Finite Group Databasebeta

← C2×#20287225 #28262698

Subgroups — C2×#20287225 #28262698

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×#16811337C211yesmaximal, characteristic
2C2×#16811315C211yesmaximal, characteristic, complemented
3#20287225C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16810939C211yesmaximal, characteristic, complemented
6C2×#16810963C211yesmaximal, characteristic, complemented
7C2×#16810961C211yesmaximal, characteristic, complemented
8C2×#16810946C211yesmaximal, characteristic, complemented
9C2×#16810906C211yesmaximal, characteristic, complemented
10C2×#16810921C211yesmaximal, characteristic, complemented
11C2×#16810849C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810692C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C2×#16810660C211yesmaximal, characteristic, complemented
16C2×C53×#468C211yesmaximal, characteristic, complemented
17C22×C8×D53C2211yescharacteristic
18#16811337—24no—
19#16811337C2218yes—
20#16811315—24no—
21#16811315C2218yescomplemented
22C2×#13133216C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133208—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133204—21no—
27C2×#13133203—21no—
28C2×#13133201—21no—
29C2×#13133193C2211yescharacteristic
30C2×#13133189—21no—
31C2×#13133188C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×C4×C22⋊D53C2211yescharacteristic
35C2×#13133176C2211yescharacteristic
36C2×#13133175C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133173—21no—
39C2×#13133173—21no—
40C22×C4⋊Dic53C2211yescharacteristic
41#16811031C2218yescomplemented
42#16810963C2218yescomplemented
43#16810961C2218yescomplemented
44#16810946C2218yescomplemented
45#16810939C2218yescomplemented
46#16810921C2218yescomplemented
47#16810906C2218yescomplemented
48#16810849C2218yescomplemented
49#16810724C2218yescomplemented
50#16810692C2218yescomplemented
51#16810665C2218yescomplemented
52#16810660C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#468C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×C22⋊D53—21no—
79C22×C22⋊D53D411yescharacteristic
80C23×Dic53—21no—
81C23×Dic53—21no—
82C22×C4×D53C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C2×C8×D53—24no—
86C2×C8×D53C2314yes—
87#13133216—22no—
88#13133216C2314yes—
89#13133212—28no—
90#13133208—28no—
91#13133208—22no—
92#13133208C2314yes—
93#13133204—28no—
94#13133203—28no—
95#13133201—28no—
96#13133193—22no—
97#13133193C2314yes—
98#13133189—28no—
99#13133188—22no—
100#13133188C2314yes—
101Q8×Dic53—22no—
102Q8×Dic53C2314yes—
103D4×Dic53—22no—
104D4×Dic53C2314yes—
105C4×C22⋊D53D414yes—
106C4×C22⋊D53C2314yes—
107#13133176—22no—
108#13133176C2314yes—
109#13133175—22no—
110#13133175—22no—
111#13133175C2314yes—
112#13133175C2314yes—
113#13133173—28no—
114#13133173—28no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53C2314yes—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919D411yescharacteristic
128C2×C22⋊Dic53—21no—
129C2×C22⋊Dic53—21no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53D411yescharacteristic
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921D411yescharacteristic
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133150C2314yes—
144#13133149C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
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—
163C2×M16×C53—24no—
164C2×M16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
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#107×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—42no—
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—44no—
212C22×Dic53—44no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53C2×D412yes—
219C2×C4×D53C2412yes—
220C2×Dic106—24no—
221C2×Dic106—82no—
222SD16×C53—28no—
223M16×C53—28no—
224C2×C8×C53—22no—
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⋊Dic53C2×D414yes—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921C2×D414yes—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—24no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919C2×D414yes—
258C4×Dic53—24no—
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—22no—
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—44no—
305C22⋊D53—84no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—48no—
314C2×Dic53—48no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322C4×D53—24no—
323C4×D53—22no—
324C4×D53—22no—
325Dic106—84no—
326C8×C53—22no—
327C8×C53C2×#4114yes—
328#88322—22no—
329#88322—22no—
330C2×#3348—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×C53#57512yes—
341C22×C53#57712yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—44no—
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×#555—531no—
362C2×#552—531no—
363#3348—5316no—
364C2×#501—531no—
365C2×#481—531no—
366C2×#485—531no—
367C2×#485—531no—
368C2×#482—531no—
369C2×#475—531no—
370C2×#478—531no—
371C2×#468D5311yescharacteristic, complemented
372C2×#465—531no—
373C2×#440—531no—
374C2×#435—531no—
375C2×#428—531no—
376C2×#427—531no—
377C2×C53—42no—
378C2×C53—82no—
379C2×C53#334814yescomplemented
380C2×C53C2×#54711yescharacteristic
381C2×C53C2×#57511yescharacteristic
382C2×C53C2×#57711yescharacteristic
383D53—42no—
384C22×SD16C2×D5311yescharacteristic
385C22×M16C2×D5311yescharacteristic
386C23×C8—531no—
387#555—538no—
388#555—1064no—
389#552—538no—
390#552—1064no—
391C2×C4⋊Q8—531no—
392C2×#126—1061no—
393C2×#125—531no—
394C2×#125—1061no—
395C2×#124—1061no—
396C2×#124—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×#117—531no—
407C2×#117—531no—
408C2×#117—531no—
409C2×#117—1061no—
410C2×#117—1061no—
411C22×C4⋊C4—531no—
412#501—538no—
413#485—538no—
414#485—538no—
415#482—538no—
416#481—538no—
417#478—538no—
418#475—538no—
419#468C2×D5318yescomplemented
420#465—538no—
421#440—538no—
422#435—538no—
423#428—538no—
424#427—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#107C2×D5311yescharacteristic
429C2×#106—531no—
430C2×#106—531no—
431C2×#106—531no—
432C2×#106—531no—
433C2×#106—531no—
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×#97—531no—
444C53C2×#334811yescharacteristic, complemented, Sylow
445C22×Q8—1061no—
446C22×Q8C22×D5311yescharacteristic
447C22×D4—21no—
448C22×D4—531no—
449C22×D4—1061no—
450C22×D4C22×D5311yescharacteristic
451C23×C4—531no—
452C23×C4—1061no—
453C23×C4—1061no—
454C23×C4C22×D5311yescharacteristic
455C2×SD16—24no—
456C2×SD16C22×D5314yes—
457C2×M16—24no—
458C2×M16C22×D5314yes—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—534no—
462C22×C8—1064no—
463C22×C8C22×D5311yescharacteristic
464C22×C8C22×D5311yescharacteristic
465C4⋊Q8—534no—
466C4⋊Q8—1062no—
467#126—1068no—
468#125—534no—
469#125—1062no—
470#125—1068no—
471#124—1068no—
472#124—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—
489#117—534no—
490#117—534no—
491#117—534no—
492#117—1068no—
493#117—1068no—
494#117—1062no—
495#117—1062no—
496#117—1062no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
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—1062no—
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—531no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C42—531no—
524C2×C42—1061no—
525C2×C42—1061no—
526C2×C42—1061no—
527C2×C42—1061no—
528#107—534no—
529#107—534no—
530#107—534no—
531#107C22×D5314yes—
532#106—534no—
533#106—534no—
534#106—534no—
535#106—534no—
536#106—534no—
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—
546#97—534no—
547C24—21no—
548C24—531no—
549C24D4×D5311yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—1064no—
554C2×Q8—4242no—
555C2×Q8C23×D5312yes—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—82no—
561C2×D4—534no—
562C2×D4—1064no—
563C2×D4—4242no—
564C2×D4—2122no—
565C2×D4C23×D5312yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—1064no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1064no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—2124no—
585C22×C4—2124no—
586C22×C4D4×D5312yes—
587C22×C4D4×D5311yescharacteristic
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—28no—
591M16—28no—
592C2×C8—22no—
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—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1064no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4C23×D5312yes—
620C4⋊C4C23×D5312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—534no—
624C22⋊C4—534no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C42—532no—
632C42—532no—
633C42—1064no—
634C42—1064no—
635C42—1064no—
636C42—1064no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—532no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—4244no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—84no—
658D4—4244no—
659D4—2124no—
660C2×C4—22no—
661C2×C4—24no—
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—532no—
671C2×C4—532no—
672C2×C4—532no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1064no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—2128no—
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—1062no—
707C22—1062no—
708C22—1062no—
709C22—2124no—
710C22#1681127312yes—
711C22#1681142212yes—
712C22#1681143312yes—
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—2122no—
731C2#2028722514yesdirect product factor
732C2C2×#1681127311yescharacteristic
733C2C2×#1681142211yescharacteristic
734C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#468C2
socleC23×C53C22×D4
prime radicalC2×#16811337C2
hypercenterC2×#468D53
hypocenterC53C2×#3348
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
2. C2×#16811315C2semidirect
3. #20287225C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16810939C2semidirect
6. C2×#16810963C2semidirect
7. C2×#16810961C2semidirect
8. C2×#16810946C2semidirect
9. C2×#16810906C2semidirect
10. C2×#16810921C2semidirect
11. C2×#16810849C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810692C2semidirect
14. C2×#16810665C2semidirect
15. C2×#16810660C2semidirect
16. C2×C53×#468C2semidirect
21. #16811315C22semidirect
41. #16811031C22semidirect
42. #16810963C22semidirect
43. #16810961C22semidirect
44. #16810946C22semidirect
45. #16810939C22semidirect
46. #16810921C22semidirect
47. #16810906C22semidirect
48. #16810849C22semidirect
49. #16810724C22semidirect
50. #16810692C22semidirect
51. #16810665C22semidirect
52. #16810660C22semidirect
73. C53×#468C22semidirect
371. C2×#468D53semidirect
379. C2×C53#3348semidirect
419. #468C2×D53semidirect
444. C53C2×#3348semidirect
731. C2#20287225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113372
C2×#168113152
#202872252
C2×#168110312
C2×#168109392
C2×#168109632
C2×#168109612
C2×#168109462
C2×#168109062
C2×#168109212
C2×#168108492
C2×#168107242
C2×#168106922
C2×#168106652
C2×#168106602
C2×C53×#4682
C2×#334853