Finite Group Databasebeta

← C2×#20286850 #28260644

Subgroups — C2×#20286850 #28260644

Order 13568.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D212C211yesmaximal, characteristic, complemented
2#20286850C2116yesmaximal, direct product factor
3C2×#16810989C211yesmaximal, characteristic, complemented
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810874C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810818C211yesmaximal, characteristic, complemented
10C2×#16810756C211yesmaximal, characteristic, complemented
11C2×#16810756C211yesmaximal, characteristic, complemented
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810627C211yesmaximal, characteristic, complemented
15C22×#13133137C211yesmaximal, characteristic, complemented
16C2×C53×#553C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×D4×D53—21no—
20C22×#11719922C2211yescharacteristic
21C22×#11719922C2211yescharacteristic, complemented
22C22×#11719922C2211yescharacteristic, complemented
23C22×#11719917C2211yescharacteristic, complemented
24C23×#88322C2211yescharacteristic, complemented
25D4×D212—24no—
26D4×D212C2218yescomplemented
27C2×#13133214C2211yescharacteristic
28C2×#13133192—21no—
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133187—21no—
32C2×#13133187—21no—
33C2×C4×D212C2211yescharacteristic
34#16810989C2218yescomplemented
35#16810947C2218yescomplemented
36#16810941C2218yescomplemented
37#16810920C2218yescomplemented
38#16810874C2218yescomplemented
39#16810857C2218yescomplemented
40#16810818C2218yescomplemented
41#16810756C2218yescomplemented
42#16810756C2218yescomplemented
43#16810733C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic, complemented
46C2×#13133148C2211yescharacteristic, complemented
47C2×#13133148C2211yescharacteristic, complemented
48C2×C4⋊#88322C2211yescharacteristic, complemented
49#16810627C2218yescomplemented
50C2×#13133138C2211yescharacteristic, complemented
51C2×#13133137C2211yescharacteristic
52C2×#13133137C2211yescharacteristic
53C2×#13133137C2211yescharacteristic
54C2×#13133137C2211yescharacteristic, complemented
55C2×#13133137C2211yescharacteristic, complemented
56C2×#13133137C2211yescharacteristic, complemented
57C2×#13133137C2211yescharacteristic, complemented
58C2×#13133137C2211yescharacteristic, complemented
59C2×#13133137C2211yescharacteristic, complemented
60C2×#13133137C2218yescomplemented
61C2×C22⋊#88322C2211yescharacteristic, complemented
62C2×C22⋊#88322C2211yescharacteristic, complemented
63C2×#13133128C2211yescharacteristic, complemented
64C53×#553—24no—
65C53×#553C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic, complemented
68C2×#123×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53C2211yescharacteristic, complemented
71C2×#121×C53C2211yescharacteristic, complemented
72C2×C4×D4×C53—21no—
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic, complemented
75C2×#117×C53C2211yescharacteristic, complemented
76C22×C4⋊C4×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C24×D53—21no—
79C22×D212—24no—
80C22×D212—24no—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212—21no—
84C22×D212—22no—
85C22×D212—22no—
86C22×D212—21no—
87C22×D212—42no—
88C22×D212—42no—
89C22×D212C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×D212C2314yes—
92C22×D212C2314yes—
93C22×D212C2311yescharacteristic
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C2×D4×D53—28no—
97C2×D4×D53—48no—
98C22×C4×D53—21no—
99C2×#11719922—24no—
100C2×#11719922—42no—
101C2×#11719922—42no—
102C2×#11719922C2314yes—
103C2×#11719922C2314yescomplemented
104C2×#11719922C2314yescomplemented
105C2×#11719917—42no—
106C2×#11719917C2314yescomplemented
107C22×#88322—42no—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111C22×#88322C2311yescharacteristic
112C22×#88322C2314yescomplemented
113#13133214—22no—
114#13133214C2314yes—
115#13133192—28no—
116#13133191—22no—
117#13133191—22no—
118#13133191C2314yes—
119#13133191C2314yes—
120#13133187—28no—
121#13133187—28no—
122C4×D212—22no—
123C4×D212C2314yes—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719921—21no—
126C2×#11719921—21no—
127C2×#11719921—21no—
128#13133150C2314yescomplemented
129#13133148C2314yescomplemented
130#13133148C2314yescomplemented
131C4⋊#88322C2314yescomplemented
132#13133138C2314yescomplemented
133#13133137C2314yes—
134#13133137C2314yes—
135#13133137C2314yes—
136#13133137C2314yescomplemented
137#13133137C2314yescomplemented
138#13133137C2314yescomplemented
139#13133137C2314yescomplemented
140#13133137C2314yescomplemented
141#13133137C2314yescomplemented
142C22⋊#88322C2314yescomplemented
143C22⋊#88322C2314yescomplemented
144#13133128C2314yescomplemented
145C22×D4×C53—21no—
146C22×D4×C53—21no—
147C22×D4×C53D411yescharacteristic
148C22×D4×C53C2311yescharacteristic
149C23×C4×C53—21no—
150C23×C4×C53—21no—
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153#126×C53—28no—
154#125×C53—22no—
155#125×C53C2314yescomplemented
156#123×C53—28no—
157#121×C53—28no—
158#121×C53—22no—
159#121×C53—22no—
160#121×C53C2314yescomplemented
161#121×C53C2314yescomplemented
162C4×D4×C53—28no—
163C4×D4×C53—22no—
164C4×D4×C53D414yes—
165C4×D4×C53C2314yes—
166C4×D4×C53C2314yescomplemented
167#117×C53—22no—
168#117×C53C2314yescomplemented
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—22no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2314yescomplemented
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C42×C53—21no—
185C2×C42×C53C2311yescharacteristic
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—24no—
194C23×D53—44no—
195C23×D53—44no—
196C23×D53—44no—
197C23×D53—44no—
198C23×D53—82no—
199C23×D53—82no—
200C2×D4×C53—24no—
201C2×D4×C53—24no—
202C2×D4×C53—24no—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—44no—
207C2×D4×C53—82no—
208C2×D4×C53C2×D414yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—22no—
213C22×C4×C53—22no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—24no—
218C22×C4×C53—24no—
219C22×C4×C53—82no—
220C22×C4×C53—82no—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2412yes—
228C22×C4×C53C2412yes—
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53—24no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—44no—
233C2×C22⋊D53—44no—
234C22×Dic53—21no—
235D4×D53—432no—
236C2×D212—21no—
237C2×D212—22no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—28no—
243C2×D212—28no—
244C2×D212—24no—
245C2×D212—24no—
246C2×D212—21no—
247C2×D212—21no—
248C2×D212—24no—
249C2×D212—24no—
250C2×D212—44no—
251C2×D212—44no—
252C2×D212—48no—
253C2×D212—48no—
254C2×D212—44no—
255C2×D212—44no—
256C2×D212—44no—
257C2×D212—82no—
258C2×D212#4114yes—
259C2×D212C2412yes—
260C2×D212C2412yes—
261C2×D212C2412yes—
262C2×C4×D53—24no—
263C2×C4×D53—44no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53—21no—
266C4⋊C4×C53—24no—
267C4⋊C4×C53—24no—
268C4⋊C4×C53—24no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53C2×D414yes—
271C4⋊C4×C53C2412yes—
272C4⋊C4×C53C2412yes—
273C4⋊C4×C53C2412yes—
274C22⋊C4×C53—24no—
275C22⋊C4×C53—24no—
276C22⋊C4×C53—24no—
277C22⋊C4×C53—24no—
278C22⋊C4×C53C2×D414yes—
279C22⋊C4×C53C2×D414yes—
280C42×C53—24no—
281C42×C53C2×D412yes—
282C42×C53C2412yes—
283#11719922—28no—
284#11719922—44no—
285#11719922—44no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289C4⋊Dic53—21no—
290C4⋊Dic53C2412yes—
291#11719917—44no—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322—22no—
295C2×#88322—22no—
296C2×#88322—44no—
297C2×#88322C2412yes—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300C2×#88322C2412yes—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53AGL(1,ℤ/8)14yes—
311C23×C53C22×D412yes—
312C23×C53C22×D412yes—
313C23×C53C22×D411yescharacteristic
314C22×D53—24no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—48no—
319C22×D53—48no—
320C22×D53—42no—
321C22×D53—42no—
322C22×D53—48no—
323C22×D53—42no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—48no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—84no—
331C22×D53—84no—
332C22×D53—816no—
333C22×D53—816no—
334D4×C53—28no—
335D4×C53—22no—
336D4×C53—22no—
337D4×C53—48no—
338D4×C53—42no—
339D4×C53—84no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—42no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53—84no—
357C2×C4×C53—84no—
358C2×C4×C53C22×D412yes—
359C2×C4×C53C22×D412yes—
360C2×C4×C53C22×D412yes—
361C2×C4×C53C22×D412yes—
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C2×#4112yes—
364C2×C4×C53H(5,𝔽2)12yes—
365C2×C4×C53C2511yescharacteristic
366C22⋊D53—48no—
367C22⋊D53—48no—
368C2×Dic53—22no—
369C2×Dic53—42no—
370D212—24no—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—22no—
376D212—48no—
377D212—48no—
378D212—48no—
379D212—42no—
380D212—42no—
381D212—84no—
382D212C2×#4114yes—
383C4×D53—48no—
384#88322—22no—
385#88322—22no—
386#88322—22no—
387#88322—22no—
388C2×#3318—531nomaximal, Sylow
389C22×C53—22no—
390C22×C53—28no—
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—22no—
394C22×C53—22no—
395C22×C53—44no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—84no—
400C22×C53#54612yes—
401C22×C53C2×AGL(1,ℤ/8)14yes—
402C22×C53C2×AGL(1,ℤ/8)12yes—
403C22×C53#57612yes—
404C22×C53C23×D411yescharacteristic
405C2×D53—24no—
406C2×D53—48no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—816no—
416C2×D53—816no—
417C2×D53—84no—
418C2×D53—84no—
419C4×C53—22no—
420C4×C53—22no—
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—42no—
424C4×C53—42no—
425C4×C53—42no—
426C4×C53#54612yes—
427C4×C53C22×#4111yescharacteristic
428C4×C53C2×H(5,𝔽2)11yescharacteristic
429Dic53—42no—
430C2×#553D5311yescharacteristic, complemented
431C2×D42—531no—
432#3318—5316no—
433C2×#490—531no—
434C2×#481—531no—
435C2×#482—531no—
436C2×#478—531no—
437C2×#469—531no—
438C2×#466—531no—
439C2×#459—531no—
440C2×#447—531no—
441C2×#447—531no—
442C2×#442—531no—
443C2×#435—531no—
444C2×#418—531no—
445C22×#102—531no—
446C2×C53—24no—
447C2×C53—42no—
448C2×C53—82no—
449C2×C53#331814yescomplemented
450C2×C53C2×#54611yescharacteristic
451C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C53C2×#57611yescharacteristic
453D53—44no—
454D53—82no—
455D53—82no—
456C23×D4—531no—
457C23×D4—531no—
458C23×D4—1061no—
459C22×D8—531no—
460C22×D8—531no—
461C22×D8—531no—
462C22×M16—531no—
463C23×C8—531no—
464#553—24no—
465#553C2×D5318yescomplemented
466D42—538no—
467D42—1064no—
468C2×#127—531no—
469C2×#126—21no—
470C2×#125C2×D5311yescharacteristic, complemented
471C2×#123—21no—
472C2×#121—21no—
473C2×#121—531no—
474C2×#121—531no—
475C2×#121—1061no—
476C2×#121C2×D5311yescharacteristic, complemented
477C2×#121C2×D5311yescharacteristic, complemented
478C2×#120—1061no—
479C2×#120—1061no—
480C2×C4×D4—21no—
481C2×C4×D4—531no—
482C2×C4×D4C2×D5311yescharacteristic
483C2×C4×D4C2×D5311yescharacteristic, complemented
484C2×#117C2×D5311yescharacteristic, complemented
485C22×C4⋊C4C2×D5311yescharacteristic, complemented
486#490—538no—
487#482—538no—
488#481—538no—
489#478—538no—
490#469—538no—
491#466—538no—
492#459—538no—
493#447—538no—
494#447—538no—
495#442—538no—
496#435—538no—
497C2×#107—531no—
498C2×#106—531no—
499C2×#106—531no—
500C2×C4⋊C8—531no—
501#418—538no—
502C2×#102—531no—
503C2×#102—531no—
504C2×#102—531no—
505C2×#102—531no—
506C2×#102—531no—
507C2×#102—531no—
508C2×#102—531no—
509C2×#102—531no—
510C2×#102—531no—
511C2×#102—531no—
512C2×#102—538no—
513C2×C22⋊C8—531no—
514C2×C22⋊C8—531no—
515C2×#97—531no—
516C53C2×#331811yescharacteristic, complemented, Sylow
517C25—1061no—
518C25—1061no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—531no—
522C22×D4—531no—
523C22×D4—531no—
524C22×D4—534no—
525C22×D4—534no—
526C22×D4—1064no—
527C22×D4—1064no—
528C22×D4—1061no—
529C22×D4—1061no—
530C22×D4—1068no—
531C22×D4—1061no—
532C22×D4—1061no—
533C22×D4—1061no—
534C22×D4—1061no—
535C22×D4—1062no—
536C22×D4—1062no—
537C22×D4—2122no—
538C22×D4—2122no—
539C22×D4—2128no—
540C22×D4C22⋊D5311yescharacteristic
541C22×D4C22×D5311yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—1061no—
545C23×C4C22×D5311yescharacteristic
546C23×C4C22×D5311yescharacteristic
547C2×D8—534no—
548C2×D8—534no—
549C2×D8—534no—
550C2×D8—1064no—
551C2×D8—2122no—
552C2×D8—2122no—
553C2×M16—534no—
554C2×M16—2122no—
555C22×C8—531no—
556C22×C8—531no—
557C22×C8—531no—
558C22×C8—531no—
559C22×C8—534no—
560C22×C8—2122no—
561#127—534no—
562#127—1062no—
563#126—28no—
564#125—22no—
565#125C22×D5314yescomplemented
566#123—28no—
567#121—28no—
568#121—22no—
569#121—22no—
570#121—534no—
571#121—534no—
572#121—1062no—
573#121—1062no—
574#121—1068no—
575#121C22×D5314yescomplemented
576#121C22×D5314yescomplemented
577#120—1068no—
578#120—1068no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—534no—
582C4×D4—1062no—
583C4×D4C22⋊D5314yes—
584C4×D4C22×D5314yes—
585C4×D4C22×D5314yescomplemented
586#117—22no—
587#117C22×D5314yescomplemented
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—531no—
593C2×C4⋊C4C22⋊D5311yescharacteristic
594C2×C4⋊C4C22×D5311yescharacteristic
595C2×C4⋊C4C22×D5311yescharacteristic
596C2×C4⋊C4C22×D5311yescharacteristic
597C2×C4⋊C4C22×D5314yescomplemented
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—1061no—
603C2×C22⋊C4—1061no—
604C2×C22⋊C4—1061no—
605C2×C22⋊C4C22⋊D5311yescharacteristic
606C2×C22⋊C4C22⋊D5311yescharacteristic
607C2×C42—21no—
608C2×C42C22×D5311yescharacteristic
609#107—534no—
610#106—534no—
611#106—534no—
612C4⋊C8—534no—
613#102—534no—
614#102—534no—
615#102—534no—
616#102—534no—
617#102—534no—
618#102—534no—
619#102—534no—
620#102—534no—
621#102—534no—
622#102—534no—
623C22⋊C8—534no—
624C22⋊C8—534no—
625#97—534no—
626C24—21no—
627C24—1061no—
628C24—1064no—
629C24—1064no—
630C24—1061no—
631C24—1061no—
632C24—4242no—
633C24—4242no—
634C24—2124no—
635C24—2124no—
636C24—2124no—
637C24—2124no—
638C24C2×C22⋊D5311yescharacteristic
639C24C2×C22⋊D5311yescharacteristic
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—534no—
649C2×D4—532no—
650C2×D4—532no—
651C2×D4—532no—
652C2×D4—1068no—
653C2×D4—1068no—
654C2×D4—1064no—
655C2×D4—1064no—
656C2×D4—1061no—
657C2×D4—1064no—
658C2×D4—1064no—
659C2×D4—1064no—
660C2×D4—1064no—
661C2×D4—1061no—
662C2×D4—1061no—
663C2×D4—1062no—
664C2×D4—1062no—
665C2×D4—1062no—
666C2×D4—1062no—
667C2×D4—1062no—
668C2×D4—4242no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4—2128no—
672C2×D4—2128no—
673C2×D4—2124no—
674C2×D4—2124no—
675C2×D4—2124no—
676C2×D4—21232no—
677C2×D4—2124no—
678C2×D4—2124no—
679C2×D4C2×C22⋊D5314yes—
680C2×D4C23×D5312yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—82no—
691C22×C4—82no—
692C22×C4—1061no—
693C22×C4—1064no—
694C22×C4—2124no—
695C22×C4C2×C22⋊D5312yes—
696C22×C4C2×C22⋊D5312yes—
697C22×C4C2×C22⋊D5311yescharacteristic
698C22×C4C2×C22⋊D5311yescharacteristic
699C22×C4C2×C22⋊D5311yescharacteristic
700C22×C4C2×C22⋊D5311yescharacteristic
701C22×C4C23×D5312yes—
702C22×C4C23×D5312yes—
703C22×C4C23×D5311yescharacteristic
704D8—1068no—
705D8—2124no—
706D8—2124no—
707M16—2124no—
708C2×C8—532no—
709C2×C8—532no—
710C2×C8—532no—
711C2×C8—532no—
712C2×C8—1062no—
713C2×C8—1062no—
714C2×C8—1062no—
715C2×C8—1062no—
716C2×C8—2124no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—532no—
724C4⋊C4—1061no—
725C4⋊C4C2×C22⋊D5314yes—
726C4⋊C4C23×D5312yes—
727C4⋊C4C23×D5312yes—
728C4⋊C4C23×D5312yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—1064no—
734C22⋊C4—1064no—
735C22⋊C4—1064no—
736C22⋊C4C2×C22⋊D5314yes—
737C22⋊C4C2×C22⋊D5314yes—
738C42—24no—
739C42C2×C22⋊D5312yes—
740C42C23×D5312yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—1062no—
751C23—1064no—
752C23—1062no—
753C23—1062no—
754C23—42416no—
755C23—4244no—
756C23—4244no—
757C23—42416no—
758C23—2128no—
759C23—2128no—
760C23—2128no—
761C23—2128no—
762C23—2122no—
763C23—2122no—
764C23—2122no—
765C23—2122no—
766C23—2122no—
767C23—2122no—
768C23—2122no—
769C23—2122no—
770C23#1313324214yes—
771C23C22×C22⋊D5312yes—
772C23C22×C22⋊D5312yes—
773C23C22×C22⋊D5311yescharacteristic
774D4—28no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—84no—
780D4—534no—
781D4—1062no—
782D4—1062no—
783D4—1062no—
784D4—1062no—
785D4—1062no—
786D4—1064no—
787D4—4244no—
788D4—2128no—
789D4—2128no—
790D4—2128no—
791D4—2128no—
792D4—2128no—
793D4—2122no—
794D4—2122no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—1062no—
814C2×C4—2128no—
815C2×C4—2122no—
816C2×C4C22×C22⋊D5312yes—
817C2×C4C22×C22⋊D5312yes—
818C2×C4C22×C22⋊D5312yes—
819C2×C4C22×C22⋊D5312yes—
820C2×C4C22×C22⋊D5311yescharacteristic
821C2×C4#41×D5312yes—
822C2×C4#1313326312yes—
823C2×C4C24×D5311yescharacteristic
824C8—1062no—
825C8—1062no—
826C8—1062no—
827C8—1062no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—84no—
839C22—1064no—
840C22—42416no—
841C22—42416no—
842C22—4244no—
843C22—4244no—
844C22—2122no—
845C22—2122no—
846C22—2122no—
847C22—2122no—
848C22—2122no—
849C22—2122no—
850C22—2128no—
851C22—2122no—
852C22—2122no—
853C22#1681126112yes—
854C22C2×#1313324214yes—
855C22C2×#1313324212yes—
856C22#1681142612yes—
857C22C23×C22⋊D5311yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—2122no—
866C4#1681126112yes—
867C4C2×#41×D5311yescharacteristic
868C4C2×#1313326311yescharacteristic
869C2—24no—
870C2—42no—
871C2—82no—
872C2—4242no—
873C2—4242no—
874C2—2124no—
875C2#2028685014yesdirect product factor
876C2C2×#1681126111yescharacteristic
877C2C22×#1313324211yescharacteristic
878C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53C2×#3318
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×D212C2semidirect
2. #20286850C2direct (N × H)
3. C2×#16810989C2semidirect
4. C2×#16810941C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810874C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810818C2semidirect
10. C2×#16810756C2semidirect
11. C2×#16810756C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810627C2semidirect
15. C22×#13133137C2semidirect
16. C2×C53×#553C2semidirect
21. C22×#11719922C22semidirect
22. C22×#11719922C22semidirect
23. C22×#11719917C22semidirect
24. C23×#88322C22semidirect
26. D4×D212C22semidirect
34. #16810989C22semidirect
35. #16810947C22semidirect
36. #16810941C22semidirect
37. #16810920C22semidirect
38. #16810874C22semidirect
39. #16810857C22semidirect
40. #16810818C22semidirect
41. #16810756C22semidirect
42. #16810756C22semidirect
43. #16810733C22semidirect
44. #16810695C22semidirect
45. C2×#13133150C22semidirect
46. C2×#13133148C22semidirect
47. C2×#13133148C22semidirect
48. C2×C4⋊#88322C22semidirect
49. #16810627C22semidirect
50. C2×#13133138C22semidirect
54. C2×#13133137C22semidirect
55. C2×#13133137C22semidirect
56. C2×#13133137C22semidirect
57. C2×#13133137C22semidirect
58. C2×#13133137C22semidirect
59. C2×#13133137C22semidirect
60. C2×#13133137C22semidirect
61. C2×C22⋊#88322C22semidirect
62. C2×C22⋊#88322C22semidirect
63. C2×#13133128C22semidirect
65. C53×#553C22semidirect
67. C2×#125×C53C22semidirect
70. C2×#121×C53C22semidirect
71. C2×#121×C53C22semidirect
74. C2×C4×D4×C53C22semidirect
75. C2×#117×C53C22semidirect
76. C22×C4⋊C4×C53C22semidirect
103. C2×#11719922C23semidirect
104. C2×#11719922C23semidirect
106. C2×#11719917C23semidirect
112. C22×#88322C23semidirect
128. #13133150C23semidirect
129. #13133148C23semidirect
130. #13133148C23semidirect
131. C4⋊#88322C23semidirect
132. #13133138C23semidirect
136. #13133137C23semidirect
137. #13133137C23semidirect
138. #13133137C23semidirect
139. #13133137C23semidirect
140. #13133137C23semidirect
141. #13133137C23semidirect
142. C22⋊#88322C23semidirect
143. C22⋊#88322C23semidirect
144. #13133128C23semidirect
155. #125×C53C23semidirect
160. #121×C53C23semidirect
161. #121×C53C23semidirect
166. C4×D4×C53C23semidirect
168. #117×C53C23semidirect
177. C2×C4⋊C4×C53C23semidirect
430. C2×#553D53semidirect
449. C2×C53#3318semidirect
465. #553C2×D53semidirect
470. C2×#125C2×D53semidirect
476. C2×#121C2×D53semidirect
477. C2×#121C2×D53semidirect
483. C2×C4×D4C2×D53semidirect
484. C2×#117C2×D53semidirect
485. C22×C4⋊C4C2×D53semidirect
516. C53C2×#3318semidirect
565. #125C22×D53semidirect
575. #121C22×D53semidirect
576. #121C22×D53semidirect
585. C4×D4C22×D53semidirect
587. #117C22×D53semidirect
597. C2×C4⋊C4C22×D53semidirect
875. C2#20286850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D2122
#202868502
C2×#168109892
C2×#168109412
C2×#168109472
C2×#168109202
C2×#168108742
C2×#168108572
C2×#168108182
C2×#168107562
C2×#168107332
C2×#168106952
C2×#168106272
C22×#131331372
C2×C53×#5532
C2×#331853