Finite Group Databasebeta

← C2×#20285675 #28255259

Subgroups — C2×#20285675 #28255259

Order 13568.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811152C211yesmaximal, characteristic, complemented
2C2×#124×D53C211yesmaximal, characteristic, complemented
3#20285675C2116yesmaximal, direct product factor
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810978C211yesmaximal, characteristic, complemented
6C2×#16810977C211yesmaximal, characteristic, complemented
7C2×#16810847C211yesmaximal, characteristic, complemented
8C2×#16810843C211yesmaximal, characteristic, complemented
9C2×#16810840C211yesmaximal, characteristic, complemented
10C2×#16810836C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810760C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic
15C2×#16810674C211yesmaximal, characteristic, complemented
16C2×C53×#495C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719923C2211yescharacteristic, complemented
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23#16811152—24no—
24#16811152C2218yescomplemented
25C2×#13133210—21no—
26C2×#13133209C2211yescharacteristic, complemented
27C2×#13133206C2211yescharacteristic
28C2×#13133205C2211yescharacteristic
29C2×#13133204C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133203—21no—
32#124×D53—24no—
33#124×D53C2218yescomplemented
34C2×#13133199—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic, complemented
38C2×D4×Dic53C2211yescharacteristic, complemented
39C2×#13133177—21no—
40C2×#13133173—21no—
41C2×C22⋊C4×D53—21no—
42C2×C22⋊C4×D53—21no—
43C2×C42×D53C2211yescharacteristic
44#16811005C2218yescomplemented
45#16810978C2218yescomplemented
46#16810977C2218yescomplemented
47#16810847C2218yescomplemented
48#16810843C2218yescomplemented
49#16810840C2218yescomplemented
50#16810836C2218yescomplemented
51#16810777C2218yescomplemented
52#16810772C2218yescomplemented
53#16810760C2218yescomplemented
54#16810755C2218yes—
55#16810674C2218yescomplemented
56C2×#13133146C2211yescharacteristic, complemented
57C2×#13133146C2211yescharacteristic, complemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133141C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic, complemented
69C22×Q16×C53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic, complemented
72C22×D8×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic, complemented
75C53×#495C2218yescomplemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—22no—
81C2×Q8×D53—42no—
82C2×Q8×D53—42no—
83C2×Q8×D53C2314yes—
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C2×D4×D53—22no—
88C2×D4×D53—42no—
89C2×D4×D53—42no—
90C2×D4×D53C2314yes—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53D411yescharacteristic
94C22×C4×D53D411yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×#11719925—42no—
97C2×#11719925C2314yescomplemented
98C2×#11719923—42no—
99C2×#11719923C2314yescomplemented
100C2×#11719924—42no—
101C2×#11719924C2314yes—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106#13133210—28no—
107#13133209—22no—
108#13133209C2314yescomplemented
109#13133206—22no—
110#13133206C2314yes—
111#13133205—22no—
112#13133205C2314yes—
113#13133204—22no—
114#13133204C2314yes—
115#13133203—28no—
116#13133203—28no—
117#13133199—28no—
118#13133193—22no—
119#13133193C2314yes—
120#13133188—22no—
121#13133188C2314yes—
122Q8×Dic53—22no—
123Q8×Dic53C2314yescomplemented
124D4×Dic53—22no—
125D4×Dic53C2314yescomplemented
126#13133177—28no—
127#13133173—28no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C22⋊C4×D53—28no—
144C22⋊C4×D53—28no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53D411yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149C42×D53D414yes—
150C42×D53C2314yes—
151#13133146C2314yescomplemented
152#13133146C2314yescomplemented
153#13133142C2314yescomplemented
154#13133142C2314yescomplemented
155#13133141C2314yescomplemented
156#13133141C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yes—
159#13133138C2314yes—
160#13133138C2314yes—
161#13133129C2314yes—
162#13133129C2314yes—
163C4×#88322C2314yescomplemented
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C2×Q16×C53—42no—
169C2×Q16×C53C2314yescomplemented
170C2×SD16×C53—42no—
171C2×SD16×C53—42no—
172C2×SD16×C53C2314yes—
173C2×SD16×C53C2314yescomplemented
174C2×D8×C53—42no—
175C2×D8×C53C2314yes—
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178#124×C53—22no—
179#124×C53—22no—
180#124×C53C2314yes—
181#124×C53C2314yescomplemented
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C42×C53C2311yescharacteristic
187C4×C8×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53—21no—
190C23×D53—21no—
191C23×D53—24no—
192C23×D53—44no—
193C23×D53—44no—
194C23×D53—44no—
195C23×D53C2×D411yescharacteristic
196C2×Q8×C53—21no—
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C2×D4×C53—21no—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53C2412yes—
211C2×D4×C53C2412yes—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—24no—
225C22×Dic53—44no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229Q8×D53—44no—
230Q8×D53—44no—
231Q8×D53—48no—
232D4×D53—44no—
233D4×D53—44no—
234D4×D53—48no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—21no—
238C2×D212C2412yes—
239C2×C4×D53—24no—
240C2×C4×D53—22no—
241C2×C4×D53—22no—
242C2×C4×D53—24no—
243C2×C4×D53—42no—
244C2×C4×D53—44no—
245C2×C4×D53C2×D412yes—
246C2×C4×D53C2×D414yes—
247C2×C4×D53C2×D414yes—
248C2×C4×D53C2412yes—
249C2×Dic106—22no—
250C2×Dic106—22no—
251C2×Dic106—21no—
252C2×Dic106—24no—
253C2×Dic106—44no—
254C2×Dic106C2412yes—
255Q16×C53—44no—
256SD16×C53—44no—
257SD16×C53—44no—
258D8×C53—44no—
259C2×C8×C53—22no—
260C2×C8×C53—22no—
261C2×C8×C53C2412yes—
262C2×C8×C53C2412yes—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—24no—
265C22⋊C4×C53—24no—
266C22⋊C4×C53—24no—
267C42×C53C2×D412yes—
268C42×C53C2412yes—
269C22⋊Dic53—24no—
270C22⋊Dic53—24no—
271C22⋊Dic53—24no—
272C22⋊Dic53—24no—
273#11719925—44no—
274#11719924—44no—
275#11719923—44no—
276#11719922—44no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921—24no—
281#11719921—24no—
282C4⋊Dic53—21no—
283C4⋊Dic53—21no—
284C4⋊Dic53—24no—
285C4⋊Dic53C2412yes—
286C4⋊Dic53C2412yes—
287#11719919—24no—
288#11719919—24no—
289#11719919—24no—
290C4×Dic53—24no—
291C4×Dic53C2×D412yes—
292C4×Dic53C2×D414yes—
293C4×Dic53C2×D414yes—
294C4×Dic53C2412yes—
295C2×#88322—22no—
296C2×#88322—22no—
297C2×#88322C2412yes—
298C2×#88322C2412yes—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53C22×D411yescharacteristic
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—48no—
312C22×D53—48no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—48no—
317C22×D53—816no—
318C22×D53#13514yes—
319C22×D53C22×D412yes—
320Q8×C53—22no—
321Q8×C53—22no—
322Q8×C53—22no—
323Q8×C53—22no—
324Q8×C53—42no—
325Q8×C53—42no—
326D4×C53—22no—
327D4×C53—22no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—42no—
331D4×C53—42no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—42no—
337C2×C4×C53—42no—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53H(5,𝔽2)12yes—
343C2×C4×C53C2511yescharacteristic
344C22⋊D53—48no—
345C22⋊D53—48no—
346C2×Dic53—22no—
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—
358C2×Dic53C22×D412yes—
359D212—22no—
360D212—22no—
361D212—42no—
362C4×D53—28no—
363C4×D53—24no—
364C4×D53—22no—
365C4×D53—22no—
366C4×D53—44no—
367C4×D53—48no—
368Dic106—22no—
369Dic106—22no—
370Dic106—48no—
371Dic106—42no—
372C8×C53—22no—
373C8×C53—22no—
374#88322—22no—
375#88322—22no—
376C2×#3211—531nomaximal, Sylow
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53—42no—
383C22×C53—84no—
384C22×C53—84no—
385C22×C53#53512yes—
386C22×C53C2×#13512yes—
387C22×C53#57512yes—
388C22×C53C23×D411yescharacteristic
389C2×D53—22no—
390C2×D53—28no—
391C2×D53—22no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—816no—
396C2×D53—84no—
397C2×D53C2×#13514yes—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53#53512yes—
403C4×C53C2×H(5,𝔽2)11yescharacteristic
404C4×C53C2×H(5,𝔽2)11yescharacteristic
405Dic53—22no—
406Dic53—22no—
407Dic53—22no—
408Dic53—42no—
409Dic53—42no—
410Dic53—42no—
411C2×#529—531no—
412C22×#124—531no—
413#3211—5316no—
414C2×#495—531no—
415C2×#495D5311yescharacteristic, complemented
416C2×#488—531no—
417C2×#488—531no—
418C2×#464—531no—
419C2×#464—531no—
420C2×#463—531no—
421C2×#463—531no—
422C2×#451—531no—
423C2×#448—531no—
424C2×#450—531no—
425C2×#447—531no—
426C2×#431—531no—
427C2×C53—82no—
428C2×C53—82no—
429C2×C53#321114yescomplemented
430C2×C53C2×#53511yescharacteristic
431C2×C53C22×#13511yescharacteristic
432C2×C53C2×#57511yescharacteristic
433D53—24no—
434D53—82no—
435C23×Q8—531no—
436C23×D4—531no—
437C22×Q16—531no—
438C22×Q16C2×D5311yescharacteristic, complemented
439C22×SD16—531no—
440C22×SD16—531no—
441C22×SD16C2×D5311yescharacteristic
442C22×SD16C2×D5311yescharacteristic, complemented
443C22×D8—531no—
444C22×D8C2×D5311yescharacteristic
445#529—538no—
446#529—1064no—
447C2×#126—1061no—
448C2×#125—531no—
449C2×#124—531no—
450C2×#124—531no—
451C2×#124—538no—
452C2×#124—531no—
453C2×#124—1061no—
454C2×#124—1061no—
455C2×#124—1064no—
456C2×#124C2×D5311yescharacteristic
457C2×#124C2×D5311yescharacteristic, complemented
458C2×#123—1061no—
459C2×C22⋊Q8—531no—
460C2×#121—531no—
461C2×C4×Q8—531no—
462C2×C4×D4—531no—
463C2×C4×D4—1061no—
464C2×#117—1061no—
465C22×C22⋊C4—1061no—
466C22×C22⋊C4—1061no—
467C22×C42—531no—
468#495—538no—
469#495C2×D5318yescomplemented
470#488—538no—
471#488—538no—
472#464—538no—
473#464—538no—
474#463—538no—
475#463—538no—
476#451—538no—
477#450—538no—
478#448—538no—
479#447—538no—
480#431—538no—
481C2×C4⋊C8—531no—
482C2×C4⋊C8—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#103—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×C22⋊C8—531no—
492C2×C22⋊C8—531no—
493C2×C4×C8—531no—
494C2×C4×C8C2×D5311yescharacteristic, complemented
495C53C2×#321111yescharacteristic, complemented, Sylow
496C25—1061no—
497C22×Q8—534no—
498C22×Q8—531no—
499C22×Q8—1061no—
500C22×Q8—1062no—
501C22×Q8—2122no—
502C22×Q8—2122no—
503C22×Q8C22×D5311yescharacteristic
504C22×Q8C22×D5311yescharacteristic
505C22×D4—534no—
506C22×D4—531no—
507C22×D4—1062no—
508C22×D4—1061no—
509C22×D4—1061no—
510C22×D4—2122no—
511C22×D4—2122no—
512C22×D4C22×D5311yescharacteristic
513C22×D4C22×D5311yescharacteristic
514C23×C4—531no—
515C23×C4—531no—
516C23×C4—531no—
517C23×C4—1061no—
518C23×C4—1061no—
519C2×Q16—42no—
520C2×Q16—534no—
521C2×Q16—2122no—
522C2×Q16C22×D5314yescomplemented
523C2×SD16—42no—
524C2×SD16—42no—
525C2×SD16—534no—
526C2×SD16—534no—
527C2×SD16—2122no—
528C2×SD16—2122no—
529C2×SD16C22×D5314yes—
530C2×SD16C22×D5314yescomplemented
531C2×D8—42no—
532C2×D8—534no—
533C2×D8—2122no—
534C2×D8C22×D5314yes—
535C22×C8—531no—
536C22×C8—531no—
537C22×C8C22×D5311yescharacteristic
538C22×C8C22×D5311yescharacteristic
539#126—1068no—
540#125—534no—
541#125—1062no—
542#124—22no—
543#124—22no—
544#124—534no—
545#124—534no—
546#124—534no—
547#124—1068no—
548#124—1068no—
549#124—1062no—
550#124—1062no—
551#124—1062no—
552#124C22×D5314yes—
553#124C22×D5314yescomplemented
554#123—1068no—
555C22⋊Q8—534no—
556C22⋊Q8—1062no—
557#121—534no—
558#121—1062no—
559C4×Q8—534no—
560C4×Q8—1062no—
561C4×D4—534no—
562C4×D4—1062no—
563C4×D4—1068no—
564#117—1068no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4—1061no—
569C2×C4⋊C4—1061no—
570C2×C4⋊C4—1061no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—1068no—
576C2×C22⋊C4—1068no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4—1061no—
580C2×C22⋊C4—1061no—
581C2×C22⋊C4—1061no—
582C2×C22⋊C4—1061no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C42—531no—
587C2×C42—531no—
588C2×C42—531no—
589C2×C42—534no—
590C2×C42—534no—
591C2×C42—1061no—
592C2×C42C22×D5311yescharacteristic
593C4⋊C8—534no—
594C4⋊C8—534no—
595#103—534no—
596#103—534no—
597#103—534no—
598#103—534no—
599#102—534no—
600#102—534no—
601#102—534no—
602#102—534no—
603C22⋊C8—534no—
604C22⋊C8—534no—
605C4×C8—534no—
606C4×C8C22×D5314yescomplemented
607C24—21no—
608C24—21no—
609C24—531no—
610C24—1064no—
611C24—1061no—
612C24—2124no—
613C24—2124no—
614C24—2124no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—532no—
622C2×Q8—1064no—
623C2×Q8—1061no—
624C2×Q8—1062no—
625C2×Q8—1062no—
626C2×Q8—2124no—
627C2×Q8—2124no—
628C2×Q8—2124no—
629C2×Q8—2128no—
630C2×Q8C23×D5312yes—
631C2×Q8C23×D5312yes—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—532no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1061no—
642C2×D4—1062no—
643C2×D4—1062no—
644C2×D4—2124no—
645C2×D4—2124no—
646C2×D4—2128no—
647C2×D4—2124no—
648C2×D4—2124no—
649C2×D4C23×D5312yes—
650C2×D4C23×D5312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—531no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—534no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—534no—
660C22×C4—1064no—
661C22×C4—1064no—
662C22×C4—1064no—
663C22×C4—1062no—
664C22×C4—1062no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—2122no—
669C22×C4—2124no—
670C22×C4—2124no—
671C22×C4D4×D5311yescharacteristic
672C22×C4D4×D5311yescharacteristic
673C22×C4C23×D5311yescharacteristic
674Q16—44no—
675Q16—2124no—
676SD16—44no—
677SD16—44no—
678SD16—2124no—
679SD16—2124no—
680D8—44no—
681D8—2124no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—532no—
685C2×C8—532no—
686C2×C8—1062no—
687C2×C8—1062no—
688C2×C8C23×D5312yes—
689C2×C8C23×D5312yes—
690C4⋊C4—532no—
691C4⋊C4—532no—
692C4⋊C4—1064no—
693C4⋊C4—1064no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1064no—
697C4⋊C4—1064no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—1064no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4—1064no—
710C22⋊C4—1064no—
711C42—534no—
712C42—532no—
713C42—534no—
714C42—532no—
715C42—1064no—
716C42D4×D5312yes—
717C42C23×D5312yes—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—534no—
727C23—532no—
728C23—1062no—
729C23—1062no—
730C23—1062no—
731C23—42416no—
732C23—2128no—
733C23—2128no—
734C23—2128no—
735C23—2122no—
736C23—2122no—
737C23—2122no—
738C23C2×D4×D5311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—1062no—
746Q8—1062no—
747Q8—2128no—
748Q8—2122no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—42no—
754D4—42no—
755D4—1062no—
756D4—1062no—
757D4—2128no—
758D4—2128no—
759D4—2122no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—532no—
767C2×C4—532no—
768C2×C4—532no—
769C2×C4—1068no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1064no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—1062no—
779C2×C4—2124no—
780C2×C4—2128no—
781C2×C4—2128no—
782C2×C4—2122no—
783C2×C4—2122no—
784C2×C4—2122no—
785C2×C4C2×D4×D5312yes—
786C2×C4C2×D4×D5312yes—
787C2×C4C2×D4×D5311yescharacteristic
788C2×C4#1313326212yes—
789C2×C4#1313326212yes—
790C2×C4C24×D5311yescharacteristic
791C8—22no—
792C8—22no—
793C8—1062no—
794C8—1062no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—84no—
803C22—534no—
804C22—1062no—
805C22—1062no—
806C22—1068no—
807C22—42416no—
808C22—4244no—
809C22—2122no—
810C22—2122no—
811C22—2122no—
812C22#1681118612yes—
813C22#135×D5312yes—
814C22#1681142012yes—
815C22C22×D4×D5311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—1062no—
821C4—1062no—
822C4—1062no—
823C4—2122no—
824C4—2122no—
825C4—2122no—
826C4#1681118612yes—
827C4C2×#1313326211yescharacteristic
828C4C2×#1313326211yescharacteristic
829C2—82no—
830C2—82no—
831C2—1064no—
832C2—4242no—
833C2#2028567514yesdirect product factor
834C2C2×#1681118611yescharacteristic
835C2C2×#135×D5311yescharacteristic
836C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#495C2
socleC23×C53C22×D4
prime radicalC2×#16810755C2
hypercenterC2×#495D53
hypocenterC53C2×#3211
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#16811152C2semidirect
2. C2×#124×D53C2semidirect
3. #20285675C2direct (N × H)
4. C2×#16811005C2semidirect
5. C2×#16810978C2semidirect
6. C2×#16810977C2semidirect
7. C2×#16810847C2semidirect
8. C2×#16810843C2semidirect
9. C2×#16810840C2semidirect
10. C2×#16810836C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810760C2semidirect
13. C2×#16810772C2semidirect
15. C2×#16810674C2semidirect
16. C2×C53×#495C2semidirect
19. C22×#11719925C22semidirect
20. C22×#11719923C22semidirect
24. #16811152C22semidirect
26. C2×#13133209C22semidirect
33. #124×D53C22semidirect
37. C2×Q8×Dic53C22semidirect
38. C2×D4×Dic53C22semidirect
44. #16811005C22semidirect
45. #16810978C22semidirect
46. #16810977C22semidirect
47. #16810847C22semidirect
48. #16810843C22semidirect
49. #16810840C22semidirect
50. #16810836C22semidirect
51. #16810777C22semidirect
52. #16810772C22semidirect
53. #16810760C22semidirect
55. #16810674C22semidirect
56. C2×#13133146C22semidirect
57. C2×#13133146C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133141C22semidirect
61. C2×#13133141C22semidirect
68. C2×C4×#88322C22semidirect
69. C22×Q16×C53C22semidirect
71. C22×SD16×C53C22semidirect
74. C2×#124×C53C22semidirect
75. C53×#495C22semidirect
76. C2×C4×C8×C53C22semidirect
97. C2×#11719925C23semidirect
99. C2×#11719923C23semidirect
108. #13133209C23semidirect
123. Q8×Dic53C23semidirect
125. D4×Dic53C23semidirect
151. #13133146C23semidirect
152. #13133146C23semidirect
153. #13133142C23semidirect
154. #13133142C23semidirect
155. #13133141C23semidirect
156. #13133141C23semidirect
163. C4×#88322C23semidirect
169. C2×Q16×C53C23semidirect
173. C2×SD16×C53C23semidirect
181. #124×C53C23semidirect
187. C4×C8×C53C23semidirect
415. C2×#495D53semidirect
429. C2×C53#3211semidirect
438. C22×Q16C2×D53semidirect
442. C22×SD16C2×D53semidirect
457. C2×#124C2×D53semidirect
469. #495C2×D53semidirect
494. C2×C4×C8C2×D53semidirect
495. C53C2×#3211semidirect
522. C2×Q16C22×D53semidirect
530. C2×SD16C22×D53semidirect
553. #124C22×D53semidirect
606. C4×C8C22×D53semidirect
833. C2#20285675direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111522
C2×#124×D532
#202856752
C2×#168110052
C2×#168109782
C2×#168109772
C2×#168108472
C2×#168108432
C2×#168108402
C2×#168108362
C2×#168107772
C2×#168107602
C2×#168107722
C2×#168107552
C2×#168106742
C2×C53×#4952
C2×#321153