Finite Group Databasebeta

← C2×#20287323 #28262823

Subgroups — C2×#20287323 #28262823

Order 13568.

1866 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×#16811344C211yesmaximal, characteristic
2C2×#16811328C211yesmaximal, characteristic
3#20287323C2116yesmaximal, direct product factor
4C2×#16811020C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810952C211yesmaximal, characteristic, complemented
8C2×#16810916C211yesmaximal, characteristic, complemented
9C2×#16810907C211yesmaximal, characteristic, complemented
10C2×#16810880C211yesmaximal, characteristic, complemented
11C2×#16810879C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic
14C2×#16810663C211yesmaximal, characteristic, complemented
15C2×#16810662C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20#16811344—24no—
21#16811344C2218yes—
22#16811328—24no—
23#16811328C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133210—21no—
28C2×#13133207—21no—
29C2×#13133203—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133195—21no—
34C2×#13133193C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133182—21no—
37C2×#13133182C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×#13133176C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811020C2218yescomplemented
44#16810967C2218yescomplemented
45#16810965C2218yescomplemented
46#16810952C2218yescomplemented
47#16810916C2218yescomplemented
48#16810907C2218yescomplemented
49#16810880C2218yescomplemented
50#16810879C2218yescomplemented
51#16810715C2218yescomplemented
52#16810698C2218yes—
53#16810663C2218yescomplemented
54#16810662C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
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×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×C22⋊D53D411yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C2×#11719925—24no—
84C2×#11719925C2314yes—
85C2×#11719917—24no—
86C2×#11719917C2314yes—
87C2×#11719912—24no—
88C2×#11719912C2314yes—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133216—22no—
92#13133216—22no—
93#13133216C2314yes—
94#13133216C2314yes—
95#13133212—28no—
96#13133210—28no—
97#13133207—28no—
98#13133203—28no—
99#13133197—22no—
100#13133197C2314yes—
101#13133196—28no—
102#13133196—22no—
103#13133196C2314yes—
104#13133195—28no—
105#13133193—22no—
106#13133193C2314yes—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109#13133182—28no—
110#13133182—22no—
111#13133182C2314yes—
112C4×C22⋊D53—28no—
113C4×C22⋊D53D414yes—
114C4×C22⋊D53C2314yes—
115#13133176—22no—
116#13133176C2314yes—
117#13133175—22no—
118#13133175C2314yes—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
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⋊Dic53—21no—
135C2×C22⋊Dic53D411yescharacteristic
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#13133151C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
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×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2314yes—
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—82no—
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×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205C22×Dic53C2×D411yescharacteristic
206C2×C4×D53—22no—
207C2×C4×D53—22no—
208C2×C4×D53—24no—
209C2×C4×D53—82no—
210C2×C4×D53C2×D412yes—
211C2×C4×D53C2412yes—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—21no—
215C2×Dic106—24no—
216C2×Dic106—24no—
217C2×Dic106—44no—
218C2×Dic106—82no—
219C2×Dic106C2412yes—
220C2×C8×C53—22no—
221C2×C8×C53—22no—
222C2×C8×C53C2412yes—
223C2×C8×C53C2412yes—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2412yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊Dic53—24no—
234C22⋊Dic53—24no—
235C22⋊Dic53C2×D414yes—
236#11719925—28no—
237#11719921—24no—
238#11719921—24no—
239#11719921—24no—
240#11719921C2×D414yes—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919C2×D414yes—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53C2×D412yes—
261C4×Dic53C2412yes—
262#11719917—28no—
263C2×#88322—22no—
264C2×#88322#4114yes—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267#11719912—28no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53C22×D412yes—
272C23×C53C22×D411yescharacteristic
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53C22×D412yes—
277Q8×C53—22no—
278Q8×C53—22no—
279Q8×C53—42no—
280C2×C4×C53—22no—
281C2×C4×C53—24no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—84no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4112yes—
296C2×C4×C532−1+412yes—
297C2×C4×C53C2511yescharacteristic
298C22⋊D53—28no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53#13714yes—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313C4×D53—24no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—84no—
317Dic106—22no—
318Dic106—22no—
319Dic106—42no—
320Dic106—48no—
321Dic106—84no—
322C8×C53—22no—
323C8×C53—22no—
324#88322—22no—
325#88322C2×#4114yes—
326C2×#3356—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—44no—
331C22×C53#54712yes—
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—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53C2×#13714yes—
354C2×#556—531no—
355C2×#554—531no—
356#3356—5316no—
357C2×#498—531no—
358C2×#485—531no—
359C2×#485—531no—
360C2×#483—531no—
361C2×#483D5311yescharacteristic, complemented
362C2×#477—531no—
363C2×#475—531no—
364C2×#470—531no—
365C2×#470—531no—
366C2×C4×Q16—531no—
367C2×#436—531no—
368C2×#428—531no—
369C2×#428—531no—
370C2×C53—42no—
371C2×C53#335614yescomplemented
372C2×C53C2×#54711yescharacteristic
373C2×C53C22×#13711yescharacteristic
374C2×C53C2×#57711yescharacteristic
375D53—42no—
376C22×Q16—531no—
377C22×M16—531no—
378C22×M16—531no—
379#556—538no—
380#556—1064no—
381#554—538no—
382#554—1064no—
383C2×C4⋊Q8—531no—
384C2×C4⋊Q8—531no—
385C2×#126—1061no—
386C2×#126—1061no—
387C2×#125—1061no—
388C2×#124—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391C2×C22⋊Q8—531no—
392C2×C22⋊Q8—1061no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8C2×D5311yescharacteristic
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×Q8—1061no—
398C2×C4×D4—531no—
399C2×C4×D4—1061no—
400C2×#117—531no—
401C2×#117—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4C2×D5311yescharacteristic
404#498—538no—
405#485—538no—
406#485—538no—
407#483—538no—
408#483C2×D5318yescomplemented
409#477—538no—
410#475—538no—
411#470—538no—
412#470—538no—
413C4×Q16—538no—
414#436—538no—
415#428—538no—
416#428—538no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—531no—
424C2×#106C2×D5311yescharacteristic
425C2×#106C2×D5311yescharacteristic
426C2×C4⋊C8—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#103C2×D5311yescharacteristic
432C2×#103C2×D5311yescharacteristic
433C2×C22⋊C8—531no—
434C2×C22⋊C8C2×D5311yescharacteristic
435C2×C4×C8—531no—
436C53C2×#335611yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8—1061no—
439C22×Q8—1061no—
440C22×Q8C22×D5311yescharacteristic
441C22×D4—531no—
442C23×C4—21no—
443C23×C4—531no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×Q16—534no—
447C2×Q16—1064no—
448C2×M16—534no—
449C2×M16—534no—
450C2×M16—1064no—
451C2×M16—1064no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—534no—
457C4⋊Q8—534no—
458C4⋊Q8—1062no—
459C4⋊Q8—1062no—
460#126—1068no—
461#126—1068no—
462#125—1068no—
463#124—1068no—
464C22⋊Q8—22no—
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⋊Q8C22×D5314yes—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×Q8—1068no—
479C4×D4—534no—
480C4×D4—534no—
481C4×D4—1068no—
482#117—534no—
483#117—534no—
484#117—1062no—
485#117—1062no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—534no—
494C2×C4⋊C4—1062no—
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×D5314yes—
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—531no—
509C2×C22⋊C4—531no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—531no—
516C2×C42—1061no—
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#106—534no—
526#106—534no—
527#106C22×D5314yes—
528#106C22×D5314yes—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103C22×D5314yes—
535#103C22×D5314yes—
536C22⋊C8—534no—
537C22⋊C8C22×D5314yes—
538C4×C8—534no—
539C24—531no—
540C24D4×D5311yescharacteristic
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—532no—
545C2×Q8—1064no—
546C2×Q8—1064no—
547C2×Q8—1061no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—4242no—
551C2×Q8—2124no—
552C2×Q8C23×D5312yes—
553C2×D4—534no—
554C2×D4—1064no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
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—
582M16—1068no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—534no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1062no—
589C2×C8C23×D5312yes—
590C2×C8C23×D5312yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—534no—
597C4⋊C4—532no—
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—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1064no—
611C4⋊C4C23×D5312yes—
612C4⋊C4C23×D5312yes—
613C4⋊C4C23×D5312yes—
614C22⋊C4—24no—
615C22⋊C4—534no—
616C22⋊C4—534no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C42—532no—
623C42—532no—
624C42—1064no—
625C42—1064no—
626C42—1064no—
627C42—1064no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—532no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23C2×D4×D5312yes—
636C23C2×D4×D5311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—1062no—
641Q8—1062no—
642Q8—4244no—
643Q8—2128no—
644Q8—2122no—
645D4—1068no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—534no—
660C2×C4—532no—
661C2×C4—532no—
662C2×C4—532no—
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×C4#41×D5312yes—
680C2×C4#1313326412yes—
681C2×C4C24×D5311yescharacteristic
682C8—22no—
683C8—22no—
684C8—534no—
685C8—1062no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—1062no—
691C22—1062no—
692C22—1062no—
693C22—2124no—
694C22#1681127112yes—
695C22#137×D5312yes—
696C22#1681142912yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—534no—
704C4—1062no—
705C4—1062no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681127112yes—
711C4C2×#41×D5311yescharacteristic
712C4C2×#1313326411yescharacteristic
713C2—42no—
714C2—2122no—
715C2#2028732314yesdirect product factor
716C2C2×#1681127111yescharacteristic
717C2C2×#137×D5311yescharacteristic
718C2C2×#1681142911yescharacteristic
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×#3356
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. #20287323C2direct (N × H)
4. C2×#16811020C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810952C2semidirect
8. C2×#16810916C2semidirect
9. C2×#16810907C2semidirect
10. C2×#16810880C2semidirect
11. C2×#16810879C2semidirect
12. C2×#16810715C2semidirect
14. C2×#16810663C2semidirect
15. C2×#16810662C2semidirect
16. C2×C53×#483C2semidirect
43. #16811020C22semidirect
44. #16810967C22semidirect
45. #16810965C22semidirect
46. #16810952C22semidirect
47. #16810916C22semidirect
48. #16810907C22semidirect
49. #16810880C22semidirect
50. #16810879C22semidirect
51. #16810715C22semidirect
53. #16810663C22semidirect
54. #16810662C22semidirect
71. C53×#483C22semidirect
361. C2×#483D53semidirect
371. C2×C53#3356semidirect
408. #483C2×D53semidirect
436. C53C2×#3356semidirect
715. C2#20287323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113442
C2×#168113282
#202873232
C2×#168110202
C2×#168109672
C2×#168109652
C2×#168109522
C2×#168109162
C2×#168109072
C2×#168108802
C2×#168108792
C2×#168107152
C2×#168106982
C2×#168106632
C2×#168106622
C2×C53×#4832
C2×#335653