Finite Group Databasebeta

← C2×#20285000 #28252432

Subgroups — C2×#20285000 #28252432

Order 13568.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811226C211yesmaximal, characteristic
2C2×#16811101C211yesmaximal, characteristic, complemented
3#20285000C2116yesmaximal, direct product factor
4C2×#16810948C211yesmaximal, characteristic, complemented
5C2×#16810944C211yesmaximal, characteristic, complemented
6C2×#16810932C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810821C211yesmaximal, characteristic, complemented
9C2×#16810821C211yesmaximal, characteristic, complemented
10C2×#16810762C211yesmaximal, characteristic, complemented
11C2×#16810726C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×SD16×Dic53C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#448C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19#16811226—24no—
20#16811226C2218yes—
21C2×#13133213C2211yescharacteristic
22C2×#13133208C2211yescharacteristic
23C2×#13133201—21no—
24C2×#13133199—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133189—21no—
27C2×#13133188—21no—
28#16811101—24no—
29#16811101C2218yescomplemented
30C2×Q8×Dic53—21no—
31C2×Q8×Dic53—21no—
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133176—21no—
39C2×#13133176—21no—
40C2×#13133176C2211yescharacteristic
41C2×#13133176C2211yescharacteristic
42#16810948C2218yescomplemented
43#16810944C2218yescomplemented
44#16810932C2218yescomplemented
45#16810928C2218yescomplemented
46#16810821C2218yescomplemented
47#16810821C2218yescomplemented
48#16810762C2218yescomplemented
49#16810726C2218yescomplemented
50#16810724C2218yescomplemented
51SD16×Dic53C2218yescomplemented
52#16810708C2218yescomplemented
53#16810681C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#448C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C23×Dic53—21no—
82C22×C4×D53—21no—
83C2×#11719924—24no—
84C2×#11719924—24no—
85C2×#11719924C2314yes—
86C2×#11719924C2314yes—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89#13133213—22no—
90#13133213C2314yes—
91#13133208—22no—
92#13133208C2314yes—
93#13133201—28no—
94#13133199—28no—
95#13133191—22no—
96#13133191C2314yes—
97#13133189—28no—
98#13133188—28no—
99Q8×Dic53—28no—
100Q8×Dic53—28no—
101Q8×Dic53—22no—
102Q8×Dic53—22no—
103Q8×Dic53—22no—
104Q8×Dic53—22no—
105Q8×Dic53C2314yes—
106Q8×Dic53C2314yes—
107Q8×Dic53C2314yes—
108Q8×Dic53C2314yes—
109D4×Dic53—22no—
110D4×Dic53C2314yes—
111#13133179—22no—
112#13133179C2314yes—
113#13133176—28no—
114#13133176—28no—
115#13133176—22no—
116#13133176D414yes—
117#13133176C2314yes—
118#13133176C2314yes—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53D411yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53D411yescharacteristic
133C2×C22⋊Dic53D411yescharacteristic
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
147#13133146C2314yes—
148#13133146C2314yes—
149#13133141C2314yes—
150#13133141C2314yes—
151#13133139C2314yes—
152#13133139C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53—24no—
159C22×Q8×C53—24no—
160C22×Q8×C53—21no—
161C22×Q8×C53—22no—
162C22×Q8×C53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53C2311yescharacteristic
169C2×SD16×C53—24no—
170C2×SD16×C53—24no—
171C2×SD16×C53C2314yes—
172C2×SD16×C53C2314yes—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175#121×C53—22no—
176#121×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C2×Q8×C53—216no—
186C2×Q8×C53—28no—
187C2×Q8×C53—28no—
188C2×Q8×C53—28no—
189C2×Q8×C53—24no—
190C2×Q8×C53—21no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53#4114yes—
195C2×Q8×C53#4114yes—
196C2×Q8×C53C2412yes—
197C2×Q8×C53C2412yes—
198C2×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—82no—
203C2×D4×C53C2412yes—
204C22×C4×C53—28no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—24no—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—82no—
219C2×C22⋊D53—82no—
220C2×C22⋊D53—82no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—24no—
225C22×Dic53—82no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212C2412yes—
234C2×C4×D53—24no—
235C2×C4×D53—82no—
236SD16×C53—28no—
237SD16×C53—28no—
238C2×C8×C53—22no—
239C2×C8×C53—22no—
240C2×C8×C53C2412yes—
241C2×C8×C53C2412yes—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247C22⋊Dic53C2×D414yes—
248C22⋊Dic53C2×D414yes—
249#11719924—28no—
250#11719924—28no—
251#11719921—24no—
252#11719921—24no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53—24no—
260C4⋊Dic53—24no—
261C4⋊Dic53C2×D414yes—
262C4⋊Dic53C2×D414yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266#11719919—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293Q8×C53—216no—
294Q8×C53—24no—
295Q8×C53—24no—
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53C2×#4114yes—
299Q8×C53C2×#4114yes—
300D4×C53—22no—
301D4×C53—22no—
302D4×C53—42no—
303D4×C53—84no—
304C2×C4×C53—216no—
305C2×C4×C53—24no—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4112yes—
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2511yescharacteristic
320C22⋊D53—84no—
321C22⋊D53—84no—
322C22⋊D53—84no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—84no—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—22no—
339D212—22no—
340D212—42no—
341C4×D53—84no—
342C8×C53—22no—
343C8×C53—22no—
344#88322—22no—
345#88322—22no—
346C2×#3126—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—44no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—84no—
355C22×C53#52512yes—
356C22×C53#57712yes—
357C22×C53#57712yes—
358C22×C53C23×D411yescharacteristic
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C4×C53—24no—
364C4×C53—24no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53#52512yes—
368C4×C53C22×#4111yescharacteristic
369C4×C53C22×#4111yescharacteristic
370Dic53—22no—
371Dic53—22no—
372Dic53—22no—
373Dic53—22no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C2×#540—531no—
378C2×#519—531no—
379#3126—5316no—
380C2×#482—531no—
381C2×#482—531no—
382C2×#479—531no—
383C2×#479—531no—
384C2×#460—531no—
385C2×#460—531no—
386C2×#448—531no—
387C2×#448D5311yescharacteristic, complemented
388C2×#440—531no—
389C2×#440—531no—
390C2×C4×SD16—531no—
391C2×C4×SD16—531no—
392C2×#433—531no—
393C2×C53—42no—
394C2×C53—82no—
395C2×C53#312614yescomplemented
396C2×C53C2×#52511yescharacteristic
397C2×C53C2×#57711yescharacteristic
398C2×C53C2×#57711yescharacteristic
399D53—82no—
400C23×Q8C2×D5311yescharacteristic
401C22×SD16—531no—
402C22×SD16—531no—
403C22×SD16C2×D5311yescharacteristic
404C22×SD16C2×D5311yescharacteristic
405#540—538no—
406#540—1064no—
407C2×#127—531no—
408C2×#125—531no—
409C2×#123—1061no—
410C2×#123—1061no—
411C2×#121—531no—
412C2×#121—1061no—
413C2×#121—1061no—
414C2×#121C2×D5311yescharacteristic
415#519—538no—
416#519—1064no—
417C2×C4×Q8—531no—
418C2×C4×Q8—531no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×Q8—1061no—
422C2×C4×Q8—1061no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×#117—531no—
426C2×#117—531no—
427C2×#117—1061no—
428C2×#117—1061no—
429#482—538no—
430#482—538no—
431#479—538no—
432#479—538no—
433#460—538no—
434#460—538no—
435#448—538no—
436#448C2×D5318yescomplemented
437#440—538no—
438#440—538no—
439C4×SD16—538no—
440C4×SD16—538no—
441#433—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103C2×D5311yescharacteristic
451C2×#103C2×D5311yescharacteristic
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8C2×D5311yescharacteristic
458C2×#97—531no—
459C2×C4×C8—531no—
460C53C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—24no—
462C22×Q8—24no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8C22×D5314yes—
466C22×Q8C22×D5311yescharacteristic
467C22×Q8C22×D5311yescharacteristic
468C22×D4—21no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4C22×D5311yescharacteristic
474C23×C4—21no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16C22×D5314yes—
485C2×SD16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490#127—534no—
491#127—1062no—
492#125—534no—
493#125—1062no—
494#123—1068no—
495#123—1068no—
496#121—22no—
497#121—534no—
498#121—1068no—
499#121—1068no—
500#121—1062no—
501#121C22×D5314yes—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—534no—
506C4×Q8—1062no—
507C4×Q8—1062no—
508C4×Q8—1062no—
509C4×Q8—1062no—
510C4×Q8—1068no—
511C4×Q8—1068no—
512C4×D4—534no—
513C4×D4—534no—
514C4×D4—1062no—
515C4×D4—1062no—
516#117—534no—
517#117—534no—
518#117—534no—
519#117—1068no—
520#117—1068no—
521#117—1062no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C42—531no—
542C2×C42—531no—
543C2×C42—1061no—
544C2×C42—1061no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42—1061no—
548#107—534no—
549#107—534no—
550#106—534no—
551#106—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103C22×D5314yes—
557#103C22×D5314yes—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562C22⋊C8—534no—
563C22⋊C8C22×D5314yes—
564#97—534no—
565C4×C8—534no—
566C24—21no—
567C24—1061no—
568C24D4×D5311yescharacteristic
569C2×Q8—216no—
570C2×Q8—28no—
571C2×Q8—28no—
572C2×Q8—28no—
573C2×Q8—24no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8#1171994714yes—
579C2×Q8#1171994714yes—
580C2×Q8C23×D5312yes—
581C2×Q8C23×D5312yes—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—82no—
587C2×D4—532no—
588C2×D4—1064no—
589C2×D4—1064no—
590C2×D4—1064no—
591C2×D4—1061no—
592C2×D4—1062no—
593C2×D4—1062no—
594C2×D4—4242no—
595C2×D4—4242no—
596C2×D4—4242no—
597C2×D4C23×D5312yes—
598C22×C4—28no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—531no—
606C22×C4—531no—
607C22×C4—531no—
608C22×C4—531no—
609C22×C4—1064no—
610C22×C4—1064no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620SD16—28no—
621SD16—28no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—21no—
633C4⋊C4—534no—
634C4⋊C4—534no—
635C4⋊C4—532no—
636C4⋊C4—532no—
637C4⋊C4—532no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4C23×D5312yes—
648C22⋊C4—24no—
649C22⋊C4—534no—
650C22⋊C4—534no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C42—532no—
656C42—532no—
657C42—532no—
658C42—532no—
659C42—1064no—
660C42—1064no—
661C42—1064no—
662C42—1064no—
663C42—1064no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1062no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23C2×D4×D5312yes—
676C23C2×D4×D5311yescharacteristic
677Q8—216no—
678Q8—24no—
679Q8—24no—
680Q8—22no—
681Q8—22no—
682Q8C2×#1171994714yes—
683Q8C2×#1171994714yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—84no—
688D4—1062no—
689D4—1062no—
690D4—4244no—
691D4—4244no—
692D4—4244no—
693D4—2122no—
694C2×C4—216no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—532no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—532no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—4244no—
717C2×C4—4244no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4C2×#1171994712yes—
724C2×C4C2×#1171994712yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1062no—
729C8—1062no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—4244no—
739C22—2122no—
740C22—2122no—
741C22—2122no—
742C22#1681112912yes—
743C22#1681142912yes—
744C22#1681143212yes—
745C22C22×D4×D5311yescharacteristic
746C4—24no—
747C4—24no—
748C4—22no—
749C4—42no—
750C4—1062no—
751C4—1062no—
752C4—1062no—
753C4—1062no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C4#1681112912yes—
758C4C22×#1171994711yescharacteristic
759C4C22×#1171994711yescharacteristic
760C2—42no—
761C2—82no—
762C2—4242no—
763C2#2028500014yesdirect product factor
764C2C2×#1681112911yescharacteristic
765C2C2×#1681142911yescharacteristic
766C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#448C2
socleC23×C53C22×D4
prime radicalC2×#16811226C2
hypercenterC2×#448D53
hypocenterC53C2×#3126
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#16811101C2semidirect
3. #20285000C2direct (N × H)
4. C2×#16810948C2semidirect
5. C2×#16810944C2semidirect
6. C2×#16810932C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810821C2semidirect
9. C2×#16810821C2semidirect
10. C2×#16810762C2semidirect
11. C2×#16810726C2semidirect
12. C2×#16810724C2semidirect
13. C2×SD16×Dic53C2semidirect
14. C2×#16810708C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#448C2semidirect
29. #16811101C22semidirect
42. #16810948C22semidirect
43. #16810944C22semidirect
44. #16810932C22semidirect
45. #16810928C22semidirect
46. #16810821C22semidirect
47. #16810821C22semidirect
48. #16810762C22semidirect
49. #16810726C22semidirect
50. #16810724C22semidirect
51. SD16×Dic53C22semidirect
52. #16810708C22semidirect
53. #16810681C22semidirect
73. C53×#448C22semidirect
387. C2×#448D53semidirect
395. C2×C53#3126semidirect
436. #448C2×D53semidirect
460. C53C2×#3126semidirect
763. C2#20285000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112262
C2×#168111012
#202850002
C2×#168109482
C2×#168109442
C2×#168109322
C2×#168109282
C2×#168108212
C2×#168107622
C2×#168107262
C2×#168107242
C2×SD16×Dic532
C2×#168107082
C2×#168106812
C2×C53×#4482
C2×#312653