Finite Group Databasebeta

← C2×#20287229 #28262702

Subgroups — C2×#20287229 #28262702

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×#16811339C211yesmaximal, characteristic
2C2×#16811311C211yesmaximal, characteristic, complemented
3#20287229C2116yesmaximal, direct product factor
4C2×#16810943C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810966C211yesmaximal, characteristic, complemented
7C2×#16810950C211yesmaximal, characteristic, complemented
8C2×#16810905C211yesmaximal, characteristic, complemented
9C2×#16810920C211yesmaximal, characteristic, complemented
10C2×#16810870C211yesmaximal, characteristic, complemented
11C2×#16810853C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C2×#16810660C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811339—24no—
21#16811339C2218yes—
22#16811311—24no—
23#16811311C2218yescomplemented
24C2×#13133212—21no—
25C2×#13133208—21no—
26C2×#13133206—21no—
27C2×#13133206—21no—
28C2×#13133202—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133197C2211yescharacteristic
31C2×#13133192—21no—
32C2×#13133192C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133175—21no—
38C2×#13133175—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810967C2218yescomplemented
44#16810966C2218yescomplemented
45#16810950C2218yescomplemented
46#16810943C2218yescomplemented
47#16810920C2218yescomplemented
48#16810905C2218yescomplemented
49#16810870C2218yescomplemented
50#16810853C2218yescomplemented
51#16810725C2218yescomplemented
52#16810696C2218yescomplemented
53#16810662C2218yescomplemented
54#16810660C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212D411yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C22×C4×D53C2311yescharacteristic
86C2×#11719913—24no—
87C2×#11719913C2314yes—
88C2×#11719912—24no—
89C2×#11719912C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C2×C8×D53—24no—
93C2×C8×D53C2314yes—
94#13133212—28no—
95#13133208—28no—
96#13133206—28no—
97#13133206—28no—
98#13133202—28no—
99#13133197—22no—
100#13133197—22no—
101#13133197C2314yes—
102#13133197C2314yes—
103#13133192—28no—
104#13133192—22no—
105#13133192—22no—
106#13133192C2314yes—
107#13133192C2314yes—
108C4×Dic106—22no—
109C4×Dic106C2314yes—
110C4×D212—22no—
111C4×D212D414yes—
112C4×D212C2314yes—
113C4×D212C2314yes—
114#13133175—28no—
115#13133175—28no—
116#13133175—22no—
117#13133175—22no—
118#13133175—22no—
119#13133175C2314yes—
120#13133175C2314yes—
121#13133175C2314yes—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53C2314yes—
131C2×#11719921—21no—
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×#11719921D411yescharacteristic
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145#13133151C2314yes—
146#13133150C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150C4⋊#88322C2314yes—
151#13133142C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133139C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133129C2314yes—
158#13133129C2314yes—
159C22×Q8×C53—21no—
160C22×C8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C4⋊Q8×C53—22no—
163C4⋊Q8×C53C2314yes—
164#125×C53—22no—
165#125×C53C2314yes—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#107×C53C2314yes—
175#107×C53C2314yes—
176#106×C53C2314yes—
177#106×C53C2314yes—
178#97×C53C2314yes—
179C23×D53—21no—
180C23×D53C2×D411yescharacteristic
181C23×D53C2×D411yescharacteristic
182C2×Q8×C53—24no—
183C2×Q8×C53—82no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2411yescharacteristic
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53C2×D411yescharacteristic
195C22×Dic53C2×D411yescharacteristic
196C2×D212—22no—
197C2×D212—22no—
198C2×D212—21no—
199C2×D212—24no—
200C2×D212—24no—
201C2×D212—42no—
202C2×D212—82no—
203C2×D212—82no—
204C2×D212C2×D414yes—
205C2×D212C2412yes—
206C2×C4×D53—22no—
207C2×C4×D53—22no—
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—24no—
211C2×C4×D53—24no—
212C2×C4×D53—44no—
213C2×C4×D53—44no—
214C2×C4×D53C2×D412yes—
215C2×C4×D53C2×D412yes—
216C2×C4×D53C2412yes—
217C2×C4×D53C2412yes—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—21no—
221C2×Dic106C2412yes—
222C2×C8×C53—22no—
223C2×C8×C53#4114yes—
224C2×C8×C53C2412yes—
225C2×C8×C53C2412yes—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C42×C53C2×D412yes—
238C42×C53C2412yes—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921C2×D414yes—
248#11719921C2×D414yes—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2×D414yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266#11719913—28no—
267#11719912—28no—
268C8×D53—28no—
269C23×C53C22×D411yescharacteristic
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53C22×D412yes—
281C22×D53C22×D412yes—
282Q8×C53—84no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C2×#4112yes—
297C2×C4×C532−1+412yes—
298C2×C4×C53C2511yescharacteristic
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53C22×D412yes—
308C2×Dic53C22×D412yes—
309D212—22no—
310D212—22no—
311D212—44no—
312D212—42no—
313D212—84no—
314D212—84no—
315C4×D53—24no—
316C4×D53—24no—
317C4×D53—22no—
318C4×D53—22no—
319C4×D53—22no—
320C4×D53—22no—
321C4×D53—48no—
322C4×D53—48no—
323Dic106—22no—
324Dic106—22no—
325Dic106—42no—
326C8×C53—22no—
327C8×C53C2×#4114yes—
328#88322—22no—
329#88322—22no—
330C2×#3348—531nomaximal, Sylow
331C22×C53#54712yes—
332C22×C53#57512yes—
333C22×C53#57712yes—
334C22×C53C23×D411yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—22no—
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—44no—
342C2×D53—44no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53#54712yes—
354C4×C53C22×#4111yescharacteristic
355C4×C53C2×2−1+411yescharacteristic
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#555—531no—
362C2×#552—531no—
363#3348—5316no—
364C2×#501D5311yescharacteristic, complemented
365C2×#481—531no—
366C2×#485—531no—
367C2×#485—531no—
368C2×#482—531no—
369C2×#475—531no—
370C2×#478—531no—
371C2×#468—531no—
372C2×#465—531no—
373C2×#440—531no—
374C2×#435—531no—
375C2×#428—531no—
376C2×#427—531no—
377C2×C53#334814yescomplemented
378C2×C53C2×#54711yescharacteristic
379C2×C53C2×#57511yescharacteristic
380C2×C53C2×#57711yescharacteristic
381D53—42no—
382D53—42no—
383D53—82no—
384C22×SD16—531no—
385C22×M16—531no—
386C23×C8—531no—
387#555—538no—
388#555—1064no—
389#552—538no—
390#552—1064no—
391C2×C4⋊Q8C2×D5311yescharacteristic
392C2×#126—1061no—
393C2×#125—1061no—
394C2×#125C2×D5311yescharacteristic
395C2×#124—1061no—
396C2×#124—1061no—
397C2×#123—1061no—
398C2×C22⋊Q8—531no—
399C2×C22⋊Q8—531no—
400C2×#121—531no—
401C2×#121—531no—
402C2×#121—1061no—
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#501C2×D5318yescomplemented
413#485—538no—
414#485—538no—
415#482—538no—
416#481—538no—
417#478—538no—
418#475—538no—
419#468—538no—
420#465—538no—
421#440—538no—
422#435—538no—
423#428—538no—
424#427—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107C2×D5311yescharacteristic
428C2×#107C2×D5311yescharacteristic
429C2×#106—531no—
430C2×#106—531no—
431C2×#106—531no—
432C2×#106C2×D5311yescharacteristic
433C2×#106C2×D5311yescharacteristic
434C2×C4⋊C8—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×#97C2×D5311yescharacteristic
444C53C2×#334811yescharacteristic, complemented, Sylow
445C22×Q8—21no—
446C22×Q8—531no—
447C22×D4—531no—
448C22×D4—531no—
449C22×D4—1061no—
450C22×D4—1061no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—1061no—
454C23×C4—1061no—
455C2×SD16—534no—
456C2×SD16—1064no—
457C2×M16—534no—
458C2×M16—1064no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—534no—
462C22×C8—1064no—
463C22×C8C22×D5311yescharacteristic
464C22×C8C22×D5311yescharacteristic
465C4⋊Q8—22no—
466C4⋊Q8C22×D5314yes—
467#126—1068no—
468#125—22no—
469#125—1068no—
470#125C22×D5314yes—
471#124—1068no—
472#124—1068no—
473#123—1068no—
474C22⋊Q8—534no—
475C22⋊Q8—534no—
476C22⋊Q8—1062no—
477C22⋊Q8—1062no—
478#121—534no—
479#121—534no—
480#121—1062no—
481#121—1062no—
482#121—1068no—
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—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4C22×D5311yescharacteristic
510C2×C4⋊C4C22×D5311yescharacteristic
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C22⋊C4—531no—
514C2×C22⋊C4—531no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
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—1061no—
524C2×C42—1061no—
525C2×C42—1061no—
526C2×C42—1061no—
527C2×C42C22×D5311yescharacteristic
528#107—534no—
529#107—534no—
530#107C22×D5314yes—
531#107C22×D5314yes—
532#106—534no—
533#106—534no—
534#106—534no—
535#106C22×D5314yes—
536#106C22×D5314yes—
537C4⋊C8—534no—
538#103—534no—
539#103—534no—
540#103—534no—
541#102—534no—
542#102—534no—
543#102—534no—
544C22⋊C8—534no—
545C22⋊C8—534no—
546#97C22×D5314yes—
547C24—531no—
548C24—531no—
549C24—1061no—
550C2×Q8—24no—
551C2×Q8—82no—
552C2×Q8—532no—
553C2×Q8—1061no—
554C2×Q8—1062no—
555C2×Q8—1062no—
556C2×D4—534no—
557C2×D4—532no—
558C2×D4—1064no—
559C2×D4—1064no—
560C2×D4—1061no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—4242no—
564C2×D4—4242no—
565C2×D4—2122no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—531no—
571C22×C4—531no—
572C22×C4—532no—
573C22×C4—532no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—1064no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1064no—
585C22×C4—2124no—
586C22×C4—2124no—
587C22×C4D4×D5311yescharacteristic
588C22×C4D4×D5311yescharacteristic
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591M16—1068no—
592C2×C8—22no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—1062no—
596C2×C8—1062no—
597C2×C8—1068no—
598C2×C8#1171994914yes—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—534no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1064no—
617C4⋊C4C23×D5312yes—
618C4⋊C4C23×D5312yes—
619C4⋊C4C23×D5312yes—
620C4⋊C4C23×D5312yes—
621C22⋊C4—534no—
622C22⋊C4—534no—
623C22⋊C4—1064no—
624C22⋊C4—1064no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C42—1064no—
632C42—1064no—
633C42—1064no—
634C42—1064no—
635C42D4×D5312yes—
636C42C23×D5312yes—
637C23—532no—
638C23—532no—
639C23—1062no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—2122no—
647C23—2122no—
648C23—2122no—
649C23C2×D4×D5311yescharacteristic
650Q8—84no—
651Q8—1062no—
652Q8—1062no—
653Q8—2122no—
654D4—1062no—
655D4—1062no—
656D4—4244no—
657D4—4244no—
658D4—2124no—
659D4—2122no—
660C2×C4—22no—
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—42no—
670C2×C4—532no—
671C2×C4—532no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—1062no—
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×C4C2×D4×D5312yes—
689C2×C4C2×D4×D5312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×#1171994912yes—
692C2×C4#1313326512yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—1062no—
696C8—1062no—
697C8C2×#1171994914yes—
698C22—1062no—
699C22—1062no—
700C22—1062no—
701C22—1062no—
702C22—1062no—
703C22—1062no—
704C22—4244no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22—2124no—
709C22—2124no—
710C22#1681127612yes—
711C22#1681142212yes—
712C22#1681143312yes—
713C22C22×D4×D5311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—1062no—
721C4—1062no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127612yes—
726C4C22×#1171994911yescharacteristic
727C4C2×#1313326511yescharacteristic
728C2—4242no—
729C2—2122no—
730C2—2122no—
731C2#2028722914yesdirect product factor
732C2C2×#1681127611yescharacteristic
733C2C2×#1681142211yescharacteristic
734C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
prime radicalC2×#16811339C2
hypercenterC2×#501D53
hypocenterC53C2×#3348
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
2. C2×#16811311C2semidirect
3. #20287229C2direct (N × H)
4. C2×#16810943C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810966C2semidirect
7. C2×#16810950C2semidirect
8. C2×#16810905C2semidirect
9. C2×#16810920C2semidirect
10. C2×#16810870C2semidirect
11. C2×#16810853C2semidirect
12. C2×#16810725C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810662C2semidirect
15. C2×#16810660C2semidirect
16. C2×C53×#501C2semidirect
23. #16811311C22semidirect
43. #16810967C22semidirect
44. #16810966C22semidirect
45. #16810950C22semidirect
46. #16810943C22semidirect
47. #16810920C22semidirect
48. #16810905C22semidirect
49. #16810870C22semidirect
50. #16810853C22semidirect
51. #16810725C22semidirect
52. #16810696C22semidirect
53. #16810662C22semidirect
54. #16810660C22semidirect
71. C53×#501C22semidirect
364. C2×#501D53semidirect
377. C2×C53#3348semidirect
412. #501C2×D53semidirect
444. C53C2×#3348semidirect
731. C2#20287229direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113392
C2×#168113112
#202872292
C2×#168109432
C2×#168109672
C2×#168109662
C2×#168109502
C2×#168109052
C2×#168109202
C2×#168108702
C2×#168108532
C2×#168107252
C2×#168106962
C2×#168106622
C2×#168106602
C2×C53×#5012
C2×#334853