Finite Group Databasebeta

← C2×#20287539 #28263854

Subgroups — C2×#20287539 #28263854

Order 13568.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811342C211yesmaximal, characteristic, complemented
2C2×#16811330C211yesmaximal, characteristic, complemented
3#20287539C2116yesmaximal, direct product factor
4C2×#16810990C211yesmaximal, characteristic, complemented
5C2×#16810982C211yesmaximal, characteristic, complemented
6C2×#16810976C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810909C211yesmaximal, characteristic, complemented
9C2×#16810925C211yesmaximal, characteristic, complemented
10C2×#16810836C211yesmaximal, characteristic
11C2×#16810826C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810735C211yesmaximal, characteristic
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×SD16×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic
17C22×#11719923C2211yescharacteristic
18#16811342—24no—
19#16811342C2218yescomplemented
20#16811330—24no—
21#16811330C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133215C2211yescharacteristic
24C2×#13133210—21no—
25C2×#13133210—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133204C2211yescharacteristic
29C2×#13133196—21no—
30C2×#13133194—21no—
31C2×#13133194—21no—
32C2×#13133194—21no—
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133173—21no—
40C22×C4⋊Dic53—21no—
41#16810990C2218yescomplemented
42#16810982C2218yescomplemented
43#16810976C2218yescomplemented
44#16810928C2218yescomplemented
45#16810925C2218yescomplemented
46#16810909C2218yescomplemented
47#16810836C2218yes—
48#16810826C2218yescomplemented
49#16810752C2218yescomplemented
50#16810735C2218yes—
51#16810723C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53C2×#13133150C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yes—
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C23×Dic53—21no—
81C23×Dic53—21no—
82C23×Dic53—21no—
83C2×#11719923—24no—
84C2×#11719923C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133217—22no—
88#13133217C2314yes—
89#13133215—22no—
90#13133215C2314yes—
91#13133210—28no—
92#13133210—28no—
93#13133208—22no—
94#13133208—22no—
95#13133208C2314yes—
96#13133208C2314yes—
97#13133204—22no—
98#13133204C2314yes—
99#13133196—28no—
100#13133194—28no—
101#13133194—28no—
102#13133194—28no—
103Q8×Dic53—22no—
104Q8×Dic53C2314yes—
105C4×Dic106—22no—
106C4×Dic106D414yes—
107C4×Dic106C2314yes—
108C4×Dic106C2314yes—
109D4×Dic53—22no—
110D4×Dic53—22no—
111D4×Dic53—22no—
112D4×Dic53C2314yes—
113D4×Dic53C2314yes—
114D4×Dic53C2314yes—
115#13133173—28no—
116C2×C4⋊Dic53—28no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53C2311yescharacteristic
140C2×C4×Dic53C2311yescharacteristic
141#13133150C2314yes—
142#13133149C2314yes—
143#13133149C2314yes—
144#13133146C2314yes—
145#13133146C2314yes—
146#13133142C2314yes—
147#13133142C2314yes—
148#13133141C2314yes—
149#13133141C2314yes—
150#13133140C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133128C2314yes—
155#13133127C2314yes—
156C8×Dic53C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×D4×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C2×SD16×C53—24no—
162C2×SD16×C53C2314yes—
163C2×D8×C53—24no—
164C2×D8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#124×C53—22no—
168#124×C53C2314yes—
169C4×D4×C53—22no—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53C2311yescharacteristic
176C4⋊C8×C53C2314yes—
177#103×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C24×C53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53#4114yes—
191C2×D4×C53C2412yes—
192C2×D4×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—24no—
205C22×Dic53—24no—
206C22×Dic53—24no—
207C22×Dic53—44no—
208C22×Dic53—82no—
209C22×Dic53—82no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—21no—
217C2×Dic106—24no—
218C2×Dic106—42no—
219C2×Dic106—82no—
220C2×Dic106C2×D414yes—
221C2×Dic106C2412yes—
222SD16×C53—28no—
223D8×C53—28no—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2412yes—
230C22⋊C4×C53—24no—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—24no—
233C42×C53C2×D412yes—
234C42×C53C2412yes—
235C22⋊Dic53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240#11719923—28no—
241C4⋊Dic53—24no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53C2×D414yes—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919C2×D414yes—
258#11719919C2×D414yes—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2×D412yes—
263C4×Dic53C2412yes—
264C4×Dic53C2412yes—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C23×C53—24no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53C22×D411yescharacteristic
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—42no—
281D4×C53—24no—
282D4×C53—22no—
283D4×C53—22no—
284D4×C53—22no—
285D4×C53—42no—
286D4×C53C2×#4114yes—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—48no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4112yes—
298C2×C4×C532−1+412yes—
299C2×C4×C53C2511yescharacteristic
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—48no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—84no—
314C2×Dic53—84no—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319Dic106—22no—
320Dic106—22no—
321Dic106—44no—
322Dic106—42no—
323Dic106—84no—
324C8×C53—22no—
325C8×C53—22no—
326#88322—22no—
327#88322—22no—
328C2×#3376—531nomaximal, Sylow
329C22×C53—24no—
330C22×C53—48no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—84no—
337C22×C53#54812yes—
338C22×C53#57512yes—
339C22×C53#57712yes—
340C22×C53C23×D411yescharacteristic
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53#54812yes—
346C4×C53C22×#4111yescharacteristic
347C4×C53C2×2−1+411yescharacteristic
348Dic53—22no—
349Dic53—22no—
350Dic53—22no—
351Dic53—22no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#556—531no—
357C2×#554—531no—
358#3376—5316no—
359C2×#491—531no—
360C2×#489—531no—
361C2×#488—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#478—531no—
365C2×#463—531no—
366C2×#463D5311yescharacteristic
367C2×#461—531no—
368C2×#446—531no—
369C2×#442—531no—
370C2×#440—531no—
371C2×C4×SD16—531no—
372C2×C53—44no—
373C2×C53—82no—
374C2×C53#337614yescomplemented
375C2×C53C2×#54811yescharacteristic
376C2×C53C2×#57511yescharacteristic
377C2×C53C2×#57711yescharacteristic
378C22×SD16—531no—
379C22×SD16C2×D5311yescharacteristic
380C22×D8C2×D5311yescharacteristic
381#556—538no—
382#556—1064no—
383#554—538no—
384#554—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8—531no—
387C2×#126—1061no—
388C2×#126—1061no—
389C2×#125—531no—
390C2×#125—531no—
391C2×#124—531no—
392C2×#124C2×D5311yescharacteristic
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×C22⋊Q8—1061no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8—531no—
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4C2×D5311yescharacteristic
404C2×#117—1061no—
405C22×C4⋊C4—1061no—
406#491—538no—
407#489—538no—
408#488—538no—
409#479—538no—
410#478—538no—
411#475—538no—
412#463—538no—
413#463C2×D5318yes—
414#461—538no—
415#446—538no—
416#442—538no—
417#440—538no—
418C4×SD16—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×C4⋊C8C2×D5311yescharacteristic
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103C2×D5311yescharacteristic
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102C2×D5311yescharacteristic
435C2×#97—531no—
436C2×#97—531no—
437C2×C4×C8—531no—
438C53C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—531no—
440C22×Q8—531no—
441C22×Q8—1061no—
442C22×Q8C22×D5311yescharacteristic
443C22×D4C22×D5311yescharacteristic
444C22×D4C22×D5311yescharacteristic
445C23×C4—21no—
446C23×C4—1061no—
447C23×C4—1061no—
448C23×C4—1061no—
449C2×SD16—24no—
450C2×SD16—534no—
451C2×SD16—1064no—
452C2×SD16C22×D5314yes—
453C2×D8—24no—
454C2×D8C22×D5314yes—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8C22×D5311yescharacteristic
458C22×C8C22×D5311yescharacteristic
459C4⋊Q8—534no—
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462C4⋊Q8—1062no—
463#126—1068no—
464#126—1068no—
465#125—534no—
466#125—534no—
467#125—1062no—
468#125—1062no—
469#124—22no—
470#124—534no—
471#124—1062no—
472#124C22×D5314yes—
473C22⋊Q8—1068no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C22⋊Q8—1068no—
477C4×Q8—534no—
478C4×Q8—534no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×D4—22no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4C22×D5314yes—
491#117—1068no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—1068no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C42—531no—
518C2×C42—531no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8C22×D5314yes—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103C22×D5314yes—
534#102—534no—
535#102—534no—
536#102—534no—
537#102C22×D5314yes—
538#97—534no—
539#97—534no—
540C4×C8—534no—
541C24—21no—
542C24—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—534no—
547C2×Q8—532no—
548C2×Q8—1064no—
549C2×Q8—1061no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—4242no—
553C2×Q8—2122no—
554C2×Q8C23×D5312yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4#1171994714yes—
561C2×D4C23×D5312yes—
562C2×D4C23×D5312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—1064no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—4242no—
579C22×C4—4242no—
580C22×C4—2124no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584SD16—28no—
585SD16—1068no—
586D8—28no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8C23×D5312yes—
594C2×C8C23×D5312yes—
595C4⋊C4—21no—
596C4⋊C4—534no—
597C4⋊C4—534no—
598C4⋊C4—534no—
599C4⋊C4—532no—
600C4⋊C4—532no—
601C4⋊C4—532no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—532no—
624C42—532no—
625C42—532no—
626C42—532no—
627C42—1064no—
628C42—1064no—
629C42D4×D5312yes—
630C42C23×D5312yes—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C2×D4×D5311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—1062no—
644Q8—1062no—
645Q8—4244no—
646Q8—2124no—
647Q8—2122no—
648D4—24no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—42no—
653D4C2×#1171994714yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—532no—
662C2×C4—532no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—4244no—
674C2×C4—4244no—
675C2×C4—2128no—
676C2×C4—2122no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4C2×D4×D5312yes—
681C2×C4C2×D4×D5312yes—
682C2×C4C2×D4×D5311yescharacteristic
683C2×C4C2×#1171994712yes—
684C2×C4#1313326412yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—24no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—84no—
698C22#1681127912yes—
699C22#1681141912yes—
700C22#1681143012yes—
701C22C22×D4×D5311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—1062no—
707C4—1062no—
708C4—1062no—
709C4—1062no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4#1681127912yes—
715C4C22×#1171994711yescharacteristic
716C4C2×#1313326411yescharacteristic
717C2—44no—
718C2—82no—
719C2#2028753914yesdirect product factor
720C2C2×#1681127911yescharacteristic
721C2C2×#1681141911yescharacteristic
722C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC22×D8×C53C22
hypercenterC2×#463D53
hypocenterC53C2×#3376
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811342C2semidirect
2. C2×#16811330C2semidirect
3. #20287539C2direct (N × H)
4. C2×#16810990C2semidirect
5. C2×#16810982C2semidirect
6. C2×#16810976C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810909C2semidirect
9. C2×#16810925C2semidirect
11. C2×#16810826C2semidirect
12. C2×#16810752C2semidirect
14. C2×#16810723C2semidirect
15. C2×SD16×Dic53C2semidirect
19. #16811342C22semidirect
21. #16811330C22semidirect
41. #16810990C22semidirect
42. #16810982C22semidirect
43. #16810976C22semidirect
44. #16810928C22semidirect
45. #16810925C22semidirect
46. #16810909C22semidirect
48. #16810826C22semidirect
49. #16810752C22semidirect
51. #16810723C22semidirect
52. SD16×Dic53C22semidirect
374. C2×C53#3376semidirect
438. C53C2×#3376semidirect
719. C2#20287539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113422
C2×#168113302
#202875392
C2×#168109902
C2×#168109822
C2×#168109762
C2×#168109282
C2×#168109092
C2×#168109252
C2×#168108362
C2×#168108262
C2×#168107522
C2×#168107352
C2×#168107232
C2×SD16×Dic532
C2×C53×#4632
C2×#337653