Finite Group Databasebeta

← C2×#20285809 #28255447

Subgroups — C2×#20285809 #28255447

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic, complemented
2#20285809C2116yesmaximal, direct product factor
3C2×#16811010C211yesmaximal, characteristic, complemented
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810982C211yesmaximal, characteristic, complemented
6C2×#16810969C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810820C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810815C211yesmaximal, characteristic, complemented
11C2×#16810785C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810774C211yesmaximal, characteristic, complemented
14C2×#16810757C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#535C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic, complemented
18C22×#11719923C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic, complemented
21C22×#11719924C2211yescharacteristic, complemented
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719922C2211yescharacteristic, complemented
25#16811244—24no—
26#16811244C2218yescomplemented
27C2×#13133217C2211yescharacteristic, complemented
28C2×#13133212—21no—
29C2×#13133205C2211yescharacteristic, complemented
30C2×#13133203—21no—
31C2×#13133199—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133195—21no—
34C2×#13133191C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic, complemented
36C2×C4×D212C2211yescharacteristic, complemented
37#16811010C2218yescomplemented
38#16811005C2218yescomplemented
39#16810982C2218yescomplemented
40#16810969C2218yescomplemented
41#16810842C2218yescomplemented
42#16810835C2218yescomplemented
43#16810820C2218yescomplemented
44#16810815C2218yescomplemented
45#16810785C2218yescomplemented
46#16810774C2218yescomplemented
47#16810768C2218yescomplemented
48#16810757C2218yescomplemented
49#16810684C2218yescomplemented
50C2×C4⋊#88322C2211yescharacteristic, complemented
51C2×C4⋊#88322C2211yescharacteristic, complemented
52C2×#13133141C2211yescharacteristic, complemented
53C2×#13133141C2211yescharacteristic, complemented
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic, complemented
59C2×#13133138C2211yescharacteristic, complemented
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic, complemented
63C2×C4×#88322C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C23×D4×C53C2211yescharacteristic
66C53×#535—24no—
67C53×#535C2218yescomplemented
68C2×#127×C53C2211yescharacteristic
69C2×#127×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×#121×C53—21no—
73C2×#121×C53—21no—
74C2×#120×C53—21no—
75C2×#120×C53—21no—
76C2×#117×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C4×D53—21no—
82C2×#11719925—42no—
83C2×#11719925C2314yescomplemented
84C2×#11719923—42no—
85C2×#11719923—42no—
86C2×#11719923—42no—
87C2×#11719923C2314yes—
88C2×#11719923C2314yes—
89C2×#11719923C2314yescomplemented
90C2×#11719924—42no—
91C2×#11719924C2314yescomplemented
92C2×#11719922—42no—
93C2×#11719922—42no—
94C2×#11719922—42no—
95C2×#11719922C2314yes—
96C2×#11719922C2314yes—
97C2×#11719922C2314yescomplemented
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102#13133217—22no—
103#13133217C2314yescomplemented
104#13133212—28no—
105#13133205—22no—
106#13133205C2314yescomplemented
107#13133203—28no—
108#13133199—28no—
109#13133196—22no—
110#13133196C2314yes—
111#13133195—28no—
112#13133191—22no—
113#13133191C2314yes—
114C4×Dic106—22no—
115C4×Dic106C2314yescomplemented
116C4×D212—22no—
117C4×D212C2314yescomplemented
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2311yescharacteristic
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×C22⋊Dic53—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×#11719921—21no—
127C2×#11719921—21no—
128C2×C4×Dic53—21no—
129C4⋊#88322C2314yescomplemented
130C4⋊#88322C2314yescomplemented
131#13133141C2314yescomplemented
132#13133141C2314yescomplemented
133#13133138C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137#13133138C2314yescomplemented
138#13133138C2314yescomplemented
139C22⋊#88322C2314yes—
140C22⋊#88322C2314yes—
141#13133128C2314yescomplemented
142C4×#88322C2314yescomplemented
143C25×C53—21no—
144C2×#41×C53—22no—
145C2×#41×C53—42no—
146C2×#41×C53—42no—
147C2×#41×C53C2314yes—
148C22×Q8×C53C2311yescharacteristic
149C22×D4×C53—21no—
150C22×D4×C53—21no—
151C22×D4×C53—22no—
152C22×D4×C53—21no—
153C22×D4×C53—21no—
154C22×D4×C53—21no—
155C22×D4×C53—21no—
156C22×D4×C53—42no—
157C22×D4×C53—42no—
158C22×D4×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C22×D4×C53C2314yes—
162C23×C4×C53—21no—
163C23×C4×C53C2311yescharacteristic
164#127×C53—22no—
165#127×C53—22no—
166#127×C53C2314yes—
167#127×C53C2314yes—
168#124×C53—22no—
169#124×C53—22no—
170#124×C53C2314yes—
171#124×C53C2314yes—
172#121×C53—28no—
173#121×C53—28no—
174#120×C53—28no—
175#120×C53—28no—
176#117×C53D414yes—
177#117×C53C2314yes—
178C2×C4⋊C4×C53D411yescharacteristic
179C2×C4⋊C4×C53D411yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53D411yescharacteristic
185C2×C22⋊C4×C53D411yescharacteristic
186C2×C42×C53C2311yescharacteristic
187C2×C42×C53C2311yescharacteristic
188C24×C53—21no—
189C24×C53—21no—
190C24×C53—21no—
191C24×C53—24no—
192C24×C53—44no—
193C24×C53—82no—
194C24×C53—82no—
195C24×C53C2×D411yescharacteristic
196C23×D53—21no—
197#41×C53—44no—
198#41×C53—44no—
199#41×C53—48no—
200C2×Q8×C53—21no—
201C2×Q8×C53—22no—
202C2×Q8×C53—22no—
203C2×Q8×C53C2412yes—
204C2×D4×C53—24no—
205C2×D4×C53—24no—
206C2×D4×C53—21no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—24no—
210C2×D4×C53—24no—
211C2×D4×C53—24no—
212C2×D4×C53—24no—
213C2×D4×C53—22no—
214C2×D4×C53—22no—
215C2×D4×C53—22no—
216C2×D4×C53—22no—
217C2×D4×C53—22no—
218C2×D4×C53—22no—
219C2×D4×C53—44no—
220C2×D4×C53—44no—
221C2×D4×C53—44no—
222C2×D4×C53—48no—
223C2×D4×C53—44no—
224C2×D4×C53—82no—
225C2×D4×C53—82no—
226C2×D4×C53—82no—
227C2×D4×C53—82no—
228C2×D4×C53C2412yes—
229C2×D4×C53C2412yes—
230C2×D4×C53C2412yes—
231C22×C4×C53—22no—
232C22×C4×C53—22no—
233C22×C4×C53—21no—
234C22×C4×C53—24no—
235C22×C4×C53—44no—
236C22×C4×C53C2×D411yescharacteristic
237C22×C4×C53C2×D411yescharacteristic
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D412yes—
242C22×C4×C53C2412yes—
243C22×C4×C53C2411yescharacteristic
244C2×C22⋊D53—24no—
245C2×C22⋊D53—82no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—21no—
252C2×D212C2412yes—
253C2×C4×D53—24no—
254C2×C4×D53—82no—
255C2×Dic106—22no—
256C2×Dic106—22no—
257C2×Dic106—21no—
258C2×Dic106—24no—
259C2×Dic106—82no—
260C2×Dic106C2412yes—
261C4⋊C4×C53C2×D414yes—
262C4⋊C4×C53C2×D414yes—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—24no—
265C22⋊C4×C53—24no—
266C22⋊C4×C53—24no—
267C22⋊C4×C53C2×D414yes—
268C22⋊C4×C53C2×D414yes—
269C42×C53C2×D412yes—
270C42×C53C2×D412yes—
271C42×C53C2412yes—
272C42×C53C2412yes—
273C22⋊Dic53—24no—
274#11719925—44no—
275#11719924—44no—
276#11719923—44no—
277#11719923—44no—
278#11719923—44no—
279#11719922—44no—
280#11719922—44no—
281#11719922—44no—
282#11719921—24no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286C4⋊Dic53—24no—
287C4⋊Dic53—21no—
288C4⋊Dic53—21no—
289C4⋊Dic53C2412yes—
290C4⋊Dic53C2412yes—
291#11719919—24no—
292#11719919—24no—
293C4×Dic53—24no—
294C2×#88322—22no—
295C2×#88322—22no—
296C2×#88322—22no—
297C2×#88322—22no—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300C2×#88322C2412yes—
301C2×#88322C2412yes—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—48no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53—84no—
319C23×C53—84no—
320C23×C53—816no—
321C23×C53C22×D412yes—
322C23×C53C22×D411yescharacteristic
323C22×D53—22no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327Q8×C53—22no—
328Q8×C53—22no—
329Q8×C53—42no—
330D4×C53—22no—
331D4×C53—22no—
332D4×C53—22no—
333D4×C53—22no—
334D4×C53—22no—
335D4×C53—22no—
336D4×C53—48no—
337D4×C53—48no—
338D4×C53—42no—
339D4×C53—42no—
340D4×C53—42no—
341D4×C53—84no—
342D4×C53—84no—
343D4×C53—84no—
344D4×C53—84no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—24no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—48no—
355C2×C4×C53—42no—
356C2×C4×C53C22×D412yes—
357C2×C4×C53C22×D412yes—
358C2×C4×C53C22×D412yes—
359C2×C4×C53C22×D412yes—
360C2×C4×C53C22×D412yes—
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53H(5,𝔽2)12yes—
363C2×C4×C53H(5,𝔽2)12yes—
364C2×C4×C53C2511yescharacteristic
365C22⋊D53—84no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—42no—
370C2×Dic53—42no—
371C2×Dic53—42no—
372D212—22no—
373D212—22no—
374D212—42no—
375C4×D53—84no—
376Dic106—22no—
377Dic106—22no—
378Dic106—42no—
379Dic106—84no—
380#88322—22no—
381#88322—22no—
382#88322—22no—
383#88322—22no—
384C2×#3224—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—44no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—816no—
399C22×C53—84no—
400C22×C53—84no—
401C22×C53—84no—
402C22×C53#53512yes—
403C22×C53#57612yes—
404C22×C53#57712yes—
405C22×C53C23×D411yescharacteristic
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—22no—
415C4×C53—42no—
416C4×C53#53512yes—
417C4×C53C2×H(5,𝔽2)11yescharacteristic
418C4×C53C2×H(5,𝔽2)11yescharacteristic
419Dic53—42no—
420Dic53—42no—
421Dic53—42no—
422C2×#542—531no—
423C2×#535D5311yescharacteristic, complemented
424#3224—5316no—
425C2×#496—531no—
426C2×#495—531no—
427C2×#489—531no—
428C2×#486—531no—
429C2×#464—531no—
430C2×#460—531no—
431C2×#463—531no—
432C2×#459—531no—
433C2×#452—531no—
434C2×#449—531no—
435C2×#450—531no—
436C2×#447—531no—
437C2×#433—531no—
438C2×C53—42no—
439C2×C53—82no—
440C2×C53—82no—
441C2×C53—82no—
442C2×C53#322414yescomplemented
443C2×C53C2×#53511yescharacteristic
444C2×C53C2×#57611yescharacteristic
445C2×C53C2×#57711yescharacteristic
446D53—82no—
447C22×#41C2×D5311yescharacteristic
448C23×D4C2×D5311yescharacteristic
449C22×Q16—531no—
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16—531no—
454C22×D8—531no—
455C22×D8—531no—
456C22×D8—531no—
457#542—538no—
458#542—1064no—
459#535—24no—
460#535C2×D5318yescomplemented
461C2×C4⋊Q8—531no—
462C2×#127C2×D5311yescharacteristic
463C2×#127C2×D5311yescharacteristic
464C2×#126—1061no—
465C2×#124—531no—
466C2×#124—1061no—
467C2×#124C2×D5311yescharacteristic
468C2×#124C2×D5311yescharacteristic
469C2×#123—1061no—
470C2×C22⋊Q8—531no—
471C2×C22⋊Q8—1061no—
472C2×#121—21no—
473C2×#121—21no—
474C2×#121—531no—
475C2×#120—21no—
476C2×#120—21no—
477C2×C4×Q8—531no—
478C2×C4×D4—531no—
479C2×#117C2×D5311yescharacteristic
480#496—538no—
481#495—538no—
482#489—538no—
483#486—538no—
484#464—538no—
485#463—538no—
486#460—538no—
487#459—538no—
488#452—538no—
489#450—538no—
490#449—538no—
491#447—538no—
492#433—538no—
493C2×C4⋊C8—531no—
494C2×C4⋊C8—531no—
495C2×#103—531no—
496C2×#103—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×C22⋊C8—531no—
504C2×C22⋊C8—531no—
505C2×#97—531no—
506C2×C4×C8—531no—
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—21no—
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41C22×D5314yes—
513C22×Q8—531no—
514C22×Q8—1061no—
515C22×Q8C22×D5311yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—531no—
526C22×D4—1061no—
527C22×D4C22×D5311yescharacteristic
528C22×D4C22×D5311yescharacteristic
529C22×D4C22×D5311yescharacteristic
530C22×D4C22×D5314yes—
531C23×C4—21no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C2×Q16—534no—
535C2×Q16—2122no—
536C2×SD16—534no—
537C2×SD16—534no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16—2122no—
543C2×SD16—2122no—
544C2×D8—534no—
545C2×D8—534no—
546C2×D8—534no—
547C2×D8—2122no—
548C2×D8—2122no—
549C2×D8—2122no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—531no—
554C4⋊Q8—534no—
555C4⋊Q8—1062no—
556#127—22no—
557#127—22no—
558#127C22×D5314yes—
559#127C22×D5314yes—
560#126—1068no—
561#124—22no—
562#124—22no—
563#124—534no—
564#124—1068no—
565#124—1062no—
566#124C22×D5314yes—
567#124C22×D5314yes—
568#123—1068no—
569C22⋊Q8—534no—
570C22⋊Q8—1062no—
571C22⋊Q8—1068no—
572#121—28no—
573#121—28no—
574#121—534no—
575#121—1062no—
576#120—28no—
577#120—28no—
578C4×Q8—534no—
579C4×Q8—1062no—
580C4×D4—534no—
581C4×D4—1062no—
582#117C22⋊D5314yes—
583#117C22×D5314yes—
584C2×C4⋊C4—531no—
585C2×C4⋊C4—531no—
586C2×C4⋊C4—1061no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4C22⋊D5311yescharacteristic
590C2×C4⋊C4C22⋊D5311yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1061no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4C22⋊D5311yescharacteristic
601C2×C22⋊C4C22⋊D5311yescharacteristic
602C2×C42—1061no—
603C2×C42C22×D5311yescharacteristic
604C2×C42C22×D5311yescharacteristic
605C4⋊C8—534no—
606C4⋊C8—534no—
607#103—534no—
608#103—534no—
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102—534no—
614#102—534no—
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97—534no—
618C4×C8—534no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—24no—
623C24—44no—
624C24—82no—
625C24—82no—
626C24—1061no—
627C24C2×C22⋊D5311yescharacteristic
628#41—44no—
629#41—44no—
630#41—48no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—532no—
635C2×Q8—1064no—
636C2×Q8—1061no—
637C2×Q8—1062no—
638C2×Q8—1062no—
639C2×Q8—4242no—
640C2×Q8C23×D5312yes—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—48no—
660C2×D4—44no—
661C2×D4—82no—
662C2×D4—82no—
663C2×D4—82no—
664C2×D4—82no—
665C2×D4—532no—
666C2×D4—1064no—
667C2×D4—1061no—
668C2×D4—1062no—
669C2×D4—1062no—
670C2×D4—4242no—
671C2×D4C23×D5312yes—
672C2×D4C23×D5312yes—
673C2×D4C23×D5312yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—44no—
679C22×C4—1061no—
680C22×C4—1061no—
681C22×C4—1061no—
682C22×C4—1064no—
683C22×C4—4242no—
684C22×C4C2×C22⋊D5312yes—
685C22×C4C2×C22⋊D5311yescharacteristic
686C22×C4C2×C22⋊D5311yescharacteristic
687C22×C4C2×C22⋊D5311yescharacteristic
688C22×C4C2×C22⋊D5311yescharacteristic
689C22×C4C2×C22⋊D5311yescharacteristic
690C22×C4C23×D5312yes—
691C22×C4C23×D5311yescharacteristic
692Q16—2124no—
693SD16—2124no—
694SD16—2124no—
695SD16—2124no—
696SD16—2124no—
697D8—2124no—
698D8—2124no—
699D8—2124no—
700C2×C8—532no—
701C2×C8—532no—
702C2×C8—532no—
703C2×C8—532no—
704C2×C8—1062no—
705C2×C8—1062no—
706C2×C8—1062no—
707C2×C8—1062no—
708C4⋊C4—532no—
709C4⋊C4—532no—
710C4⋊C4—1061no—
711C4⋊C4—1061no—
712C4⋊C4—1064no—
713C4⋊C4—1064no—
714C4⋊C4—1064no—
715C4⋊C4C2×C22⋊D5314yes—
716C4⋊C4C2×C22⋊D5314yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1064no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4C2×C22⋊D5314yes—
727C22⋊C4C2×C22⋊D5314yes—
728C42—1064no—
729C42C2×C22⋊D5312yes—
730C42C2×C22⋊D5312yes—
731C42C23×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—48no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—84no—
750C23—84no—
751C23—816no—
752C23—1062no—
753C23—2122no—
754C23—2122no—
755C23—2122no—
756C23C22×C22⋊D5312yes—
757C23C22×C22⋊D5311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—1062no—
762Q8—1062no—
763Q8—4244no—
764Q8—2122no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—84no—
777D4—84no—
778D4—84no—
779D4—84no—
780D4—1062no—
781D4—1062no—
782D4—4244no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—4244no—
799C2×C4—2122no—
800C2×C4—2122no—
801C2×C4—2122no—
802C2×C4C22×C22⋊D5312yes—
803C2×C4C22×C22⋊D5312yes—
804C2×C4C22×C22⋊D5312yes—
805C2×C4C22×C22⋊D5312yes—
806C2×C4C22×C22⋊D5312yes—
807C2×C4C22×C22⋊D5311yescharacteristic
808C2×C4#1313326212yes—
809C2×C4#1313326212yes—
810C2×C4C24×D5311yescharacteristic
811C8—1062no—
812C8—1062no—
813C8—1062no—
814C8—1062no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—816no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—4244no—
833C22—2122no—
834C22—2122no—
835C22—2122no—
836C22#1681119012yes—
837C22#1681142612yes—
838C22#1681143412yes—
839C22C23×C22⋊D5311yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—2122no—
847C4—2122no—
848C4—2122no—
849C4#1681119012yes—
850C4C2×#1313326211yescharacteristic
851C4C2×#1313326211yescharacteristic
852C2—42no—
853C2—82no—
854C2—82no—
855C2—82no—
856C2—4242no—
857C2#2028580914yesdirect product factor
858C2C2×#1681119011yescharacteristic
859C2C2×#1681142611yescharacteristic
860C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#535C2
socleC23×C53C22×D4
hypercenterC2×#535D53
hypocenterC53C2×#3224
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#16811244C2semidirect
2. #20285809C2direct (N × H)
3. C2×#16811010C2semidirect
4. C2×#16811005C2semidirect
5. C2×#16810982C2semidirect
6. C2×#16810969C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810820C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810815C2semidirect
11. C2×#16810785C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810774C2semidirect
14. C2×#16810757C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#535C2semidirect
17. C22×#11719925C22semidirect
20. C22×#11719923C22semidirect
21. C22×#11719924C22semidirect
24. C22×#11719922C22semidirect
26. #16811244C22semidirect
27. C2×#13133217C22semidirect
29. C2×#13133205C22semidirect
35. C2×C4×Dic106C22semidirect
36. C2×C4×D212C22semidirect
37. #16811010C22semidirect
38. #16811005C22semidirect
39. #16810982C22semidirect
40. #16810969C22semidirect
41. #16810842C22semidirect
42. #16810835C22semidirect
43. #16810820C22semidirect
44. #16810815C22semidirect
45. #16810785C22semidirect
46. #16810774C22semidirect
47. #16810768C22semidirect
48. #16810757C22semidirect
49. #16810684C22semidirect
50. C2×C4⋊#88322C22semidirect
51. C2×C4⋊#88322C22semidirect
52. C2×#13133141C22semidirect
53. C2×#13133141C22semidirect
58. C2×#13133138C22semidirect
59. C2×#13133138C22semidirect
62. C2×#13133128C22semidirect
63. C2×C4×#88322C22semidirect
67. C53×#535C22semidirect
83. C2×#11719925C23semidirect
89. C2×#11719923C23semidirect
91. C2×#11719924C23semidirect
97. C2×#11719922C23semidirect
103. #13133217C23semidirect
106. #13133205C23semidirect
115. C4×Dic106C23semidirect
117. C4×D212C23semidirect
129. C4⋊#88322C23semidirect
130. C4⋊#88322C23semidirect
131. #13133141C23semidirect
132. #13133141C23semidirect
137. #13133138C23semidirect
138. #13133138C23semidirect
141. #13133128C23semidirect
142. C4×#88322C23semidirect
423. C2×#535D53semidirect
442. C2×C53#3224semidirect
460. #535C2×D53semidirect
507. C53C2×#3224semidirect
857. C2#20285809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
#202858092
C2×#168110102
C2×#168110052
C2×#168109822
C2×#168109692
C2×#168108422
C2×#168108202
C2×#168108352
C2×#168108152
C2×#168107852
C2×#168107682
C2×#168107742
C2×#168107572
C2×#168106842
C2×C53×#5352
C2×#322453