Finite Group Databasebeta

← C2×#20287166 #28262635

Subgroups — C2×#20287166 #28262635

Order 13568.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic
2C2×#16811308C211yesmaximal, characteristic
3#20287166C2116yesmaximal, direct product factor
4C2×#16811030C211yesmaximal, characteristic, complemented
5C2×#16810958C211yesmaximal, characteristic, complemented
6C2×#16810967C211yesmaximal, characteristic, complemented
7C2×#16810955C211yesmaximal, characteristic, complemented
8C2×#16810953C211yesmaximal, characteristic, complemented
9C2×#16810933C211yesmaximal, characteristic, complemented
10C2×#16810907C211yesmaximal, characteristic, complemented
11C2×#16810882C211yesmaximal, characteristic, complemented
12C2×#16810864C211yesmaximal, characteristic, complemented
13C2×#16810729C211yesmaximal, characteristic, complemented
14C2×#16810694C211yesmaximal, characteristic
15C2×#16810662C211yesmaximal, characteristic, complemented
16C22×#106×C53C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19#16811328—24no—
20#16811328C2218yes—
21#16811308—24no—
22#16811308C2218yes—
23C2×#13133216C2211yescharacteristic
24C2×#13133212—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133207—21no—
28C2×#13133200—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133197C2211yescharacteristic
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133182C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133176—21no—
40C2×#13133175C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16811030C2218yescomplemented
43#16810967C2218yescomplemented
44#16810958C2218yescomplemented
45#16810955C2218yescomplemented
46#16810953C2218yescomplemented
47#16810933C2218yescomplemented
48#16810907C2218yescomplemented
49#16810882C2218yescomplemented
50#16810864C2218yescomplemented
51#16810729C2218yescomplemented
52#16810694C2218yes—
53#16810662C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C23×C8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#106×C53C2218yescomplemented
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×C22⋊D53D411yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C2×Dic212—24no—
84C2×Dic212C2314yes—
85C2×#11719912—24no—
86C2×#11719912C2314yes—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89#13133216—22no—
90#13133216C2314yes—
91#13133212—28no—
92#13133208—22no—
93#13133208C2314yes—
94#13133207—28no—
95#13133207—28no—
96#13133200—28no—
97#13133197—22no—
98#13133197—22no—
99#13133197C2314yes—
100#13133197C2314yes—
101#13133196—28no—
102#13133196—22no—
103#13133196—22no—
104#13133196C2314yes—
105#13133196C2314yes—
106#13133195—28no—
107#13133182—22no—
108#13133182—22no—
109#13133182C2314yes—
110#13133182C2314yes—
111C4×C22⋊D53—28no—
112C4×C22⋊D53D414yes—
113C4×C22⋊D53C2314yes—
114#13133176—28no—
115#13133175—22no—
116#13133175C2314yes—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C4⋊C4×D53—22no—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53D411yescharacteristic
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yes—
144#13133150C2314yes—
145#13133150C2314yes—
146#13133148C2314yes—
147#13133148C2314yes—
148#13133146C2314yes—
149#13133142C2314yes—
150#13133142C2314yes—
151#13133140C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133140C2314yes—
155C22⋊#88322C2314yes—
156#13133129C2314yes—
157#13133127C2314yes—
158C23×C4×C53—21no—
159C23×C4×C53—21no—
160C23×C4×C53C2311yescharacteristic
161C22×C8×C53—24no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2314yes—
164C22×C8×C53C2311yescharacteristic
165C2×C4⋊C4×C53—22no—
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×C53C2314yes—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175#106×C53C2314yes—
176#106×C53C2314yes—
177#106×C53C2314yes—
178#106×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53C2×D411yescharacteristic
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—24no—
188C22×C4×C53—24no—
189C22×C4×C53—44no—
190C22×C4×C53—82no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53C2×D414yes—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×C4×D53—22no—
205C2×C4×D53—22no—
206C2×C4×D53—24no—
207C2×C4×D53—82no—
208C2×C4×D53C2×D412yes—
209C2×C4×D53C2412yes—
210C2×Dic106—22no—
211C2×Dic106—22no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—21no—
215C2×Dic106—21no—
216C2×Dic106—24no—
217C2×Dic106—82no—
218C2×Dic106C2412yes—
219C2×Dic106C2412yes—
220C2×C8×C53—22no—
221C2×C8×C53—28no—
222C2×C8×C53#4114yes—
223C2×C8×C53C2412yes—
224C2×C8×C53C2412yes—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C22⋊Dic53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53C2×D414yes—
238#11719921—24no—
239#11719921—24no—
240#11719921—24no—
241#11719921C2×D414yes—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919C2×D414yes—
257C4×Dic53—24no—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53C2×D412yes—
261C4×Dic53C2412yes—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266Dic212—28no—
267#11719912—28no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53#13714yes—
271C23×C53C22×D412yes—
272C23×C53C22×D411yescharacteristic
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53C22×D412yes—
277C2×C4×C53—22no—
278C2×C4×C53—24no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—48no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—84no—
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—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53C22×D412yes—
309C2×Dic53C22×D412yes—
310C2×Dic53C22×D412yes—
311C4×D53—24no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—84no—
315Dic106—22no—
316Dic106—22no—
317Dic106—22no—
318Dic106—22no—
319Dic106—42no—
320Dic106—42no—
321Dic106—84no—
322C8×C53—22no—
323C8×C53C2×#4114yes—
324#88322—22no—
325#88322—22no—
326C2×#3344—531nomaximal, Sylow
327C22×C53—28no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53#54712yes—
331C22×C53C2×#13714yes—
332C22×C53C2×#13712yes—
333C22×C53#57712yes—
334C22×C53C23×D411yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—44no—
339C4×C53—22no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53#54712yes—
345C4×C53C22×#4111yescharacteristic
346C4×C53C2×2−1+411yescharacteristic
347Dic53—22no—
348Dic53—22no—
349Dic53—22no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354C2×#554—531no—
355C2×#552—531no—
356#3344—5316no—
357C2×#501—531no—
358C2×#484—531no—
359C2×#485—531no—
360C2×#483—531no—
361C2×#483—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#470—531no—
365C2×#467—531no—
366C2×#441—531no—
367C2×#435—531no—
368C2×#428—531no—
369C22×#106D5311yescharacteristic, complemented
370C2×C53—24no—
371C2×C53#334414yescomplemented
372C2×C53C2×#54711yescharacteristic
373C2×C53C22×#13711yescharacteristic
374C2×C53C2×#57711yescharacteristic
375D53—42no—
376C22×Q16—531no—
377C22×M16—531no—
378C23×C8C2×D5311yescharacteristic
379#554—538no—
380#554—1064no—
381#552—538no—
382#552—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#125—531no—
386C2×#125—1061no—
387C2×#125—1061no—
388C2×#123—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391C2×C22⋊Q8—531no—
392C2×C22⋊Q8—531no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×D4—531no—
398C2×C4×D4—1061no—
399C2×#117—531no—
400C2×#117—1061no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4C2×D5311yescharacteristic
403C22×C4⋊C4C2×D5311yescharacteristic
404#501—538no—
405#485—538no—
406#484—538no—
407#483—538no—
408#483—538no—
409#479—538no—
410#475—538no—
411#470—538no—
412#467—538no—
413#441—538no—
414#435—538no—
415#428—538no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106C2×D5311yescharacteristic
422C2×#106C2×D5311yescharacteristic
423C2×#106C2×D5311yescharacteristic
424C2×#106C2×D5311yescharacteristic
425C2×#106C2×D5318yescomplemented
426C2×C4⋊C8—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×C22⋊C8—531no—
434C2×C22⋊C8—531no—
435C2×#97—531no—
436C53C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8—531no—
439C22×Q8—1061no—
440C22×D4—531no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—531no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×Q16—534no—
447C2×Q16—1064no—
448C2×M16—534no—
449C2×M16—1064no—
450C22×C8—24no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5314yes—
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—534no—
457C4⋊Q8—1062no—
458#126—1068no—
459#125—534no—
460#125—1062no—
461#125—1068no—
462#125—1068no—
463#123—1068no—
464C22⋊Q8—534no—
465C22⋊Q8—534no—
466C22⋊Q8—534no—
467C22⋊Q8—534no—
468C22⋊Q8—1068no—
469C22⋊Q8—1068no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C22⋊Q8—1062no—
473C22⋊Q8—1062no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×D4—534no—
479C4×D4—534no—
480C4×D4—1068no—
481#117—534no—
482#117—1068no—
483#117—1062no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C4⋊C4C22×D5314yes—
508C2×C4⋊C4C22×D5314yes—
509C2×C22⋊C4—531no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520#107—534no—
521#107—534no—
522#107—534no—
523#106—534no—
524#106—534no—
525#106C22×D5314yes—
526#106C22×D5314yes—
527#106C22×D5314yes—
528#106C22×D5314yes—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536C22⋊C8—534no—
537C22⋊C8—534no—
538#97—534no—
539C24—531no—
540C24D4×D5311yescharacteristic
541C2×Q8—532no—
542C2×Q8—532no—
543C2×Q8—1064no—
544C2×Q8—1061no—
545C2×Q8—1061no—
546C2×Q8—1062no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—4242no—
551C2×D4—534no—
552C2×D4—1064no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—531no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—1064no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—4242no—
576C22×C4D4×D5312yes—
577C22×C4D4×D5311yescharacteristic
578C22×C4C23×D5312yes—
579C22×C4C23×D5311yescharacteristic
580Q16—1068no—
581M16—1068no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—1062no—
587C2×C8—1062no—
588C2×C8#1171994514yes—
589C2×C8C23×D5312yes—
590C2×C8C23×D5312yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—534no—
598C4⋊C4—532no—
599C4⋊C4—532no—
600C4⋊C4—1064no—
601C4⋊C4—1064no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4C23×D5312yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C4⋊C4C23×D5312yes—
616C22⋊C4—534no—
617C22⋊C4—534no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—532no—
624C42—532no—
625C42—1064no—
626C42—1064no—
627C42—1064no—
628C23—22no—
629C23—22no—
630C23—532no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23#1313324614yes—
635C23C2×D4×D5312yes—
636C23C2×D4×D5311yescharacteristic
637Q8—1062no—
638Q8—1062no—
639Q8—1062no—
640Q8—1062no—
641Q8—4244no—
642Q8—2122no—
643Q8—2122no—
644D4—1068no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—532no—
660C2×C4—532no—
661C2×C4—532no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1064no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—4244no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4—2122no—
677C2×C4C2×D4×D5312yes—
678C2×C4C2×D4×D5311yescharacteristic
679C2×C4C2×#1171994512yes—
680C2×C4#1313326512yes—
681C2×C4C24×D5311yescharacteristic
682C8—22no—
683C8—1062no—
684C8—1062no—
685C8C2×#1171994514yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—1062no—
690C22—1062no—
691C22—1062no—
692C22—2124no—
693C22#1681127412yes—
694C22C2×#1313324614yes—
695C22C2×#1313324612yes—
696C22#1681142912yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681127412yes—
711C4C22×#1171994511yescharacteristic
712C4C2×#1313326511yescharacteristic
713C2—24no—
714C2—2122no—
715C2#2028716614yesdirect product factor
716C2C2×#1681127411yescharacteristic
717C2C22×#1313324611yescharacteristic
718C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#106×C53C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC22×#106D53
hypocenterC53C2×#3344
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #20287166C2direct (N × H)
4. C2×#16811030C2semidirect
5. C2×#16810958C2semidirect
6. C2×#16810967C2semidirect
7. C2×#16810955C2semidirect
8. C2×#16810953C2semidirect
9. C2×#16810933C2semidirect
10. C2×#16810907C2semidirect
11. C2×#16810882C2semidirect
12. C2×#16810864C2semidirect
13. C2×#16810729C2semidirect
15. C2×#16810662C2semidirect
16. C22×#106×C53C2semidirect
42. #16811030C22semidirect
43. #16810967C22semidirect
44. #16810958C22semidirect
45. #16810955C22semidirect
46. #16810953C22semidirect
47. #16810933C22semidirect
48. #16810907C22semidirect
49. #16810882C22semidirect
50. #16810864C22semidirect
51. #16810729C22semidirect
53. #16810662C22semidirect
76. C2×#106×C53C22semidirect
369. C22×#106D53semidirect
371. C2×C53#3344semidirect
425. C2×#106C2×D53semidirect
436. C53C2×#3344semidirect
715. C2#20287166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168113082
#202871662
C2×#168110302
C2×#168109582
C2×#168109672
C2×#168109552
C2×#168109532
C2×#168109332
C2×#168109072
C2×#168108822
C2×#168108642
C2×#168107292
C2×#168106942
C2×#168106622
C22×#106×C532
C2×#334453