Finite Group Databasebeta

← C2×#20285437 #28254039

Subgroups — C2×#20285437 #28254039

Order 13568.

2018 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×#16811159C211yesmaximal, characteristic, complemented
2C2×#16811154C211yesmaximal, characteristic, complemented
3#20285437C2116yesmaximal, direct product factor
4C2×#16811024C211yesmaximal, characteristic, complemented
5C2×#16811004C211yesmaximal, characteristic, complemented
6C2×#16810979C211yesmaximal, characteristic, complemented
7C2×#16810976C211yesmaximal, characteristic, complemented
8C2×#16810879C211yesmaximal, characteristic, complemented
9C2×#16810874C211yesmaximal, characteristic
10C2×#16810869C211yesmaximal, characteristic, complemented
11C2×#16810732C211yesmaximal, characteristic, complemented
12C2×#16810727C211yesmaximal, characteristic, complemented
13C2×#16810724C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×M16×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#468C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16811159—24no—
22#16811159C2218yescomplemented
23#16811154—24no—
24#16811154C2218yescomplemented
25C2×#13133212—21no—
26C2×#13133210—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133208C2211yescharacteristic
29C2×#13133206C2211yescharacteristic
30C2×#13133204C2211yescharacteristic
31C2×#13133201—21no—
32C2×#13133198—21no—
33C2×#13133196C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×D4×Dic53—21no—
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133177—21no—
41C2×#13133175—21no—
42C2×#13133173—21no—
43C22×C4×Dic53C2211yescharacteristic
44#16811024C2218yescomplemented
45#16811004C2218yescomplemented
46#16810979C2218yescomplemented
47#16810976C2218yescomplemented
48#16810879C2218yescomplemented
49#16810874C2218yes—
50#16810869C2218yescomplemented
51#16810732C2218yescomplemented
52#16810727C2218yescomplemented
53#16810724C2218yescomplemented
54#16810722C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64M16×Dic53C2218yescomplemented
65C2×#13133127C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#468C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C23×Dic53D411yescharacteristic
82C23×Dic53D411yescharacteristic
83C22×C4×D53—21no—
84C2×#11719925—24no—
85C2×#11719925C2314yes—
86C2×#11719913—24no—
87C2×#11719913C2314yes—
88C2×#11719922—24no—
89C2×#11719922C2314yes—
90C2×#11719917—24no—
91C2×#11719917C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133212—28no—
95#13133210—28no—
96#13133208—22no—
97#13133208—22no—
98#13133208C2314yes—
99#13133208C2314yes—
100#13133206—22no—
101#13133206C2314yes—
102#13133204—22no—
103#13133204C2314yes—
104#13133201—28no—
105#13133198—28no—
106#13133196—22no—
107#13133196C2314yes—
108#13133191—22no—
109#13133191C2314yes—
110Q8×Dic53—22no—
111Q8×Dic53C2314yes—
112#13133182—22no—
113#13133182C2314yes—
114D4×Dic53—22no—
115D4×Dic53—28no—
116D4×Dic53C2314yes—
117#13133179—22no—
118#13133179C2314yes—
119#13133177—28no—
120#13133175—28no—
121#13133173—28no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D414yes—
144C2×C4×Dic53C2311yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2314yes—
147#13133151C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133142C2314yes—
151#13133141C2314yes—
152#13133140C2314yes—
153#13133139C2314yes—
154#13133138C2314yes—
155#13133137C2314yes—
156#13133127C2314yes—
157#13133127C2314yes—
158C8×Dic53C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×D4×C53—21no—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C2×M16×C53—24no—
167C2×M16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172#121×C53—22no—
173#121×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179#107×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C2×D4×C53—24no—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—44no—
194C2×D4×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—44no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—42no—
211C22×Dic53—42no—
212C22×Dic53—44no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D414yes—
218C22×Dic53C2×D414yes—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—21no—
222C2×D212C2412yes—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106C2412yes—
229SD16×C53—28no—
230M16×C53—28no—
231C2×C8×C53—22no—
232C2×C8×C53#4114yes—
233C2×C8×C53C2412yes—
234C2×C8×C53C2412yes—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C22⋊C4×C53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719925—28no—
247#11719922—28no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53C2×D414yes—
266C4×Dic53C2×D414yes—
267C4×Dic53C2×D412yes—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C4×Dic53C2412yes—
271#11719917—28no—
272C2×#88322—22no—
273C2×#88322#4114yes—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276#11719913—28no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D412yes—
285C23×C53C22×D411yescharacteristic
286C22×D53—22no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—48no—
296D4×C53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2×#4112yes—
311C2×C4×C53C2511yescharacteristic
312C22⋊D53—48no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—44no—
321C2×Dic53—44no—
322C2×Dic53—48no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330D212—22no—
331D212—22no—
332D212—42no—
333C4×D53—48no—
334Dic106—22no—
335Dic106—22no—
336Dic106—42no—
337C8×C53—22no—
338C8×C53C2×#4114yes—
339#88322—22no—
340#88322C2×#4114yes—
341C2×#3183—531nomaximal, Sylow
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—44no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—84no—
350C22×C53#53212yes—
351C22×C53#57512yes—
352C22×C53#57512yes—
353C22×C53C23×D411yescharacteristic
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—84no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#53212yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C22×#4111yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#529—531no—
373C2×#529—531no—
374#3183—5316no—
375C2×#499—531no—
376C2×#495—531no—
377C2×#488—531no—
378C2×#488—531no—
379C2×#470—531no—
380C2×#469—531no—
381C2×#468—531no—
382C2×#468D5311yescharacteristic, complemented
383C2×#442—531no—
384C2×#441—531no—
385C2×#440—531no—
386C2×#440—531no—
387C2×C4×M16—531no—
388C2×C53—42no—
389C2×C53—82no—
390C2×C53#318314yescomplemented
391C2×C53C2×#53211yescharacteristic
392C2×C53C2×#57511yescharacteristic
393C2×C53C2×#57511yescharacteristic
394D53—82no—
395C22×Q16—531no—
396C22×SD16—531no—
397C22×SD16C2×D5311yescharacteristic
398C22×D8—531no—
399C22×M16—531no—
400C22×M16C2×D5311yescharacteristic
401#529—538no—
402#529—538no—
403#529—1064no—
404#529—1064no—
405C2×#126—1061no—
406C2×#126—1061no—
407C2×#125—531no—
408C2×#125—531no—
409C2×#124—531no—
410C2×#124—531no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—531no—
414C2×C22⋊Q8C2×D5311yescharacteristic
415C2×#121—531no—
416C2×#121C2×D5311yescharacteristic
417C2×C4×Q8—531no—
418C2×C4×Q8—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×#117—1061no—
424C2×#117—1061no—
425C22×C42—531no—
426#499—538no—
427#495—538no—
428#488—538no—
429#488—538no—
430#470—538no—
431#469—538no—
432#468—538no—
433#468C2×D5318yescomplemented
434#442—538no—
435#441—538no—
436#440—538no—
437#440—538no—
438C2×#107—531no—
439C2×#107C2×D5311yescharacteristic
440C2×#106—531no—
441C2×#106—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103—531no—
445C2×#103C2×D5311yescharacteristic
446C2×#102—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102C2×D5311yescharacteristic
450C4×M16—538no—
451C2×#97—531no—
452C2×#97—531no—
453C2×C4×C8—531no—
454C2×C4×C8—531no—
455C53C2×#318311yescharacteristic, complemented, Sylow
456C22×Q8—531no—
457C22×Q8C22×D5311yescharacteristic
458C22×D4—21no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4C22×D5311yescharacteristic
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—1061no—
465C23×C4—1061no—
466C23×C4C22×D5311yescharacteristic
467C2×Q16—534no—
468C2×Q16—1064no—
469C2×SD16—24no—
470C2×SD16—534no—
471C2×SD16—1064no—
472C2×SD16C22×D5314yes—
473C2×D8—534no—
474C2×D8—1064no—
475C2×M16—24no—
476C2×M16—534no—
477C2×M16—1064no—
478C2×M16C22×D5314yes—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483#126—1068no—
484#126—1068no—
485#125—534no—
486#125—534no—
487#125—1062no—
488#125—1062no—
489#124—534no—
490#124—534no—
491#124—1062no—
492#124—1062no—
493#123—1068no—
494#123—1068no—
495C22⋊Q8—22no—
496C22⋊Q8—534no—
497C22⋊Q8—1062no—
498C22⋊Q8C22×D5314yes—
499#121—22no—
500#121—534no—
501#121—1062no—
502#121C22×D5314yes—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×Q8—1062no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—1062no—
510C4×D4—1062no—
511C4×D4—1068no—
512C4×D4—1068no—
513#117—1068no—
514#117—1068no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—531no—
538C2×C42—531no—
539C2×C42—534no—
540C2×C42—531no—
541C2×C42—531no—
542C2×C42—534no—
543C2×C42—1061no—
544C2×C42—1061no—
545#107—534no—
546#107C22×D5314yes—
547#106—534no—
548#106—534no—
549#103—534no—
550#103—534no—
551#103—534no—
552#103C22×D5314yes—
553#102—534no—
554#102—534no—
555#102—534no—
556#102C22×D5314yes—
557#97—534no—
558#97—534no—
559C4×C8—534no—
560C4×C8—534no—
561C24—21no—
562C24—1061no—
563C24D4×D5311yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—532no—
568C2×Q8—1061no—
569C2×Q8—1062no—
570C2×Q8—1062no—
571C2×Q8C23×D5312yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—532no—
578C2×D4—1064no—
579C2×D4—1061no—
580C2×D4—1062no—
581C2×D4—1062no—
582C2×D4—2124no—
583C2×D4C23×D5312yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—531no—
592C22×C4—531no—
593C22×C4—534no—
594C22×C4—534no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—2124no—
601C22×C4—2122no—
602C22×C4—2122no—
603C22×C4—2124no—
604C22×C4D4×D5312yes—
605C22×C4D4×D5311yescharacteristic
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608Q16—1068no—
609SD16—28no—
610SD16—1068no—
611D8—1068no—
612M16—28no—
613M16—1068no—
614C2×C8—22no—
615C2×C8—534no—
616C2×C8—532no—
617C2×C8—532no—
618C2×C8—1062no—
619C2×C8#1171994714yes—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1061no—
634C4⋊C4—1061no—
635C4⋊C4—1064no—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C42—534no—
649C42—534no—
650C42—532no—
651C42—532no—
652C42—532no—
653C42—532no—
654C42—1064no—
655C42—1064no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—1062no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23C2×D4×D5312yes—
668C23C2×D4×D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1062no—
673Q8—1062no—
674Q8—2122no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—1062no—
680D4—1062no—
681D4—2128no—
682D4—2122no—
683C2×C4—22no—
684C2×C4—24no—
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—532no—
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—1062no—
703C2×C4—1062no—
704C2×C4—2128no—
705C2×C4—2124no—
706C2×C4—2124no—
707C2×C4—2128no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4C2×D4×D5312yes—
712C2×C4C2×D4×D5311yescharacteristic
713C2×C4#41×D5312yes—
714C2×C4C2×#1171994712yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—534no—
718C8—1062no—
719C8C2×#1171994714yes—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—4244no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22#1681116812yes—
733C22#1681141912yes—
734C22#1681142212yes—
735C22C22×D4×D5311yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—1062no—
741C4—1062no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4#1681116812yes—
748C4C2×#41×D5311yescharacteristic
749C4C22×#1171994711yescharacteristic
750C2—42no—
751C2—82no—
752C2—4242no—
753C2#2028543714yesdirect product factor
754C2C2×#1681116811yescharacteristic
755C2C2×#1681141911yescharacteristic
756C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#468C2
socleC23×C53C22×D4
prime radicalC2×#16810874C2
hypercenterC2×#468D53
hypocenterC53C2×#3183
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16811159C2semidirect
2. C2×#16811154C2semidirect
3. #20285437C2direct (N × H)
4. C2×#16811024C2semidirect
5. C2×#16811004C2semidirect
6. C2×#16810979C2semidirect
7. C2×#16810976C2semidirect
8. C2×#16810879C2semidirect
10. C2×#16810869C2semidirect
11. C2×#16810732C2semidirect
12. C2×#16810727C2semidirect
13. C2×#16810724C2semidirect
14. C2×#16810722C2semidirect
15. C2×M16×Dic53C2semidirect
16. C2×C53×#468C2semidirect
22. #16811159C22semidirect
24. #16811154C22semidirect
44. #16811024C22semidirect
45. #16811004C22semidirect
46. #16810979C22semidirect
47. #16810976C22semidirect
48. #16810879C22semidirect
50. #16810869C22semidirect
51. #16810732C22semidirect
52. #16810727C22semidirect
53. #16810724C22semidirect
54. #16810722C22semidirect
64. M16×Dic53C22semidirect
73. C53×#468C22semidirect
382. C2×#468D53semidirect
390. C2×C53#3183semidirect
433. #468C2×D53semidirect
455. C53C2×#3183semidirect
753. C2#20285437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111592
C2×#168111542
#202854372
C2×#168110242
C2×#168110042
C2×#168109792
C2×#168109762
C2×#168108792
C2×#168108742
C2×#168108692
C2×#168107322
C2×#168107272
C2×#168107242
C2×#168107222
C2×M16×Dic532
C2×C53×#4682
C2×#318353