Finite Group Databasebeta

← C2×#20285504 #28254653

Subgroups — C2×#20285504 #28254653

Order 13568.

2394 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811136C211yesmaximal, characteristic, complemented
2C2×#16811133C211yesmaximal, characteristic, complemented
3#20285504C2116yesmaximal, direct product factor
4C2×#16810967C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810949C211yesmaximal, characteristic, complemented
7C2×#16810946C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810857C211yesmaximal, characteristic, complemented
10C2×#16810852C211yesmaximal, characteristic, complemented
11C2×#16810788C211yesmaximal, characteristic, complemented
12C2×#16810782C211yesmaximal, characteristic, complemented
13C2×#16810769C211yesmaximal, characteristic, complemented
14C2×#16810767C211yesmaximal, characteristic, complemented
15C22×#13133129C211yesmaximal, characteristic, complemented
16C2×C53×#465C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C22×#11719925C2211yescharacteristic, complemented
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719922C2211yescharacteristic, complemented
23C23×#88322C2211yescharacteristic
24#16811136—24no—
25#16811136C2218yescomplemented
26#16811133—24no—
27#16811133C2218yescomplemented
28C2×#13133202—21no—
29C2×#13133199—21no—
30C2×#13133197C2211yescharacteristic
31C2×#13133196C2211yescharacteristic
32C2×#13133193C2211yescharacteristic
33C2×#13133192C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133188C2211yescharacteristic
36C2×#13133187—21no—
37C2×#13133185—21no—
38C2×D4×Dic53—21no—
39C2×#13133179—21no—
40C2×#13133177—21no—
41C2×#13133177—21no—
42C2×#13133175C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44#16810967C2218yescomplemented
45#16810962C2218yescomplemented
46#16810949C2218yescomplemented
47#16810946C2218yescomplemented
48#16810862C2218yescomplemented
49#16810857C2218yescomplemented
50#16810852C2218yescomplemented
51#16810788C2218yescomplemented
52#16810782C2218yescomplemented
53#16810769C2218yescomplemented
54#16810767C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133149C2211yescharacteristic, complemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic, complemented
63C2×#13133137C2211yescharacteristic, complemented
64C2×#13133129C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2218yescomplemented
69C22×SD16×C53C2211yescharacteristic, complemented
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#465C2218yescomplemented
74C2×#106×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic, complemented
77C24×D53D411yescharacteristic
78C2×#11719949—22no—
79C2×#11719949—42no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C2×#11719947—22no—
83C2×#11719947—42no—
84C2×#11719947—42no—
85C2×#11719947C2314yes—
86C22×Dic106C2311yescharacteristic
87C22×D212—21no—
88C22×D212—21no—
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C23×Dic53D411yescharacteristic
95C22×C4×D53—21no—
96C22×C4×D53—42no—
97C22×C4×D53—42no—
98C22×C4×D53D411yescharacteristic
99C22×C4×D53D411yescharacteristic
100C22×C4×D53D414yes—
101C22×C4×D53C2311yescharacteristic
102C22×C4×D53C2311yescharacteristic
103C22×C4×D53C2314yes—
104C2×#11719925—42no—
105C2×#11719925C2314yescomplemented
106C2×#11719913—42no—
107C2×#11719913C2314yescomplemented
108C2×#11719922—42no—
109C2×#11719922C2314yescomplemented
110C22×#88322—42no—
111C22×#88322C2311yescharacteristic
112C22×#88322C2311yescharacteristic
113C22×#88322C2314yes—
114#13133202—28no—
115#13133199—28no—
116#13133197—22no—
117#13133197C2314yes—
118#13133196—22no—
119#13133196C2314yes—
120#13133193—22no—
121#13133193C2314yes—
122#13133192—22no—
123#13133192C2314yes—
124#13133191—22no—
125#13133191C2314yes—
126#13133188—22no—
127#13133188C2314yes—
128#13133187—28no—
129#13133185—28no—
130D4×Dic53—28no—
131#13133179—28no—
132#13133177—28no—
133#13133177—28no—
134#13133175—22no—
135#13133175—22no—
136#13133175C2314yes—
137#13133175C2314yes—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53C2311yescharacteristic
140C2×C4⋊Dic53C2311yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153#13133150C2314yescomplemented
154#13133150C2314yescomplemented
155#13133149C2314yescomplemented
156#13133142C2314yescomplemented
157#13133141C2314yescomplemented
158#13133140C2314yescomplemented
159#13133139C2314yescomplemented
160#13133138C2314yescomplemented
161#13133137C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164#13133129C2314yes—
165#13133129C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53C2311yescharacteristic
170C2×SD16×C53—42no—
171C2×SD16×C53C2314yescomplemented
172C22×C8×C53—42no—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2314yes—
176C22⋊Q8×C53—22no—
177C22⋊Q8×C53C2314yes—
178#121×C53—22no—
179#121×C53C2314yes—
180C2×C4⋊C4×C53—21no—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C4⋊C4×C53C2311yescharacteristic
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185#106×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—24no—
191C23×D53—21no—
192C23×D53—42no—
193C23×D53—42no—
194C23×D53C2×D411yescharacteristic
195C23×D53C2×D411yescharacteristic
196C23×D53C2×D414yes—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×D4×C53—24no—
202C2×D4×C53—21no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53C2412yes—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
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—44no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—24no—
226C22×Dic53—42no—
227C22×Dic53—44no—
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C22×Dic53C2×D414yes—
231#11719949—44no—
232#11719949—44no—
233#11719949—48no—
234#11719947—44no—
235#11719947—44no—
236#11719947—48no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—24no—
240C2×D212—24no—
241C2×D212—21no—
242C2×D212—44no—
243C2×D212—44no—
244C2×D212C2412yes—
245C2×C4×D53—22no—
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—22no—
249C2×C4×D53—24no—
250C2×C4×D53—48no—
251C2×C4×D53—44no—
252C2×C4×D53—44no—
253C2×C4×D53—42no—
254C2×C4×D53—42no—
255C2×C4×D53—44no—
256C2×C4×D53C2×D412yes—
257C2×C4×D53C2×D412yes—
258C2×C4×D53C2×D414yes—
259C2×C4×D53C2×D414yes—
260C2×C4×D53C2412yes—
261C2×C4×D53C2412yes—
262C2×Dic106—22no—
263C2×Dic106—22no—
264C2×Dic106—21no—
265C2×Dic106C2412yes—
266SD16×C53—44no—
267C2×C8×C53—22no—
268C2×C8×C53—22no—
269C2×C8×C53—44no—
270C2×C8×C53C2412yes—
271C2×C8×C53C2412yes—
272C4⋊C4×C53—24no—
273C4⋊C4×C53—21no—
274C4⋊C4×C53—21no—
275C4⋊C4×C53C2412yes—
276C4⋊C4×C53C2412yes—
277C22⋊C4×C53—24no—
278C22⋊C4×C53—24no—
279C22⋊Dic53—24no—
280C22⋊Dic53—24no—
281#11719925—44no—
282#11719922—44no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289C4⋊Dic53—21no—
290C4⋊Dic53—21no—
291C4⋊Dic53—24no—
292C4⋊Dic53C2412yes—
293C4⋊Dic53C2412yes—
294#11719919—24no—
295#11719919—24no—
296C4×Dic53—24no—
297C4×Dic53—24no—
298C2×#88322—22no—
299C2×#88322—22no—
300C2×#88322—44no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303#11719913—44no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53#13514yes—
311C23×C53C22×D412yes—
312C23×C53C22×D411yescharacteristic
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—28no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—44no—
322C22×D53—44no—
323C22×D53—416no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53C22×D412yes—
328C22×D53C22×D412yes—
329Q8×C53—22no—
330Q8×C53—22no—
331Q8×C53—42no—
332D4×C53—22no—
333D4×C53—22no—
334D4×C53—48no—
335D4×C53—42no—
336C2×C4×C53—22no—
337C2×C4×C53—24no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—42no—
344C2×C4×C53—42no—
345C2×C4×C53—42no—
346C2×C4×C53C22×D412yes—
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53H(5,𝔽2)12yes—
349C2×C4×C53H(5,𝔽2)12yes—
350C2×C4×C53C2511yescharacteristic
351C22⋊D53—48no—
352C22⋊D53—48no—
353C22⋊D53—48no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—44no—
360C2×Dic53—48no—
361C2×Dic53—42no—
362C2×Dic53—42no—
363C2×Dic53—42no—
364C2×Dic53C22×D412yes—
365C2×Dic53C22×D412yes—
366D212—22no—
367D212—22no—
368D212—48no—
369D212—48no—
370D212—42no—
371C4×D53—24no—
372C4×D53—24no—
373C4×D53—22no—
374C4×D53—22no—
375C4×D53—22no—
376C4×D53—22no—
377C4×D53—44no—
378C4×D53—44no—
379C4×D53—48no—
380Dic106—22no—
381Dic106—22no—
382Dic106—42no—
383C8×C53—22no—
384C8×C53—22no—
385#88322—22no—
386#88322—22no—
387C2×#3191—531nomaximal, Sylow
388C22×C53—22no—
389C22×C53—28no—
390C22×C53—22no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—84no—
395C22×C53#53412yes—
396C22×C53C2×#13514yes—
397C22×C53C2×#13512yes—
398C22×C53#57512yes—
399C22×C53C23×D411yescharacteristic
400C2×D53—22no—
401C2×D53—22no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—22no—
405C2×D53—22no—
406C2×D53—416no—
407C2×D53—44no—
408C2×D53—44no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—84no—
413C4×C53—22no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53—42no—
417C4×C53#53412yes—
418C4×C53C2×H(5,𝔽2)11yescharacteristic
419C4×C53C2×H(5,𝔽2)11yescharacteristic
420Dic53—22no—
421Dic53—22no—
422Dic53—42no—
423Dic53—42no—
424Dic53—42no—
425C2×#525—531no—
426C2×#525—531no—
427#3191—5316no—
428C2×#485—531no—
429C2×#485—531no—
430C2×#482—531no—
431C2×#482—531no—
432C2×#467—531no—
433C2×#466—531no—
434C2×#465—531no—
435C2×#465D5311yescharacteristic, complemented
436C2×#452—531no—
437C2×#452—531no—
438C2×#449—531no—
439C2×#449—531no—
440C22×C22⋊C8—531no—
441C2×C53—24no—
442C2×C53—82no—
443C2×C53#319114yescomplemented
444C2×C53C2×#53411yescharacteristic
445C2×C53C22×#13511yescharacteristic
446C2×C53C2×#57511yescharacteristic
447D53—42no—
448D53—42no—
449D53—82no—
450C22×#41—531no—
451C22×#41—531no—
452C24×C4—531no—
453C22×Q16—531no—
454C22×SD16—531no—
455C22×SD16C2×D5311yescharacteristic, complemented
456C22×D8—531no—
457C23×C8—531no—
458C23×C8C2×D5311yescharacteristic
459#525—538no—
460#525—538no—
461#525—1064no—
462#525—1064no—
463C2×#123—1061no—
464C2×#123—1061no—
465C2×C22⋊Q8—531no—
466C2×C22⋊Q8—531no—
467C2×C22⋊Q8—531no—
468C2×C22⋊Q8C2×D5311yescharacteristic
469C2×#121—531no—
470C2×#121—531no—
471C2×#121—531no—
472C2×#121C2×D5311yescharacteristic
473C2×#120—1061no—
474C2×#120—1061no—
475C2×C4×D4—1061no—
476C2×C4×D4—1061no—
477C2×C4×D4—1061no—
478C2×C4×D4—1061no—
479C2×#117—531no—
480C2×#117—531no—
481#485—538no—
482#485—538no—
483#482—538no—
484#482—538no—
485#467—538no—
486#466—538no—
487#465—538no—
488#465C2×D5318yescomplemented
489#452—538no—
490#452—538no—
491#449—538no—
492#449—538no—
493C2×#107—531no—
494C2×#107—531no—
495C2×#106—531no—
496C2×#106C2×D5311yescharacteristic, complemented
497C2×#103—531no—
498C2×#103—531no—
499C2×#103—531no—
500C2×#103C2×D5311yescharacteristic, complemented
501C2×#102—531no—
502C2×#102—531no—
503C2×#102—531no—
504C2×#102C2×D5311yescharacteristic, complemented
505C2×C22⋊C8—531no—
506C2×C22⋊C8—531no—
507C2×C22⋊C8—531no—
508C2×C22⋊C8—531no—
509C2×C22⋊C8—538no—
510C53C2×#319111yescharacteristic, complemented, Sylow
511C25—531no—
512C2×#41—534no—
513C2×#41—534no—
514C2×#41—1062no—
515C2×#41—1062no—
516C2×#41—2122no—
517C2×#41—2122no—
518C2×#41—2122no—
519C2×#41—2122no—
520C22×Q8—531no—
521C22×Q8C22×D5311yescharacteristic
522C22×D4—21no—
523C22×D4—531no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—1061no—
528C22×D4—1061no—
529C22×D4C22×D5311yescharacteristic
530C23×C4—531no—
531C23×C4—531no—
532C23×C4—531no—
533C23×C4—531no—
534C23×C4—531no—
535C23×C4—534no—
536C23×C4—534no—
537C23×C4—1061no—
538C23×C4—1061no—
539C23×C4—2122no—
540C23×C4—2122no—
541C23×C4C22×D5311yescharacteristic
542C2×Q16—534no—
543C2×Q16—2122no—
544C2×SD16—42no—
545C2×SD16—534no—
546C2×SD16—2122no—
547C2×SD16C22×D5314yescomplemented
548C2×D8—534no—
549C2×D8—2122no—
550C22×C8—42no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—534no—
554C22×C8—2122no—
555C22×C8C22×D5311yescharacteristic
556C22×C8C22×D5311yescharacteristic
557C22×C8C22×D5314yes—
558#123—1068no—
559#123—1068no—
560C22⋊Q8—22no—
561C22⋊Q8—534no—
562C22⋊Q8—534no—
563C22⋊Q8—534no—
564C22⋊Q8—1062no—
565C22⋊Q8—1062no—
566C22⋊Q8—1062no—
567C22⋊Q8C22×D5314yes—
568#121—22no—
569#121—534no—
570#121—534no—
571#121—534no—
572#121—1062no—
573#121—1062no—
574#121—1062no—
575#121C22×D5314yes—
576#120—1068no—
577#120—1068no—
578C4×D4—1068no—
579C4×D4—1068no—
580C4×D4—1068no—
581C4×D4—1068no—
582#117—534no—
583#117—534no—
584#117—1062no—
585#117—1062no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—531no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C4⋊C4—1061no—
592C2×C4⋊C4C22×D5311yescharacteristic
593C2×C4⋊C4C22×D5311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4—1061no—
601C2×C22⋊C4—1061no—
602C2×C22⋊C4—1061no—
603C2×C22⋊C4—1061no—
604C2×C42—1061no—
605C2×C42—1061no—
606#107—534no—
607#107—534no—
608#106—534no—
609#106C22×D5314yescomplemented
610#103—534no—
611#103—534no—
612#103—534no—
613#103C22×D5314yescomplemented
614#102—534no—
615#102—534no—
616#102—534no—
617#102C22×D5314yescomplemented
618C22⋊C8—534no—
619C22⋊C8—534no—
620C22⋊C8—534no—
621C22⋊C8—534no—
622C24—21no—
623C24—531no—
624C24—531no—
625C24—534no—
626C24—1064no—
627C24—1061no—
628C24—2122no—
629C24—2122no—
630C24D4×D5311yescharacteristic
631#41—2124no—
632#41—2124no—
633#41—2128no—
634#41—2124no—
635#41—2124no—
636#41—2128no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—532no—
641C2×Q8—1061no—
642C2×Q8—1062no—
643C2×Q8—1062no—
644C2×Q8C23×D5312yes—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—532no—
651C2×D4—1064no—
652C2×D4—1064no—
653C2×D4—1064no—
654C2×D4—1064no—
655C2×D4—1064no—
656C2×D4—1061no—
657C2×D4—1062no—
658C2×D4—1062no—
659C2×D4—2124no—
660C2×D4—2124no—
661C2×D4—2124no—
662C2×D4—2124no—
663C2×D4—2124no—
664C2×D4C23×D5312yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—531no—
671C22×C4—531no—
672C22×C4—534no—
673C22×C4—532no—
674C22×C4—532no—
675C22×C4—532no—
676C22×C4—532no—
677C22×C4—534no—
678C22×C4—534no—
679C22×C4—1064no—
680C22×C4—1064no—
681C22×C4—1062no—
682C22×C4—1062no—
683C22×C4—1062no—
684C22×C4—1062no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—2128no—
689C22×C4—2124no—
690C22×C4—2124no—
691C22×C4—2122no—
692C22×C4—2122no—
693C22×C4—2124no—
694C22×C4—2122no—
695C22×C4—2124no—
696C22×C4D4×D5312yes—
697C22×C4D4×D5311yescharacteristic
698C22×C4C23×D5312yes—
699C22×C4C23×D5311yescharacteristic
700Q16—2124no—
701SD16—44no—
702SD16—2124no—
703D8—2124no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—44no—
707C2×C8—532no—
708C2×C8—532no—
709C2×C8—1062no—
710C2×C8—1062no—
711C2×C8—2124no—
712C2×C8C23×D5312yes—
713C2×C8C23×D5312yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—532no—
718C4⋊C4—532no—
719C4⋊C4—1064no—
720C4⋊C4—1064no—
721C4⋊C4—1061no—
722C4⋊C4—1061no—
723C4⋊C4—1064no—
724C4⋊C4C23×D5312yes—
725C4⋊C4C23×D5312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1064no—
729C22⋊C4—1064no—
730C22⋊C4—1064no—
731C22⋊C4—1064no—
732C22⋊C4—1064no—
733C22⋊C4—1064no—
734C22⋊C4—1064no—
735C22⋊C4—1064no—
736C42—1064no—
737C42—1064no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—532no—
745C23—532no—
746C23—1068no—
747C23—1062no—
748C23—1062no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—2124no—
755C23—2124no—
756C23—21216no—
757C23—2122no—
758C23—2122no—
759C23—2122no—
760C23#1313323814yes—
761C23C2×D4×D5312yes—
762C23C2×D4×D5311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—1062no—
767Q8—1062no—
768Q8—2122no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—1062no—
774D4—1062no—
775D4—2128no—
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—532no—
792C2×C4—532no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1064no—
796C2×C4—1064no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—2124no—
805C2×C4—2124no—
806C2×C4—2128no—
807C2×C4—2124no—
808C2×C4—2128no—
809C2×C4—2122no—
810C2×C4—2122no—
811C2×C4—2122no—
812C2×C4C2×D4×D5312yes—
813C2×C4C2×D4×D5311yescharacteristic
814C2×C4#1313326212yes—
815C2×C4#1313326312yes—
816C2×C4C24×D5311yescharacteristic
817C8—22no—
818C8—22no—
819C8—1062no—
820C8—1062no—
821C22—22no—
822C22—28no—
823C22—22no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—84no—
828C22—1062no—
829C22—1062no—
830C22—1062no—
831C22—1062no—
832C22—1062no—
833C22—1062no—
834C22—4244no—
835C22—21216no—
836C22—2122no—
837C22—2122no—
838C22—2122no—
839C22—2124no—
840C22—2124no—
841C22#1681118112yes—
842C22C2×#1313323814yes—
843C22C2×#1313323812yes—
844C22#1681142012yes—
845C22C22×D4×D5311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—1062no—
851C4—1062no—
852C4—2122no—
853C4—2122no—
854C4—2122no—
855C4#1681118112yes—
856C4C2×#1313326211yescharacteristic
857C4C2×#1313326311yescharacteristic
858C2—24no—
859C2—82no—
860C2—4242no—
861C2—2122no—
862C2—2122no—
863C2#2028550414yesdirect product factor
864C2C2×#1681118111yescharacteristic
865C2C22×#1313323811yescharacteristic
866C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
hypercenterC2×#465D53
hypocenterC53C2×#3191
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16811136C2semidirect
2. C2×#16811133C2semidirect
3. #20285504C2direct (N × H)
4. C2×#16810967C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810949C2semidirect
7. C2×#16810946C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810857C2semidirect
10. C2×#16810852C2semidirect
11. C2×#16810788C2semidirect
12. C2×#16810782C2semidirect
13. C2×#16810769C2semidirect
14. C2×#16810767C2semidirect
15. C22×#13133129C2semidirect
16. C2×C53×#465C2semidirect
20. C22×#11719925C22semidirect
21. C22×#11719913C22semidirect
22. C22×#11719922C22semidirect
25. #16811136C22semidirect
27. #16811133C22semidirect
44. #16810967C22semidirect
45. #16810962C22semidirect
46. #16810949C22semidirect
47. #16810946C22semidirect
48. #16810862C22semidirect
49. #16810857C22semidirect
50. #16810852C22semidirect
51. #16810788C22semidirect
52. #16810782C22semidirect
53. #16810769C22semidirect
54. #16810767C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133149C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133139C22semidirect
62. C2×#13133138C22semidirect
63. C2×#13133137C22semidirect
68. C2×#13133129C22semidirect
69. C22×SD16×C53C22semidirect
73. C53×#465C22semidirect
74. C2×#106×C53C22semidirect
75. C2×#103×C53C22semidirect
76. C2×#102×C53C22semidirect
105. C2×#11719925C23semidirect
107. C2×#11719913C23semidirect
109. C2×#11719922C23semidirect
153. #13133150C23semidirect
154. #13133150C23semidirect
155. #13133149C23semidirect
156. #13133142C23semidirect
157. #13133141C23semidirect
158. #13133140C23semidirect
159. #13133139C23semidirect
160. #13133138C23semidirect
161. #13133137C23semidirect
171. C2×SD16×C53C23semidirect
185. #106×C53C23semidirect
186. #103×C53C23semidirect
187. #102×C53C23semidirect
435. C2×#465D53semidirect
443. C2×C53#3191semidirect
455. C22×SD16C2×D53semidirect
488. #465C2×D53semidirect
496. C2×#106C2×D53semidirect
500. C2×#103C2×D53semidirect
504. C2×#102C2×D53semidirect
510. C53C2×#3191semidirect
547. C2×SD16C22×D53semidirect
609. #106C22×D53semidirect
613. #103C22×D53semidirect
617. #102C22×D53semidirect
863. C2#20285504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111362
C2×#168111332
#202855042
C2×#168109672
C2×#168109622
C2×#168109492
C2×#168109462
C2×#168108622
C2×#168108572
C2×#168108522
C2×#168107882
C2×#168107822
C2×#168107692
C2×#168107672
C22×#131331292
C2×C53×#4652
C2×#319153