Finite Group Databasebeta

← C2×#20286611 #28260509

Subgroups — C2×#20286611 #28260509

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811282C211yesmaximal, characteristic, complemented
2#20286611C2116yesmaximal, direct product factor
3C2×#16810980C211yesmaximal, characteristic, complemented
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810964C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810857C211yesmaximal, characteristic, complemented
8C2×#16810850C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic, complemented
11C2×#16810761C211yesmaximal, characteristic, complemented
12C2×C4×#11719923C211yesmaximal, characteristic, complemented
13C2×D4×#88322C211yesmaximal, characteristic, complemented
14C2×#16810617C211yesmaximal, characteristic, complemented
15C22×#13133140C211yesmaximal, characteristic, complemented
16C2×C53×#553C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811282—24no—
25#16811282C2218yescomplemented
26C2×#13133205C2211yescharacteristic
27C2×#13133203—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133195—21no—
30C2×#13133191C2211yescharacteristic
31C2×#13133189—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133177—21no—
34#16810980C2218yescomplemented
35#16810964C2218yescomplemented
36#16810941C2218yescomplemented
37#16810927C2218yescomplemented
38#16810857C2218yescomplemented
39#16810850C2218yescomplemented
40#16810838C2218yescomplemented
41#16810766C2218yescomplemented
42#16810761C2218yescomplemented
43C4×#11719923C2218yescomplemented
44D4×#88322C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810617C2218yescomplemented
50C2×#13133140C2211yescharacteristic
51C2×#13133140C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2218yescomplemented
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#553—24no—
65C53×#553C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic
68C2×#123×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×D4×C53—21no—
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—24no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2314yes—
87C22×Dic106C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C2×#11719923—24no—
94C2×#11719923—42no—
95C2×#11719923C2314yes—
96C2×#11719923C2314yes—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C22×#88322—42no—
100C22×#88322—42no—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2314yes—
106C22×#88322C2314yes—
107#13133205—22no—
108#13133205C2314yes—
109#13133203—28no—
110#13133196—22no—
111#13133196C2314yes—
112#13133195—28no—
113#13133191—22no—
114#13133191C2314yes—
115#13133189—28no—
116C4×Dic106—22no—
117C4×Dic106C2314yes—
118#13133177—28no—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×#11719919—21no—
121C2×#11719919—21no—
122C2×C22⋊Dic53—21no—
123C2×#11719921—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×C4×Dic53—21no—
127#13133150C2314yes—
128#13133148C2314yes—
129#13133148C2314yes—
130C4⋊#88322C2314yes—
131#13133140C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133138C2314yes—
138#13133137C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141C22⋊#88322C2314yes—
142C22⋊#88322C2314yes—
143C4×#88322C2314yes—
144C22×D4×C53—21no—
145C22×D4×C53—21no—
146C22×D4×C53D411yescharacteristic
147C22×D4×C53C2311yescharacteristic
148C23×C4×C53—21no—
149C23×C4×C53—21no—
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152#126×C53—28no—
153#125×C53—22no—
154#125×C53C2314yes—
155#123×C53—28no—
156#121×C53—28no—
157#121×C53—22no—
158#121×C53—22no—
159#121×C53C2314yes—
160#121×C53C2314yes—
161C4×D4×C53—28no—
162C4×D4×C53—22no—
163C4×D4×C53D414yes—
164C4×D4×C53C2314yes—
165C4×D4×C53C2314yes—
166#117×C53—22no—
167#117×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—22no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2314yes—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C2×D4×C53—24no—
190C2×D4×C53—24no—
191C2×D4×C53—24no—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—44no—
196C2×D4×C53—82no—
197C2×D4×C53C2×D414yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—24no—
207C22×C4×C53—24no—
208C22×C4×C53—82no—
209C22×C4×C53—82no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53—44no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—44no—
228#11719945—28no—
229#11719945—44no—
230#11719945—48no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—21no—
234C2×D212C2412yes—
235C2×C4×D53—24no—
236C2×C4×D53—44no—
237C2×Dic106—21no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—28no—
242C2×Dic106—24no—
243C2×Dic106—21no—
244C2×Dic106—44no—
245C2×Dic106—48no—
246C2×Dic106—44no—
247C2×Dic106#4114yes—
248C2×Dic106C2412yes—
249C2×Dic106C2412yes—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2×D414yes—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—24no—
264C22⋊C4×C53C2×D414yes—
265C22⋊C4×C53C2×D414yes—
266C42×C53—24no—
267C42×C53C2×D412yes—
268C42×C53C2412yes—
269C22⋊Dic53—24no—
270#11719923—28no—
271#11719923—44no—
272#11719922—44no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276C4⋊Dic53—21no—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279#11719919—24no—
280C4×Dic53—24no—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—44no—
286C2×#88322—44no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53#13514yes—
301C23×C53C22×D412yes—
302C23×C53C22×D412yes—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308D4×C53—28no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—48no—
312D4×C53—42no—
313D4×C53—84no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—24no—
319C2×C4×C53—24no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—84no—
331C2×C4×C53—84no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C2×#4112yes—
338C2×C4×C53H(5,𝔽2)12yes—
339C2×C4×C53C2511yescharacteristic
340C22⋊D53—48no—
341C22⋊D53—48no—
342C2×Dic53—24no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—48no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349D212—22no—
350D212—22no—
351D212—42no—
352C4×D53—48no—
353Dic106—24no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—48no—
358Dic106—42no—
359Dic106C2×#4114yes—
360#88322—22no—
361#88322—22no—
362#88322—22no—
363#88322—22no—
364C2×#3301—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—28no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—84no—
376C22×C53#54612yes—
377C22×C53C2×#13514yes—
378C22×C53C2×#13512yes—
379C22×C53#57712yes—
380C22×C53C23×D411yescharacteristic
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#54612yes—
393C4×C53C22×#4111yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—24no—
396Dic53—42no—
397Dic53—42no—
398C2×#553D5311yescharacteristic, complemented
399C2×#548—531no—
400#3301—5316no—
401C2×#488—531no—
402C2×#481—531no—
403C2×#485—531no—
404C2×#479—531no—
405C2×#466—531no—
406C2×#465—531no—
407C2×#463—531no—
408C2×#449—531no—
409C2×#448—531no—
410C2×C4×SD16—531no—
411C2×C8×D4—531no—
412C2×#416—531no—
413C22×#103—531no—
414C2×C53—24no—
415C2×C53—42no—
416C2×C53—82no—
417C2×C53#330114yescomplemented
418C2×C53C2×#54611yescharacteristic
419C2×C53C22×#13511yescharacteristic
420C2×C53C2×#57711yescharacteristic
421D53—82no—
422C22×#41—531no—
423C23×Q8—531no—
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C23×C8—531no—
428C23×C8—531no—
429#553—24no—
430#553C2×D5318yescomplemented
431#548—538no—
432#548—1064no—
433C2×#126—21no—
434C2×#125C2×D5311yescharacteristic
435C2×#124—531no—
436C2×#124—1061no—
437C2×#123—21no—
438C2×C22⋊Q8—531no—
439C2×C22⋊Q8—1061no—
440C2×#121—21no—
441C2×#121—531no—
442C2×#121—1061no—
443C2×#121C2×D5311yescharacteristic
444C2×#121C2×D5311yescharacteristic
445C2×C4×Q8—531no—
446C2×C4×D4—21no—
447C2×C4×D4—1061no—
448C2×C4×D4C2×D5311yescharacteristic
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117C2×D5311yescharacteristic
451C22×C4⋊C4C2×D5311yescharacteristic
452#488—538no—
453#485—538no—
454#481—538no—
455#479—538no—
456#466—538no—
457#465—538no—
458#463—538no—
459#449—538no—
460#448—538no—
461C4×SD16—538no—
462C8×D4—538no—
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8—531no—
467#416—538no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—538no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×C4×C8—531no—
482C53C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—1064no—
485C2×#41—1062no—
486C2×#41—2122no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8—534no—
490C22×Q8—1064no—
491C22×Q8—1061no—
492C22×Q8—1062no—
493C22×Q8—2122no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4C22⋊D5311yescharacteristic
500C22×D4C22×D5311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—2122no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—534no—
519C22×C8—2122no—
520C22×C8—2122no—
521#126—28no—
522#125—22no—
523#125C22×D5314yes—
524#124—534no—
525#124—1068no—
526#124—1062no—
527#123—28no—
528C22⋊Q8—534no—
529C22⋊Q8—1062no—
530C22⋊Q8—1068no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—534no—
535#121—1068no—
536#121—1062no—
537#121C22×D5314yes—
538#121C22×D5314yes—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—28no—
542C4×D4—22no—
543C4×D4—1068no—
544C4×D4C22⋊D5314yes—
545C4×D4C22×D5314yes—
546C4×D4C22×D5314yes—
547#117—22no—
548#117C22×D5314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4C22⋊D5311yescharacteristic
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5314yes—
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4C22⋊D5311yescharacteristic
570C2×C22⋊C4C22⋊D5311yescharacteristic
571C2×C42—21no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C4×C8—534no—
591C24—21no—
592C24—1061no—
593C24C2×C22⋊D5311yescharacteristic
594C24C2×C22⋊D5311yescharacteristic
595#41—1068no—
596#41—2124no—
597#41—2128no—
598C2×Q8—534no—
599C2×Q8—532no—
600C2×Q8—532no—
601C2×Q8—1068no—
602C2×Q8—1061no—
603C2×Q8—1064no—
604C2×Q8—1061no—
605C2×Q8—1062no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8—2124no—
609C2×Q8—2124no—
610C2×Q8—2128no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—532no—
620C2×D4—1064no—
621C2×D4—1064no—
622C2×D4—1061no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—2124no—
626C2×D4—2124no—
627C2×D4C2×C22⋊D5314yes—
628C2×D4C23×D5312yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—82no—
639C22×C4—82no—
640C22×C4—1061no—
641C22×C4—1064no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1064no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4C2×C22⋊D5312yes—
648C22×C4C2×C22⋊D5312yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—1068no—
657SD16—2124no—
658D8—2124no—
659C2×C8—532no—
660C2×C8—532no—
661C2×C8—532no—
662C2×C8—532no—
663C2×C8—1062no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—2124no—
668C2×C8—2124no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—532no—
676C4⋊C4—1061no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4C2×C22⋊D5314yes—
680C4⋊C4C23×D5312yes—
681C4⋊C4C23×D5312yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4C2×C22⋊D5314yes—
692C22⋊C4C2×C22⋊D5314yes—
693C42—24no—
694C42—1064no—
695C42C2×C22⋊D5312yes—
696C42C23×D5312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—1062no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23#1313323714yes—
711C23C22×C22⋊D5312yes—
712C23C22×C22⋊D5312yes—
713C23C22×C22⋊D5311yescharacteristic
714Q8—534no—
715Q8—1062no—
716Q8—1064no—
717Q8—1062no—
718Q8—1062no—
719Q8—2128no—
720Q8—2122no—
721D4—28no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—42no—
726D4—84no—
727D4—1062no—
728D4—1062no—
729D4—2128no—
730D4—2128no—
731D4—2122no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—1062no—
751C2×C4—1064no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—2128no—
755C2×C4—2128no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4C22×C22⋊D5312yes—
759C2×C4C22×C22⋊D5312yes—
760C2×C4C22×C22⋊D5312yes—
761C2×C4C22×C22⋊D5312yes—
762C2×C4C22×C22⋊D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326312yes—
765C2×C4C24×D5311yescharacteristic
766C8—1062no—
767C8—1062no—
768C8—1062no—
769C8—1062no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—4244no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22#1681126112yes—
786C22C2×#1313323714yes—
787C22C2×#1313323712yes—
788C22#1681143412yes—
789C22C23×C22⋊D5311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—1064no—
798C4—2122no—
799C4—2122no—
800C4#1681126112yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326311yescharacteristic
803C2—24no—
804C2—42no—
805C2—82no—
806C2—4242no—
807C2#2028661114yesdirect product factor
808C2C2×#1681126111yescharacteristic
809C2C22×#1313323711yescharacteristic
810C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53C2×#3301
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16811282C2semidirect
2. #20286611C2direct (N × H)
3. C2×#16810980C2semidirect
4. C2×#16810941C2semidirect
5. C2×#16810964C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810857C2semidirect
8. C2×#16810850C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810766C2semidirect
11. C2×#16810761C2semidirect
12. C2×C4×#11719923C2semidirect
13. C2×D4×#88322C2semidirect
14. C2×#16810617C2semidirect
15. C22×#13133140C2semidirect
16. C2×C53×#553C2semidirect
25. #16811282C22semidirect
34. #16810980C22semidirect
35. #16810964C22semidirect
36. #16810941C22semidirect
37. #16810927C22semidirect
38. #16810857C22semidirect
39. #16810850C22semidirect
40. #16810838C22semidirect
41. #16810766C22semidirect
42. #16810761C22semidirect
43. C4×#11719923C22semidirect
44. D4×#88322C22semidirect
49. #16810617C22semidirect
56. C2×#13133140C22semidirect
65. C53×#553C22semidirect
398. C2×#553D53semidirect
417. C2×C53#3301semidirect
430. #553C2×D53semidirect
482. C53C2×#3301semidirect
807. C2#20286611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112822
#202866112
C2×#168109802
C2×#168109412
C2×#168109642
C2×#168109272
C2×#168108572
C2×#168108502
C2×#168108382
C2×#168107662
C2×#168107612
C2×C4×#117199232
C2×D4×#883222
C2×#168106172
C22×#131331402
C2×C53×#5532
C2×#330153