Finite Group Databasebeta

← #26218106

Subgroups — #26218106

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic, complemented
2C2×#15689630C211yesmaximal, characteristic
3C2×#15689107C211yesmaximal, characteristic, complemented
4C2×#15689086C211yesmaximal, characteristic, complemented
5#20243853C214yesmaximal, complemented
6#20243848C214yesmaximal, complemented
7#20243126C211yesmaximal, characteristic, complemented
8#20243126C211yesmaximal, characteristic, complemented
9C2×C47×#413C211yesmaximal, characteristic, complemented
10C23×C4×D47C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C22×#10625329C2211yescharacteristic
13C22×#10625324—21no—
14C2×M16×D47—22no—
15C2×M16×D47—24no—
16C2×M16×D47—24no—
17C2×M16×D47C2214yes—
18C22×C8×D47—21no—
19#15689630—22no—
20#15689630—21no—
21#15689630—21no—
22#15689630—21no—
23#15689630—22no—
24#15689630—21no—
25C2×#13094005C412yes—
26C2×#13094000C2212yes—
27C2×#13093995C2212yes—
28C2×#13093992C412yes—
29C2×C4×C22⋊D47C414yes—
30C2×#13093983C2211yescharacteristic
31#15689107—24no—
32C2×#13093943C2212yescomplemented
33C2×#13093941C2212yescomplemented
34#15689086—21no—
35#15689086—21no—
36#15689086C2214yes—
37C2×(C2×D47)⋊C8—22no—
38#15688891C2214yescomplemented
39#15688891C2214yescomplemented
40C22×#41×C47C2211yescharacteristic
41C22×M16×C47C2211yescharacteristic
42C22×M16×C47C2211yescharacteristic
43C47×#413—24no—
44C2×#101×C47C2212yescomplemented
45C2×#100×C47C2212yescomplemented
46C24×D47C2×C411yescharacteristic
47C22×C22⋊D47C2×C414yes—
48C23×Dic47C2×C411yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47C2×C412yes—
54C22×C4×D47D412yes—
55C22×C4×D47D411yescharacteristic
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47D412yes—
59C22×C4×D47D411yescharacteristic
60C22×C4×D47C2312yes—
61C2×#10625329—22no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329D414yescomplemented
67C2×#10625329C2312yes—
68C2×#10625329C2312yes—
69C2×#10625324—28no—
70C2×#10625324—24no—
71M16×D47—216no—
72M16×D47—28no—
73M16×D47—28no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—28no—
77C2×C8×D47—24no—
78#13094005—24no—
79#13094005—22no—
80#13094005—22no—
81#13094000—22no—
82#13094000—22no—
83#13094000—22no—
84#13094000—22no—
85#13093995—22no—
86#13093995—22no—
87#13093995—22no—
88#13093995—22no—
89#13093992—22no—
90#13093992—24no—
91#13093992—22no—
92C4×C22⋊D47—24no—
93C4×C22⋊D47—24no—
94C4×C22⋊D47—24no—
95C4×C22⋊D47—24no—
96#13093983—21no—
97#13093983—21no—
98#13093983—21no—
99#13093983—21no—
100C2×C4⋊Dic47C2312yes—
101C2×Dic47⋊C4C2×C414yes—
102C2×C22⋊Dic47C2×C412yes—
103C2×C22⋊Dic47C2×C414yes—
104C2×(C2×D47)⋊C4C2×C414yes—
105C2×C4×Dic47C2×C412yes—
106#13093943—24no—
107#13093941—24no—
108(C2×D47)⋊C8—24no—
109(C2×D47)⋊C8—24no—
110C2×#41×C47—22no—
111C2×#41×C47—21no—
112C2×#41×C47—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—22no—
116C2×#41×C47—22no—
117C2×#41×C47—22no—
118C22×Q8×C47C2311yescharacteristic
119C22×D4×C47C2×C412yes—
120C22×D4×C47C2311yescharacteristic
121C23×C4×C47C2×C412yes—
122C23×C4×C47C2311yescharacteristic
123C2×M16×C47—22no—
124C2×M16×C47—21no—
125C2×M16×C47—21no—
126C2×M16×C47—22no—
127C2×M16×C47—22no—
128C2×M16×C47D414yescomplemented
129C2×M16×C47C2312yes—
130C2×M16×C47C2312yes—
131C22×C8×C47—21no—
132C22×C8×C47—21no—
133#101×C47—24no—
134#100×C47—24no—
135C24×C47C22×C412yes—
136C24×C47C22×C411yescharacteristic
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—44no—
140C23×D47C22⋊C411yescharacteristic
141C23×D47C22⋊C412yes—
142C23×D47C22⋊C411yescharacteristic
143C23×D47C22×C412yes—
144#41×C47—42no—
145#41×C47—42no—
146#41×C47—42no—
147#41×C47—42no—
148#41×C47—42no—
149#41×C47—42no—
150#41×C47—42no—
151#41×C47—42no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—24no—
161C2×D4×C47—24no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—24no—
171C22×C4×C47—24no—
172C22×C4×C47C22×C412yes—
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D412yes—
180C22×C4×C47#4112yes—
181C22×C4×C47#4112yes—
182C22×C4×C47C2411yescharacteristic
183C2×C22⋊D47—24no—
184C2×C22⋊D47—24no—
185C2×C22⋊D47—48no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47C22⋊C412yes—
189C22×Dic47C22⋊C411yescharacteristic
190C22×Dic47C22⋊C411yescharacteristic
191C22×Dic47C22×C412yes—
192C22×Dic47C22×C414yes—
193C2×C4×D47—24no—
194C2×C4×D47—24no—
195C2×C4×D47—22no—
196C2×C4×D47—24no—
197C2×C4×D47—22no—
198C2×C4×D47—24no—
199C2×C4×D47—22no—
200C2×C4×D47—22no—
201C2×C4×D47—24no—
202C2×C4×D47—22no—
203C2×C4×D47—22no—
204C2×C4×D47—22no—
205C2×C4×D47—24no—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47C22⋊C412yes—
212C2×C4×D47C22⋊C412yes—
213C2×C4×D47C22⋊C412yes—
214C2×C4×D47C22⋊C412yes—
215C2×C4×D47C2×D412yes—
216C2×C4×D47C2×D412yes—
217C2×C4×D47C2×D412yes—
218C2×C4×D47C2×D412yes—
219M16×C47—24no—
220M16×C47—22no—
221M16×C47—22no—
222M16×C47—22no—
223M16×C47—42no—
224M16×C47C2×D414yes—
225C2×C8×C47—24no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47—42no—
229C22⋊Dic47—22no—
230C22⋊Dic47—22no—
231C22⋊Dic47—24no—
232C22⋊Dic47—24no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235C4⋊Dic47—22no—
236C4⋊Dic47—22no—
237Dic47⋊C4—24no—
238Dic47⋊C4—24no—
239C4×Dic47—22no—
240C4×Dic47—22no—
241#10625329—24no—
242#10625329—22no—
243#10625329—22no—
244#10625329—22no—
245#10625329—42no—
246#10625329C2×D414yes—
247C2×C47⋊C8—24no—
248C2×C47⋊C8—22no—
249C2×C47⋊C8—22no—
250C2×C47⋊C8—42no—
251#10625324—216no—
252C8×D47—216no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—42no—
257C23×C47—44no—
258C23×C47C2×C22⋊C411yescharacteristic
259C23×C47C2×C22⋊C411yescharacteristic
260C23×C47C4×D412yes—
261C23×C47C4×D412yes—
262C23×C47C23×C411yescharacteristic
263C22×D47—22no—
264C22×D47—24no—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—24no—
268C22×D47—22no—
269C22×D47—24no—
270C22×D47—24no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—48no—
275C22×D47—48no—
276C22×D47C2×C22⋊C412yes—
277C22×D47C2×C22⋊C412yes—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47—41no—
282D4×C47—44no—
283D4×C47—44no—
284D4×C47—41no—
285D4×C47—41no—
286D4×C47—41no—
287D4×C47—41no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—44no—
292C2×C4×C47—44no—
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C4×D412yes—
296C2×C4×C47C4×D412yes—
297C2×C4×C47#12012yes—
298C2×C4×C47#12012yes—
299C2×C4×C47#12112yes—
300C2×C4×C47#12112yes—
301C2×C4×C47#12112yes—
302C2×C4×C47#12112yes—
303C2×C4×C47#12312yes—
304C2×C4×C47#12312yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C2×#4111yescharacteristic
310C2×C4×C47C2×#4111yescharacteristic
311C22⋊D47—48no—
312C22⋊D47—48no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—44no—
320C2×Dic47C2×C22⋊C412yes—
321C2×Dic47C2×C22⋊C412yes—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—22no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—24no—
331C4×D47—24no—
332C4×D47—24no—
333C4×D47—24no—
334C8×C47—24no—
335C8×C47—42no—
336C47⋊C8—24no—
337C47⋊C8—42no—
338#20989—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—44no—
345C22×C47—42no—
346C22×C47—82no—
347C22×C47—82no—
348C22×C47#38612yes—
349C22×C47#38612yes—
350C22×C47C22×C22⋊C411yescharacteristic
351C22×C47C2×C4×D411yescharacteristic
352C22×C47C2×C4×D411yescharacteristic
353C2×D47—28no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—22no—
359C2×D47—44no—
360C2×D47—44no—
361C2×D47—48no—
362C2×D47—44no—
363C2×D47#41314yescomplemented
364C4×C47—42no—
365C4×C47#38612yes—
366C4×C47#38612yes—
367C4×C47C2×#12011yescharacteristic
368C4×C47C2×#12111yescharacteristic
369C4×C47C2×#12111yescharacteristic
370C4×C47C2×#12311yescharacteristic
371Dic47—22no—
372Dic47—22no—
373Dic47—44no—
374C23×M16—471no—
375C2×#525—471no—
376C2×#413—471no—
377C2×#413D4711yescharacteristic, complemented
378C2×#407—471no—
379#1901—474no—
380#1900—474no—
381#1742—471no—
382#1742—471no—
383C2×C47—22no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—22no—
387C2×C47—82no—
388C2×C47C2×#38611yescharacteristic
389C2×C47C2×#41312yes—
390D47—24no—
391D47—42no—
392C22×#41C2×D4711yescharacteristic
393C24×C4—471no—
394C22×M16—471no—
395C22×M16—471no—
396C22×M16—474no—
397C22×M16—941no—
398C22×M16—944no—
399C22×M16—942no—
400C22×M16—944no—
401C22×M16C2×D4711yescharacteristic
402C22×M16C2×D4711yescharacteristic
403C23×C8—941no—
404#525—941no—
405#525—942no—
406#525—941no—
407#525—942no—
408#525—941no—
409#525—941no—
410C2×#123—472no—
411C2×C22⋊Q8—472no—
412C2×#121—472no—
413C2×#120—472no—
414C2×C4×D4—474no—
415C2×#117—471no—
416#413—24no—
417#413—944no—
418C2×#101—472no—
419C2×#101C2×D4712yescomplemented
420C2×#100—472no—
421C2×#100C2×D4712yescomplemented
422#407—474no—
423#407—941no—
424#407—941no—
425C2×C22⋊C8—942no—
426#343—474no—
427#343—474no—
428C47#2098911yescharacteristic, complemented, Sylow
429C25—471no—
430C2×#41—22no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—22no—
436C2×#41—22no—
437C2×#41—22no—
438C22×Q8C22×D4711yescharacteristic
439C22×D4—474no—
440C22×D4C4×D4712yes—
441C22×D4C22×D4711yescharacteristic
442C23×C4—471no—
443C23×C4—472no—
444C23×C4—471no—
445C23×C4—472no—
446C23×C4—471no—
447C23×C4—472no—
448C23×C4—471no—
449C23×C4—471no—
450C23×C4—472no—
451C23×C4—942no—
452C23×C4—942no—
453C23×C4—942no—
454C23×C4—942no—
455C23×C4C4×D4712yes—
456C23×C4C22×D4711yescharacteristic
457C2×M16—22no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—474no—
463C2×M16—472no—
464C2×M16—472no—
465C2×M16—944no—
466C2×M16—948no—
467C2×M16—948no—
468C2×M16—9416no—
469C2×M16—941no—
470C2×M16—942no—
471C2×M16—948no—
472C2×M16—941no—
473C2×M16—942no—
474C2×M16—942no—
475C2×M16C22⋊D4714yescomplemented
476C2×M16C22×D4712yes—
477C2×M16C22×D4712yes—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—944no—
481C22×C8—948no—
482C22×C8—941no—
483C22×C8—941no—
484#123—942no—
485#123—944no—
486#123—942no—
487C22⋊Q8—942no—
488C22⋊Q8—942no—
489C22⋊Q8—942no—
490C22⋊Q8—942no—
491#121—942no—
492#121—942no—
493#121—942no—
494#121—942no—
495#120—942no—
496#120—944no—
497#120—942no—
498C4×D4—944no—
499C4×D4—944no—
500C4×D4—944no—
501C4×D4—944no—
502#117—941no—
503#117—941no—
504#117—941no—
505#117—941no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—472no—
508C2×C22⋊C4—472no—
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C42—472no—
512#101—24no—
513#101—944no—
514#100—24no—
515#100—944no—
516C22⋊C8—944no—
517C22⋊C8—944no—
518C24—471no—
519C24—472no—
520C24—472no—
521C24—471no—
522C24—942no—
523C24—942no—
524C24—1884no—
525C24C2×C4×D4712yes—
526C24C2×C4×D4711yescharacteristic
527#41—42no—
528#41—42no—
529#41—42no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—42no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—944no—
552C2×D4—944no—
553C2×D4—1888no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—471no—
559C22×C4—472no—
560C22×C4—471no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—474no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—944no—
574C22×C4—944no—
575C22×C4—942no—
576C22×C4—944no—
577C22×C4—942no—
578C22×C4—944no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—944no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—944no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4C2×C4×D4712yes—
592C22×C4C2×C4×D4711yescharacteristic
593C22×C4#1062535012yes—
594C22×C4D4×D4711yescharacteristic
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4D4×D4711yescharacteristic
598C22×C4D4×D4712yes—
599C22×C4#1062535212yes—
600C22×C4C2×C22⋊D4712yes—
601C22×C4C23×D4711yescharacteristic
602M16—24no—
603M16—22no—
604M16—22no—
605M16—22no—
606M16—42no—
607M16—474no—
608M16—9416no—
609M16—944no—
610M16—942no—
611M16—942no—
612M16—942no—
613M16—1882no—
614M16C2×C22⋊D4714yes—
615C2×C8—24no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—42no—
619C2×C8—9416no—
620C2×C8—944no—
621C2×C8—942no—
622C2×C8—942no—
623C2×C8—1882no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—942no—
627C4⋊C4—942no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—942no—
633C22⋊C4—942no—
634C42—942no—
635C42—942no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—42no—
640C23—44no—
641C23—472no—
642C23—472no—
643C23—944no—
644C23—944no—
645C23—944no—
646C23—942no—
647C23—944no—
648C23—942no—
649C23—942no—
650C23—942no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23—1888no—
655C23—1888no—
656C23C22⋊C4×D4711yescharacteristic
657C23C22⋊C4×D4711yescharacteristic
658C23(C22⋊D47)⋊C412yes—
659C23C4×C22⋊D4712yes—
660C23C22×C4×D4711yescharacteristic
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665D4—44no—
666D4—44no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—1888no—
672D4—1888no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—942no—
681C2×C4—944no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—944no—
686C2×C4—944no—
687C2×C4—944no—
688C2×C4—944no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—944no—
698C2×C4—1884no—
699C2×C4C22⋊C4×D4711yescharacteristic
700C2×C4C22⋊C4×D4711yescharacteristic
701C2×C4(C22⋊D47)⋊C412yes—
702C2×C4C4×C22⋊D4712yes—
703C2×C4#1309399212yes—
704C2×C4#1309399212yes—
705C2×C4#1309399512yes—
706C2×C4#1309399512yes—
707C2×C4#1309399712yes—
708C2×C4#1309399712yes—
709C2×C4#1309400612yes—
710C2×C4#1309400612yes—
711C2×C4C2×D4×D4711yescharacteristic
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4C2×D4×D4711yescharacteristic
714C2×C4C22×C22⋊D4711yescharacteristic
715C2×C4C2×#1062535211yescharacteristic
716C2×C4C2×#1062535011yescharacteristic
717C8—24no—
718C8—42no—
719C8—944no—
720C8—1882no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—82no—
729C22—82no—
730C22—474no—
731C22—948no—
732C22—942no—
733C22—942no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—1884no—
738C22—1884no—
739C22—1888no—
740C22—1884no—
741C22#1568899912yes—
742C22#1568899912yes—
743C22C2×C22⋊C4×D4711yescharacteristic
744C22C2×(C22⋊D47)⋊C411yescharacteristic
745C22C2×C4×C22⋊D4711yescharacteristic
746C4—42no—
747C4—942no—
748C4—942no—
749C4—1884no—
750C4#1568899912yes—
751C4#1568899912yes—
752C4C2×#1309399211yescharacteristic
753C4C2×#1309399511yescharacteristic
754C4C2×#1309399711yescharacteristic
755C4C2×#1309400611yescharacteristic
756C2—21no—
757C2—21no—
758C2—22no—
759C2—22no—
760C2—82no—
761C2—944no—
762C2—1882no—
763C2C2×#1568899911yescharacteristic
764C2#413×D4712yes—
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#413C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689630C2
cosocleC22×C4×C47C24
hypercenterC2×#413D47
hypocenterC47#20989
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C22×M16×D47C2semidirect
3. C2×#15689107C2semidirect
4. C2×#15689086C2semidirect
5. #20243853C2semidirect
6. #20243848C2semidirect
7. #20243126C2semidirect
8. #20243126C2semidirect
9. C2×C47×#413C2semidirect
32. C2×#13093943C22semidirect
33. C2×#13093941C22semidirect
38. #15688891C22semidirect
39. #15688891C22semidirect
44. C2×#101×C47C22semidirect
45. C2×#100×C47C22semidirect
66. C2×#10625329D4semidirect
128. C2×M16×C47D4semidirect
363. C2×D47#413semidirect
377. C2×#413D47semidirect
419. C2×#101C2×D47semidirect
421. C2×#100C2×D47semidirect
428. C47#20989semidirect
475. C2×M16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156896302
C2×#156891072
C2×#156890862
#202438532
#202438482
#202431262
C2×C47×#4132
#2098947