Finite Group Databasebeta

← C2×#20285064 #28253323

Subgroups — C2×#20285064 #28253323

Order 13568.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811250C211yesmaximal, characteristic, complemented
2C2×#16811186C211yesmaximal, characteristic
3#20285064C2116yesmaximal, direct product factor
4C2×#16810987C211yesmaximal, characteristic, complemented
5C2×#16810986C211yesmaximal, characteristic, complemented
6C2×#16810985C211yesmaximal, characteristic, complemented
7C2×#16810981C211yesmaximal, characteristic, complemented
8C2×#16810978C211yesmaximal, characteristic, complemented
9C2×#16810976C211yesmaximal, characteristic, complemented
10C2×#16810968C211yesmaximal, characteristic, complemented
11C2×#16810621C211yesmaximal, characteristic, complemented
12C2×#16810626C211yesmaximal, characteristic, complemented
13C2×#16810616C211yesmaximal, characteristic, complemented
14C2×#102×D53C211yesmaximal, characteristic, complemented
15C2×#16810577C211yesmaximal, characteristic, complemented
16C2×C53×#486C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811250—24no—
22#16811250C2218yescomplemented
23#16811186—24no—
24#16811186C2218yes—
25C2×#13133216C2211yescharacteristic, complemented
26C2×#13133215—21no—
27C2×#13133213C2211yescharacteristic
28C2×#13133209C2211yescharacteristic, complemented
29C2×#13133208C2211yescharacteristic, complemented
30C2×#13133207—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133204C2211yescharacteristic
33C2×#13133195—21no—
34C2×#13133193—21no—
35C2×#13133189—21no—
36C2×#13133189—21no—
37C2×#13133185—21no—
38C2×#13133185—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810987C2218yescomplemented
43#16810986C2218yescomplemented
44#16810985C2218yescomplemented
45#16810981C2218yescomplemented
46#16810978C2218yescomplemented
47#16810976C2218yescomplemented
48#16810968C2218yescomplemented
49#16810626C2218yescomplemented
50#16810621C2218yescomplemented
51#16810616C2218yescomplemented
52C2×#13133142C2211yescharacteristic, complemented
53C2×#13133142C2211yescharacteristic, complemented
54C2×#13133140C2211yescharacteristic, complemented
55C2×#13133140C2211yescharacteristic, complemented
56C2×#13133139C2211yescharacteristic
57C2×#13133139C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic, complemented
61C2×#13133138C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64#102×D53C2218yescomplemented
65#16810577C2218yescomplemented
66C2×#13133128C2211yescharacteristic, complemented
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×C4⋊Q8×C53C2211yescharacteristic, complemented
70C2×#127×C53C2211yescharacteristic
71C53×#486C2218yescomplemented
72C2×#102×C53C2211yescharacteristic
73C2×#102×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947—24no—
81C2×#11719947C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C2×D4×D53—22no—
90C2×D4×D53—24no—
91C2×D4×D53—24no—
92C2×D4×D53C2314yes—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C2×#11719912—24no—
97C2×#11719912C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C2×C8×D53—24no—
101C2×C8×D53C2314yes—
102#13133216—22no—
103#13133216C2314yescomplemented
104#13133215—28no—
105#13133213—22no—
106#13133213C2314yes—
107#13133209—22no—
108#13133209C2314yescomplemented
109#13133208—22no—
110#13133208C2314yescomplemented
111#13133207—28no—
112#13133205—22no—
113#13133205C2314yes—
114#13133204—22no—
115#13133204C2314yes—
116#13133195—28no—
117#13133193—28no—
118#13133189—28no—
119#13133189—28no—
120#13133185—28no—
121#13133185—28no—
122#13133175—22no—
123#13133175C2314yes—
124#13133174D414yes—
125#13133174C2314yes—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×#11719919D411yescharacteristic
136C4⋊C4×D53—22no—
137C4⋊C4×D53C2314yes—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921D411yescharacteristic
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133142C2314yescomplemented
148#13133142C2314yescomplemented
149#13133140C2314yescomplemented
150#13133140C2314yescomplemented
151#13133139C2314yes—
152#13133139C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133138C2314yescomplemented
156#13133138C2314yescomplemented
157#13133137C2314yes—
158#13133137C2314yes—
159#13133128C2314yescomplemented
160#13133127C2314yescomplemented
161C8×Dic53C2314yescomplemented
162C22×Q8×C53—21no—
163C22×D4×C53—21no—
164C22×D4×C53—21no—
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yescomplemented
171#127×C53—22no—
172#127×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C42×C53C2311yescharacteristic
177#102×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yescomplemented
180#102×C53C2314yescomplemented
181C4×C8×C53C2314yescomplemented
182C24×C53—21no—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—24no—
186C23×D53—44no—
187C23×D53—82no—
188C23×D53—82no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—24no—
191C2×Q8×C53—82no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—24no—
195C2×D4×C53—24no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53—82no—
201C2×D4×C53—82no—
202C2×D4×C53C2412yes—
203C2×D4×C53C2412yes—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—24no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—44no—
215C2×C22⋊D53—82no—
216C2×C22⋊D53—82no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—24no—
221C22×Dic53—44no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225#11719947—28no—
226#11719947—28no—
227#11719947—48no—
228D4×D53—28no—
229D4×D53—28no—
230D4×D53—48no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—21no—
234C2×D212C2412yes—
235C2×C4×D53—24no—
236C2×C4×D53—82no—
237C2×C4×D53C2×D412yes—
238C2×C4×D53#4114yes—
239C2×C4×D53#4114yes—
240C2×C4×D53C2412yes—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—21no—
244C2×Dic106—24no—
245C2×Dic106—82no—
246C2×Dic106C2412yes—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C42×C53C2×D412yes—
257C42×C53C2412yes—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921C2×D414yes—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919C2×D414yes—
276#11719919C2×D414yes—
277C4×Dic53—24no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2412yes—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284#11719912—28no—
285C8×D53—28no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—48no—
302C22×D53—84no—
303C22×D53—84no—
304C22×D53—816no—
305C22×D53#12414yes—
306C22×D53C22×D412yes—
307Q8×C53—84no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—42no—
313D4×C53—42no—
314D4×C53—84no—
315D4×C53—84no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4112yes—
326C2×C4×C53C2×#4112yes—
327C2×C4×C53C2511yescharacteristic
328C22⋊D53—48no—
329C22⋊D53—48no—
330C22⋊D53—84no—
331C22⋊D53—84no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—48no—
341C2×Dic53#12414yes—
342C2×Dic53C22×D412yes—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345D212—22no—
346D212—22no—
347D212—42no—
348C4×D53—84no—
349C4×D53#12418yes—
350C4×D53C2×#4114yes—
351C4×D53C2×#4114yes—
352Dic106—22no—
353Dic106—22no—
354Dic106—42no—
355Dic106—84no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3136—531nomaximal, Sylow
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—84no—
368C22×C53—84no—
369C22×C53C2×#12412yes—
370C22×C53#57612yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—28no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—816no—
380C2×D53—84no—
381C2×D53C2×#12414yes—
382C4×C53—22no—
383C4×C53—22no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53C2×#12412yes—
387C4×C53C22×#4111yescharacteristic
388C4×C53C22×#4111yescharacteristic
389Dic53—22no—
390Dic53—22no—
391Dic53—42no—
392Dic53—42no—
393Dic53—42no—
394Dic53C2×#12414yes—
395C2×#544—531no—
396C2×#535—531no—
397#3136—5316no—
398C2×#490—531no—
399C2×#490—531no—
400C2×#489—531no—
401C2×#489—531no—
402C2×#488—531no—
403C2×#488—531no—
404C2×#486—531no—
405C2×#486D5311yescharacteristic, complemented
406C2×#417—531no—
407C2×#418—531no—
408C2×#416—531no—
409C22×#102—531no—
410C2×#405—531no—
411C2×C53—82no—
412C2×C53—82no—
413C2×C53#313614yescomplemented
414C2×C53C22×#12411yescharacteristic
415C2×C53C2×#57611yescharacteristic
416C2×C53C2×#57711yescharacteristic
417D53—24no—
418D53—82no—
419C22×#41—531no—
420C23×D4—531no—
421C22×M16—531no—
422C23×C8—531no—
423#544—538no—
424#544—1064no—
425#535—538no—
426#535—1064no—
427C2×C4⋊Q8—531no—
428C2×C4⋊Q8—1061no—
429C2×C4⋊Q8C2×D5311yescharacteristic, complemented
430C2×#127—531no—
431C2×#127C2×D5311yescharacteristic
432C2×#125—531no—
433C2×#125—531no—
434C2×#125—1061no—
435C2×#124—531no—
436C2×#124—531no—
437C2×C22⋊Q8—1061no—
438C2×C22⋊Q8—1061no—
439C2×#121—1061no—
440C2×#121—1061no—
441C2×#120—1061no—
442C2×#120—1061no—
443C2×#117—531no—
444C2×#117—531no—
445C22×C4⋊C4—531no—
446#490—538no—
447#490—538no—
448#489—538no—
449#489—538no—
450#488—538no—
451#488—538no—
452#486—538no—
453#486C2×D5318yescomplemented
454#418—538no—
455#417—538no—
456#416—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—538no—
470C2×#102C2×D5311yescharacteristic
471C2×#102C2×D5311yescharacteristic
472C2×#102C2×D5311yescharacteristic, complemented
473C2×#102C2×D5311yescharacteristic, complemented
474#405—538no—
475C2×#97—531no—
476C2×#97—531no—
477C2×C4×C8—531no—
478C2×C4×C8C2×D5311yescharacteristic, complemented
479C53C2×#313611yescharacteristic, complemented, Sylow
480C25—1061no—
481C2×#41—534no—
482C2×#41—1062no—
483C2×#41—1064no—
484C2×#41—1064no—
485C22×Q8—21no—
486C22×Q8—531no—
487C22×Q8—1061no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—534no—
491C22×D4—531no—
492C22×D4—1064no—
493C22×D4—1064no—
494C22×D4—1062no—
495C22×D4—1061no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C22×D4C22×D5311yescharacteristic
501C23×C4—531no—
502C23×C4—1061no—
503C23×C4—1061no—
504C2×M16—534no—
505C2×M16—1064no—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8—534no—
509C22×C8—1064no—
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5311yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—534no—
514C4⋊Q8—1062no—
515C4⋊Q8—1068no—
516C4⋊Q8C22×D5314yescomplemented
517#127—22no—
518#127—534no—
519#127—1062no—
520#127C22×D5314yes—
521#125—534no—
522#125—534no—
523#125—1062no—
524#125—1068no—
525#125—1062no—
526#124—534no—
527#124—534no—
528#124—1062no—
529#124—1062no—
530C22⋊Q8—1068no—
531C22⋊Q8—1068no—
532#121—1068no—
533#121—1068no—
534#120—1068no—
535#120—1068no—
536#117—534no—
537#117—534no—
538#117—534no—
539#117—1062no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—534no—
546C2×C4⋊C4—1062no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—531no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C42—531no—
563C2×C42—1061no—
564C2×C42C22×D5311yescharacteristic
565#103—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#102—534no—
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102—534no—
575#102—534no—
576#102—534no—
577#102C22×D5314yes—
578#102C22×D5314yes—
579#102C22×D5314yescomplemented
580#102C22×D5314yescomplemented
581#97—534no—
582#97—534no—
583C4×C8—534no—
584C4×C8C22×D5314yescomplemented
585C24—21no—
586C24—21no—
587C24—531no—
588C24—1064no—
589C24—1061no—
590C24—4242no—
591C24—4242no—
592C24—2124no—
593#41—1068no—
594#41—1068no—
595#41—2128no—
596C2×Q8—24no—
597C2×Q8—82no—
598C2×Q8—532no—
599C2×Q8—1064no—
600C2×Q8—1061no—
601C2×Q8—1062no—
602C2×Q8—1062no—
603C2×Q8—4242no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—532no—
615C2×D4—1068no—
616C2×D4—1068no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—2128no—
627C2×D4—2124no—
628C2×D4—2124no—
629C2×D4C23×D5312yes—
630C2×D4C23×D5312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—531no—
634C22×C4—532no—
635C22×C4—534no—
636C22×C4—534no—
637C22×C4—532no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—1064no—
641C22×C4—1064no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—4242no—
646C22×C4—2124no—
647C22×C4D4×D5311yescharacteristic
648C22×C4D4×D5311yescharacteristic
649C22×C4C23×D5311yescharacteristic
650M16—1068no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—532no—
654C2×C8—532no—
655C2×C8—1068no—
656C2×C8—1062no—
657C2×C8—1062no—
658C2×C8C23×D5312yes—
659C2×C8C23×D5312yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—534no—
664C4⋊C4—534no—
665C4⋊C4—532no—
666C4⋊C4—532no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1061no—
672C4⋊C4—1061no—
673C4⋊C4—1064no—
674C4⋊C4—1064no—
675C4⋊C4C23×D5312yes—
676C4⋊C4C23×D5312yes—
677C22⋊C4—534no—
678C22⋊C4—534no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42D4×D5312yes—
688C42C23×D5312yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—534no—
698C23—532no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—4244no—
703C23—4244no—
704C23—42416no—
705C23—2128no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23C2×D4×D5311yescharacteristic
710Q8—84no—
711Q8—1062no—
712Q8—1062no—
713Q8—4244no—
714Q8—2122no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—1062no—
724D4—1062no—
725D4—4244no—
726D4—4244no—
727D4—2128no—
728D4—2128no—
729D4—2122no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—534no—
737C2×C4—532no—
738C2×C4—538no—
739C2×C4—534no—
740C2×C4—534no—
741C2×C4—532no—
742C2×C4—532no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—4244no—
749C2×C4—2128no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5312yes—
755C2×C4C2×D4×D5311yescharacteristic
756C2×C4#41×D5312yes—
757C2×C4#41×D5312yes—
758C2×C4C24×D5311yescharacteristic
759C8—22no—
760C8—22no—
761C8—1062no—
762C8—1062no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—534no—
772C22—1068no—
773C22—1062no—
774C22—1062no—
775C22—42416no—
776C22—4244no—
777C22—2122no—
778C22—2122no—
779C22—2122no—
780C22#124×D5312yes—
781C22#1681142412yes—
782C22#1681142912yes—
783C22C22×D4×D5311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—534no—
789C4—1062no—
790C4—1062no—
791C4—2122no—
792C4—2122no—
793C4—2122no—
794C4#124×D5312yes—
795C4C2×#41×D5311yescharacteristic
796C4C2×#41×D5311yescharacteristic
797C2—82no—
798C2—82no—
799C2—1064no—
800C2—4242no—
801C2#2028506414yesdirect product factor
802C2C2×#124×D5311yescharacteristic
803C2C2×#1681142411yescharacteristic
804C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#486C2
socleC23×C53C22×D4
prime radicalC2×#16811186C2
hypercenterC2×#486D53
hypocenterC53C2×#3136
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16811250C2semidirect
3. #20285064C2direct (N × H)
4. C2×#16810987C2semidirect
5. C2×#16810986C2semidirect
6. C2×#16810985C2semidirect
7. C2×#16810981C2semidirect
8. C2×#16810978C2semidirect
9. C2×#16810976C2semidirect
10. C2×#16810968C2semidirect
11. C2×#16810621C2semidirect
12. C2×#16810626C2semidirect
13. C2×#16810616C2semidirect
14. C2×#102×D53C2semidirect
15. C2×#16810577C2semidirect
16. C2×C53×#486C2semidirect
22. #16811250C22semidirect
25. C2×#13133216C22semidirect
28. C2×#13133209C22semidirect
29. C2×#13133208C22semidirect
42. #16810987C22semidirect
43. #16810986C22semidirect
44. #16810985C22semidirect
45. #16810981C22semidirect
46. #16810978C22semidirect
47. #16810976C22semidirect
48. #16810968C22semidirect
49. #16810626C22semidirect
50. #16810621C22semidirect
51. #16810616C22semidirect
52. C2×#13133142C22semidirect
53. C2×#13133142C22semidirect
54. C2×#13133140C22semidirect
55. C2×#13133140C22semidirect
60. C2×#13133138C22semidirect
61. C2×#13133138C22semidirect
64. #102×D53C22semidirect
65. #16810577C22semidirect
66. C2×#13133128C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
69. C2×C4⋊Q8×C53C22semidirect
71. C53×#486C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
103. #13133216C23semidirect
108. #13133209C23semidirect
110. #13133208C23semidirect
147. #13133142C23semidirect
148. #13133142C23semidirect
149. #13133140C23semidirect
150. #13133140C23semidirect
155. #13133138C23semidirect
156. #13133138C23semidirect
159. #13133128C23semidirect
160. #13133127C23semidirect
161. C8×Dic53C23semidirect
170. C4⋊Q8×C53C23semidirect
179. #102×C53C23semidirect
180. #102×C53C23semidirect
181. C4×C8×C53C23semidirect
405. C2×#486D53semidirect
413. C2×C53#3136semidirect
429. C2×C4⋊Q8C2×D53semidirect
453. #486C2×D53semidirect
472. C2×#102C2×D53semidirect
473. C2×#102C2×D53semidirect
478. C2×C4×C8C2×D53semidirect
479. C53C2×#3136semidirect
516. C4⋊Q8C22×D53semidirect
579. #102C22×D53semidirect
580. #102C22×D53semidirect
584. C4×C8C22×D53semidirect
801. C2#20285064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112502
C2×#168111862
#202850642
C2×#168109872
C2×#168109862
C2×#168109852
C2×#168109812
C2×#168109782
C2×#168109762
C2×#168109682
C2×#168106212
C2×#168106262
C2×#168106162
C2×#102×D532
C2×#168105772
C2×C53×#4862
C2×#313653