Finite Group Databasebeta

← C2×#20287305 #28262803

Subgroups — C2×#20287305 #28262803

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811337C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic, complemented
3#20287305C2116yesmaximal, direct product factor
4C2×#16811020C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810939C211yesmaximal, characteristic, complemented
7C2×#16810945C211yesmaximal, characteristic, complemented
8C2×#16810944C211yesmaximal, characteristic, complemented
9C2×#16810911C211yesmaximal, characteristic, complemented
10C2×#16810901C211yesmaximal, characteristic, complemented
11C2×#16810873C211yesmaximal, characteristic, complemented
12C2×D8×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810699C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C2×#16810662C211yesmaximal, characteristic, complemented
16C2×C53×#469C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719912C2211yescharacteristic
19#16811337—24no—
20#16811337C2218yescomplemented
21#16811273—24no—
22#16811273C2218yescomplemented
23C2×#13133216C2211yescharacteristic
24C2×#13133216C2211yescharacteristic
25C2×#13133204—21no—
26C2×#13133203—21no—
27C2×#13133199—21no—
28C2×#13133198—21no—
29C2×#13133194—21no—
30C2×#13133189—21no—
31C2×#13133188C2211yescharacteristic
32C2×#13133188C2211yescharacteristic
33C2×D4×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133176C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133173—21no—
39C22×C4⋊Dic53C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41#16811020C2218yescomplemented
42#16810945C2218yescomplemented
43#16810944C2218yescomplemented
44#16810940C2218yescomplemented
45#16810939C2218yescomplemented
46#16810911C2218yescomplemented
47#16810901C2218yescomplemented
48#16810873C2218yescomplemented
49D8×Dic53C2218yescomplemented
50#16810699C2218yescomplemented
51#16810665C2218yescomplemented
52#16810662C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#469C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53D411yescharacteristic
84C23×Dic53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719912—24no—
90C2×#11719912C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133204—28no—
98#13133203—28no—
99#13133199—28no—
100#13133198—28no—
101#13133194—28no—
102#13133189—28no—
103#13133188—22no—
104#13133188—22no—
105#13133188C2314yes—
106#13133188C2314yes—
107D4×Dic53—22no—
108D4×Dic53—22no—
109D4×Dic53C2314yes—
110D4×Dic53C2314yes—
111C4×C22⋊D53D414yes—
112C4×C22⋊D53C2314yes—
113#13133176—22no—
114#13133176C2314yes—
115#13133175—22no—
116#13133175C2314yes—
117#13133173—28no—
118C2×C4⋊Dic53—22no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2314yes—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919D411yescharacteristic
129C4⋊C4×D53—22no—
130C4⋊C4×D53C2314yes—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53D411yescharacteristic
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142#13133151C2314yes—
143#13133151C2314yes—
144#13133150C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155C22⋊#88322C2314yes—
156#13133129C2314yes—
157C8×Dic53C2314yes—
158C22×D4×C53—21no—
159C22×D4×C53—21no—
160C22×D4×C53C2311yescharacteristic
161C22×D4×C53C2311yescharacteristic
162C23×C4×C53C2311yescharacteristic
163C2×D8×C53—24no—
164C2×D8×C53C2314yes—
165C2×M16×C53—24no—
166C2×M16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169#121×C53—22no—
170#121×C53—22no—
171#121×C53C2314yes—
172#121×C53C2314yes—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177#106×C53C2314yes—
178#102×C53C2314yes—
179#102×C53C2314yes—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53C2×D411yescharacteristic
183C23×D53C2×D411yescharacteristic
184C2×D4×C53—24no—
185C2×D4×C53—24no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—44no—
193C2×D4×C53—82no—
194C2×D4×C53C2412yes—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2412yes—
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—82no—
209C2×C22⋊D53C2×D414yes—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—24no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223#11719947—432no—
224C2×C4×D53—22no—
225C2×C4×D53—22no—
226C2×C4×D53—24no—
227C2×C4×D53—44no—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2412yes—
230C2×Dic106—24no—
231C2×Dic106—24no—
232C2×Dic106—44no—
233C2×Dic106—82no—
234D8×C53—28no—
235M16×C53—28no—
236C2×C8×C53—22no—
237C2×C8×C53#4114yescomplemented
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊Dic53—24no—
247C22⋊Dic53—24no—
248C22⋊Dic53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251C22⋊Dic53C2×D414yes—
252#11719921—24no—
253#11719921C2×D414yes—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53C2412yes—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53C2×D412yes—
270C4×Dic53C2412yes—
271C2×#88322—22no—
272C2×#88322—22no—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275#11719912—28no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53C22×D412yes—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—22no—
297D4×C53—48no—
298D4×C53—42no—
299D4×C53—42no—
300D4×C53—84no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C532−1+412yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—28no—
315C22⋊D53—48no—
316C22⋊D53—84no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—48no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—48no—
329C2×Dic53—48no—
330C2×Dic53AGL(1,ℤ/8)14yes—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C4×D53—24no—
335C4×D53—22no—
336C4×D53—22no—
337C4×D53—48no—
338Dic106—48no—
339Dic106—84no—
340C8×C53—22no—
341C8×C53C2×#4114yescomplemented
342#88322—22no—
343#88322—22no—
344C2×#3354—531nomaximal, Sylow
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—44no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—84no—
356C22×C53—84no—
357C22×C53#54712yes—
358C22×C53C2×AGL(1,ℤ/8)12yes—
359C22×C53#57712yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—22no—
364C2×D53—44no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53#54712yes—
369C4×C53C22×#4111yescharacteristic
370C4×C53C2×2−1+411yescharacteristic
371Dic53—22no—
372Dic53—22no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377Dic53C2×AGL(1,ℤ/8)14yes—
378C2×#555—531no—
379C2×#547—531no—
380#3354—5316no—
381C2×#498—531no—
382C2×#481—531no—
383C2×#481—531no—
384C2×#482—531no—
385C2×#482—531no—
386C2×#476—531no—
387C2×#474—531no—
388C2×#469—531no—
389C2×#469D5311yescharacteristic, complemented
390C2×C4×D8—531no—
391C2×#436—531no—
392C2×#428—531no—
393C2×#428—531no—
394C2×C53—42no—
395C2×C53—82no—
396C2×C53—82no—
397C2×C53#335414yescomplemented
398C2×C53C2×#54711yescharacteristic
399C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C53C2×#57711yescharacteristic
401D53—42no—
402C22×#41—1061no—
403C22×D8C2×D5311yescharacteristic
404C22×M16—531no—
405C22×M16C2×D5311yescharacteristic
406#555—538no—
407#555—1064no—
408#547—538no—
409#547—1064no—
410C2×C4⋊Q8—531no—
411C2×C4⋊Q8—531no—
412C2×#124—1061no—
413C2×#124—1061no—
414C2×#123—1061no—
415C2×#123—1061no—
416C2×C22⋊Q8—1061no—
417C2×#121—531no—
418C2×#121—531no—
419C2×#121—1061no—
420C2×#121C2×D5311yescharacteristic
421C2×#121C2×D5311yescharacteristic
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—531no—
425C2×#117—531no—
426C2×#117—531no—
427C2×#117—1061no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430#498—538no—
431#482—538no—
432#482—538no—
433#481—538no—
434#481—538no—
435#476—538no—
436#474—538no—
437#469—538no—
438#469C2×D5318yescomplemented
439C4×D8—538no—
440#436—538no—
441#428—538no—
442#428—538no—
443C2×#107—531no—
444C2×#107—531no—
445C2×#107—531no—
446C2×#106—531no—
447C2×#106—531no—
448C2×#106—531no—
449C2×#106—531no—
450C2×#106—531no—
451C2×#106C2×D5311yescharacteristic
452C2×C4⋊C8—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102C2×D5311yescharacteristic
458C2×#102C2×D5311yescharacteristic
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×C4×C8—531no—
462C53C2×#335411yescharacteristic, complemented, Sylow
463C2×#41—1068no—
464C2×#41—2128no—
465C22×Q8—1061no—
466C22×Q8—1061no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4C22×D5311yescharacteristic
473C22×D4C22×D5311yescharacteristic
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4C22×D5311yescharacteristic
480C2×D8—24no—
481C2×D8C22×D5314yes—
482C2×M16—24no—
483C2×M16—534no—
484C2×M16—1064no—
485C2×M16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—534no—
491C4⋊Q8—534no—
492C4⋊Q8—1062no—
493C4⋊Q8—1062no—
494#124—1068no—
495#124—1068no—
496#123—1068no—
497#123—1068no—
498C22⋊Q8—1068no—
499#121—22no—
500#121—22no—
501#121—534no—
502#121—534no—
503#121—1062no—
504#121—1062no—
505#121—1068no—
506#121C22×D5314yes—
507#121C22×D5314yes—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—534no—
511C4×D4—534no—
512C4×D4—1062no—
513C4×D4—1062no—
514#117—534no—
515#117—534no—
516#117—1068no—
517#117—1062no—
518#117—1062no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—534no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—1062no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1062no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—531no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C42—531no—
545C2×C42—1061no—
546C2×C42—1061no—
547#107—534no—
548#107—534no—
549#107—534no—
550#106—534no—
551#106—534no—
552#106—534no—
553#106—534no—
554#106—534no—
555#106C22×D5314yes—
556C4⋊C8—534no—
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102C22×D5314yes—
562#102C22×D5314yes—
563C22⋊C8—534no—
564C22⋊C8—534no—
565C4×C8—534no—
566C24—21no—
567C24—21no—
568C24—531no—
569C24D4×D5311yescharacteristic
570#41—21232no—
571C2×Q8—1064no—
572C2×Q8—1064no—
573C2×Q8—4242no—
574C2×Q8—2124no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—44no—
584C2×D4—82no—
585C2×D4—534no—
586C2×D4—1064no—
587C2×D4—1064no—
588C2×D4—1064no—
589C2×D4—4242no—
590C2×D4—2124no—
591C2×D4C23×D5312yes—
592C2×D4C23×D5312yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1064no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—2124no—
613C22×C4—2124no—
614C22×C4—2124no—
615C22×C4—2124no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620D8—28no—
621M16—28no—
622M16—1068no—
623C2×C8—22no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—1062no—
627C2×C8—1062no—
628C2×C8#1171994714yescomplemented
629C2×C8C23×D5312yes—
630C2×C8C23×D5312yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—534no—
634C4⋊C4—532no—
635C4⋊C4—532no—
636C4⋊C4—532no—
637C4⋊C4—532no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1064no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—534no—
651C22⋊C4—534no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C42—532no—
659C42—532no—
660C42—1064no—
661C42—1064no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—532no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23C2×D4×D5312yes—
678C23C2×D4×D5311yescharacteristic
679Q8—4244no—
680Q8—2128no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—84no—
689D4—1068no—
690D4—4244no—
691D4—2128no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—534no—
701C2×C4—532no—
702C2×C4—532no—
703C2×C4—532no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1064no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—2128no—
714C2×C4—2128no—
715C2×C4—2128no—
716C2×C4—2128no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4C2×#1171994712yes—
724C2×C4#1313326412yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—1062no—
728C8—1062no—
729C8C2×#1171994714yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—84no—
742C22—1062no—
743C22—1062no—
744C22—1062no—
745C22—2124no—
746C22#1681127312yes—
747C22AGL(1,ℤ/8)×D5312yes—
748C22#1681143312yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—534no—
754C4—1062no—
755C4—1062no—
756C4—2122no—
757C4—2122no—
758C4—2122no—
759C4—2122no—
760C4#1681127312yes—
761C4C22×#1171994711yescharacteristic
762C4C2×#1313326411yescharacteristic
763C2—42no—
764C2—82no—
765C2—82no—
766C2—2122no—
767C2#2028730514yesdirect product factor
768C2C2×#1681127311yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
770C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#469C2
socleC23×C53C22×D4
hypercenterC2×#469D53
hypocenterC53C2×#3354
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16811337C2semidirect
2. C2×#16811273C2semidirect
3. #20287305C2direct (N × H)
4. C2×#16811020C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810939C2semidirect
7. C2×#16810945C2semidirect
8. C2×#16810944C2semidirect
9. C2×#16810911C2semidirect
10. C2×#16810901C2semidirect
11. C2×#16810873C2semidirect
12. C2×D8×Dic53C2semidirect
13. C2×#16810699C2semidirect
14. C2×#16810665C2semidirect
15. C2×#16810662C2semidirect
16. C2×C53×#469C2semidirect
20. #16811337C22semidirect
22. #16811273C22semidirect
41. #16811020C22semidirect
42. #16810945C22semidirect
43. #16810944C22semidirect
44. #16810940C22semidirect
45. #16810939C22semidirect
46. #16810911C22semidirect
47. #16810901C22semidirect
48. #16810873C22semidirect
49. D8×Dic53C22semidirect
50. #16810699C22semidirect
51. #16810665C22semidirect
52. #16810662C22semidirect
73. C53×#469C22semidirect
237. C2×C8×C53#41semidirect
341. C8×C53C2×#41semidirect
389. C2×#469D53semidirect
397. C2×C53#3354semidirect
438. #469C2×D53semidirect
462. C53C2×#3354semidirect
628. C2×C8#11719947semidirect
729. C8C2×#11719947semidirect
767. C2#20287305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113372
C2×#168112732
#202873052
C2×#168110202
C2×#168109402
C2×#168109392
C2×#168109452
C2×#168109442
C2×#168109112
C2×#168109012
C2×#168108732
C2×D8×Dic532
C2×#168106992
C2×#168106652
C2×#168106622
C2×C53×#4692
C2×#335453