Finite Group Databasebeta

← C2×#20243687 #26217449

Subgroups — C2×#20243687 #26217449

Order 12032.

2050 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic, complemented
2C2×#15689630C211yesmaximal, characteristic
3C22×#13093951C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5#20243687C218yesmaximal, direct product factor
6C2×#15688884C211yesmaximal, characteristic, complemented
7C2×#15688883C211yesmaximal, characteristic, complemented
8C22×#104×C47C211yesmaximal, characteristic, complemented
9C23×C4×D47C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625324—21no—
12C2×M16×D47—22no—
13C2×M16×D47—24no—
14C2×M16×D47—24no—
15C2×M16×D47C2214yescomplemented
16C22×C8×D47—21no—
17#15689630—22no—
18#15689630—22no—
19#15689630C414yescomplemented
20#15689630C2214yes—
21C2×#13094005—21no—
22C2×#13094000C411yescharacteristic, complemented
23C2×#13094000C411yescharacteristic, complemented
24C2×#13093995C411yescharacteristic, complemented
25C2×#13093995C411yescharacteristic, complemented
26C2×#13093992—21no—
27C2×C4×C22⋊D47—21no—
28C2×C4×C22⋊D47—21no—
29C2×#13093983C2211yescharacteristic
30C22×(C2×D47)⋊C4—21no—
31C22×C4×Dic47C2211yescharacteristic
32C2×#13093951—24no—
33C2×#13093951C2214yescomplemented
34C4×(C2×D47)⋊C4—22no—
35C4×(C2×D47)⋊C4C2214yescomplemented
36C2×C47⋊#95—21no—
37#15688884C2214yescomplemented
38#15688883C2214yescomplemented
39C22×#41×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C22×C42×C47C2211yescharacteristic
42C2×#104×C47—24no—
43C2×#104×C47C2214yescomplemented
44C24×D47D411yescharacteristic
45C22×C22⋊D47—21no—
46C22×C22⋊D47—21no—
47C23×Dic47—21no—
48C23×Dic47D411yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47C2×C411yescharacteristic
54C22×C4×D47C2×C411yescharacteristic
55C22×C4×D47C2×C412yes—
56C22×C4×D47D412yes—
57C22×C4×D47D411yescharacteristic
58C22×C4×D47D411yescharacteristic
59C22×C4×D47D412yes—
60C22×C4×D47C2312yes—
61C2×#10625329—22no—
62C2×#10625329—21no—
63C2×#10625329D414yescomplemented
64C2×#10625329C2312yes—
65C2×#10625324—28no—
66C2×#10625324—24no—
67M16×D47—216no—
68M16×D47—28no—
69M16×D47—28no—
70C22×C47⋊C8—21no—
71C2×C8×D47—28no—
72C2×C8×D47—24no—
73#13094005—24no—
74#13094005—24no—
75#13094000—22no—
76#13094000—22no—
77#13094000C2×C414yescomplemented
78#13094000C2×C414yescomplemented
79#13093995—22no—
80#13093995—22no—
81#13093995C2×C414yescomplemented
82#13093995C2×C414yescomplemented
83#13093992—24no—
84#13093992—24no—
85C4×C22⋊D47—24no—
86C4×C22⋊D47—24no—
87C4×C22⋊D47—24no—
88C4×C22⋊D47—24no—
89#13093983—21no—
90#13093983—21no—
91#13093983C2×C412yes—
92#13093983C2312yes—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×(C2×D47)⋊C4—28no—
101C2×(C2×D47)⋊C4—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—24no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—22no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47C2312yes—
109#13093951—28no—
110C47⋊#95—24no—
111C2×#41×C47—21no—
112C2×#41×C47—21no—
113C2×#41×C47—22no—
114C2×#41×C47—22no—
115C2×#41×C47—22no—
116C2×#41×C47—22no—
117C2×#41×C47C2×C412yes—
118C2×#41×C47C2312yes—
119C22×Q8×C47C2×C411yescharacteristic
120C22×D4×C47—21no—
121C22×D4×C47C2×C411yescharacteristic
122C23×C4×C47—21no—
123C23×C4×C47—21no—
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—21no—
127C2×M16×C47D414yescomplemented
128C2×M16×C47C2312yes—
129C22×C8×C47—21no—
130C2×C42×C47—22no—
131C2×C42×C47—22no—
132C2×C42×C47—21no—
133C2×C42×C47C2312yes—
134#104×C47—28no—
135C24×C47—21no—
136C24×C47C2×D411yescharacteristic
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—24no—
140C23×D47—42no—
141C23×D47C22⋊C411yescharacteristic
142C23×D47C22⋊C412yes—
143C23×D47C22⋊C411yescharacteristic
144C23×D47C2×D412yes—
145#41×C47—24no—
146#41×C47—24no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—42no—
152#41×C47—42no—
153#41×C47—42no—
154#41×C47—42no—
155C2×Q8×C47—21no—
156C2×Q8×C47—22no—
157C2×Q8×C47—22no—
158C2×Q8×C47C22×C412yes—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—21no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47C22×C412yes—
167C22×C4×C47—24no—
168C22×C4×C47—21no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—42no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D412yes—
182C22×C4×C47C2×D412yes—
183C22×C4×C47#4112yes—
184C22×C4×C47#4112yes—
185C22×C4×C47C2411yescharacteristic
186C2×C22⋊D47—24no—
187C2×C22⋊D47—24no—
188C2×C22⋊D47—44no—
189C2×C22⋊D47—44no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—24no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—22no—
196C22×Dic47—42no—
197C22×Dic47—42no—
198C22×Dic47C22⋊C411yescharacteristic
199C22×Dic47C22⋊C411yescharacteristic
200C22×Dic47C22⋊C412yes—
201C22×Dic47C2×D412yes—
202C2×C4×D47—22no—
203C2×C4×D47—22no—
204C2×C4×D47—24no—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—24no—
208C2×C4×D47—22no—
209C2×C4×D47—24no—
210C2×C4×D47—22no—
211C2×C4×D47—24no—
212C2×C4×D47—24no—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—24no—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47C22⋊C412yes—
221C2×C4×D47C22⋊C412yes—
222C2×C4×D47C22⋊C412yes—
223C2×C4×D47C22⋊C412yes—
224C2×C4×D47C22×C412yes—
225C2×C4×D47C22×C412yes—
226C2×C4×D47C2×D412yes—
227C2×C4×D47C2×D412yes—
228M16×C47—24no—
229M16×C47—22no—
230M16×C47C2×D414yescomplemented
231C2×C8×C47—24no—
232C2×C8×C47—22no—
233C42×C47—22no—
234C42×C47—22no—
235C42×C47—42no—
236C22⋊Dic47—22no—
237C22⋊Dic47—22no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240(C2×D47)⋊C4—216no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47C22×C412yes—
246C4⋊Dic47C22×C412yes—
247Dic47⋊C4—24no—
248Dic47⋊C4—24no—
249C4×Dic47—22no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47—42no—
254#10625329—24no—
255#10625329—22no—
256#10625329C2×D414yescomplemented
257C2×C47⋊C8—24no—
258C2×C47⋊C8—22no—
259#10625324—216no—
260C8×D47—216no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—42no—
265C23×C47—42no—
266C23×C47—42no—
267C23×C47C2×C22⋊C411yescharacteristic
268C23×C47C2×C22⋊C411yescharacteristic
269C23×C47#12112yes—
270C23×C47#12112yes—
271C23×C47C22×D411yescharacteristic
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—24no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—24no—
281C22×D47—24no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—48no—
285C22×D47—48no—
286C22×D47#10414yescomplemented
287C22×D47C2×C22⋊C412yes—
288C22×D47C2×C22⋊C412yes—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—42no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—44no—
297D4×C47—42no—
298C2×C4×C47—24no—
299C2×C4×C47—22no—
300C2×C4×C47—48no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—44no—
307C2×C4×C47C2×C22⋊C411yescharacteristic
308C2×C4×C47C2×C22⋊C411yescharacteristic
309C2×C4×C47C4×D412yes—
310C2×C4×C47C4×D412yes—
311C2×C4×C47C4×D412yes—
312C2×C4×C47C4×D412yes—
313C2×C4×C47#12012yes—
314C2×C4×C47#12012yes—
315C2×C4×C47#12112yes—
316C2×C4×C47#12112yes—
317C2×C4×C47#12312yes—
318C2×C4×C47#12312yes—
319C2×C4×C47C23×C411yescharacteristic
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C22×D411yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4111yescharacteristic
324C2×C4×C47C2×#4111yescharacteristic
325C22⋊D47—48no—
326C22⋊D47—48no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—24no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—24no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—48no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47C2×C22⋊C412yes—
341C2×Dic47C2×C22⋊C412yes—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—22no—
346C4×D47—22no—
347C4×D47—22no—
348C4×D47—22no—
349C4×D47—22no—
350C4×D47—24no—
351C4×D47—24no—
352C4×D47—24no—
353C4×D47—24no—
354C8×C47—24no—
355C47⋊C8—24no—
356C2×#1871—471nomaximal, Sylow
357C22×C47—24no—
358C22×C47—24no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—84no—
367C22×C47#38612yes—
368C22×C47#38612yes—
369C22×C47C2×#10412yes—
370C22×C47#42112yes—
371C22×C47C22×C22⋊C411yescharacteristic
372C22×C47C2×#12111yescharacteristic
373C22×C47C2×#12111yescharacteristic
374C2×D47—28no—
375C2×D47—22no—
376C2×D47—22no—
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—44no—
381C2×D47—44no—
382C2×D47—48no—
383C2×D47—44no—
384C2×D47C2×#10414yescomplemented
385C4×C47—44no—
386C4×C47—42no—
387C4×C47#38612yes—
388C4×C47#38612yes—
389C4×C47C2×C4×D411yescharacteristic
390C4×C47C2×C4×D411yescharacteristic
391C4×C47C2×#12011yescharacteristic
392C4×C47C2×#12311yescharacteristic
393Dic47—22no—
394Dic47—22no—
395Dic47—44no—
396Dic47—42no—
397Dic47—42no—
398C23×M16—471no—
399C2×#525—471no—
400C22×#104—471no—
401C22×#104D4711yescharacteristic, complemented
402C2×C4×C22⋊C4—471no—
403#1871—478no—
404C2×#339—471no—
405C2×#339—471no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—22no—
409C2×C47—82no—
410C2×C47#187114yescomplemented
411C2×C47C2×#38611yescharacteristic
412C2×C47C22×#10411yescharacteristic
413C2×C47C2×#42111yescharacteristic
414D47—24no—
415D47—42no—
416C22×#41C2×D4711yescharacteristic
417C24×C4—471no—
418C22×M16—471no—
419C22×M16—474no—
420C22×M16—941no—
421C22×M16—944no—
422C22×M16—942no—
423C22×M16—944no—
424C22×M16C2×D4711yescharacteristic
425C23×C8—941no—
426#525—474no—
427#525—474no—
428#525—942no—
429#525—942no—
430C2×#123—941no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—471no—
433C2×#121—471no—
434C2×#121—471no—
435C2×#120—941no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×#117—471no—
439C22×C22⋊C4—941no—
440C22×C42—471no—
441C22×C42C2×D4711yescharacteristic
442C2×#104—24no—
443C2×#104—474no—
444C2×#104—944no—
445C2×#104C2×D4714yescomplemented
446C4×C22⋊C4—474no—
447C4×C22⋊C4—942no—
448C2×#95—941no—
449#339—474no—
450#339—474no—
451C47C2×#187111yescharacteristic, complemented, Sylow
452C25—471no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41C4×D4712yes—
460C2×#41C22×D4712yes—
461C22×Q8C4×D4711yescharacteristic
462C22×D4—21no—
463C22×D4—941no—
464C22×D4—941no—
465C22×D4C4×D4711yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—472no—
472C23×C4—472no—
473C23×C4—472no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—472no—
477C23×C4—942no—
478C23×C4—942no—
479C23×C4—942no—
480C23×C4—942no—
481C23×C4—941no—
482C23×C4C22×D4711yescharacteristic
483C2×M16—22no—
484C2×M16—21no—
485C2×M16—474no—
486C2×M16—472no—
487C2×M16—944no—
488C2×M16—948no—
489C2×M16—948no—
490C2×M16—9416no—
491C2×M16—941no—
492C2×M16—942no—
493C2×M16—948no—
494C2×M16C22⋊D4714yescomplemented
495C2×M16C22×D4712yes—
496C22×C8—21no—
497C22×C8—944no—
498C22×C8—948no—
499C22×C8—941no—
500#123—944no—
501#123—944no—
502C22⋊Q8—474no—
503C22⋊Q8—474no—
504C22⋊Q8—942no—
505C22⋊Q8—942no—
506#121—474no—
507#121—474no—
508#121—942no—
509#121—942no—
510#120—944no—
511#120—944no—
512C4×D4—944no—
513C4×D4—944no—
514C4×D4—944no—
515C4×D4—944no—
516#117—472no—
517#117—472no—
518#117—941no—
519#117—941no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—948no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—21no—
534C2×C42—472no—
535C2×C42—941no—
536C2×C42—942no—
537C2×C42—942no—
538C2×C42—941no—
539C2×C42C22×D4712yes—
540#104—28no—
541#104—948no—
542#95—944no—
543C24—21no—
544C24—471no—
545C24—471no—
546C24—472no—
547C24—472no—
548C24—944no—
549C24—942no—
550C24—942no—
551C24—1882no—
552C24D4×D4711yescharacteristic
553#41—24no—
554#41—24no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—42no—
560#41—42no—
561#41—42no—
562#41—42no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8C2×C4×D4712yes—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—944no—
575C2×D4—944no—
576C2×D4—1884no—
577C2×D4—1884no—
578C2×D4C2×C4×D4712yes—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—944no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—944no—
608C22×C4—942no—
609C22×C4—944no—
610C22×C4—942no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—944no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—944no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—942no—
624C22×C4—1882no—
625C22×C4—1882no—
626C22×C4C2×C4×D4711yescharacteristic
627C22×C4C2×C4×D4711yescharacteristic
628C22×C4#1062535012yes—
629C22×C4D4×D4711yescharacteristic
630C22×C4D4×D4711yescharacteristic
631C22×C4D4×D4712yes—
632C22×C4D4×D4711yescharacteristic
633C22×C4#1062535212yes—
634C22×C4C2×C22⋊D4712yes—
635C22×C4C23×D4711yescharacteristic
636M16—24no—
637M16—22no—
638M16—474no—
639M16—9416no—
640M16—944no—
641M16—942no—
642M16C2×C22⋊D4714yescomplemented
643C2×C8—24no—
644C2×C8—22no—
645C2×C8—9416no—
646C2×C8—944no—
647C2×C8—942no—
648C4⋊C4—472no—
649C4⋊C4—472no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4—941no—
653C4⋊C4—941no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—9416no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C22⋊C4—942no—
660C22⋊C4—942no—
661C42—22no—
662C42—22no—
663C42—42no—
664C42—942no—
665C42—942no—
666C42—942no—
667C42—942no—
668C42—1882no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—472no—
676C23—474no—
677C23—472no—
678C23—944no—
679C23—944no—
680C23—942no—
681C23—942no—
682C23—944no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—942no—
688C23—1882no—
689C23—1882no—
690C23—1888no—
691C23—1888no—
692C23C22⋊C4×D4711yescharacteristic
693C23C22⋊C4×D4711yescharacteristic
694C23#1309399512yes—
695C23#1309399712yes—
696C23C2×D4×D4711yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—42no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—1888no—
707D4—1888no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—472no—
718C2×C4—472no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—944no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—944no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—1882no—
740C2×C4—1888no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4C22⋊C4×D4711yescharacteristic
745C2×C4C22⋊C4×D4711yescharacteristic
746C2×C4(C22⋊D47)⋊C412yes—
747C2×C4(C22⋊D47)⋊C412yes—
748C2×C4C4×C22⋊D4712yes—
749C2×C4C4×C22⋊D4712yes—
750C2×C4#1309399212yes—
751C2×C4#1309399212yes—
752C2×C4#1309399512yes—
753C2×C4#1309399712yes—
754C2×C4#1309400612yes—
755C2×C4#1309400612yes—
756C2×C4C22×C4×D4711yescharacteristic
757C2×C4C2×D4×D4711yescharacteristic
758C2×C4C2×D4×D4711yescharacteristic
759C2×C4C22×C22⋊D4711yescharacteristic
760C2×C4C2×#1062535211yescharacteristic
761C2×C4C2×#1062535011yescharacteristic
762C8—24no—
763C8—944no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—474no—
775C22—942no—
776C22—942no—
777C22—948no—
778C22—942no—
779C22—942no—
780C22—942no—
781C22—1884no—
782C22—1884no—
783C22—1888no—
784C22—1884no—
785C22#1568899912yes—
786C22#1568899912yes—
787C22#104×D4712yes—
788C22#1568913812yes—
789C22C2×C22⋊C4×D4711yescharacteristic
790C22C2×#1309399511yescharacteristic
791C22C2×#1309399711yescharacteristic
792C4—44no—
793C4—42no—
794C4—942no—
795C4—942no—
796C4—1884no—
797C4—1882no—
798C4—1882no—
799C4#1568899912yes—
800C4#1568899912yes—
801C4C2×(C22⋊D47)⋊C411yescharacteristic
802C4C2×C4×C22⋊D4711yescharacteristic
803C4C2×#1309399211yescharacteristic
804C4C2×#1309400611yescharacteristic
805C2—21no—
806C2—21no—
807C2—22no—
808C2—82no—
809C2—944no—
810C2—1882no—
811C2#2024368714yesdirect product factor
812C2C2×#1568899911yescharacteristic
813C2C2×#104×D4711yescharacteristic
814C2C2×#1568913811yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#104×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689630C2
cosocleC22×C4×C47C24
hypercenterC22×#104D47
hypocenterC47C2×#1871
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C22×M16×D47C2semidirect
3. C22×#13093951C2semidirect
4. C2×C4×(C2×D47)⋊C4C2semidirect
5. #20243687C2direct (N × H)
6. C2×#15688884C2semidirect
7. C2×#15688883C2semidirect
8. C22×#104×C47C2semidirect
15. C2×M16×D47C22semidirect
19. #15689630C4semidirect
22. C2×#13094000C4semidirect
23. C2×#13094000C4semidirect
24. C2×#13093995C4semidirect
25. C2×#13093995C4semidirect
33. C2×#13093951C22semidirect
35. C4×(C2×D47)⋊C4C22semidirect
37. #15688884C22semidirect
38. #15688883C22semidirect
43. C2×#104×C47C22semidirect
63. C2×#10625329D4semidirect
77. #13094000C2×C4semidirect
78. #13094000C2×C4semidirect
81. #13093995C2×C4semidirect
82. #13093995C2×C4semidirect
127. C2×M16×C47D4semidirect
230. M16×C47C2×D4semidirect
256. #10625329C2×D4semidirect
286. C22×D47#104semidirect
384. C2×D47C2×#104semidirect
401. C22×#104D47semidirect
410. C2×C47#1871semidirect
445. C2×#104C2×D47semidirect
451. C47C2×#1871semidirect
494. C2×M16C22⋊D47semidirect
642. M16C2×C22⋊D47semidirect
811. C2#20243687direct (N × H)

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
C22×#130939512
C2×C4×(C2×D47)⋊C42
#202436872
C2×#156888842
C2×#156888832
C22×#104×C472
C2×#187147