Finite Group Databasebeta

← C2×#20287314 #28262813

Subgroups — C2×#20287314 #28262813

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×#16811325C211yesmaximal, characteristic, complemented
2C2×#16811317C211yesmaximal, characteristic, complemented
3#20287314C2116yesmaximal, direct product factor
4C2×#16811024C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic, complemented
6C2×#16810937C211yesmaximal, characteristic, complemented
7C2×#16810935C211yesmaximal, characteristic, complemented
8C2×#16810922C211yesmaximal, characteristic, complemented
9C2×#16810921C211yesmaximal, characteristic, complemented
10C2×#16810875C211yesmaximal, characteristic, complemented
11C2×#16810874C211yesmaximal, characteristic, complemented
12C2×#16810703C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810666C211yesmaximal, characteristic, complemented
15C2×#16810662C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719922C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20#16811325—24no—
21#16811325C2218yescomplemented
22#16811317—24no—
23#16811317C2218yescomplemented
24C2×#13133211—21no—
25C2×#13133210—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133201—21no—
29C2×#13133199—21no—
30C2×#13133192C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133190—21no—
33C2×#13133189—21no—
34C2×#13133188C2211yescharacteristic
35C2×C4×D212—21no—
36C2×D4×Dic53—21no—
37C2×D4×Dic53C2211yescharacteristic
38C2×#13133179C2211yescharacteristic
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811024C2218yescomplemented
44#16810950C2218yescomplemented
45#16810937C2218yescomplemented
46#16810935C2218yescomplemented
47#16810922C2218yescomplemented
48#16810921C2218yescomplemented
49#16810875C2218yescomplemented
50#16810874C2218yescomplemented
51#16810703C2218yescomplemented
52#16810698C2218yescomplemented
53#16810666C2218yescomplemented
54#16810662C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×D212—21no—
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C22×C22⋊D53D411yescharacteristic
82C23×Dic53—21no—
83C23×Dic53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C2×#11719922—24no—
88C2×#11719922C2314yes—
89C2×#11719917—24no—
90C2×#11719917C2314yes—
91C2×#11719912—24no—
92C2×#11719912C2314yes—
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95#13133211—28no—
96#13133210—28no—
97#13133208—22no—
98#13133208—22no—
99#13133208C2314yes—
100#13133208C2314yes—
101#13133201—28no—
102#13133199—28no—
103#13133192—22no—
104#13133192C2314yes—
105#13133191—22no—
106#13133191C2314yes—
107#13133190—28no—
108#13133189—28no—
109#13133188—22no—
110#13133188C2314yes—
111C4×D212—28no—
112D4×Dic53—28no—
113D4×Dic53—22no—
114D4×Dic53C2314yes—
115#13133179—22no—
116#13133179C2314yes—
117C4×C22⋊D53D414yes—
118C4×C22⋊D53C2314yes—
119#13133175—22no—
120#13133175C2314yes—
121C2×C4⋊Dic53—22no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2314yes—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133151C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133146C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155#13133138C2314yes—
156#13133137C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C22×D4×C53—21no—
160C22×D4×C53C2311yescharacteristic
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164#121×C53—22no—
165#121×C53C2314yes—
166#117×C53—22no—
167#117×C53C2314yes—
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C42×C53—21no—
174#107×C53C2314yes—
175#106×C53C2314yes—
176#102×C53C2314yes—
177#102×C53C2314yes—
178C22⋊C8×C53C2314yes—
179C24×C53—21no—
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C23×D53C2×D411yescharacteristic
183C2×D4×C53—24no—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53—44no—
188C2×D4×C53C2412yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—42no—
201C2×C22⋊D53—82no—
202C2×C22⋊D53—82no—
203C2×C22⋊D53C2×D414yes—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—24no—
209C22×Dic53—82no—
210C22×Dic53—82no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—24no—
217C2×D212—21no—
218C2×D212—44no—
219C2×D212C2412yes—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—82no—
225C2×C4×D53—82no—
226C2×C4×D53C2×D412yes—
227C2×C4×D53C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C42×C53—24no—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53C2×D414yes—
244#11719922—28no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921C2×D414yes—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919C2×D414yes—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266#11719917—28no—
267C2×#88322—22no—
268C2×#88322#4114yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271#11719912—28no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53C22×D412yes—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53C22×D412yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—48no—
292D4×C53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—44no—
309C22⋊D53—84no—
310C22⋊D53—84no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—84no—
321C2×Dic53—84no—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—22no—
326D212—22no—
327D212—48no—
328D212—42no—
329C4×D53—24no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—84no—
333C4×D53—84no—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322C2×#4114yes—
338C2×#3355—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—84no—
347C22×C53#54712yes—
348C22×C53#57512yes—
349C22×C53#57612yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—44no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#54712yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#553—531no—
373C2×#553—531no—
374#3355—5316no—
375C2×#499—531no—
376C2×#482—531no—
377C2×#482D5311yescharacteristic, complemented
378C2×#480—531no—
379C2×#480—531no—
380C2×#478—531no—
381C2×#478—531no—
382C2×#469—531no—
383C2×#469—531no—
384C2×C4×D8—531no—
385C2×#436—531no—
386C2×#428—531no—
387C2×#428—531no—
388C2×C53—42no—
389C2×C53—82no—
390C2×C53#335514yescomplemented
391C2×C53C2×#54711yescharacteristic
392C2×C53C2×#57511yescharacteristic
393C2×C53C2×#57611yescharacteristic
394D53—42no—
395D53—82no—
396C22×D8—531no—
397C22×M16—531no—
398C22×M16—531no—
399#553—538no—
400#553—538no—
401#553—1064no—
402#553—1064no—
403C2×#126—1061no—
404C2×#126—1061no—
405C2×#125—531no—
406C2×#125—531no—
407C2×#123—1061no—
408C2×#123—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#121—531no—
412C2×#121—1061no—
413C2×#121—1061no—
414C2×#121C2×D5311yescharacteristic
415C2×C4×D4—531no—
416C2×C4×D4—531no—
417C2×C4×D4—531no—
418C2×C4×D4—1061no—
419C2×C4×D4—1061no—
420C2×#117—531no—
421C2×#117C2×D5311yescharacteristic
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424#499—538no—
425#482—538no—
426#482C2×D5318yescomplemented
427#480—538no—
428#480—538no—
429#478—538no—
430#478—538no—
431#469—538no—
432#469—538no—
433C4×D8—538no—
434#436—538no—
435#428—538no—
436#428—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107—531no—
441C2×#107C2×D5311yescharacteristic
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⋊C8C2×D5311yescharacteristic
455C2×C4×C8—531no—
456C53C2×#335511yescharacteristic, complemented, Sylow
457C22×D4—21no—
458C22×D4—531no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—531no—
465C23×C4—1061no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4C22×D5311yescharacteristic
470C2×D8—534no—
471C2×D8—1064no—
472C2×M16—534no—
473C2×M16—534no—
474C2×M16—1064no—
475C2×M16—1064no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5311yescharacteristic
480#126—1068no—
481#126—1068no—
482#125—534no—
483#125—534no—
484#125—1062no—
485#125—1062no—
486#123—1068no—
487#123—1068no—
488#121—22no—
489#121—534no—
490#121—534no—
491#121—534no—
492#121—1068no—
493#121—1062no—
494#121—1062no—
495#121—1068no—
496#121—1062no—
497#121C22×D5314yes—
498C4×D4—534no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1068no—
503C4×D4—1062no—
504C4×D4—1062no—
505C4×D4—1068no—
506#117—22no—
507#117—534no—
508#117—1062no—
509#117C22×D5314yes—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—534no—
515C2×C4⋊C4—534no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1062no—
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—531no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—21no—
538C2×C42—531no—
539C2×C42—1061no—
540#107—534no—
541#107—534no—
542#107—534no—
543#107—534no—
544#107C22×D5314yes—
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⋊C8C22×D5314yes—
558C4×C8—534no—
559C24—21no—
560C24—531no—
561C24—1061no—
562C24D4×D5311yescharacteristic
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—534no—
569C2×D4—532no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—1064no—
573C2×D4—1061no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—4242no—
577C2×D4—4242no—
578C2×D4—2124no—
579C2×D4—2122no—
580C2×D4C23×D5312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—1064no—
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—4242no—
601C22×C4—4242no—
602C22×C4—4242no—
603C22×C4—4242no—
604C22×C4D4×D5312yes—
605C22×C4D4×D5311yescharacteristic
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608D8—1068no—
609M16—1068no—
610M16—1068no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—534no—
614C2×C8—532no—
615C2×C8—532no—
616C2×C8—1062no—
617C2×C8C23×D5312yes—
618C2×C8C23×D5312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—534no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—1064no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1061no—
632C4⋊C4—1061no—
633C4⋊C4—1061no—
634C4⋊C4—1064no—
635C4⋊C4C23×D5312yes—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—534no—
641C22⋊C4—534no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C42—24no—
649C42—532no—
650C42—532no—
651C42—1064no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—532no—
660C23—1062no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23C2×D4×D5312yes—
668C23C2×D4×D5311yescharacteristic
669D4—22no—
670D4—22no—
671D4—48no—
672D4—42no—
673D4—1062no—
674D4—1062no—
675D4—4244no—
676D4—4244no—
677D4—2128no—
678D4—2124no—
679D4—2122no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—532no—
691C2×C4—532no—
692C2×C4—532no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1064no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—4244no—
703C2×C4—4244no—
704C2×C4—4244no—
705C2×C4—4244no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4#41×D5312yes—
712C2×C4#1313326412yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—22no—
716C8—534no—
717C8—1062no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—1062no—
727C22—1062no—
728C22—1062no—
729C22—4244no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22—2124no—
734C22#1681127112yes—
735C22#1681141912yes—
736C22#1681142512yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—1062no—
743C4—1062no—
744C4—1062no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127112yes—
749C4C2×#41×D5311yescharacteristic
750C4C2×#1313326411yescharacteristic
751C2—42no—
752C2—82no—
753C2—4242no—
754C2—2122no—
755C2#2028731414yesdirect product factor
756C2C2×#1681127111yescharacteristic
757C2C2×#1681141911yescharacteristic
758C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
hypercenterC2×#482D53
hypocenterC53C2×#3355
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811325C2semidirect
2. C2×#16811317C2semidirect
3. #20287314C2direct (N × H)
4. C2×#16811024C2semidirect
5. C2×#16810950C2semidirect
6. C2×#16810937C2semidirect
7. C2×#16810935C2semidirect
8. C2×#16810922C2semidirect
9. C2×#16810921C2semidirect
10. C2×#16810875C2semidirect
11. C2×#16810874C2semidirect
12. C2×#16810703C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810666C2semidirect
15. C2×#16810662C2semidirect
16. C2×C53×#482C2semidirect
21. #16811325C22semidirect
23. #16811317C22semidirect
43. #16811024C22semidirect
44. #16810950C22semidirect
45. #16810937C22semidirect
46. #16810935C22semidirect
47. #16810922C22semidirect
48. #16810921C22semidirect
49. #16810875C22semidirect
50. #16810874C22semidirect
51. #16810703C22semidirect
52. #16810698C22semidirect
53. #16810666C22semidirect
54. #16810662C22semidirect
71. C53×#482C22semidirect
377. C2×#482D53semidirect
390. C2×C53#3355semidirect
426. #482C2×D53semidirect
456. C53C2×#3355semidirect
755. C2#20287314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113252
C2×#168113172
#202873142
C2×#168110242
C2×#168109502
C2×#168109372
C2×#168109352
C2×#168109222
C2×#168109212
C2×#168108752
C2×#168108742
C2×#168107032
C2×#168106982
C2×#168106662
C2×#168106622
C2×C53×#4822
C2×#335553