Finite Group Databasebeta

← C2×#20286163 #28257042

Subgroups — C2×#20286163 #28257042

Order 13568.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811236C211yesmaximal, characteristic, complemented
2C2×#16811224C211yesmaximal, characteristic
3#20286163C2116yesmaximal, direct product factor
4C2×#16810933C211yesmaximal, characteristic, complemented
5C2×#16810929C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810868C211yesmaximal, characteristic, complemented
9C2×#16810853C211yesmaximal, characteristic, complemented
10C2×#16810851C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic, complemented
12C2×#16810822C211yesmaximal, characteristic, complemented
13C2×#16810829C211yesmaximal, characteristic, complemented
14C2×#16810828C211yesmaximal, characteristic, complemented
15C2×#16810648C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811236—24no—
24#16811236C2218yescomplemented
25#16811224—24no—
26#16811224C2218yes—
27C2×#13133217C2211yescharacteristic
28C2×#13133213C2211yescharacteristic
29C2×#13133212—21no—
30C2×#13133212—21no—
31C2×#13133208—21no—
32C2×#13133208—21no—
33C2×#13133208C2211yescharacteristic
34C2×#13133200—21no—
35C2×#13133199—21no—
36C2×#13133197C2211yescharacteristic
37C2×#13133197C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×#13133191—21no—
40C2×#13133190—21no—
41C2×#13133188C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×C4×D212C2211yescharacteristic
45C2×#13133174C2211yescharacteristic
46#16810933C2218yescomplemented
47#16810929C2218yescomplemented
48#16810920C2218yescomplemented
49#16810870C2218yescomplemented
50#16810868C2218yescomplemented
51#16810853C2218yescomplemented
52#16810851C2218yescomplemented
53#16810829C2218yescomplemented
54#16810828C2218yescomplemented
55#16810822C2218yescomplemented
56#16810822C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53C2311yescharacteristic
86C2×#11719913—42no—
87C2×#11719913—42no—
88C2×#11719913C2314yes—
89C2×#11719913C2314yes—
90C2×#11719923—42no—
91C2×#11719923—42no—
92C2×#11719923C2314yes—
93C2×#11719923C2314yes—
94C2×#11719912—42no—
95C2×#11719912C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C2×C8×D53—42no—
99C2×C8×D53C2314yes—
100#13133217—22no—
101#13133217C2314yes—
102#13133213—22no—
103#13133213C2314yes—
104#13133212—28no—
105#13133212—28no—
106#13133208—28no—
107#13133208—28no—
108#13133208—22no—
109#13133208C2314yes—
110#13133200—28no—
111#13133199—28no—
112#13133197—22no—
113#13133197—22no—
114#13133197C2314yes—
115#13133197C2314yes—
116#13133192—22no—
117#13133192C2314yes—
118#13133191—28no—
119#13133190—28no—
120#13133188—22no—
121#13133188C2314yes—
122#13133182—22no—
123#13133182—22no—
124#13133182C2314yes—
125#13133182C2314yes—
126C4×D212—22no—
127C4×D212C2314yes—
128#13133174D414yes—
129#13133174C2314yes—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×#11719921D411yescharacteristic
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#125×C53—22no—
167#125×C53C2314yes—
168C4×D4×C53—22no—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—82no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—82no—
201C2×C22⋊D53—82no—
202C2×C22⋊D53—82no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—21no—
212C2×D212—24no—
213C2×D212—82no—
214C2×D212C2412yes—
215C2×C4×D53—22no—
216C2×C4×D53—22no—
217C2×C4×D53—24no—
218C2×C4×D53—82no—
219C2×C4×D53C2×D412yes—
220C2×C4×D53C2412yes—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—21no—
226C2×Dic106—21no—
227C2×Dic106C2412yes—
228C2×Dic106C2412yes—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C22⋊C4×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2412yes—
244C22⋊Dic53—24no—
245#11719923—44no—
246#11719923—44no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921C2×D414yes—
252#11719921C2×D414yes—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919C2×D414yes—
264#11719919C2×D414yes—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273#11719913—44no—
274#11719913—44no—
275#11719912—44no—
276C8×D53—44no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53C22×D412yes—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—84no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53H(5,𝔽2)12yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—84no—
309C22⋊D53—84no—
310C22⋊D53—84no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322C2×Dic53C22×D412yes—
323D212—22no—
324D212—22no—
325D212—42no—
326D212—84no—
327C4×D53—24no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—84no—
331Dic106—22no—
332Dic106—22no—
333Dic106—22no—
334Dic106—22no—
335Dic106—42no—
336Dic106—42no—
337C8×C53—22no—
338C8×C53—22no—
339#88322—22no—
340#88322—22no—
341C2×#3260—531nomaximal, Sylow
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—84no—
346C22×C53#53712yes—
347C22×C53#57712yes—
348C22×C53#57712yes—
349C22×C53C23×D411yescharacteristic
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—44no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—84no—
358C4×C53—22no—
359C4×C53—22no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#53712yes—
364C4×C53C2×H(5,𝔽2)11yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#541—531no—
373C2×#540—531no—
374#3260—5316no—
375C2×#479—531no—
376C2×#479—531no—
377C2×#478—531no—
378C2×#478D5311yescharacteristic, complemented
379C2×#468—531no—
380C2×#468—531no—
381C2×#465—531no—
382C2×#465—531no—
383C2×#460—531no—
384C2×#460—531no—
385C2×#461—531no—
386C2×#461—531no—
387C2×#424—531no—
388C2×C53—82no—
389C2×C53#326014yescomplemented
390C2×C53C2×#53711yescharacteristic
391C2×C53C2×#57711yescharacteristic
392C2×C53C2×#57711yescharacteristic
393D53—42no—
394D53—82no—
395C22×SD16—531no—
396C22×SD16—531no—
397C22×SD16—531no—
398C22×SD16—531no—
399C22×M16—531no—
400C23×C8—531no—
401#541—538no—
402#541—1064no—
403#540—538no—
404#540—1064no—
405C2×C4⋊Q8—531no—
406C2×#127—531no—
407C2×#126—1061no—
408C2×#126—1061no—
409C2×#125—531no—
410C2×#125—1061no—
411C2×#125—1061no—
412C2×#125C2×D5311yescharacteristic
413C2×#123—1061no—
414C2×#123—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8—531no—
417C2×#121—531no—
418C2×#121—531no—
419C2×#121—1061no—
420C2×#121—1061no—
421C2×C4×Q8—531no—
422C2×C4×Q8—531no—
423C2×C4×D4—531no—
424C2×C4×D4C2×D5311yescharacteristic
425C2×#117—531no—
426#479—538no—
427#479—538no—
428#478—538no—
429#478C2×D5318yescomplemented
430#468—538no—
431#468—538no—
432#465—538no—
433#465—538no—
434#461—538no—
435#461—538no—
436#460—538no—
437#460—538no—
438C2×#107—531no—
439C2×#107C2×D5311yescharacteristic
440C2×#106—531no—
441C2×#106C2×D5311yescharacteristic
442#424—538no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×C4⋊C8—531no—
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×#103—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102C2×D5311yescharacteristic
454C2×#102C2×D5311yescharacteristic
455C53C2×#326011yescharacteristic, complemented, Sylow
456C22×Q8—531no—
457C22×Q8—531no—
458C22×D4—531no—
459C22×D4—1061no—
460C22×D4—1061no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—21no—
465C23×C4—531no—
466C23×C4—1061no—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—534no—
470C2×SD16—534no—
471C2×SD16—2122no—
472C2×SD16—2122no—
473C2×SD16—2122no—
474C2×SD16—2122no—
475C2×M16—534no—
476C2×M16—2122no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—534no—
480C22×C8—2122no—
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483C4⋊Q8—534no—
484C4⋊Q8—1062no—
485#127—534no—
486#127—1062no—
487#126—1068no—
488#126—1068no—
489#125—22no—
490#125—534no—
491#125—1062no—
492#125—1068no—
493#125—1068no—
494#125C22×D5314yes—
495#123—1068no—
496#123—1068no—
497C22⋊Q8—534no—
498C22⋊Q8—534no—
499C22⋊Q8—1062no—
500C22⋊Q8—1062no—
501#121—534no—
502#121—534no—
503#121—1068no—
504#121—1068no—
505#121—1062no—
506#121—1062no—
507C4×Q8—534no—
508C4×Q8—534no—
509C4×Q8—1062no—
510C4×Q8—1062no—
511C4×D4—22no—
512C4×D4—534no—
513C4×D4—1062no—
514C4×D4C22×D5314yes—
515#117—534no—
516#117—534no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4C22×D5311yescharacteristic
531C2×C4⋊C4C22×D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—531no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C42—531no—
542C2×C42—1061no—
543C2×C42—1061no—
544C2×C42C22×D5311yescharacteristic
545#107—534no—
546#107C22×D5314yes—
547#106—534no—
548#106C22×D5314yes—
549C4⋊C8—534no—
550C4⋊C8—534no—
551C4⋊C8—534no—
552C4⋊C8C22×D5314yes—
553#103—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#102—534no—
558#102—534no—
559#102C22×D5314yes—
560#102C22×D5314yes—
561C24—21no—
562C24—531no—
563C24—1061no—
564C2×Q8—532no—
565C2×Q8—532no—
566C2×Q8—1061no—
567C2×Q8—1061no—
568C2×Q8—1062no—
569C2×Q8—1062no—
570C2×Q8—1062no—
571C2×Q8—1062no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—532no—
576C2×D4—1064no—
577C2×D4—1064no—
578C2×D4—1064no—
579C2×D4—1064no—
580C2×D4—1061no—
581C2×D4—1062no—
582C2×D4—1062no—
583C2×D4—4242no—
584C2×D4—4242no—
585C2×D4—4242no—
586C2×D4—4242no—
587C2×D4C23×D5312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1064no—
604C22×C4—4242no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608SD16—2124no—
609SD16—2124no—
610SD16—2124no—
611SD16—2124no—
612M16—2124no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—532no—
616C2×C8—532no—
617C2×C8—1062no—
618C2×C8—1062no—
619C2×C8—2124no—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—532no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1061no—
637C4⋊C4—1064no—
638C4⋊C4—1064no—
639C4⋊C4C23×D5312yes—
640C4⋊C4C23×D5312yes—
641C4⋊C4C23×D5312yes—
642C22⋊C4—24no—
643C22⋊C4—534no—
644C22⋊C4—534no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—532no—
651C42—532no—
652C42—1064no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—532no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—1062no—
670Q8—1062no—
671Q8—1062no—
672Q8—1062no—
673Q8—2122no—
674Q8—2122no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—1062no—
679D4—1062no—
680D4—4244no—
681D4—4244no—
682D4—4244no—
683D4—4244no—
684D4—2122no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—532no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—4244no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4C2×D4×D5312yes—
711C2×C4C2×D4×D5312yes—
712C2×C4C2×D4×D5311yescharacteristic
713C2×C4#1313326312yes—
714C2×C4#1313326512yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1062no—
719C8—1062no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—1062no—
725C22—1062no—
726C22—1062no—
727C22—4244no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2124no—
732C22#1681120312yes—
733C22#1681143012yes—
734C22#1681143312yes—
735C22C22×D4×D5311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—1062no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4#1681120312yes—
748C4C2×#1313326311yescharacteristic
749C4C2×#1313326511yescharacteristic
750C2—82no—
751C2—4242no—
752C2—2122no—
753C2#2028616314yesdirect product factor
754C2C2×#1681120311yescharacteristic
755C2C2×#1681143011yescharacteristic
756C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC2×#16811224C2
hypercenterC2×#478D53
hypocenterC53C2×#3260
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811236C2semidirect
3. #20286163C2direct (N × H)
4. C2×#16810933C2semidirect
5. C2×#16810929C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810868C2semidirect
9. C2×#16810853C2semidirect
10. C2×#16810851C2semidirect
11. C2×#16810822C2semidirect
12. C2×#16810822C2semidirect
13. C2×#16810829C2semidirect
14. C2×#16810828C2semidirect
15. C2×#16810648C2semidirect
16. C2×C53×#478C2semidirect
24. #16811236C22semidirect
46. #16810933C22semidirect
47. #16810929C22semidirect
48. #16810920C22semidirect
49. #16810870C22semidirect
50. #16810868C22semidirect
51. #16810853C22semidirect
52. #16810851C22semidirect
53. #16810829C22semidirect
54. #16810828C22semidirect
55. #16810822C22semidirect
56. #16810822C22semidirect
59. #16810648C22semidirect
71. C53×#478C22semidirect
378. C2×#478D53semidirect
389. C2×C53#3260semidirect
429. #478C2×D53semidirect
455. C53C2×#3260semidirect
753. C2#20286163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112362
C2×#168112242
#202861632
C2×#168109332
C2×#168109292
C2×#168109202
C2×#168108702
C2×#168108682
C2×#168108532
C2×#168108512
C2×#168108222
C2×#168108292
C2×#168108282
C2×#168106482
C2×C53×#4782
C2×#326053