Finite Group Databasebeta

← C2×#20287179 #28262649

Subgroups — C2×#20287179 #28262649

Order 13568.

2158 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×#16811277C211yesmaximal, characteristic, complemented
2#20287179C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810939C211yesmaximal, characteristic, complemented
6C2×#16810947C211yesmaximal, characteristic, complemented
7C2×#16810934C211yesmaximal, characteristic, complemented
8C2×#16810920C211yesmaximal, characteristic, complemented
9C2×#16810913C211yesmaximal, characteristic, complemented
10C2×#16810874C211yesmaximal, characteristic, complemented
11C2×#16810857C211yesmaximal, characteristic, complemented
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810666C211yesmaximal, characteristic, complemented
15C22×#13133148C211yesmaximal, characteristic, complemented
16C2×C53×#553C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719922C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811277—24no—
22#16811277C2218yescomplemented
23C2×#13133217C2211yescharacteristic
24C2×#13133201—21no—
25C2×#13133201—21no—
26C2×#13133197—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811033C2218yescomplemented
33#16810947C2218yescomplemented
34#16810941C2218yescomplemented
35#16810939C2218yescomplemented
36#16810934C2218yescomplemented
37#16810920C2218yescomplemented
38#16810913C2218yescomplemented
39#16810874C2218yescomplemented
40#16810857C2218yescomplemented
41#16810733C2218yescomplemented
42#16810695C2218yescomplemented
43#16810666C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2218yescomplemented
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#553—24no—
65C53×#553C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic
68C2×#123×C53—21no—
69C2×#121×C53—21no—
70C2×#121×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×D4×C53—21no—
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719922—24no—
87C2×#11719922C2314yes—
88C2×#11719917—24no—
89C2×#11719917C2314yes—
90C22×#88322—24no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95C22×#88322C2311yescharacteristic
96#13133217—22no—
97#13133217C2314yes—
98#13133201—28no—
99#13133201—28no—
100#13133197—28no—
101#13133191—22no—
102#13133191—22no—
103#13133191C2314yes—
104#13133191C2314yes—
105C4×D212—22no—
106C4×D212C2314yes—
107C2×C4⋊Dic53—22no—
108C2×C4⋊Dic53—22no—
109C2×C4⋊Dic53—21no—
110C2×C4⋊Dic53—21no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2314yes—
113C2×C4⋊Dic53C2314yes—
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2311yescharacteristic
116C2×C4⋊Dic53C2311yescharacteristic
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133148C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128#13133148C2314yes—
129C4⋊#88322C2314yes—
130#13133138C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133137C2314yes—
136C22⋊#88322C2314yes—
137C22⋊#88322C2314yes—
138#13133128C2314yes—
139C22×D4×C53—21no—
140C22×D4×C53—21no—
141C22×D4×C53D411yescharacteristic
142C22×D4×C53C2311yescharacteristic
143C23×C4×C53—21no—
144C23×C4×C53—21no—
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147#126×C53—28no—
148#125×C53—22no—
149#125×C53C2314yes—
150#123×C53—28no—
151#121×C53—28no—
152#121×C53—22no—
153#121×C53—22no—
154#121×C53C2314yes—
155#121×C53C2314yes—
156C4×D4×C53—28no—
157C4×D4×C53—22no—
158C4×D4×C53D414yes—
159C4×D4×C53C2314yes—
160C4×D4×C53C2314yes—
161#117×C53—22no—
162#117×C53C2314yes—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—22no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53C2311yescharacteristic
180C24×C53—21no—
181C24×C53C2×D411yescharacteristic
182C24×C53C2×D411yescharacteristic
183C23×D53—21no—
184C2×D4×C53—24no—
185C2×D4×C53—24no—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—44no—
191C2×D4×C53—82no—
192C2×D4×C53C2×D414yes—
193C2×D4×C53C2412yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—24no—
203C22×C4×C53—82no—
204C22×C4×C53—82no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53—44no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—24no—
222C22×Dic53—24no—
223C22×Dic53—44no—
224C22×Dic53—44no—
225#11719947—432no—
226C2×D212—22no—
227C2×D212—22no—
228C2×D212—21no—
229C2×D212C2412yes—
230C2×C4×D53—24no—
231C2×C4×D53—44no—
232C2×Dic106—24no—
233C2×Dic106—44no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53C2×D414yes—
241C4⋊C4×C53C2412yes—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53C2×D414yes—
249C22⋊C4×C53C2×D414yes—
250C42×C53—24no—
251C42×C53C2×D412yes—
252C42×C53C2412yes—
253#11719922—28no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53—24no—
262C4⋊Dic53—24no—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266#11719917—28no—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322—28no—
271C2×#88322#4114yescomplemented
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53—42no—
285C23×C53AGL(1,ℤ/8)14yes—
286C23×C53C22×D412yes—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293D4×C53—28no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—48no—
297D4×C53—42no—
298D4×C53—84no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—24no—
304C2×C4×C53—24no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—84no—
316C2×C4×C53—84no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D411yescharacteristic
322C2×C4×C53C2×#4112yes—
323C2×C4×C532−1+412yes—
324C2×C4×C53C2511yescharacteristic
325C22⋊D53—48no—
326C22⋊D53—48no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—48no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—48no—
335D212—22no—
336D212—22no—
337D212—42no—
338C4×D53—48no—
339Dic106—48no—
340#88322—22no—
341#88322—22no—
342#88322—22no—
343#88322C2×#4114yescomplemented
344C2×#3345—531nomaximal, Sylow
345C22×C53—28no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—44no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—84no—
356C22×C53#54712yes—
357C22×C53C2×AGL(1,ℤ/8)14yes—
358C22×C53C2×AGL(1,ℤ/8)12yes—
359C22×C53#57712yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—84no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—22no—
368C4×C53—22no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53#54712yes—
373C4×C53C22×#4111yescharacteristic
374C4×C53C2×2−1+411yescharacteristic
375Dic53—42no—
376Dic53—42no—
377Dic53—42no—
378C2×#553D5311yescharacteristic, complemented
379C2×#547—531no—
380#3345—5316no—
381C2×#501—531no—
382C2×#481—531no—
383C2×#481—531no—
384C2×#482—531no—
385C2×#480—531no—
386C2×#478—531no—
387C2×#476—531no—
388C2×#469—531no—
389C2×#466—531no—
390C2×#442—531no—
391C2×#435—531no—
392C2×#428—531no—
393C22×#106—531no—
394C2×C53—24no—
395C2×C53—42no—
396C2×C53—82no—
397C2×C53#334514yescomplemented
398C2×C53C2×#54711yescharacteristic
399C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C53C2×#57711yescharacteristic
401D53—82no—
402C22×#41—1061no—
403C22×D8—531no—
404C22×M16—531no—
405C23×C8—531no—
406#553—24no—
407#553C2×D5318yescomplemented
408#547—538no—
409#547—1064no—
410C2×C4⋊Q8—531no—
411C2×#126—21no—
412C2×#125C2×D5311yescharacteristic
413C2×#123—21no—
414C2×#123—1061no—
415C2×#123—1061no—
416C2×C22⋊Q8—1061no—
417C2×#121—21no—
418C2×#121—531no—
419C2×#121—531no—
420C2×#121C2×D5311yescharacteristic
421C2×#121C2×D5311yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4—531no—
424C2×C4×D4C2×D5311yescharacteristic
425C2×C4×D4C2×D5311yescharacteristic
426C2×#117C2×D5311yescharacteristic
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4C2×D5311yescharacteristic
430#501—538no—
431#482—538no—
432#481—538no—
433#481—538no—
434#480—538no—
435#478—538no—
436#476—538no—
437#469—538no—
438#466—538no—
439#442—538no—
440#435—538no—
441#428—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#107—531no—
445C2×#106—531no—
446C2×#106—531no—
447C2×#106—531no—
448C2×#106—531no—
449C2×#106—538no—
450C2×#106—531no—
451C2×#106—531no—
452C2×C4⋊C8—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×#97—531no—
462C53C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1068no—
464C2×#41—2128no—
465C22×Q8—1061no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4C22⋊D5311yescharacteristic
472C22×D4C22×D5311yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4C22×D5311yescharacteristic
479C23×C4C22×D5311yescharacteristic
480C2×D8—534no—
481C2×D8—1064no—
482C2×M16—534no—
483C2×M16—1064no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8—534no—
487C22×C8—531no—
488C22×C8—531no—
489C22×C8—1064no—
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—28no—
493#125—22no—
494#125C22×D5314yes—
495#123—28no—
496#123—1068no—
497#123—1068no—
498C22⋊Q8—1068no—
499#121—28no—
500#121—22no—
501#121—22no—
502#121—534no—
503#121—534no—
504#121—1062no—
505#121—1062no—
506#121C22×D5314yes—
507#121C22×D5314yes—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—534no—
511C4×D4—1062no—
512C4×D4C22⋊D5314yes—
513C4×D4C22×D5314yes—
514C4×D4C22×D5314yes—
515#117—22no—
516#117C22×D5314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—534no—
525C2×C4⋊C4—534no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1062no—
529C2×C4⋊C4—1062no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4C22⋊D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C4⋊C4C22×D5314yes—
535C2×C4⋊C4C22×D5311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4C22⋊D5311yescharacteristic
544C2×C22⋊C4C22⋊D5311yescharacteristic
545C2×C42—21no—
546C2×C42C22×D5311yescharacteristic
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#106—534no—
556C4⋊C8—534no—
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562#102—534no—
563C22⋊C8—534no—
564C22⋊C8—534no—
565#97—534no—
566C24—21no—
567C24—1061no—
568C24C2×C22⋊D5311yescharacteristic
569C24C2×C22⋊D5311yescharacteristic
570#41—21232no—
571C2×Q8—1064no—
572C2×Q8—2124no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—532no—
582C2×D4—1064no—
583C2×D4—1064no—
584C2×D4—1061no—
585C2×D4—1062no—
586C2×D4—1062no—
587C2×D4—2124no—
588C2×D4—2124no—
589C2×D4C2×C22⋊D5314yes—
590C2×D4C23×D5312yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—1064no—
603C22×C4—1064no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1064no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4C2×C22⋊D5312yes—
612C22×C4C2×C22⋊D5312yes—
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C22×C4C2×C22⋊D5311yescharacteristic
617C22×C4C23×D5312yes—
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620D8—1068no—
621M16—1068no—
622C2×C8—534no—
623C2×C8—532no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—532no—
627C2×C8—1068no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8—1062no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—532no—
640C4⋊C4—1061no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1064no—
644C4⋊C4—1064no—
645C4⋊C4—1064no—
646C4⋊C4C2×C22⋊D5314yes—
647C4⋊C4C23×D5312yes—
648C4⋊C4C23×D5312yes—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4C2×C22⋊D5314yes—
658C22⋊C4C2×C22⋊D5314yes—
659C42—24no—
660C42C2×C22⋊D5312yes—
661C42C23×D5312yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1062no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23#1313324214yes—
676C23C22×C22⋊D5312yes—
677C23C22×C22⋊D5312yes—
678C23C22×C22⋊D5311yescharacteristic
679Q8—2128no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—1062no—
687D4—1062no—
688D4—2128no—
689D4—2128no—
690D4—2122no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—2128no—
713C2×C4—2128no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2128no—
718C2×C4C22×C22⋊D5312yes—
719C2×C4C22×C22⋊D5312yes—
720C2×C4C22×C22⋊D5312yes—
721C2×C4C22×C22⋊D5312yes—
722C2×C4C22×C22⋊D5311yescharacteristic
723C2×C4#41×D5312yes—
724C2×C4#1313326412yes—
725C2×C4C24×D5311yescharacteristic
726C8—534no—
727C8—1062no—
728C8—1062no—
729C8—1062no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—4244no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22#1681127212yes—
746C22C2×#1313324214yes—
747C22C2×#1313324212yes—
748C22#1681143412yes—
749C22C23×C22⋊D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—2122no—
758C4—2122no—
759C4—2122no—
760C4#1681127212yes—
761C4C2×#41×D5311yescharacteristic
762C4C2×#1313326411yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—4242no—
767C2#2028717914yesdirect product factor
768C2C2×#1681127211yescharacteristic
769C2C22×#1313324211yescharacteristic
770C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53C2×#3345
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16811277C2semidirect
2. #20287179C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16810941C2semidirect
5. C2×#16810939C2semidirect
6. C2×#16810947C2semidirect
7. C2×#16810934C2semidirect
8. C2×#16810920C2semidirect
9. C2×#16810913C2semidirect
10. C2×#16810874C2semidirect
11. C2×#16810857C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810666C2semidirect
15. C22×#13133148C2semidirect
16. C2×C53×#553C2semidirect
22. #16811277C22semidirect
32. #16811033C22semidirect
33. #16810947C22semidirect
34. #16810941C22semidirect
35. #16810939C22semidirect
36. #16810934C22semidirect
37. #16810920C22semidirect
38. #16810913C22semidirect
39. #16810874C22semidirect
40. #16810857C22semidirect
41. #16810733C22semidirect
42. #16810695C22semidirect
43. #16810666C22semidirect
53. C2×#13133148C22semidirect
65. C53×#553C22semidirect
271. C2×#88322#41semidirect
343. #88322C2×#41semidirect
378. C2×#553D53semidirect
397. C2×C53#3345semidirect
407. #553C2×D53semidirect
462. C53C2×#3345semidirect
767. C2#20287179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112772
#202871792
C2×#168110332
C2×#168109412
C2×#168109392
C2×#168109472
C2×#168109342
C2×#168109202
C2×#168109132
C2×#168108742
C2×#168108572
C2×#168107332
C2×#168106952
C2×#168106662
C22×#131331482
C2×C53×#5532
C2×#334553