Finite Group Databasebeta

← C2×#20288634 #28292596

Subgroups — C2×#20288634 #28292596

Order 13568.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288634C2132yesmaximal, direct product factor
2C2×#16811320C214yesmaximal, complemented
3C2×#16811318C214yesmaximal, complemented
4C2×#16811316C214yesmaximal, complemented
5C2×#16811310C214yesmaximal, complemented
6C2×#16811236C211yesmaximal, characteristic, complemented
7C2×#16811235C211yesmaximal, characteristic, complemented
8C2×#16811227C211yesmaximal, characteristic, complemented
9C2×#16811202C212yesmaximal, complemented
10C2×#16811171C211yesmaximal, characteristic, complemented
11C2×#16811155C212yesmaximal, complemented
12C2×#16811154C212yesmaximal, complemented
13C2×#125×D53C211yesmaximal, characteristic, complemented
14C2×#16811102C212yesmaximal, complemented
15C2×#16811091C211yesmaximal, characteristic, complemented
16C2×C53×#540C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2212yes—
19#16811320C22164yescomplemented
20#16811318C22164yescomplemented
21#16811316C22164yescomplemented
22#16811310C22164yescomplemented
23#16811236C22116yescomplemented
24#16811235C22116yescomplemented
25#16811227C22116yescomplemented
26#16811202C22132yescomplemented
27#16811171C22116yescomplemented
28C2×#13133217C2211yescharacteristic
29#16811155C22132yescomplemented
30#16811154C22132yescomplemented
31C2×#13133212C2214yes—
32C2×#13133210C2214yes—
33C2×#13133210C2214yes—
34C2×#13133210C2214yes—
35C2×#13133209C2211yescharacteristic
36C2×#13133208C2214yes—
37C2×#13133208C2212yes—
38C2×#13133207C2214yes—
39C2×#13133207C2214yes—
40#125×D53C22116yescomplemented
41C2×#13133204C2212yes—
42C2×#13133199C2214yes—
43C2×#13133198C2214yes—
44C2×#13133198C2214yes—
45C2×#13133197C2212yes—
46C2×#13133196C2212yes—
47C2×#13133194C2214yes—
48C2×#13133190C2214yes—
49C2×#13133189C2214yes—
50C2×#13133189C2214yes—
51C2×#13133188C2212yes—
52C2×#13133188C2214yes—
53C2×#13133188C2214yes—
54#16811102C22132yescomplemented
55#16811091C22116yescomplemented
56C2×C4×Dic106C2212yes—
57C2×#13133182C2212yes—
58C2×#13133182C2212yes—
59C2×D4×Dic53C2212yes—
60C2×D4×Dic53C2214yes—
61C2×D4×Dic53C2214yes—
62C2×#13133179C2212yes—
63C2×C4×C22⋊D53C2214yes—
64C2×C4×C22⋊D53C2214yes—
65C2×#13133177C2212yes—
66C2×#13133177C2212yes—
67C2×#13133177C2214yes—
68C2×#13133176C2214yes—
69C2×#13133174C2211yescharacteristic
70C2×#13133174C2211yescharacteristic
71C2×#13133173C2214yes—
72C2×#13133173C2214yes—
73C22×#11719919C2214yes—
74C2×C4⋊C4×D53C2212yes—
75C2×C4⋊C4×D53C2214yes—
76C22×C4×Dic53C2211yescharacteristic
77C2×C42×D53C2211yescharacteristic
78C2×C42×D53C2211yescharacteristic
79C53×#540C22116yescomplemented
80C2×#127×C53C2211yescharacteristic
81C2×#125×C53C2211yescharacteristic
82C2×#123×C53C2214yes—
83C2×#121×C53C2212yes—
84C2×#121×C53C2214yes—
85C2×C4×D4×C53C2212yes—
86C2×#117×C53C2211yescharacteristic
87C2×#11719945—28no—
88C2×#11719945C2318yes—
89C2×#11719947—216no—
90C2×#11719947C23116yes—
91C22×Dic106C2311yescharacteristic
92C22×Dic106C2312yes—
93C22×D212C2311yescharacteristic
94C22×C22⋊D53C2311yescharacteristic
95C22×C22⋊D53C2311yescharacteristic
96C22×C22⋊D53C2314yes—
97C22×C22⋊D53C2314yes—
98C23×Dic53C2314yes—
99C23×Dic53C2312yes—
100C23×Dic53C2314yes—
101C22×C4×D53C2311yescharacteristic
102C22×C4×D53C2312yes—
103C22×C4×D53C2312yes—
104C22×C4×D53C2314yes—
105C22×C4×D53C2311yescharacteristic
106#13133217C2318yes—
107#13133212C23132yes—
108#13133210C23132yes—
109#13133210C23132yes—
110#13133210C23132yes—
111#13133209C2318yes—
112#13133208C23132yes—
113#13133208C23116yes—
114#13133207C23132yes—
115#13133207C23132yes—
116#13133204C23116yes—
117#13133199C23132yes—
118#13133198C23132yes—
119#13133198C23132yes—
120#13133197C23116yes—
121#13133196C23116yes—
122#13133194C23132yes—
123#13133190C23132yes—
124#13133189C23132yes—
125#13133189C23132yes—
126#13133188C23132yes—
127#13133188C23132yes—
128#13133188C23116yes—
129C4×Dic106C23116yes—
130#13133182C23116yes—
131#13133182C23116yes—
132D4×Dic53C23132yes—
133D4×Dic53C23132yes—
134D4×Dic53C23116yes—
135#13133179C23116yes—
136C4×C22⋊D53C23132yes—
137C4×C22⋊D53C23132yes—
138#13133177C23116yes—
139#13133177C23132yes—
140#13133177C23116yes—
141#13133176C23132yes—
142#13133174C2318yes—
143#13133174C2318yes—
144#13133173C23132yes—
145#13133173C23132yes—
146C2×C4⋊Dic53C2314yes—
147C2×C4⋊Dic53C2312yes—
148C2×C4⋊Dic53C2314yes—
149C2×C4⋊Dic53C2314yes—
150C2×#11719919C23132yes—
151C2×#11719919C2314yes—
152C2×#11719919C2314yes—
153C2×#11719919C2314yes—
154C2×#11719919C2312yes—
155C2×#11719919C2314yes—
156C2×#11719919C2314yes—
157C2×#11719919C2314yes—
158C2×#11719919C2312yes—
159C4⋊C4×D53C23132yes—
160C4⋊C4×D53C23116yes—
161C2×C22⋊Dic53C2314yes—
162C2×C22⋊Dic53C2314yes—
163C2×C22⋊Dic53C2314yes—
164C2×C22⋊Dic53C2314yes—
165C2×C22⋊Dic53C2314yes—
166C2×#11719921C2312yes—
167C2×#11719921C2312yes—
168C2×#11719921C2314yes—
169C2×C4×Dic53C2311yescharacteristic
170C2×C4×Dic53C2312yes—
171C2×C4×Dic53C2312yes—
172C2×C4×Dic53C2312yes—
173C2×C4×Dic53C2311yescharacteristic
174C2×C4×Dic53C2318yes—
175C2×C4×Dic53C2314yes—
176C2×C4×Dic53C2314yes—
177C42×D53C2318yes—
178C42×D53C2318yes—
179C22×D4×C53C2312yes—
180C22×D4×C53C2314yes—
181C22×D4×C53C2314yes—
182C23×C4×C53C2311yescharacteristic
183C23×C4×C53C2314yes—
184#127×C53C2318yes—
185#125×C53C2318yes—
186#123×C53C23132yes—
187#121×C53C23132yes—
188#121×C53C23116yes—
189C4×D4×C53C23116yes—
190#117×C53C2318yes—
191C2×C4⋊C4×C53C2312yes—
192C2×C4⋊C4×C53C2312yes—
193C2×C4⋊C4×C53C2314yes—
194C2×C22⋊C4×C53C2312yes—
195C2×C22⋊C4×C53C2314yes—
196C2×C22⋊C4×C53C2314yes—
197C2×C42×C53C2311yescharacteristic
198C2×C42×C53C2311yescharacteristic
199C24×C53C2414yes—
200C24×C53C2411yescharacteristic
201C23×D53C2411yescharacteristic
202C23×D53C2411yescharacteristic
203C2×D4×C53—28no—
204C2×D4×C53—48no—
205C2×D4×C53—48no—
206C2×D4×C53C2418yes—
207C2×D4×C53C24116yes—
208C2×D4×C53C24116yes—
209C22×C4×C53—24no—
210C22×C4×C53—48no—
211C22×C4×C53C2412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C22×C4×C53C2414yes—
215C22×C4×C53C2414yes—
216C22×C4×C53C24116yes—
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—216no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—48no—
222C2×C22⋊D53C2414yes—
223C2×C22⋊D53C2414yes—
224C2×C22⋊D53C24116yes—
225C2×C22⋊D53C24116yes—
226C22×Dic53—216no—
227C22×Dic53—44no—
228C22×Dic53—48no—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2414yes—
232C22×Dic53C2411yescharacteristic
233C22×Dic53C2414yes—
234C22×Dic53C24116yes—
235C22×Dic53C2418yes—
236C22×Dic53C24116yes—
237C22×Dic53C2411yescharacteristic
238#11719947—264no—
239#11719945—232no—
240C2×D212—24no—
241C2×D212C2414yes—
242C2×C4×D53—24no—
243C2×C4×D53—44no—
244C2×C4×D53—44no—
245C2×C4×D53—48no—
246C2×C4×D53#4118yes—
247C2×C4×D53C2414yes—
248C2×C4×D53C2418yes—
249C2×C4×D53C2418yes—
250C2×C4×D53C24116yes—
251C2×C4×D53C2414yes—
252C2×Dic106—28no—
253C2×Dic106—24no—
254C2×Dic106C2414yes—
255C2×Dic106C2418yes—
256C4⋊C4×C53C2418yes—
257C4⋊C4×C53C2418yes—
258C4⋊C4×C53C24116yes—
259C22⋊C4×C53C2418yes—
260C22⋊C4×C53C24116yes—
261C22⋊C4×C53C24116yes—
262C42×C53C2414yes—
263C42×C53C2414yes—
264C22⋊Dic53C24116yes—
265C22⋊Dic53C24116yes—
266C22⋊Dic53C24116yes—
267C22⋊Dic53C24116yes—
268C22⋊Dic53C24116yes—
269#11719921C2418yes—
270#11719921C2418yes—
271#11719921C24116yes—
272C4⋊Dic53C24116yes—
273C4⋊Dic53C2418yes—
274C4⋊Dic53C24116yes—
275C4⋊Dic53C24116yes—
276#11719919C24116yes—
277#11719919C24116yes—
278#11719919C24116yes—
279#11719919C2418yes—
280#11719919C24116yes—
281#11719919C24116yes—
282#11719919C24116yes—
283#11719919C2418yes—
284C4×Dic53C2414yes—
285C4×Dic53C2418yes—
286C4×Dic53C2418yes—
287C4×Dic53C2418yes—
288C4×Dic53C2414yes—
289C4×Dic53C24116yes—
290C4×Dic53C24116yes—
291C23×C53—28no—
292C23×C53—22no—
293C23×C53—28no—
294C23×C53—24no—
295C23×C53—28no—
296C23×C53C2518yes—
297C23×C53C2512yes—
298C23×C53C2511yescharacteristic
299C22×D53—24no—
300C22×D53—22no—
301C22×D53—24no—
302C22×D53C2×#4114yes—
303C22×D53C2512yes—
304C22×D53C2512yes—
305D4×C53—216no—
306D4×C53—416no—
307D4×C53—416no—
308C2×C4×C53—22no—
309C2×C4×C53—24no—
310C2×C4×C53—28no—
311C2×C4×C53—24no—
312C2×C4×C53—28no—
313C2×C4×C53—416no—
314C2×C4×C53C2×#4114yes—
315C2×C4×C53C2512yes—
316C2×C4×C53C2514yes—
317C2×C4×C53C2518yes—
318C2×C4×C53C2514yes—
319C2×C4×C53C2512yes—
320C22⋊D53—28no—
321C22⋊D53—232no—
322C22⋊D53—28no—
323C22⋊D53—416no—
324C2×Dic53—22no—
325C2×Dic53—28no—
326C2×Dic53—24no—
327C2×Dic53—28no—
328C2×Dic53—24no—
329C2×Dic53—232no—
330C2×Dic53—48no—
331C2×Dic53—416no—
332C2×Dic53C2×#4114yes—
333C2×Dic53C2512yes—
334C2×Dic53C2518yes—
335C2×Dic53C2514yes—
336C2×Dic53C2518yes—
337C2×Dic53C2514yes—
338C2×Dic53C2512yes—
339D212—28no—
340C4×D53—28no—
341C4×D53—48no—
342C4×D53—48no—
343C4×D53—416no—
344C4×D53C2×#41116yes—
345Dic106—216no—
346Dic106—28no—
347C2×#3512—531nomaximal, Sylow
348C22×C53—28no—
349C22×C53—22no—
350C22×C53—28no—
351C22×C53—24no—
352C22×C53—28no—
353C22×C53—416no—
354C22×C53—44no—
355C22×C53C22×#4112yes—
356C22×C53#58514yes—
357C22×C53C2611yescharacteristic
358C2×D53—24no—
359C2×D53—28no—
360C2×D53—22no—
361C2×D53—24no—
362C2×D53—44no—
363C2×D53C22×#4114yes—
364C4×C53—22no—
365C4×C53—24no—
366C4×C53—28no—
367C4×C53—24no—
368C4×C53C22×#4114yes—
369Dic53—22no—
370Dic53—28no—
371Dic53—24no—
372Dic53—28no—
373Dic53—24no—
374Dic53C22×#4114yes—
375#3512—5332no—
376C2×#553—534no—
377C2×#553—534no—
378C2×#553—534no—
379C2×#552—534no—
380C2×#541—531no—
381C2×#541—531no—
382C2×#540—531no—
383C2×#540D5311yescharacteristic, complemented
384C2×#537—532no—
385C2×#532—531no—
386C2×#529—532no—
387C2×#529—532no—
388C22×#125—531no—
389C2×#520—532no—
390C2×C4×#41—531no—
391C2×C53—48no—
392C2×C53—42no—
393C2×C53#351214yescomplemented
394C2×C53C23×#4111yescharacteristic
395C2×C53C2×#58512yes—
396D53—24no—
397D53—42no—
398C22×#41—532no—
399C22×#41—531no—
400#553—5364no—
401#553—5364no—
402#553—5364no—
403#552—5364no—
404#541—5316no—
405#541—5316no—
406#540—5316no—
407#540C2×D53116yescomplemented
408#537—5332no—
409#532—5316no—
410C2×C4⋊Q8—531no—
411C2×#127C2×D5311yescharacteristic
412#529—5332no—
413#529—5332no—
414C2×#126—534no—
415C2×#126—534no—
416C2×#126—534no—
417C2×#126—534no—
418C2×#125—5316no—
419C2×#125—532no—
420C2×#125—534no—
421C2×#125—534no—
422C2×#125—534no—
423C2×#125—531no—
424C2×#125C2×D5311yescharacteristic
425C2×#124—532no—
426C2×#123—534no—
427C2×#123—534no—
428C2×#123—534no—
429C2×#123C2×D5314yes—
430C2×C22⋊Q8—532no—
431C2×C22⋊Q8—532no—
432C2×C22⋊Q8—534no—
433C2×#121—532no—
434C2×#121—534no—
435C2×#121—534no—
436C2×#121—534no—
437C2×#121—534no—
438C2×#121—534no—
439C2×#121C2×D5312yes—
440C2×#121C2×D5314yes—
441#520—5332no—
442C4×#41—5316no—
443C2×C4×Q8—532no—
444C2×C4×Q8—532no—
445C2×C4×Q8—532no—
446C2×C4×D4—532no—
447C2×C4×D4—534no—
448C2×C4×D4—534no—
449C2×C4×D4—534no—
450C2×C4×D4—534no—
451C2×C4×D4—532no—
452C2×C4×D4—532no—
453C2×C4×D4—532no—
454C2×C4×D4—534no—
455C2×C4×D4C2×D5312yes—
456C2×#117—534no—
457C2×#117—534no—
458C2×#117—534no—
459C2×#117—531no—
460C2×#117—531no—
461C2×#117C2×D5311yescharacteristic
462C22×C4⋊C4—534no—
463C22×C4⋊C4—532no—
464C22×C4⋊C4—534no—
465C22×C42—531no—
466C22×C42—531no—
467C22×C42—531no—
468C53C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—5316no—
470C2×#41—538no—
471C2×#41—1068no—
472C2×#41—10616no—
473C22×Q8—531no—
474C22×Q8—532no—
475C22×D4—531no—
476C22×D4—534no—
477C22×D4—531no—
478C22×D4—534no—
479C22×D4—531no—
480C22×D4C22×D5312yes—
481C22×D4C22×D5314yes—
482C22×D4C22×D5314yes—
483C23×C4—531no—
484C23×C4—534no—
485C23×C4—534no—
486C23×C4—532no—
487C23×C4—531no—
488C23×C4—534no—
489C23×C4—532no—
490C23×C4—532no—
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5314yes—
493C4⋊Q8—538no—
494#127C22×D5318yes—
495#126—5332no—
496#126—5332no—
497#126—5332no—
498#126—5332no—
499#125—5316no—
500#125—5332no—
501#125—5332no—
502#125—5332no—
503#125—538no—
504#125C22×D5318yes—
505#124—5316no—
506#123—5332no—
507#123—5332no—
508#123—5332no—
509#123C22×D53132yes—
510C22⋊Q8—5316no—
511C22⋊Q8—5316no—
512C22⋊Q8—5332no—
513#121—5316no—
514#121—5332no—
515#121—5332no—
516#121—5332no—
517#121—5332no—
518#121—5332no—
519#121C22×D53116yes—
520#121C22×D53132yes—
521C4×Q8—5316no—
522C4×Q8—5316no—
523C4×Q8—5316no—
524C4×D4—5316no—
525C4×D4—5332no—
526C4×D4—5332no—
527C4×D4—5332no—
528C4×D4—5332no—
529C4×D4—5316no—
530C4×D4—5316no—
531C4×D4—5316no—
532C4×D4—5332no—
533C4×D4C22×D53116yes—
534#117—5332no—
535#117—5332no—
536#117—5332no—
537#117—538no—
538#117—538no—
539#117C22×D5318yes—
540C2×C4⋊C4—532no—
541C2×C4⋊C4—534no—
542C2×C4⋊C4—534no—
543C2×C4⋊C4—534no—
544C2×C4⋊C4—532no—
545C2×C4⋊C4—534no—
546C2×C4⋊C4—534no—
547C2×C4⋊C4—5332no—
548C2×C4⋊C4—534no—
549C2×C4⋊C4—532no—
550C2×C4⋊C4—534no—
551C2×C4⋊C4—534no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—5316no—
554C2×C4⋊C4—5332no—
555C2×C4⋊C4C22×D5312yes—
556C2×C4⋊C4C22×D5314yes—
557C2×C4⋊C4C22×D5312yes—
558C2×C22⋊C4—534no—
559C2×C22⋊C4—534no—
560C2×C22⋊C4—534no—
561C2×C22⋊C4—534no—
562C2×C22⋊C4—534no—
563C2×C22⋊C4—532no—
564C2×C22⋊C4—532no—
565C2×C22⋊C4—534no—
566C2×C22⋊C4C22×D5314yes—
567C2×C22⋊C4C22×D5314yes—
568C2×C22⋊C4C22×D5312yes—
569C2×C42—531no—
570C2×C42—534no—
571C2×C42—534no—
572C2×C42—532no—
573C2×C42—532no—
574C2×C42—532no—
575C2×C42—538no—
576C2×C42—531no—
577C2×C42—538no—
578C2×C42—538no—
579C2×C42C22×D5311yescharacteristic
580C2×C42C22×D5311yescharacteristic
581C24—531no—
582C24—531no—
583C24C23×D5311yescharacteristic
584C24C23×D5314yes—
585#41—10632no—
586#41—10664no—
587C2×Q8—534no—
588C2×Q8—538no—
589C2×Q8—1064no—
590C2×Q8—1068no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—534no—
595C2×D4—534no—
596C2×D4—5316no—
597C2×D4—5316no—
598C2×D4—534no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—10616no—
603C2×D4—2128no—
604C2×D4C23×D5318yes—
605C2×D4C23×D53116yes—
606C2×D4C23×D53116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—531no—
610C22×C4—538no—
611C22×C4—534no—
612C22×C4—5316no—
613C22×C4—532no—
614C22×C4—532no—
615C22×C4—534no—
616C22×C4—531no—
617C22×C4—534no—
618C22×C4—538no—
619C22×C4—5316no—
620C22×C4—534no—
621C22×C4—538no—
622C22×C4—538no—
623C22×C4—5316no—
624C22×C4—10616no—
625C22×C4—1064no—
626C22×C4—2124no—
627C22×C4—2128no—
628C22×C4—2124no—
629C22×C4—2124no—
630C22×C4—2128no—
631C22×C4C23×D5314yes—
632C22×C4C23×D5312yes—
633C22×C4C23×D5311yescharacteristic
634C22×C4C23×D5312yes—
635C22×C4C23×D5314yes—
636C22×C4C23×D53116yes—
637C22×C4C23×D5311yescharacteristic
638C4⋊C4—538no—
639C4⋊C4—5316no—
640C4⋊C4—5316no—
641C4⋊C4—5316no—
642C4⋊C4—538no—
643C4⋊C4—5316no—
644C4⋊C4—5316no—
645C4⋊C4—5316no—
646C4⋊C4—538no—
647C4⋊C4—5316no—
648C4⋊C4—5316no—
649C4⋊C4—5316no—
650C4⋊C4C23×D5318yes—
651C4⋊C4C23×D53116yes—
652C4⋊C4C23×D5318yes—
653C22⋊C4—5316no—
654C22⋊C4—5316no—
655C22⋊C4—5316no—
656C22⋊C4—5316no—
657C22⋊C4—5316no—
658C22⋊C4—538no—
659C22⋊C4—538no—
660C22⋊C4—5316no—
661C22⋊C4C23×D53116yes—
662C22⋊C4C23×D53116yes—
663C22⋊C4C23×D5318yes—
664C42—534no—
665C42—534no—
666C42—538no—
667C42—538no—
668C42—538no—
669C42—5316no—
670C42—5316no—
671C42C23×D5314yes—
672C42C23×D5314yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—534no—
679C23—532no—
680C23—532no—
681C23—1064no—
682C23—1062no—
683C23—1064no—
684C23C24×D5312yes—
685C23C24×D5318yes—
686C23C24×D5311yescharacteristic
687Q8—1068no—
688Q8—10616no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—1068no—
693D4—1068no—
694D4—1068no—
695D4—10632no—
696D4—21216no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—534no—
704C2×C4—532no—
705C2×C4—5316no—
706C2×C4—534no—
707C2×C4—534no—
708C2×C4—532no—
709C2×C4—538no—
710C2×C4—538no—
711C2×C4—10632no—
712C2×C4—1062no—
713C2×C4—1068no—
714C2×C4—1064no—
715C2×C4—1064no—
716C2×C4—1068no—
717C2×C4—1068no—
718C2×C4—2128no—
719C2×C4—21216no—
720C2×C4—2128no—
721C2×C4—2128no—
722C2×C4—21216no—
723C2×C4#41×D5314yes—
724C2×C4C24×D5314yes—
725C2×C4C24×D5312yes—
726C2×C4C24×D5314yes—
727C2×C4C24×D5318yes—
728C2×C4C24×D5312yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—534no—
737C22—1068no—
738C22—1064no—
739C22—1062no—
740C22—1064no—
741C22—2124no—
742C22C2×#41×D5312yes—
743C22#1681145814yes—
744C22C25×D5311yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—534no—
750C4—1068no—
751C4—1062no—
752C4—1064no—
753C4—1064no—
754C4—1068no—
755C4C2×#41×D5314yes—
756C2—42no—
757C2—48no—
758C2—1064no—
759C2—2122no—
760C2#2028863414yesdirect product factor
761C2C22×#41×D5311yescharacteristic
762C2C2×#1681145812yes—
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#540C2
socleC23×C53C25
hypercenterC2×#540D53
hypocenterC53C2×#3512
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #20288634C2direct (N × H)
2. C2×#16811320C2semidirect
3. C2×#16811318C2semidirect
4. C2×#16811316C2semidirect
5. C2×#16811310C2semidirect
6. C2×#16811236C2semidirect
7. C2×#16811235C2semidirect
8. C2×#16811227C2semidirect
9. C2×#16811202C2semidirect
10. C2×#16811171C2semidirect
11. C2×#16811155C2semidirect
12. C2×#16811154C2semidirect
13. C2×#125×D53C2semidirect
14. C2×#16811102C2semidirect
15. C2×#16811091C2semidirect
16. C2×C53×#540C2semidirect
19. #16811320C22semidirect
20. #16811318C22semidirect
21. #16811316C22semidirect
22. #16811310C22semidirect
23. #16811236C22semidirect
24. #16811235C22semidirect
25. #16811227C22semidirect
26. #16811202C22semidirect
27. #16811171C22semidirect
29. #16811155C22semidirect
30. #16811154C22semidirect
40. #125×D53C22semidirect
54. #16811102C22semidirect
55. #16811091C22semidirect
79. C53×#540C22semidirect
383. C2×#540D53semidirect
393. C2×C53#3512semidirect
407. #540C2×D53semidirect
468. C53C2×#3512semidirect
760. C2#20288634direct (N × H)

Maximal subgroups

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

subgroupindex
#202886342
C2×#168113202
C2×#168113182
C2×#168113162
C2×#168113102
C2×#168112362
C2×#168112352
C2×#168112272
C2×#168112022
C2×#168111712
C2×#168111552
C2×#168111542
C2×#125×D532
C2×#168111022
C2×#168110912
C2×C53×#5402
C2×#351253