Finite Group Databasebeta

← #26183927

Subgroups — #26183927

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257068C211yesmaximal, characteristic
2#20251837C211yesmaximal, characteristic, complemented
3#20241959C211yesmaximal, characteristic, complemented
4#20241942C212yesmaximal, complemented
5#20241929C211yesmaximal, characteristic, complemented
6#20241920C212yesmaximal, complemented
7#20241907C211yesmaximal, characteristic, complemented
8#20241890C212yesmaximal, complemented
9#20241877C211yesmaximal, characteristic, complemented
10C2×#15688859C212yesmaximal, complemented
11C47×#2339C211yesmaximal, characteristic, complemented
12C2×#13094071C411yescharacteristic, complemented
13C2×#13094031—21no—
14Q8×C22⋊D47—21no—
15#15689780—21no—
16#15689772—21no—
17#15689772—22no—
18#15689767—21no—
19#15689767—22no—
20#15689701C411yescharacteristic, complemented
21#15689701C412yescomplemented
22#15689694C411yescharacteristic, complemented
23#15689694C412yescomplemented
24#15689634C2211yescharacteristic
25#15689634C2212yes—
26C2×#13094003C2212yes—
27C2×#13094003C2211yescharacteristic
28#15689606C411yescharacteristic, complemented
29#15689090—22no—
30#15689090—21no—
31#15689087C2212yes—
32#15689087C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2212yes—
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35#15688859C2211yescharacteristic
36#15688859C2212yes—
37#15688859C2212yes—
38#15688859C2212yes—
39#15688859C2212yes—
40#15688859C2211yescharacteristic
41#15688859C2212yes—
42#15688856C2212yes—
43#15688856C2211yescharacteristic
44#15688856C2211yescharacteristic
45C22×#41×C47C2211yescharacteristic
46C2×C4×D4×C47—21no—
47C47×#391—21no—
48C47×#386—22no—
49C47×#381C2212yes—
50C47×#380C2211yescharacteristic
51C4×C22⋊C4×C47C2211yescharacteristic
52C2×#95×C47C2212yes—
53#13094071—44no—
54C2×#10625350C2×C412yescomplemented
55C2×#10625350C2×C411yescharacteristic, complemented
56C2×#10625352—22no—
57C2×#10625352—21no—
58C22×Dic94C2×C412yescomplemented
59C22×Dic94C2×C411yescharacteristic, complemented
60C2×Q8×D47—21no—
61#13094031—44no—
62C2×#10625329—22no—
63C2×#10625329—21no—
64C22×C47⋊C8—22no—
65C22×C47⋊C8—21no—
66#13094022—21no—
67#13094022—22no—
68#13094011—21no—
69#13094011—22no—
70#13094007—22no—
71#13094007—21no—
72#13094005—22no—
73#13094005—22no—
74#13094005—22no—
75#13094003—21no—
76#13094003—22no—
77#13094003—21no—
78#13094003—22no—
79#13094003C2×C412yescomplemented
80#13094003C2×C412yescomplemented
81#13094003C2×C412yescomplemented
82#13094003C2×C411yescharacteristic, complemented
83#13094003C2×C412yescomplemented
84#13094003C2311yescharacteristic
85#13094003C2312yes—
86#13094000—21no—
87#13094000—22no—
88#13093998C2×C411yescharacteristic, complemented
89#13093998C2×C412yescomplemented
90#13093998C2311yescharacteristic
91#13093996—22no—
92#13093996—22no—
93#13093996—22no—
94#13093995—21no—
95#13093995—22no—
96#13093993—22no—
97#13093993—21no—
98Q8×Dic47—21no—
99D4×Dic47—22no—
100D4×Dic47—21no—
101C4×C22⋊D47—21no—
102C4×C22⋊D47—22no—
103C4×C22⋊D47—21no—
104C4×C22⋊D47—22no—
105#13093983C2×C411yescharacteristic, complemented
106#13093983C2×C412yescomplemented
107C2×C4⋊Dic47C2×C412yescomplemented
108C2×C4⋊Dic47C2×C411yescharacteristic, complemented
109C2×Dic47⋊C4—22no—
110C2×Dic47⋊C4—21no—
111C2×C22⋊Dic47—22no—
112C2×C22⋊Dic47—21no—
113C22⋊(C47⋊C8)—21no—
114C22⋊(C47⋊C8)—22no—
115C22⋊(C47⋊C8)—21no—
116C22⋊(C47⋊C8)—22no—
117C22⋊(C47⋊C8)C2311yescharacteristic
118C22⋊(C47⋊C8)C2312yes—
119C22⋊(C47⋊C8)C2311yescharacteristic
120C2×#41×C47—44no—
121C2×#41×C47C2×C411yescharacteristic
122C2×#41×C47C2×C411yescharacteristic
123C2×#41×C47C2×C412yes—
124C2×#41×C47D411yescharacteristic
125C2×#41×C47D412yes—
126C2×#41×C47D411yescharacteristic
127C22×Q8×C47D411yescharacteristic
128C22×D4×C47D411yescharacteristic
129C22×D4×C47D412yes—
130C23×C4×C47—22no—
131C23×C4×C47C2312yes—
132C23×C4×C47C2311yescharacteristic
133C4×D4×C47—44no—
134C2×C4⋊C4×C47—21no—
135C2×C22⋊C4×C47—22no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C42×C47—21no—
139#95×C47—22no—
140#95×C47—22no—
141#95×C47C2311yescharacteristic
142#95×C47C2312yes—
143#95×C47C2311yescharacteristic
144C24×C47C2×D412yes—
145C24×C47C2×D411yescharacteristic
146#41×C47—24no—
147#41×C47—24no—
148#41×C47—44no—
149#41×C47—44no—
150#41×C47—42no—
151#41×C47—42no—
152C2×Q8×C47—42no—
153C2×Q8×C47C22⋊C411yescharacteristic
154C2×Q8×C47C22⋊C411yescharacteristic
155C2×Q8×C47C22⋊C412yes—
156C2×D4×C47—24no—
157C2×D4×C47—44no—
158C2×D4×C47C22⋊C412yes—
159C2×D4×C47C22⋊C411yescharacteristic
160C2×D4×C47C22⋊C412yes—
161C2×D4×C47C22⋊C412yes—
162C2×D4×C47C22⋊C412yes—
163C2×D4×C47C22⋊C412yes—
164C2×D4×C47C22⋊C411yescharacteristic
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—22no—
168C22×C4×C47—42no—
169C22×C4×C47—44no—
170C22×C4×C47—44no—
171C22×C4×C47—44no—
172C22×C4×C47—82no—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C412yes—
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D412yes—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D412yes—
183C22×C4×C47C2411yescharacteristic
184C2×C22⋊D47—21no—
185C2×C22⋊D47—22no—
186C2×C22⋊D47—21no—
187C2×C22⋊D47—21no—
188C2×C22⋊D47—22no—
189C22×Dic47—21no—
190C22×Dic47—22no—
191C22×Dic47—21no—
192C22×Dic47—22no—
193Q8×D47—44no—
194#10625352—48no—
195#10625352—44no—
196#10625350—44no—
197#10625350—42no—
198C2×D188C22×C411yescharacteristic
199C2×C4×D47—22no—
200C2×C4×D47—21no—
201C2×Dic94—22no—
202C2×Dic94—21no—
203C2×Dic94—44no—
204C2×Dic94—42no—
205C2×Dic94C22×C411yescharacteristic
206C2×Dic94C22×C412yes—
207C4⋊C4×C47—42no—
208C22⋊C4×C47—42no—
209C22⋊C4×C47—44no—
210C22⋊C4×C47—81no—
211C42×C47—42no—
212C22⋊Dic47—22no—
213C22⋊Dic47—22no—
214C22⋊Dic47—22no—
215C22⋊Dic47—21no—
216C22⋊Dic47—22no—
217C22⋊Dic47—21no—
218C22⋊Dic47—22no—
219C22⋊Dic47—21no—
220C22⋊Dic47—22no—
221(C2×D47)⋊C4—21no—
222(C2×D47)⋊C4—22no—
223(C2×D47)⋊C4—21no—
224C4⋊Dic47—22no—
225C4⋊Dic47—21no—
226C4⋊Dic47C22×C411yescharacteristic
227C4⋊Dic47C22×C412yes—
228C4⋊Dic47C22×C411yescharacteristic
229Dic47⋊C4—22no—
230Dic47⋊C4—22no—
231Dic47⋊C4—22no—
232Dic47⋊C4—21no—
233Dic47⋊C4—22no—
234Dic47⋊C4—21no—
235Dic47⋊C4—22no—
236C4×Dic47—22no—
237C4×Dic47—21no—
238#10625329—44no—
239#10625329—42no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—22no—
243C2×C47⋊C8—44no—
244C2×C47⋊C8—42no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—24no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—42no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47C2×C22⋊C411yescharacteristic
254C23×C47C2×C22⋊C412yes—
255C23×C47C2×C22⋊C411yescharacteristic
256C23×C47C2×C22⋊C412yes—
257C23×C47C22×D411yescharacteristic
258C22×D47—21no—
259Q8×C47—22no—
260Q8×C47—22no—
261Q8×C47—42no—
262D4×C47—24no—
263D4×C47—24no—
264D4×C47—24no—
265D4×C47—22no—
266D4×C47—42no—
267D4×C47—42no—
268D4×C47#9914yes—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—41no—
289C2×C4×C47—88no—
290C2×C4×C47C2×C22⋊C412yes—
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C23×C411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C22⋊D47—42no—
297C22⋊D47—41no—
298C22⋊D47—41no—
299C22⋊D47—44no—
300C22⋊D47—82no—
301C22⋊D47—81no—
302C2×Dic47—21no—
303C2×Dic47—22no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—22no—
307C2×Dic47—42no—
308C2×Dic47—44no—
309C2×Dic47—82no—
310C2×Dic47—81no—
311D188—41no—
312C4×D47—44no—
313C4×D47—42no—
314Dic94—44no—
315Dic94—42no—
316Dic94—41no—
317Dic94—42no—
318C47⋊C8—41no—
319C47⋊C8—42no—
320C47⋊C8—41no—
321#17608—471nomaximal, Sylow
322C22×C47—21no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—21no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—21no—
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—22no—
334C22×C47—21no—
335C22×C47—44no—
336C22×C47—44no—
337C22×C47—81no—
338C22×C47—81no—
339C22×C47C2×#9914yes—
340C22×C47C22×C22⋊C411yescharacteristic
341C22×C47#57711yescharacteristic
342C22×C47#57811yescharacteristic
343C2×D47—41no—
344C2×D47—41no—
345C2×D47—41no—
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—22no—
349C4×C47—21no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—81no—
353C4×C47—82no—
354C4×C47C2×#9912yes—
355Dic47—41no—
356Dic47—42no—
357Dic47—41no—
358Dic47—41no—
359Dic47—42no—
360#3489—471no—
361#2880—471no—
362#2339D4711yescharacteristic, complemented
363#1520—471no—
364#1516—472no—
365#1513—471no—
366#1511—472no—
367#1508—471no—
368#1504—472no—
369#1501—471no—
370C2×#328—472no—
371C2×C47—21no—
372C2×C47—21no—
373C2×C47—24no—
374C2×C47—42no—
375C2×C47—41no—
376C2×C47—41no—
377C2×C47C22×#9911yescharacteristic
378C2×C47#289811yescharacteristic
379C2×C47#290111yescharacteristic
380D47—81no—
381C2×2−1+4—471no—
382C22×#41C2×D4711yescharacteristic
383C2×#131—941no—
384D4×Q8—941no—
385#548—941no—
386#547—941no—
387#547—942no—
388#546—941no—
389#546—942no—
390#537—472no—
391#537—471no—
392#536—471no—
393#536—472no—
394#525—471no—
395#525—472no—
396C2×C22⋊Q8—472no—
397C2×C22⋊Q8—471no—
398#520—471no—
399C2×C4×D4—21no—
400#408—942no—
401#408—941no—
402#407—472no—
403#407—471no—
404C2×C22⋊C8—472no—
405C2×C22⋊C8—471no—
406#391—21no—
407#386—22no—
408#381C2×D4712yes—
409#380C2×D4711yescharacteristic
410C4×C22⋊C4C2×D4711yescharacteristic
411C2×#95C2×D4712yes—
412#328—471no—
413#328—472no—
414#328—472no—
415#328—472no—
416#328—471no—
417#328—472no—
418#328—472no—
419#327—471no—
420#327—471no—
421#327—472no—
422C47#1760811yescharacteristic, complemented, Sylow
4232−1+4—1884no—
424C2×#41—44no—
425C2×#41—472no—
426C2×#41—471no—
427C2×#41—942no—
428C2×#41—941no—
429C2×#41C4×D4711yescharacteristic
430C2×#41C4×D4712yes—
431C2×#41C4×D4711yescharacteristic
432C2×#41D18811yescharacteristic
433C2×#41D18812yes—
434C2×#41D18811yescharacteristic
435C22×Q8—471no—
436C22×Q8—472no—
437C22×Q8—941no—
438C22×Q8C22⋊D4711yescharacteristic
439C22×D4C22⋊D4711yescharacteristic
440C22×D4C22⋊D4712yes—
441C23×C4—22no—
442C23×C4C22×D4712yes—
443C23×C4C22×D4711yescharacteristic
444#131—1884no—
445C2×M16—942no—
446C2×M16—941no—
447C22×C8—942no—
448C22×C8—941no—
449C4⋊Q8—941no—
450C4⋊Q8—942no—
451#124—941no—
452#124—942no—
453#123—942no—
454#123—942no—
455#123—942no—
456#123—942no—
457#123—941no—
458C22⋊Q8—472no—
459C22⋊Q8—472no—
460C22⋊Q8—472no—
461C22⋊Q8—471no—
462C22⋊Q8—472no—
463C22⋊Q8—471no—
464C22⋊Q8—472no—
465C22⋊Q8—941no—
466C22⋊Q8—942no—
467C22⋊Q8—941no—
468C22⋊Q8—942no—
469C22⋊Q8—941no—
470C22⋊Q8—942no—
471#121—471no—
472#121—472no—
473#121—471no—
474#121—942no—
475#121—942no—
476#121—942no—
477#121—941no—
478#121—942no—
479#120—942no—
480#120—941no—
481C4×Q8—941no—
482C4×D4—44no—
483C4×D4—942no—
484C4×D4—941no—
485C4×D4—941no—
486C4×D4—942no—
487C4×D4—941no—
488C4×D4—942no—
489#117—471no—
490#117—472no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—472no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—941no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—942no—
500C2×C22⋊C4—941no—
501C2×C42—21no—
502C22⋊C8—471no—
503C22⋊C8—471no—
504C22⋊C8—472no—
505C22⋊C8—941no—
506C22⋊C8—942no—
507C22⋊C8—941no—
508C22⋊C8—942no—
509#95—22no—
510#95—22no—
511#95C22×D4711yescharacteristic
512#95C22×D4712yes—
513#95C22×D4711yescharacteristic
514C24C2×C22⋊D4712yes—
515C24C2×C22⋊D4711yescharacteristic
516#41—24no—
517#41—24no—
518#41—44no—
519#41—44no—
520#41—42no—
521#41—42no—
522#41—1884no—
523#41—1882no—
524#41—1888no—
525#41—1884no—
526C2×Q8—42no—
527C2×Q8—472no—
528C2×Q8—471no—
529C2×Q8—942no—
530C2×Q8—941no—
531C2×Q8—1882no—
532C2×Q8—1884no—
533C2×Q8—1884no—
534C2×Q8(C2×D47)⋊C411yescharacteristic
535C2×Q8(C2×D47)⋊C411yescharacteristic
536C2×Q8(C2×D47)⋊C412yes—
537C2×D4—24no—
538C2×D4—44no—
539C2×D4—471no—
540C2×D4—941no—
541C2×D4—942no—
542C2×D4—941no—
543C2×D4—942no—
544C2×D4—941no—
545C2×D4(C2×D47)⋊C412yes—
546C2×D4(C2×D47)⋊C412yes—
547C2×D4(C2×D47)⋊C412yes—
548C2×D4(C2×D47)⋊C411yescharacteristic
549C2×D4(C2×D47)⋊C412yes—
550C2×D4(C2×D47)⋊C412yes—
551C2×D4(C2×D47)⋊C411yescharacteristic
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—42no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—82no—
560C22×C4—941no—
561C22×C4—942no—
562C22×C4—941no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—941no—
566C22×C4C2×C4×D4712yes—
567C22×C4C2×C4×D4711yescharacteristic
568C22×C4C2×C4×D4712yes—
569C22×C4C2×C4×D4711yescharacteristic
570C22×C4C2×D18812yes—
571C22×C4C2×D18811yescharacteristic
572C22×C4C2×D18811yescharacteristic
573C22×C4C2×D18812yes—
574C22×C4C2×C22⋊D4711yescharacteristic
575C22×C4C2×C22⋊D4712yes—
576C22×C4C23×D4711yescharacteristic
577M16—1884no—
578M16—1882no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—942no—
582C2×C8—1884no—
583C2×C8—1882no—
584C4⋊C4—42no—
585C4⋊C4—471no—
586C4⋊C4—472no—
587C4⋊C4—471no—
588C4⋊C4—942no—
589C4⋊C4—942no—
590C4⋊C4—942no—
591C4⋊C4—941no—
592C4⋊C4—942no—
593C4⋊C4—942no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—942no—
597C22⋊C4—42no—
598C22⋊C4—44no—
599C22⋊C4—81no—
600C22⋊C4—942no—
601C22⋊C4—942no—
602C22⋊C4—942no—
603C22⋊C4—941no—
604C22⋊C4—942no—
605C22⋊C4—941no—
606C22⋊C4—942no—
607C22⋊C4—941no—
608C22⋊C4—942no—
609C22⋊C4—941no—
610C22⋊C4—942no—
611C22⋊C4—941no—
612C42—42no—
613C42—942no—
614C42—941no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—941no—
624C23C2×(C2×D47)⋊C411yescharacteristic
625C23C2×(C2×D47)⋊C412yes—
626C23C2×(C2×D47)⋊C411yescharacteristic
627C23C2×(C2×D47)⋊C412yes—
628C23C22×C22⋊D4711yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—1882no—
633Q8—1881no—
634Q8—1884no—
635Q8—1882no—
636D4—24no—
637D4—24no—
638D4—24no—
639D4—22no—
640D4—42no—
641D4—42no—
642D4—3762no—
643D4—3761no—
644D4—1881no—
645D4—1882no—
646D4—1884no—
647D4—1881no—
648D4—1881no—
649D4#1309393814yes—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—88no—
671C2×C4—941no—
672C2×C4—942no—
673C2×C4—941no—
674C2×C4—942no—
675C2×C4—941no—
676C2×C4—3762no—
677C2×C4—3761no—
678C2×C4—1884no—
679C2×C4—1882no—
680C2×C4—1884no—
681C2×C4—1882no—
682C2×C4C2×(C2×D47)⋊C412yes—
683C2×C4C2×(C2×D47)⋊C411yescharacteristic
684C2×C4C2×(C2×D47)⋊C412yes—
685C2×C4C2×(C2×D47)⋊C411yescharacteristic
686C2×C4C22×C4×D4711yescharacteristic
687C2×C4C22×D18811yescharacteristic
688C8—1881no—
689C8—1882no—
690C8—1881no—
691C22—22no—
692C22—21no—
693C22—22no—
694C22—21no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—22no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—81no—
707C22—81no—
708C22—1881no—
709C22—1881no—
710C22—1881no—
711C22C2×#1309393814yes—
712C22C22×(C2×D47)⋊C411yescharacteristic
713C22#1568993411yescharacteristic
714C22#1568993811yescharacteristic
715C4—21no—
716C4—21no—
717C4—22no—
718C4—21no—
719C4—22no—
720C4—42no—
721C4—82no—
722C4—81no—
723C4—1881no—
724C4—1881no—
725C4—1882no—
726C4—1882no—
727C4—1881no—
728C4C2×#1309393812yes—
729C2—21no—
730C2—21no—
731C2—24no—
732C2—42no—
733C2—41no—
734C2—41no—
735C2—3761no—
736C2C22×#1309393811yescharacteristic
737C2#2025191811yescharacteristic
738C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2339C2
socleC22×C47C22×C22⋊C4
prime radical#20257068C2
cosocleC22×C4×C47C24
hypercenter#2339D47
hypocenterC47#17608
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #20251837C2semidirect
3. #20241959C2semidirect
4. #20241942C2semidirect
5. #20241929C2semidirect
6. #20241920C2semidirect
7. #20241907C2semidirect
8. #20241890C2semidirect
9. #20241877C2semidirect
10. C2×#15688859C2semidirect
11. C47×#2339C2semidirect
12. C2×#13094071C4semidirect
20. #15689701C4semidirect
21. #15689701C4semidirect
22. #15689694C4semidirect
23. #15689694C4semidirect
28. #15689606C4semidirect
54. C2×#10625350C2×C4semidirect
55. C2×#10625350C2×C4semidirect
58. C22×Dic94C2×C4semidirect
59. C22×Dic94C2×C4semidirect
79. #13094003C2×C4semidirect
80. #13094003C2×C4semidirect
81. #13094003C2×C4semidirect
82. #13094003C2×C4semidirect
83. #13094003C2×C4semidirect
88. #13093998C2×C4semidirect
89. #13093998C2×C4semidirect
105. #13093983C2×C4semidirect
106. #13093983C2×C4semidirect
107. C2×C4⋊Dic47C2×C4semidirect
108. C2×C4⋊Dic47C2×C4semidirect
362. #2339D47semidirect
422. C47#17608semidirect

Maximal subgroups

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

subgroupindex
#202570682
#202518372
#202419592
#202419422
#202419292
#202419202
#202419072
#202418902
#202418772
C2×#156888592
C47×#23392
#1760847