Finite Group Databasebeta

← C2×#20286537 #28260429

Subgroups — C2×#20286537 #28260429

Order 13568.

2642 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic, complemented
2C2×#16811257C211yesmaximal, characteristic
3#20286537C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810912C211yesmaximal, characteristic, complemented
7C2×#16810853C211yesmaximal, characteristic, complemented
8C2×#16810850C211yesmaximal, characteristic, complemented
9C2×#16810822C211yesmaximal, characteristic, complemented
10C2×#16810776C211yesmaximal, characteristic, complemented
11C2×#16810775C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C22×#13133137C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C53×#481C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×D4×D53—21no—
19C22×D4×D53C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic, complemented
23C23×#88322C2211yescharacteristic, complemented
24C22×C8×D53C2211yescharacteristic, complemented
25#16811328—24no—
26#16811328C2218yescomplemented
27#16811257—24no—
28#16811257C2218yes—
29C2×#13133216C2211yescharacteristic, complemented
30C2×#13133213C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133197C2211yescharacteristic, complemented
33C2×#13133196—21no—
34C2×#13133196C2211yescharacteristic, complemented
35C2×#13133195—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133187—21no—
39C2×#13133185—21no—
40C2×#13133182C2211yescharacteristic, complemented
41C2×#13133179C2211yescharacteristic
42C2×C4×C22⋊D53—21no—
43C2×C4×C22⋊D53C2211yescharacteristic
44C2×C4⋊C4×D53C2211yescharacteristic, complemented
45#16810968C2218yescomplemented
46#16810943C2218yescomplemented
47#16810912C2218yescomplemented
48#16810853C2218yescomplemented
49#16810850C2218yescomplemented
50#16810822C2218yescomplemented
51#16810776C2218yescomplemented
52#16810775C2218yescomplemented
53#16810710C2218yescomplemented
54#16810686C2218yescomplemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57C2×#13133140C2211yescharacteristic, complemented
58C2×#13133139C2211yescharacteristic
59C2×#13133139C2211yescharacteristic, complemented
60C2×#13133138C2211yescharacteristic, complemented
61C2×#13133137C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133137C2218yescomplemented
66#102×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic, complemented
71C53×#481C2218yescomplemented
72C2×#106×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C24×D53—21no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×D212—24no—
82C22×D212—21no—
83C22×D212—21no—
84C22×D212—22no—
85C22×D212—42no—
86C22×D212C2311yescharacteristic
87C22×D212C2314yes—
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53D411yescharacteristic
93C2×D4×D53—28no—
94C2×D4×D53—24no—
95C2×D4×D53—22no—
96C2×D4×D53—42no—
97C2×D4×D53—48no—
98C2×D4×D53C2314yes—
99C22×C4×D53—21no—
100C22×C4×D53—21no—
101C22×C4×D53C2311yescharacteristic
102C2×#11719913—24no—
103C2×#11719913—42no—
104C2×#11719913C2314yes—
105C2×#11719913C2314yescomplemented
106C2×#11719923—42no—
107C2×#11719923C2314yescomplemented
108C22×#88322—42no—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111C22×#88322C2314yescomplemented
112C2×C8×D53—42no—
113C2×C8×D53C2314yescomplemented
114#13133216—22no—
115#13133216C2314yescomplemented
116#13133213—22no—
117#13133213C2314yes—
118#13133207—28no—
119#13133197—22no—
120#13133197C2314yescomplemented
121#13133196—28no—
122#13133196—22no—
123#13133196C2314yescomplemented
124#13133195—28no—
125#13133192—22no—
126#13133192C2314yes—
127#13133190—28no—
128#13133187—28no—
129#13133185—28no—
130#13133182—22no—
131#13133182C2314yescomplemented
132#13133179—22no—
133#13133179C2314yes—
134C4×C22⋊D53—28no—
135C4×C22⋊D53D414yes—
136C4×C22⋊D53C2314yes—
137C2×C4⋊Dic53—21no—
138C2×C4⋊Dic53C2311yescharacteristic
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919D411yescharacteristic
144C4⋊C4×D53—22no—
145C4⋊C4×D53C2314yescomplemented
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53D411yescharacteristic
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921D411yescharacteristic
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154#13133148C2314yescomplemented
155#13133146C2314yescomplemented
156#13133140C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yescomplemented
159#13133138C2314yescomplemented
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yescomplemented
163#13133137C2314yescomplemented
164#13133129C2314yescomplemented
165C8×Dic53C2314yescomplemented
166C22×D4×C53—21no—
167C22×D4×C53C2311yescharacteristic
168C23×C4×C53—21no—
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172#121×C53—22no—
173#121×C53C2314yes—
174C2×C4⋊C4×C53—22no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2314yescomplemented
180C2×C22⋊C4×C53—21no—
181#106×C53C2314yescomplemented
182#106×C53C2314yescomplemented
183#102×C53C2314yescomplemented
184#102×C53C2314yescomplemented
185C22⋊C8×C53C2314yescomplemented
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—24no—
191C23×D53—24no—
192C23×D53—44no—
193C23×D53—44no—
194C23×D53—44no—
195C23×D53—44no—
196C23×D53—82no—
197C23×D53—82no—
198C23×D53C2×D411yescharacteristic
199C2×D4×C53—24no—
200C2×D4×C53—21no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—44no—
204C2×D4×C53C2412yes—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—82no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53—82no—
222C2×C22⋊D53SD1618yescomplemented
223C2×C22⋊D53C2×D414yes—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229D4×D53—28no—
230D4×D53—44no—
231D4×D53—48no—
232D4×D53—432no—
233C2×D212—21no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—28no—
238C2×D212—24no—
239C2×D212—24no—
240C2×D212—21no—
241C2×D212—44no—
242C2×D212—48no—
243C2×D212—44no—
244C2×D212—44no—
245C2×D212#4114yes—
246C2×D212C2412yes—
247C2×D212C2412yes—
248C2×C4×D53—22no—
249C2×C4×D53—22no—
250C2×C4×D53—24no—
251C2×C4×D53—24no—
252C2×C4×D53—44no—
253C2×C4×D53—82no—
254C2×C4×D53C2×D412yes—
255C2×C4×D53C2412yes—
256C2×Dic106—22no—
257C2×Dic106—22no—
258C2×Dic106—21no—
259C2×Dic106—24no—
260C2×Dic106—82no—
261C2×Dic106C2412yes—
262C2×C8×C53—22no—
263C2×C8×C53—22no—
264C2×C8×C53C2412yes—
265C2×C8×C53C2412yes—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—24no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53C2412yes—
271C4⋊C4×C53C2412yes—
272C4⋊C4×C53C2412yes—
273C22⋊C4×C53—24no—
274C22⋊Dic53—24no—
275C22⋊Dic53C2×D414yes—
276#11719923—44no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921C2×D414yes—
281C4⋊Dic53—21no—
282C4⋊Dic53—24no—
283C4⋊Dic53C2412yes—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287#11719919—24no—
288#11719919C2×D414yes—
289C4×Dic53—24no—
290C4×Dic53C2×D412yes—
291C4×Dic53C2412yes—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322—44no—
295C2×#88322C2412yes—
296C2×#88322C2412yes—
297#11719913—28no—
298#11719913—44no—
299C8×D53—44no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53C2×SD1614yes—
307C23×C53C22×D412yes—
308C23×C53C22×D411yescharacteristic
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—24no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—48no—
315C22×D53—48no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53—42no—
319C22×D53—42no—
320C22×D53—48no—
321C22×D53—42no—
322C22×D53—48no—
323C22×D53—84no—
324C22×D53—816no—
325C22×D53—84no—
326C22×D53—816no—
327C22×D53C2×SD1614yes—
328C22×D53C22×D412yes—
329D4×C53—22no—
330D4×C53—22no—
331D4×C53—48no—
332D4×C53—42no—
333C2×C4×C53—22no—
334C2×C4×C53—24no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53—84no—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C2×#4112yes—
347C2×C4×C53H(5,𝔽2)12yes—
348C2×C4×C53C2511yescharacteristic
349C22⋊D53—48no—
350C22⋊D53—48no—
351C22⋊D53—84no—
352C22⋊D53C2×SD16116yescomplemented
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53C2×SD1614yes—
360C2×Dic53C22×D412yes—
361C2×Dic53C22×D412yes—
362C2×Dic53C22×D412yes—
363D212—24no—
364D212—22no—
365D212—22no—
366D212—22no—
367D212—48no—
368D212—48no—
369D212—42no—
370D212C2×#4114yes—
371C4×D53—24no—
372C4×D53—22no—
373C4×D53—22no—
374C4×D53—48no—
375C4×D53—84no—
376Dic106—22no—
377Dic106—22no—
378Dic106—42no—
379Dic106—84no—
380C8×C53—22no—
381C8×C53—22no—
382#88322—22no—
383#88322—22no—
384C2×#3295—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—28no—
387C22×C53—22no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—84no—
392C22×C53#54612yes—
393C22×C53C22×SD1614yes—
394C22×C53C22×SD1612yes—
395C22×C53#57612yes—
396C22×C53C23×D411yescharacteristic
397C2×D53—22no—
398C2×D53—28no—
399C2×D53—22no—
400C2×D53—24no—
401C2×D53—48no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—816no—
408C2×D53—816no—
409C2×D53—84no—
410C2×D53C22×SD1614yes—
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—42no—
414C4×C53—42no—
415C4×C53#54612yes—
416C4×C53C22×#4111yescharacteristic
417C4×C53C2×H(5,𝔽2)11yescharacteristic
418Dic53—22no—
419Dic53—22no—
420Dic53—42no—
421Dic53—42no—
422Dic53C22×SD1614yes—
423C2×#554—531no—
424C2×D42—531no—
425#3295—5316no—
426C2×#486—531no—
427C2×#481—531no—
428C2×#481D5311yescharacteristic, complemented
429C2×#476—531no—
430C2×#465—531no—
431C2×#465—531no—
432C2×#460—531no—
433C2×#450—531no—
434C2×#450—531no—
435C2×C4×SD16—531no—
436C2×C8×D4—531no—
437C22×#102—531no—
438C22×#102—531no—
439C2×C53—24no—
440C2×C53—82no—
441C2×C53#329514yescomplemented
442C2×C53C2×#54611yescharacteristic
443C2×C53C23×SD1611yescharacteristic
444C2×C53C2×#57611yescharacteristic
445D53—24no—
446D53—44no—
447D53—82no—
448C23×D4—531no—
449C23×D4—531no—
450C23×D4—1061no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16—531no—
454C23×C8—531no—
455C23×C8—531no—
456#554—538no—
457#554—1064no—
458D42—538no—
459D42—1064no—
460C2×C4⋊Q8—531no—
461C2×#127—531no—
462C2×#125—1061no—
463C2×C22⋊Q8—531no—
464C2×C22⋊Q8—531no—
465C2×C22⋊Q8—1061no—
466C2×C22⋊Q8—1061no—
467C2×#121—531no—
468C2×#121—1061no—
469C2×#121C2×D5311yescharacteristic
470C2×#120—1061no—
471C2×#120—1061no—
472C2×C4×Q8—531no—
473C2×C4×D4—531no—
474C2×C4×D4—531no—
475C2×C4×D4—1061no—
476C22×C4⋊C4—531no—
477C22×C4⋊C4C2×D5311yescharacteristic, complemented
478#486—538no—
479#481—538no—
480#481C2×D5318yescomplemented
481#476—538no—
482#465—538no—
483#465—538no—
484#460—538no—
485#450—538no—
486#450—538no—
487C4×SD16—538no—
488C8×D4—538no—
489C2×#106—531no—
490C2×#106C2×D5311yescharacteristic, complemented
491C2×#106C2×D5311yescharacteristic, complemented
492C2×C4⋊C8—531no—
493C2×#103—531no—
494C2×#102—531no—
495C2×#102—531no—
496C2×#102—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—538no—
502C2×#102—538no—
503C2×#102C2×D5311yescharacteristic, complemented
504C2×#102C2×D5311yescharacteristic, complemented
505C2×C22⋊C8—531no—
506C2×C22⋊C8C2×D5311yescharacteristic, complemented
507C2×C4×C8—531no—
508C53C2×#329511yescharacteristic, complemented, Sylow
509C25—1061no—
510C25—1061no—
511C22×Q8—531no—
512C22×Q8—1061no—
513C22×D4—21no—
514C22×D4—531no—
515C22×D4—534no—
516C22×D4—531no—
517C22×D4—531no—
518C22×D4—534no—
519C22×D4—1064no—
520C22×D4—1061no—
521C22×D4—1062no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1064no—
526C22×D4—1068no—
527C22×D4—1061no—
528C22×D4—1062no—
529C22×D4—2122no—
530C22×D4—2122no—
531C22×D4—2128no—
532C22×D4C22×D5311yescharacteristic
533C23×C4—21no—
534C23×C4—531no—
535C23×C4—1061no—
536C23×C4—1061no—
537C23×C4C22×D5311yescharacteristic
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—534no—
541C2×SD16—1064no—
542C2×SD16—2122no—
543C2×SD16—2122no—
544C22×C8—531no—
545C22×C8—531no—
546C22×C8—534no—
547C22×C8—534no—
548C22×C8—2122no—
549C22×C8—2122no—
550C22×C8C22×D5311yescharacteristic
551C22×C8C22×D5311yescharacteristic
552C4⋊Q8—534no—
553C4⋊Q8—1062no—
554#127—534no—
555#127—1062no—
556#125—1068no—
557C22⋊Q8—534no—
558C22⋊Q8—534no—
559C22⋊Q8—1068no—
560C22⋊Q8—1068no—
561C22⋊Q8—1062no—
562C22⋊Q8—1062no—
563#121—22no—
564#121—534no—
565#121—1068no—
566#121—1062no—
567#121C22×D5314yes—
568#120—1068no—
569#120—1068no—
570C4×Q8—534no—
571C4×Q8—1062no—
572C4×D4—534no—
573C4×D4—534no—
574C4×D4—534no—
575C4×D4—1062no—
576C4×D4—1068no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—531no—
580C2×C4⋊C4—531no—
581C2×C4⋊C4—534no—
582C2×C4⋊C4—1062no—
583C2×C4⋊C4—1061no—
584C2×C4⋊C4—1061no—
585C2×C4⋊C4—1061no—
586C2×C4⋊C4—1061no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4C22×D5311yescharacteristic
589C2×C4⋊C4C22×D5311yescharacteristic
590C2×C4⋊C4C22×D5311yescharacteristic
591C2×C4⋊C4C22×D5314yescomplemented
592C2×C22⋊C4—21no—
593C2×C22⋊C4—531no—
594C2×C22⋊C4—531no—
595C2×C22⋊C4—1061no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C42—531no—
600C2×C42—1061no—
601#106—534no—
602#106C22×D5314yescomplemented
603#106C22×D5314yescomplemented
604C4⋊C8—534no—
605#103—534no—
606#102—534no—
607#102—534no—
608#102—534no—
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102C22×D5314yescomplemented
614#102C22×D5314yescomplemented
615C22⋊C8—534no—
616C22⋊C8C22×D5314yescomplemented
617C4×C8—534no—
618C24—21no—
619C24—531no—
620C24—1064no—
621C24—1061no—
622C24—1064no—
623C24—1061no—
624C24—4242no—
625C24—4242no—
626C24—2124no—
627C24—2124no—
628C24—2124no—
629C24—2124no—
630C24D4×D5311yescharacteristic
631C2×Q8—532no—
632C2×Q8—1064no—
633C2×Q8—1061no—
634C2×Q8—1062no—
635C2×Q8—1062no—
636C2×Q8—4242no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—44no—
642C2×D4—538no—
643C2×D4—534no—
644C2×D4—534no—
645C2×D4—532no—
646C2×D4—532no—
647C2×D4—1068no—
648C2×D4—1064no—
649C2×D4—1064no—
650C2×D4—1064no—
651C2×D4—1064no—
652C2×D4—1068no—
653C2×D4—1061no—
654C2×D4—1064no—
655C2×D4—1061no—
656C2×D4—1062no—
657C2×D4—1062no—
658C2×D4—1062no—
659C2×D4—4242no—
660C2×D4—2124no—
661C2×D4—2128no—
662C2×D4—2124no—
663C2×D4—2124no—
664C2×D4—2124no—
665C2×D4—2124no—
666C2×D4—2128no—
667C2×D4—2124no—
668C2×D4—21232no—
669C2×D4C23×D5312yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—82no—
677C22×C4—531no—
678C22×C4—531no—
679C22×C4—531no—
680C22×C4—532no—
681C22×C4—532no—
682C22×C4—1064no—
683C22×C4—1064no—
684C22×C4—1062no—
685C22×C4—1062no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—4242no—
689C22×C4—2124no—
690C22×C4D4×D5312yes—
691C22×C4D4×D5311yescharacteristic
692C22×C4C23×D5312yes—
693C22×C4C23×D5311yescharacteristic
694SD16—1068no—
695SD16—2124no—
696SD16—2124no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—532no—
700C2×C8—532no—
701C2×C8—1062no—
702C2×C8—1062no—
703C2×C8—2124no—
704C2×C8—2124no—
705C2×C8C23×D5312yes—
706C2×C8C23×D5312yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—534no—
712C4⋊C4—532no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4—1064no—
716C4⋊C4—1064no—
717C4⋊C4—1061no—
718C4⋊C4—1064no—
719C4⋊C4C23×D5312yes—
720C4⋊C4C23×D5312yes—
721C4⋊C4C23×D5312yes—
722C22⋊C4—24no—
723C22⋊C4—534no—
724C22⋊C4—534no—
725C22⋊C4—1064no—
726C22⋊C4—1064no—
727C22⋊C4—1064no—
728C22⋊C4—1064no—
729C42—532no—
730C42—532no—
731C42—1064no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—534no—
739C23—532no—
740C23—1062no—
741C23—1062no—
742C23—1064no—
743C23—1062no—
744C23—1062no—
745C23—42416no—
746C23—4244no—
747C23—4244no—
748C23—42416no—
749C23—2128no—
750C23—2128no—
751C23—2128no—
752C23—2122no—
753C23—2128no—
754C23—2122no—
755C23—2122no—
756C23—2122no—
757C23—2122no—
758C23SD16×D5314yes—
759C23C2×D4×D5312yes—
760C23C2×D4×D5311yescharacteristic
761Q8—1062no—
762Q8—1062no—
763Q8—4244no—
764Q8—2122no—
765D4—22no—
766D4—22no—
767D4—48no—
768D4—42no—
769D4—5316no—
770D4—534no—
771D4—1064no—
772D4—1062no—
773D4—1062no—
774D4—1062no—
775D4—4244no—
776D4—2128no—
777D4—2128no—
778D4—2128no—
779D4—2128no—
780D4—2122no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—84no—
792C2×C4—534no—
793C2×C4—532no—
794C2×C4—532no—
795C2×C4—532no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—1064no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—4244no—
804C2×C4—2128no—
805C2×C4—2122no—
806C2×C4—2122no—
807C2×C4C2×D4×D5312yes—
808C2×C4C2×D4×D5311yescharacteristic
809C2×C4#41×D5312yes—
810C2×C4#1313326312yes—
811C2×C4C24×D5311yescharacteristic
812C8—22no—
813C8—22no—
814C8—1062no—
815C8—1062no—
816C22—28no—
817C22—22no—
818C22—22no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—534no—
824C22—1068no—
825C22—1062no—
826C22—1062no—
827C22—1064no—
828C22—42416no—
829C22—42416no—
830C22—4244no—
831C22—2122no—
832C22—2122no—
833C22—2122no—
834C22—2128no—
835C22—2122no—
836C22—2122no—
837C22#1681126512yes—
838C22C2×SD16×D5314yes—
839C22C2×SD16×D5312yes—
840C22#1681142712yes—
841C22C22×D4×D5311yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—534no—
847C4—1062no—
848C4—1062no—
849C4—2122no—
850C4—2122no—
851C4#1681126512yes—
852C4C2×#41×D5311yescharacteristic
853C4C2×#1313326311yescharacteristic
854C2—24no—
855C2—82no—
856C2—1064no—
857C2—4242no—
858C2—2124no—
859C2#2028653714yesdirect product factor
860C2C2×#1681126511yescharacteristic
861C2C22×SD16×D5311yescharacteristic
862C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#481C2
socleC23×C53C22×D4
prime radicalC2×#16811257C2
hypercenterC2×#481D53
hypocenterC53C2×#3295
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16811328C2semidirect
3. #20286537C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810912C2semidirect
7. C2×#16810853C2semidirect
8. C2×#16810850C2semidirect
9. C2×#16810822C2semidirect
10. C2×#16810776C2semidirect
11. C2×#16810775C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810686C2semidirect
14. C22×#13133137C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C53×#481C2semidirect
21. C22×#11719913C22semidirect
22. C22×#11719923C22semidirect
23. C23×#88322C22semidirect
24. C22×C8×D53C22semidirect
26. #16811328C22semidirect
29. C2×#13133216C22semidirect
32. C2×#13133197C22semidirect
34. C2×#13133196C22semidirect
40. C2×#13133182C22semidirect
44. C2×C4⋊C4×D53C22semidirect
45. #16810968C22semidirect
46. #16810943C22semidirect
47. #16810912C22semidirect
48. #16810853C22semidirect
49. #16810850C22semidirect
50. #16810822C22semidirect
51. #16810776C22semidirect
52. #16810775C22semidirect
53. #16810710C22semidirect
54. #16810686C22semidirect
55. C2×#13133148C22semidirect
56. C2×#13133146C22semidirect
57. C2×#13133140C22semidirect
59. C2×#13133139C22semidirect
60. C2×#13133138C22semidirect
63. C2×#13133137C22semidirect
64. C2×#13133137C22semidirect
65. C2×#13133137C22semidirect
66. #102×D53C22semidirect
67. C2×#13133129C22semidirect
68. C2×C8×Dic53C22semidirect
70. C22×C4⋊C4×C53C22semidirect
71. C53×#481C22semidirect
72. C2×#106×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
105. C2×#11719913C23semidirect
107. C2×#11719923C23semidirect
111. C22×#88322C23semidirect
113. C2×C8×D53C23semidirect
115. #13133216C23semidirect
120. #13133197C23semidirect
123. #13133196C23semidirect
131. #13133182C23semidirect
145. C4⋊C4×D53C23semidirect
154. #13133148C23semidirect
155. #13133146C23semidirect
156. #13133140C23semidirect
158. #13133139C23semidirect
159. #13133138C23semidirect
162. #13133137C23semidirect
163. #13133137C23semidirect
164. #13133129C23semidirect
165. C8×Dic53C23semidirect
179. C2×C4⋊C4×C53C23semidirect
181. #106×C53C23semidirect
182. #106×C53C23semidirect
183. #102×C53C23semidirect
184. #102×C53C23semidirect
185. C22⋊C8×C53C23semidirect
222. C2×C22⋊D53SD16semidirect
352. C22⋊D53C2×SD16semidirect
428. C2×#481D53semidirect
441. C2×C53#3295semidirect
477. C22×C4⋊C4C2×D53semidirect
480. #481C2×D53semidirect
490. C2×#106C2×D53semidirect
491. C2×#106C2×D53semidirect
503. C2×#102C2×D53semidirect
504. C2×#102C2×D53semidirect
506. C2×C22⋊C8C2×D53semidirect
508. C53C2×#3295semidirect
591. C2×C4⋊C4C22×D53semidirect
602. #106C22×D53semidirect
603. #106C22×D53semidirect
613. #102C22×D53semidirect
614. #102C22×D53semidirect
616. C22⋊C8C22×D53semidirect
859. C2#20286537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112572
#202865372
C2×#168109682
C2×#168109432
C2×#168109122
C2×#168108532
C2×#168108502
C2×#168108222
C2×#168107762
C2×#168107752
C2×#168107102
C2×#168106862
C22×#131331372
C2×#102×D532
C2×C53×#4812
C2×#329553