Finite Group Databasebeta

← C2×#20284963 #28252392

Subgroups — C2×#20284963 #28252392

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811233C211yesmaximal, characteristic, complemented
2C2×#16811097C211yesmaximal, characteristic
3#20284963C2116yesmaximal, direct product factor
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810926C211yesmaximal, characteristic, complemented
6C2×#16810922C211yesmaximal, characteristic, complemented
7C2×#16810827C211yesmaximal, characteristic, complemented
8C2×#16810827C211yesmaximal, characteristic, complemented
9C2×#16810776C211yesmaximal, characteristic
10C2×#16810773C211yesmaximal, characteristic
11C2×#16810726C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22#16811233—24no—
23#16811233C2218yescomplemented
24C2×#13133215C2211yescharacteristic, complemented
25C2×#13133210—21no—
26C2×#13133210—21no—
27C2×#13133208—21no—
28C2×#13133208C2211yescharacteristic, complemented
29C2×#13133207—21no—
30C2×#13133196C2211yescharacteristic
31#16811097—24no—
32#16811097C2218yes—
33C2×Q8×Dic53C2211yescharacteristic, complemented
34C2×#13133182C2211yescharacteristic, complemented
35C2×C4×D212—21no—
36C2×C4×D212—21no—
37C2×#13133179C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133176C2211yescharacteristic
42C2×C22⋊C4×D53—21no—
43C2×C22⋊C4×D53—21no—
44#16810964C2218yescomplemented
45#16810926C2218yescomplemented
46#16810922C2218yescomplemented
47#16810827C2218yescomplemented
48#16810827C2218yescomplemented
49#16810776C2218yes—
50#16810773C2218yes—
51#16810726C2218yescomplemented
52#16810722C2218yescomplemented
53#16810710C2218yescomplemented
54#16810708C2218yescomplemented
55#16810681C2218yescomplemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212—22no—
81C22×D212—24no—
82C22×D212—24no—
83C22×D212C2314yes—
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C2×#11719913—24no—
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719913C2314yes—
94C2×#11719924—24no—
95C2×#11719924—24no—
96C2×#11719924C2314yes—
97C2×#11719924C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100#13133215—22no—
101#13133215C2314yescomplemented
102#13133210—28no—
103#13133210—28no—
104#13133208—28no—
105#13133208—22no—
106#13133208C2314yescomplemented
107#13133207—28no—
108#13133196—22no—
109#13133196C2314yes—
110Q8×Dic53—22no—
111Q8×Dic53C2314yescomplemented
112#13133182—22no—
113#13133182C2314yescomplemented
114C4×D212—28no—
115C4×D212—28no—
116#13133179—22no—
117#13133179—22no—
118#13133179—22no—
119#13133179—22no—
120#13133179C2314yes—
121#13133179C2314yes—
122#13133179C2314yes—
123#13133179C2314yes—
124#13133176D414yes—
125#13133176C2314yes—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53D411yescharacteristic
129C2×C4⋊Dic53D411yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53D411yescharacteristic
138C2×C22⋊Dic53D411yescharacteristic
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C22⋊C4×D53—28no—
144C22⋊C4×D53—28no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yescomplemented
150#13133148C2314yescomplemented
151#13133146C2314yescomplemented
152#13133146C2314yescomplemented
153#13133140C2314yescomplemented
154#13133140C2314yescomplemented
155#13133139C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160#13133127C2314yescomplemented
161C8×Dic53C2314yescomplemented
162C22×Q8×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53C2314yes—
168#117×C53—22no—
169#117×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yescomplemented
178#106×C53C2314yescomplemented
179#103×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181C22⋊C8×C53C2314yes—
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—28no—
186C23×D53—24no—
187C23×D53—82no—
188C23×D53—82no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C2×D212—28no—
210C2×D212—216no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212—24no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—28no—
217C2×D212—28no—
218C2×D212#4114yes—
219C2×D212#4114yes—
220C2×D212C2412yes—
221C2×D212C2412yes—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—82no—
227C2×C4×D53—82no—
228C2×C4×D53—82no—
229C2×C4×D53—82no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106C2412yes—
234C2×C8×C53—22no—
235C2×C8×C53—22no—
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C42×C53—24no—
248C22⋊Dic53—24no—
249C22⋊Dic53C2×D414yes—
250C22⋊Dic53C2×D414yes—
251#11719924—28no—
252#11719924—28no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—24no—
259C4⋊Dic53—24no—
260C4⋊Dic53C2×D414yes—
261C4⋊Dic53C2×D414yes—
262C4⋊Dic53C2412yes—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53C2×D412yes—
271C4×Dic53C2×D412yes—
272C4×Dic53C2412yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278#11719913—28no—
279#11719913—28no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53C22×D412yes—
284C23×C53C22×D411yescharacteristic
285C22×D53—24no—
286C22×D53—24no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—216no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—84no—
295C22×D53—84no—
296C22×D53—816no—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—42no—
300C2×C4×C53—22no—
301C2×C4×C53—24no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C2×#4112yes—
315C2×C4×C53C2×#4112yes—
316C2×C4×C53C2511yescharacteristic
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329D212—216no—
330D212—24no—
331D212—24no—
332D212—22no—
333D212—22no—
334D212C2×#4114yes—
335D212C2×#4114yes—
336C4×D53—84no—
337C4×D53—84no—
338C4×D53—84no—
339C4×D53—84no—
340Dic106—22no—
341Dic106—22no—
342Dic106—42no—
343C8×C53—22no—
344C8×C53—22no—
345#88322—22no—
346#88322—22no—
347C2×#3123—531nomaximal, Sylow
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—44no—
352C22×C53#52512yes—
353C22×C53#57712yes—
354C22×C53#57712yes—
355C22×C53C23×D411yescharacteristic
356C2×D53—24no—
357C2×D53—24no—
358C2×D53—48no—
359C2×D53—48no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—816no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#52512yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C22×#4111yescharacteristic
373Dic53—22no—
374Dic53—22no—
375Dic53—22no—
376Dic53—22no—
377Dic53—42no—
378Dic53—42no—
379C2×#541—531no—
380C2×#518—531no—
381#3123—5316no—
382C2×#485—531no—
383C2×#485D5311yescharacteristic, complemented
384C2×#478—531no—
385C2×#478—531no—
386C2×#461—531no—
387C2×#461—531no—
388C2×#450—531no—
389C2×#450—531no—
390C2×#440—531no—
391C2×#440—531no—
392C2×C4×SD16—531no—
393C2×C4×SD16—531no—
394C2×#433—531no—
395C2×C53—42no—
396C2×C53#312314yescomplemented
397C2×C53C2×#52511yescharacteristic
398C2×C53C2×#57711yescharacteristic
399C2×C53C2×#57711yescharacteristic
400D53—44no—
401D53—44no—
402C23×D4—531no—
403C22×SD16—531no—
404C22×SD16—531no—
405C22×SD16—531no—
406C22×SD16—531no—
407#541—538no—
408#541—1064no—
409C2×C4⋊Q8—531no—
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#125—531no—
413C2×#125—1061no—
414C2×#125—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8C2×D5311yescharacteristic
417#518—538no—
418#518—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×C4×D4—1061no—
426C2×C4×D4—1061no—
427C2×#117—531no—
428C2×#117C2×D5311yescharacteristic
429C22×C22⋊C4—1061no—
430C22×C22⋊C4—1061no—
431#485—538no—
432#485C2×D5318yescomplemented
433#478—538no—
434#478—538no—
435#461—538no—
436#461—538no—
437#450—538no—
438#450—538no—
439#440—538no—
440#440—538no—
441C4×SD16—538no—
442C4×SD16—538no—
443#433—538no—
444C2×#107—531no—
445C2×#107C2×D5311yescharacteristic, complemented
446C2×#106—531no—
447C2×#106C2×D5311yescharacteristic, complemented
448C2×C4⋊C8—531no—
449C2×C4⋊C8—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103C2×D5311yescharacteristic, complemented
453C2×#103C2×D5311yescharacteristic, complemented
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×C22⋊C8—531no—
459C2×C22⋊C8C2×D5311yescharacteristic
460C2×#97—531no—
461C2×C4×C8—531no—
462C53C2×#312311yescharacteristic, complemented, Sylow
463C25—1061no—
464C22×Q8—531no—
465C22×Q8C22×D5311yescharacteristic
466C22×D4—531no—
467C22×D4—531no—
468C22×D4—534no—
469C22×D4—1064no—
470C22×D4—1064no—
471C22×D4—1061no—
472C22×D4—1062no—
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C2×SD16—534no—
479C2×SD16—534no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16—1064no—
485C2×SD16—1064no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—1068no—
493#126—1068no—
494#125—534no—
495#125—1062no—
496#125—1068no—
497#125—1068no—
498C22⋊Q8—22no—
499C22⋊Q8—534no—
500C22⋊Q8—1062no—
501C22⋊Q8C22×D5314yes—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×D4—534no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1068no—
511C4×D4—1068no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1062no—
515C4×D4—1062no—
516#117—22no—
517#117—534no—
518#117—534no—
519#117C22×D5314yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
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×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—531no—
538C2×C22⋊C4—1068no—
539C2×C22⋊C4—1068no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C42—21no—
546C2×C42—531no—
547C2×C42—531no—
548C2×C42—1061no—
549C2×C42—1061no—
550#107—534no—
551#107C22×D5314yescomplemented
552#106—534no—
553#106C22×D5314yescomplemented
554C4⋊C8—534no—
555C4⋊C8—534no—
556#103—534no—
557#103—534no—
558#103C22×D5314yescomplemented
559#103C22×D5314yescomplemented
560#102—534no—
561#102—534no—
562#102—534no—
563#102—534no—
564C22⋊C8—534no—
565C22⋊C8C22×D5314yes—
566#97—534no—
567C4×C8—534no—
568C24—1068no—
569C24—1064no—
570C24—1061no—
571C24—1061no—
572C24—4242no—
573C24—4242no—
574C24D4×D5311yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—532no—
579C2×Q8—1061no—
580C2×Q8—1062no—
581C2×Q8—1062no—
582C2×Q8C23×D5312yes—
583C2×D4—534no—
584C2×D4—534no—
585C2×D4—532no—
586C2×D4—532no—
587C2×D4—1068no—
588C2×D4—1068no—
589C2×D4—1068no—
590C2×D4—10616no—
591C2×D4—1064no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—1062no—
595C2×D4—1062no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—531no—
603C22×C4—531no—
604C22×C4—531no—
605C22×C4—531no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1064no—
609C22×C4—1064no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—4242no—
613C22×C4—4242no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620SD16—1068no—
621SD16—1068no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—534no—
637C4⋊C4—534no—
638C4⋊C4—532no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1061no—
646C4⋊C4—1064no—
647C4⋊C4C23×D5312yes—
648C4⋊C4C23×D5312yes—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—534no—
653C22⋊C4—534no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C42—24no—
660C42—532no—
661C42—532no—
662C42—532no—
663C42—532no—
664C42—1064no—
665C42—1064no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—10616no—
670C23—1064no—
671C23—1064no—
672C23—1062no—
673C23—1062no—
674C23—4244no—
675C23—4244no—
676C23—42416no—
677C23—2122no—
678C23—2122no—
679C23—2122no—
680C23—2122no—
681C23C2×D4×D5312yes—
682C23C2×D4×D5311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—1062no—
687Q8—1062no—
688Q8—2122no—
689D4—534no—
690D4—534no—
691D4—10616no—
692D4—1064no—
693D4—1064no—
694D4—1062no—
695D4—1062no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—532no—
709C2×C4—532no—
710C2×C4—532no—
711C2×C4—532no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—4244no—
719C2×C4—4244no—
720C2×C4—4244no—
721C2×C4—4244no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4C2×D4×D5312yes—
725C2×C4C2×D4×D5311yescharacteristic
726C2×C4#41×D5312yes—
727C2×C4#41×D5312yes—
728C2×C4C24×D5311yescharacteristic
729C8—22no—
730C8—22no—
731C8—1062no—
732C8—1062no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—1064no—
738C22—1064no—
739C22—42416no—
740C22—2128no—
741C22—2128no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22#1681113112yes—
747C22#1681143012yes—
748C22#1681143212yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1062no—
756C4—1062no—
757C4—1062no—
758C4—1062no—
759C4—2122no—
760C4—2122no—
761C4#1681113112yes—
762C4C2×#41×D5311yescharacteristic
763C4C2×#41×D5311yescharacteristic
764C2—42no—
765C2—2124no—
766C2—2124no—
767C2#2028496314yesdirect product factor
768C2C2×#1681113111yescharacteristic
769C2C2×#1681143011yescharacteristic
770C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC23×D212C22
hypercenterC2×#485D53
hypocenterC53C2×#3123
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16811233C2semidirect
3. #20284963C2direct (N × H)
4. C2×#16810964C2semidirect
5. C2×#16810926C2semidirect
6. C2×#16810922C2semidirect
7. C2×#16810827C2semidirect
8. C2×#16810827C2semidirect
11. C2×#16810726C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810710C2semidirect
14. C2×#16810708C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#485C2semidirect
23. #16811233C22semidirect
24. C2×#13133215C22semidirect
28. C2×#13133208C22semidirect
33. C2×Q8×Dic53C22semidirect
34. C2×#13133182C22semidirect
44. #16810964C22semidirect
45. #16810926C22semidirect
46. #16810922C22semidirect
47. #16810827C22semidirect
48. #16810827C22semidirect
51. #16810726C22semidirect
52. #16810722C22semidirect
53. #16810710C22semidirect
54. #16810708C22semidirect
55. #16810681C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133140C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
71. C53×#485C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
101. #13133215C23semidirect
106. #13133208C23semidirect
111. Q8×Dic53C23semidirect
113. #13133182C23semidirect
149. #13133150C23semidirect
150. #13133148C23semidirect
151. #13133146C23semidirect
152. #13133146C23semidirect
153. #13133140C23semidirect
154. #13133140C23semidirect
160. #13133127C23semidirect
161. C8×Dic53C23semidirect
177. #107×C53C23semidirect
178. #106×C53C23semidirect
179. #103×C53C23semidirect
180. #103×C53C23semidirect
383. C2×#485D53semidirect
396. C2×C53#3123semidirect
432. #485C2×D53semidirect
445. C2×#107C2×D53semidirect
447. C2×#106C2×D53semidirect
452. C2×#103C2×D53semidirect
453. C2×#103C2×D53semidirect
462. C53C2×#3123semidirect
551. #107C22×D53semidirect
553. #106C22×D53semidirect
558. #103C22×D53semidirect
559. #103C22×D53semidirect
767. C2#20284963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168110972
#202849632
C2×#168109642
C2×#168109262
C2×#168109222
C2×#168108272
C2×#168107762
C2×#168107732
C2×#168107262
C2×#168107222
C2×#168107102
C2×#168107082
C2×#168106812
C2×C53×#4852
C2×#312353