Finite Group Databasebeta

← C2×#20284510 #28251601

Subgroups — C2×#20284510 #28251601

Order 13568.

2530 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811179C211yesmaximal, characteristic, complemented
2C2×C4×D4×D53C211yesmaximal, characteristic
3#20284510C2116yesmaximal, direct product factor
4C2×#16810924C211yesmaximal, characteristic, complemented
5C2×#16810923C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810912C211yesmaximal, characteristic, complemented
8C2×#16810911C211yesmaximal, characteristic, complemented
9C2×#16810902C211yesmaximal, characteristic, complemented
10C2×#16810901C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic, complemented
12C2×#16810662C211yesmaximal, characteristic, complemented
13C2×#16810645C211yesmaximal, characteristic, complemented
14C2×#16810626C211yesmaximal, characteristic
15C2×#16810626C211yesmaximal, characteristic
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C23×C4×D53—21no—
19C22×#11719912C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21#16811179—24no—
22#16811179C2218yescomplemented
23C2×#13133216C2211yescharacteristic, complemented
24C2×#13133216C2211yescharacteristic, complemented
25C2×#13133209C2211yescharacteristic, complemented
26C2×#13133195—21no—
27C2×#13133195—21no—
28C2×#13133182—21no—
29C2×#13133182—21no—
30C2×C4×D212C2211yescharacteristic
31C2×D4×Dic53C2211yescharacteristic
32C2×#13133179C2211yescharacteristic
33C2×C4×C22⋊D53—21no—
34C2×#13133177—21no—
35C4×D4×D53—24no—
36C4×D4×D53C2218yes—
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C22⋊C4×D53—21no—
41C2×C42×D53C2211yescharacteristic
42#16810924C2218yescomplemented
43#16810923C2218yescomplemented
44#16810920C2218yescomplemented
45#16810912C2218yescomplemented
46#16810911C2218yescomplemented
47#16810902C2218yescomplemented
48#16810901C2218yescomplemented
49#16810664C2218yescomplemented
50#16810662C2218yescomplemented
51C2×#13133151C2211yescharacteristic, complemented
52C2×#13133150C2211yescharacteristic, complemented
53C2×#13133150C2211yescharacteristic, complemented
54C2×#13133149C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133148C2211yescharacteristic, complemented
57#16810645C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133146C2211yescharacteristic, complemented
61#16810626C2218yes—
62#16810626C2218yes—
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic, complemented
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C2×D4×D53—22no—
83C2×D4×D53—24no—
84C2×D4×D53Q818yescomplemented
85C2×D4×D53C2314yes—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—28no—
91C22×C4×D53—48no—
92C22×C4×D53D411yescharacteristic
93C22×C4×D53D411yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C2×#11719912—24no—
96C2×#11719912—24no—
97C2×#11719912C2314yes—
98C2×#11719912C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133216—22no—
102#13133216—22no—
103#13133216C2314yescomplemented
104#13133216C2314yescomplemented
105#13133209—22no—
106#13133209C2314yescomplemented
107#13133195—28no—
108#13133195—28no—
109#13133182—28no—
110#13133182—28no—
111C4×D212—22no—
112C4×D212C2314yes—
113D4×Dic53—22no—
114D4×Dic53C2314yes—
115#13133179—22no—
116#13133179C2314yes—
117C4×C22⋊D53—28no—
118#13133177—28no—
119#13133175—22no—
120#13133175—22no—
121#13133175C2314yes—
122#13133175C2314yes—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C22⋊C4×D53—28no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144C42×D53D414yes—
145C42×D53C2314yes—
146#13133151C2314yescomplemented
147#13133150C2314yescomplemented
148#13133150C2314yescomplemented
149#13133149C2314yescomplemented
150#13133148C2314yescomplemented
151#13133148C2314yescomplemented
152C4⋊#88322C2314yescomplemented
153#13133146C2314yescomplemented
154#13133146C2314yescomplemented
155#13133139C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161C22×D4×C53C2311yescharacteristic
162C23×C4×C53—21no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#125×C53—22no—
166#125×C53C2314yescomplemented
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C42×C53C2311yescharacteristic
176#107×C53C2314yescomplemented
177#106×C53C2314yescomplemented
178C4⋊C8×C53C2314yescomplemented
179#102×C53C2314yes—
180#102×C53C2314yes—
181C24×C53—21no—
182C23×D53—21no—
183C23×D53—28no—
184C23×D53—24no—
185C23×D53—44no—
186C23×D53—44no—
187C23×D53C2×D411yescharacteristic
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53C2×Q814yes—
191C2×D4×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—28no—
201C2×C22⋊D53—24no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—24no—
206C22×Dic53—44no—
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210D4×D53—216no—
211D4×D53—28no—
212D4×D53C2×Q8116yescomplemented
213C2×D212—21no—
214C2×D212—22no—
215C2×D212C2×Q814yes—
216C2×D212C2412yes—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—432no—
222C2×C4×D53—42no—
223C2×C4×D53—44no—
224C2×C4×D53—44no—
225C2×C4×D53—44no—
226C2×C4×D53C2×D414yes—
227C2×C4×D53C2×D414yes—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2×Q814yes—
230C2×C4×D53#4114yes—
231C2×C4×D53C2412yes—
232C2×Dic106—24no—
233C2×Dic106—24no—
234C2×Dic106—44no—
235C2×Dic106—44no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53C2412yes—
246C4⋊C4×C53C2412yes—
247C4⋊C4×C53C2412yes—
248C22⋊C4×C53—24no—
249C42×C53C2×D412yes—
250C42×C53C2412yes—
251C22⋊Dic53—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53C2×D412yes—
270C4×Dic53C2×D414yes—
271C4×Dic53C2×D414yes—
272C4×Dic53C2412yes—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277#11719912—28no—
278#11719912—28no—
279C23×C53—24no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53C22×D411yescharacteristic
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—24no—
287C22×D53—22no—
288C22×D53—216no—
289C22×D53—48no—
290C22×D53—432no—
291C22×D53—48no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53C22⋊Q814yes—
295C22×D53C22×D412yes—
296D4×C53—24no—
297D4×C53—22no—
298D4×C53C22×Q814yes—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—48no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C22×Q812yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—216no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—48no—
323C2×Dic53C22⋊Q814yes—
324C2×Dic53AGL(1,ℤ/8)14yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328D212—24no—
329D212—22no—
330D212C22×Q814yes—
331C4×D53—28no—
332C4×D53—44no—
333C4×D53—48no—
334C4×D53—48no—
335C4×D53—48no—
336C4×D53C22⋊Q818yes—
337C4×D53C22×Q814yes—
338C4×D53C2×#4114yes—
339Dic106—48no—
340Dic106—48no—
341C8×C53—22no—
342C8×C53—22no—
343#88322—22no—
344#88322—22no—
345C2×#3077—531nomaximal, Sylow
346C22×C53—24no—
347C22×C53—48no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53C2×C22⋊Q812yes—
351C22×C53C2×AGL(1,ℤ/8)12yes—
352C22×C53#57512yes—
353C22×C53C23×D411yescharacteristic
354C2×D53—28no—
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—24no—
358C2×D53—432no—
359C2×D53—48no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53C2×C22⋊Q814yes—
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—42no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53C2×C22⋊Q812yes—
369C4×C53C23×Q811yescharacteristic
370C4×C53C22×#4111yescharacteristic
371Dic53—22no—
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53C2×C22⋊Q814yes—
376Dic53C2×AGL(1,ℤ/8)14yes—
377C2×#533—531no—
378C22×C4×D4—531no—
379#3077—5316no—
380C2×#478—531no—
381C2×#478—531no—
382C2×#478—531no—
383C2×#478D5311yescharacteristic, complemented
384C2×#476—531no—
385C2×#476—531no—
386C2×#474—531no—
387C2×#474—531no—
388C2×#428—531no—
389C2×#428—531no—
390C2×#423—531no—
391C2×#418—531no—
392C2×#418—531no—
393C2×C53—44no—
394C2×C53#307714yescomplemented
395C2×C53C22×C22⋊Q811yescharacteristic
396C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C53C2×#57511yescharacteristic
398D53—24no—
399D53—44no—
400C23×D4—531no—
401C24×C4—1061no—
402C22×M16—531no—
403C22×M16—531no—
404#533—538no—
405#533—1064no—
406C2×C4⋊Q8—531no—
407C2×C4⋊Q8—531no—
408C2×#125—531no—
409C2×#125C2×D5311yescharacteristic, complemented
410C2×C22⋊Q8—1061no—
411C2×C22⋊Q8—1061no—
412C2×C4×Q8—1061no—
413C2×C4×Q8—1061no—
414C2×C4×D4—531no—
415C2×C4×D4—538no—
416C2×C4×D4—531no—
417C2×C4×D4—531no—
418C2×C4×D4—1061no—
419C2×C4×D4—1064no—
420C2×C4×D4—1061no—
421C2×C4×D4C2×D5311yescharacteristic
422C2×#117—531no—
423C2×#117—531no—
424C22×C4⋊C4—531no—
425C22×C22⋊C4—1061no—
426C22×C42—531no—
427#478—538no—
428#478—538no—
429#478—538no—
430#478C2×D5318yescomplemented
431#476—538no—
432#476—538no—
433#474—538no—
434#474—538no—
435#428—538no—
436#428—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107C2×D5311yescharacteristic, complemented
441C2×#106—531no—
442C2×#106—531no—
443C2×#106—531no—
444C2×#106C2×D5311yescharacteristic, complemented
445#423—538no—
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×C4⋊C8—531no—
449C2×C4⋊C8C2×D5311yescharacteristic, complemented
450#418—538no—
451#418—538no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102C2×D5311yescharacteristic
459C2×#102C2×D5311yescharacteristic
460C53C2×#307711yescharacteristic, complemented, Sylow
461C25—1061no—
462C22×Q8—1061no—
463C22×Q8—1061no—
464C22×D4—538no—
465C22×D4—534no—
466C22×D4—531no—
467C22×D4—1062no—
468C22×D4—1064no—
469C22×D4—1061no—
470C22×D4C22×D5311yescharacteristic
471C23×C4—21no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1068no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—2128no—
481C2×M16—534no—
482C2×M16—534no—
483C2×M16—1064no—
484C2×M16—1064no—
485C22×C8—531no—
486C22×C8—531no—
487C22×C8C22×D5311yescharacteristic
488C22×C8C22×D5311yescharacteristic
489C4⋊Q8—534no—
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492C4⋊Q8—1062no—
493#125—22no—
494#125—534no—
495#125—1062no—
496#125C22×D5314yescomplemented
497C22⋊Q8—1068no—
498C22⋊Q8—1068no—
499C4×Q8—1068no—
500C4×Q8—1068no—
501C4×D4—22no—
502C4×D4—534no—
503C4×D4—534no—
504C4×D4—534no—
505C4×D4—1068no—
506C4×D4—1062no—
507C4×D4—1068no—
508C4×D4—1062no—
509C4×D4—1062no—
510C4×D4C22×D5314yes—
511#117—534no—
512#117—534no—
513#117—1062no—
514#117—1062no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—534no—
521C2×C4⋊C4—1062no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C4⋊C4C22×D5311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—1068no—
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—531no—
540C2×C42—534no—
541C2×C42—534no—
542C2×C42—1061no—
543C2×C42—1061no—
544C2×C42C22×D5311yescharacteristic
545#107—534no—
546#107—534no—
547#107—534no—
548#107C22×D5314yescomplemented
549#106—534no—
550#106—534no—
551#106—534no—
552#106C22×D5314yescomplemented
553C4⋊C8—534no—
554C4⋊C8—534no—
555C4⋊C8—534no—
556C4⋊C8C22×D5314yescomplemented
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562#102—534no—
563#102C22×D5314yes—
564#102C22×D5314yes—
565C24—21no—
566C24—531no—
567C24—1064no—
568C24—1068no—
569C24—1061no—
570C24—2124no—
571C24—2124no—
572C2×Q8—1064no—
573C2×Q8—1064no—
574C2×Q8—2124no—
575C2×Q8—2124no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—5316no—
579C2×D4—534no—
580C2×D4—532no—
581C2×D4—10616no—
582C2×D4—1068no—
583C2×D4—1064no—
584C2×D4—1068no—
585C2×D4—1061no—
586C2×D4—1062no—
587C2×D4Q8×D5314yes—
588C2×D4C23×D5312yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—44no—
594C22×C4—531no—
595C22×C4—531no—
596C22×C4—532no—
597C22×C4—534no—
598C22×C4—534no—
599C22×C4—532no—
600C22×C4—531no—
601C22×C4—534no—
602C22×C4—534no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1064no—
606C22×C4—1064no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1064no—
611C22×C4—2122no—
612C22×C4—2124no—
613C22×C4—2124no—
614C22×C4—21232no—
615C22×C4—2124no—
616C22×C4—2124no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620M16—1068no—
621M16—1068no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—1062no—
627C2×C8—1062no—
628C2×C8C23×D5312yes—
629C2×C8C23×D5312yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—532no—
636C4⋊C4—532no—
637C4⋊C4—532no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1061no—
644C4⋊C4—1064no—
645C4⋊C4—1064no—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C4⋊C4C23×D5312yes—
649C22⋊C4—24no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C42—534no—
656C42—534no—
657C42—532no—
658C42—532no—
659C42—1064no—
660C42—1064no—
661C42D4×D5312yes—
662C42C23×D5312yes—
663C23—24no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—534no—
668C23—532no—
669C23—10616no—
670C23—1062no—
671C23—1062no—
672C23—1064no—
673C23—1062no—
674C23—2128no—
675C23—21232no—
676C23—2128no—
677C23—2122no—
678C23—2122no—
679C23C2×D4×D5311yescharacteristic
680Q8—2128no—
681Q8—2128no—
682D4—24no—
683D4—22no—
684D4—534no—
685D4—10616no—
686D4—1064no—
687D4—1062no—
688D4C2×Q8×D5314yes—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—534no—
699C2×C4—534no—
700C2×C4—532no—
701C2×C4—532no—
702C2×C4—538no—
703C2×C4—534no—
704C2×C4—534no—
705C2×C4—532no—
706C2×C4—1068no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—2124no—
712C2×C4—2128no—
713C2×C4—2128no—
714C2×C4—2128no—
715C2×C4—2128no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4C2×D4×D5312yes—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5311yescharacteristic
722C2×C4C2×Q8×D5312yes—
723C2×C4#41×D5312yes—
724C2×C4C24×D5311yescharacteristic
725C8—22no—
726C8—22no—
727C8—1062no—
728C8—1062no—
729C22—24no—
730C22—48no—
731C22—42no—
732C22—42no—
733C22—534no—
734C22—1068no—
735C22—1062no—
736C22—1062no—
737C22—1064no—
738C22—21232no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22C22⋊Q8×D5312yes—
743C22AGL(1,ℤ/8)×D5312yes—
744C22#1681142012yes—
745C22C22×D4×D5311yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—534no—
752C4—534no—
753C4—1062no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C4C22⋊Q8×D5312yes—
758C4C22×Q8×D5311yescharacteristic
759C4C2×#41×D5311yescharacteristic
760C2—44no—
761C2—1064no—
762C2—2124no—
763C2#2028451014yesdirect product factor
764C2C2×C22⋊Q8×D5311yescharacteristic
765C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
766C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×#478D53
hypocenterC53C2×#3077
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×#16811179C2semidirect
3. #20284510C2direct (N × H)
4. C2×#16810924C2semidirect
5. C2×#16810923C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810912C2semidirect
8. C2×#16810911C2semidirect
9. C2×#16810902C2semidirect
10. C2×#16810901C2semidirect
11. C2×#16810664C2semidirect
12. C2×#16810662C2semidirect
13. C2×#16810645C2semidirect
16. C2×C53×#478C2semidirect
22. #16811179C22semidirect
23. C2×#13133216C22semidirect
24. C2×#13133216C22semidirect
25. C2×#13133209C22semidirect
42. #16810924C22semidirect
43. #16810923C22semidirect
44. #16810920C22semidirect
45. #16810912C22semidirect
46. #16810911C22semidirect
47. #16810902C22semidirect
48. #16810901C22semidirect
49. #16810664C22semidirect
50. #16810662C22semidirect
51. C2×#13133151C22semidirect
52. C2×#13133150C22semidirect
53. C2×#13133150C22semidirect
54. C2×#13133149C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133148C22semidirect
57. #16810645C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133146C22semidirect
60. C2×#13133146C22semidirect
69. C2×#125×C53C22semidirect
71. C53×#478C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×C4⋊C8×C53C22semidirect
84. C2×D4×D53Q8semidirect
103. #13133216C23semidirect
104. #13133216C23semidirect
106. #13133209C23semidirect
146. #13133151C23semidirect
147. #13133150C23semidirect
148. #13133150C23semidirect
149. #13133149C23semidirect
150. #13133148C23semidirect
151. #13133148C23semidirect
152. C4⋊#88322C23semidirect
153. #13133146C23semidirect
154. #13133146C23semidirect
166. #125×C53C23semidirect
176. #107×C53C23semidirect
177. #106×C53C23semidirect
178. C4⋊C8×C53C23semidirect
212. D4×D53C2×Q8semidirect
383. C2×#478D53semidirect
394. C2×C53#3077semidirect
409. C2×#125C2×D53semidirect
430. #478C2×D53semidirect
440. C2×#107C2×D53semidirect
444. C2×#106C2×D53semidirect
449. C2×C4⋊C8C2×D53semidirect
460. C53C2×#3077semidirect
496. #125C22×D53semidirect
548. #107C22×D53semidirect
552. #106C22×D53semidirect
556. C4⋊C8C22×D53semidirect
763. C2#20284510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111792
C2×C4×D4×D532
#202845102
C2×#168109242
C2×#168109232
C2×#168109202
C2×#168109122
C2×#168109112
C2×#168109022
C2×#168109012
C2×#168106642
C2×#168106622
C2×#168106452
C2×#168106262
C2×C53×#4782
C2×#307753