Finite Group Databasebeta

← C2×#20286835 #28260804

Subgroups — C2×#20286835 #28260804

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811294C211yesmaximal, characteristic
2#20286835C2116yesmaximal, direct product factor
3C2×#16810989C211yesmaximal, characteristic, complemented
4C2×#16810941C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810854C211yesmaximal, characteristic, complemented
9C2×#16810823C211yesmaximal, characteristic, complemented
10C2×#16810783C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810617C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811294—24no—
25#16811294C2218yes—
26C2×#13133214C2211yescharacteristic
27C2×#13133213—21no—
28C2×#13133191C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C2×#13133190—21no—
31C2×#13133190—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133179—21no—
34#16810989C2218yescomplemented
35#16810947C2218yescomplemented
36#16810941C2218yescomplemented
37#16810927C2218yescomplemented
38#16810871C2218yescomplemented
39#16810854C2218yescomplemented
40#16810823C2218yescomplemented
41#16810783C2218yescomplemented
42#16810783C2218yescomplemented
43#16810728C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810622C2218yescomplemented
50#16810617C2218yescomplemented
51C2×#13133141C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133137C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#552—24no—
65C53×#552C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53—21no—
68C2×#125×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×#117×C53—21no—
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—24no—
81C2×#11719945—42no—
82C2×#11719945—42no—
83C2×#11719945C2314yes—
84C2×#11719945C2314yes—
85C22×Dic106C2311yescharacteristic
86C22×D212—21no—
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C2×#11719925—24no—
97C2×#11719925C2314yes—
98C2×#11719924—42no—
99C2×#11719924—42no—
100C2×#11719924C2314yes—
101C2×#11719924C2314yes—
102C2×#11719917—42no—
103C2×#11719917C2314yes—
104C22×#88322—42no—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C22×#88322C2314yes—
110#13133214—22no—
111#13133214C2314yes—
112#13133213—28no—
113#13133191—22no—
114#13133191—22no—
115#13133191C2314yes—
116#13133191C2314yes—
117#13133190—28no—
118#13133190—28no—
119C4×Dic106—22no—
120C4×Dic106C2314yes—
121#13133179—28no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×C4×Dic53—21no—
127#13133150C2314yes—
128#13133148C2314yes—
129#13133148C2314yes—
130C4⋊#88322C2314yes—
131#13133141C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133137C2314yes—
136#13133137C2314yes—
137#13133137C2314yes—
138#13133137C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141C22⋊#88322C2314yes—
142C22⋊#88322C2314yes—
143#13133128C2314yes—
144C22×Q8×C53C2311yescharacteristic
145C22×D4×C53D411yescharacteristic
146C23×C4×C53—21no—
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149#126×C53—28no—
150#125×C53—28no—
151#125×C53—22no—
152#125×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—22no—
155C22⋊Q8×C53—22no—
156C22⋊Q8×C53C2314yes—
157C22⋊Q8×C53C2314yes—
158C4×Q8×C53—22no—
159C4×Q8×C53C2314yes—
160C4×D4×C53D414yes—
161C4×D4×C53C2314yes—
162#117×C53—28no—
163#117×C53—22no—
164#117×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2314yes—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53D411yescharacteristic
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C42×C53—21no—
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—42no—
194C2×D4×C53C2×D414yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—44no—
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—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—82no—
221C2×C22⋊D53—82no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224#11719945—28no—
225#11719945—28no—
226#11719945—44no—
227#11719945—44no—
228#11719945—48no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—24no—
235C2×D212—21no—
236C2×D212—21no—
237C2×D212—24no—
238C2×D212—44no—
239C2×D212—82no—
240C2×D212C2412yes—
241C2×D212C2412yes—
242C2×C4×D53—24no—
243C2×C4×D53—24no—
244C2×C4×D53—44no—
245C2×C4×D53—44no—
246C2×Dic106—21no—
247C2×Dic106—22no—
248C2×Dic106#4114yes—
249C2×Dic106C2412yes—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—24no—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2×D414yes—
260C4⋊C4×C53C2412yes—
261C4⋊C4×C53C2412yes—
262C4⋊C4×C53C2412yes—
263C22⋊C4×C53—24no—
264C22⋊C4×C53—24no—
265C22⋊C4×C53—24no—
266C22⋊C4×C53C2×D414yes—
267C22⋊C4×C53C2×D414yes—
268C42×C53—24no—
269C42×C53—24no—
270C42×C53C2×D412yes—
271C42×C53C2412yes—
272#11719925—28no—
273#11719924—44no—
274#11719924—44no—
275#11719921—24no—
276#11719921—24no—
277C4⋊Dic53—21no—
278C4⋊Dic53C2412yes—
279#11719919—24no—
280C4×Dic53—24no—
281#11719917—44no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322—44no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53C22×D412yes—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308Q8×C53—22no—
309Q8×C53—22no—
310Q8×C53—42no—
311D4×C53—44no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—24no—
317C2×C4×C53—24no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—48no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C2×#4112yes—
337C2×C4×C53H(5,𝔽2)12yes—
338C2×C4×C53C2511yescharacteristic
339C22⋊D53—48no—
340C22⋊D53—48no—
341C22⋊D53—84no—
342C22⋊D53—84no—
343C2×Dic53—24no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—42no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—22no—
351D212—48no—
352D212—42no—
353D212—42no—
354D212—84no—
355C4×D53—48no—
356C4×D53—48no—
357Dic106—24no—
358Dic106—22no—
359Dic106C2×#4114yes—
360#88322—22no—
361#88322—22no—
362#88322—22no—
363#88322—22no—
364C2×#3317—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53—44no—
373C22×C53#54612yes—
374C22×C53#57512yes—
375C22×C53#57712yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53#54612yes—
394C4×C53C22×#4111yescharacteristic
395C4×C53C2×H(5,𝔽2)11yescharacteristic
396Dic53—24no—
397Dic53—42no—
398C2×#552D5311yescharacteristic, complemented
399C2×#550—531no—
400#3317—5316no—
401C2×#490—531no—
402C2×#481—531no—
403C2×#482—531no—
404C2×#479—531no—
405C2×#468—531no—
406C2×#465—531no—
407C2×#460—531no—
408C2×#452—531no—
409C2×#452—531no—
410C2×#441—531no—
411C2×#435—531no—
412C2×#417—531no—
413C2×#416—531no—
414C2×C53—42no—
415C2×C53—42no—
416C2×C53#331714yescomplemented
417C2×C53C2×#54611yescharacteristic
418C2×C53C2×#57511yescharacteristic
419C2×C53C2×#57711yescharacteristic
420D53—82no—
421D53—82no—
422C22×#41—531no—
423C22×#41—531no—
424C22×Q16—531no—
425C22×SD16—531no—
426C22×SD16—531no—
427C22×M16—531no—
428C23×C8—531no—
429#552—24no—
430#552C2×D5318yescomplemented
431#550—538no—
432#550—1064no—
433C2×#127—531no—
434C2×#127—1061no—
435C2×#126—21no—
436C2×#125—21no—
437C2×#125C2×D5311yescharacteristic
438C2×#123—21no—
439C2×C22⋊Q8C2×D5311yescharacteristic
440C2×C22⋊Q8C2×D5311yescharacteristic
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8—531no—
446C2×C4×Q8C2×D5311yescharacteristic
447C2×C4×D4—1061no—
448C2×C4×D4C2×D5311yescharacteristic
449C2×#117—21no—
450C2×#117C2×D5311yescharacteristic
451C22×C4⋊C4C2×D5311yescharacteristic
452#490—538no—
453#482—538no—
454#481—538no—
455#479—538no—
456#468—538no—
457#465—538no—
458#460—538no—
459#452—538no—
460#452—538no—
461#441—538no—
462#435—538no—
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8—531no—
467#417—538no—
468#416—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×#97—531no—
482C53C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—534no—
485C2×#41—1064no—
486C2×#41—1064no—
487C2×#41—1062no—
488C2×#41—1062no—
489C2×#41—2122no—
490C2×#41—2122no—
491C22×Q8—531no—
492C22×Q8C22×D5311yescharacteristic
493C22×D4—531no—
494C22×D4—531no—
495C22×D4—1061no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4—1061no—
501C22×D4C22⋊D5311yescharacteristic
502C23×C4—21no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×Q16—534no—
508C2×Q16—1064no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—2122no—
512C2×SD16—2122no—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8—534no—
520C22×C8—2122no—
521#127—534no—
522#127—1068no—
523#127—1062no—
524#126—28no—
525#125—28no—
526#125—22no—
527#125C22×D5314yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8C22×D5314yes—
532C22⋊Q8C22×D5314yes—
533#121—534no—
534#121—534no—
535#121—1062no—
536#121—1062no—
537#121—1068no—
538#121—1068no—
539C4×Q8—22no—
540C4×Q8—534no—
541C4×Q8—1062no—
542C4×Q8C22×D5314yes—
543C4×D4—1068no—
544C4×D4C22⋊D5314yes—
545C4×D4C22×D5314yes—
546#117—22no—
547#117—28no—
548#117C22×D5314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4C22⋊D5311yescharacteristic
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5314yes—
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4C22⋊D5311yescharacteristic
569C2×C22⋊C4C22⋊D5311yescharacteristic
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#102—534no—
583#102—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590#97—534no—
591C24—1061no—
592C24—1061no—
593C24C2×C22⋊D5311yescharacteristic
594C24C2×C22⋊D5311yescharacteristic
595#41—1068no—
596#41—1068no—
597#41—2124no—
598#41—2124no—
599#41—2128no—
600#41—2128no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—534no—
605C2×Q8—532no—
606C2×Q8—1061no—
607C2×Q8—1062no—
608C2×Q8C23×D5312yes—
609C2×D4—42no—
610C2×D4—532no—
611C2×D4—532no—
612C2×D4—1064no—
613C2×D4—1064no—
614C2×D4—1064no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1061no—
619C2×D4—1061no—
620C2×D4—1062no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—4242no—
627C2×D4—2124no—
628C2×D4—2124no—
629C2×D4—2124no—
630C2×D4C2×C22⋊D5314yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—1064no—
644C22×C4—1064no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4C2×C22⋊D5312yes—
648C22×C4C2×C22⋊D5312yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—1068no—
657SD16—2124no—
658SD16—2124no—
659M16—2124no—
660C2×C8—532no—
661C2×C8—532no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—1062no—
668C2×C8—2124no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—532no—
679C4⋊C4—1061no—
680C4⋊C4—1064no—
681C4⋊C4C2×C22⋊D5314yes—
682C4⋊C4C23×D5312yes—
683C4⋊C4C23×D5312yes—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4C2×C22⋊D5314yes—
691C22⋊C4C2×C22⋊D5314yes—
692C42—24no—
693C42—24no—
694C42—1064no—
695C42C2×C22⋊D5312yes—
696C42C23×D5312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—1062no—
704C23—1062no—
705C23—2122no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23C22×C22⋊D5312yes—
712C23C22×C22⋊D5312yes—
713C23C22×C22⋊D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—534no—
718Q8—1062no—
719Q8—1064no—
720D4—44no—
721D4—1062no—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—4244no—
726D4—4244no—
727D4—4244no—
728D4—2128no—
729D4—2128no—
730D4—2128no—
731D4—2122no—
732D4—2122no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—1062no—
753C2×C4—1064no—
754C2×C4—1062no—
755C2×C4—2128no—
756C2×C4—2128no—
757C2×C4—2122no—
758C2×C4C22×C22⋊D5312yes—
759C2×C4C22×C22⋊D5312yes—
760C2×C4C22×C22⋊D5312yes—
761C2×C4C22×C22⋊D5312yes—
762C2×C4C22×C22⋊D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326312yes—
765C2×C4C24×D5311yescharacteristic
766C8—1062no—
767C8—1062no—
768C8—1062no—
769C8—1062no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—4244no—
779C22—4244no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22#1681126112yes—
787C22#1681142112yes—
788C22#1681143112yes—
789C22C23×C22⋊D5311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—1064no—
799C4—2122no—
800C4#1681126112yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326311yescharacteristic
803C2—42no—
804C2—42no—
805C2—4242no—
806C2—4242no—
807C2#2028683514yesdirect product factor
808C2C2×#1681126111yescharacteristic
809C2C2×#1681142111yescharacteristic
810C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC2×#16811294C2
hypercenterC2×#552D53
hypocenterC53C2×#3317
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #20286835C2direct (N × H)
3. C2×#16810989C2semidirect
4. C2×#16810941C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810854C2semidirect
9. C2×#16810823C2semidirect
10. C2×#16810783C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810617C2semidirect
16. C2×C53×#552C2semidirect
34. #16810989C22semidirect
35. #16810947C22semidirect
36. #16810941C22semidirect
37. #16810927C22semidirect
38. #16810871C22semidirect
39. #16810854C22semidirect
40. #16810823C22semidirect
41. #16810783C22semidirect
42. #16810783C22semidirect
43. #16810728C22semidirect
44. #16810695C22semidirect
49. #16810622C22semidirect
50. #16810617C22semidirect
65. C53×#552C22semidirect
398. C2×#552D53semidirect
416. C2×C53#3317semidirect
430. #552C2×D53semidirect
482. C53C2×#3317semidirect
807. C2#20286835direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112942
#202868352
C2×#168109892
C2×#168109412
C2×#168109472
C2×#168109272
C2×#168108712
C2×#168108542
C2×#168108232
C2×#168107832
C2×#168107282
C2×#168106952
C2×#168106222
C2×#168106172
C2×C53×#5522
C2×#331753