Finite Group Databasebeta

← C2×#20287439 #28263786

Subgroups — C2×#20287439 #28263786

Order 13568.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811349C211yesmaximal, characteristic, complemented
2C2×#16811293C211yesmaximal, characteristic
3#20287439C2116yesmaximal, direct product factor
4C2×#16810987C211yesmaximal, characteristic, complemented
5C2×#16810986C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic, complemented
7C2×#16810925C211yesmaximal, characteristic, complemented
8C2×#16810924C211yesmaximal, characteristic, complemented
9C2×#16810901C211yesmaximal, characteristic, complemented
10C2×#16810821C211yesmaximal, characteristic, complemented
11C2×#16810821C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810724C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×SD16×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#460C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719924C2211yescharacteristic
19#16811349—24no—
20#16811349C2218yescomplemented
21#16811293—24no—
22#16811293C2218yes—
23C2×#13133216—21no—
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26C2×#13133213C2211yescharacteristic
27C2×#13133209—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133208—21no—
30C2×#13133208C2211yescharacteristic
31C2×#13133189—21no—
32C2×#13133189—21no—
33C2×#13133188—21no—
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×C4×Dic106—21no—
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×D4×Dic53C2211yescharacteristic
41#16810987C2218yescomplemented
42#16810986C2218yescomplemented
43#16810968C2218yescomplemented
44#16810925C2218yescomplemented
45#16810924C2218yescomplemented
46#16810901C2218yescomplemented
47#16810821C2218yescomplemented
48#16810821C2218yescomplemented
49#16810752C2218yescomplemented
50#16810724C2218yescomplemented
51#16810721C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133139C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#127×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#460C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106D411yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C23×Dic53—21no—
87C23×Dic53—21no—
88C22×C4×D53—21no—
89C2×#11719924—24no—
90C2×#11719924C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133216—22no—
94#13133216—28no—
95#13133216C2314yes—
96#13133213—22no—
97#13133213—22no—
98#13133213C2314yes—
99#13133213C2314yes—
100#13133209—22no—
101#13133209—28no—
102#13133209C2314yes—
103#13133208—28no—
104#13133208—22no—
105#13133208C2314yes—
106#13133189—28no—
107#13133189—28no—
108#13133188—28no—
109Q8×Dic53—22no—
110Q8×Dic53—22no—
111Q8×Dic53C2314yes—
112Q8×Dic53C2314yes—
113C4×Dic106—28no—
114C4×Dic106D414yes—
115C4×Dic106C2314yes—
116C4×D212—22no—
117C4×D212C2314yes—
118D4×Dic53—22no—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121D4×Dic53C2314yes—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53D411yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141C2×C4×Dic53C2311yescharacteristic
142#13133151C2314yes—
143#13133150C2314yes—
144#13133149C2314yes—
145#13133146C2314yes—
146#13133146C2314yes—
147#13133141C2314yes—
148#13133139C2314yes—
149#13133139C2314yes—
150#13133138C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133137C2314yes—
155#13133128C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53—21no—
160C22×D4×C53—21no—
161C22×D4×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C2×SD16×C53—24no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169#127×C53—22no—
170#127×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C4⋊C8×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C24×C53—21no—
182C23×D53—21no—
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53#4114yescomplemented
186C2×Q8×C53C2412yes—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—24no—
190C2×D4×C53—24no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—44no—
196C2×D4×C53—82no—
197C2×D4×C53C2412yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—82no—
211C2×C22⋊D53—82no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—24no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223#11719947—432no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—21no—
227C2×D212C2412yes—
228C2×C4×D53—24no—
229C2×C4×D53—44no—
230C2×Dic106—24no—
231C2×Dic106—24no—
232C2×Dic106—44no—
233C2×Dic106C2×D414yes—
234SD16×C53—28no—
235SD16×C53—28no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C42×C53—24no—
244C42×C53C2×D412yes—
245C42×C53C2412yes—
246C22⋊Dic53—24no—
247C22⋊Dic53—24no—
248#11719924—28no—
249#11719921—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53C2×D414yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919C2×D414yes—
265#11719919C2×D414yes—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2×D412yes—
270C4×Dic53C2412yes—
271C4×Dic53C2412yes—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289Q8×C53—24no—
290Q8×C53—22no—
291Q8×C53C2×#4114yescomplemented
292D4×C53—22no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—48no—
297D4×C53—42no—
298D4×C53—42no—
299D4×C53—84no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—42no—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C532−1+412yes—
311C2×C4×C53C2511yescharacteristic
312C22⋊D53—48no—
313C22⋊D53—48no—
314C22⋊D53—84no—
315C22⋊D53—84no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—48no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—48no—
327C2×Dic53AGL(1,ℤ/8)14yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332D212—22no—
333D212—22no—
334D212—42no—
335C4×D53—48no—
336Dic106—28no—
337Dic106—48no—
338C8×C53—22no—
339C8×C53—22no—
340#88322—22no—
341#88322—22no—
342C2×#3368—531nomaximal, Sylow
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—84no—
350C22×C53—84no—
351C22×C53#54812yes—
352C22×C53C2×AGL(1,ℤ/8)12yes—
353C22×C53#57712yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—24no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—42no—
363C4×C53#54812yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53C2×AGL(1,ℤ/8)14yes—
373C2×#557—531no—
374C2×#550—531no—
375#3368—5316no—
376C2×#490—531no—
377C2×#490—531no—
378C2×#486—531no—
379C2×#478—531no—
380C2×#478—531no—
381C2×#474—531no—
382C2×#460—531no—
383C2×#460—531no—
384C2×#460D5311yescharacteristic, complemented
385C2×#446—531no—
386C2×#440—531no—
387C2×#440—531no—
388C2×C4×SD16—531no—
389C2×C53—82no—
390C2×C53—82no—
391C2×C53#336814yescomplemented
392C2×C53C2×#54811yescharacteristic
393C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C53C2×#57711yescharacteristic
395D53—82no—
396C22×#41—1061no—
397C22×SD16—531no—
398C22×SD16C2×D5311yescharacteristic
399C22×SD16C2×D5311yescharacteristic
400#557—538no—
401#557—1064no—
402#550—538no—
403#550—1064no—
404C2×C4⋊Q8—531no—
405C2×C4⋊Q8—1061no—
406C2×#127—531no—
407C2×#127—531no—
408C2×#127C2×D5311yescharacteristic
409C2×#125—531no—
410C2×#125—531no—
411C2×#125—1061no—
412C2×#125—1061no—
413C2×#121—1061no—
414C2×#121—1061no—
415C2×#121—1061no—
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×Q8—531no—
419C2×C4×Q8—1061no—
420C2×C4×Q8C2×D5311yescharacteristic
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424#490—538no—
425#490—538no—
426#486—538no—
427#478—538no—
428#478—538no—
429#474—538no—
430#460—538no—
431#460—538no—
432#460C2×D5318yescomplemented
433#446—538no—
434#440—538no—
435#440—538no—
436C4×SD16—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#106—531no—
440C2×C4⋊C8—531no—
441C2×C4⋊C8—531no—
442C2×C4⋊C8C2×D5311yescharacteristic
443C2×#103—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×#97—531no—
454C2×#97—531no—
455C2×C4×C8—531no—
456C53C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1068no—
458C2×#41—2128no—
459C22×Q8—531no—
460C22×Q8—1061no—
461C22×Q8C22×D5311yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—531no—
465C22×D4—1061no—
466C22×D4—1061no—
467C22×D4—1061no—
468C22×D4—1061no—
469C22×D4C22×D5311yescharacteristic
470C22×D4C22×D5311yescharacteristic
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C2×SD16—24no—
475C2×SD16—24no—
476C2×SD16—534no—
477C2×SD16—1064no—
478C2×SD16C22×D5314yes—
479C2×SD16C22×D5314yes—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8C22×D5311yescharacteristic
483C22×C8C22×D5311yescharacteristic
484C4⋊Q8—534no—
485C4⋊Q8—1062no—
486C4⋊Q8—1068no—
487#127—22no—
488#127—534no—
489#127—534no—
490#127—1062no—
491#127—1062no—
492#127C22×D5314yes—
493#125—534no—
494#125—534no—
495#125—1068no—
496#125—1062no—
497#125—1068no—
498#125—1062no—
499#121—1068no—
500#121—1068no—
501#121—1068no—
502C4×Q8—22no—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—534no—
506C4×Q8—534no—
507C4×Q8—1068no—
508C4×Q8—1062no—
509C4×Q8—1062no—
510C4×Q8C22×D5314yes—
511C4×D4—534no—
512C4×D4—534no—
513C4×D4—534no—
514C4×D4—1062no—
515C4×D4—1062no—
516C4×D4—1062no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4C22×D5311yescharacteristic
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C42—21no—
536C2×C42—531no—
537C2×C42—531no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42C22×D5311yescharacteristic
541#107—534no—
542#107—534no—
543#106—534no—
544C4⋊C8—534no—
545C4⋊C8—534no—
546C4⋊C8C22×D5314yes—
547#103—534no—
548#102—534no—
549#102—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102C22×D5314yes—
556#102C22×D5314yes—
557#97—534no—
558#97—534no—
559C4×C8—534no—
560C24—21no—
561C24—21no—
562C24—1061no—
563#41—21232no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—534no—
567C2×Q8—1064no—
568C2×Q8—1064no—
569C2×Q8—2124no—
570C2×Q8#1171994714yescomplemented
571C2×Q8C23×D5312yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—44no—
581C2×D4—82no—
582C2×D4—532no—
583C2×D4—1064no—
584C2×D4—1064no—
585C2×D4—1064no—
586C2×D4—1064no—
587C2×D4—1061no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4—4242no—
591C2×D4—4242no—
592C2×D4—2124no—
593C2×D4—2124no—
594C2×D4C23×D5312yes—
595C2×D4C23×D5312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—531no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1064no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4D4×D5311yescharacteristic
612C22×C4D4×D5311yescharacteristic
613C22×C4C23×D5311yescharacteristic
614SD16—28no—
615SD16—28no—
616SD16—1068no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—532no—
620C2×C8—532no—
621C2×C8—1062no—
622C2×C8—1062no—
623C2×C8C23×D5312yes—
624C2×C8C23×D5312yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—534no—
630C4⋊C4—532no—
631C4⋊C4—532no—
632C4⋊C4—532no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1064no—
638C4⋊C4—1061no—
639C4⋊C4—1061no—
640C4⋊C4—1061no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4C23×D5312yes—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C42—24no—
648C42—532no—
649C42—532no—
650C42—532no—
651C42—532no—
652C42—1064no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—24no—
670Q8—22no—
671Q8—1068no—
672Q8—2128no—
673Q8C2×#1171994714yescomplemented
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—1062no—
683D4—1062no—
684D4—4244no—
685D4—4244no—
686D4—2128no—
687D4—2128no—
688D4—2122no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—534no—
696C2×C4—532no—
697C2×C4—532no—
698C2×C4—532no—
699C2×C4—532no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—2128no—
707C2×C4—2128no—
708C2×C4—2128no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×D4×D5312yes—
713C2×C4C2×D4×D5312yes—
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4C2×#1171994712yes—
716C2×C4#1313326412yes—
717C2×C4C24×D5311yescharacteristic
718C8—22no—
719C8—22no—
720C8—1062no—
721C8—1062no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—4244no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22#1681127912yes—
735C22AGL(1,ℤ/8)×D5312yes—
736C22#1681142912yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—534no—
743C4—1062no—
744C4—1062no—
745C4—1062no—
746C4—2122no—
747C4—2122no—
748C4—2122no—
749C4#1681127912yes—
750C4C22×#1171994711yescharacteristic
751C4C2×#1313326411yescharacteristic
752C2—82no—
753C2—82no—
754C2—4242no—
755C2#2028743914yesdirect product factor
756C2C2×#1681127911yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
758C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#460C2
socleC23×C53C22×D4
prime radicalC2×#16811293C2
hypercenterC2×#460D53
hypocenterC53C2×#3368
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16811349C2semidirect
3. #20287439C2direct (N × H)
4. C2×#16810987C2semidirect
5. C2×#16810986C2semidirect
6. C2×#16810968C2semidirect
7. C2×#16810925C2semidirect
8. C2×#16810924C2semidirect
9. C2×#16810901C2semidirect
10. C2×#16810821C2semidirect
11. C2×#16810821C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810724C2semidirect
14. C2×#16810721C2semidirect
15. C2×SD16×Dic53C2semidirect
16. C2×C53×#460C2semidirect
20. #16811349C22semidirect
41. #16810987C22semidirect
42. #16810986C22semidirect
43. #16810968C22semidirect
44. #16810925C22semidirect
45. #16810924C22semidirect
46. #16810901C22semidirect
47. #16810821C22semidirect
48. #16810821C22semidirect
49. #16810752C22semidirect
50. #16810724C22semidirect
51. #16810721C22semidirect
52. SD16×Dic53C22semidirect
73. C53×#460C22semidirect
185. C2×Q8×C53#41semidirect
291. Q8×C53C2×#41semidirect
384. C2×#460D53semidirect
391. C2×C53#3368semidirect
432. #460C2×D53semidirect
456. C53C2×#3368semidirect
570. C2×Q8#11719947semidirect
673. Q8C2×#11719947semidirect
755. C2#20287439direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113492
C2×#168112932
#202874392
C2×#168109872
C2×#168109862
C2×#168109682
C2×#168109252
C2×#168109242
C2×#168109012
C2×#168108212
C2×#168107522
C2×#168107242
C2×#168107212
C2×SD16×Dic532
C2×C53×#4602
C2×#336853