Finite Group Databasebeta

← C2×#20287278 #28262773

Subgroups — C2×#20287278 #28262773

Order 13568.

1898 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×#16811321C211yesmaximal, characteristic
2C2×#16811307C211yesmaximal, characteristic, complemented
3#20287278C2116yesmaximal, direct product factor
4C2×#16811023C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810948C211yesmaximal, characteristic, complemented
8C2×#16810932C211yesmaximal, characteristic, complemented
9C2×#16810922C211yesmaximal, characteristic, complemented
10C2×#16810872C211yesmaximal, characteristic, complemented
11C2×#16810871C211yesmaximal, characteristic, complemented
12C2×#16810708C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810663C211yesmaximal, characteristic, complemented
15C2×#16810662C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20#16811321—24no—
21#16811321C2218yes—
22#16811307—24no—
23#16811307C2218yescomplemented
24C2×#13133212—21no—
25C2×#13133210—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133202—21no—
30C2×#13133199—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133191—21no—
34C2×#13133191C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133176C2211yescharacteristic
40C2×#13133175—21no—
41C2×#13133175C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811023C2218yescomplemented
44#16810962C2218yescomplemented
45#16810948C2218yescomplemented
46#16810943C2218yescomplemented
47#16810932C2218yescomplemented
48#16810922C2218yescomplemented
49#16810872C2218yescomplemented
50#16810871C2218yescomplemented
51#16810708C2218yescomplemented
52#16810698C2218yescomplemented
53#16810663C2218yescomplemented
54#16810662C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#483C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×D212—21no—
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53D411yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C22×C4×D53C2311yescharacteristic
84C2×#11719924—24no—
85C2×#11719924C2314yes—
86C2×#11719917—24no—
87C2×#11719917C2314yes—
88C2×#11719912—24no—
89C2×#11719912C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133212—28no—
93#13133210—28no—
94#13133208—22no—
95#13133208—22no—
96#13133208C2314yes—
97#13133208C2314yes—
98#13133207—28no—
99#13133202—28no—
100#13133199—28no—
101#13133193—22no—
102#13133193C2314yes—
103#13133192—22no—
104#13133192C2314yes—
105#13133191—22no—
106#13133191—28no—
107#13133191C2314yes—
108Q8×Dic53—22no—
109Q8×Dic53C2314yes—
110#13133179—22no—
111#13133179C2314yes—
112C4×C22⋊D53—28no—
113C4×C22⋊D53D414yes—
114C4×C22⋊D53C2314yes—
115#13133176—22no—
116#13133176C2314yes—
117#13133175—28no—
118#13133175—22no—
119#13133175C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921D411yescharacteristic
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133146C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53C2314yes—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174#106×C53C2314yes—
175#106×C53C2314yes—
176#103×C53C2314yes—
177#103×C53C2314yes—
178C22⋊C8×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53—21no—
181C23×D53C2×D411yescharacteristic
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—82no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—42no—
200C2×C22⋊D53—44no—
201C2×C22⋊D53C2×D414yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—21no—
211C2×D212—24no—
212C2×D212—82no—
213C2×D212C2412yes—
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—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53C2412yes—
225C2×C8×C53C2412yes—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C22⋊C4×C53—24no—
235C22⋊Dic53—24no—
236C22⋊Dic53C2×D414yes—
237#11719924—28no—
238#11719921—24no—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921C2×D414yes—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919C2×D414yes—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263#11719917—28no—
264C2×#88322—22no—
265C2×#88322#4114yes—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268#11719912—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53C22×D412yes—
273C23×C53C22×D411yescharacteristic
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53C22×D412yes—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—42no—
285C2×C4×C53—22no—
286C2×C4×C53—24no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—84no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C22⋊D53—44no—
304C22⋊D53—48no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317D212—22no—
318D212—22no—
319D212—42no—
320D212—84no—
321C4×D53—24no—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—48no—
325C4×D53—84no—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322C2×#4114yes—
330C2×#3351—531nomaximal, Sylow
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—44no—
335C22×C53#54712yes—
336C22×C53#57512yes—
337C22×C53#57712yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—44no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#54712yes—
353C4×C53C22×#4111yescharacteristic
354C4×C53C2×2−1+411yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#553—531no—
362C2×#552—531no—
363#3351—5316no—
364C2×#499—531no—
365C2×#481—531no—
366C2×#485—531no—
367C2×#482—531no—
368C2×#483D5311yescharacteristic, complemented
369C2×#479—531no—
370C2×#478—531no—
371C2×#468—531no—
372C2×#468—531no—
373C2×C4×SD16—531no—
374C2×#436—531no—
375C2×#428—531no—
376C2×#428—531no—
377C2×C53—42no—
378C2×C53#335114yescomplemented
379C2×C53C2×#54711yescharacteristic
380C2×C53C2×#57511yescharacteristic
381C2×C53C2×#57711yescharacteristic
382D53—42no—
383D53—82no—
384C22×SD16—531no—
385C22×M16—531no—
386C22×M16—531no—
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—531no—
402C2×#121—1061no—
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⋊C4C2×D5311yescharacteristic
412#499—538no—
413#485—538no—
414#483C2×D5318yescomplemented
415#482—538no—
416#481—538no—
417#479—538no—
418#478—538no—
419#468—538no—
420#468—538no—
421C4×SD16—538no—
422#436—538no—
423#428—538no—
424#428—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#107—531no—
429C2×#106—531no—
430C2×#106—531no—
431C2×#106—531no—
432C2×#106C2×D5311yescharacteristic
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103C2×D5311yescharacteristic
437C2×#103C2×D5311yescharacteristic
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8C2×D5311yescharacteristic
443C2×C4×C8—531no—
444C53C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8C22×D5311yescharacteristic
446C22×D4—531no—
447C22×D4—531no—
448C22×D4—1061no—
449C22×D4—1061no—
450C23×C4—21no—
451C23×C4—531no—
452C23×C4—1061no—
453C23×C4—1061no—
454C23×C4C22×D5311yescharacteristic
455C2×SD16—534no—
456C2×SD16—1064no—
457C2×M16—534no—
458C2×M16—534no—
459C2×M16—1064no—
460C2×M16—1064no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8C22×D5311yescharacteristic
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—534no—
479#121—534no—
480#121—1062no—
481#121—1068no—
482#121—1062no—
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—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1061no—
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⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C4⋊C4C22×D5314yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—1061no—
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#106C22×D5314yes—
536#106C22×D5314yes—
537C4⋊C8—534no—
538#103—534no—
539#103C22×D5314yes—
540#103C22×D5314yes—
541#102—534no—
542#102—534no—
543#102—534no—
544C22⋊C8—534no—
545C22⋊C8C22×D5314yes—
546C4×C8—534no—
547C24—531no—
548C24—1061no—
549C24D4×D5311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D5312yes—
554C2×D4—534no—
555C2×D4—532no—
556C2×D4—1064no—
557C2×D4—1064no—
558C2×D4—1061no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—4242no—
562C2×D4—2122no—
563C2×D4—2124no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—532no—
576C22×C4—532no—
577C22×C4—1064no—
578C22×C4—1064no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—4242no—
585C22×C4—2124no—
586C22×C4D4×D5312yes—
587C22×C4D4×D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591M16—1068no—
592M16—1068no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—534no—
596C2×C8—532no—
597C2×C8—532no—
598C2×C8—1062no—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—534no—
607C4⋊C4—532no—
608C4⋊C4—532no—
609C4⋊C4—532no—
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⋊C4C23×D5312yes—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C22⋊C4—24no—
624C22⋊C4—534no—
625C22⋊C4—534no—
626C22⋊C4—1064no—
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—532no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—1062no—
654D4—1062no—
655D4—4244no—
656D4—2124no—
657D4—2128no—
658D4—2122no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—84no—
672C2×C4—532no—
673C2×C4—532no—
674C2×C4—532no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1064no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—4244no—
685C2×C4—2128no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4C2×D4×D5312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4#41×D5312yes—
692C2×C4#1313326412yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—22no—
696C8—534no—
697C8—1062no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—1062no—
703C22—1062no—
704C22—1062no—
705C22—4244no—
706C22—2122no—
707C22—2122no—
708C22—2122no—
709C22—2124no—
710C22#1681127112yes—
711C22#1681142212yes—
712C22#1681142912yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1062no—
720C4—1062no—
721C4—1062no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127112yes—
726C4C2×#41×D5311yescharacteristic
727C4C2×#1313326411yescharacteristic
728C2—42no—
729C2—4242no—
730C2—2122no—
731C2#2028727814yesdirect product factor
732C2C2×#1681127111yescharacteristic
733C2C2×#1681142211yescharacteristic
734C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
prime radicalC2×#16811321C2
hypercenterC2×#483D53
hypocenterC53C2×#3351
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#16811307C2semidirect
3. #20287278C2direct (N × H)
4. C2×#16811023C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810948C2semidirect
8. C2×#16810932C2semidirect
9. C2×#16810922C2semidirect
10. C2×#16810872C2semidirect
11. C2×#16810871C2semidirect
12. C2×#16810708C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810663C2semidirect
15. C2×#16810662C2semidirect
16. C2×C53×#483C2semidirect
23. #16811307C22semidirect
43. #16811023C22semidirect
44. #16810962C22semidirect
45. #16810948C22semidirect
46. #16810943C22semidirect
47. #16810932C22semidirect
48. #16810922C22semidirect
49. #16810872C22semidirect
50. #16810871C22semidirect
51. #16810708C22semidirect
52. #16810698C22semidirect
53. #16810663C22semidirect
54. #16810662C22semidirect
71. C53×#483C22semidirect
368. C2×#483D53semidirect
378. C2×C53#3351semidirect
414. #483C2×D53semidirect
444. C53C2×#3351semidirect
731. C2#20287278direct (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×#168113072
#202872782
C2×#168110232
C2×#168109432
C2×#168109622
C2×#168109482
C2×#168109322
C2×#168109222
C2×#168108722
C2×#168108712
C2×#168107082
C2×#168106982
C2×#168106632
C2×#168106622
C2×C53×#4832
C2×#335153