Finite Group Databasebeta

← C2×#20286916 #28260889

Subgroups — C2×#20286916 #28260889

Order 13568.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic, complemented
2#20286916C2116yesmaximal, direct product factor
3C2×#16810977C211yesmaximal, characteristic, complemented
4C2×#16810961C211yesmaximal, characteristic, complemented
5C2×#16810934C211yesmaximal, characteristic, complemented
6C2×#16810923C211yesmaximal, characteristic, complemented
7C2×#16810874C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810757C211yesmaximal, characteristic, complemented
12C2×C4×#11719922C211yesmaximal, characteristic, complemented
13C2×#16810701C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C2×#16810628C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic, complemented
18C22×#11719922C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21C22×#11719917C2211yescharacteristic, complemented
22#16811319—24no—
23#16811319C2218yescomplemented
24C2×#13133212—21no—
25C2×#13133209C2211yescharacteristic, complemented
26C2×#13133199—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic, complemented
29C2×#13133189—21no—
30C2×C4×D212C2211yescharacteristic, complemented
31C2×#13133177—21no—
32C2×#13133176C2211yescharacteristic
33C22×C4⋊Dic53C2211yescharacteristic, complemented
34#16810977C2218yescomplemented
35#16810961C2218yescomplemented
36#16810934C2218yescomplemented
37#16810923C2218yescomplemented
38#16810874C2218yescomplemented
39#16810871C2218yescomplemented
40#16810835C2218yescomplemented
41#16810768C2218yescomplemented
42#16810757C2218yescomplemented
43C4×#11719922C2218yescomplemented
44#16810701C2218yescomplemented
45C2×#13133150C2211yescharacteristic, complemented
46C2×#13133150C2211yescharacteristic, complemented
47C2×#13133148C2211yescharacteristic, complemented
48C2×C4⋊#88322C2211yescharacteristic, complemented
49#16810628C2218yescomplemented
50#16810624C2218yescomplemented
51C2×#13133141C2211yescharacteristic, complemented
52C2×#13133141C2211yescharacteristic, complemented
53C2×#13133141C2211yescharacteristic, complemented
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic, complemented
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic, complemented
63C2×C4×#88322C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C23×D4×C53C2211yescharacteristic
66C53×#546—24no—
67C53×#546C2218yescomplemented
68C2×#124×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×#121×C53—21no—
72C2×#121×C53C2211yescharacteristic
73C2×#120×C53—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C22⋊C4×C53—21no—
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C2×#11719924—42no—
83C2×#11719924C2314yescomplemented
84C2×#11719922—24no—
85C2×#11719922—42no—
86C2×#11719922C2314yes—
87C2×#11719922C2314yes—
88C2×#11719917—42no—
89C2×#11719917—42no—
90C2×#11719917C2314yes—
91C2×#11719917C2314yescomplemented
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133212—28no—
97#13133209—22no—
98#13133209C2314yescomplemented
99#13133199—28no—
100#13133191—22no—
101#13133191—22no—
102#13133191C2314yes—
103#13133191C2314yescomplemented
104#13133189—28no—
105C4×D212—22no—
106C4×D212C2314yescomplemented
107#13133177—28no—
108#13133176—22no—
109#13133176C2314yes—
110C2×C4⋊Dic53—22no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2311yescharacteristic
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2314yescomplemented
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×C22⋊Dic53—21no—
119C2×#11719921—21no—
120C2×#11719921—21no—
121C2×#11719921—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yescomplemented
124#13133150C2314yescomplemented
125#13133148C2314yescomplemented
126C4⋊#88322C2314yescomplemented
127#13133141C2314yescomplemented
128#13133141C2314yescomplemented
129#13133141C2314yescomplemented
130#13133138C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133137C2314yescomplemented
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yescomplemented
139C4×#88322C2314yescomplemented
140C25×C53—21no—
141C2×#41×C53—22no—
142C2×#41×C53—24no—
143C2×#41×C53—42no—
144C2×#41×C53C2314yes—
145C22×Q8×C53C2311yescharacteristic
146C22×D4×C53—24no—
147C22×D4×C53—21no—
148C22×D4×C53—21no—
149C22×D4×C53—21no—
150C22×D4×C53—22no—
151C22×D4×C53—42no—
152C22×D4×C53D411yescharacteristic
153C22×D4×C53C2311yescharacteristic
154C22×D4×C53C2314yes—
155C22×D4×C53C2311yescharacteristic
156C23×C4×C53—21no—
157C23×C4×C53—21no—
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160#124×C53—22no—
161#124×C53C2314yes—
162#123×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53C2314yes—
165#121×C53—28no—
166#121×C53—22no—
167#121×C53C2314yes—
168#120×C53—28no—
169C4×D4×C53—22no—
170C4×D4×C53D414yes—
171C4×D4×C53C2314yes—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—28no—
177C2×C22⋊C4×C53—21no—
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×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—24no—
188C24×C53—44no—
189C24×C53—44no—
190C24×C53—82no—
191C24×C53C2×D411yescharacteristic
192C24×C53C2×D411yescharacteristic
193C23×D53—21no—
194#41×C53—28no—
195#41×C53—44no—
196#41×C53—48no—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×D4×C53—28no—
202C2×D4×C53—24no—
203C2×D4×C53—24no—
204C2×D4×C53—21no—
205C2×D4×C53—24no—
206C2×D4×C53—21no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—44no—
211C2×D4×C53—48no—
212C2×D4×C53—42no—
213C2×D4×C53—44no—
214C2×D4×C53—44no—
215C2×D4×C53—82no—
216C2×D4×C53C2×D414yes—
217C2×D4×C53#4114yes—
218C2×D4×C53C2412yes—
219C2×D4×C53C2412yes—
220C22×C4×C53—22no—
221C22×C4×C53—22no—
222C22×C4×C53—22no—
223C22×C4×C53—22no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—24no—
227C22×C4×C53—24no—
228C22×C4×C53—44no—
229C22×C4×C53—82no—
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53C2412yes—
237C22×C4×C53C2412yes—
238C22×C4×C53C2411yescharacteristic
239C2×C22⋊D53—24no—
240C2×C22⋊D53—24no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53—82no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—24no—
247C22×Dic53—82no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—21no—
251C2×D212C2412yes—
252C2×C4×D53—24no—
253C2×C4×D53—82no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2×D414yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C22⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C22⋊C4×C53C2×D414yes—
264C22⋊C4×C53C2×D414yes—
265C42×C53C2×D412yes—
266C42×C53C2412yes—
267C22⋊Dic53—24no—
268#11719924—44no—
269#11719922—28no—
270#11719922—44no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53—24no—
277C4⋊Dic53—21no—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281#11719919—24no—
282#11719919—24no—
283C4×Dic53—24no—
284#11719917—44no—
285#11719917—44no—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322C2412yes—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—24no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—48no—
304C23×C53—48no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—84no—
311C23×C53—816no—
312C23×C53C22×D412yes—
313C23×C53C22×D412yes—
314C23×C53C22×D411yescharacteristic
315C22×D53—22no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53—42no—
319Q8×C53—22no—
320Q8×C53—22no—
321Q8×C53—42no—
322D4×C53—24no—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—44no—
327D4×C53—48no—
328D4×C53—48no—
329D4×C53—42no—
330D4×C53—84no—
331D4×C53C2×#4114yes—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—24no—
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—22no—
344C2×C4×C53—48no—
345C2×C4×C53—42no—
346C2×C4×C53—42no—
347C2×C4×C53—84no—
348C2×C4×C53C22×D412yes—
349C2×C4×C53C22×D412yes—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53C2×#4112yes—
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53C2511yescharacteristic
356C22⋊D53—48no—
357C22⋊D53—84no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—42no—
362C2×Dic53—42no—
363C2×Dic53—42no—
364C2×Dic53—84no—
365D212—22no—
366D212—22no—
367D212—42no—
368C4×D53—84no—
369#88322—22no—
370#88322—22no—
371#88322—22no—
372#88322—22no—
373C2×#3322—531nomaximal, Sylow
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—24no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—44no—
382C22×C53—44no—
383C22×C53—48no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—816no—
390C22×C53—84no—
391C22×C53#54612yes—
392C22×C53#57512yes—
393C22×C53#57612yes—
394C22×C53C23×D411yescharacteristic
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—84no—
399C4×C53—22no—
400C4×C53—22no—
401C4×C53—22no—
402C4×C53—22no—
403C4×C53—42no—
404C4×C53—42no—
405C4×C53#54612yes—
406C4×C53C22×#4111yescharacteristic
407C4×C53C2×H(5,𝔽2)11yescharacteristic
408Dic53—42no—
409Dic53—42no—
410Dic53—42no—
411C2×#553—531no—
412C2×#546D5311yescharacteristic, complemented
413#3322—5316no—
414C2×#488—531no—
415C2×#485—531no—
416C2×#480—531no—
417C2×#478—531no—
418C2×#469—531no—
419C2×#468—531no—
420C2×#463—531no—
421C2×#449—531no—
422C2×#447—531no—
423C2×C4×D8—531no—
424C2×#436—531no—
425C2×#417—531no—
426C2×#418—531no—
427C2×C53—42no—
428C2×C53—42no—
429C2×C53—44no—
430C2×C53—82no—
431C2×C53#332214yescomplemented
432C2×C53C2×#54611yescharacteristic
433C2×C53C2×#57511yescharacteristic
434C2×C53C2×#57611yescharacteristic
435D53—82no—
436C22×#41C2×D5311yescharacteristic
437C23×D4C2×D5311yescharacteristic
438C22×SD16—531no—
439C22×D8—531no—
440C22×D8—531no—
441C22×M16—531no—
442C22×M16—531no—
443#553—538no—
444#553—1064no—
445#546—24no—
446#546C2×D5318yescomplemented
447C2×#126—1061no—
448C2×#125—531no—
449C2×#124C2×D5311yescharacteristic
450C2×#123—21no—
451C2×#123—1061no—
452C2×C22⋊Q8C2×D5311yescharacteristic
453C2×#121—21no—
454C2×#121—531no—
455C2×#121—531no—
456C2×#121—1061no—
457C2×#121C2×D5311yescharacteristic
458C2×#120—21no—
459C2×C4×D4—531no—
460C2×C4×D4—1061no—
461C2×C4×D4C2×D5311yescharacteristic
462C2×C4×D4C2×D5311yescharacteristic
463C2×#117—531no—
464C22×C4⋊C4—531no—
465C22×C22⋊C4—21no—
466#488—538no—
467#485—538no—
468#480—538no—
469#478—538no—
470#469—538no—
471#468—538no—
472#463—538no—
473#449—538no—
474#447—538no—
475C4×D8—538no—
476#436—538no—
477C2×#107—531no—
478C2×#107—531no—
479C2×#106—531no—
480C2×C4⋊C8—531no—
481#418—538no—
482#417—538no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×C22⋊C8—531no—
494C2×C22⋊C8—531no—
495C2×C4×C8—531no—
496C53C2×#332211yescharacteristic, complemented, Sylow
497C25—21no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D5314yes—
502C22×Q8C22×D5311yescharacteristic
503C22×D4—24no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—42no—
509C22×D4—531no—
510C22×D4—1061no—
511C22×D4—1061no—
512C22×D4C22⋊D5311yescharacteristic
513C22×D4C22×D5311yescharacteristic
514C22×D4C22×D5314yes—
515C22×D4C22×D5311yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4C22×D5311yescharacteristic
521C23×C4C22×D5311yescharacteristic
522C2×SD16—534no—
523C2×SD16—2122no—
524C2×D8—534no—
525C2×D8—534no—
526C2×D8—1064no—
527C2×D8—2122no—
528C2×M16—534no—
529C2×M16—534no—
530C2×M16—2122no—
531C2×M16—2122no—
532C22×C8—531no—
533C22×C8—531no—
534C22×C8—531no—
535C22×C8—531no—
536#126—1068no—
537#125—534no—
538#125—1062no—
539#124—22no—
540#124C22×D5314yes—
541#123—28no—
542#123—1068no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D5314yes—
545#121—22no—
546#121—28no—
547#121—534no—
548#121—534no—
549#121—1068no—
550#121—1062no—
551#121—1062no—
552#121C22×D5314yes—
553#120—28no—
554C4×D4—22no—
555C4×D4—534no—
556C4×D4—1068no—
557C4×D4—1062no—
558C4×D4C22⋊D5314yes—
559C4×D4C22×D5314yes—
560C4×D4C22×D5314yes—
561#117—534no—
562#117—1062no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—534no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1062no—
570C2×C4⋊C4—1061no—
571C2×C4⋊C4—1061no—
572C2×C4⋊C4C22⋊D5311yescharacteristic
573C2×C4⋊C4C22×D5311yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—28no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4—1061no—
582C2×C22⋊C4—1061no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4C22⋊D5311yescharacteristic
585C2×C22⋊C4C22⋊D5311yescharacteristic
586C2×C42—1061no—
587C2×C42C22×D5311yescharacteristic
588#107—534no—
589#107—534no—
590#106—534no—
591C4⋊C8—534no—
592#103—534no—
593#103—534no—
594#103—534no—
595#102—534no—
596#102—534no—
597#102—534no—
598#102—534no—
599#102—534no—
600#102—534no—
601#102—534no—
602C22⋊C8—534no—
603C22⋊C8—534no—
604C4×C8—534no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—44no—
609C24—44no—
610C24—82no—
611C24—1061no—
612C24C2×C22⋊D5311yescharacteristic
613C24C2×C22⋊D5311yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D5312yes—
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—44no—
631C2×D4—48no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—82no—
636C2×D4—532no—
637C2×D4—1064no—
638C2×D4—1064no—
639C2×D4—1061no—
640C2×D4—1062no—
641C2×D4—1062no—
642C2×D4—4242no—
643C2×D4—2124no—
644C2×D4#1171994714yes—
645C2×D4C2×C22⋊D5314yes—
646C2×D4C23×D5312yes—
647C2×D4C23×D5312yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—1064no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1064no—
663C22×C4—4242no—
664C22×C4—4242no—
665C22×C4C2×C22⋊D5312yes—
666C22×C4C2×C22⋊D5312yes—
667C22×C4C2×C22⋊D5311yescharacteristic
668C22×C4C2×C22⋊D5311yescharacteristic
669C22×C4C2×C22⋊D5311yescharacteristic
670C22×C4C2×C22⋊D5311yescharacteristic
671C22×C4C23×D5312yes—
672C22×C4C23×D5312yes—
673C22×C4C23×D5311yescharacteristic
674SD16—2124no—
675D8—1068no—
676D8—2124no—
677M16—2124no—
678M16—2124no—
679C2×C8—532no—
680C2×C8—532no—
681C2×C8—532no—
682C2×C8—532no—
683C2×C8—1062no—
684C2×C8—1062no—
685C2×C8—1062no—
686C2×C8—1062no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—532no—
690C4⋊C4—532no—
691C4⋊C4—532no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1064no—
695C4⋊C4—1061no—
696C4⋊C4—1064no—
697C4⋊C4—1064no—
698C4⋊C4C2×C22⋊D5314yes—
699C4⋊C4C23×D5312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4C2×C22⋊D5314yes—
710C22⋊C4C2×C22⋊D5314yes—
711C42—1064no—
712C42C2×C22⋊D5312yes—
713C42C23×D5312yes—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—48no—
724C23—48no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—84no—
731C23—816no—
732C23—1062no—
733C23—2122no—
734C23—2122no—
735C23—2122no—
736C23C22×C22⋊D5312yes—
737C23C22×C22⋊D5312yes—
738C23C22×C22⋊D5311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—24no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—48no—
748D4—48no—
749D4—42no—
750D4—84no—
751D4—1062no—
752D4—1062no—
753D4—4244no—
754D4—2128no—
755D4—2122no—
756D4C2×#1171994714yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—84no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—4244no—
777C2×C4—4244no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4C22×C22⋊D5312yes—
782C2×C4C22×C22⋊D5312yes—
783C2×C4C22×C22⋊D5312yes—
784C2×C4C22×C22⋊D5312yes—
785C2×C4C22×C22⋊D5311yescharacteristic
786C2×C4C2×#1171994712yes—
787C2×C4#1313326212yes—
788C2×C4C24×D5311yescharacteristic
789C8—1062no—
790C8—1062no—
791C8—1062no—
792C8—1062no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—48no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—816no—
809C22—84no—
810C22—4244no—
811C22—2122no—
812C22—2122no—
813C22—2122no—
814C22#1681126712yes—
815C22#1681142112yes—
816C22#1681142612yes—
817C22C23×C22⋊D5311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—2122no—
825C4—2122no—
826C4—2122no—
827C4#1681126712yes—
828C4C22×#1171994711yescharacteristic
829C4C2×#1313326211yescharacteristic
830C2—42no—
831C2—42no—
832C2—44no—
833C2—82no—
834C2—4242no—
835C2#2028691614yesdirect product factor
836C2C2×#1681126711yescharacteristic
837C2C2×#1681142111yescharacteristic
838C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3322
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16811319C2semidirect
2. #20286916C2direct (N × H)
3. C2×#16810977C2semidirect
4. C2×#16810961C2semidirect
5. C2×#16810934C2semidirect
6. C2×#16810923C2semidirect
7. C2×#16810874C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810757C2semidirect
12. C2×C4×#11719922C2semidirect
13. C2×#16810701C2semidirect
14. C2×#16810624C2semidirect
15. C2×#16810628C2semidirect
16. C2×C53×#546C2semidirect
17. C22×#11719924C22semidirect
21. C22×#11719917C22semidirect
23. #16811319C22semidirect
25. C2×#13133209C22semidirect
28. C2×#13133191C22semidirect
30. C2×C4×D212C22semidirect
33. C22×C4⋊Dic53C22semidirect
34. #16810977C22semidirect
35. #16810961C22semidirect
36. #16810934C22semidirect
37. #16810923C22semidirect
38. #16810874C22semidirect
39. #16810871C22semidirect
40. #16810835C22semidirect
41. #16810768C22semidirect
42. #16810757C22semidirect
43. C4×#11719922C22semidirect
44. #16810701C22semidirect
45. C2×#13133150C22semidirect
46. C2×#13133150C22semidirect
47. C2×#13133148C22semidirect
48. C2×C4⋊#88322C22semidirect
49. #16810628C22semidirect
50. #16810624C22semidirect
51. C2×#13133141C22semidirect
52. C2×#13133141C22semidirect
53. C2×#13133141C22semidirect
60. C2×#13133137C22semidirect
62. C2×C22⋊#88322C22semidirect
63. C2×C4×#88322C22semidirect
67. C53×#546C22semidirect
83. C2×#11719924C23semidirect
91. C2×#11719917C23semidirect
98. #13133209C23semidirect
103. #13133191C23semidirect
106. C4×D212C23semidirect
115. C2×C4⋊Dic53C23semidirect
123. #13133150C23semidirect
124. #13133150C23semidirect
125. #13133148C23semidirect
126. C4⋊#88322C23semidirect
127. #13133141C23semidirect
128. #13133141C23semidirect
129. #13133141C23semidirect
136. #13133137C23semidirect
138. C22⋊#88322C23semidirect
139. C4×#88322C23semidirect
412. C2×#546D53semidirect
431. C2×C53#3322semidirect
446. #546C2×D53semidirect
496. C53C2×#3322semidirect
835. C2#20286916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
#202869162
C2×#168109772
C2×#168109612
C2×#168109342
C2×#168109232
C2×#168108742
C2×#168108712
C2×#168108352
C2×#168107682
C2×#168107572
C2×C4×#117199222
C2×#168107012
C2×#168106242
C2×#168106282
C2×C53×#5462
C2×#332253