Finite Group Databasebeta

← C2×#20286074 #28256933

Subgroups — C2×#20286074 #28256933

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic, complemented
2C2×#16811152C211yesmaximal, characteristic, complemented
3#20286074C2116yesmaximal, direct product factor
4C2×#16810906C211yesmaximal, characteristic, complemented
5C2×#16810924C211yesmaximal, characteristic, complemented
6C2×#16810923C211yesmaximal, characteristic, complemented
7C2×#16810901C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810873C211yesmaximal, characteristic, complemented
10C2×#16810872C211yesmaximal, characteristic, complemented
11C2×#16810866C211yesmaximal, characteristic, complemented
12C2×#16810821C211yesmaximal, characteristic, complemented
13C2×#16810835C211yesmaximal, characteristic, complemented
14C2×#16810816C211yesmaximal, characteristic, complemented
15C2×#16810645C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22#16811170—24no—
23#16811170C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26#16811152—24no—
27#16811152C2218yescomplemented
28C2×#13133210—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133199—21no—
32C2×#13133193C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×#13133190—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×C4×C22⋊D53—21no—
41C2×#13133177—21no—
42C2×#13133173—21no—
43C2×C42×D53C2211yescharacteristic
44#16810924C2218yescomplemented
45#16810923C2218yescomplemented
46#16810906C2218yescomplemented
47#16810901C2218yescomplemented
48#16810875C2218yescomplemented
49#16810873C2218yescomplemented
50#16810872C2218yescomplemented
51#16810866C2218yescomplemented
52#16810835C2218yescomplemented
53#16810821C2218yescomplemented
54#16810816C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810645C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133138C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91C2×#11719924—42no—
92C2×#11719924C2314yes—
93C2×#11719922—42no—
94C2×#11719922C2314yes—
95C2×#11719912—42no—
96C2×#11719912—42no—
97C2×#11719912C2314yes—
98C2×#11719912C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133216—22no—
102#13133216C2314yes—
103#13133213—22no—
104#13133213C2314yes—
105#13133210—28no—
106#13133209—22no—
107#13133209C2314yes—
108#13133203—28no—
109#13133199—28no—
110#13133193—22no—
111#13133193C2314yes—
112#13133192—22no—
113#13133192C2314yes—
114#13133190—28no—
115#13133188—22no—
116#13133188—22no—
117#13133188C2314yes—
118#13133188C2314yes—
119Q8×Dic53—22no—
120Q8×Dic53C2314yes—
121C4×D212—22no—
122C4×D212C2314yes—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125C4×C22⋊D53—28no—
126#13133177—28no—
127#13133173—28no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53D411yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146C42×D53D414yes—
147C42×D53C2314yes—
148#13133151C2314yes—
149#13133150C2314yes—
150#13133149C2314yes—
151#13133148C2314yes—
152C4⋊#88322C2314yes—
153#13133146C2314yes—
154#13133146C2314yes—
155#13133141C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160#13133138C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C2×SD16×C53—42no—
166C2×SD16×C53C2314yes—
167C2×D8×C53—42no—
168C2×D8×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171#124×C53—22no—
172#124×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53C2311yescharacteristic
180C4⋊C8×C53C2314yes—
181#103×C53C2314yes—
182#102×C53C2314yes—
183C24×C53—21no—
184C24×C53—21no—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53C2412yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C2×C22⋊D53—44no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—24no—
218C22×Dic53—44no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222#11719945—432no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—24no—
226C2×D212—21no—
227C2×D212—44no—
228C2×D212C2412yes—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—42no—
234C2×C4×D53—44no—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2×D414yes—
237C2×C4×D53C2×D414yes—
238C2×C4×D53C2412yes—
239C2×Dic106—24no—
240C2×Dic106—44no—
241SD16×C53—44no—
242D8×C53—44no—
243C2×C8×C53—22no—
244C2×C8×C53—22no—
245C2×C8×C53C2412yes—
246C2×C8×C53C2412yes—
247C4⋊C4×C53—21no—
248C4⋊C4×C53C2412yes—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C42×C53C2×D412yes—
253C42×C53C2412yes—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257#11719924—44no—
258#11719922—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—24no—
266C4⋊Dic53C2412yes—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273C4×Dic53—24no—
274C4×Dic53C2×D412yes—
275C4×Dic53C2×D414yes—
276C4×Dic53C2×D414yes—
277C4×Dic53C2412yes—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322C2412yes—
281C2×#88322C2412yes—
282#11719912—44no—
283#11719912—44no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53C22×D412yes—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—42no—
304D4×C53—22no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—42no—
309D4×C53—42no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—48no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53H(5,𝔽2)12yes—
321C2×C4×C532−1+412yes—
322C2×C4×C53C2511yescharacteristic
323C22⋊D53—48no—
324C22⋊D53—48no—
325C22⋊D53—48no—
326C22⋊D53—48no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—48no—
336C2×Dic53AGL(1,ℤ/8)14yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339C2×Dic53C22×D412yes—
340D212—22no—
341D212—22no—
342D212—48no—
343D212—42no—
344C4×D53—24no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—28no—
348C4×D53—44no—
349C4×D53—48no—
350Dic106—48no—
351C8×C53—22no—
352C8×C53—22no—
353#88322—22no—
354#88322—22no—
355C2×#3251—531nomaximal, Sylow
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—84no—
363C22×C53—84no—
364C22×C53#53712yes—
365C22×C53C2×AGL(1,ℤ/8)12yes—
366C22×C53#57512yes—
367C22×C53C23×D411yescharacteristic
368C2×D53—22no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—44no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—84no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53#53712yes—
381C4×C53C2×H(5,𝔽2)11yescharacteristic
382C4×C53C2×2−1+411yescharacteristic
383Dic53—22no—
384Dic53—22no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388Dic53C2×AGL(1,ℤ/8)14yes—
389C2×#532—531no—
390C2×#529—531no—
391#3251—5316no—
392C2×#475—531no—
393C2×#478—531no—
394C2×#478—531no—
395C2×#474—531no—
396C2×#469—531no—
397C2×#469—531no—
398C2×#468—531no—
399C2×#468—531no—
400C2×#460—531no—
401C2×#463—531no—
402C2×#463D5311yescharacteristic, complemented
403C2×#459—531no—
404C2×#423—531no—
405C2×C53—82no—
406C2×C53—82no—
407C2×C53#325114yescomplemented
408C2×C53C2×#53711yescharacteristic
409C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C53C2×#57511yescharacteristic
411D53—42no—
412D53—82no—
413C22×#41—1061no—
414C22×SD16—531no—
415C22×SD16C2×D5311yescharacteristic
416C22×D8—531no—
417C22×D8C2×D5311yescharacteristic
418C22×M16—531no—
419C22×M16—531no—
420#532—538no—
421#532—1064no—
422C2×C4⋊Q8—531no—
423C2×#127—531no—
424#529—538no—
425#529—1064no—
426C2×#126—1061no—
427C2×#125—531no—
428C2×#124—1061no—
429C2×#124C2×D5311yescharacteristic
430C2×#123—1061no—
431C2×C22⋊Q8—531no—
432C2×#121—531no—
433C2×#121—531no—
434C2×#121—531no—
435C2×#121—1061no—
436C2×C4×Q8—531no—
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×#117—1061no—
443C22×C42—531no—
444#478—538no—
445#478—538no—
446#475—538no—
447#474—538no—
448#469—538no—
449#469—538no—
450#468—538no—
451#468—538no—
452#463—538no—
453#463C2×D5318yescomplemented
454#460—538no—
455#459—538no—
456C2×#107—531no—
457C2×#107—531no—
458C2×#106—531no—
459C2×#106—531no—
460#423—538no—
461C2×C4⋊C8—531no—
462C2×C4⋊C8—531no—
463C2×C4⋊C8—531no—
464C2×C4⋊C8C2×D5311yescharacteristic
465C2×#103—531no—
466C2×#103C2×D5311yescharacteristic
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102C2×D5311yescharacteristic
473C53C2×#325111yescharacteristic, complemented, Sylow
474C2×#41—1068no—
475C2×#41—2128no—
476C22×Q8—1061no—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—531no—
479C22×D4—1061no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4C22×D5311yescharacteristic
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4—1061no—
492C2×SD16—42no—
493C2×SD16—534no—
494C2×SD16—2122no—
495C2×SD16C22×D5314yes—
496C2×D8—42no—
497C2×D8—534no—
498C2×D8—2122no—
499C2×D8C22×D5314yes—
500C2×M16—534no—
501C2×M16—534no—
502C2×M16—2122no—
503C2×M16—2122no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C4⋊Q8—534no—
509C4⋊Q8—1062no—
510#127—534no—
511#127—1062no—
512#126—1068no—
513#125—534no—
514#125—1062no—
515#124—22no—
516#124—1068no—
517#124C22×D5314yes—
518#123—1068no—
519C22⋊Q8—534no—
520C22⋊Q8—1062no—
521#121—534no—
522#121—534no—
523#121—534no—
524#121—1068no—
525#121—1062no—
526#121—1062no—
527#121—1062no—
528C4×Q8—534no—
529C4×Q8—1062no—
530C4×D4—22no—
531C4×D4—534no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1062no—
535C4×D4—1068no—
536C4×D4—1062no—
537C4×D4C22×D5314yes—
538#117—1068no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—531no—
558C2×C42—531no—
559C2×C42—531no—
560C2×C42—534no—
561C2×C42—534no—
562C2×C42—1061no—
563C2×C42C22×D5311yescharacteristic
564#107—534no—
565#107—534no—
566#106—534no—
567#106—534no—
568C4⋊C8—534no—
569C4⋊C8—534no—
570C4⋊C8—534no—
571C4⋊C8C22×D5314yes—
572#103—534no—
573#103C22×D5314yes—
574#102—534no—
575#102—534no—
576#102—534no—
577#102—534no—
578#102—534no—
579#102C22×D5314yes—
580C24—21no—
581C24—21no—
582C24—531no—
583C24—1061no—
584#41—21232no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—1064no—
589C2×Q8—2124no—
590C2×Q8C23×D5312yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—532no—
598C2×D4—1064no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1064no—
603C2×D4—1061no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—2124no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4—2124no—
610C2×D4—2124no—
611C2×D4C23×D5312yes—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—534no—
621C22×C4—532no—
622C22×C4—532no—
623C22×C4—534no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1064no—
632C22×C4—2122no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—44no—
639SD16—2124no—
640D8—44no—
641D8—2124no—
642M16—2124no—
643M16—2124no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—532no—
647C2×C8—532no—
648C2×C8—1062no—
649C2×C8—1062no—
650C2×C8C23×D5312yes—
651C2×C8C23×D5312yes—
652C4⋊C4—21no—
653C4⋊C4—532no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1061no—
660C4⋊C4—1061no—
661C4⋊C4—1061no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C42—534no—
675C42—534no—
676C42—532no—
677C42—532no—
678C42—1064no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—532no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23C2×D4×D5311yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—2128no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—1062no—
709D4—1062no—
710D4—2128no—
711D4—2128no—
712D4—2128no—
713D4—2128no—
714D4—2128no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—534no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—1068no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—2124no—
737C2×C4—2128no—
738C2×C4—2128no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4C2×D4×D5312yes—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4#1313326212yes—
746C2×C4#1313326412yes—
747C2×C4C24×D5311yescharacteristic
748C8—22no—
749C8—22no—
750C8—1062no—
751C8—1062no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—1062no—
761C22—1062no—
762C22—1062no—
763C22—4244no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22—2124no—
768C22#1681120212yes—
769C22AGL(1,ℤ/8)×D5312yes—
770C22#1681142012yes—
771C22C22×D4×D5311yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—534no—
777C4—1062no—
778C4—1062no—
779C4—2122no—
780C4—2122no—
781C4—2122no—
782C4#1681120212yes—
783C4C2×#1313326211yescharacteristic
784C4C2×#1313326411yescharacteristic
785C2—82no—
786C2—82no—
787C2—4242no—
788C2—2122no—
789C2#2028607414yesdirect product factor
790C2C2×#1681120211yescharacteristic
791C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
792C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
hypercenterC2×#463D53
hypocenterC53C2×#3251
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811170C2semidirect
2. C2×#16811152C2semidirect
3. #20286074C2direct (N × H)
4. C2×#16810906C2semidirect
5. C2×#16810924C2semidirect
6. C2×#16810923C2semidirect
7. C2×#16810901C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810873C2semidirect
10. C2×#16810872C2semidirect
11. C2×#16810866C2semidirect
12. C2×#16810821C2semidirect
13. C2×#16810835C2semidirect
14. C2×#16810816C2semidirect
15. C2×#16810645C2semidirect
16. C2×C53×#463C2semidirect
23. #16811170C22semidirect
27. #16811152C22semidirect
44. #16810924C22semidirect
45. #16810923C22semidirect
46. #16810906C22semidirect
47. #16810901C22semidirect
48. #16810875C22semidirect
49. #16810873C22semidirect
50. #16810872C22semidirect
51. #16810866C22semidirect
52. #16810835C22semidirect
53. #16810821C22semidirect
54. #16810816C22semidirect
59. #16810645C22semidirect
73. C53×#463C22semidirect
402. C2×#463D53semidirect
407. C2×C53#3251semidirect
453. #463C2×D53semidirect
473. C53C2×#3251semidirect
789. C2#20286074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111702
C2×#168111522
#202860742
C2×#168109062
C2×#168109242
C2×#168109232
C2×#168109012
C2×#168108752
C2×#168108732
C2×#168108722
C2×#168108662
C2×#168108212
C2×#168108352
C2×#168108162
C2×#168106452
C2×C53×#4632
C2×#325153