Finite Group Databasebeta

← C2×#20287067 #28262510

Subgroups — C2×#20287067 #28262510

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic
3#20287067C2116yesmaximal, direct product factor
4C2×#16811020C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810939C211yesmaximal, characteristic, complemented
7C2×#16810952C211yesmaximal, characteristic, complemented
8C2×#16810951C211yesmaximal, characteristic, complemented
9C2×#16810906C211yesmaximal, characteristic, complemented
10C2×#16810911C211yesmaximal, characteristic, complemented
11C2×#16810849C211yesmaximal, characteristic, complemented
12C2×SD16×Dic53C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
14C22×#13133149C211yesmaximal, characteristic, complemented
15C2×#106×D53C211yesmaximal, characteristic, complemented
16C2×C53×#465C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×C8×D53C2211yescharacteristic
19#16811331—24no—
20#16811331C2218yescomplemented
21#16811273—24no—
22#16811273C2218yes—
23C2×#13133216C2211yescharacteristic
24C2×#13133216C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133199—21no—
27C2×#13133198—21no—
28C2×#13133197—21no—
29C2×#13133194—21no—
30C2×#13133194—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133188C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133177—21no—
37C22×C4⋊Dic53C2211yescharacteristic
38C22×C4⋊Dic53C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811020C2218yescomplemented
42#16810952C2218yescomplemented
43#16810951C2218yescomplemented
44#16810940C2218yescomplemented
45#16810939C2218yescomplemented
46#16810911C2218yescomplemented
47#16810906C2218yescomplemented
48#16810849C2218yescomplemented
49SD16×Dic53C2218yescomplemented
50C8×C22⋊D53C2218yescomplemented
51C2×#13133149C2211yescharacteristic
52C2×#13133149C2211yescharacteristic
53C2×#13133149C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2218yescomplemented
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60#106×D53C2218yescomplemented
61C2×#13133146C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#465C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53D411yescharacteristic
83C23×Dic53—21no—
84C23×Dic53—21no—
85C23×Dic53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C2×C8×D53—24no—
92C2×C8×D53C2314yes—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133207—28no—
98#13133199—28no—
99#13133198—28no—
100#13133197—28no—
101#13133194—28no—
102#13133194—28no—
103#13133193—22no—
104#13133193C2314yes—
105#13133188—22no—
106#13133188C2314yes—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109D4×Dic53—22no—
110D4×Dic53C2314yes—
111C4×C22⋊D53D414yes—
112C4×C22⋊D53C2314yes—
113#13133177—28no—
114C2×C4⋊Dic53—22no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53C2314yes—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2314yes—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C4⋊C4×D53—22no—
132C4⋊C4×D53—22no—
133C4⋊C4×D53C2314yes—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142#13133149C2314yes—
143#13133149C2314yes—
144#13133149C2314yes—
145#13133149C2314yes—
146#13133148C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133129C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53—21no—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C2×SD16×C53—24no—
163C2×SD16×C53C2314yes—
164C22×C8×C53—24no—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22⋊Q8×C53—22no—
169C22⋊Q8×C53C2314yes—
170#121×C53—22no—
171#121×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#103×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C24×C53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53C2412yes—
187C2×D4×C53—24no—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—44no—
192C2×D4×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C2×C22⋊D53SD1618yescomplemented
205C2×C22⋊D53C2×D414yes—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53—82no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719947—432no—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×C4×D53—82no—
226C2×C4×D53C2×D412yes—
227C2×C4×D53C2412yes—
228C2×Dic106—24no—
229C2×Dic106—24no—
230C2×Dic106—44no—
231C2×Dic106—82no—
232SD16×C53—28no—
233C2×C8×C53—22no—
234C2×C8×C53—28no—
235C2×C8×C53#4114yescomplemented
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C2412yes—
242C4⋊C4×C53C2412yes—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C22⋊Dic53—24no—
246C22⋊Dic53—24no—
247C22⋊Dic53C2×D414yes—
248#11719921—24no—
249#11719921C2×D414yes—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—24no—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274C8×D53—28no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53C2×SD1614yes—
282C23×C53C22×D412yes—
283C23×C53C22×D411yescharacteristic
284C22×D53—22no—
285C22×D53—22no—
286C22×D53C2×SD1614yes—
287C22×D53C22×D412yes—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—48no—
294D4×C53—42no—
295C2×C4×C53—22no—
296C2×C4×C53—24no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C2×#4112yes—
308C2×C4×C532−1+412yes—
309C2×C4×C53C2511yescharacteristic
310C22⋊D53—48no—
311C22⋊D53C2×SD16116yescomplemented
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—48no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—48no—
324C2×Dic53—84no—
325C2×Dic53C2×SD1614yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C4×D53—24no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—48no—
333C4×D53—84no—
334Dic106—48no—
335Dic106—84no—
336C8×C53—22no—
337C8×C53C2×#4114yescomplemented
338#88322—22no—
339#88322—22no—
340C2×#3335—531nomaximal, Sylow
341C22×C53—28no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—84no—
348C22×C53#54712yes—
349C22×C53C22×SD1614yes—
350C22×C53C22×SD1612yes—
351C22×C53#57712yes—
352C22×C53C23×D411yescharacteristic
353C2×D53—28no—
354C2×D53—22no—
355C2×D53—22no—
356C2×D53C22×SD1614yes—
357C4×C53—22no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53#54712yes—
362C4×C53C22×#4111yescharacteristic
363C4×C53C2×2−1+411yescharacteristic
364Dic53—22no—
365Dic53—22no—
366Dic53—42no—
367Dic53—42no—
368Dic53—42no—
369Dic53—42no—
370Dic53C22×SD1614yes—
371C2×#554—531no—
372C2×#547—531no—
373#3335—5316no—
374C2×#498—531no—
375C2×#481—531no—
376C2×#481—531no—
377C2×#483—531no—
378C2×#483—531no—
379C2×#475—531no—
380C2×#476—531no—
381C2×#465—531no—
382C2×#465D5311yescharacteristic, complemented
383C2×C4×SD16—531no—
384C2×C8×D4—531no—
385C22×#106—531no—
386C22×#106—531no—
387C2×C53—24no—
388C2×C53—82no—
389C2×C53#333514yescomplemented
390C2×C53C2×#54711yescharacteristic
391C2×C53C23×SD1611yescharacteristic
392C2×C53C2×#57711yescharacteristic
393D53—24no—
394C22×#41—1061no—
395C22×SD16C2×D5311yescharacteristic
396C23×C8—531no—
397C23×C8C2×D5311yescharacteristic
398#554—538no—
399#554—1064no—
400#547—538no—
401#547—1064no—
402C2×C4⋊Q8—531no—
403C2×C4⋊Q8—531no—
404C2×#125—1061no—
405C2×#123—1061no—
406C2×#123—1061no—
407C2×C22⋊Q8—531no—
408C2×C22⋊Q8—1061no—
409C2×C22⋊Q8—1061no—
410C2×C22⋊Q8—1061no—
411C2×C22⋊Q8C2×D5311yescharacteristic
412C2×#121—531no—
413C2×#121C2×D5311yescharacteristic
414C2×C4×Q8—531no—
415C2×C4×D4—531no—
416C2×C4×D4—531no—
417C2×C4×D4—1061no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
422#498—538no—
423#483—538no—
424#483—538no—
425#481—538no—
426#481—538no—
427#476—538no—
428#475—538no—
429#465—538no—
430#465C2×D5318yescomplemented
431C4×SD16—538no—
432C8×D4—538no—
433C2×#106—531no—
434C2×#106—538no—
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#106—531no—
440C2×#106—531no—
441C2×#106—531no—
442C2×#106—538no—
443C2×#106C2×D5311yescharacteristic
444C2×C4⋊C8—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#103C2×D5311yescharacteristic
448C2×#102—531no—
449C2×#102—531no—
450C2×#102C2×D5311yescharacteristic
451C2×C22⋊C8—531no—
452C2×C22⋊C8—531no—
453C2×C4×C8—531no—
454C53C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—1068no—
456C2×#41—2128no—
457C22×Q8—1061no—
458C22×Q8—1061no—
459C22×Q8C22×D5311yescharacteristic
460C22×D4—21no—
461C22×D4—531no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—531no—
465C23×C4—1061no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4—1061no—
470C23×C4C22×D5311yescharacteristic
471C2×SD16—24no—
472C2×SD16C22×D5314yes—
473C22×C8—24no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—534no—
477C22×C8—1064no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5314yes—
480C22×C8C22×D5311yescharacteristic
481C4⋊Q8—534no—
482C4⋊Q8—534no—
483C4⋊Q8—1062no—
484C4⋊Q8—1062no—
485#125—1068no—
486#123—1068no—
487#123—1068no—
488C22⋊Q8—22no—
489C22⋊Q8—534no—
490C22⋊Q8—1068no—
491C22⋊Q8—1068no—
492C22⋊Q8—1068no—
493C22⋊Q8—1062no—
494C22⋊Q8C22×D5314yes—
495#121—22no—
496#121—534no—
497#121—1062no—
498#121C22×D5314yes—
499C4×Q8—534no—
500C4×Q8—1062no—
501C4×D4—534no—
502C4×D4—534no—
503C4×D4—534no—
504C4×D4—1062no—
505C4×D4—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—534no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1062no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1062no—
527C2×C4⋊C4—1062no—
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C4⋊C4C22×D5311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—531no—
533C2×C22⋊C4—531no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—531no—
538C2×C42—1061no—
539#106—534no—
540#106—534no—
541#106—534no—
542#106—534no—
543#106—534no—
544#106—534no—
545#106—534no—
546#106—534no—
547#106C22×D5314yes—
548C4⋊C8—534no—
549#103—534no—
550#103—534no—
551#103C22×D5314yes—
552#102—534no—
553#102—534no—
554#102C22×D5314yes—
555C22⋊C8—534no—
556C22⋊C8—534no—
557C4×C8—534no—
558C24—21no—
559C24—531no—
560C24D4×D5311yescharacteristic
561#41—21232no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—1064no—
566C2×Q8—1064no—
567C2×Q8—4242no—
568C2×Q8—2124no—
569C2×Q8C23×D5312yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—538no—
576C2×D4—534no—
577C2×D4—1064no—
578C2×D4—2124no—
579C2×D4C23×D5312yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—1064no—
591C22×C4—1064no—
592C22×C4—1064no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—4242no—
602C22×C4—4242no—
603C22×C4—2124no—
604C22×C4—2124no—
605C22×C4—2124no—
606C22×C4D4×D5312yes—
607C22×C4D4×D5311yescharacteristic
608C22×C4C23×D5312yes—
609C22×C4C23×D5311yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—532no—
614C2×C8—532no—
615C2×C8—1062no—
616C2×C8—1062no—
617C2×C8—1068no—
618C2×C8#1171994714yescomplemented
619C2×C8C23×D5312yes—
620C2×C8C23×D5312yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—534no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—532no—
628C4⋊C4—532no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1061no—
636C4⋊C4—1061no—
637C4⋊C4—1061no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1061no—
641C4⋊C4C23×D5312yes—
642C4⋊C4C23×D5312yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—534no—
646C22⋊C4—534no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C42—532no—
651C42—532no—
652C42—1064no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—534no—
660C23—532no—
661C23—1062no—
662C23—1062no—
663C23SD16×D5314yes—
664C23C2×D4×D5312yes—
665C23C2×D4×D5311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—4244no—
670Q8—2128no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—5316no—
676D4—2128no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—534no—
688C2×C4—532no—
689C2×C4—532no—
690C2×C4—532no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1064no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—4244no—
701C2×C4—4244no—
702C2×C4—2128no—
703C2×C4—2128no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2128no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4C2×#1171994712yes—
712C2×C4#1313326412yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—1062no—
716C8—1062no—
717C8C2×#1171994714yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—534no—
726C22—1068no—
727C22—1062no—
728C22—1062no—
729C22#1681127312yes—
730C22C2×SD16×D5314yes—
731C22C2×SD16×D5312yes—
732C22#1681143012yes—
733C22C22×D4×D5311yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—534no—
739C4—1062no—
740C4—1062no—
741C4—2122no—
742C4—2122no—
743C4—2122no—
744C4—2122no—
745C4#1681127312yes—
746C4C22×#1171994711yescharacteristic
747C4C2×#1313326411yescharacteristic
748C2—24no—
749C2—82no—
750C2—1064no—
751C2#2028706714yesdirect product factor
752C2C2×#1681127311yescharacteristic
753C2C22×SD16×D5311yescharacteristic
754C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#465C2
socleC23×C53C22×D4
prime radicalC2×#16811273C2
hypercenterC2×#465D53
hypocenterC53C2×#3335
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16811331C2semidirect
3. #20287067C2direct (N × H)
4. C2×#16811020C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810939C2semidirect
7. C2×#16810952C2semidirect
8. C2×#16810951C2semidirect
9. C2×#16810906C2semidirect
10. C2×#16810911C2semidirect
11. C2×#16810849C2semidirect
12. C2×SD16×Dic53C2semidirect
13. C2×C8×C22⋊D53C2semidirect
14. C22×#13133149C2semidirect
15. C2×#106×D53C2semidirect
16. C2×C53×#465C2semidirect
20. #16811331C22semidirect
41. #16811020C22semidirect
42. #16810952C22semidirect
43. #16810951C22semidirect
44. #16810940C22semidirect
45. #16810939C22semidirect
46. #16810911C22semidirect
47. #16810906C22semidirect
48. #16810849C22semidirect
49. SD16×Dic53C22semidirect
50. C8×C22⋊D53C22semidirect
55. C2×#13133149C22semidirect
60. #106×D53C22semidirect
73. C53×#465C22semidirect
204. C2×C22⋊D53SD16semidirect
235. C2×C8×C53#41semidirect
311. C22⋊D53C2×SD16semidirect
337. C8×C53C2×#41semidirect
382. C2×#465D53semidirect
389. C2×C53#3335semidirect
430. #465C2×D53semidirect
454. C53C2×#3335semidirect
618. C2×C8#11719947semidirect
717. C8C2×#11719947semidirect
751. C2#20287067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168112732
#202870672
C2×#168110202
C2×#168109402
C2×#168109392
C2×#168109522
C2×#168109512
C2×#168109062
C2×#168109112
C2×#168108492
C2×SD16×Dic532
C2×C8×C22⋊D532
C22×#131331492
C2×#106×D532
C2×C53×#4652
C2×#333553