes—
47C23×Dic47C2312yes—
48C23×Dic47C2312yes—
49C23×Dic47C2312yes—
50C23×Dic47C2312yes—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47C2×C414yes—
59C2×C4⋊Dic47D414yes—
60C2×C4×Dic47—24no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—42no—
63C47⋊#95—24no—
64C47⋊#95—24no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—24no—
69C47⋊#95—24no—
70C47⋊#95—42no—
71C47⋊#95—42no—
72C47⋊#95C2×C418yes—
73C47⋊#95C2×C418yes—
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47—22no—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—22no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47Q814yescomplemented
87C2×C42×C47—22no—
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47C2×C414yes—
95C2×C42×C47D414yes—
96#95×C47—22no—
97#95×C47—22no—
98C24×C47C2411yescharacteristic
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×Q812yes—
139C22×C4×C47C2×Q812yes—
140C22×C4×C47C2×Q812yes—
141C22×C4×C47#4112yes—
142C22×C4×C47#4112yes—
143C22×C4×C47#4112yes—
144C22×C4×C47#4112yes—
145C22×C4×C47#4112yes—
146C22×C4×C47#4112yes—
147C22×C4×C47#4112yes—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47C22×C414yes—
174C22×Dic47C22×C414yes—
175C22×Dic47C2×D414yes—
176C2×Dic94—28no—
177C2×Dic94—28no—
178C2×Dic94—28no—
179C2×Dic94—44no—
180C2×Dic94—44no—
181C2×Dic94—44no—
182C2×Dic94—44no—
183C4⋊C4×C47—28no—
184C4⋊C4×C47—28no—
185C42×C47—28no—
186C42×C47—28no—
187C42×C47—44no—
188C4⋊Dic47—28no—
189C4⋊Dic47—28no—
190C4⋊Dic47—44no—
191C4×Dic47—48no—
192C23×C47C23×C411yescharacteristic
193C23×C47C22×D411yescharacteristic
194C23×C47C22×D411yescharacteristic
195C23×C47C22×Q811yescharacteristic
196C23×C47C2×#4111yescharacteristic
197C23×C47C2×#4111yescharacteristic
198C23×C47C2×#4111yescharacteristic
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C23×C47C2×#4111yescharacteristic
202C23×C47C2×#4111yescharacteristic
203C23×C47H(5,𝔽2)11yescharacteristic
204C23×C472−1+411yescharacteristic
205C23×C472−1+411yescharacteristic
206C23×C472−1+411yescharacteristic
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47#11714yes—
248C2×C4×C47C4×D414yes—
249C2×C4×C47C4×D414yes—
250C2×C4×C47C4×Q814yes—
251C2×C4×C47#12114yes—
252C2×C4×C47C22⋊Q814yes—
253C2×C4×C47#12314yes—
254C2×C4×C47#12414yes—
255C2×C4×C47#12614yes—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—42no—
266C2×Dic47—42no—
267C2×Dic47—42no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284Dic94—416no—
285#14021—471nomaximal, Sylow
286C22×C47C2×#11711yescharacteristic
287C22×C47C2×C4×D411yescharacteristic
288C22×C47C2×C4×D411yescharacteristic
289C22×C47C2×C4×Q811yescharacteristic
290C22×C47C4×#4111yescharacteristic
291C22×C47#51911yescharacteristic
292C22×C47#52011yescharacteristic
293C22×C47C2×#12111yescharacteristic
294C22×C47C2×C22⋊Q811yescharacteristic
295C22×C47C2×#12311yescharacteristic
296C22×C47#52511yescharacteristic
297C22×C47C2×#12411yescharacteristic
298C22×C47C2×#12611yescharacteristic
299C22×C47#52911yescharacteristic
300C22×C47#53311yescharacteristic
301C22×C47#53611yescharacteristic
302C22×C47#53711yescharacteristic
303C22×C47#54111yescharacteristic
304C22×C47#54211yescharacteristic
305C22×C47#54611yescharacteristic
306C22×C47#54711yescharacteristic
307C22×C47#54811yescharacteristic
308C22×C47D4×Q811yescharacteristic
309C22×C47#55211yescharacteristic
310C22×C47#55211yescharacteristic
311C22×C47#55411yescharacteristic
312C22×C47#55611yescharacteristic
313C22×C47#55611yescharacteristic
314C22×C47#55611yescharacteristic
315C22×C47#55611yescharacteristic
316C22×C47#55611yescharacteristic
317C22×C47#55711yescharacteristic
318C22×C47#55711yescharacteristic
319C22×C47#55911yescharacteristic
320C22×C47#55911yescharacteristic
321C4×C47—24no—
322C4×C47—24no—
323C4×C47—42no—
324C4×C47—42no—
325C4×C47—42no—
326C4×C47—42no—
327C4×C47#38818yes—
328Dic47—44no—
329Dic47—44no—
330Dic47—44no—
331Dic47—82no—
332C2×#391—471no—
333C2×#391—471no—
334C2×#391—471no—
335C2×C4×C4⋊C4—471no—
336C2×C4×C4⋊C4D4711yescharacteristic
337#1443—472no—
338#1442—472no—
339#1436—472no—
340C4⋊#95—471no—
341C4⋊#95—471no—
342#1434—472no—
343C2×C47C2×#38811yescharacteristic
344C2×C47C4×C22⋊Q811yescharacteristic
345C2×C47#232311yescharacteristic
346C2×C47#235511yescharacteristic
347C2×C47#235611yescharacteristic
348C2×C47#236511yescharacteristic
349C2×C47#236711yescharacteristic
350C2×C47#241511yescharacteristic
351C2×C47#241711yescharacteristic
352C2×C47#244611yescharacteristic
353C2×C47#244711yescharacteristic
354C2×C47#251111yescharacteristic
355C2×C47#251411yescharacteristic
356C2×C47#256811yescharacteristic
357C2×C47#259211yescharacteristic
358C23×Q8—471no—
359C22×C4⋊C4—471no—
360C22×C4⋊C4—471no—
361C22×C4⋊C4—471no—
362C22×C4⋊C4C2×D4711yescharacteristic
363C22×C4⋊C4C2×D4711yescharacteristic
364C22×C42—472no—
365C22×C42C2×D4711yescharacteristic
366C22×C42C2×D4711yescharacteristic
367C22×C42C2×D4711yescharacteristic
368#391—478no—
369#391—944no—
370#391—944no—
371C4×C4⋊C4—24no—
372C4×C4⋊C4—944no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95—472no—
376C2×#95—472no—
377C2×#95—472no—
378C2×#95—472no—
379C2×#95—472no—
380C2×#95—472no—
381C2×#95—472no—
382C2×#95—472no—
383C2×#95—472no—
384C2×#95C2×D4711yescharacteristic
385C2×#95C2×D4711yescharacteristic
386C47#1402111yescharacteristic, complemented, Sylow
387C22×Q8—474no—
388C22×Q8—942no—
389C22×Q8—942no—
390C22×Q8—942no—
391C22×Q8—942no—
392C22×Q8—942no—
393C22×Q8—942no—
394C23×C4—472no—
395C23×C4—472no—
396C23×C4—472no—
397C23×C4—472no—
398C23×C4C22×D4711yescharacteristic
399C23×C4C22×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C23×C4C22×D4711yescharacteristic
402C23×C4C22×D4711yescharacteristic
403C23×C4C22×D4711yescharacteristic
404C23×C4C22×D4711yescharacteristic
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—474no—
411C2×C4⋊C4—474no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—942no—
414C2×C4⋊C4—942no—
415C2×C4⋊C4—942no—
416C2×C4⋊C4—942no—
417C2×C4⋊C4—942no—
418C2×C4⋊C4—942no—
419C2×C4⋊C4Dic9414yescomplemented
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—944no—
428C2×C42—944no—
429C2×C42—1882no—
430C2×C42C4×D4714yes—
431C2×C42C22⋊D4714yes—
432#95—22no—
433#95—22no—
434#95—478no—
435#95—478no—
436#95—944no—
437#95—944no—
438#95—944no—
439#95—944no—
440#95—944no—
441#95—944no—
442#95—944no—
443#95—1882no—
444#95—1882no—
445C24C23×D4711yescharacteristic
446C2×Q8—948no—
447C2×Q8—948no—
448C2×Q8—948no—
449C2×Q8—1884no—
450C2×Q8—1884no—
451C2×Q8—1884no—
452C2×Q8—1884no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—474no—
486C22×C4—474no—
487C22×C4—474no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4C2×Dic9412yes—
514C22×C4C2×Dic9412yes—
515C22×C4C2×Dic9412yes—
516C22×C4C2×C4×D4712yes—
517C22×C4C2×C4×D4712yes—
518C22×C4C2×C4×D4712yes—
519C22×C4#1062535012yes—
520C22×C4#1062535012yes—
521C22×C4#1062535012yes—
522C22×C4#1062535012yes—
523C22×C4D4×D4712yes—
524C22×C4#1062535212yes—
525C22×C4#1062535412yes—
526C22×C4#1062535412yes—
527C22×C4C2×C22⋊D4712yes—
528C22×C4C2×C22⋊D4712yes—
529C22×C4C2×C22⋊D4712yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—948no—
533C4⋊C4—948no—
534C4⋊C4—1884no—
535C42—28no—
536C42—28no—
537C42—44no—
538C42—1888no—
539C23C22×C4×D4711yescharacteristic
540C23C2×D4×D4711yescharacteristic
541C23C22×C22⋊D4711yescharacteristic
542C23C22×Dic9411yescharacteristic
543C23C2×#1062535211yescharacteristic
544C23C2×#1062535011yescharacteristic
545C23C2×#1062535011yescharacteristic
546C23C2×#1062535011yescharacteristic
547C23C2×#1062535011yescharacteristic
548C23C2×#1062535411yescharacteristic
549C23C2×#1062535411yescharacteristic
550C23#1309407011yescharacteristic
551C23#1309407111yescharacteristic
552C23#1309407111yescharacteristic
553C23#1309407111yescharacteristic
554Q8—18816no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—944no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—1882no—
605C2×C4—1882no—
606C2×C4—1882no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4—1882no—
612C2×C4—1882no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1882no—
618C2×C4—1882no—
619C2×C4—1882no—
620C2×C4—1882no—
621C2×C4—1882no—
622C2×C4—1882no—
623C2×C4#1309398214yes—
624C2×C4C4×C22⋊D4714yes—
625C2×C4#1309398614yes—
626C2×C4C4×Dic9414yes—
627C2×C4#1309399614yes—
628C2×C4#1309400314yes—
629C2×C4#1309400914yes—
630C2×C4#1309401314yes—
631C2×C4#1309401914yes—
632C22C2×#1309398211yescharacteristic
633C22C2×C4×C22⋊D4711yescharacteristic
634C22C2×#1309398611yescharacteristic
635C22C2×C4×Dic9411yescharacteristic
636C22C4×#1062535011yescharacteristic
637C22#1568960011yescharacteristic
638C22#1568960311yescharacteristic
639C22C2×#1309399611yescharacteristic
640C22C2×#1309400311yescharacteristic
641C22C2×#1309400911yescharacteristic
642C22#1568963411yescharacteristic
643C22C2×#1309401311yescharacteristic
644C22C2×#1309401911yescharacteristic
645C22#1568965711yescharacteristic
646C22#1568968011yescharacteristic
647C22#1568969411yescharacteristic
648C22#1568970111yescharacteristic
649C22#1568973511yescharacteristic
650C22#1568974411yescharacteristic
651C22#1568976911yescharacteristic
652C22#1568977811yescharacteristic
653C22#1568978211yescharacteristic
654C22D4×Dic9411yescharacteristic
655C22#1568981311yescharacteristic
656C22#1568981311yescharacteristic
657C22#1568983011yescharacteristic
658C22#1568984311yescharacteristic
659C22#1568984611yescharacteristic
660C22#1568984611yescharacteristic
661C22#1568984611yescharacteristic
662C22#1568984611yescharacteristic
663C22#1568985211yescharacteristic
664C22#1568985211yescharacteristic
665C22#1568985811yescharacteristic
666C22#1568985811yescharacteristic
667C4—24no—
668C4—24no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—3762no—
674C4—1884no—
675C4—1884no—
676C4—1884no—
677C4#1568901318yes—
678C2C2×#1568901311yescharacteristic
679C2C4×#1309400311yescharacteristic
680C2#2024607011yescharacteristic
681C2#2024634311yescharacteristic
682C2#2024635111yescharacteristic
683C2#2024644411yescharacteristic
684C2#2024645711yescharacteristic
685C2#2024681711yescharacteristic
686C2#2024683911yescharacteristic
687C2#2024716411yescharacteristic
688C2#2024717511yescharacteristic
689C2#2024796311yescharacteristic
690C2#2024799611yescharacteristic
691C2#2024860011yescharacteristic
692C2#2024887611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#14021
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
19. #15689029C4semidirect
86. C2×C4⋊C4×C47Q8semidirect
386. C47#14021semidirect
419. C2×C4⋊C4Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156890292
C2×C4×C4⋊Dic472
#202416492
#202416472
#202416202
#202416182
#202416142
C2×C4×C4⋊C4×C472
#1402147