Finite Group Databasebeta

← C2×#20287089 #28262534

Subgroups — C2×#20287089 #28262534

Order 13568.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811320C211yesmaximal, characteristic
2C2×#16811307C211yesmaximal, characteristic, complemented
3#20287089C2116yesmaximal, direct product factor
4C2×#16811023C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810961C211yesmaximal, characteristic, complemented
7C2×#16810944C211yesmaximal, characteristic, complemented
8C2×#16810935C211yesmaximal, characteristic, complemented
9C2×#16810932C211yesmaximal, characteristic, complemented
10C2×#16810921C211yesmaximal, characteristic, complemented
11C2×#16810849C211yesmaximal, characteristic, complemented
12C2×SD16×Dic53C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
14C2×#16810661C211yesmaximal, characteristic, complemented
15C2×#106×D53C211yesmaximal, characteristic, complemented
16C2×C53×#465C211yesmaximal, characteristic, complemented
17C22×C8×D53C2211yescharacteristic
18#16811320—24no—
19#16811320C2218yes—
20#16811307—24no—
21#16811307C2218yescomplemented
22C2×#13133210—21no—
23C2×#13133210—21no—
24C2×#13133208C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133199—21no—
28C2×#13133198—21no—
29C2×#13133193C2211yescharacteristic
30C2×#13133188—21no—
31C2×#13133188C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×C4×C22⋊D53C2211yescharacteristic
35C2×#13133177—21no—
36C2×#13133176C2211yescharacteristic
37C2×#13133176C2211yescharacteristic
38C2×#13133175—21no—
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811023C2218yescomplemented
42#16810961C2218yescomplemented
43#16810957C2218yescomplemented
44#16810944C2218yescomplemented
45#16810935C2218yescomplemented
46#16810932C2218yescomplemented
47#16810921C2218yescomplemented
48#16810849C2218yescomplemented
49SD16×Dic53C2218yescomplemented
50C8×C22⋊D53C2218yescomplemented
51#16810661C2218yescomplemented
52C2×#13133151C2211yescharacteristic
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60#106×D53C2218yescomplemented
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
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×C22⋊D53—21no—
78C22×C22⋊D53D411yescharacteristic
79C23×Dic53—21no—
80C22×C4×D53—21no—
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C2×C8×D53—24no—
86C2×C8×D53C2314yes—
87#13133210—28no—
88#13133210—28no—
89#13133208—22no—
90#13133208—22no—
91#13133208C2314yes—
92#13133208C2314yes—
93#13133207—28no—
94#13133199—28no—
95#13133198—28no—
96#13133193—22no—
97#13133193C2314yes—
98#13133188—28no—
99#13133188—22no—
100#13133188C2314yes—
101Q8×Dic53—22no—
102Q8×Dic53C2314yes—
103D4×Dic53—22no—
104D4×Dic53C2314yes—
105C4×C22⋊D53D414yes—
106C4×C22⋊D53C2314yes—
107#13133177—28no—
108#13133176—22no—
109#13133176—22no—
110#13133176C2314yes—
111#13133176C2314yes—
112#13133175—28no—
113C2×C4⋊Dic53—21no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53C2311yescharacteristic
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×#11719919—21no—
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919D411yescharacteristic
126C4⋊C4×D53—22no—
127C4⋊C4×D53—22no—
128C4⋊C4×D53C2314yes—
129C4⋊C4×D53C2314yes—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921D411yescharacteristic
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133150C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154C22⋊#88322C2314yes—
155#13133129C2314yes—
156C8×Dic53C2314yes—
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—82no—
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—44no—
204C2×C22⋊D53C2×D414yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—82no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53—24no—
217C2×C4×D53—24no—
218C2×C4×D53—44no—
219C2×C4×D53—82no—
220C2×C4×D53C2×D412yes—
221C2×C4×D53C2412yes—
222SD16×C53—28no—
223C2×C8×C53—22no—
224C2×C8×C53—28no—
225C2×C8×C53#4114yes—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—24no—
235C22⋊Dic53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53C2×D414yes—
240#11719921—24no—
241#11719921C2×D414yes—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919C2×D414yes—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53C2×D412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C8×D53—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D412yes—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53#13514yes—
281C22×D53C22×D412yes—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—42no—
285D4×C53—22no—
286D4×C53—22no—
287D4×C53—42no—
288D4×C53—84no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C2×#4112yes—
302C2×C4×C532−1+412yes—
303C2×C4×C53C2511yescharacteristic
304C22⋊D53—28no—
305C22⋊D53—48no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—84no—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C4×D53—24no—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—48no—
325C4×D53—84no—
326C8×C53—22no—
327C8×C53C2×#4114yes—
328#88322—22no—
329#88322—22no—
330C2×#3337—531nomaximal, Sylow
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—44no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—84no—
339C22×C53#54712yes—
340C22×C53C2×#13512yes—
341C22×C53#57712yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—28no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53C2×#13514yes—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53#54712yes—
352C4×C53C22×#4111yescharacteristic
353C4×C53C2×2−1+411yescharacteristic
354Dic53—22no—
355Dic53—22no—
356Dic53—22no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#553—531no—
362C2×#552—531no—
363#3337—5316no—
364C2×#499—531no—
365C2×#484—531no—
366C2×#485—531no—
367C2×#482—531no—
368C2×#480—531no—
369C2×#479—531no—
370C2×#478—531no—
371C2×#465—531no—
372C2×#465D5311yescharacteristic, complemented
373C2×C4×SD16—531no—
374C2×C8×D4—531no—
375C2×#427—531no—
376C22×#106—531no—
377C2×C53—42no—
378C2×C53—82no—
379C2×C53#333714yescomplemented
380C2×C53C2×#54711yescharacteristic
381C2×C53C22×#13511yescharacteristic
382C2×C53C2×#57711yescharacteristic
383D53—24no—
384C22×SD16C2×D5311yescharacteristic
385C23×C8—531no—
386C23×C8C2×D5311yescharacteristic
387#553—538no—
388#553—1064no—
389#552—538no—
390#552—1064no—
391C2×#126—1061no—
392C2×#126—1061no—
393C2×#125—531no—
394C2×#125—531no—
395C2×#125—1061no—
396C2×#123—1061no—
397C2×#123—1061no—
398C2×C22⋊Q8—531no—
399C2×C22⋊Q8C2×D5311yescharacteristic
400C2×#121—531no—
401C2×#121—1061no—
402C2×#121C2×D5311yescharacteristic
403C2×C4×Q8—531no—
404C2×C4×D4—531no—
405C2×C4×D4—531no—
406C2×C4×D4—1061no—
407C2×#117—531no—
408C2×#117—531no—
409C2×#117—1061no—
410C22×C4⋊C4—531no—
411C22×C4⋊C4—531no—
412#499—538no—
413#485—538no—
414#484—538no—
415#482—538no—
416#480—538no—
417#479—538no—
418#478—538no—
419#465—538no—
420#465C2×D5318yescomplemented
421C4×SD16—538no—
422C8×D4—538no—
423#427—538no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#106—531no—
429C2×#106—531no—
430C2×#106—531no—
431C2×#106—531no—
432C2×#106—538no—
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103C2×D5311yescharacteristic
438C2×#102—531no—
439C2×#102—531no—
440C2×#102C2×D5311yescharacteristic
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C4×C8—531no—
444C53C2×#333711yescharacteristic, complemented, Sylow
445C22×Q8C22×D5311yescharacteristic
446C22×D4—21no—
447C22×D4—531no—
448C22×D4—1061no—
449C22×D4C22×D5311yescharacteristic
450C23×C4—531no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4—1061no—
454C23×C4C22×D5311yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D5314yes—
457C22×C8—24no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—534no—
461C22×C8—1064no—
462C22×C8C22×D5311yescharacteristic
463C22×C8C22×D5314yes—
464C22×C8C22×D5311yescharacteristic
465#126—1068no—
466#126—1068no—
467#125—534no—
468#125—534no—
469#125—1062no—
470#125—1062no—
471#125—1068no—
472#123—1068no—
473#123—1068no—
474C22⋊Q8—22no—
475C22⋊Q8—534no—
476C22⋊Q8—1062no—
477C22⋊Q8C22×D5314yes—
478#121—22no—
479#121—534no—
480#121—1062no—
481#121—1068no—
482#121C22×D5314yes—
483C4×Q8—534no—
484C4×Q8—1062no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—534no—
488C4×D4—1062no—
489C4×D4—1068no—
490#117—534no—
491#117—534no—
492#117—1068no—
493#117—1062no—
494#117—1062no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C4⋊C4C22×D5311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—531no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C42—531no—
525C2×C42—1061no—
526C2×C42—1061no—
527C2×C42—1061no—
528#107—534no—
529#107—534no—
530#107—534no—
531#107—534no—
532#106—534no—
533#106—534no—
534#106—534no—
535#106—534no—
536#106C22×D5314yes—
537C4⋊C8—534no—
538#103—534no—
539#103—534no—
540#103C22×D5314yes—
541#102—534no—
542#102—534no—
543#102C22×D5314yes—
544C22⋊C8—534no—
545C22⋊C8—534no—
546C4×C8—534no—
547C24—21no—
548C24—531no—
549C24D4×D5311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D5312yes—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—82no—
559C2×D4—534no—
560C2×D4—1064no—
561C2×D4—1064no—
562C2×D4—2124no—
563C2×D4C23×D5312yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—531no—
572C22×C4—532no—
573C22×C4—532no—
574C22×C4—1064no—
575C22×C4—1064no—
576C22×C4—1064no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—4242no—
584C22×C4—4242no—
585C22×C4—2124no—
586C22×C4D4×D5312yes—
587C22×C4D4×D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—28no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—1062no—
596C2×C8—1062no—
597C2×C8—1068no—
598C2×C8#1171994714yes—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—534no—
605C4⋊C4—532no—
606C4⋊C4—532no—
607C4⋊C4—532no—
608C4⋊C4—532no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—534no—
626C22⋊C4—534no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C22⋊C4—1064no—
632C42—532no—
633C42—532no—
634C42—1064no—
635C42—1064no—
636C42—1064no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—534no—
645C23—532no—
646C23—1062no—
647C23—1062no—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—84no—
657D4—1068no—
658D4—2128no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—532no—
670C2×C4—532no—
671C2×C4—532no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1064no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—4244no—
683C2×C4—4244no—
684C2×C4—2128no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4C2×D4×D5312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×#1171994712yes—
692C2×C4#1313326412yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—1062no—
696C8—1062no—
697C8C2×#1171994714yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—84no—
706C22—534no—
707C22—1068no—
708C22—1062no—
709C22—1062no—
710C22#1681127312yes—
711C22#135×D5312yes—
712C22#1681142912yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—1062no—
719C4—1062no—
720C4—1062no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127312yes—
726C4C22×#1171994711yescharacteristic
727C4C2×#1313326411yescharacteristic
728C2—42no—
729C2—82no—
730C2—1064no—
731C2#2028708914yesdirect product factor
732C2C2×#1681127311yescharacteristic
733C2C2×#135×D5311yescharacteristic
734C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
prime radicalC2×#16811320C2
hypercenterC2×#465D53
hypocenterC53C2×#3337
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
2. C2×#16811307C2semidirect
3. #20287089C2direct (N × H)
4. C2×#16811023C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810961C2semidirect
7. C2×#16810944C2semidirect
8. C2×#16810935C2semidirect
9. C2×#16810932C2semidirect
10. C2×#16810921C2semidirect
11. C2×#16810849C2semidirect
12. C2×SD16×Dic53C2semidirect
13. C2×C8×C22⋊D53C2semidirect
14. C2×#16810661C2semidirect
15. C2×#106×D53C2semidirect
16. C2×C53×#465C2semidirect
21. #16811307C22semidirect
41. #16811023C22semidirect
42. #16810961C22semidirect
43. #16810957C22semidirect
44. #16810944C22semidirect
45. #16810935C22semidirect
46. #16810932C22semidirect
47. #16810921C22semidirect
48. #16810849C22semidirect
49. SD16×Dic53C22semidirect
50. C8×C22⋊D53C22semidirect
51. #16810661C22semidirect
60. #106×D53C22semidirect
73. C53×#465C22semidirect
372. C2×#465D53semidirect
379. C2×C53#3337semidirect
420. #465C2×D53semidirect
444. C53C2×#3337semidirect
731. C2#20287089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113202
C2×#168113072
#202870892
C2×#168110232
C2×#168109572
C2×#168109612
C2×#168109442
C2×#168109352
C2×#168109322
C2×#168109212
C2×#168108492
C2×SD16×Dic532
C2×C8×C22⋊D532
C2×#168106612
C2×#106×D532
C2×C53×#4652
C2×#333753