Finite Group Databasebeta

← #26217493

Subgroups — #26217493

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689630C211yesmaximal, characteristic
2C2×#117×D47C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
5#20243707C212yesmaximal, complemented
6#20243702C212yesmaximal, complemented
7#20243697C212yesmaximal, complemented
8#20243692C212yesmaximal, complemented
9#20243105C211yesmaximal, characteristic, complemented
10#20243104C211yesmaximal, characteristic, complemented
11C2×C47×#416C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C23×C47⋊C8C2211yescharacteristic
14#15689630—24no—
15#15689630C418yescomplemented
16C2×#13094005—21no—
17C2×#13094000C2211yescharacteristic
18C2×#13094000C2211yescharacteristic
19C2×#13093995C2211yescharacteristic
20C2×#13093995C2211yescharacteristic
21C2×#13093992—21no—
22C2×C4×C22⋊D47—21no—
23C2×C4×C22⋊D47—21no—
24C2×#13093983C2211yescharacteristic
25C2×#13093983C2211yescharacteristic
26C2×#13093982C2212yes—
27C2×#13093981—21no—
28C2×#13093980—21no—
29#117×D47—24no—
30#117×D47—24no—
31C2×C4⋊C4×D47C2212yes—
32C2×C22⋊C4×D47—21no—
33C2×C42×D47—21no—
34#15689119—24no—
35C2×#13093948C2212yescomplemented
36C2×#13093945C2212yescomplemented
37C2×(C2×D47)⋊C8—24no—
38C2×(C2×D47)⋊C8C2212yes—
39C2×(C2×D47)⋊C8C2212yes—
40#15688886C2212yescomplemented
41#15688886C2212yescomplemented
42#15688885C2212yescomplemented
43#15688885C2212yescomplemented
44C22×#41×C47C2211yescharacteristic
45C23×C8×C47C2211yescharacteristic
46C2×#117×C47C2211yescharacteristic
47C47×#416—24no—
48C2×#103×C47C2212yescomplemented
49C2×#102×C47C2212yescomplemented
50C24×D47D411yescharacteristic
51C22×C22⋊D47—21no—
52C22×C22⋊D47—21no—
53C23×Dic47D411yescharacteristic
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47C2×C414yes—
60C22×C4×D47D411yescharacteristic
61C22×C4×D47D411yescharacteristic
62C22×C4×D47D414yes—
63C22×C4×D47C2311yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C22×C47⋊C8—22no—
66C22×C47⋊C8—22no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8C2312yes—
69#13094005—28no—
70#13094000—22no—
71#13094000—22no—
72#13094000C2×C414yes—
73#13094000C2×C414yescomplemented
74#13093995—22no—
75#13093995—22no—
76#13093995C2×C414yes—
77#13093995C2×C414yescomplemented
78#13093992—28no—
79C4×C22⋊D47—28no—
80C4×C22⋊D47—28no—
81#13093983—22no—
82#13093983—22no—
83#13093983C2×C414yescomplemented
84#13093983D414yescomplemented
85#13093982—24no—
86#13093982—24no—
87#13093981—28no—
88#13093980—28no—
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2312yes—
92C2×Dic47⋊C4—22no—
93C2×Dic47⋊C4—21no—
94C2×Dic47⋊C4—21no—
95C4⋊C4×D47—24no—
96C4⋊C4×D47—24no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C22⋊C4×D47—28no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—22no—
108C42×D47—28no—
109#13093948—24no—
110#13093945—24no—
111(C2×D47)⋊C8—24no—
112(C2×D47)⋊C8—24no—
113C2×#41×C47—22no—
114C2×#41×C47—22no—
115C2×#41×C47—22no—
116C2×#41×C47—22no—
117C2×#41×C47—22no—
118C2×#41×C47C2×C414yescomplemented
119C22×Q8×C47C2311yescharacteristic
120C22×D4×C47—21no—
121C22×D4×C47C2311yescharacteristic
122C23×C4×C47—21no—
123C23×C4×C47C2311yescharacteristic
124C22×C8×C47—22no—
125C22×C8×C47—22no—
126C22×C8×C47—22no—
127C22×C8×C47C2312yes—
128#117×C47—22no—
129#117×C47D414yescomplemented
130C2×C4⋊C4×C47C2312yes—
131C2×C22⋊C4×C47—21no—
132C2×C42×C47—21no—
133#103×C47—24no—
134#102×C47—24no—
135C24×C47—21no—
136C24×C47C2×D411yescharacteristic
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—24no—
140C23×D47—42no—
141C23×D47C22⋊C414yes—
142C23×D47C2×D411yescharacteristic
143C23×D47C2×D411yescharacteristic
144#41×C47—28no—
145#41×C47—28no—
146#41×C47—44no—
147#41×C47—44no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47C22×C412yes—
154C2×D4×C47—24no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—42no—
161C2×D4×C47—42no—
162C2×D4×C47C22×C412yes—
163C22×C4×C47—22no—
164C22×C4×C47—21no—
165C22×C4×C47—24no—
166C22×C4×C47—42no—
167C22×C4×C47—42no—
168C22×C4×C47C22×C412yes—
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47C2×D412yes—
173C22×C4×C47#4112yes—
174C22×C4×C47#4112yes—
175C22×C4×C47C2411yescharacteristic
176C2×C22⋊D47—24no—
177C2×C22⋊D47—24no—
178C2×C22⋊D47—44no—
179C2×C22⋊D47—44no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47C22⋊C414yes—
186C22×Dic47C2×D411yescharacteristic
187C22×Dic47C2×D411yescharacteristic
188C2×C4×D47—28no—
189C2×C4×D47—28no—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—22no—
195C2×C4×D47—22no—
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47—21no—
199C2×C4×D47—21no—
200C2×C4×D47—21no—
201C2×C4×D47—21no—
202C2×C4×D47—21no—
203C2×C4×D47—21no—
204C2×C4×D47—28no—
205C2×C4×D47—44no—
206C2×C4×D47—44no—
207C2×C4×D47C22⋊C414yes—
208C2×C4×D47C22⋊C414yes—
209C2×C4×D47C22×C412yes—
210C2×C4×D47C22×C412yes—
211C2×C4×D47C2×D412yes—
212C2×C4×D47C2×D412yes—
213C2×C8×C47—22no—
214C2×C8×C47—22no—
215C2×C8×C47—22no—
216C2×C8×C47—44no—
217C4⋊C4×C47—22no—
218C4⋊C4×C47C2×D414yes—
219C22⋊C4×C47—24no—
220C42×C47—24no—
221C22⋊Dic47—24no—
222C22⋊Dic47—24no—
223C22⋊Dic47—24no—
224C22⋊Dic47—24no—
225(C2×D47)⋊C4—28no—
226(C2×D47)⋊C4—24no—
227(C2×D47)⋊C4—24no—
228C4⋊Dic47—22no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47C22×C412yes—
232C4⋊Dic47C22×C412yes—
233C4⋊Dic47C2×D414yes—
234Dic47⋊C4—28no—
235Dic47⋊C4—24no—
236Dic47⋊C4—24no—
237C4×Dic47—28no—
238C4×Dic47—24no—
239C4×Dic47—24no—
240C2×C47⋊C8—22no—
241C2×C47⋊C8—22no—
242C2×C47⋊C8—22no—
243C2×C47⋊C8—44no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47C2×C22⋊C412yes—
252C23×C47#12012yes—
253C23×C47#12312yes—
254C23×C47C22×D411yescharacteristic
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—22no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—28no—
263C22×D47—28no—
264C22×D47—44no—
265C22×D47—48no—
266C22×D47—48no—
267C22×D47C2×C22⋊C412yes—
268C22×D47C2×C22⋊C412yes—
269C22×D47#13514yes—
270Q8×C47—22no—
271Q8×C47—22no—
272Q8×C47—41no—
273Q8×C47—41no—
274D4×C47—22no—
275D4×C47—22no—
276D4×C47—48no—
277D4×C47—41no—
278D4×C47—41no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—48no—
286C2×C4×C47C2×C22⋊C412yes—
287C2×C4×C47C4×D414yes—
288C2×C4×C47C4×D414yes—
289C2×C4×C47#12012yes—
290C2×C4×C47#12114yes—
291C2×C4×C47#12114yes—
292C2×C4×C47#12312yes—
293C2×C4×C47C23×C411yescharacteristic
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C22⋊D47—48no—
300C22⋊D47—48no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—28no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—24no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47C2×C22⋊C412yes—
314C2×Dic47C2×C22⋊C412yes—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—22no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—28no—
324C4×D47—28no—
325C4×D47—416no—
326C8×C47—42no—
327C47⋊C8—42no—
328#20908—471nomaximal, Sylow
329C22×C47—24no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—24no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—82no—
337C22×C47—82no—
338C22×C47#38614yes—
339C22×C47C22×C22⋊C411yescharacteristic
340C22×C47C2×#12011yescharacteristic
341C22×C47C2×#12311yescharacteristic
342C22×C47C2×#13512yes—
343C22×C47#57512yes—
344C2×D47—24no—
345C2×D47—22no—
346C2×D47—24no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—416no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47#41614yescomplemented
355C4×C47—44no—
356C4×C47—42no—
357C4×C47#38614yes—
358C4×C47C2×C4×D411yescharacteristic
359C4×C47C2×C4×D411yescharacteristic
360C4×C47C2×#12111yescharacteristic
361C4×C47C2×#12111yescharacteristic
362Dic47—22no—
363Dic47—22no—
364Dic47—42no—
365Dic47—42no—
366Dic47—44no—
367C2×#525—471no—
368C22×#117—471no—
369C2×#416—471no—
370C2×#416D4711yescharacteristic, complemented
371C22×C22⋊C8—471no—
372#1875—472no—
373#1874—472no—
374#1873—472no—
375#1872—472no—
376#1735—471no—
377#1735—471no—
378C2×C47—24no—
379C2×C47—82no—
380C2×C47C2×#38611yescharacteristic
381C2×C47C2×#41611yescharacteristic
382C2×C47#289611yescharacteristic
383C2×C47#300212yes—
384C2×C47#309112yes—
385D47—24no—
386D47—42no—
387C22×#41C2×D4711yescharacteristic
388C24×C4—471no—
389C23×C8—471no—
390C23×C8C2×D4711yescharacteristic
391#525—478no—
392#525—944no—
393C2×#123—941no—
394C2×C22⋊Q8—471no—
395C2×C22⋊Q8—471no—
396C2×#121—471no—
397C2×#121—471no—
398C2×#120—941no—
399C2×C4×D4—941no—
400C2×C4×D4—941no—
401C2×#117—471no—
402C2×#117—471no—
403C2×#117—472no—
404C2×#117—941no—
405C2×#117—941no—
406C2×#117—944no—
407C2×#117—944no—
408C2×#117C2×D4711yescharacteristic
409C22×C4⋊C4—472no—
410C22×C22⋊C4—941no—
411C22×C42—941no—
412#416—24no—
413#416—944no—
414C2×#103—472no—
415C2×#103C2×D4712yescomplemented
416C2×#102—472no—
417C2×#102C2×D4712yescomplemented
418C2×C22⋊C8—472no—
419C2×C22⋊C8—472no—
420C2×C22⋊C8—944no—
421#340—472no—
422#340—472no—
423#340—472no—
424#340—472no—
425C47#2090811yescharacteristic, complemented, Sylow
426C25—471no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41C4×D4714yescomplemented
433C22×Q8C22×D4711yescharacteristic
434C22×D4—21no—
435C22×D4—941no—
436C22×D4—941no—
437C22×D4C22×D4711yescharacteristic
438C23×C4—21no—
439C23×C4—471no—
440C23×C4—474no—
441C23×C4—474no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—942no—
447C23×C4—942no—
448C23×C4—942no—
449C23×C4—942no—
450C23×C4—942no—
451C23×C4C22×D4711yescharacteristic
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8—472no—
456C22×C8—942no—
457C22×C8—942no—
458C22×C8—942no—
459C22×C8C22×D4712yes—
460#123—948no—
461C22⋊Q8—474no—
462C22⋊Q8—474no—
463C22⋊Q8—942no—
464C22⋊Q8—942no—
465#121—474no—
466#121—474no—
467#121—942no—
468#121—942no—
469#120—948no—
470C4×D4—948no—
471C4×D4—948no—
472#117—22no—
473#117—474no—
474#117—474no—
475#117—948no—
476#117—948no—
477#117—944no—
478#117—942no—
479#117—942no—
480#117—944no—
481#117C22⋊D4714yescomplemented
482C2×C4⋊C4—472no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—942no—
487C2×C4⋊C4—941no—
488C2×C4⋊C4—941no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4C22×D4712yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—948no—
493C2×C22⋊C4—942no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C22⋊C4—941no—
500C2×C42—21no—
501C2×C42—948no—
502C2×C42—942no—
503C2×C42—941no—
504C2×C42—941no—
505#103—24no—
506#103—944no—
507#102—24no—
508#102—944no—
509C22⋊C8—944no—
510C22⋊C8—944no—
511C24—21no—
512C24—471no—
513C24—471no—
514C24—474no—
515C24—944no—
516C24—942no—
517C24—942no—
518C24—1882no—
519C24D4×D4711yescharacteristic
520#41—28no—
521#41—28no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×C4×D4712yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—944no—
539C2×D4—944no—
540C2×D4—1884no—
541C2×D4—1884no—
542C2×D4C2×C4×D4712yes—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—474no—
549C22×C4—471no—
550C22×C4—471no—
551C22×C4—474no—
552C22×C4—474no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—948no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—948no—
561C22×C4—948no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—948no—
565C22×C4—948no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—942no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—1884no—
580C22×C4—1884no—
581C22×C4C2×C4×D4712yes—
582C22×C4#1062535012yes—
583C22×C4D4×D4712yes—
584C22×C4D4×D4712yes—
585C22×C4D4×D4711yescharacteristic
586C22×C4#1062535212yes—
587C22×C4C2×C22⋊D4712yes—
588C22×C4C23×D4711yescharacteristic
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—942no—
594C2×C8—942no—
595C2×C8—942no—
596C2×C8—1884no—
597C4⋊C4—22no—
598C4⋊C4—472no—
599C4⋊C4—472no—
600C4⋊C4—474no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—948no—
604C4⋊C4—941no—
605C4⋊C4—941no—
606C4⋊C4—942no—
607C4⋊C4C2×C22⋊D4714yes—
608C22⋊C4—24no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C22⋊C4—948no—
612C22⋊C4—944no—
613C22⋊C4—944no—
614C22⋊C4—944no—
615C22⋊C4—944no—
616C42—24no—
617C42—948no—
618C42—944no—
619C42—944no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—472no—
628C23—474no—
629C23—472no—
630C23—948no—
631C23—941no—
632C23—941no—
633C23—942no—
634C23—948no—
635C23—941no—
636C23—941no—
637C23—942no—
638C23—942no—
639C23—1884no—
640C23—1888no—
641C23—1888no—
642C23C22⋊C4×D4712yes—
643C23#1309399212yes—
644C23#1309400612yes—
645C23C2×D4×D4711yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—41no—
654D4—41no—
655D4—1888no—
656D4—1888no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—48no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—948no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—948no—
672C2×C4—948no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—18816no—
685C2×C4—1882no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4C22⋊C4×D4712yes—
690C2×C4(C22⋊D47)⋊C414yes—
691C2×C4C4×C22⋊D4714yes—
692C2×C4#1309399212yes—
693C2×C4#1309399514yes—
694C2×C4#1309399714yes—
695C2×C4#1309400612yes—
696C2×C4C22×C4×D4711yescharacteristic
697C2×C4C2×D4×D4711yescharacteristic
698C2×C4C2×D4×D4711yescharacteristic
699C2×C4C22×C22⋊D4711yescharacteristic
700C2×C4C2×#1062535211yescharacteristic
701C2×C4C2×#1062535011yescharacteristic
702C8—42no—
703C8—1882no—
704C22—24no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—82no—
712C22—82no—
713C22—474no—
714C22—942no—
715C22—944no—
716C22—944no—
717C22—942no—
718C22—942no—
719C22—942no—
720C22—942no—
721C22—18816no—
722C22—1882no—
723C22—1882no—
724C22#1568899914yes—
725C22C2×C22⋊C4×D4711yescharacteristic
726C22C2×#1309399211yescharacteristic
727C22C2×#1309400611yescharacteristic
728C22#135×D4712yes—
729C22#1568992012yes—
730C4—42no—
731C4—44no—
732C4—942no—
733C4—942no—
734C4—1884no—
735C4—1882no—
736C4—1882no—
737C4#1568899914yes—
738C4C2×(C22⋊D47)⋊C411yescharacteristic
739C4C2×C4×C22⋊D4711yescharacteristic
740C4C2×#1309399511yescharacteristic
741C4C2×#1309399711yescharacteristic
742C2—24no—
743C2—82no—
744C2—944no—
745C2—1882no—
746C2C2×#1568899911yescharacteristic
747C2#416×D4711yescharacteristic
748C2#2025190311yescharacteristic
749C2#2025260212yes—
750C2#2025329912yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC2×#15689630C2
cosocleC22×C4×C47C24
hypercenterC2×#416D47
hypocenterC47#20908
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#117×D47C2semidirect
3. C2×#15689119C2semidirect
4. C22×(C2×D47)⋊C8C2semidirect
5. #20243707C2semidirect
6. #20243702C2semidirect
7. #20243697C2semidirect
8. #20243692C2semidirect
9. #20243105C2semidirect
10. #20243104C2semidirect
11. C2×C47×#416C2semidirect
15. #15689630C4semidirect
35. C2×#13093948C22semidirect
36. C2×#13093945C22semidirect
40. #15688886C22semidirect
41. #15688886C22semidirect
42. #15688885C22semidirect
43. #15688885C22semidirect
48. C2×#103×C47C22semidirect
49. C2×#102×C47C22semidirect
73. #13094000C2×C4semidirect
77. #13093995C2×C4semidirect
83. #13093983C2×C4semidirect
84. #13093983D4semidirect
118. C2×#41×C47C2×C4semidirect
129. #117×C47D4semidirect
354. C2×D47#416semidirect
370. C2×#416D47semidirect
415. C2×#103C2×D47semidirect
417. C2×#102C2×D47semidirect
425. C47#20908semidirect
432. C2×#41C4×D47semidirect
481. #117C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896302
C2×#117×D472
C2×#156891192
C22×(C2×D47)⋊C82
#202437072
#202437022
#202436972
#202436922
#202431052
#202431042
C2×C47×#4162
#2090847