Finite Group Databasebeta

← C2×#20286613 #28260511

Subgroups — C2×#20286613 #28260511

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×#16811321C211yesmaximal, characteristic, complemented
2C2×#16811284C211yesmaximal, characteristic, complemented
3#20286613C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810941C211yesmaximal, characteristic, complemented
6C2×#16810963C211yesmaximal, characteristic, complemented
7C2×#16810932C211yesmaximal, characteristic, complemented
8C2×#16810859C211yesmaximal, characteristic, complemented
9C2×#16810855C211yesmaximal, characteristic, complemented
10C2×#16810841C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810762C211yesmaximal, characteristic, complemented
13C2×#16810708C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C22×#103×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811321—24no—
23#16811321C2218yescomplemented
24#16811284—24no—
25#16811284C2218yescomplemented
26C2×#13133212—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133206—21no—
29C2×#13133206C2211yescharacteristic
30C2×#13133202—21no—
31C2×#13133193—21no—
32C2×#13133193C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×#13133191—21no—
35C2×#13133191—21no—
36C2×#13133191C2211yescharacteristic
37C2×#13133191C2211yescharacteristic
38C2×Q8×Dic53C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×C4×C22⋊D53—21no—
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44#16810979C2218yescomplemented
45#16810963C2218yescomplemented
46#16810941C2218yescomplemented
47#16810932C2218yescomplemented
48#16810859C2218yescomplemented
49#16810855C2218yescomplemented
50#16810841C2218yescomplemented
51#16810771C2218yescomplemented
52#16810762C2218yescomplemented
53#16810708C2218yescomplemented
54C8×C22⋊D53C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59#16810618C2218yescomplemented
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2218yescomplemented
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53C2311yescharacteristic
91C2×#11719924—24no—
92C2×#11719924—42no—
93C2×#11719924C2314yes—
94C2×#11719924C2314yes—
95C2×D424—42no—
96C2×D424C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—42no—
100C2×C8×D53C2314yes—
101#13133212—28no—
102#13133208—22no—
103#13133208C2314yes—
104#13133206—28no—
105#13133206—22no—
106#13133206C2314yes—
107#13133202—28no—
108#13133193—28no—
109#13133193—22no—
110#13133193C2314yes—
111#13133192—22no—
112#13133192C2314yes—
113#13133191—22no—
114#13133191—22no—
115#13133191—28no—
116#13133191—28no—
117#13133191C2314yes—
118#13133191C2314yes—
119Q8×Dic53—22no—
120Q8×Dic53C2314yes—
121#13133179—22no—
122#13133179C2314yes—
123C4×C22⋊D53—28no—
124C4×C22⋊D53—28no—
125C4×C22⋊D53D414yes—
126C4×C22⋊D53C2314yes—
127#13133175—22no—
128#13133175C2314yes—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×C22⋊Dic53D411yescharacteristic
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133151C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133146C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53—22no—
163C22×Q8×C53—21no—
164C22×Q8×C53—24no—
165C22×Q8×C53—42no—
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C22×C8×C53—42no—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2314yes—
176C2×C4⋊C4×C53—22no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2314yes—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181#103×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—24no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—28no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—44no—
197C2×Q8×C53—44no—
198C2×Q8×C53—48no—
199C2×Q8×C53#4114yes—
200C2×Q8×C53C2412yes—
201C2×Q8×C53C2412yes—
202C22×C4×C53—21no—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—24no—
209C22×C4×C53—24no—
210C22×C4×C53—44no—
211C22×C4×C53—82no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53C2×D414yes—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227#11719949—28no—
228#11719949—44no—
229#11719949—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—24no—
235C2×D212—21no—
236C2×D212—21no—
237C2×D212—24no—
238C2×D212—44no—
239C2×D212—82no—
240C2×D212C2412yes—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—24no—
245C2×C4×D53—24no—
246C2×C4×D53—44no—
247C2×C4×D53—82no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2412yes—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53—44no—
253C2×C8×C53C2412yes—
254C2×C8×C53C2412yes—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—24no—
258C4⋊C4×C53C2412yes—
259C4⋊C4×C53C2412yes—
260C22⋊Dic53C2×D414yes—
261#11719924—28no—
262#11719924—44no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272C4⋊Dic53—21no—
273C4⋊Dic53—21no—
274C4⋊Dic53—24no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279#11719919—24no—
280#11719919C2×D414yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289D424—44no—
290C8×D53—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53#13514yes—
294C23×C53C22×D412yes—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53C22×D412yes—
308Q8×C53—24no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—48no—
313Q8×C53—42no—
314Q8×C53C2×#4114yes—
315C2×C4×C53—24no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—48no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—84no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—28no—
335C22⋊D53—48no—
336C22⋊D53—48no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—22no—
351D212—48no—
352D212—42no—
353D212—42no—
354D212—84no—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—48no—
359C4×D53—84no—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3301—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—28no—
367C22×C53—22no—
368C22×C53#54612yes—
369C22×C53C2×#13514yes—
370C22×C53C2×#13512yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—44no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C2×D53—84no—
385C4×C53—24no—
386C4×C53—22no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53#54612yes—
391C4×C53C22×#4111yescharacteristic
392C4×C53C2×H(5,𝔽2)11yescharacteristic
393Dic53—22no—
394Dic53—22no—
395Dic53—22no—
396Dic53—42no—
397Dic53—42no—
398C2×#553—531no—
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×#103D5311yescharacteristic, complemented
414C2×C53—24no—
415C2×C53#330114yescomplemented
416C2×C53C2×#54611yescharacteristic
417C2×C53C22×#13511yescharacteristic
418C2×C53C2×#57711yescharacteristic
419D53—42no—
420D53—82no—
421D53—82no—
422C22×#41—531no—
423C23×Q8C2×D5311yescharacteristic
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C23×C8—531no—
428C23×C8C2×D5311yescharacteristic
429#553—538no—
430#553—1064no—
431#548—538no—
432#548—1064no—
433C2×#126—1061no—
434C2×#125—531no—
435C2×#124—531no—
436C2×#124—1061no—
437C2×#123—1061no—
438C2×C22⋊Q8—531no—
439C2×C22⋊Q8—1061no—
440C2×#121—531no—
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×C4×D4—1061no—
450C2×#117—531no—
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×#103C2×D5311yescharacteristic
471C2×#103C2×D5311yescharacteristic
472C2×#103C2×D5311yescharacteristic
473C2×#103C2×D5311yescharacteristic
474C2×#103C2×D5318yescomplemented
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—1062no—
485C2×#41—1064no—
486C2×#41—2122no—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C22×D5311yescharacteristic
492C22×Q8C22×D5314yes—
493C22×Q8C22×D5311yescharacteristic
494C22×D4—531no—
495C22×D4—531no—
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4—1061no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—2122no—
513C22×C8—42no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—534no—
517C22×C8—2122no—
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5314yes—
521#126—1068no—
522#125—534no—
523#125—1062no—
524#124—534no—
525#124—1062no—
526#124—1068no—
527#123—1068no—
528C22⋊Q8—534no—
529C22⋊Q8—1068no—
530C22⋊Q8—1062no—
531#121—534no—
532#121—534no—
533#121—534no—
534#121—1062no—
535#121—1068no—
536#121—1068no—
537#121—1062no—
538#121—1062no—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1062no—
545C4×D4—1068no—
546C4×D4—1068no—
547#117—534no—
548#117—1062no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5314yes—
561C2×C22⋊C4—531no—
562C2×C22⋊C4—531no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—531no—
572C2×C42—1061no—
573C2×C42—1061no—
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103C22×D5314yes—
581#103C22×D5314yes—
582#103C22×D5314yes—
583#103C22×D5314yes—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C4×C8—534no—
591C24—531no—
592C24—1061no—
593C24—1061no—
594C24D4×D5311yescharacteristic
595#41—1068no—
596#41—2124no—
597#41—2128no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8#1171994514yes—
609C2×Q8C23×D5312yes—
610C2×Q8C23×D5312yes—
611C2×D4—534no—
612C2×D4—532no—
613C2×D4—532no—
614C2×D4—1064no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1061no—
620C2×D4—1061no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—4242no—
626C2×D4—2124no—
627C2×D4—2124no—
628C2×D4—2124no—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—82no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—531no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—1064no—
645C22×C4—1064no—
646C22×C4—1062no—
647C22×C4—1062no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—1068no—
657SD16—2124no—
658D8—2124no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—44no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—534no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1061no—
680C4⋊C4—1061no—
681C4⋊C4C23×D5312yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—534no—
684C22⋊C4—534no—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C42—532no—
694C42—532no—
695C42—1064no—
696C42—1064no—
697C23—22no—
698C23—22no—
699C23—532no—
700C23—1062no—
701C23—1062no—
702C23—1062no—
703C23—1062no—
704C23—1062no—
705C23—2122no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23#1313324014yes—
712C23C2×D4×D5312yes—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#1171994514yes—
721D4—1068no—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—1062no—
726D4—4244no—
727D4—2128no—
728D4—2128no—
729D4—2128no—
730D4—2122no—
731D4—2122no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—84no—
746C2×C4—532no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1064no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—4244no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4C2×#1171994512yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—1062no—
774C22—1062no—
775C22—1062no—
776C22—4244no—
777C22—4244no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2124no—
785C22#1681126312yes—
786C22C2×#1313324014yes—
787C22C2×#1313324012yes—
788C22#1681142912yes—
789C22C22×D4×D5311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—1062no—
796C4—1062no—
797C4—1062no—
798C4—2122no—
799C4—2122no—
800C4#1681126312yes—
801C4C22×#1171994511yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—24no—
804C2—4242no—
805C2—4242no—
806C2—2122no—
807C2#2028661314yesdirect product factor
808C2C2×#1681126311yescharacteristic
809C2C22×#1313324011yescharacteristic
810C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#103×C53C2
socleC23×C53C22×D4
hypercenterC22×#103D53
hypocenterC53C2×#3301
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16811321C2semidirect
2. C2×#16811284C2semidirect
3. #20286613C2direct (N × H)
4. C2×#16810979C2semidirect
5. C2×#16810941C2semidirect
6. C2×#16810963C2semidirect
7. C2×#16810932C2semidirect
8. C2×#16810859C2semidirect
9. C2×#16810855C2semidirect
10. C2×#16810841C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810762C2semidirect
13. C2×#16810708C2semidirect
14. C2×C8×C22⋊D53C2semidirect
15. C2×#16810618C2semidirect
16. C22×#103×C53C2semidirect
23. #16811321C22semidirect
25. #16811284C22semidirect
44. #16810979C22semidirect
45. #16810963C22semidirect
46. #16810941C22semidirect
47. #16810932C22semidirect
48. #16810859C22semidirect
49. #16810855C22semidirect
50. #16810841C22semidirect
51. #16810771C22semidirect
52. #16810762C22semidirect
53. #16810708C22semidirect
54. C8×C22⋊D53C22semidirect
59. #16810618C22semidirect
76. C2×#103×C53C22semidirect
413. C22×#103D53semidirect
415. C2×C53#3301semidirect
474. C2×#103C2×D53semidirect
482. C53C2×#3301semidirect
807. C2#20286613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113212
C2×#168112842
#202866132
C2×#168109792
C2×#168109412
C2×#168109632
C2×#168109322
C2×#168108592
C2×#168108552
C2×#168108412
C2×#168107712
C2×#168107622
C2×#168107082
C2×C8×C22⋊D532
C2×#168106182
C22×#103×C532
C2×#330153