Finite Group Databasebeta

← C2×#20287210 #28262682

Subgroups — C2×#20287210 #28262682

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811337C211yesmaximal, characteristic, complemented
2C2×#16811325C211yesmaximal, characteristic, complemented
3#20287210C2116yesmaximal, direct product factor
4C2×#16811030C211yesmaximal, characteristic, complemented
5C2×#16810946C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810944C211yesmaximal, characteristic, complemented
8C2×#16810934C211yesmaximal, characteristic, complemented
9C2×#16810925C211yesmaximal, characteristic, complemented
10C2×#16810901C211yesmaximal, characteristic, complemented
11C2×#16810856C211yesmaximal, characteristic, complemented
12C2×#16810735C211yesmaximal, characteristic, complemented
13C2×#16810692C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C2×#16810658C211yesmaximal, characteristic, complemented
16C2×C53×#469C211yesmaximal, characteristic, complemented
17C22×C8×D53C2211yescharacteristic
18#16811337—24no—
19#16811337C2218yescomplemented
20#16811325—24no—
21#16811325C2218yescomplemented
22C2×#13133216C2211yescharacteristic
23C2×#13133210—21no—
24C2×#13133208C2211yescharacteristic
25C2×#13133204—21no—
26C2×#13133203—21no—
27C2×#13133201—21no—
28C2×#13133189—21no—
29C2×#13133189—21no—
30C2×#13133188C2211yescharacteristic
31C2×#13133188C2211yescharacteristic
32C2×D4×Dic53—21no—
33C2×D4×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×C4×C22⋊D53C2211yescharacteristic
36C2×#13133176C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×#13133173—21no—
40C22×C4⋊Dic53C2211yescharacteristic
41#16811030C2218yescomplemented
42#16810946C2218yescomplemented
43#16810945C2218yescomplemented
44#16810944C2218yescomplemented
45#16810934C2218yescomplemented
46#16810925C2218yescomplemented
47#16810901C2218yescomplemented
48#16810856C2218yescomplemented
49#16810735C2218yescomplemented
50#16810692C2218yescomplemented
51#16810665C2218yescomplemented
52#16810658C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#469C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C22×C22⋊D53D411yescharacteristic
81C23×Dic53—21no—
82C23×Dic53—21no—
83C23×Dic53—21no—
84C22×C4×D53C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C2×C8×D53—24no—
88C2×C8×D53C2314yes—
89#13133216—22no—
90#13133216C2314yes—
91#13133210—28no—
92#13133208—22no—
93#13133208C2314yes—
94#13133204—28no—
95#13133203—28no—
96#13133201—28no—
97#13133189—28no—
98#13133189—28no—
99#13133188—22no—
100#13133188—22no—
101#13133188C2314yes—
102#13133188C2314yes—
103D4×Dic53—28no—
104D4×Dic53—22no—
105D4×Dic53—22no—
106D4×Dic53C2314yes—
107D4×Dic53C2314yes—
108C4×C22⋊D53D414yes—
109C4×C22⋊D53C2314yes—
110#13133176—22no—
111#13133176C2314yes—
112#13133175—22no—
113#13133175—22no—
114#13133175C2314yes—
115#13133175C2314yes—
116#13133173—28no—
117C2×C4⋊Dic53—22no—
118C2×C4⋊Dic53—21no—
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×#11719919D411yescharacteristic
128C2×C22⋊Dic53—21no—
129C2×C22⋊Dic53—21no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53D411yescharacteristic
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921D411yescharacteristic
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133150C2314yes—
144#13133150C2314yes—
145#13133150C2314yes—
146#13133149C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149#13133146C2314yes—
150#13133138C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154C22⋊#88322C2314yes—
155#13133129C2314yes—
156#13133127C2314yes—
157C22×D4×C53—21no—
158C22×D4×C53—21no—
159C22×D4×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C2×D8×C53—24no—
163C2×D8×C53C2314yes—
164C2×M16×C53—24no—
165C2×M16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168#121×C53—22no—
169#121×C53—22no—
170#121×C53C2314yes—
171#121×C53C2314yes—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176#106×C53C2314yes—
177#102×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×D4×C53—24no—
184C2×D4×C53—24no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—44no—
192C2×D4×C53—82no—
193C2×D4×C53C2412yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—42no—
206C2×C22⋊D53—82no—
207C2×C22⋊D53—82no—
208C2×C22⋊D53C2×D414yes—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—24no—
214C22×Dic53—24no—
215C22×Dic53—24no—
216C22×Dic53—44no—
217C22×Dic53—82no—
218C22×Dic53—82no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C2×C4×D53—22no—
223C2×C4×D53—22no—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2412yes—
226C2×Dic106—24no—
227C2×Dic106—82no—
228D8×C53—28no—
229M16×C53—28no—
230C2×C8×C53—22no—
231C2×C8×C53#4114yes—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53C2×D414yes—
246#11719921—24no—
247#11719921—24no—
248#11719921C2×D414yes—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919C2×D414yes—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53C2×D412yes—
266C4×Dic53C2412yes—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C8×D53—28no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53C22×D412yes—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53C22×D412yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—48no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—84no—
297C2×C4×C53—22no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
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—44no—
311C22⋊D53—84no—
312C22⋊D53—84no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—48no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—84no—
326C2×Dic53—84no—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330C4×D53—24no—
331C4×D53—22no—
332C4×D53—22no—
333Dic106—84no—
334C8×C53—22no—
335C8×C53C2×#4114yes—
336#88322—22no—
337#88322—22no—
338C2×#3347—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—44no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—84no—
350C22×C53—84no—
351C22×C53#54712yes—
352C22×C53#57512yes—
353C22×C53#57612yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—22no—
358C2×D53—44no—
359C4×C53—22no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#54712yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C2×2−1+411yescharacteristic
365Dic53—22no—
366Dic53—22no—
367Dic53—22no—
368Dic53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#555—531no—
373C2×#553—531no—
374#3347—5316no—
375C2×#501—531no—
376C2×#482—531no—
377C2×#482—531no—
378C2×#482—531no—
379C2×#480—531no—
380C2×#478—531no—
381C2×#474—531no—
382C2×#469D5311yescharacteristic, complemented
383C2×#466—531no—
384C2×#442—531no—
385C2×#435—531no—
386C2×#428—531no—
387C2×#427—531no—
388C2×C53—42no—
389C2×C53—82no—
390C2×C53—82no—
391C2×C53#334714yescomplemented
392C2×C53C2×#54711yescharacteristic
393C2×C53C2×#57511yescharacteristic
394C2×C53C2×#57611yescharacteristic
395D53—42no—
396C22×D8C2×D5311yescharacteristic
397C22×M16C2×D5311yescharacteristic
398C23×C8—531no—
399#555—538no—
400#555—1064no—
401#553—538no—
402#553—1064no—
403C2×C4⋊Q8—531no—
404C2×#126—1061no—
405C2×#125—531no—
406C2×#124—1061no—
407C2×#124—1061no—
408C2×#123—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#121—1061no—
412C2×#121—1061no—
413C2×#121C2×D5311yescharacteristic
414C2×#121C2×D5311yescharacteristic
415C2×C4×D4—531no—
416C2×C4×D4—531no—
417C2×C4×D4—531no—
418C2×C4×D4—1061no—
419C2×#117—531no—
420C2×#117—531no—
421C2×#117—531no—
422C2×#117—1061no—
423C22×C4⋊C4—531no—
424#501—538no—
425#482—538no—
426#482—538no—
427#482—538no—
428#480—538no—
429#478—538no—
430#474—538no—
431#469C2×D5318yescomplemented
432#466—538no—
433#442—538no—
434#435—538no—
435#428—538no—
436#427—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107—531no—
441C2×#107—531no—
442C2×#106—531no—
443C2×#106—531no—
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×#97—531no—
456C53C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1061no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—531no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C22×D4C22×D5311yescharacteristic
465C23×C4—531no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4C22×D5311yescharacteristic
470C2×D8—24no—
471C2×D8C22×D5314yes—
472C2×M16—24no—
473C2×M16C22×D5314yes—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—534no—
477C22×C8—1064no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5311yescharacteristic
480C4⋊Q8—534no—
481C4⋊Q8—1062no—
482#126—1068no—
483#125—534no—
484#125—1062no—
485#124—1068no—
486#124—1068no—
487#123—1068no—
488#121—22no—
489#121—22no—
490#121—534no—
491#121—534no—
492#121—1062no—
493#121—1062no—
494#121—1068no—
495#121—1068no—
496#121C22×D5314yes—
497#121C22×D5314yes—
498C4×D4—534no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1068no—
505#117—534no—
506#117—534no—
507#117—534no—
508#117—1068no—
509#117—1062no—
510#117—1062no—
511#117—1062no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1062no—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C42—531no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540#107—534no—
541#107—534no—
542#107—534no—
543#107—534no—
544#107—534no—
545#106—534no—
546#106—534no—
547#106—534no—
548#106C22×D5314yes—
549C4⋊C8—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102C22×D5314yes—
555#102C22×D5314yes—
556C22⋊C8—534no—
557C22⋊C8—534no—
558#97—534no—
559C24—21no—
560C24—21no—
561C24—531no—
562C24D4×D5311yescharacteristic
563C2×Q8—1064no—
564C2×Q8—4242no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4—534no—
576C2×D4—1064no—
577C2×D4—1064no—
578C2×D4—4242no—
579C2×D4—4242no—
580C2×D4—2122no—
581C2×D4C23×D5312yes—
582C2×D4C23×D5312yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—1064no—
593C22×C4—1064no—
594C22×C4—1062no—
595C22×C4—1062no—
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×C4D4×D5312yes—
605C22×C4D4×D5311yescharacteristic
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608D8—28no—
609M16—28no—
610C2×C8—22no—
611C2×C8—532no—
612C2×C8—532no—
613C2×C8—1062no—
614C2×C8—1062no—
615C2×C8—1068no—
616C2×C8#1171994714yes—
617C2×C8C23×D5312yes—
618C2×C8C23×D5312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—534no—
622C4⋊C4—532no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1061no—
630C4⋊C4—1061no—
631C4⋊C4—1064no—
632C4⋊C4—1061no—
633C4⋊C4—1061no—
634C4⋊C4C23×D5312yes—
635C4⋊C4C23×D5312yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—534no—
639C22⋊C4—534no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C42—532no—
648C42—532no—
649C42—1064no—
650C42—1064no—
651C42—1064no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—532no—
664C23—1062no—
665C23—1062no—
666C23—1062no—
667C23C2×D4×D5312yes—
668C23C2×D4×D5311yescharacteristic
669Q8—4244no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—48no—
675D4—42no—
676D4—42no—
677D4—84no—
678D4—4244no—
679D4—4244no—
680D4—2124no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—532no—
690C2×C4—532no—
691C2×C4—532no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1064no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—4244no—
703C2×C4—4244no—
704C2×C4—2128no—
705C2×C4—2122no—
706C2×C4—2122no—
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×#1171994714yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—1062no—
731C22—1062no—
732C22—1062no—
733C22—2124no—
734C22#1681127312yes—
735C22#1681141912yes—
736C22#1681142712yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—1062no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127312yes—
749C4C22×#1171994711yescharacteristic
750C4C2×#1313326411yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—2122no—
755C2#2028721014yesdirect product factor
756C2C2×#1681127311yescharacteristic
757C2C2×#1681141911yescharacteristic
758C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#469C2
socleC23×C53C22×D4
hypercenterC2×#469D53
hypocenterC53C2×#3347
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×#16811325C2semidirect
3. #20287210C2direct (N × H)
4. C2×#16811030C2semidirect
5. C2×#16810946C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810944C2semidirect
8. C2×#16810934C2semidirect
9. C2×#16810925C2semidirect
10. C2×#16810901C2semidirect
11. C2×#16810856C2semidirect
12. C2×#16810735C2semidirect
13. C2×#16810692C2semidirect
14. C2×#16810665C2semidirect
15. C2×#16810658C2semidirect
16. C2×C53×#469C2semidirect
19. #16811337C22semidirect
21. #16811325C22semidirect
41. #16811030C22semidirect
42. #16810946C22semidirect
43. #16810945C22semidirect
44. #16810944C22semidirect
45. #16810934C22semidirect
46. #16810925C22semidirect
47. #16810901C22semidirect
48. #16810856C22semidirect
49. #16810735C22semidirect
50. #16810692C22semidirect
51. #16810665C22semidirect
52. #16810658C22semidirect
73. C53×#469C22semidirect
382. C2×#469D53semidirect
391. C2×C53#3347semidirect
431. #469C2×D53semidirect
456. C53C2×#3347semidirect
755. C2#20287210direct (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×#168113252
#202872102
C2×#168110302
C2×#168109462
C2×#168109452
C2×#168109442
C2×#168109342
C2×#168109252
C2×#168109012
C2×#168108562
C2×#168107352
C2×#168106922
C2×#168106652
C2×#168106582
C2×C53×#4692
C2×#334753