Finite Group Databasebeta

← C2×#20285341 #28253900

Subgroups — C2×#20285341 #28253900

Order 13568.

1970 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×#16811231C211yesmaximal, characteristic, complemented
2C2×#16811224C211yesmaximal, characteristic
3#20285341C2116yesmaximal, direct product factor
4C2×#16811024C211yesmaximal, characteristic, complemented
5C2×#16810994C211yesmaximal, characteristic, complemented
6C2×#16810990C211yesmaximal, characteristic, complemented
7C2×#16810986C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810866C211yesmaximal, characteristic, complemented
10C2×#16810855C211yesmaximal, characteristic, complemented
11C2×#16810851C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×C4×#11719924C211yesmaximal, characteristic, complemented
14C2×C4×#11719923C211yesmaximal, characteristic, complemented
15C2×#16810580C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811231—24no—
23#16811231C2218yescomplemented
24#16811224—24no—
25#16811224C2218yes—
26C2×#13133215C2211yescharacteristic
27C2×#13133213C2211yescharacteristic
28C2×#13133212—21no—
29C2×#13133211—21no—
30C2×#13133209—21no—
31C2×#13133208C2211yescharacteristic
32C2×#13133208C2211yescharacteristic
33C2×#13133207—21no—
34C2×#13133200—21no—
35C2×#13133199—21no—
36C2×#13133197C2211yescharacteristic
37C2×#13133193C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×#13133191—21no—
40C2×#13133190—21no—
41C2×#13133188C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×C4×D212C2211yescharacteristic
44C2×#13133174C2211yescharacteristic
45#16811024C2218yescomplemented
46#16810994C2218yescomplemented
47#16810990C2218yescomplemented
48#16810986C2218yescomplemented
49#16810870C2218yescomplemented
50#16810866C2218yescomplemented
51#16810855C2218yescomplemented
52#16810851C2218yescomplemented
53#16810725C2218yescomplemented
54C4×#11719924C2218yescomplemented
55C4×#11719923C2218yescomplemented
56C2×#13133151C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810580C2218yescomplemented
66C2×#13133127C2211yescharacteristic
67C2×C4×#88322C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719913—24no—
86C2×#11719913C2314yes—
87C2×#11719923—24no—
88C2×#11719923C2314yes—
89C2×#11719924—24no—
90C2×#11719924C2314yes—
91C2×#11719912—24no—
92C2×#11719912C2314yes—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C2×C8×D53—24no—
96C2×C8×D53C2314yes—
97#13133215—22no—
98#13133215C2314yes—
99#13133213—22no—
100#13133213C2314yes—
101#13133212—28no—
102#13133211—28no—
103#13133209—28no—
104#13133208—22no—
105#13133208—22no—
106#13133208C2314yes—
107#13133208C2314yes—
108#13133207—28no—
109#13133200—28no—
110#13133199—28no—
111#13133197—22no—
112#13133197C2314yes—
113#13133193—22no—
114#13133193C2314yes—
115#13133192—22no—
116#13133192C2314yes—
117#13133191—28no—
118#13133190—28no—
119#13133188—22no—
120#13133188C2314yes—
121C4×Dic106—22no—
122C4×Dic106C2314yes—
123C4×D212—22no—
124C4×D212C2314yes—
125#13133174D414yes—
126#13133174C2314yes—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133151C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133127C2314yes—
159C4×#88322C2314yes—
160C8×Dic53C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#102×C53C2314yes—
181#97×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—82no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—82no—
205C2×C22⋊D53—82no—
206C2×C22⋊D53—82no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—21no—
216C2×D212—24no—
217C2×D212—82no—
218C2×D212C2412yes—
219C2×C4×D53—22no—
220C2×C4×D53—22no—
221C2×C4×D53—24no—
222C2×C4×D53—82no—
223C2×C4×D53C2×D412yes—
224C2×C4×D53C2412yes—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106C2412yes—
229SD16×C53—28no—
230C2×C8×C53—22no—
231C2×C8×C53#4114yes—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C42×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244#11719924—28no—
245#11719923—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921C2×D414yes—
251#11719921C2×D414yes—
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—
263#11719919—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322#4114yes—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274#11719913—28no—
275#11719912—28no—
276C8×D53—28no—
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—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—42no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—84no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4112yes—
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2511yescharacteristic
311C22⋊D53—84no—
312C22⋊D53—84no—
313C22⋊D53—84no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326D212—22no—
327D212—22no—
328D212—42no—
329D212—84no—
330C4×D53—24no—
331C4×D53—22no—
332C4×D53—22no—
333C4×D53—84no—
334Dic106—22no—
335Dic106—22no—
336Dic106—42no—
337C8×C53—22no—
338C8×C53C2×#4114yes—
339#88322—22no—
340#88322C2×#4114yes—
341C2×#3174—531nomaximal, Sylow
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—84no—
346C22×C53#53212yes—
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#53212yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C22×#4111yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#541—531no—
373C2×#540—531no—
374#3174—5316no—
375C2×#499—531no—
376C2×#492—531no—
377C2×#491—531no—
378C2×#490—531no—
379C2×#468—531no—
380C2×#468—531no—
381C2×#465—531no—
382C2×#465—531no—
383C2×#440—531no—
384C2×#440D5311yescharacteristic, complemented
385C2×C4×SD16—531no—
386C2×C4×SD16—531no—
387C2×#405—531no—
388C2×C53—82no—
389C2×C53#317414yescomplemented
390C2×C53C2×#53211yescharacteristic
391C2×C53C2×#57711yescharacteristic
392C2×C53C2×#57711yescharacteristic
393D53—42no—
394D53—82no—
395C22×SD16—531no—
396C22×SD16—531no—
397C22×SD16—531no—
398C22×SD16C2×D5311yescharacteristic
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—531no—
411C2×#125—1061no—
412C2×#125—1061no—
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×Q8C2×D5311yescharacteristic
423C2×C4×D4—531no—
424C2×C4×D4C2×D5311yescharacteristic
425C2×#117—531no—
426#499—538no—
427#492—538no—
428#491—538no—
429#490—538no—
430#468—538no—
431#468—538no—
432#465—538no—
433#465—538no—
434#440—538no—
435#440C2×D5318yescomplemented
436C4×SD16—538no—
437C4×SD16—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
450#405—538no—
451C2×#97—531no—
452C2×#97C2×D5311yescharacteristic
453C2×C4×C8—531no—
454C2×C4×C8—531no—
455C53C2×#317411yescharacteristic, complemented, Sylow
456C22×Q8—531no—
457C22×Q8C22×D5311yescharacteristic
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—24no—
468C2×SD16—534no—
469C2×SD16—534no—
470C2×SD16—534no—
471C2×SD16—1064no—
472C2×SD16—1064no—
473C2×SD16—1064no—
474C2×SD16C22×D5314yes—
475C2×M16—534no—
476C2×M16—1064no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—534no—
480C22×C8—1064no—
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—534no—
490#125—534no—
491#125—1068no—
492#125—1062no—
493#125—1062no—
494#125—1068no—
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—22no—
508C4×Q8—534no—
509C4×Q8—1062no—
510C4×Q8C22×D5314yes—
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—531no—
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⋊C4—1061no—
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—21no—
542C2×C42—531no—
543C2×C42—1061no—
544C2×C42C22×D5311yescharacteristic
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#97C22×D5314yes—
559C4×C8—534no—
560C4×C8—534no—
561C24—21no—
562C24—531no—
563C24—1061no—
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—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—28no—
609SD16—1068no—
610SD16—1068no—
611SD16—1068no—
612M16—1068no—
613C2×C8—22no—
614C2×C8—534no—
615C2×C8—532no—
616C2×C8—532no—
617C2×C8—1068no—
618C2×C8—1062no—
619C2×C8#1171994514yes—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—534no—
626C4⋊C4—534no—
627C4⋊C4—532no—
628C4⋊C4—532no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4—1064no—
637C4⋊C4—1061no—
638C4⋊C4—1061no—
639C4⋊C4—1064no—
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—24no—
651C42—532no—
652C42—532no—
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—22no—
670Q8—22no—
671Q8—42no—
672Q8—1062no—
673Q8—1062no—
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—1064no—
701C2×C4—1062no—
702C2×C4—1062no—
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#41×D5312yes—
714C2×C4C2×#1171994512yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—534no—
718C8—1062no—
719C8C2×#1171994514yes—
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#1681117012yes—
733C22#1681143212yes—
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#1681117012yes—
748C4C2×#41×D5311yescharacteristic
749C4C22×#1171994511yescharacteristic
750C2—82no—
751C2—4242no—
752C2—2122no—
753C2#2028534114yesdirect product factor
754C2C2×#1681117011yescharacteristic
755C2C2×#1681143211yescharacteristic
756C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#16811224C2
hypercenterC2×#440D53
hypocenterC53C2×#3174
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811231C2semidirect
3. #20285341C2direct (N × H)
4. C2×#16811024C2semidirect
5. C2×#16810994C2semidirect
6. C2×#16810990C2semidirect
7. C2×#16810986C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810866C2semidirect
10. C2×#16810855C2semidirect
11. C2×#16810851C2semidirect
12. C2×#16810725C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810580C2semidirect
16. C2×C53×#440C2semidirect
23. #16811231C22semidirect
45. #16811024C22semidirect
46. #16810994C22semidirect
47. #16810990C22semidirect
48. #16810986C22semidirect
49. #16810870C22semidirect
50. #16810866C22semidirect
51. #16810855C22semidirect
52. #16810851C22semidirect
53. #16810725C22semidirect
54. C4×#11719924C22semidirect
55. C4×#11719923C22semidirect
65. #16810580C22semidirect
72. C53×#440C22semidirect
384. C2×#440D53semidirect
389. C2×C53#3174semidirect
435. #440C2×D53semidirect
455. C53C2×#3174semidirect
753. C2#20285341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112312
C2×#168112242
#202853412
C2×#168110242
C2×#168109942
C2×#168109902
C2×#168109862
C2×#168108702
C2×#168108662
C2×#168108552
C2×#168108512
C2×#168107252
C2×C4×#117199242
C2×C4×#117199232
C2×#168105802
C2×C53×#4402
C2×#317453