Finite Group Databasebeta

← C2×#20287081 #28262525

Subgroups — C2×#20287081 #28262525

Order 13568.

1866 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811315C211yesmaximal, characteristic
2C2×#16811308C211yesmaximal, characteristic
3#20287081C2116yesmaximal, direct product factor
4C2×#16811023C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810954C211yesmaximal, characteristic, complemented
8C2×#16810933C211yesmaximal, characteristic, complemented
9C2×#16810928C211yesmaximal, characteristic, complemented
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810862C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic
14C2×#16810658C211yesmaximal, characteristic, complemented
15C22×#13133150C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811315—24no—
21#16811315C2218yes—
22#16811308—24no—
23#16811308C2218yes—
24C2×#13133212—21no—
25C2×#13133212—21no—
26C2×#13133208—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133208C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133201—21no—
31C2×#13133200—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133193C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×C4×C22⋊D53C2211yescharacteristic
38C2×#13133176—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×#13133173—21no—
42C22×C4⋊Dic53C2211yescharacteristic
43#16811023C2218yescomplemented
44#16810967C2218yescomplemented
45#16810962C2218yescomplemented
46#16810954C2218yescomplemented
47#16810933C2218yescomplemented
48#16810928C2218yescomplemented
49#16810863C2218yescomplemented
50#16810862C2218yescomplemented
51#16810715C2218yescomplemented
52#16810686C2218yes—
53#16810658C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133150C2218yescomplemented
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
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×Dic106C2311yescharacteristic
78C22×C22⋊D53D411yescharacteristic
79C23×Dic53—21no—
80C22×C4×D53C2311yescharacteristic
81C2×#11719925—24no—
82C2×#11719925C2314yes—
83C22×#88322—24no—
84C22×#88322C2311yescharacteristic
85C22×#88322C2314yes—
86C22×#88322C2311yescharacteristic
87C2×C8×D53—24no—
88C2×C8×D53C2314yes—
89#13133212—28no—
90#13133212—28no—
91#13133208—28no—
92#13133208—22no—
93#13133208—22no—
94#13133208C2314yes—
95#13133208C2314yes—
96#13133207—28no—
97#13133201—28no—
98#13133200—28no—
99#13133197—22no—
100#13133197C2314yes—
101#13133196—22no—
102#13133196C2314yes—
103#13133193—22no—
104#13133193C2314yes—
105Q8×Dic53—22no—
106Q8×Dic53C2314yes—
107#13133182—22no—
108#13133182C2314yes—
109C4×C22⋊D53D414yes—
110C4×C22⋊D53C2314yes—
111#13133176—28no—
112#13133175—22no—
113#13133175—22no—
114#13133175C2314yes—
115#13133175C2314yes—
116#13133173—28no—
117C2×C4⋊Dic53—22no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2314yes—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
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×D53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—24no—
192C22×C4×C53—44no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53C2×D414yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—24no—
204C22×Dic53—44no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53C2×D412yes—
211C2×C4×D53C2412yes—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—21no—
215C2×Dic106C2412yes—
216C2×C8×C53—22no—
217C2×C8×C53—22no—
218C2×C8×C53C2412yes—
219C2×C8×C53C2412yes—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C2412yes—
226C4⋊C4×C53C2412yes—
227C4⋊C4×C53C2412yes—
228C22⋊C4×C53—24no—
229C22⋊Dic53—24no—
230C22⋊Dic53C2×D414yes—
231#11719925—28no—
232#11719921—24no—
233#11719921—24no—
234#11719921—24no—
235#11719921—24no—
236#11719921C2×D414yes—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—24no—
240C4⋊Dic53—21no—
241C4⋊Dic53—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53—24no—
244C4⋊Dic53—24no—
245C4⋊Dic53C2412yes—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248#11719919—24no—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919C2×D414yes—
254C4×Dic53—24no—
255C4×Dic53—24no—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53C2×D412yes—
259C4×Dic53C2412yes—
260C2×#88322—22no—
261C2×#88322—28no—
262C2×#88322#4114yes—
263C2×#88322C2412yes—
264C2×#88322C2412yes—
265C8×D53—28no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53#13514yes—
269C23×C53C22×D412yes—
270C23×C53C22×D411yescharacteristic
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53C22×D412yes—
275Q8×C53—22no—
276Q8×C53—22no—
277Q8×C53—42no—
278C2×C4×C53—22no—
279C2×C4×C53—24no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—42no—
287C2×C4×C53—48no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D411yescharacteristic
293C2×C4×C53C2×#4112yes—
294C2×C4×C532−1+412yes—
295C2×C4×C53C2511yescharacteristic
296C22⋊D53—28no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—42no—
305C2×Dic53—48no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53C22×D412yes—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C4×D53—24no—
313C4×D53—22no—
314C4×D53—22no—
315Dic106—22no—
316Dic106—22no—
317Dic106—42no—
318C8×C53—22no—
319C8×C53—22no—
320#88322—22no—
321#88322C2×#4114yes—
322C2×#3336—531nomaximal, Sylow
323C22×C53—28no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53#54712yes—
327C22×C53C2×#13514yes—
328C22×C53C2×#13512yes—
329C22×C53#57812yes—
330C22×C53C23×D411yescharacteristic
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—22no—
334C2×D53—44no—
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53#54712yes—
341C4×C53C22×#4111yescharacteristic
342C4×C53C2×2−1+411yescharacteristic
343Dic53—22no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350C2×#552—531no—
351C2×#552—531no—
352#3336—5316no—
353C2×#499—531no—
354C2×#485—531no—
355C2×#485—531no—
356C2×#483—531no—
357C2×#483D5311yescharacteristic, complemented
358C2×#479—531no—
359C2×#479—531no—
360C2×#467—531no—
361C2×#467—531no—
362C2×C4×Q16—531no—
363C2×C8×D4—531no—
364C2×#427—531no—
365C22×#107—531no—
366C2×C53—24no—
367C2×C53#333614yescomplemented
368C2×C53C2×#54711yescharacteristic
369C2×C53C22×#13511yescharacteristic
370C2×C53C2×#57811yescharacteristic
371D53—42no—
372C22×Q16—531no—
373C23×C8—531no—
374C23×C8—531no—
375#552—538no—
376#552—538no—
377#552—1064no—
378#552—1064no—
379C2×#126—1061no—
380C2×#126—1061no—
381C2×#125—531no—
382C2×#125—531no—
383C2×#125—1061no—
384C2×#125—1061no—
385C2×#123—1061no—
386C2×#123—1061no—
387C2×C22⋊Q8—531no—
388C2×C22⋊Q8—531no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×C4×Q8—531no—
392C2×C4×Q8—531no—
393C2×C4×D4—531no—
394C2×#117—531no—
395C2×#117—531no—
396C2×#117—1061no—
397C2×#117—1061no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4C2×D5311yescharacteristic
400#499—538no—
401#485—538no—
402#485—538no—
403#483—538no—
404#483C2×D5318yescomplemented
405#479—538no—
406#479—538no—
407#467—538no—
408#467—538no—
409C4×Q16—538no—
410C8×D4—538no—
411#427—538no—
412C2×#107—531no—
413C2×#107—531no—
414C2×#107—538no—
415C2×#107—531no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#106—531no—
419C2×#106—531no—
420C2×#106C2×D5311yescharacteristic
421C2×#106C2×D5311yescharacteristic
422C2×C4⋊C8—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103C2×D5311yescharacteristic
428C2×#103C2×D5311yescharacteristic
429C2×C22⋊C8—531no—
430C2×C22⋊C8C2×D5311yescharacteristic
431C2×C4×C8—531no—
432C53C2×#333611yescharacteristic, complemented, Sylow
433C22×Q8—531no—
434C22×Q8C22×D5311yescharacteristic
435C22×D4—531no—
436C23×C4—21no—
437C23×C4—531no—
438C23×C4—1061no—
439C23×C4C22×D5311yescharacteristic
440C2×Q16—534no—
441C2×Q16—1064no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—534no—
445C22×C8—534no—
446C22×C8—1064no—
447C22×C8—1064no—
448C22×C8C22×D5311yescharacteristic
449C22×C8C22×D5311yescharacteristic
450#126—1068no—
451#126—1068no—
452#125—534no—
453#125—534no—
454#125—1062no—
455#125—1062no—
456#125—1068no—
457#125—1068no—
458#123—1068no—
459#123—1068no—
460C22⋊Q8—22no—
461C22⋊Q8—534no—
462C22⋊Q8—534no—
463C22⋊Q8—534no—
464C22⋊Q8—1062no—
465C22⋊Q8—1062no—
466C22⋊Q8—1062no—
467C22⋊Q8C22×D5314yes—
468C4×Q8—534no—
469C4×Q8—534no—
470C4×Q8—1062no—
471C4×Q8—1062no—
472C4×D4—534no—
473C4×D4—534no—
474#117—534no—
475#117—534no—
476#117—1068no—
477#117—1068no—
478#117—1062no—
479#117—1062no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—534no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—1061no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1062no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C4⋊C4C22×D5314yes—
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—531no—
505C2×C22⋊C4—531no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C42—531no—
512C2×C42—1061no—
513C2×C42—1061no—
514C2×C42—1061no—
515C2×C42—1061no—
516#107—534no—
517#107—534no—
518#107—534no—
519#107—534no—
520#107—534no—
521#106—534no—
522#106—534no—
523#106C22×D5314yes—
524#106C22×D5314yes—
525C4⋊C8—534no—
526#103—534no—
527#103—534no—
528#103—534no—
529#103—534no—
530#103C22×D5314yes—
531#103C22×D5314yes—
532C22⋊C8—534no—
533C22⋊C8C22×D5314yes—
534C4×C8—534no—
535C24—531no—
536C24D4×D5311yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—532no—
541C2×Q8—1061no—
542C2×Q8—1062no—
543C2×Q8—1062no—
544C2×Q8C23×D5312yes—
545C2×D4—534no—
546C2×D4—1064no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—44no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1064no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—2124no—
568C22×C4D4×D5312yes—
569C22×C4D4×D5311yescharacteristic
570C22×C4C23×D5312yes—
571C22×C4C23×D5311yescharacteristic
572Q16—1068no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—534no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1068no—
579C2×C8—1068no—
580C2×C8—1062no—
581C2×C8C23×D5312yes—
582C2×C8C23×D5312yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—534no—
589C4⋊C4—532no—
590C4⋊C4—532no—
591C4⋊C4—532no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1064no—
603C4⋊C4—1061no—
604C4⋊C4—1064no—
605C4⋊C4C23×D5312yes—
606C4⋊C4C23×D5312yes—
607C4⋊C4C23×D5312yes—
608C22⋊C4—24no—
609C22⋊C4—534no—
610C22⋊C4—534no—
611C22⋊C4—1064no—
612C22⋊C4—1064no—
613C22⋊C4—1064no—
614C22⋊C4—1064no—
615C22⋊C4—1064no—
616C42—532no—
617C42—532no—
618C42—1064no—
619C42—1064no—
620C42—1064no—
621C42—1064no—
622C23—22no—
623C23—22no—
624C23—532no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23#1313323814yes—
629C23C2×D4×D5312yes—
630C23C2×D4×D5311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—1062no—
635Q8—1062no—
636Q8—2122no—
637D4—1068no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—48no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—532no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1064no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—2122no—
665C2×C4—2128no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4C2×D4×D5312yes—
670C2×C4C2×D4×D5311yescharacteristic
671C2×C4#41×D5312yes—
672C2×C4#1313326412yes—
673C2×C4C24×D5311yescharacteristic
674C8—22no—
675C8—22no—
676C8—534no—
677C8—1062no—
678C22—28no—
679C22—22no—
680C22—22no—
681C22—1062no—
682C22—1062no—
683C22—1062no—
684C22—2124no—
685C22#1681127112yes—
686C22C2×#1313323814yes—
687C22C2×#1313323812yes—
688C22#1681143912yes—
689C22C22×D4×D5311yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1062no—
696C4—1062no—
697C4—1062no—
698C4—2122no—
699C4—2122no—
700C4—2122no—
701C4—2122no—
702C4#1681127112yes—
703C4C2×#41×D5311yescharacteristic
704C4C2×#1313326411yescharacteristic
705C2—24no—
706C2—2122no—
707C2#2028708114yesdirect product factor
708C2C2×#1681127111yescharacteristic
709C2C22×#1313323811yescharacteristic
710C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#483D53
hypocenterC53C2×#3336
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
3. #20287081C2direct (N × H)
4. C2×#16811023C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810954C2semidirect
8. C2×#16810933C2semidirect
9. C2×#16810928C2semidirect
10. C2×#16810863C2semidirect
11. C2×#16810862C2semidirect
12. C2×#16810715C2semidirect
14. C2×#16810658C2semidirect
15. C22×#13133150C2semidirect
16. C2×C53×#483C2semidirect
43. #16811023C22semidirect
44. #16810967C22semidirect
45. #16810962C22semidirect
46. #16810954C22semidirect
47. #16810933C22semidirect
48. #16810928C22semidirect
49. #16810863C22semidirect
50. #16810862C22semidirect
51. #16810715C22semidirect
53. #16810658C22semidirect
59. C2×#13133150C22semidirect
71. C53×#483C22semidirect
357. C2×#483D53semidirect
367. C2×C53#3336semidirect
404. #483C2×D53semidirect
432. C53C2×#3336semidirect
707. C2#20287081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113152
C2×#168113082
#202870812
C2×#168110232
C2×#168109672
C2×#168109622
C2×#168109542
C2×#168109332
C2×#168109282
C2×#168108632
C2×#168108622
C2×#168107152
C2×#168106862
C2×#168106582
C22×#131331502
C2×C53×#4832
C2×#333653