Finite Group Databasebeta

← C2×#20284896 #28252320

Subgroups — C2×#20284896 #28252320

Order 13568.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811242C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic, complemented
3#20284896C2116yesmaximal, direct product factor
4C2×#16810963C211yesmaximal, characteristic, complemented
5C2×#16810945C211yesmaximal, characteristic, complemented
6C2×#16810913C211yesmaximal, characteristic, complemented
7C2×#16810904C211yesmaximal, characteristic, complemented
8C2×#16810835C211yesmaximal, characteristic, complemented
9C2×#16810772C211yesmaximal, characteristic, complemented
10C2×#16810755C211yesmaximal, characteristic
11C2×#16810732C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810708C211yesmaximal, characteristic, complemented
14C2×D8×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811242—24no—
21#16811242C2218yescomplemented
22C2×#13133217C2211yescharacteristic, complemented
23C2×#13133210—21no—
24C2×#13133203—21no—
25C2×#13133201—21no—
26C2×#13133194—21no—
27C2×#13133193C2211yescharacteristic
28C2×#13133188C2211yescharacteristic
29#16811095—24no—
30#16811095C2218yescomplemented
31C2×Q8×Dic53C2211yescharacteristic, complemented
32C2×C4×D212C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic, complemented
35C2×#13133179C2211yescharacteristic
36C2×C4×C22⋊D53—21no—
37C2×#13133177—21no—
38C2×#13133175C2211yescharacteristic
39C2×#13133174C2211yescharacteristic
40C22×#11719921—21no—
41C2×C22⋊C4×D53—21no—
42#16810963C2218yescomplemented
43#16810945C2218yescomplemented
44#16810913C2218yescomplemented
45#16810904C2218yescomplemented
46#16810835C2218yescomplemented
47#16810772C2218yescomplemented
48#16810755C2218yes—
49#16810732C2218yescomplemented
50#16810724C2218yescomplemented
51#16810708C2218yescomplemented
52D8×Dic53C2218yescomplemented
53#16810683C2218yescomplemented
54C2×#13133151C2211yescharacteristic, complemented
55C2×#13133151C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic, complemented
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×Dic106—21no—
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C2×D4×D53—24no—
83C2×D4×D53—24no—
84C2×D4×D53—22no—
85C2×D4×D53C2314yes—
86C23×Dic53—21no—
87C23×Dic53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53C2311yescharacteristic
91C2×#11719924—24no—
92C2×#11719924C2314yes—
93C2×#11719922—24no—
94C2×#11719922C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133217—22no—
98#13133217C2314yescomplemented
99#13133210—28no—
100#13133203—28no—
101#13133201—28no—
102#13133194—28no—
103#13133193—22no—
104#13133193C2314yes—
105#13133188—22no—
106#13133188C2314yes—
107Q8×Dic53—22no—
108Q8×Dic53C2314yescomplemented
109C4×D212—22no—
110C4×D212C2314yes—
111D4×Dic53—22no—
112D4×Dic53—22no—
113D4×Dic53C2314yes—
114D4×Dic53C2314yescomplemented
115#13133179—22no—
116#13133179C2314yes—
117C4×C22⋊D53—28no—
118#13133177—28no—
119#13133175—22no—
120#13133175C2314yes—
121#13133174D414yes—
122#13133174C2314yes—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C2×#11719919D411yescharacteristic
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×#11719921—28no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×#11719921D411yescharacteristic
141C22⋊C4×D53—28no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yescomplemented
146#13133151C2314yescomplemented
147#13133148C2314yescomplemented
148#13133148C2314yescomplemented
149C4⋊#88322C2314yescomplemented
150#13133141C2314yescomplemented
151#13133139C2314yes—
152#13133139C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133138C2314yescomplemented
156#13133129C2314yes—
157#13133129C2314yes—
158#13133127C2314yescomplemented
159C8×Dic53C2314yescomplemented
160C22×Q8×C53C2311yescharacteristic
161C22×D4×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C2×D8×C53—24no—
167C2×D8×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170#124×C53—22no—
171#124×C53C2314yescomplemented
172C4×D4×C53—22no—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181#102×C53C2314yescomplemented
182C24×C53—21no—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—28no—
186C23×D53—24no—
187C23×D53—82no—
188C23×D53—82no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53#4114yes—
200C2×D4×C53C2412yes—
201C2×D4×C53C2412yes—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—82no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—28no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—82no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—24no—
218C22×Dic53—82no—
219C22×Dic53—82no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223D4×D53—216no—
224D4×D53—28no—
225D4×D53—28no—
226C2×D212—21no—
227C2×D212—22no—
228C2×D212#4114yes—
229C2×D212C2412yes—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—82no—
235C2×C4×D53—82no—
236C2×C4×D53C2×D412yes—
237C2×C4×D53C2412yes—
238C2×Dic106—24no—
239C2×Dic106—82no—
240SD16×C53—28no—
241D8×C53—28no—
242C2×C8×C53—22no—
243C2×C8×C53—22no—
244C2×C8×C53C2412yes—
245C2×C8×C53C2412yes—
246C4⋊C4×C53—21no—
247C4⋊C4×C53C2412yes—
248C22⋊C4×C53—24no—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C42×C53C2×D412yes—
252C42×C53C2412yes—
253C22⋊Dic53—24no—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256#11719924—28no—
257#11719922—28no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921C2×D414yes—
263#11719921C2×D414yes—
264C4⋊Dic53—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919C2×D414yes—
274#11719919C2×D414yes—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53C2×D412yes—
278C4×Dic53C2412yes—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322C2412yes—
282C2×#88322C2412yes—
283C23×C53—24no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—24no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—216no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—84no—
301C22×D53—84no—
302C22×D53—816no—
303C22×D53C22×D412yes—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—42no—
307D4×C53—24no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—42no—
312D4×C53C2×#4114yes—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—84no—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4112yes—
324C2×C4×C53C2×#4112yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—216no—
327C22⋊D53—84no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—84no—
338C2×Dic53—84no—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342D212—24no—
343D212—22no—
344D212C2×#4114yes—
345C4×D53—24no—
346C4×D53—22no—
347C4×D53—22no—
348C4×D53—84no—
349C4×D53—84no—
350Dic106—84no—
351C8×C53—22no—
352C8×C53—22no—
353#88322—22no—
354#88322—22no—
355C2×#3118—531nomaximal, Sylow
356C22×C53—24no—
357C22×C53—48no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—84no—
364C22×C53#52512yes—
365C22×C53#57612yes—
366C22×C53#57712yes—
367C22×C53C23×D411yescharacteristic
368C2×D53—22no—
369C2×D53—24no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—44no—
373C2×D53—48no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—816no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#52512yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C22×#4111yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390C2×#542—531no—
391C2×#518—531no—
392#3118—5316no—
393C2×#485—531no—
394C2×#482—531no—
395C2×#476—531no—
396C2×#474—531no—
397C2×#463—531no—
398C2×#463D5311yescharacteristic, complemented
399C2×#450—531no—
400C2×#447—531no—
401C2×#442—531no—
402C2×#440—531no—
403C2×C4×SD16—531no—
404C2×C4×D8—531no—
405C2×#433—531no—
406C2×C53—44no—
407C2×C53—82no—
408C2×C53#311814yescomplemented
409C2×C53C2×#52511yescharacteristic
410C2×C53C2×#57611yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—42no—
413D53—44no—
414C23×D4—531no—
415C22×SD16—531no—
416C22×SD16C2×D5311yescharacteristic
417C22×D8—531no—
418C22×D8C2×D5311yescharacteristic
419#542—538no—
420#542—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—1061no—
423C2×#124—1061no—
424C2×#124C2×D5311yescharacteristic, complemented
425C2×#123—1061no—
426C2×C22⋊Q8—531no—
427C2×C22⋊Q8—1061no—
428C2×#121—531no—
429#518—538no—
430#518—1064no—
431C2×C4×Q8—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×C4×D4—1061no—
438C2×C4×D4C2×D5311yescharacteristic
439C2×#117—531no—
440C2×#117—531no—
441C22×C22⋊C4—1061no—
442C22×C22⋊C4—1061no—
443#485—538no—
444#482—538no—
445#476—538no—
446#474—538no—
447#463—538no—
448#463C2×D5318yescomplemented
449#450—538no—
450#447—538no—
451#442—538no—
452#440—538no—
453C4×SD16—538no—
454C4×D8—538no—
455#433—538no—
456C2×#107—531no—
457C2×#107—531no—
458C2×#106—531no—
459C2×#106—531no—
460C2×C4⋊C8—531no—
461C2×C4⋊C8C2×D5311yescharacteristic, complemented
462C2×#103—531no—
463C2×#103C2×D5311yescharacteristic, complemented
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102C2×D5311yescharacteristic, complemented
470C2×C22⋊C8—531no—
471C2×C22⋊C8—531no—
472C2×#97—531no—
473C2×C4×C8—531no—
474C53C2×#311811yescharacteristic, complemented, Sylow
475C25—1061no—
476C22×Q8—1061no—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—534no—
479C22×D4—531no—
480C22×D4—1062no—
481C22×D4—1061no—
482C22×D4—1064no—
483C22×D4—1064no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C22×D4C22×D5311yescharacteristic
487C23×C4—21no—
488C23×C4—531no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4—1061no—
493C2×SD16—24no—
494C2×SD16—534no—
495C2×SD16—1064no—
496C2×SD16C22×D5314yes—
497C2×D8—24no—
498C2×D8—534no—
499C2×D8—1064no—
500C2×D8C22×D5314yes—
501C22×C8—531no—
502C22×C8—531no—
503C22×C8C22×D5311yescharacteristic
504C22×C8C22×D5311yescharacteristic
505C4⋊Q8—534no—
506C4⋊Q8—1062no—
507#126—1068no—
508#124—22no—
509#124—1068no—
510#124C22×D5314yescomplemented
511#123—1068no—
512C22⋊Q8—534no—
513C22⋊Q8—1068no—
514C22⋊Q8—1062no—
515#121—534no—
516#121—1062no—
517C4×Q8—534no—
518C4×Q8—1062no—
519C4×D4—22no—
520C4×D4—534no—
521C4×D4—534no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—1062no—
525C4×D4—1062no—
526C4×D4—1062no—
527C4×D4—1068no—
528C4×D4—1068no—
529C4×D4—1062no—
530C4×D4C22×D5314yes—
531#117—534no—
532#117—534no—
533#117—534no—
534#117—1062no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—531no—
548C2×C22⋊C4—531no—
549C2×C22⋊C4—1068no—
550C2×C22⋊C4—1068no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—531no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107—534no—
564#106—534no—
565#106—534no—
566C4⋊C8—534no—
567C4⋊C8C22×D5314yescomplemented
568#103—534no—
569#103C22×D5314yescomplemented
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102—534no—
575#102C22×D5314yescomplemented
576C22⋊C8—534no—
577C22⋊C8—534no—
578#97—534no—
579C4×C8—534no—
580C24—21no—
581C24—21no—
582C24—531no—
583C24—1064no—
584C24—1068no—
585C24—1061no—
586C24—4242no—
587C24—4242no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—1064no—
592C2×Q8—4242no—
593C2×Q8C23×D5312yes—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—534no—
600C2×D4—532no—
601C2×D4—1064no—
602C2×D4—1068no—
603C2×D4—10616no—
604C2×D4—1068no—
605C2×D4—1068no—
606C2×D4—1064no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—4242no—
610C2×D4#1171994714yes—
611C2×D4C23×D5312yes—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—82no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—532no—
621C22×C4—532no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1064no—
631C22×C4—4242no—
632C22×C4—4242no—
633C22×C4—4242no—
634C22×C4—4242no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—28no—
639SD16—1068no—
640D8—28no—
641D8—1068no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8C23×D5312yes—
649C2×C8C23×D5312yes—
650C4⋊C4—21no—
651C4⋊C4—534no—
652C4⋊C4—534no—
653C4⋊C4—532no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1061no—
659C4⋊C4—1061no—
660C4⋊C4—1061no—
661C4⋊C4—1064no—
662C4⋊C4C23×D5312yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—534no—
667C22⋊C4—534no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C42—532no—
676C42—532no—
677C42—1064no—
678C42—1064no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—532no—
690C23—10616no—
691C23—1062no—
692C23—1064no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—4244no—
697C23—4244no—
698C23—42416no—
699C23—2122no—
700C23—2122no—
701C23C2×D4×D5311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—4244no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—534no—
712D4—10616no—
713D4—1064no—
714D4—1062no—
715D4—4244no—
716D4C2×#1171994714yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1064no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—4244no—
737C2×C4—4244no—
738C2×C4—4244no—
739C2×C4—4244no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5312yes—
745C2×C4C2×D4×D5311yescharacteristic
746C2×C4#41×D5312yes—
747C2×C4C2×#1171994712yes—
748C2×C4C24×D5311yescharacteristic
749C8—22no—
750C8—22no—
751C8—1062no—
752C8—1062no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—1062no—
762C22—1062no—
763C22—1062no—
764C22—1064no—
765C22—42416no—
766C22—2122no—
767C22—2122no—
768C22—2124no—
769C22—2128no—
770C22#1681113312yes—
771C22#1681142512yes—
772C22#1681143312yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—1062no—
779C4—1062no—
780C4—1062no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4#1681113312yes—
785C4C2×#41×D5311yescharacteristic
786C4C22×#1171994711yescharacteristic
787C2—44no—
788C2—82no—
789C2—2122no—
790C2—2124no—
791C2#2028489614yesdirect product factor
792C2C2×#1681113311yescharacteristic
793C2C2×#1681142511yescharacteristic
794C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC2×#16810755C2
hypercenterC2×#463D53
hypocenterC53C2×#3118
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×#16811242C2semidirect
2. C2×#16811095C2semidirect
3. #20284896C2direct (N × H)
4. C2×#16810963C2semidirect
5. C2×#16810945C2semidirect
6. C2×#16810913C2semidirect
7. C2×#16810904C2semidirect
8. C2×#16810835C2semidirect
9. C2×#16810772C2semidirect
11. C2×#16810732C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810708C2semidirect
14. C2×D8×Dic53C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#463C2semidirect
21. #16811242C22semidirect
22. C2×#13133217C22semidirect
30. #16811095C22semidirect
31. C2×Q8×Dic53C22semidirect
34. C2×D4×Dic53C22semidirect
42. #16810963C22semidirect
43. #16810945C22semidirect
44. #16810913C22semidirect
45. #16810904C22semidirect
46. #16810835C22semidirect
47. #16810772C22semidirect
49. #16810732C22semidirect
50. #16810724C22semidirect
51. #16810708C22semidirect
52. D8×Dic53C22semidirect
53. #16810683C22semidirect
54. C2×#13133151C22semidirect
55. C2×#13133151C22semidirect
56. C2×#13133148C22semidirect
57. C2×#13133148C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133141C22semidirect
64. C2×#13133138C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
71. C2×#124×C53C22semidirect
73. C53×#463C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
76. C2×#102×C53C22semidirect
98. #13133217C23semidirect
108. Q8×Dic53C23semidirect
114. D4×Dic53C23semidirect
145. #13133151C23semidirect
146. #13133151C23semidirect
147. #13133148C23semidirect
148. #13133148C23semidirect
149. C4⋊#88322C23semidirect
150. #13133141C23semidirect
155. #13133138C23semidirect
158. #13133127C23semidirect
159. C8×Dic53C23semidirect
171. #124×C53C23semidirect
179. C4⋊C8×C53C23semidirect
180. #103×C53C23semidirect
181. #102×C53C23semidirect
398. C2×#463D53semidirect
408. C2×C53#3118semidirect
424. C2×#124C2×D53semidirect
448. #463C2×D53semidirect
461. C2×C4⋊C8C2×D53semidirect
463. C2×#103C2×D53semidirect
469. C2×#102C2×D53semidirect
474. C53C2×#3118semidirect
510. #124C22×D53semidirect
567. C4⋊C8C22×D53semidirect
569. #103C22×D53semidirect
575. #102C22×D53semidirect
791. C2#20284896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112422
C2×#168110952
#202848962
C2×#168109632
C2×#168109452
C2×#168109132
C2×#168109042
C2×#168108352
C2×#168107722
C2×#168107552
C2×#168107322
C2×#168107242
C2×#168107082
C2×D8×Dic532
C2×#168106832
C2×C53×#4632
C2×#311853