Finite Group Databasebeta

← #26244121

Subgroups — #26244121

Order 12032.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689171C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic, complemented
3#20251907C211yesmaximal, characteristic, complemented
4C2×#15689107C211yesmaximal, characteristic, complemented
5C2×#15689107C211yesmaximal, characteristic, complemented
6#20244665C214yesmaximal, complemented
7#20244658C214yesmaximal, complemented
8C2×#15688895C211yesmaximal, characteristic, complemented
9C2×C47×#575C211yesmaximal, characteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C22×#10625329C2211yescharacteristic
13C2×#13093983C2211yescharacteristic
14#15689171—22no—
15#15689171C2214yescomplemented
16C2×#13093959—22no—
17#15689140—22no—
18#15689140C2214yes—
19C2×#13093951—22no—
20#15689132C2212yescomplemented
21#15689128C2212yescomplemented
22#15689124—22no—
23#15689119—22no—
24#15689107—22no—
25#15689107—22no—
26#15689107—22no—
27#15689107C2214yes—
28C2×#13093943—21no—
29C2×#13093943C2212yescomplemented
30C2×#13093941—21no—
31C2×#13093941C2212yescomplemented
32#15688895C2214yescomplemented
33C22×#41×C47C2211yescharacteristic
34C22×#41×C47C2211yescharacteristic
35C47×#575—22no—
36C47×#575—22no—
37C47×#575—22no—
38C47×#575—22no—
39C2×#137×C47—21no—
40C2×#137×C47C2212yes—
41C2×AGL(1,ℤ/8)×C47—21no—
42C2×AGL(1,ℤ/8)×C47C2212yes—
43C2×#135×C47—22no—
44C22×M16×C47C2211yescharacteristic
45C2×#10625329—21no—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329D412yes—
59C2×#10625329D412yes—
60C2×#10625329C2312yes—
61C2×#10625329C2312yes—
62C2×#10625329C2312yes—
63C22×C47⋊C8—21no—
64C22×C47⋊C8—21no—
65C22×C47⋊C8—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983C2312yes—
70C2×C4⋊Dic47—21no—
71C2×C22⋊Dic47—21no—
72C2×C4×Dic47—21no—
73#13093959—28no—
74#13093951—28no—
75#13093948—24no—
76#13093945—24no—
77#13093943—24no—
78#13093943—24no—
79#13093941—24no—
80#13093941—24no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47—21no—
86C2×#41×C47—21no—
87C2×#41×C47—21no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—21no—
92C2×#41×C47—21no—
93C2×#41×C47—21no—
94C2×#41×C47—21no—
95C2×#41×C47—21no—
96C2×#41×C47—21no—
97C2×#41×C47—21no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47D412yes—
102C2×#41×C47D412yes—
103C2×#41×C47D412yes—
104C2×#41×C47C2312yes—
105C22×Q8×C47D411yescharacteristic
106C22×Q8×C47C2311yescharacteristic
107C22×D4×C47—21no—
108C22×D4×C47—21no—
109C22×D4×C47D411yescharacteristic
110C22×D4×C47C2311yescharacteristic
111C23×C4×C47—21no—
112C23×C4×C47—21no—
113C23×C4×C47C2311yescharacteristic
114#137×C47—24no—
115#137×C47—24no—
116#137×C47—24no—
117#137×C47—24no—
118AGL(1,ℤ/8)×C47—24no—
119AGL(1,ℤ/8)×C47—24no—
120AGL(1,ℤ/8)×C47—24no—
121AGL(1,ℤ/8)×C47—24no—
122#135×C47—28no—
123#135×C47—28no—
124C2×Q16×C47—22no—
125C2×SD16×C47—22no—
126C2×SD16×C47—22no—
127C2×D8×C47—22no—
128C2×M16×C47—21no—
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47D412yes—
132C2×M16×C47D412yes—
133C2×M16×C47C2312yes—
134C22×C8×C47—21no—
135C24×C47—21no—
136C24×C47—21no—
137C24×C47#4111yescharacteristic
138#41×C47—22no—
139#41×C47—22no—
140#41×C47—22no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—22no—
154#41×C47—41no—
155#41×C47—41no—
156#41×C47—41no—
157#41×C47—41no—
158#41×C47—41no—
159#41×C47—41no—
160#41×C47—41no—
161#41×C47—41no—
162#41×C47—41no—
163#41×C47—41no—
164#41×C47—41no—
165#41×C47—41no—
166#41×C47—41no—
167#41×C47—41no—
168#41×C47—41no—
169#41×C47—41no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47C2×D412yes—
181C2×Q8×C47C2×D412yes—
182C2×D4×C47—22no—
183C2×D4×C47—22no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—41no—
197C2×D4×C47—41no—
198C2×D4×C47—41no—
199C2×D4×C47—41no—
200C2×D4×C47—41no—
201C2×D4×C47—41no—
202C2×D4×C47—41no—
203C2×D4×C47—41no—
204C2×D4×C47C2×D412yes—
205C2×D4×C47C2×D412yes—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—41no—
213C22×C4×C47—41no—
214C22×C4×C47—41no—
215C22×C4×C47—41no—
216C22×C4×C47—41no—
217C22×C4×C47—41no—
218C22×C4×C47—41no—
219C22×C4×C47—41no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47#4111yescharacteristic
229C22×C4×C47#4111yescharacteristic
230C22×C4×C47#4111yescharacteristic
231C22×C4×C47#4111yescharacteristic
232C22×C4×C47#4111yescharacteristic
233C22×C4×C47C2411yescharacteristic
234C22×Dic47—41no—
235Q16×C47—28no—
236SD16×C47—28no—
237SD16×C47—28no—
238D8×C47—28no—
239M16×C47—22no—
240M16×C47—22no—
241M16×C47—22no—
242M16×C47C2×D414yes—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C22⋊Dic47—22no—
247C22⋊Dic47—41no—
248C4⋊Dic47—22no—
249C4⋊Dic47—41no—
250C4×Dic47—22no—
251C4×Dic47—41no—
252#10625329—22no—
253#10625329—22no—
254#10625329—22no—
255#10625329—22no—
256#10625329—22no—
257#10625329—22no—
258#10625329—22no—
259#10625329—41no—
260#10625329—41no—
261#10625329—41no—
262#10625329—41no—
263#10625329C2×D414yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—41no—
270C2×C47⋊C8—41no—
271C2×C47⋊C8—41no—
272C2×C47⋊C8—41no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—81no—
280C23×C47—82no—
281C23×C47—82no—
282C23×C47#12111yescharacteristic
283C23×C47#12111yescharacteristic
284C23×C47#12311yescharacteristic
285C23×C47#12311yescharacteristic
286C23×C47#12411yescharacteristic
287C23×C47#12411yescharacteristic
288C23×C47C2×#4111yescharacteristic
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—41no—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47—22no—
300D4×C47—22no—
301D4×C47—42no—
302D4×C47—42no—
303D4×C47—42no—
304D4×C47—42no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12011yescharacteristic
329C2×C4×C47#12011yescharacteristic
330C2×C4×C47#12011yescharacteristic
331C2×C4×C47#12111yescharacteristic
332C2×C4×C47#12111yescharacteristic
333C2×C4×C47#12111yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12111yescharacteristic
341C2×C4×C47#12311yescharacteristic
342C2×C4×C47#12311yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47#12311yescharacteristic
345C2×C4×C47#12311yescharacteristic
346C2×C4×C47#12311yescharacteristic
347C2×C4×C47#12411yescharacteristic
348C2×C4×C47#12411yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C2×#4111yescharacteristic
354C2×C4×C47C2×#4111yescharacteristic
355C2×Dic47—42no—
356C2×Dic47—82no—
357C8×C47—24no—
358C47⋊C8—24no—
359C47⋊C8—42no—
360C47⋊C8—42no—
361#23525—471nomaximal, Sylow
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—82no—
372C22×C47—82no—
373C22×C47—82no—
374C22×C47—82no—
375C22×C47—82no—
376C22×C47—82no—
377C22×C47#39411yescharacteristic
378C22×C47#39411yescharacteristic
379C22×C47#39411yescharacteristic
380C22×C47#39411yescharacteristic
381C22×C47C2×#12111yescharacteristic
382C22×C47C2×#12311yescharacteristic
383C22×C47C2×#12411yescharacteristic
384C4×C47—42no—
385C4×C47—42no—
386C4×C47#39411yescharacteristic
387C4×C47#39411yescharacteristic
388C4×C47#39411yescharacteristic
389C4×C47#39411yescharacteristic
390C4×C47C2×#12011yescharacteristic
391C4×C47C2×#12111yescharacteristic
392C4×C47C2×#12111yescharacteristic
393C4×C47C2×#12311yescharacteristic
394Dic47—82no—
395C2×#575D4711yescharacteristic
396C2×#430—471no—
397C2×#421—471no—
398#2896—471no—
399C2×#413—471no—
400C2×#413—471no—
401#2049—474no—
402#2048—474no—
403C2×#344—471no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—21no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—82no—
412C2×C47—82no—
413C2×C47C2×#39411yescharacteristic
414C22×#41C2×D4711yescharacteristic
415C22×#41C2×D4711yescharacteristic
416#575—22no—
417#575—22no—
418#575—22no—
419#575—22no—
420C2×#137—21no—
421C2×#137C2×D4712yes—
422C2×AGL(1,ℤ/8)—21no—
423C2×AGL(1,ℤ/8)C2×D4712yes—
424C2×#135—22no—
425C22×M16—471no—
426C22×M16—471no—
427C22×M16—471no—
428C22×M16C2×D4711yescharacteristic
429C2×#117—471no—
430#430—474no—
431#430—942no—
432C2×#108—942no—
433#421—474no—
434#421—942no—
435C2×#104—942no—
436#419—472no—
437#418—472no—
438#417—942no—
439#416—942no—
440#413—474no—
441#413—942no—
442#413—942no—
443#413—942no—
444C2×#101—472no—
445C2×#101—941no—
446C2×#100—472no—
447C2×#100—941no—
448#344—474no—
449C47#2352511yescharacteristic, complemented, Sylow
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41C22⋊D4712yes—
471C2×#41C22⋊D4712yes—
472C2×#41C22⋊D4712yes—
473C2×#41C22×D4712yes—
474C22×Q8C22⋊D4711yescharacteristic
475C22×Q8C22×D4711yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C22⋊D4711yescharacteristic
479C22×D4C22×D4711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C22×D4711yescharacteristic
483#137—24no—
484#137—24no—
485#137—24no—
486#137—24no—
487AGL(1,ℤ/8)—24no—
488AGL(1,ℤ/8)—24no—
489AGL(1,ℤ/8)—24no—
490AGL(1,ℤ/8)—24no—
491#135—28no—
492#135—28no—
493C2×Q16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×D8—22no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—472no—
501C2×M16—472no—
502C2×M16—472no—
503C2×M16—472no—
504C2×M16—472no—
505C2×M16—941no—
506C2×M16—941no—
507C2×M16—941no—
508C2×M16—941no—
509C2×M16—941no—
510C2×M16—941no—
511C2×M16—941no—
512C2×M16—941no—
513C2×M16—941no—
514C2×M16—941no—
515C2×M16—941no—
516C2×M16—941no—
517C2×M16—941no—
518C2×M16C22⋊D4712yes—
519C2×M16C22⋊D4712yes—
520C2×M16C22×D4712yes—
521C22×C8—21no—
522C22×C8—941no—
523C22×C8—941no—
524C22×C8—941no—
525#117—472no—
526#117—941no—
527#117—941no—
528#117—941no—
529C2×C4⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C42—941no—
532#108—948no—
533#104—948no—
534#103—944no—
535#102—944no—
536#101—944no—
537#101—944no—
538#100—944no—
539#100—944no—
540C24—21no—
541C24—21no—
542C24#1062535211yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×C22⋊D4712yes—
586C2×Q8C2×C22⋊D4712yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4C2×C22⋊D4712yes—
610C2×D4C2×C22⋊D4712yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—1881no—
626C22×C4D4×D4711yescharacteristic
627C22×C4D4×D4711yescharacteristic
628C22×C4#1062535211yescharacteristic
629C22×C4#1062535211yescharacteristic
630C22×C4#1062535211yescharacteristic
631C22×C4#1062535211yescharacteristic
632C22×C4#1062535211yescharacteristic
633C22×C4C2×C22⋊D4711yescharacteristic
634C22×C4C2×C22⋊D4711yescharacteristic
635C22×C4C2×C22⋊D4711yescharacteristic
636C22×C4C2×C22⋊D4711yescharacteristic
637C22×C4C2×C22⋊D4711yescharacteristic
638C22×C4C2×C22⋊D4711yescharacteristic
639C22×C4C23×D4711yescharacteristic
640Q16—28no—
641SD16—28no—
642SD16—28no—
643D8—28no—
644M16—22no—
645M16—22no—
646M16—22no—
647M16—474no—
648M16—942no—
649M16—942no—
650M16—942no—
651M16—942no—
652M16—942no—
653M16—942no—
654M16—942no—
655M16—1881no—
656M16—1881no—
657M16—1881no—
658M16—1881no—
659M16C2×C22⋊D4714yes—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—942no—
664C2×C8—942no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—942no—
668C2×C8—1881no—
669C2×C8—1881no—
670C2×C8—1881no—
671C2×C8—1881no—
672C4⋊C4—942no—
673C4⋊C4—1881no—
674C22⋊C4—942no—
675C22⋊C4—1881no—
676C42—942no—
677C42—1881no—
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—82no—
686C23—82no—
687C23#1309399611yescharacteristic
688C23#1309399611yescharacteristic
689C23#1309400511yescharacteristic
690C23#1309400511yescharacteristic
691C23#1309401111yescharacteristic
692C23#1309401111yescharacteristic
693C23C2×#1062535211yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—3762no—
733C2×C4—1882no—
734C2×C4#1309399311yescharacteristic
735C2×C4#1309399311yescharacteristic
736C2×C4#1309399311yescharacteristic
737C2×C4#1309399311yescharacteristic
738C2×C4#1309399511yescharacteristic
739C2×C4#1309399511yescharacteristic
740C2×C4#1309399511yescharacteristic
741C2×C4#1309399511yescharacteristic
742C2×C4#1309399611yescharacteristic
743C2×C4#1309399611yescharacteristic
744C2×C4#1309399611yescharacteristic
745C2×C4#1309399611yescharacteristic
746C2×C4#1309399611yescharacteristic
747C2×C4#1309399611yescharacteristic
748C2×C4#1309400511yescharacteristic
749C2×C4#1309400511yescharacteristic
750C2×C4#1309400511yescharacteristic
751C2×C4#1309400511yescharacteristic
752C2×C4#1309400511yescharacteristic
753C2×C4#1309400511yescharacteristic
754C2×C4#1309401111yescharacteristic
755C2×C4#1309401111yescharacteristic
756C2×C4C2×D4×D4711yescharacteristic
757C2×C4C22×C22⋊D4711yescharacteristic
758C2×C4C22×C22⋊D4711yescharacteristic
759C2×C4C22×C22⋊D4711yescharacteristic
760C2×C4C2×#1062535211yescharacteristic
761C2×C4C2×#1062535211yescharacteristic
762C8—24no—
763C8—944no—
764C8—1882no—
765C8—1882no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22#1568903711yescharacteristic
782C22#1568903711yescharacteristic
783C22#1568903711yescharacteristic
784C22#1568903711yescharacteristic
785C22C2×#1309399611yescharacteristic
786C22C2×#1309400511yescharacteristic
787C22C2×#1309401111yescharacteristic
788C4—42no—
789C4—42no—
790C4—3762no—
791C4#1568903711yescharacteristic
792C4#1568903711yescharacteristic
793C4#1568903711yescharacteristic
794C4#1568903711yescharacteristic
795C4C2×#1309399311yescharacteristic
796C4C2×#1309399511yescharacteristic
797C4C2×#1309399611yescharacteristic
798C4C2×#1309400511yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—82no—
808C2C2×#1568903711yescharacteristic
subgroupG/H
centerC4#15689037
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#575C2
socleC2×C47C2×#394
hypercenterC2×#575D47
hypocenterC47#23525
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#15689171C2semidirect
2. C2×#15689140C2semidirect
3. #20251907C2semidirect
4. C2×#15689107C2semidirect
5. C2×#15689107C2semidirect
6. #20244665C2semidirect
7. #20244658C2semidirect
8. C2×#15688895C2semidirect
15. #15689171C22semidirect
20. #15689132C22semidirect
21. #15689128C22semidirect
29. C2×#13093943C22semidirect
31. C2×#13093941C22semidirect
32. #15688895C22semidirect
449. C47#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#156891712
C2×#156891402
#202519072
C2×#156891072
#202446652
#202446582
C2×#156888952
C2×C47×#5752
#2352547