Finite Group Databasebeta

← C2×#20286801 #28260623

Subgroups — C2×#20286801 #28260623

Order 13568.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811333C211yesmaximal, characteristic, complemented
2C2×#16811268C211yesmaximal, characteristic
3#20286801C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810903C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810863C211yesmaximal, characteristic, complemented
10C2×#16810845C211yesmaximal, characteristic, complemented
11C2×#16810782C211yesmaximal, characteristic, complemented
12C2×#16810772C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719924C2211yescharacteristic
21C22×#11719912C2211yescharacteristic, complemented
22C22×C8×D53C2211yescharacteristic
23#16811333—24no—
24#16811333C2218yescomplemented
25#16811268—24no—
26#16811268C2218yes—
27C2×#13133217C2211yescharacteristic, complemented
28C2×#13133209—21no—
29C2×#13133205C2211yescharacteristic
30C2×#13133201—21no—
31C2×#13133197C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic, complemented
36C2×#13133192C2211yescharacteristic
37C2×#13133191—21no—
38C2×#13133187—21no—
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic, complemented
43C22×#11719921—21no—
44#16810983C2218yescomplemented
45#16810960C2218yescomplemented
46#16810938C2218yescomplemented
47#16810903C2218yescomplemented
48#16810872C2218yescomplemented
49#16810863C2218yescomplemented
50#16810845C2218yescomplemented
51#16810782C2218yescomplemented
52#16810772C2218yescomplemented
53#16810696C2218yescomplemented
54C2×#13133150C2211yescharacteristic, complemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×C4⋊#88322C2211yescharacteristic, complemented
57#16810621C2218yescomplemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66#102×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic, complemented
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719947—24no—
79C2×#11719947—22no—
80C2×#11719947—42no—
81C2×#11719947C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×D212—21no—
85C22×D212D411yescharacteristic
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C2×D4×D53—24no—
90C2×D4×D53—22no—
91C2×D4×D53—42no—
92C2×D4×D53C2314yes—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97C22×C4×D53C2311yescharacteristic
98C2×#11719925—42no—
99C2×#11719925C2314yescomplemented
100C2×#11719924—42no—
101C2×#11719924C2314yes—
102C2×#11719912—42no—
103C2×#11719912C2314yescomplemented
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106C2×C8×D53—42no—
107C2×C8×D53C2314yes—
108#13133217—22no—
109#13133217C2314yescomplemented
110#13133209—28no—
111#13133205—22no—
112#13133205C2314yes—
113#13133201—28no—
114#13133197—22no—
115#13133197C2314yes—
116#13133195—28no—
117#13133195—28no—
118#13133193—22no—
119#13133193—22no—
120#13133193C2314yes—
121#13133193C2314yescomplemented
122#13133192—22no—
123#13133192C2314yes—
124#13133191—28no—
125#13133187—28no—
126C4×D212—28no—
127C4×D212D414yes—
128C4×D212C2314yes—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53—22no—
140C4⋊C4×D53C2314yes—
141C4⋊C4×D53C2314yescomplemented
142C2×#11719921—28no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×#11719921D411yescharacteristic
151#13133150C2314yescomplemented
152#13133150C2314yescomplemented
153C4⋊#88322C2314yescomplemented
154#13133142C2314yescomplemented
155#13133142C2314yescomplemented
156#13133140C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160#13133138C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yescomplemented
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yescomplemented
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yescomplemented
182#103×C53C2314yescomplemented
183#102×C53C2314yes—
184#97×C53C2314yescomplemented
185C24×C53—21no—
186C23×D53—21no—
187C23×D53—24no—
188C23×D53—44no—
189C23×D53—44no—
190C23×D53—82no—
191C23×D53C2×D411yescharacteristic
192C23×D53C2×D411yescharacteristic
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53#4114yes—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
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—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220#11719947—28no—
221#11719947—44no—
222#11719947—48no—
223D4×D53—28no—
224D4×D53—44no—
225D4×D53—48no—
226C2×D212—24no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—21no—
230C2×D212—24no—
231C2×D212—82no—
232C2×D212C2×D414yes—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—82no—
241C2×C4×D53—82no—
242C2×C4×D53C2×D412yes—
243C2×C4×D53C2×D412yes—
244C2×C4×D53C2412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106—24no—
250C2×Dic106—82no—
251C2×Dic106C2412yes—
252SD16×C53—28no—
253C2×C8×C53—22no—
254C2×C8×C53—22no—
255C2×C8×C53C2412yes—
256C2×C8×C53C2412yes—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53C2412yes—
261C4⋊C4×C53C2412yes—
262C22⋊C4×C53—24no—
263C42×C53—24no—
264C42×C53C2×D412yes—
265C42×C53C2412yes—
266#11719925—44no—
267#11719924—44no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921C2×D414yes—
275#11719921C2×D414yes—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53—24no—
279C4⋊Dic53—24no—
280C4⋊Dic53C2×D414yes—
281C4⋊Dic53C2412yes—
282C4⋊Dic53C2412yes—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291#11719912—44no—
292C8×D53—44no—
293C23×C53—24no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—48no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—48no—
309C22×D53—84no—
310C22×D53—816no—
311C22×D53#13714yes—
312C22×D53C22×D412yes—
313C22×D53C22×D412yes—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—42no—
317D4×C53—24no—
318D4×C53—22no—
319D4×C53C2×#4114yes—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—84no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53C2×#4112yes—
333C2×C4×C53H(5,𝔽2)12yes—
334C2×C4×C53C2511yescharacteristic
335C22⋊D53—48no—
336C22⋊D53—48no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—48no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348D212—28no—
349D212—22no—
350D212—22no—
351D212—42no—
352D212—84no—
353C4×D53—24no—
354C4×D53—24no—
355C4×D53—22no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—22no—
359C4×D53—84no—
360C4×D53—84no—
361Dic106—22no—
362Dic106—22no—
363Dic106—42no—
364Dic106—84no—
365C8×C53—22no—
366C8×C53—22no—
367#88322—22no—
368#88322—22no—
369C2×#3314—531nomaximal, Sylow
370C22×C53—24no—
371C22×C53—48no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53#54612yes—
375C22×C53C2×#13712yes—
376C22×C53#57612yes—
377C22×C53C23×D411yescharacteristic
378C2×D53—22no—
379C2×D53—28no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—44no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—816no—
389C2×D53—84no—
390C2×D53C2×#13714yes—
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53#54612yes—
397C4×C53C22×#4111yescharacteristic
398C4×C53C2×H(5,𝔽2)11yescharacteristic
399Dic53—22no—
400Dic53—22no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#554—531no—
405C2×#546—531no—
406#3314—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480—531no—
410C2×#474—531no—
411C2×#468—531no—
412C2×#467—531no—
413C2×#464—531no—
414C2×#452—531no—
415C2×#450—531no—
416C2×#440D5311yescharacteristic, complemented
417C2×#435—531no—
418C2×#417—531no—
419C22×#102—531no—
420C2×C53—44no—
421C2×C53#331414yescomplemented
422C2×C53C2×#54611yescharacteristic
423C2×C53C22×#13711yescharacteristic
424C2×C53C2×#57611yescharacteristic
425D53—24no—
426D53—42no—
427D53—82no—
428C22×#41—531no—
429C23×D4—531no—
430C22×Q16—531no—
431C22×SD16—531no—
432C22×SD16C2×D5311yescharacteristic
433C22×M16—531no—
434C23×C8—531no—
435#554—538no—
436#554—1064no—
437#546—538no—
438#546—1064no—
439C2×C4⋊Q8—531no—
440C2×#125—1061no—
441C2×#124—531no—
442C2×#123—1061no—
443C2×C22⋊Q8—531no—
444C2×C22⋊Q8—531no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8—1061no—
448C2×#121—531no—
449C2×#121—1061no—
450C2×#120—1061no—
451C2×C4×Q8C2×D5311yescharacteristic, complemented
452C2×C4×D4—531no—
453C2×C4×D4—1061no—
454C2×C4×D4C2×D5311yescharacteristic
455C22×C4⋊C4—531no—
456C22×C4⋊C4—531no—
457C22×C22⋊C4—1061no—
458#489—538no—
459#484—538no—
460#480—538no—
461#474—538no—
462#468—538no—
463#467—538no—
464#464—538no—
465#452—538no—
466#450—538no—
467#440C2×D5318yescomplemented
468#435—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107C2×D5311yescharacteristic, complemented
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103C2×D5311yescharacteristic, complemented
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—538no—
484C2×#102C2×D5311yescharacteristic
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×#97C2×D5311yescharacteristic, complemented
488C53C2×#331411yescharacteristic, complemented, Sylow
489C25—1061no—
490C2×#41—534no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2122no—
494C22×Q8—531no—
495C22×Q8—1061no—
496C22×Q8C22×D5311yescharacteristic
497C22×D4—534no—
498C22×D4—531no—
499C22×D4—531no—
500C22×D4—1061no—
501C22×D4—1062no—
502C22×D4—1061no—
503C22×D4—1064no—
504C22×D4—1061no—
505C22×D4—2122no—
506C22×D4C22×D5311yescharacteristic
507C23×C4—21no—
508C23×C4—531no—
509C23×C4—531no—
510C23×C4—1061no—
511C23×C4—1061no—
512C23×C4—1061no—
513C2×Q16—534no—
514C2×Q16—2122no—
515C2×SD16—24no—
516C2×SD16—534no—
517C2×SD16—2122no—
518C2×SD16C22×D5314yes—
519C2×M16—534no—
520C2×M16—2122no—
521C22×C8—531no—
522C22×C8—531no—
523C22×C8—534no—
524C22×C8—2122no—
525C22×C8C22×D5311yescharacteristic
526C22×C8C22×D5311yescharacteristic
527C4⋊Q8—534no—
528C4⋊Q8—1062no—
529#125—1068no—
530#124—534no—
531#124—1062no—
532#123—1068no—
533C22⋊Q8—534no—
534C22⋊Q8—534no—
535C22⋊Q8—534no—
536C22⋊Q8—1068no—
537C22⋊Q8—1068no—
538C22⋊Q8—1062no—
539C22⋊Q8—1062no—
540C22⋊Q8—1062no—
541#121—534no—
542#121—1068no—
543#121—1062no—
544#120—1068no—
545C4×Q8—22no—
546C4×Q8C22×D5314yescomplemented
547C4×D4—22no—
548C4×D4—534no—
549C4×D4—534no—
550C4×D4—1068no—
551C4×D4C22×D5314yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—534no—
557C2×C4⋊C4—534no—
558C2×C4⋊C4—1062no—
559C2×C4⋊C4—1062no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—531no—
570C2×C22⋊C4—531no—
571C2×C22⋊C4—1068no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C42—21no—
579C2×C42C22×D5311yescharacteristic
580#107—534no—
581#107—534no—
582#107C22×D5314yescomplemented
583C4⋊C8—534no—
584#103—534no—
585#103—534no—
586#103—534no—
587#103C22×D5314yescomplemented
588#102—534no—
589#102—534no—
590#102—534no—
591#102—534no—
592#102—534no—
593#102C22×D5314yes—
594C22⋊C8—534no—
595C22⋊C8—534no—
596#97C22×D5314yescomplemented
597C24—21no—
598C24—531no—
599C24—531no—
600C24—1064no—
601C24—1061no—
602C24—4242no—
603C24—2124no—
604C24—2124no—
605#41—1068no—
606#41—2124no—
607#41—2128no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—532no—
612C2×Q8—1064no—
613C2×Q8—1061no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—4242no—
617C2×Q8C23×D5312yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—534no—
621C2×D4—532no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1068no—
626C2×D4—1064no—
627C2×D4—1061no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—4242no—
631C2×D4—2124no—
632C2×D4—2128no—
633C2×D4—2124no—
634C2×D4—2124no—
635C2×D4#1171994514yes—
636C2×D4C23×D5312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—531no—
643C22×C4—531no—
644C22×C4—532no—
645C22×C4—532no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—1064no—
649C22×C4—1064no—
650C22×C4—1064no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—4242no—
659C22×C4—4242no—
660C22×C4—2124no—
661C22×C4D4×D5311yescharacteristic
662C22×C4D4×D5311yescharacteristic
663C22×C4C23×D5311yescharacteristic
664Q16—2124no—
665SD16—28no—
666SD16—2124no—
667M16—2124no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—532no—
671C2×C8—532no—
672C2×C8—1062no—
673C2×C8—1062no—
674C2×C8—2124no—
675C2×C8C23×D5312yes—
676C2×C8C23×D5312yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—534no—
681C4⋊C4—532no—
682C4⋊C4—532no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1061no—
689C4⋊C4—1061no—
690C4⋊C4—1064no—
691C4⋊C4C23×D5312yes—
692C4⋊C4C23×D5312yes—
693C22⋊C4—24no—
694C22⋊C4—534no—
695C22⋊C4—534no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C42—24no—
703C42D4×D5312yes—
704C42C23×D5312yes—
705C23—24no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—534no—
710C23—532no—
711C23—532no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—42416no—
719C23—4244no—
720C23—2128no—
721C23—2128no—
722C23—2122no—
723C23—2122no—
724C23—2122no—
725C23C2×D4×D5311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1062no—
730Q8—1062no—
731Q8—4244no—
732Q8—2122no—
733D4—24no—
734D4—22no—
735D4—1068no—
736D4—1062no—
737D4—1062no—
738D4—4244no—
739D4—2128no—
740D4—2128no—
741D4—2122no—
742D4C2×#1171994514yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1064no—
757C2×C4—1064no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—4244no—
766C2×C4—4244no—
767C2×C4—2128no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4—2122no—
771C2×C4C2×D4×D5312yes—
772C2×C4C2×D4×D5312yes—
773C2×C4C2×D4×D5311yescharacteristic
774C2×C4C2×#1171994512yes—
775C2×C4#1313326312yes—
776C2×C4C24×D5311yescharacteristic
777C8—22no—
778C8—22no—
779C8—1062no—
780C8—1062no—
781C22—24no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—534no—
786C22—1068no—
787C22—1062no—
788C22—1062no—
789C22—1062no—
790C22—1062no—
791C22—1062no—
792C22—42416no—
793C22—4244no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2124no—
798C22#1681126912yes—
799C22#137×D5312yes—
800C22#1681142712yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1062no—
808C4—1062no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126912yes—
813C4C22×#1171994511yescharacteristic
814C4C2×#1313326311yescharacteristic
815C2—44no—
816C2—1064no—
817C2—4242no—
818C2—2122no—
819C2#2028680114yesdirect product factor
820C2C2×#1681126911yescharacteristic
821C2C2×#137×D5311yescharacteristic
822C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#16811268C2
hypercenterC2×#440D53
hypocenterC53C2×#3314
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×#16811333C2semidirect
3. #20286801C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810903C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810863C2semidirect
10. C2×#16810845C2semidirect
11. C2×#16810782C2semidirect
12. C2×#16810772C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810621C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C53×#440C2semidirect
19. C22×#11719925C22semidirect
21. C22×#11719912C22semidirect
24. #16811333C22semidirect
27. C2×#13133217C22semidirect
35. C2×#13133193C22semidirect
42. C2×C4⋊C4×D53C22semidirect
44. #16810983C22semidirect
45. #16810960C22semidirect
46. #16810938C22semidirect
47. #16810903C22semidirect
48. #16810872C22semidirect
49. #16810863C22semidirect
50. #16810845C22semidirect
51. #16810782C22semidirect
52. #16810772C22semidirect
53. #16810696C22semidirect
54. C2×#13133150C22semidirect
55. C2×#13133150C22semidirect
56. C2×C4⋊#88322C22semidirect
57. #16810621C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
66. #102×D53C22semidirect
68. C2×#13133129C22semidirect
70. C2×C4×Q8×C53C22semidirect
72. C53×#440C22semidirect
73. C2×#107×C53C22semidirect
74. C2×#103×C53C22semidirect
76. C2×#97×C53C22semidirect
99. C2×#11719925C23semidirect
103. C2×#11719912C23semidirect
109. #13133217C23semidirect
121. #13133193C23semidirect
141. C4⋊C4×D53C23semidirect
151. #13133150C23semidirect
152. #13133150C23semidirect
153. C4⋊#88322C23semidirect
154. #13133142C23semidirect
155. #13133142C23semidirect
156. #13133140C23semidirect
163. #13133129C23semidirect
172. C4×Q8×C53C23semidirect
181. #107×C53C23semidirect
182. #103×C53C23semidirect
184. #97×C53C23semidirect
416. C2×#440D53semidirect
421. C2×C53#3314semidirect
451. C2×C4×Q8C2×D53semidirect
467. #440C2×D53semidirect
471. C2×#107C2×D53semidirect
477. C2×#103C2×D53semidirect
487. C2×#97C2×D53semidirect
488. C53C2×#3314semidirect
546. C4×Q8C22×D53semidirect
582. #107C22×D53semidirect
587. #103C22×D53semidirect
596. #97C22×D53semidirect
819. C2#20286801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113332
C2×#168112682
#202868012
C2×#168109832
C2×#168109602
C2×#168109382
C2×#168109032
C2×#168108722
C2×#168108632
C2×#168108452
C2×#168107822
C2×#168107722
C2×#168106962
C2×#168106212
C2×#102×D532
C2×C53×#4402
C2×#331453