Finite Group Databasebeta

← C2×#20286963 #28260940

Subgroups — C2×#20286963 #28260940

Order 13568.

2178 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×#16811325C211yesmaximal, characteristic, complemented
2C2×#16811283C211yesmaximal, characteristic, complemented
3#20286963C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic, complemented
6C2×#16810951C211yesmaximal, characteristic, complemented
7C2×#16810929C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810840C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×#16810714C211yesmaximal, characteristic, complemented
13C2×#16810699C211yesmaximal, characteristic, complemented
14C2×#16810625C211yesmaximal, characteristic, complemented
15C2×#16810630C211yesmaximal, characteristic, complemented
16C2×C53×#468C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22#16811325—24no—
23#16811325C2218yescomplemented
24#16811283—24no—
25#16811283C2218yescomplemented
26C2×#13133210—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133206C2211yescharacteristic
29C2×#13133203—21no—
30C2×#13133201—21no—
31C2×#13133195—21no—
32C2×#13133192C2211yescharacteristic
33C2×#13133190—21no—
34C2×#13133189—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×D4×Dic53—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133179—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C22×C4⋊Dic53C2211yescharacteristic
43#16810979C2218yescomplemented
44#16810951C2218yescomplemented
45#16810950C2218yescomplemented
46#16810929C2218yescomplemented
47#16810875C2218yescomplemented
48#16810840C2218yescomplemented
49#16810766C2218yescomplemented
50#16810760C2218yescomplemented
51#16810714C2218yescomplemented
52#16810699C2218yescomplemented
53C2×#13133148C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133146C2211yescharacteristic
56#16810630C2218yescomplemented
57#16810625C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#468C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106C2311yescharacteristic
83C2×Q8×D53—22no—
84C2×Q8×D53—24no—
85C2×Q8×D53—42no—
86C2×Q8×D53C2314yes—
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53D411yescharacteristic
92C23×Dic53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719923—24no—
98C2×#11719923C2314yes—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133210—28no—
106#13133208—22no—
107#13133208C2314yes—
108#13133206—22no—
109#13133206C2314yes—
110#13133203—28no—
111#13133201—28no—
112#13133195—28no—
113#13133192—22no—
114#13133192C2314yes—
115#13133190—28no—
116#13133189—28no—
117#13133188—22no—
118#13133188C2314yes—
119#13133182—22no—
120#13133182C2314yes—
121D4×Dic53—28no—
122D4×Dic53—22no—
123D4×Dic53C2314yes—
124#13133179—28no—
125C4×C22⋊D53D414yes—
126C4×C22⋊D53C2314yes—
127#13133175—22no—
128#13133175C2314yes—
129C2×C4⋊Dic53—22no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2314yes—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919D411yescharacteristic
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53D411yescharacteristic
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#13133148C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53—21no—
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C2×SD16×C53—42no—
168C2×SD16×C53C2314yes—
169C2×M16×C53—42no—
170C2×M16×C53C2314yes—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22⋊Q8×C53—22no—
174C22⋊Q8×C53C2314yes—
175#121×C53—22no—
176#121×C53C2314yes—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182#107×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—24no—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53—44no—
198C2×D4×C53C2412yes—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2412yes—
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—42no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—82no—
213C2×C22⋊D53C2×D414yes—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—24no—
218C22×Dic53—24no—
219C22×Dic53—82no—
220C22×Dic53—82no—
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224Q8×D53—28no—
225Q8×D53—44no—
226Q8×D53—48no—
227#11719945—28no—
228#11719945—44no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—24no—
233C2×D212—21no—
234C2×D212—44no—
235C2×D212C2412yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×C4×D53C2×D412yes—
243C2×C4×D53C2412yes—
244C2×Dic106—21no—
245C2×Dic106—22no—
246C2×Dic106—24no—
247C2×Dic106—44no—
248C2×Dic106#4114yes—
249C2×Dic106C2412yes—
250SD16×C53—44no—
251M16×C53—44no—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2412yes—
260C4⋊C4×C53C2412yes—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53C2×D414yes—
266#11719923—28no—
267#11719922—44no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921C2×D414yes—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53—24no—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279#11719919—24no—
280#11719919—24no—
281#11719919C2×D414yes—
282C4×Dic53—24no—
283C4×Dic53—24no—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290#11719912—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53C22×D412yes—
308Q8×C53—22no—
309Q8×C53—22no—
310Q8×C53—42no—
311D4×C53—22no—
312D4×C53—22no—
313D4×C53—48no—
314D4×C53—42no—
315C2×C4×C53—22no—
316C2×C4×C53—24no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4112yes—
328C2×C4×C53H(5,𝔽2)12yes—
329C2×C4×C53C2511yescharacteristic
330C22⋊D53—44no—
331C22⋊D53—48no—
332C22⋊D53—84no—
333C2×Dic53—24no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—84no—
343C2×Dic53—84no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347D212—22no—
348D212—22no—
349D212—48no—
350D212—42no—
351C4×D53—24no—
352C4×D53—22no—
353C4×D53—22no—
354C4×D53—48no—
355C4×D53—48no—
356Dic106—24no—
357Dic106—22no—
358Dic106—48no—
359Dic106C2×#4114yes—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3326—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—44no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—84no—
373C22×C53#54612yes—
374C22×C53#57512yes—
375C22×C53#57712yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—44no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53#54612yes—
390C4×C53C22×#4111yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—24no—
393Dic53—22no—
394Dic53—22no—
395Dic53—22no—
396Dic53—42no—
397Dic53—42no—
398C2×#553—531no—
399C2×#548—531no—
400#3326—5316no—
401C2×#488—531no—
402C2×#482—531no—
403C2×#483—531no—
404C2×#479—531no—
405C2×#469—531no—
406C2×#468D5311yescharacteristic, complemented
407C2×#463—531no—
408C2×#449—531no—
409C2×#448—531no—
410C2×C4×SD16—531no—
411C2×#436—531no—
412C2×#417—531no—
413C2×#419—531no—
414C2×C53—42no—
415C2×C53—82no—
416C2×C53#332614yescomplemented
417C2×C53C2×#54611yescharacteristic
418C2×C53C2×#57511yescharacteristic
419C2×C53C2×#57711yescharacteristic
420D53—42no—
421D53—82no—
422C22×#41—531no—
423C23×Q8—531no—
424C22×SD16—531no—
425C22×SD16C2×D5311yescharacteristic
426C22×D8—531no—
427C22×M16—531no—
428C22×M16C2×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—1061no—
439C2×C22⋊Q8C2×D5311yescharacteristic
440C2×#121—531no—
441C2×#121—531no—
442C2×#121—1061no—
443C2×#121—1061no—
444C2×#121C2×D5311yescharacteristic
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⋊C4—531no—
452#488—538no—
453#483—538no—
454#482—538no—
455#479—538no—
456#469—538no—
457#468C2×D5318yescomplemented
458#463—538no—
459#449—538no—
460#448—538no—
461C4×SD16—538no—
462#436—538no—
463C2×#107C2×D5311yescharacteristic
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8—531no—
467#419—538no—
468#417—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103C2×D5311yescharacteristic
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102C2×D5311yescharacteristic
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×C4×C8—531no—
482C53C2×#332611yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—1064no—
485C2×#41—1062no—
486C2×#41—2122no—
487C22×Q8—534no—
488C22×Q8—531no—
489C22×Q8—1061no—
490C22×Q8—1062no—
491C22×Q8—1064no—
492C22×Q8—2122no—
493C22×Q8C22×D5311yescharacteristic
494C22×D4—21no—
495C22×D4—531no—
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4C22×D5311yescharacteristic
501C23×C4—531no—
502C23×C4—1061no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×SD16—42no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16C22×D5314yes—
511C2×D8—534no—
512C2×D8—2122no—
513C2×M16—42no—
514C2×M16—534no—
515C2×M16—2122no—
516C2×M16C22×D5314yes—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521#126—1068no—
522#125—534no—
523#125—1062no—
524#124—534no—
525#124—1062no—
526#124—1068no—
527#123—1068no—
528C22⋊Q8—22no—
529C22⋊Q8—1068no—
530C22⋊Q8C22×D5314yes—
531#121—22no—
532#121—534no—
533#121—534no—
534#121—1068no—
535#121—1062no—
536#121—1062no—
537#121—1068no—
538#121C22×D5314yes—
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—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—534no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1062no—
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—531no—
564C2×C22⋊C4—531no—
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#107C22×D5314yes—
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#103C22×D5314yes—
584#102—534no—
585#102—534no—
586#102—534no—
587#102C22×D5314yes—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C4×C8—534no—
591C24—21no—
592C24—531no—
593C24—1061no—
594C24D4×D5311yescharacteristic
595#41—1068no—
596#41—2124no—
597#41—2128no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—534no—
602C2×Q8—532no—
603C2×Q8—1064no—
604C2×Q8—1061no—
605C2×Q8—1062no—
606C2×Q8—1068no—
607C2×Q8—2124no—
608C2×Q8—2124no—
609C2×Q8—2128no—
610C2×Q8C23×D5312yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—534no—
617C2×D4—532no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—2124no—
626C2×D4—2122no—
627C2×D4—2124no—
628C2×D4C23×D5312yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—531no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—532no—
638C22×C4—532no—
639C22×C4—1064no—
640C22×C4—1064no—
641C22×C4—1061no—
642C22×C4—1062no—
643C22×C4—1062no—
644C22×C4—1064no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—1064no—
648C22×C4—4242no—
649C22×C4—4242no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—44no—
657SD16—1068no—
658D8—2124no—
659M16—44no—
660M16—2124no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—532no—
664C2×C8—532no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—534no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1061no—
679C4⋊C4—1061no—
680C4⋊C4—1064no—
681C4⋊C4C23×D5312yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—534no—
686C22⋊C4—534no—
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—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—532no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C2×D4×D5312yes—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—534no—
718Q8—1062no—
719Q8—1064no—
720Q8—2128no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—42no—
725D4—1062no—
726D4—1062no—
727D4—4244no—
728D4—2128no—
729D4—2124no—
730D4—2128no—
731D4—2122no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—532no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1064no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1064no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—4244no—
756C2×C4—4244no—
757C2×C4—2128no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—1062no—
779C22—1062no—
780C22—1062no—
781C22—4244no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2124no—
786C22#1681126212yes—
787C22#1681141912yes—
788C22#1681143212yes—
789C22C22×D4×D5311yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—1062no—
795C4—1064no—
796C4—1062no—
797C4—1062no—
798C4—2122no—
799C4—2122no—
800C4#1681126212yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—42no—
804C2—82no—
805C2—4242no—
806C2—2122no—
807C2#2028696314yesdirect product factor
808C2C2×#1681126211yescharacteristic
809C2C2×#1681141911yescharacteristic
810C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#468C2
socleC23×C53C22×D4
hypercenterC2×#468D53
hypocenterC53C2×#3326
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16811325C2semidirect
2. C2×#16811283C2semidirect
3. #20286963C2direct (N × H)
4. C2×#16810979C2semidirect
5. C2×#16810950C2semidirect
6. C2×#16810951C2semidirect
7. C2×#16810929C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810840C2semidirect
10. C2×#16810766C2semidirect
11. C2×#16810760C2semidirect
12. C2×#16810714C2semidirect
13. C2×#16810699C2semidirect
14. C2×#16810625C2semidirect
15. C2×#16810630C2semidirect
16. C2×C53×#468C2semidirect
23. #16811325C22semidirect
25. #16811283C22semidirect
43. #16810979C22semidirect
44. #16810951C22semidirect
45. #16810950C22semidirect
46. #16810929C22semidirect
47. #16810875C22semidirect
48. #16810840C22semidirect
49. #16810766C22semidirect
50. #16810760C22semidirect
51. #16810714C22semidirect
52. #16810699C22semidirect
56. #16810630C22semidirect
57. #16810625C22semidirect
73. C53×#468C22semidirect
406. C2×#468D53semidirect
416. C2×C53#3326semidirect
457. #468C2×D53semidirect
482. C53C2×#3326semidirect
807. C2#20286963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113252
C2×#168112832
#202869632
C2×#168109792
C2×#168109502
C2×#168109512
C2×#168109292
C2×#168108752
C2×#168108402
C2×#168107662
C2×#168107602
C2×#168107142
C2×#168106992
C2×#168106252
C2×#168106302
C2×C53×#4682
C2×#332653