Finite Group Databasebeta

← C2×#20286222 #28259070

Subgroups — C2×#20286222 #28259070

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C23×#11719913C211yesmaximal, characteristic, complemented
3C2×#16811286C211yesmaximal, characteristic, complemented
4C2×#16811264C211yesmaximal, characteristic
5#20286222C2116yesmaximal, direct product factor
6C2×#16811016C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810848C211yesmaximal, characteristic, complemented
9C2×#16810827C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810778C211yesmaximal, characteristic, complemented
12C2×#16810763C211yesmaximal, characteristic, complemented
13C2×#16810773C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×#16810694C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic, complemented
20C23×D212C2211yescharacteristic
21C2×#13133249—28no—
22C2×#13133249C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719925C2211yescharacteristic, complemented
25C22×#11719913—28no—
26C22×#11719913C2211yescharacteristic
27C22×#11719913C2211yescharacteristic
28C22×#11719913C2211yescharacteristic
29C22×#11719913C2211yescharacteristic
30C22×#11719913C2218yescomplemented
31C22×#11719924C2211yescharacteristic
32C22×#11719924C2211yescharacteristic
33C22×#11719912C2211yescharacteristic, complemented
34#16811286—24no—
35#16811286C2218yescomplemented
36#16811264—24no—
37#16811264C2218yes—
38C2×#13133216—21no—
39C2×#13133215C2211yescharacteristic, complemented
40C2×#13133206C2211yescharacteristic
41C2×#13133202—21no—
42C2×#13133197C2211yescharacteristic, complemented
43C2×#13133195—21no—
44C2×#13133194—21no—
45C2×#13133192—21no—
46C2×#13133192C2211yescharacteristic
47C2×#13133187—21no—
48C2×#13133182C2211yescharacteristic, complemented
49C2×#13133179C2211yescharacteristic
50C2×C4×C22⋊D53C2211yescharacteristic
51C2×#13133177—21no—
52C2×C22⋊C4×D53—21no—
53#16811016C2218yescomplemented
54#16810870C2218yescomplemented
55#16810848C2218yescomplemented
56#16810827C2218yescomplemented
57#16810788C2218yescomplemented
58#16810778C2218yescomplemented
59#16810773C2218yescomplemented
60#16810763C2218yescomplemented
61#16810722C2218yescomplemented
62#16810694C2218yescomplemented
63C2×#13133146C2211yescharacteristic, complemented
64C2×#13133140C2211yescharacteristic, complemented
65C2×#13133140C2211yescharacteristic, complemented
66C2×#13133137C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68C2×C22⋊#88322C2211yescharacteristic
69C2×#13133129C2211yescharacteristic, complemented
70C2×#13133127C2211yescharacteristic, complemented
71C22×Q16×C53C2211yescharacteristic, complemented
72C23×C8×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C53×#467C2218yescomplemented
76C2×#107×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#103×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—42no—
83C2×#11719949C2314yes—
84C22×Dic106—24no—
85C22×Dic106—22no—
86C22×Dic106—21no—
87C22×Dic106—21no—
88C22×Dic106—42no—
89C22×Dic106C2311yescharacteristic
90C22×Dic106C2314yes—
91C22×Dic106C2311yescharacteristic
92C2×Q8×D53—22no—
93C2×Q8×D53—24no—
94C2×Q8×D53—42no—
95C2×Q8×D53C2314yescomplemented
96C22×D212—24no—
97C22×D212—21no—
98C22×D212—22no—
99C22×D212—21no—
100C22×D212—21no—
101C22×D212—42no—
102C22×D212C2311yescharacteristic
103C22×D212C2314yes—
104C22×D212C2311yescharacteristic
105C22×C22⋊D53D411yescharacteristic
106C23×Dic53—21no—
107C22×C4×D53—21no—
108C22×C4×D53—21no—
109C22×C4×D53—21no—
110C22×C4×D53C2311yescharacteristic
111#13133249—232no—
112C2×#11719925—24no—
113C2×#11719925—42no—
114C2×#11719925C2314yescomplemented
115C2×#11719925C2314yescomplemented
116C2×#11719913—24no—
117C2×#11719913—232no—
118C2×#11719913—24no—
119C2×#11719913—24no—
120C2×#11719913D418yescomplemented
121C2×#11719913C2314yes—
122C2×#11719913C2314yes—
123C2×#11719913C2314yes—
124C2×#11719913C2314yes—
125C2×#11719924—24no—
126C2×#11719924—42no—
127C2×#11719924C2314yes—
128C2×#11719924C2314yes—
129C2×#11719912—24no—
130C2×#11719912C2314yescomplemented
131C22×#88322C2311yescharacteristic
132C22×#88322C2311yescharacteristic
133#13133216—28no—
134#13133215—22no—
135#13133215C2314yescomplemented
136#13133206—22no—
137#13133206C2314yes—
138#13133202—28no—
139#13133197—22no—
140#13133197C2314yescomplemented
141#13133195—28no—
142#13133194—28no—
143#13133192—28no—
144#13133192—22no—
145#13133192C2314yes—
146#13133187—28no—
147#13133182—22no—
148#13133182C2314yescomplemented
149#13133179—22no—
150#13133179C2314yes—
151C4×C22⋊D53D414yes—
152C4×C22⋊D53C2314yes—
153#13133177—28no—
154C2×C4⋊Dic53—21no—
155C2×#11719919—21no—
156C2×#11719919—21no—
157C2×#11719919—21no—
158C2×#11719919D411yescharacteristic
159C2×C22⋊Dic53D411yescharacteristic
160C2×#11719921—21no—
161C2×#11719921—21no—
162C2×#11719921—21no—
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921D411yescharacteristic
166C22⋊C4×D53—28no—
167C2×C4×Dic53—21no—
168C2×C4×Dic53C2311yescharacteristic
169#13133146C2314yescomplemented
170#13133140C2314yescomplemented
171#13133140C2314yescomplemented
172#13133137C2314yes—
173#13133137C2314yes—
174C22⋊#88322C2314yes—
175#13133129C2314yescomplemented
176#13133127C2314yescomplemented
177C22×Q8×C53C2311yescharacteristic
178C22×Q8×C53C2311yescharacteristic
179C23×C4×C53C2311yescharacteristic
180C2×Q16×C53—24no—
181C2×Q16×C53C2314yescomplemented
182C22×C8×C53—24no—
183C22×C8×C53C2311yescharacteristic
184C22×C8×C53C2314yes—
185C22×C8×C53C2311yescharacteristic
186C22⋊Q8×C53—22no—
187C22⋊Q8×C53—22no—
188C22⋊Q8×C53C2314yes—
189C22⋊Q8×C53C2314yes—
190C2×C4⋊C4×C53—21no—
191C2×C4⋊C4×C53—21no—
192C2×C4⋊C4×C53C2311yescharacteristic
193C2×C4⋊C4×C53C2311yescharacteristic
194C2×C22⋊C4×C53—21no—
195C2×C22⋊C4×C53—21no—
196#107×C53C2314yescomplemented
197#103×C53C2314yescomplemented
198#103×C53C2314yescomplemented
199C24×C53C2×D411yescharacteristic
200C23×D53—21no—
201C23×D53—21no—
202C23×D53—24no—
203C23×D53—44no—
204C23×D53—44no—
205C23×D53—82no—
206C23×D53C2×D411yescharacteristic
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53—22no—
210C2×Q8×C53—22no—
211C2×Q8×C53—22no—
212C2×Q8×C53—22no—
213C2×Q8×C53C2412yes—
214C2×Q8×C53C2412yes—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D412yes—
223C22×C4×C53C2412yes—
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53C2×D414yes—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—24no—
230C22×Dic53—44no—
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719949—28no—
235#11719949—44no—
236#11719949—48no—
237Q8×D53—28no—
238Q8×D53—44no—
239Q8×D53—48no—
240C2×D212—21no—
241C2×D212—22no—
242C2×D212—22no—
243C2×D212—22no—
244C2×D212—28no—
245C2×D212—24no—
246C2×D212—24no—
247C2×D212—21no—
248C2×D212—24no—
249C2×D212—44no—
250C2×D212—48no—
251C2×D212—44no—
252C2×D212—44no—
253C2×D212—82no—
254C2×D212C2×D414yes—
255C2×D212C2412yes—
256C2×D212C2412yes—
257C2×C4×D53—22no—
258C2×C4×D53—22no—
259C2×C4×D53—24no—
260C2×C4×D53—24no—
261C2×C4×D53—24no—
262C2×C4×D53—44no—
263C2×C4×D53—44no—
264C2×C4×D53—82no—
265C2×C4×D53C2×D412yes—
266C2×C4×D53C2412yes—
267C2×Dic106—21no—
268C2×Dic106—22no—
269C2×Dic106—22no—
270C2×Dic106—22no—
271C2×Dic106—28no—
272C2×Dic106—24no—
273C2×Dic106—21no—
274C2×Dic106—24no—
275C2×Dic106—44no—
276C2×Dic106—48no—
277C2×Dic106—44no—
278C2×Dic106—44no—
279C2×Dic106C2×D414yes—
280C2×Dic106C2412yes—
281C2×Dic106C2412yes—
282Q16×C53—28no—
283C2×C8×C53—22no—
284C2×C8×C53—28no—
285C2×C8×C53C2×D414yes—
286C2×C8×C53C2412yes—
287C2×C8×C53C2412yes—
288C4⋊C4×C53—24no—
289C4⋊C4×C53—24no—
290C4⋊C4×C53—21no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53C2412yes—
293C4⋊C4×C53C2412yes—
294C22⋊C4×C53—24no—
295C22⋊C4×C53—24no—
296C22⋊Dic53C2×D414yes—
297#11719925—28no—
298#11719925—44no—
299#11719924—28no—
300#11719924—44no—
301#11719921—24no—
302#11719921—24no—
303#11719921—24no—
304#11719921—24no—
305#11719921—24no—
306#11719921C2×D414yes—
307C4⋊Dic53—24no—
308#11719919—24no—
309#11719919—24no—
310#11719919—24no—
311#11719919C2×D414yes—
312C4×Dic53—24no—
313C4×Dic53C2×D412yes—
314C4×Dic53C2412yes—
315C2×#88322—22no—
316C2×#88322—22no—
317C2×#88322C2412yes—
318C2×#88322C2412yes—
319#11719913—28no—
320#11719913—28no—
321#11719913—28no—
322#11719913C2×D4116yescomplemented
323#11719912—28no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53#13714yescomplemented
327C23×C53C22×D412yes—
328C23×C53C22×D411yescharacteristic
329C22×D53—22no—
330C22×D53—24no—
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—48no—
336C22×D53—42no—
337C22×D53—42no—
338C22×D53—42no—
339C22×D53—42no—
340C22×D53—48no—
341C22×D53—42no—
342C22×D53—84no—
343C22×D53—816no—
344C22×D53C22×D412yes—
345Q8×C53—22no—
346Q8×C53—22no—
347Q8×C53—22no—
348Q8×C53—22no—
349Q8×C53—42no—
350Q8×C53—42no—
351C2×C4×C53—22no—
352C2×C4×C53—24no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—42no—
360C2×C4×C53—42no—
361C2×C4×C53—42no—
362C2×C4×C53—42no—
363C2×C4×C53C22×D412yes—
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C22×D412yes—
366C2×C4×C53H(5,𝔽2)12yes—
367C2×C4×C53C2511yescharacteristic
368C22⋊D53—28no—
369C2×Dic53—24no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—48no—
376C2×Dic53—42no—
377C2×Dic53C22×D412yes—
378C2×Dic53C22×D412yes—
379C2×Dic53C22×D412yes—
380D212—24no—
381D212—22no—
382D212—22no—
383D212—22no—
384D212—48no—
385D212—48no—
386D212—42no—
387D212—84no—
388D212C22×D414yes—
389C4×D53—24no—
390C4×D53—22no—
391C4×D53—22no—
392C4×D53—48no—
393C4×D53—48no—
394C4×D53—84no—
395Dic106—24no—
396Dic106—22no—
397Dic106—22no—
398Dic106—22no—
399Dic106—48no—
400Dic106—48no—
401Dic106—42no—
402Dic106C22×D414yes—
403C8×C53—22no—
404C8×C53C22×D414yes—
405#88322—22no—
406#88322—22no—
407C2×#3266—531nomaximal, Sylow
408C22×C53—22no—
409C22×C53—28no—
410C22×C53—22no—
411C22×C53D4212yes—
412C22×C53C2×#13712yes—
413C22×C53C2×#13714yescomplemented
414C22×C53#57712yes—
415C22×C53C23×D411yescharacteristic
416C2×D53—22no—
417C2×D53—24no—
418C2×D53—22no—
419C2×D53—22no—
420C2×D53—44no—
421C2×D53—48no—
422C2×D53—42no—
423C2×D53—42no—
424C2×D53—42no—
425C2×D53—42no—
426C2×D53—42no—
427C2×D53—816no—
428C2×D53—84no—
429C4×C53—22no—
430C4×C53—42no—
431C4×C53—42no—
432C4×C53—42no—
433C4×C53—42no—
434C4×C53D4212yes—
435C4×C53C23×D411yescharacteristic
436C4×C53C2×H(5,𝔽2)11yescharacteristic
437Dic53—24no—
438Dic53—22no—
439Dic53—22no—
440Dic53—22no—
441Dic53—42no—
442C22×#137—531no—
443C23×SD16—531no—
444C2×D4×Q8—531no—
445C2×#546—531no—
446#3266—5316no—
447C2×#497—531no—
448C2×#468—531no—
449C2×#467D5311yescharacteristic, complemented
450C2×#464—531no—
451C2×#461—531no—
452C2×#452—531no—
453C2×#451—531no—
454C2×#448—531no—
455C2×#450—531no—
456C2×#440—531no—
457C2×#435—531no—
458C2×C53—24no—
459C2×C53#326614yescomplemented
460C2×C53C2×D4211yescharacteristic
461C2×C53C22×#13711yescharacteristic
462C2×C53C2×#57711yescharacteristic
463D53—42no—
464D53—44no—
465D53—82no—
466C22×#41—531no—
467C23×Q8—531no—
468C23×Q8—531no—
469C23×D4—531no—
470C2×#137—538no—
471C2×#137—1068no—
472C22×Q16—531no—
473C22×Q16—531no—
474C22×Q16C2×D5311yescharacteristic, complemented
475C22×SD16—531no—
476C22×SD16—531no—
477C22×SD16—531no—
478C22×SD16—531no—
479C22×SD16—531no—
480C22×SD16—531no—
481C22×SD16—538no—
482C22×SD16—1068no—
483C22×M16—531no—
484C23×C8C2×D5311yescharacteristic
485D4×Q8—538no—
486D4×Q8—1064no—
487#546—538no—
488#546—1064no—
489C2×C4⋊Q8—531no—
490C2×C4⋊Q8—1061no—
491C2×#124—531no—
492C2×#123—1061no—
493C2×C22⋊Q8—531no—
494C2×C22⋊Q8—1061no—
495C2×C22⋊Q8—1061no—
496C2×C22⋊Q8C2×D5311yescharacteristic
497C2×C22⋊Q8C2×D5311yescharacteristic
498C2×#121—531no—
499C2×#121—1061no—
500C2×#120—1061no—
501C2×C4×Q8—531no—
502C2×C4×D4—531no—
503C2×C4×D4—531no—
504C2×C4×D4—1061no—
505C22×C22⋊C4—1061no—
506#497—538no—
507#468—538no—
508#467C2×D5318yescomplemented
509#464—538no—
510#461—538no—
511#452—538no—
512#451—538no—
513#450—538no—
514#448—538no—
515#440—538no—
516#435—538no—
517C2×#107C2×D5311yescharacteristic, complemented
518C2×C4⋊C8—531no—
519C2×#103—531no—
520C2×#103—531no—
521C2×#103C2×D5311yescharacteristic, complemented
522C2×#103C2×D5311yescharacteristic, complemented
523C2×#102—531no—
524C2×#102—531no—
525C2×C22⋊C8—531no—
526C2×C22⋊C8—531no—
527C2×#97—531no—
528C53C2×#326611yescharacteristic, complemented, Sylow
529C25—1061no—
530C2×#41—534no—
531C2×#41—1062no—
532C2×#41—1064no—
533C2×#41—2122no—
534C22×Q8—534no—
535C22×Q8—531no—
536C22×Q8—531no—
537C22×Q8—534no—
538C22×Q8—1061no—
539C22×Q8—1064no—
540C22×Q8—1062no—
541C22×Q8—1061no—
542C22×Q8—1062no—
543C22×Q8—1064no—
544C22×Q8—2122no—
545C22×Q8—2122no—
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5311yescharacteristic
548C22×D4—531no—
549C22×D4—531no—
550C22×D4—531no—
551C22×D4—534no—
552C22×D4—1064no—
553C22×D4—1061no—
554C22×D4—1061no—
555C22×D4—1061no—
556C22×D4—1062no—
557C22×D4—2122no—
558C23×C4—531no—
559C23×C4—1061no—
560C23×C4—1061no—
561C23×C4—1061no—
562C23×C4—1061no—
563C23×C4C22×D5311yescharacteristic
564#137—10632no—
565C2×Q16—24no—
566C2×Q16—534no—
567C2×Q16—534no—
568C2×Q16—1064no—
569C2×Q16—2122no—
570C2×Q16C22×D5314yescomplemented
571C2×SD16—534no—
572C2×SD16—534no—
573C2×SD16—538no—
574C2×SD16—534no—
575C2×SD16—534no—
576C2×SD16—534no—
577C2×SD16—534no—
578C2×SD16—10632no—
579C2×SD16—1064no—
580C2×SD16—1064no—
581C2×SD16—1064no—
582C2×SD16—1064no—
583C2×SD16—2122no—
584C2×M16—534no—
585C2×M16—1064no—
586C22×C8—24no—
587C22×C8—531no—
588C22×C8—531no—
589C22×C8C22×D5311yescharacteristic
590C22×C8C22×D5314yes—
591C22×C8C22×D5311yescharacteristic
592C4⋊Q8—534no—
593C4⋊Q8—1062no—
594C4⋊Q8—1068no—
595#124—534no—
596#124—1062no—
597#123—1068no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—534no—
601C22⋊Q8—1068no—
602C22⋊Q8—1068no—
603C22⋊Q8—1062no—
604C22⋊Q8C22×D5314yes—
605C22⋊Q8C22×D5314yes—
606#121—534no—
607#121—1068no—
608#121—1062no—
609#120—1068no—
610C4×Q8—534no—
611C4×Q8—1062no—
612C4×D4—534no—
613C4×D4—534no—
614C4×D4—534no—
615C4×D4—1062no—
616C4×D4—1068no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—531no—
620C2×C4⋊C4—1061no—
621C2×C4⋊C4—1061no—
622C2×C4⋊C4—1061no—
623C2×C4⋊C4—1061no—
624C2×C4⋊C4C22×D5311yescharacteristic
625C2×C4⋊C4C22×D5311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—531no—
629C2×C22⋊C4—531no—
630C2×C22⋊C4—1068no—
631C2×C22⋊C4—1061no—
632C2×C22⋊C4—1061no—
633C2×C22⋊C4—1061no—
634C2×C22⋊C4—1061no—
635C2×C22⋊C4—1061no—
636C2×C42—531no—
637C2×C42—1061no—
638#107C22×D5314yescomplemented
639C4⋊C8—534no—
640#103—534no—
641#103—534no—
642#103C22×D5314yescomplemented
643#103C22×D5314yescomplemented
644#102—534no—
645#102—534no—
646C22⋊C8—534no—
647C22⋊C8—534no—
648#97—534no—
649C24—531no—
650C24—1061no—
651C24—1064no—
652C24—1061no—
653C24—4242no—
654C24—2124no—
655C24—2124no—
656C24D4×D5311yescharacteristic
657#41—1068no—
658#41—2124no—
659#41—2128no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—534no—
667C2×Q8—532no—
668C2×Q8—532no—
669C2×Q8—1064no—
670C2×Q8—1068no—
671C2×Q8—1061no—
672C2×Q8—1064no—
673C2×Q8—1061no—
674C2×Q8—1062no—
675C2×Q8—1068no—
676C2×Q8—1062no—
677C2×Q8—1062no—
678C2×Q8—2124no—
679C2×Q8—2124no—
680C2×Q8—2128no—
681C2×Q8—2124no—
682C2×Q8—2124no—
683C2×Q8—2128no—
684C2×Q8C23×D5312yes—
685C2×Q8C23×D5312yes—
686C2×D4—534no—
687C2×D4—534no—
688C2×D4—532no—
689C2×D4—532no—
690C2×D4—1068no—
691C2×D4—1064no—
692C2×D4—1064no—
693C2×D4—1064no—
694C2×D4—1061no—
695C2×D4—1062no—
696C2×D4—1064no—
697C2×D4—1061no—
698C2×D4—1062no—
699C2×D4—1062no—
700C2×D4—4242no—
701C2×D4—2124no—
702C2×D4—2128no—
703C2×D4—2124no—
704C2×D4—2124no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—531no—
712C22×C4—531no—
713C22×C4—531no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—1064no—
717C22×C4—1064no—
718C22×C4—1064no—
719C22×C4—1061no—
720C22×C4—1062no—
721C22×C4—1062no—
722C22×C4—1064no—
723C22×C4—1061no—
724C22×C4—4242no—
725C22×C4—2124no—
726C22×C4—2124no—
727C22×C4—2124no—
728C22×C4D4×D5312yes—
729C22×C4D4×D5311yescharacteristic
730C22×C4C23×D5312yes—
731C22×C4C23×D5311yescharacteristic
732Q16—28no—
733Q16—1068no—
734Q16—2124no—
735SD16—5316no—
736SD16—1068no—
737SD16—1068no—
738SD16—1068no—
739SD16—1068no—
740SD16—2124no—
741M16—1068no—
742C2×C8—22no—
743C2×C8—28no—
744C2×C8—532no—
745C2×C8—532no—
746C2×C8—1062no—
747C2×C8—1062no—
748C2×C8D4×D5314yes—
749C2×C8C23×D5312yes—
750C2×C8C23×D5312yes—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—534no—
756C4⋊C4—1064no—
757C4⋊C4—1064no—
758C4⋊C4—1064no—
759C4⋊C4—1064no—
760C4⋊C4C23×D5312yes—
761C4⋊C4C23×D5312yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—534no—
765C22⋊C4—534no—
766C22⋊C4—1064no—
767C22⋊C4—1064no—
768C22⋊C4—1064no—
769C22⋊C4—1064no—
770C22⋊C4—1064no—
771C42—532no—
772C42—532no—
773C42—1064no—
774C23—22no—
775C23—22no—
776C23—532no—
777C23—1062no—
778C23—1062no—
779C23—1062no—
780C23—1062no—
781C23—1064no—
782C23—1062no—
783C23—42416no—
784C23—4244no—
785C23—2128no—
786C23—2122no—
787C23—2128no—
788C23—2122no—
789C23—2122no—
790C23—2122no—
791C23—2122no—
792C23#1313324914yescomplemented
793C23C2×D4×D5312yes—
794C23C2×D4×D5311yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—42no—
800Q8—42no—
801Q8—534no—
802Q8—1062no—
803Q8—1064no—
804Q8—1062no—
805Q8—1062no—
806Q8—2128no—
807Q8—2128no—
808Q8—2122no—
809D4—534no—
810D4—1068no—
811D4—1062no—
812D4—1062no—
813D4—1062no—
814D4—1064no—
815D4—4244no—
816D4—2128no—
817D4—2128no—
818D4—2122no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—532no—
832C2×C4—532no—
833C2×C4—532no—
834C2×C4—1062no—
835C2×C4—1062no—
836C2×C4—1062no—
837C2×C4—1062no—
838C2×C4—1064no—
839C2×C4—1062no—
840C2×C4—1062no—
841C2×C4—1064no—
842C2×C4—1062no—
843C2×C4—4244no—
844C2×C4—2128no—
845C2×C4—2128no—
846C2×C4—2128no—
847C2×C4—2122no—
848C2×C4C2×D4×D5312yes—
849C2×C4C2×D4×D5312yes—
850C2×C4C2×D4×D5311yescharacteristic
851C2×C4#1313326312yes—
852C2×C4C24×D5311yescharacteristic
853C8—22no—
854C8—1062no—
855C8—1062no—
856C8C2×D4×D5314yes—
857C22—28no—
858C22—22no—
859C22—22no—
860C22—1062no—
861C22—1064no—
862C22—1062no—
863C22—1062no—
864C22—42416no—
865C22—4244no—
866C22—2122no—
867C22—2122no—
868C22—2122no—
869C22—2124no—
870C22—2128no—
871C22—2122no—
872C22—2122no—
873C22#1681125712yes—
874C22C2×#1313324912yes—
875C22C2×#1313324914yescomplemented
876C22#1681143012yes—
877C22C22×D4×D5311yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—1062no—
884C4—1064no—
885C4—1062no—
886C4—1062no—
887C4—2122no—
888C4#1681125712yes—
889C4C22×D4×D5311yescharacteristic
890C4C2×#1313326311yescharacteristic
891C2—24no—
892C2—4242no—
893C2—2122no—
894C2—2124no—
895C2#2028622214yesdirect product factor
896C2C2×#1681125711yescharacteristic
897C2C22×#1313324911yescharacteristic
898C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC2×#16811264C2
hypercenterC2×#467D53
hypocenterC53C2×#3266
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C23×#11719913C2semidirect
3. C2×#16811286C2semidirect
5. #20286222C2direct (N × H)
6. C2×#16811016C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810848C2semidirect
9. C2×#16810827C2semidirect
10. C2×#16810788C2semidirect
11. C2×#16810778C2semidirect
12. C2×#16810763C2semidirect
13. C2×#16810773C2semidirect
14. C2×#16810722C2semidirect
15. C2×#16810694C2semidirect
16. C2×C53×#467C2semidirect
19. C22×Q8×D53C22semidirect
22. C2×#13133249C22semidirect
23. C22×#11719925C22semidirect
24. C22×#11719925C22semidirect
30. C22×#11719913C22semidirect
33. C22×#11719912C22semidirect
35. #16811286C22semidirect
39. C2×#13133215C22semidirect
42. C2×#13133197C22semidirect
48. C2×#13133182C22semidirect
53. #16811016C22semidirect
54. #16810870C22semidirect
55. #16810848C22semidirect
56. #16810827C22semidirect
57. #16810788C22semidirect
58. #16810778C22semidirect
59. #16810773C22semidirect
60. #16810763C22semidirect
61. #16810722C22semidirect
62. #16810694C22semidirect
63. C2×#13133146C22semidirect
64. C2×#13133140C22semidirect
65. C2×#13133140C22semidirect
69. C2×#13133129C22semidirect
70. C2×#13133127C22semidirect
71. C22×Q16×C53C22semidirect
75. C53×#467C22semidirect
76. C2×#107×C53C22semidirect
77. C2×#103×C53C22semidirect
78. C2×#103×C53C22semidirect
95. C2×Q8×D53C23semidirect
114. C2×#11719925C23semidirect
115. C2×#11719925C23semidirect
120. C2×#11719913D4semidirect
130. C2×#11719912C23semidirect
135. #13133215C23semidirect
140. #13133197C23semidirect
148. #13133182C23semidirect
169. #13133146C23semidirect
170. #13133140C23semidirect
171. #13133140C23semidirect
175. #13133129C23semidirect
176. #13133127C23semidirect
181. C2×Q16×C53C23semidirect
196. #107×C53C23semidirect
197. #103×C53C23semidirect
198. #103×C53C23semidirect
322. #11719913C2×D4semidirect
326. C23×C53#137semidirect
413. C22×C53C2×#137semidirect
449. C2×#467D53semidirect
459. C2×C53#3266semidirect
474. C22×Q16C2×D53semidirect
508. #467C2×D53semidirect
517. C2×#107C2×D53semidirect
521. C2×#103C2×D53semidirect
522. C2×#103C2×D53semidirect
528. C53C2×#3266semidirect
570. C2×Q16C22×D53semidirect
638. #107C22×D53semidirect
642. #103C22×D53semidirect
643. #103C22×D53semidirect
792. C23#13133249semidirect
875. C22C2×#13133249semidirect
895. C2#20286222direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C23×#117199132
C2×#168112862
C2×#168112642
#202862222
C2×#168110162
C2×#168108702
C2×#168108482
C2×#168108272
C2×#168107882
C2×#168107782
C2×#168107632
C2×#168107732
C2×#168107222
C2×#168106942
C2×C53×#4672
C2×#326653