Finite Group Databasebeta

← #26218040

Subgroups — #26218040

Order 12032.

1954 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#15689140C211yesmaximal, characteristic, complemented
4C2×#15689086C211yesmaximal, characteristic, complemented
5#20243833C214yesmaximal, complemented
6#20243828C214yesmaximal, complemented
7#20243099C211yesmaximal, characteristic, complemented
8#20243098C211yesmaximal, characteristic, complemented
9C2×C47×#421C211yesmaximal, characteristic, complemented
10C23×C4×D47C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689630—21no—
13#15689630—21no—
14#15689630—22no—
15#15689630C414yescomplemented
16#15689630C2212yes—
17#15689630C2212yes—
18C2×#13094005—21no—
19C2×#13094000C412yescomplemented
20C2×#13093995C412yescomplemented
21C2×#13093992—21no—
22C2×C4×C22⋊D47—22no—
23C2×#13093983C2211yescharacteristic
24C2×#13093983C2211yescharacteristic
25C2×#13093982—21no—
26C2×#13093981C2212yescomplemented
27C2×#13093980—21no—
28#117×D47—24no—
29#117×D47—24no—
30C2×C4⋊C4×D47—21no—
31C2×C22⋊C4×D47—21no—
32C2×C42×D47C2212yescomplemented
33#15689140—24no—
34C2×#13093951C2214yescomplemented
35#15689086—22no—
36#15689086C2212yescomplemented
37#15689086C2212yescomplemented
38C2×(C2×D47)⋊C8—22no—
39#15688884C2214yescomplemented
40#15688883C2214yescomplemented
41C22×#41×C47C2211yescharacteristic
42C22×M16×C47C2211yescharacteristic
43C2×#117×C47C2211yescharacteristic
44C47×#421—24no—
45C2×#104×C47C2214yescomplemented
46C24×D47D411yescharacteristic
47C22×C22⋊D47—22no—
48C23×Dic47D411yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47C2×C412yes—
55C22×C4×D47C2×C412yes—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47D412yes—
59C22×C4×D47D412yes—
60C22×C4×D47C2311yescharacteristic
61C22×C4×D47C2311yescharacteristic
62C2×#10625329—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329C2312yes—
66C22×C47⋊C8—21no—
67#13094005—24no—
68#13094005—22no—
69#13094005—22no—
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—24no—
79#13093992—22no—
80#13093992—22no—
81C4×C22⋊D47—24no—
82C4×C22⋊D47—24no—
83C4×C22⋊D47—24no—
84C4×C22⋊D47—24no—
85#13093983—22no—
86#13093983—21no—
87#13093983—21no—
88#13093983C2×C412yescomplemented
89#13093983D414yescomplemented
90#13093983C2312yes—
91#13093982—28no—
92#13093981—24no—
93#13093981—24no—
94#13093980—28no—
95C2×C4⋊Dic47—21no—
96C2×C4⋊Dic47C2×C412yescomplemented
97C2×Dic47⋊C4—22no—
98C2×Dic47⋊C4—22no—
99C4⋊C4×D47—28no—
100C2×C22⋊Dic47—21no—
101C2×C22⋊Dic47—21no—
102C2×C22⋊Dic47—22no—
103C2×(C2×D47)⋊C4—22no—
104C2×(C2×D47)⋊C4—22no—
105C22⋊C4×D47—28no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—22no—
108C2×C4×Dic47C2312yes—
109C42×D47—24no—
110C42×D47—24no—
111#13093951—28no—
112(C2×D47)⋊C8—24no—
113(C2×D47)⋊C8—24no—
114C2×#41×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—22no—
117C2×#41×C47—22no—
118C2×#41×C47—22no—
119C2×#41×C47—22no—
120C2×#41×C47C2×C412yescomplemented
121C2×#41×C47C2312yes—
122C22×Q8×C47C2×C411yescharacteristic, complemented
123C22×D4×C47—21no—
124C22×D4×C47C2×C411yescharacteristic, complemented
125C23×C4×C47—21no—
126C23×C4×C47C2311yescharacteristic
127C2×M16×C47—21no—
128C2×M16×C47—22no—
129C2×M16×C47—22no—
130C2×M16×C47C2312yes—
131C22×C8×C47—21no—
132#117×C47—22no—
133#117×C47D414yescomplemented
134C2×C4⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C42×C47C2312yes—
137#104×C47—28no—
138C24×C47—21no—
139C24×C47C2×D411yescharacteristic
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—44no—
143C23×D47C22⋊C412yes—
144C23×D47C22⋊C412yes—
145C23×D47C2×D411yescharacteristic
146C23×D47C2×D411yescharacteristic
147#41×C47—24no—
148#41×C47—24no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—42no—
154#41×C47—42no—
155#41×C47—42no—
156#41×C47—42no—
157C2×Q8×C47—21no—
158C2×Q8×C47—22no—
159C2×Q8×C47—22no—
160C2×Q8×C47C22×C412yes—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—42no—
167C2×D4×C47—42no—
168C2×D4×C47C22×C412yes—
169C22×C4×C47—21no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D412yes—
181C22×C4×C47C2×D412yes—
182C22×C4×C47#4112yes—
183C22×C4×C47#4112yes—
184C22×C4×C47C2411yescharacteristic
185C2×C22⋊D47—24no—
186C2×C22⋊D47—24no—
187C2×C22⋊D47—48no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47C22⋊C412yes—
193C22×Dic47C22⋊C412yes—
194C22×Dic47C2×D411yescharacteristic
195C22×Dic47C2×D411yescharacteristic
196C2×C4×D47—24no—
197C2×C4×D47—24no—
198C2×C4×D47—24no—
199C2×C4×D47—24no—
200C2×C4×D47—22no—
201C2×C4×D47—22no—
202C2×C4×D47—24no—
203C2×C4×D47—24no—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—21no—
209C2×C4×D47—21no—
210C2×C4×D47—21no—
211C2×C4×D47—21no—
212C2×C4×D47—21no—
213C2×C4×D47—21no—
214C2×C4×D47—21no—
215C2×C4×D47—21no—
216C2×C4×D47—28no—
217C2×C4×D47—48no—
218C2×C4×D47C22⋊C412yes—
219C2×C4×D47C22⋊C412yes—
220C2×C4×D47C22⋊C412yes—
221C2×C4×D47C22⋊C412yes—
222C2×C4×D47C22×C412yes—
223C2×C4×D47C22×C412yes—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2×D412yes—
226M16×C47—22no—
227M16×C47—22no—
228M16×C47—42no—
229C2×C8×C47—22no—
230C2×C8×C47—42no—
231C4⋊C4×C47—24no—
232C22⋊C4×C47—24no—
233C42×C47—22no—
234C42×C47C2×D414yescomplemented
235C22⋊Dic47—22no—
236C22⋊Dic47—24no—
237C22⋊Dic47—22no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243C4⋊Dic47—22no—
244C4⋊Dic47—24no—
245C4⋊Dic47C22×C414yes—
246Dic47⋊C4—28no—
247Dic47⋊C4—24no—
248Dic47⋊C4—24no—
249C4×Dic47—28no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47C2×D414yescomplemented
254#10625329—22no—
255#10625329—22no—
256#10625329—42no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—42no—
259C23×C47—22no—
260C23×C47—42no—
261C23×C47—44no—
262C23×C47—42no—
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47#12012yes—
266C23×C47#12312yes—
267C23×C47C22×D411yescharacteristic
268C22×D47—21no—
269C22×D47—21no—
270C22×D47—24no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47—42no—
280C22×D47—48no—
281C22×D47—48no—
282C22×D47C2×C22⋊C412yes—
283C22×D47C2×C22⋊C412yes—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—42no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—42no—
290D4×C47—42no—
291D4×C47—44no—
292D4×C47—42no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—44no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—44no—
300C2×C4×C47C2×C22⋊C411yescharacteristic
301C2×C4×C47C2×C22⋊C411yescharacteristic
302C2×C4×C47C4×D412yes—
303C2×C4×C47C4×D412yes—
304C2×C4×C47C4×D412yes—
305C2×C4×C47C4×D412yes—
306C2×C4×C47#12012yes—
307C2×C4×C47#12112yes—
308C2×C4×C47#12112yes—
309C2×C4×C47#12112yes—
310C2×C4×C47#12112yes—
311C2×C4×C47#12312yes—
312C2×C4×C47C23×C411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C22⋊D47—48no—
319C22⋊D47—48no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47C2×C22⋊C412yes—
331C2×Dic47C2×C22⋊C412yes—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—24no—
341C4×D47—24no—
342C4×D47—24no—
343C4×D47—24no—
344C4×D47—416no—
345C8×C47—42no—
346C47⋊C8—42no—
347#20979—471nomaximal, Sylow
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—44no—
354C22×C47—42no—
355C22×C47—84no—
356C22×C47#38612yes—
357C22×C47#38612yes—
358C22×C47C22×C22⋊C411yescharacteristic
359C22×C47C2×#12011yescharacteristic
360C22×C47C2×#12311yescharacteristic
361C2×D47—24no—
362C2×D47—24no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—48no—
369C2×D47—48no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47#42114yescomplemented
373C4×C47—44no—
374C4×C47—42no—
375C4×C47#38612yes—
376C4×C47#38612yes—
377C4×C47C2×C4×D411yescharacteristic
378C4×C47C2×C4×D411yescharacteristic
379C4×C47C2×#12111yescharacteristic
380C4×C47C2×#12111yescharacteristic
381Dic47—22no—
382Dic47—22no—
383Dic47—44no—
384Dic47—44no—
385C2×#525—471no—
386C22×#117—471no—
387C2×#421—471no—
388C2×#421D4711yescharacteristic, complemented
389C2×#407—471no—
390#1897—474no—
391#1896—474no—
392#1733—471no—
393#1733—471no—
394C2×C47—21no—
395C2×C47—21no—
396C2×C47—22no—
397C2×C47—22no—
398C2×C47—82no—
399C2×C47C2×#38611yescharacteristic
400C2×C47C2×#42112yes—
401D47—24no—
402D47—42no—
403C22×#41C2×D4711yescharacteristic
404C24×C4—471no—
405C22×M16—471no—
406C22×M16C2×D4711yescharacteristic
407#525—474no—
408#525—472no—
409#525—472no—
410#525—941no—
411#525—941no—
412#525—942no—
413C2×#123—941no—
414C2×C22⋊Q8—472no—
415C2×#121—472no—
416C2×#120—941no—
417C2×C4×D4—942no—
418C2×#117—471no—
419C2×#117—472no—
420C2×#117—471no—
421C2×#117—941no—
422C2×#117—941no—
423C2×#117—944no—
424C2×#117—944no—
425C2×#117C2×D4711yescharacteristic
426C22×C4⋊C4—941no—
427C22×C22⋊C4—941no—
428C22×C42—472no—
429#421—24no—
430#421—944no—
431C2×#104—474no—
432C2×#104C2×D4714yescomplemented
433#407—472no—
434#407—472no—
435#407—942no—
436C2×C22⋊C8—942no—
437#339—474no—
438#339—474no—
439C47#2097911yescharacteristic, complemented, Sylow
440C25—471no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41C4×D4712yescomplemented
448C2×#41C22×D4712yes—
449C22×Q8C4×D4711yescharacteristic, complemented
450C22×D4—21no—
451C22×D4—942no—
452C22×D4C4×D4711yescharacteristic, complemented
453C23×C4—21no—
454C23×C4—471no—
455C23×C4—472no—
456C23×C4—472no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—472no—
460C23×C4—472no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—942no—
464C23×C4—942no—
465C23×C4—942no—
466C23×C4—942no—
467C23×C4—942no—
468C23×C4C22×D4711yescharacteristic
469C2×M16—21no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—472no—
473C2×M16—941no—
474C2×M16—942no—
475C2×M16—942no—
476C2×M16C22×D4712yes—
477C22×C8—21no—
478C22×C8—941no—
479#123—944no—
480#123—942no—
481#123—942no—
482C22⋊Q8—474no—
483C22⋊Q8—474no—
484C22⋊Q8—942no—
485C22⋊Q8—942no—
486#121—474no—
487#121—474no—
488#121—942no—
489#121—942no—
490#120—944no—
491#120—942no—
492#120—942no—
493C4×D4—944no—
494C4×D4—944no—
495C4×D4—944no—
496C4×D4—944no—
497#117—22no—
498#117—474no—
499#117—472no—
500#117—472no—
501#117—944no—
502#117—948no—
503#117—948no—
504#117—941no—
505#117—941no—
506#117—942no—
507#117—944no—
508#117C22⋊D4714yescomplemented
509C2×C4⋊C4—21no—
510C2×C4⋊C4—472no—
511C2×C4⋊C4—948no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—942no—
514C2×C4⋊C4—941no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—948no—
517C2×C22⋊C4—942no—
518C2×C22⋊C4—942no—
519C2×C22⋊C4—942no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C42—472no—
523C2×C42—944no—
524C2×C42—942no—
525C2×C42—941no—
526C2×C42—944no—
527C2×C42C22×D4712yes—
528#104—28no—
529#104—948no—
530C22⋊C8—944no—
531C22⋊C8—944no—
532C24—21no—
533C24—471no—
534C24—472no—
535C24—472no—
536C24—471no—
537C24—942no—
538C24—942no—
539C24—1884no—
540C24D4×D4711yescharacteristic
541#41—24no—
542#41—24no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—42no—
548#41—42no—
549#41—42no—
550#41—42no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8C2×C4×D4712yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—944no—
563C2×D4—944no—
564C2×D4—1888no—
565C2×D4C2×C4×D4712yes—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—948no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—944no—
588C22×C4—944no—
589C22×C4—944no—
590C22×C4—944no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—944no—
594C22×C4—944no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—1888no—
610C22×C4C2×C4×D4711yescharacteristic
611C22×C4C2×C4×D4711yescharacteristic
612C22×C4#1062535012yes—
613C22×C4D4×D4711yescharacteristic
614C22×C4D4×D4711yescharacteristic
615C22×C4D4×D4711yescharacteristic
616C22×C4D4×D4712yes—
617C22×C4#1062535212yes—
618C22×C4C2×C22⋊D4712yes—
619C22×C4C23×D4711yescharacteristic
620M16—22no—
621M16—22no—
622M16—42no—
623M16—942no—
624M16—942no—
625M16—1882no—
626C2×C8—22no—
627C2×C8—42no—
628C2×C8—942no—
629C2×C8—1882no—
630C4⋊C4—24no—
631C4⋊C4—474no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—948no—
635C4⋊C4—942no—
636C4⋊C4—944no—
637C22⋊C4—24no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—948no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—942no—
644C22⋊C4—944no—
645C22⋊C4—942no—
646C42—22no—
647C42—474no—
648C42—948no—
649C42—942no—
650C42—942no—
651C42—942no—
652C42C2×C22⋊D4714yescomplemented
653C23—22no—
654C23—42no—
655C23—44no—
656C23—42no—
657C23—472no—
658C23—472no—
659C23—944no—
660C23—944no—
661C23—944no—
662C23—941no—
663C23—941no—
664C23—944no—
665C23—944no—
666C23—941no—
667C23—941no—
668C23—1882no—
669C23—1882no—
670C23—1882no—
671C23—1888no—
672C23—1888no—
673C23C22⋊C4×D4711yescharacteristic
674C23C22⋊C4×D4711yescharacteristic
675C23#1309399212yes—
676C23#1309400612yes—
677C23C2×D4×D4711yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—42no—
681D4—22no—
682D4—22no—
683D4—44no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—1888no—
688D4—1888no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—472no—
697C2×C4—472no—
698C2×C4—944no—
699C2×C4—944no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4—941no—
704C2×C4—944no—
705C2×C4—944no—
706C2×C4—944no—
707C2×C4—944no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—944no—
717C2×C4—944no—
718C2×C4—18816no—
719C2×C4—1884no—
720C2×C4—1884no—
721C2×C4C22⋊C4×D4711yescharacteristic
722C2×C4C22⋊C4×D4711yescharacteristic
723C2×C4(C22⋊D47)⋊C412yes—
724C2×C4(C22⋊D47)⋊C412yes—
725C2×C4C4×C22⋊D4712yes—
726C2×C4C4×C22⋊D4712yes—
727C2×C4#1309399212yes—
728C2×C4#1309399512yes—
729C2×C4#1309399512yes—
730C2×C4#1309399712yes—
731C2×C4#1309399712yes—
732C2×C4#1309400612yes—
733C2×C4C22×C4×D4711yescharacteristic
734C2×C4C2×D4×D4711yescharacteristic
735C2×C4C2×D4×D4711yescharacteristic
736C2×C4C22×C22⋊D4711yescharacteristic
737C2×C4C2×#1062535211yescharacteristic
738C2×C4C2×#1062535011yescharacteristic
739C8—42no—
740C8—1882no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—84no—
749C22—474no—
750C22—944no—
751C22—944no—
752C22—942no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—942no—
757C22—1888no—
758C22—1888no—
759C22—1882no—
760C22—1882no—
761C22#1568899912yes—
762C22#1568899912yes—
763C22C2×C22⋊C4×D4711yescharacteristic
764C22C2×#1309399211yescharacteristic
765C22C2×#1309400611yescharacteristic
766C4—44no—
767C4—42no—
768C4—942no—
769C4—942no—
770C4—1884no—
771C4—1884no—
772C4#1568899912yes—
773C4#1568899912yes—
774C4C2×(C22⋊D47)⋊C411yescharacteristic
775C4C2×C4×C22⋊D4711yescharacteristic
776C4C2×#1309399511yescharacteristic
777C4C2×#1309399711yescharacteristic
778C2—21no—
779C2—22no—
780C2—21no—
781C2—22no—
782C2—82no—
783C2—944no—
784C2—1882no—
785C2C2×#1568899911yescharacteristic
786C2#421×D4712yes—
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689630C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47#20979
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#117×D47C2semidirect
3. C2×#15689140C2semidirect
4. C2×#15689086C2semidirect
5. #20243833C2semidirect
6. #20243828C2semidirect
7. #20243099C2semidirect
8. #20243098C2semidirect
9. C2×C47×#421C2semidirect
15. #15689630C4semidirect
19. C2×#13094000C4semidirect
20. C2×#13093995C4semidirect
26. C2×#13093981C22semidirect
32. C2×C42×D47C22semidirect
34. C2×#13093951C22semidirect
36. #15689086C22semidirect
37. #15689086C22semidirect
39. #15688884C22semidirect
40. #15688883C22semidirect
45. C2×#104×C47C22semidirect
73. #13094000C2×C4semidirect
77. #13093995C2×C4semidirect
88. #13093983C2×C4semidirect
89. #13093983D4semidirect
96. C2×C4⋊Dic47C2×C4semidirect
120. C2×#41×C47C2×C4semidirect
122. C22×Q8×C47C2×C4semidirect
124. C22×D4×C47C2×C4semidirect
133. #117×C47D4semidirect
234. C42×C47C2×D4semidirect
253. C4×Dic47C2×D4semidirect
372. C2×D47#421semidirect
388. C2×#421D47semidirect
432. C2×#104C2×D47semidirect
439. C47#20979semidirect
447. C2×#41C4×D47semidirect
449. C22×Q8C4×D47semidirect
452. C22×D4C4×D47semidirect
508. #117C22⋊D47semidirect
652. C42C2×C22⋊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×#156891402
C2×#156890862
#202438332
#202438282
#202430992
#202430982
C2×C47×#4212
#2097947