Finite Group Databasebeta

← C2×#20287206 #28262677

Subgroups — C2×#20287206 #28262677

Order 13568.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic, complemented
2C2×#16811325C211yesmaximal, characteristic
3#20287206C2116yesmaximal, direct product factor
4C2×#16811030C211yesmaximal, characteristic, complemented
5C2×#16810956C211yesmaximal, characteristic, complemented
6C2×#16810939C211yesmaximal, characteristic, complemented
7C2×#16810963C211yesmaximal, characteristic, complemented
8C2×#16810935C211yesmaximal, characteristic, complemented
9C2×#16810932C211yesmaximal, characteristic, complemented
10C2×#16810901C211yesmaximal, characteristic, complemented
11C2×#16810866C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810694C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C22×#13133151C211yesmaximal, characteristic, complemented
16C2×C53×#465C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18#16811331—24no—
19#16811331C2218yescomplemented
20#16811325—24no—
21#16811325C2218yes—
22C2×#13133216C2211yescharacteristic
23C2×#13133210—21no—
24C2×#13133208C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133201—21no—
27C2×#13133197—21no—
28C2×#13133194—21no—
29C2×#13133193C2211yescharacteristic
30C2×#13133189—21no—
31C2×#13133188C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×D4×Dic53—21no—
34C2×D4×Dic53C2211yescharacteristic
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133177—21no—
37C2×#13133175C2211yescharacteristic
38C22×C4⋊Dic53C2211yescharacteristic
39C22×C4⋊Dic53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811030C2218yescomplemented
42#16810963C2218yescomplemented
43#16810956C2218yescomplemented
44#16810939C2218yescomplemented
45#16810935C2218yescomplemented
46#16810932C2218yescomplemented
47#16810901C2218yescomplemented
48#16810866C2218yescomplemented
49#16810724C2218yescomplemented
50#16810694C2218yescomplemented
51#16810662C2218yescomplemented
52C2×#13133151C2211yescharacteristic
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#465C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C23×Dic53—21no—
81C23×Dic53—21no—
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719912—24no—
86C2×#11719912C2314yes—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89#13133216—22no—
90#13133216C2314yes—
91#13133210—28no—
92#13133208—22no—
93#13133208C2314yes—
94#13133207—28no—
95#13133201—28no—
96#13133197—28no—
97#13133194—28no—
98#13133193—22no—
99#13133193C2314yes—
100#13133189—28no—
101#13133188—22no—
102#13133188C2314yes—
103Q8×Dic53—22no—
104Q8×Dic53C2314yes—
105D4×Dic53—28no—
106D4×Dic53—22no—
107D4×Dic53C2314yes—
108C4×C22⋊D53D414yes—
109C4×C22⋊D53C2314yes—
110#13133177—28no—
111#13133175—22no—
112#13133175C2314yes—
113C2×C4⋊Dic53—22no—
114C2×C4⋊Dic53—22no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53C2314yes—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2314yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C4⋊C4×D53—22no—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921D411yescharacteristic
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133150C2314yes—
146#13133150C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154C22⋊#88322C2314yes—
155#13133129C2314yes—
156#13133127C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×D4×C53—21no—
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C2×SD16×C53—24no—
162C2×SD16×C53C2314yes—
163C22×C8×C53—24no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169#121×C53—22no—
170#121×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176#106×C53C2314yes—
177#103×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C24×C53C2×D411yescharacteristic
181C23×D53C2×D411yescharacteristic
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—44no—
191C2×D4×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—82no—
204C2×C22⋊D53C2×D414yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—82no—
213C22×Dic53—82no—
214C22×Dic53—82no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C2×C4×D53—22no—
219C2×C4×D53—22no—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C2×C4×D53C2×D412yes—
223C2×C4×D53C2412yes—
224C2×Dic106—24no—
225C2×Dic106—82no—
226SD16×C53—28no—
227C2×C8×C53—22no—
228C2×C8×C53—28no—
229C2×C8×C53#4114yes—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊Dic53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53C2×D414yes—
242#11719921—24no—
243#11719921—24no—
244#11719921C2×D414yes—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919C2×D414yes—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719912—28no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53#13714yes—
278C23×C53C22×D412yes—
279C23×C53C22×D411yescharacteristic
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53C22×D412yes—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—42no—
287D4×C53—22no—
288D4×C53—22no—
289D4×C53—48no—
290D4×C53—42no—
291C2×C4×C53—22no—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C2×#4112yes—
304C2×C4×C532−1+412yes—
305C2×C4×C53C2511yescharacteristic
306C22⋊D53—28no—
307C22⋊D53—84no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—84no—
320C2×Dic53—84no—
321C2×Dic53—84no—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C4×D53—24no—
326C4×D53—22no—
327C4×D53—22no—
328C4×D53—84no—
329Dic106—84no—
330C8×C53—22no—
331C8×C53C2×#4114yes—
332#88322—22no—
333#88322—22no—
334C2×#3346—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—84no—
342C22×C53#54712yes—
343C22×C53C2×#13714yes—
344C22×C53C2×#13712yes—
345C22×C53#57612yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—44no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#54712yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C2×2−1+411yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#554—531no—
366C2×#553—531no—
367#3346—5316no—
368C2×#501—531no—
369C2×#484—531no—
370C2×#481—531no—
371C2×#485—531no—
372C2×#480—531no—
373C2×#479—531no—
374C2×#474—531no—
375C2×#468—531no—
376C2×#465D5311yescharacteristic, complemented
377C2×#440—531no—
378C2×#435—531no—
379C2×#428—531no—
380C22×#107—531no—
381C2×C53—24no—
382C2×C53—82no—
383C2×C53#334614yescomplemented
384C2×C53C2×#54711yescharacteristic
385C2×C53C22×#13711yescharacteristic
386C2×C53C2×#57611yescharacteristic
387D53—42no—
388C22×SD16C2×D5311yescharacteristic
389C22×M16—531no—
390C23×C8C2×D5311yescharacteristic
391#554—538no—
392#554—1064no—
393#553—538no—
394#553—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#125—531no—
398C2×#125—1061no—
399C2×#123—1061no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—1061no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8C2×D5311yescharacteristic
404C2×#121—531no—
405C2×#121—1061no—
406C2×#121C2×D5311yescharacteristic
407C2×C4×Q8—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4—1061no—
411C2×C4×D4—1061no—
412C2×#117—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416#501—538no—
417#485—538no—
418#484—538no—
419#481—538no—
420#480—538no—
421#479—538no—
422#474—538no—
423#468—538no—
424#465C2×D5318yescomplemented
425#440—538no—
426#435—538no—
427#428—538no—
428C2×#107—531no—
429C2×#107—531no—
430C2×#107—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107—531no—
434C2×#107—531no—
435C2×#106—531no—
436C2×#106—531no—
437C2×#106C2×D5311yescharacteristic
438C2×C4⋊C8—531no—
439C2×#103—531no—
440C2×#103—531no—
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102—531no—
444C2×#102C2×D5311yescharacteristic
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×#97—531no—
448C53C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—1061no—
450C22×Q8C22×D5311yescharacteristic
451C22×D4—21no—
452C22×D4—531no—
453C22×D4—1061no—
454C22×D4C22×D5311yescharacteristic
455C23×C4—531no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4C22×D5311yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D5314yes—
463C2×M16—534no—
464C2×M16—1064no—
465C22×C8—24no—
466C22×C8—531no—
467C22×C8—531no—
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5314yes—
470C22×C8C22×D5311yescharacteristic
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#126—1068no—
474#125—534no—
475#125—1062no—
476#125—1068no—
477#123—1068no—
478C22⋊Q8—22no—
479C22⋊Q8—534no—
480C22⋊Q8—1068no—
481C22⋊Q8—1068no—
482C22⋊Q8—1062no—
483C22⋊Q8C22×D5314yes—
484#121—22no—
485#121—534no—
486#121—1062no—
487#121—1068no—
488#121C22×D5314yes—
489C4×Q8—534no—
490C4×Q8—1062no—
491C4×D4—534no—
492C4×D4—534no—
493C4×D4—534no—
494C4×D4—1062no—
495C4×D4—1068no—
496C4×D4—1068no—
497#117—534no—
498#117—1062no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1062no—
518C2×C4⋊C4—1062no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—531no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C42—531no—
530C2×C42—1061no—
531C2×C42—1061no—
532#107—534no—
533#107—534no—
534#107—534no—
535#107—534no—
536#107—534no—
537#107—534no—
538#106—534no—
539#106—534no—
540#106C22×D5314yes—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103C22×D5314yes—
545#102—534no—
546#102—534no—
547#102C22×D5314yes—
548C22⋊C8—534no—
549C22⋊C8—534no—
550#97—534no—
551C24—21no—
552C24—531no—
553C24D4×D5311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—1064no—
558C2×Q8—4242no—
559C2×Q8C23×D5312yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—44no—
565C2×D4—534no—
566C2×D4—1064no—
567C2×D4—1064no—
568C2×D4—4242no—
569C2×D4C23×D5312yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—531no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—1064no—
581C22×C4—1064no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—4242no—
591C22×C4—4242no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4D4×D5312yes—
595C22×C4D4×D5311yescharacteristic
596C22×C4C23×D5312yes—
597C22×C4C23×D5311yescharacteristic
598SD16—28no—
599M16—1068no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—532no—
603C2×C8—532no—
604C2×C8—1062no—
605C2×C8—1062no—
606C2×C8#1171994714yes—
607C2×C8C23×D5312yes—
608C2×C8C23×D5312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—534no—
613C4⋊C4—532no—
614C4⋊C4—532no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1061no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—534no—
634C22⋊C4—534no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—532no—
640C42—532no—
641C42—1064no—
642C42—1064no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—532no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23#1313324614yes—
654C23C2×D4×D5312yes—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—4244no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—1068no—
665D4—4244no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—532no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1064no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—4244no—
690C2×C4—4244no—
691C2×C4—4244no—
692C2×C4—4244no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4C2×D4×D5312yes—
698C2×C4C2×D4×D5311yescharacteristic
699C2×C4C2×#1171994712yes—
700C2×C4#1313326412yes—
701C2×C4C24×D5311yescharacteristic
702C8—22no—
703C8—1062no—
704C8—1062no—
705C8C2×#1171994714yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—1062no—
714C22—1062no—
715C22—1062no—
716C22—2124no—
717C22#1681127312yes—
718C22C2×#1313324614yes—
719C22C2×#1313324612yes—
720C22#1681142512yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1062no—
727C4—1062no—
728C4—1062no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681127312yes—
734C4C22×#1171994711yescharacteristic
735C4C2×#1313326411yescharacteristic
736C2—24no—
737C2—82no—
738C2—2122no—
739C2#2028720614yesdirect product factor
740C2C2×#1681127311yescharacteristic
741C2C22×#1313324611yescharacteristic
742C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
prime radicalC2×#16811325C2
hypercenterC2×#465D53
hypocenterC53C2×#3346
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16811331C2semidirect
3. #20287206C2direct (N × H)
4. C2×#16811030C2semidirect
5. C2×#16810956C2semidirect
6. C2×#16810939C2semidirect
7. C2×#16810963C2semidirect
8. C2×#16810935C2semidirect
9. C2×#16810932C2semidirect
10. C2×#16810901C2semidirect
11. C2×#16810866C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810694C2semidirect
14. C2×#16810662C2semidirect
15. C22×#13133151C2semidirect
16. C2×C53×#465C2semidirect
19. #16811331C22semidirect
41. #16811030C22semidirect
42. #16810963C22semidirect
43. #16810956C22semidirect
44. #16810939C22semidirect
45. #16810935C22semidirect
46. #16810932C22semidirect
47. #16810901C22semidirect
48. #16810866C22semidirect
49. #16810724C22semidirect
50. #16810694C22semidirect
51. #16810662C22semidirect
56. C2×#13133151C22semidirect
73. C53×#465C22semidirect
376. C2×#465D53semidirect
383. C2×C53#3346semidirect
424. #465C2×D53semidirect
448. C53C2×#3346semidirect
739. C2#20287206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168113252
#202872062
C2×#168110302
C2×#168109562
C2×#168109392
C2×#168109632
C2×#168109352
C2×#168109322
C2×#168109012
C2×#168108662
C2×#168107242
C2×#168106942
C2×#168106622
C22×#131331512
C2×C53×#4652
C2×#334653