Finite Group Databasebeta

← C2×#20286681 #28260607

Subgroups — C2×#20286681 #28260607

Order 13568.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811278C211yesmaximal, characteristic, complemented
2C2×#16811268C211yesmaximal, characteristic, complemented
3#20286681C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810955C211yesmaximal, characteristic, complemented
7C2×#16810913C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810851C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810765C211yesmaximal, characteristic, complemented
12C2×#16810755C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#102×D53C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719947C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C22×#11719923C2211yescharacteristic, complemented
21C22×#11719922C2211yescharacteristic
22C22×#11719912C2211yescharacteristic, complemented
23C22×C8×D53C2211yescharacteristic
24#16811278—24no—
25#16811278C2218yescomplemented
26#16811268—24no—
27#16811268C2218yescomplemented
28C2×#13133217C2211yescharacteristic, complemented
29C2×#13133205C2211yescharacteristic
30C2×#13133201—21no—
31C2×#13133199—21no—
32C2×#13133199—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133196—21no—
35C2×#13133192C2211yescharacteristic
36C2×#13133191—21no—
37C2×#13133188C2211yescharacteristic
38C2×#13133188C2211yescharacteristic, complemented
39C2×#13133187—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic, complemented
43C22×#11719921—21no—
44#16810983C2218yescomplemented
45#16810955C2218yescomplemented
46#16810943C2218yescomplemented
47#16810913C2218yescomplemented
48#16810875C2218yescomplemented
49#16810851C2218yescomplemented
50#16810838C2218yescomplemented
51#16810765C2218yescomplemented
52#16810755C2218yescomplemented
53#16810696C2218yescomplemented
54C2×#13133148C2211yescharacteristic, complemented
55C2×#13133148C2211yescharacteristic, 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×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic, complemented
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic, complemented
76C2×#97×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—28no—
79C2×#11719945—48no—
80C2×#11719947—24no—
81C2×#11719947—22no—
82C2×#11719947—42no—
83C2×#11719947C2314yes—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C22×D212—21no—
87C22×D212D411yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C2×D4×D53—24no—
94C2×D4×D53—22no—
95C2×D4×D53—42no—
96C2×D4×D53C2314yes—
97C23×Dic53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C22×C4×D53C2311yescharacteristic
102C2×#11719923—42no—
103C2×#11719923C2314yescomplemented
104C2×#11719922—42no—
105C2×#11719922C2314yes—
106C2×#11719912—42no—
107C2×#11719912C2314yescomplemented
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110C2×C8×D53—42no—
111C2×C8×D53C2314yes—
112#13133217—22no—
113#13133217C2314yescomplemented
114#13133205—22no—
115#13133205C2314yes—
116#13133201—28no—
117#13133199—28no—
118#13133199—28no—
119#13133197—22no—
120#13133197C2314yes—
121#13133196—28no—
122#13133192—22no—
123#13133192C2314yes—
124#13133191—28no—
125#13133188—22no—
126#13133188—22no—
127#13133188C2314yes—
128#13133188C2314yescomplemented
129#13133187—28no—
130C4×D212D414yes—
131C4×D212C2314yes—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53D411yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C4⋊C4×D53—22no—
140C4⋊C4×D53—22no—
141C4⋊C4×D53C2314yes—
142C4⋊C4×D53C2314yescomplemented
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—28no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921D411yescharacteristic
151C2×#11719921D411yescharacteristic
152#13133148C2314yescomplemented
153#13133148C2314yescomplemented
154C4⋊#88322C2314yescomplemented
155#13133142C2314yescomplemented
156#13133142C2314yescomplemented
157#13133140C2314yescomplemented
158#13133139C2314yes—
159#13133139C2314yes—
160#13133138C2314yes—
161#13133138C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164#13133129C2314yescomplemented
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53—21no—
169C2×D8×C53—24no—
170C2×D8×C53C2314yes—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C4×D4×C53—22no—
174C4×D4×C53—22no—
175C4×D4×C53C2314yes—
176C4×D4×C53C2314yescomplemented
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C42×C53C2311yescharacteristic
182#106×C53C2314yescomplemented
183#102×C53C2314yes—
184#102×C53C2314yescomplemented
185#97×C53C2314yescomplemented
186C24×C53—21no—
187C24×C53—21no—
188C23×D53—21no—
189C23×D53—24no—
190C23×D53—44no—
191C23×D53—44no—
192C23×D53—82no—
193C23×D53C2×D411yescharacteristic
194C23×D53C2×D411yescharacteristic
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53#4114yescomplemented
201C2×D4×C53C2412yes—
202C2×D4×C53C2412yes—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—24no—
206C22×C4×C53—24no—
207C22×C4×C53—44no—
208C22×C4×C53—82no—
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2411yescharacteristic
212C2×C22⋊D53—24no—
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53—44no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—24no—
224C22×Dic53—44no—
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227#11719947—28no—
228#11719947—44no—
229#11719947—48no—
230D4×D53—28no—
231D4×D53—44no—
232D4×D53—48no—
233#11719945—432no—
234C2×D212—24no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—21no—
238C2×D212—24no—
239C2×D212—82no—
240C2×D212C2×D414yes—
241C2×D212C2412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—44no—
249C2×C4×D53—44no—
250C2×C4×D53C2×D412yes—
251C2×C4×D53C2×D412yes—
252C2×C4×D53C2412yes—
253C2×C4×D53C2412yes—
254C2×Dic106—22no—
255C2×Dic106—22no—
256C2×Dic106—24no—
257C2×Dic106—21no—
258C2×Dic106—44no—
259C2×Dic106C2412yes—
260D8×C53—28no—
261C2×C8×C53—22no—
262C2×C8×C53—22no—
263C2×C8×C53C2412yes—
264C2×C8×C53C2412yes—
265C4⋊C4×C53—21no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53C2412yes—
268C4⋊C4×C53C2412yes—
269C22⋊C4×C53—24no—
270C22⋊C4×C53—24no—
271C42×C53C2×D412yes—
272C42×C53C2412yes—
273C22⋊Dic53—24no—
274C22⋊Dic53—24no—
275#11719923—44no—
276#11719922—44no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921—24no—
281#11719921C2×D414yes—
282#11719921C2×D414yes—
283C4⋊Dic53—21no—
284C4⋊Dic53—21no—
285C4⋊Dic53—24no—
286C4⋊Dic53—24no—
287C4⋊Dic53C2×D414yes—
288C4⋊Dic53C2412yes—
289C4⋊Dic53C2412yes—
290#11719919—24no—
291#11719919—24no—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296#11719912—44no—
297C8×D53—44no—
298C23×C53—24no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—48no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—48no—
318C22×D53—84no—
319C22×D53—816no—
320C22×D53AGL(1,ℤ/8)14yes—
321C22×D53C22×D412yes—
322C22×D53C22×D412yes—
323D4×C53—24no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—22no—
327D4×C53—42no—
328D4×C53C2×#4114yescomplemented
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—48no—
334C2×C4×C53—42no—
335C2×C4×C53—42no—
336C2×C4×C53—84no—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C2×#4112yes—
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53C2511yescharacteristic
343C22⋊D53—48no—
344C22⋊D53—48no—
345C22⋊D53—48no—
346C22⋊D53—48no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—48no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—42no—
356C2×Dic53C22×D412yes—
357C2×Dic53C22×D412yes—
358D212—28no—
359D212—22no—
360D212—22no—
361D212—42no—
362D212—84no—
363C4×D53—24no—
364C4×D53—24no—
365C4×D53—22no—
366C4×D53—22no—
367C4×D53—22no—
368C4×D53—22no—
369C4×D53—48no—
370C4×D53—48no—
371Dic106—22no—
372Dic106—22no—
373Dic106—48no—
374Dic106—42no—
375C8×C53—22no—
376C8×C53—22no—
377#88322—22no—
378#88322—22no—
379C2×#3306—531nomaximal, Sylow
380C22×C53—24no—
381C22×C53—48no—
382C22×C53—42no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—84no—
388C22×C53#54612yes—
389C22×C53C2×AGL(1,ℤ/8)12yes—
390C22×C53#57712yes—
391C22×C53C23×D411yescharacteristic
392C2×D53—22no—
393C2×D53—28no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—22no—
398C2×D53—44no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—816no—
403C2×D53—84no—
404C2×D53C2×AGL(1,ℤ/8)14yes—
405C4×C53—22no—
406C4×C53—22no—
407C4×C53—42no—
408C4×C53—42no—
409C4×C53#54612yes—
410C4×C53C22×#4111yescharacteristic
411C4×C53C2×H(5,𝔽2)11yescharacteristic
412Dic53—22no—
413Dic53—22no—
414Dic53—42no—
415Dic53—42no—
416Dic53—42no—
417C2×#547—531no—
418C2×#546—531no—
419#3306—5316no—
420C2×#489—531no—
421C2×#481—531no—
422C2×#483—531no—
423C2×#476—531no—
424C2×#469—531no—
425C2×#465—531no—
426C2×#463—531no—
427C2×#449—531no—
428C2×#447—531no—
429C2×#442D5311yescharacteristic, complemented
430C2×#435—531no—
431C2×#417—531no—
432C22×#102—531no—
433C2×C53—44no—
434C2×C53—82no—
435C2×C53#330614yescomplemented
436C2×C53C2×#54611yescharacteristic
437C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C53C2×#57711yescharacteristic
439D53—24no—
440D53—42no—
441D53—82no—
442C22×#41—531no—
443C22×#41—1061no—
444C23×D4—531no—
445C22×SD16—531no—
446C22×D8—531no—
447C22×D8C2×D5311yescharacteristic
448C22×M16—531no—
449C23×C8—531no—
450#547—538no—
451#547—1064no—
452#546—538no—
453#546—1064no—
454C2×C4⋊Q8—531no—
455C2×#124—531no—
456C2×#123—1061no—
457C2×#123—1061no—
458C2×#123—1061no—
459C2×C22⋊Q8—531no—
460C2×C22⋊Q8—1061no—
461C2×#121—531no—
462C2×#121—531no—
463C2×#121—531no—
464C2×#121—1061no—
465C2×#120—1061no—
466C2×C4×D4—531no—
467C2×C4×D4C2×D5311yescharacteristic
468C2×C4×D4C2×D5311yescharacteristic, complemented
469C22×C4⋊C4—531no—
470C22×C4⋊C4—531no—
471C22×C22⋊C4—1061no—
472#489—538no—
473#483—538no—
474#481—538no—
475#476—538no—
476#469—538no—
477#465—538no—
478#463—538no—
479#449—538no—
480#447—538no—
481#442C2×D5318yescomplemented
482#435—538no—
483C2×#106—531no—
484C2×#106—531no—
485C2×#106C2×D5311yescharacteristic, complemented
486C2×C4⋊C8—531no—
487#417—538no—
488C2×#103—531no—
489C2×#103—531no—
490C2×#103—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×#102—531no—
495C2×#102—531no—
496C2×#102—538no—
497C2×#102C2×D5311yescharacteristic
498C2×#102C2×D5311yescharacteristic, complemented
499C2×C22⋊C8—531no—
500C2×C22⋊C8—531no—
501C2×#97C2×D5311yescharacteristic, complemented
502C53C2×#330611yescharacteristic, complemented, Sylow
503C25—1061no—
504C2×#41—534no—
505C2×#41—1068no—
506C2×#41—1062no—
507C2×#41—1064no—
508C2×#41—2128no—
509C2×#41—2122no—
510C22×Q8—531no—
511C22×Q8—1061no—
512C22×D4—534no—
513C22×D4—531no—
514C22×D4—531no—
515C22×D4—1061no—
516C22×D4—1062no—
517C22×D4—1061no—
518C22×D4—1064no—
519C22×D4—1061no—
520C22×D4—1061no—
521C22×D4—1061no—
522C22×D4—2122no—
523C22×D4C22×D5311yescharacteristic
524C22×D4C22×D5311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—531no—
528C23×C4—531no—
529C23×C4—1061no—
530C23×C4—1061no—
531C23×C4—1061no—
532C2×SD16—534no—
533C2×SD16—2122no—
534C2×D8—24no—
535C2×D8—534no—
536C2×D8—2122no—
537C2×D8C22×D5314yes—
538C2×M16—534no—
539C2×M16—2122no—
540C22×C8—531no—
541C22×C8—531no—
542C22×C8—534no—
543C22×C8—2122no—
544C22×C8C22×D5311yescharacteristic
545C22×C8C22×D5311yescharacteristic
546C4⋊Q8—534no—
547C4⋊Q8—1062no—
548#124—534no—
549#124—1062no—
550#123—1068no—
551#123—1068no—
552#123—1068no—
553C22⋊Q8—534no—
554C22⋊Q8—1062no—
555C22⋊Q8—1068no—
556#121—534no—
557#121—534no—
558#121—534no—
559#121—1068no—
560#121—1062no—
561#121—1062no—
562#121—1062no—
563#120—1068no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—534no—
567C4×D4—534no—
568C4×D4C22×D5314yes—
569C4×D4C22×D5314yescomplemented
570C2×C4⋊C4—531no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—531no—
573C2×C4⋊C4—534no—
574C2×C4⋊C4—534no—
575C2×C4⋊C4—1062no—
576C2×C4⋊C4—1062no—
577C2×C4⋊C4—1061no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4—1061no—
581C2×C4⋊C4C22×D5311yescharacteristic
582C2×C4⋊C4C22×D5311yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—531no—
586C2×C22⋊C4—531no—
587C2×C22⋊C4—1068no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C22⋊C4—1061no—
592C2×C22⋊C4—1061no—
593C2×C22⋊C4—1061no—
594C2×C42C22×D5311yescharacteristic
595#106—534no—
596#106—534no—
597#106C22×D5314yescomplemented
598C4⋊C8—534no—
599#103—534no—
600#103—534no—
601#103—534no—
602#102—534no—
603#102—534no—
604#102—534no—
605#102—534no—
606#102—534no—
607#102C22×D5314yes—
608#102C22×D5314yescomplemented
609C22⋊C8—534no—
610C22⋊C8—534no—
611#97C22×D5314yescomplemented
612C24—21no—
613C24—21no—
614C24—531no—
615C24—531no—
616C24—1064no—
617C24—1061no—
618C24—4242no—
619C24—2124no—
620C24—2124no—
621#41—1068no—
622#41—21232no—
623#41—2124no—
624#41—2128no—
625C2×Q8—532no—
626C2×Q8—1061no—
627C2×Q8—1064no—
628C2×Q8—1062no—
629C2×Q8—1062no—
630C2×Q8—2124no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—534no—
637C2×D4—532no—
638C2×D4—1064no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1068no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1064no—
645C2×D4—1061no—
646C2×D4—1062no—
647C2×D4—1062no—
648C2×D4—4242no—
649C2×D4—2124no—
650C2×D4—2128no—
651C2×D4—2124no—
652C2×D4—2124no—
653C2×D4—2124no—
654C2×D4—2124no—
655C2×D4#1171994514yescomplemented
656C2×D4C23×D5312yes—
657C2×D4C23×D5312yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—44no—
663C22×C4—82no—
664C22×C4—531no—
665C22×C4—531no—
666C22×C4—532no—
667C22×C4—532no—
668C22×C4—532no—
669C22×C4—532no—
670C22×C4—1064no—
671C22×C4—1064no—
672C22×C4—1064no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—2124no—
681C22×C4—2124no—
682C22×C4—2124no—
683C22×C4D4×D5311yescharacteristic
684C22×C4D4×D5311yescharacteristic
685C22×C4C23×D5311yescharacteristic
686SD16—2124no—
687D8—28no—
688D8—2124no—
689M16—2124no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—532no—
693C2×C8—532no—
694C2×C8—1062no—
695C2×C8—1062no—
696C2×C8—2124no—
697C2×C8C23×D5312yes—
698C2×C8C23×D5312yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—534no—
702C4⋊C4—532no—
703C4⋊C4—532no—
704C4⋊C4—1064no—
705C4⋊C4—1064no—
706C4⋊C4—1064no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1064no—
710C4⋊C4C23×D5312yes—
711C4⋊C4C23×D5312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—534no—
715C22⋊C4—534no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4—1064no—
720C22⋊C4—1064no—
721C22⋊C4—1064no—
722C42D4×D5312yes—
723C42C23×D5312yes—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—534no—
733C23—532no—
734C23—532no—
735C23—1062no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1062no—
740C23—1062no—
741C23—42416no—
742C23—4244no—
743C23—2128no—
744C23—2128no—
745C23—2122no—
746C23—2122no—
747C23—2122no—
748C23C2×D4×D5311yescharacteristic
749Q8—1062no—
750Q8—1062no—
751Q8—2128no—
752Q8—2122no—
753D4—24no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—42no—
758D4—1068no—
759D4—1062no—
760D4—1062no—
761D4—4244no—
762D4—2128no—
763D4—2128no—
764D4—2128no—
765D4—2128no—
766D4—2122no—
767D4C2×#1171994514yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—84no—
776C2×C4—532no—
777C2×C4—532no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1064no—
781C2×C4—1064no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—2128no—
790C2×C4—2128no—
791C2×C4—2128no—
792C2×C4—2122no—
793C2×C4—2122no—
794C2×C4—2122no—
795C2×C4C2×D4×D5312yes—
796C2×C4C2×D4×D5312yes—
797C2×C4C2×D4×D5311yescharacteristic
798C2×C4C2×#1171994512yes—
799C2×C4#1313326312yes—
800C2×C4C24×D5311yescharacteristic
801C8—22no—
802C8—22no—
803C8—1062no—
804C8—1062no—
805C22—24no—
806C22—42no—
807C22—42no—
808C22—48no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—84no—
813C22—534no—
814C22—1062no—
815C22—1062no—
816C22—1068no—
817C22—1062no—
818C22—1062no—
819C22—1062no—
820C22—42416no—
821C22—4244no—
822C22—2122no—
823C22—2122no—
824C22—2122no—
825C22—2124no—
826C22#1681126912yes—
827C22AGL(1,ℤ/8)×D5312yes—
828C22#1681143312yes—
829C22C22×D4×D5311yescharacteristic
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—1062no—
835C4—1062no—
836C4—2122no—
837C4—2122no—
838C4—2122no—
839C4#1681126912yes—
840C4C22×#1171994511yescharacteristic
841C4C2×#1313326311yescharacteristic
842C2—44no—
843C2—82no—
844C2—1064no—
845C2—4242no—
846C2—2122no—
847C2#2028668114yesdirect product factor
848C2C2×#1681126911yescharacteristic
849C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
850C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
hypercenterC2×#442D53
hypocenterC53C2×#3306
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811278C2semidirect
2. C2×#16811268C2semidirect
3. #20286681C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810955C2semidirect
7. C2×#16810913C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810851C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810765C2semidirect
12. C2×#16810755C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810621C2semidirect
15. C2×#102×D53C2semidirect
16. C2×C53×#442C2semidirect
20. C22×#11719923C22semidirect
22. C22×#11719912C22semidirect
25. #16811278C22semidirect
27. #16811268C22semidirect
28. C2×#13133217C22semidirect
38. C2×#13133188C22semidirect
42. C2×C4⋊C4×D53C22semidirect
44. #16810983C22semidirect
45. #16810955C22semidirect
46. #16810943C22semidirect
47. #16810913C22semidirect
48. #16810875C22semidirect
49. #16810851C22semidirect
50. #16810838C22semidirect
51. #16810765C22semidirect
52. #16810755C22semidirect
53. #16810696C22semidirect
54. C2×#13133148C22semidirect
55. C2×#13133148C22semidirect
56. C2×C4⋊#88322C22semidirect
57. #16810621C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
66. #102×D53C22semidirect
68. C2×#13133129C22semidirect
71. C2×C4×D4×C53C22semidirect
72. C53×#442C22semidirect
73. C2×#106×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×#97×C53C22semidirect
103. C2×#11719923C23semidirect
107. C2×#11719912C23semidirect
113. #13133217C23semidirect
128. #13133188C23semidirect
142. C4⋊C4×D53C23semidirect
152. #13133148C23semidirect
153. #13133148C23semidirect
154. C4⋊#88322C23semidirect
155. #13133142C23semidirect
156. #13133142C23semidirect
157. #13133140C23semidirect
164. #13133129C23semidirect
176. C4×D4×C53C23semidirect
182. #106×C53C23semidirect
184. #102×C53C23semidirect
185. #97×C53C23semidirect
200. C2×D4×C53#41semidirect
328. D4×C53C2×#41semidirect
429. C2×#442D53semidirect
435. C2×C53#3306semidirect
468. C2×C4×D4C2×D53semidirect
481. #442C2×D53semidirect
485. C2×#106C2×D53semidirect
498. C2×#102C2×D53semidirect
501. C2×#97C2×D53semidirect
502. C53C2×#3306semidirect
569. C4×D4C22×D53semidirect
597. #106C22×D53semidirect
608. #102C22×D53semidirect
611. #97C22×D53semidirect
655. C2×D4#11719945semidirect
767. D4C2×#11719945semidirect
847. C2#20286681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112782
C2×#168112682
#202866812
C2×#168109832
C2×#168109432
C2×#168109552
C2×#168109132
C2×#168108752
C2×#168108512
C2×#168108382
C2×#168107652
C2×#168107552
C2×#168106962
C2×#168106212
C2×#102×D532
C2×C53×#4422
C2×#330653