Finite Group Databasebeta

← C2×#20284767 #28252144

Subgroups — C2×#20284767 #28252144

Order 13568.

2602 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811158C211yesmaximal, characteristic, complemented
2C2×C4×D4×D53C211yesmaximal, characteristic, complemented
3#20284767C2116yesmaximal, direct product factor
4C2×#16810960C211yesmaximal, characteristic, complemented
5C2×#16810943C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810839C211yesmaximal, characteristic, complemented
8C2×#16810838C211yesmaximal, characteristic, complemented
9C2×#16810775C211yesmaximal, characteristic, complemented
10C2×#16810758C211yesmaximal, characteristic
11C2×#16810714C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810705C211yesmaximal, characteristic, complemented
14C2×#16810703C211yesmaximal, characteristic, complemented
15C2×#16810675C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C23×C4×D53—21no—
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23#16811158—24no—
24#16811158C2218yescomplemented
25C2×#13133212—21no—
26C2×#13133205C2211yescharacteristic, complemented
27C2×#13133202—21no—
28C2×#13133197C2211yescharacteristic
29C2×#13133192C2211yescharacteristic
30C2×#13133182C2211yescharacteristic, complemented
31C2×C4×D212C2211yescharacteristic
32C2×D4×Dic53C2211yescharacteristic
33C2×#13133179—21no—
34C2×#13133179C2211yescharacteristic
35C2×#13133179C2211yescharacteristic, complemented
36C2×C4×C22⋊D53—21no—
37C2×#13133177—21no—
38C4×D4×D53—24no—
39C4×D4×D53C2218yescomplemented
40C2×#13133175—21no—
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C22⋊C4×D53—21no—
43C2×C42×D53C2211yescharacteristic
44#16810960C2218yescomplemented
45#16810943C2218yescomplemented
46#16810920C2218yescomplemented
47#16810839C2218yescomplemented
48#16810838C2218yescomplemented
49#16810775C2218yescomplemented
50#16810758C2218yes—
51#16810714C2218yescomplemented
52#16810710C2218yescomplemented
53#16810705C2218yescomplemented
54#16810703C2218yescomplemented
55#16810675C2218yescomplemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×#125×C53C2211yescharacteristic, complemented
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C2×D4×D53—24no—
84C2×D4×D53—24no—
85C2×D4×D53—22no—
86C2×D4×D53C2314yes—
87C23×Dic53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—28no—
93C22×C4×D53—48no—
94C22×C4×D53D411yescharacteristic
95C22×C4×D53D411yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C2×#11719913—24no—
98C2×#11719913C2314yes—
99C2×#11719923—24no—
100C2×#11719923C2314yes—
101C2×D424—24no—
102C2×D424C2314yes—
103C2×#11719922—24no—
104C2×#11719922C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133212—28no—
108#13133205—22no—
109#13133205C2314yescomplemented
110#13133202—28no—
111#13133197—22no—
112#13133197C2314yes—
113#13133192—22no—
114#13133192C2314yes—
115#13133182—22no—
116#13133182C2314yescomplemented
117C4×D212—22no—
118C4×D212C2314yes—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121#13133179—22no—
122#13133179—22no—
123#13133179—28no—
124#13133179C2314yes—
125#13133179C2314yescomplemented
126C4×C22⋊D53—28no—
127#13133177—28no—
128#13133175—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C22⋊C4×D53—28no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53C2311yescharacteristic
148C42×D53D414yes—
149C42×D53C2314yes—
150#13133150C2314yescomplemented
151#13133148C2314yescomplemented
152C4⋊#88322C2314yescomplemented
153#13133142C2314yescomplemented
154#13133140C2314yescomplemented
155#13133139C2314yescomplemented
156#13133137C2314yes—
157#13133137C2314yes—
158#13133137C2314yescomplemented
159#13133129C2314yes—
160#13133129C2314yes—
161C8×Dic53C2314yescomplemented
162C8×Dic53C2314yescomplemented
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#125×C53—22no—
168#125×C53C2314yescomplemented
169C4×D4×C53—22no—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yescomplemented
179#106×C53C2314yescomplemented
180C4⋊C8×C53C2314yescomplemented
181#102×C53C2314yes—
182#102×C53C2314yes—
183C24×C53—21no—
184C23×D53—28no—
185C23×D53—21no—
186C23×D53—24no—
187C23×D53—21no—
188C23×D53—44no—
189C23×D53—44no—
190C23×D53C2×D411yescharacteristic
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53#4114yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—28no—
204C2×C22⋊D53—24no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—44no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212D4×D53—216no—
213D4×D53—28no—
214D4×D53—28no—
215C2×D212—21no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—24no—
220C2×D212—21no—
221C2×D212—44no—
222C2×D212#4114yes—
223C2×D212C2412yes—
224C2×D212C2412yes—
225C2×C4×D53—24no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—432no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2×D414yes—
240C2×C4×D53C2×D414yes—
241C2×C4×D53C2412yes—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106C2412yes—
246C2×C8×C53—22no—
247C2×C8×C53—22no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C42×C53C2×D412yes—
260C42×C53C2412yes—
261C22⋊Dic53—24no—
262#11719923—28no—
263#11719922—28no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2412yes—
274#11719919—24no—
275#11719919—24no—
276C4×Dic53—24no—
277C4×Dic53C2×D412yes—
278C4×Dic53C2×D414yes—
279C4×Dic53C2×D414yes—
280C4×Dic53C2412yes—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285D424—28no—
286#11719913—28no—
287C23×C53—24no—
288C23×C53—22no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—216no—
295C22×D53—24no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—48no—
299C22×D53—432no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—48no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53#13514yes—
307C22×D53C22×D412yes—
308D4×C53—24no—
309D4×C53—22no—
310D4×C53C2×#4114yes—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—48no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4112yes—
324C2×C4×C53C2×#4112yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—216no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—48no—
334C2×Dic53AGL(1,ℤ/8)14yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—24no—
339D212—22no—
340D212—22no—
341D212—22no—
342D212—48no—
343D212—42no—
344D212C2×#4114yes—
345C4×D53—28no—
346C4×D53—24no—
347C4×D53—22no—
348C4×D53—22no—
349C4×D53—28no—
350C4×D53—48no—
351C4×D53—48no—
352C4×D53—48no—
353C4×D53—48no—
354Dic106—22no—
355Dic106—22no—
356Dic106—42no—
357C8×C53—22no—
358C8×C53—22no—
359#88322—22no—
360#88322—22no—
361C2×#3105—531nomaximal, Sylow
362C22×C53—24no—
363C22×C53—48no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53#52512yes—
367C22×C53C2×#13512yes—
368C22×C53C2×AGL(1,ℤ/8)12yes—
369C22×C53C23×D411yescharacteristic
370C2×D53—28no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—24no—
374C2×D53—432no—
375C2×D53—48no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—84no—
382C2×D53C2×#13514yes—
383C4×C53—22no—
384C4×C53—22no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53#52512yes—
389C4×C53C22×#4111yescharacteristic
390C4×C53C22×#4111yescharacteristic
391Dic53—22no—
392Dic53—22no—
393Dic53—42no—
394Dic53—42no—
395Dic53C2×AGL(1,ℤ/8)14yes—
396C2×#529—531no—
397C22×C4×D4—531no—
398#3105—5316no—
399C2×#484—531no—
400C2×#481—531no—
401C2×#478—531no—
402C2×#478D5311yescharacteristic, complemented
403C2×#463—531no—
404C2×#463—531no—
405C2×#450—531no—
406C2×#447—531no—
407C2×C4×SD16—531no—
408C2×C4×SD16—531no—
409C2×C4×D8—531no—
410C2×C4×D8—531no—
411C2×#431—531no—
412C2×C53—44no—
413C2×C53#310514yescomplemented
414C2×C53C2×#52511yescharacteristic
415C2×C53C22×#13511yescharacteristic
416C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
417D53—24no—
418D53—44no—
419D53—82no—
420C23×D4—531no—
421C24×C4—1061no—
422C22×SD16—531no—
423C22×SD16—531no—
424C22×D8—531no—
425C22×D8—531no—
426#529—538no—
427#529—1064no—
428C2×#126—1061no—
429C2×#125C2×D5311yescharacteristic, complemented
430C2×#124—531no—
431C2×#123—1061no—
432C2×C22⋊Q8—531no—
433C2×#121—531no—
434C2×C4×Q8—531no—
435C2×C4×D4—531no—
436C2×C4×D4—538no—
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1064no—
442C2×C4×D4—1061no—
443C2×C4×D4—1061no—
444C2×C4×D4C2×D5311yescharacteristic
445C2×#117—1061no—
446C22×C4⋊C4—531no—
447C22×C22⋊C4—1061no—
448C22×C42—531no—
449#484—538no—
450#481—538no—
451#478—538no—
452#478C2×D5318yescomplemented
453#463—538no—
454#463—538no—
455#450—538no—
456#447—538no—
457C4×SD16—538no—
458C4×SD16—538no—
459C4×D8—538no—
460C4×D8—538no—
461#431—538no—
462C2×#107—531no—
463C2×#107C2×D5311yescharacteristic, complemented
464C2×#106—531no—
465C2×#106C2×D5311yescharacteristic, complemented
466C2×C4⋊C8—531no—
467C2×C4⋊C8C2×D5311yescharacteristic, complemented
468C2×#103—531no—
469C2×#103—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102C2×D5311yescharacteristic
475C2×#102C2×D5311yescharacteristic
476C2×C22⋊C8—531no—
477C2×C22⋊C8—531no—
478C2×C4×C8—531no—
479C2×C4×C8—531no—
480C53C2×#310511yescharacteristic, complemented, Sylow
481C25—1061no—
482C22×Q8—531no—
483C22×D4—534no—
484C22×D4—531no—
485C22×D4—531no—
486C22×D4—1061no—
487C22×D4—1062no—
488C22×D4—1061no—
489C22×D4—1064no—
490C22×D4—1064no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—531no—
494C23×C4—531no—
495C23×C4—531no—
496C23×C4—1061no—
497C23×C4—1061no—
498C23×C4—1068no—
499C23×C4—1061no—
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4—2128no—
503C2×SD16—534no—
504C2×SD16—534no—
505C2×SD16—1064no—
506C2×SD16—1064no—
507C2×D8—534no—
508C2×D8—534no—
509C2×D8—1064no—
510C2×D8—1064no—
511C22×C8—531no—
512C22×C8—531no—
513C22×C8C22×D5311yescharacteristic
514C22×C8C22×D5311yescharacteristic
515#126—1068no—
516#125—22no—
517#125C22×D5314yescomplemented
518#124—534no—
519#124—1062no—
520#123—1068no—
521C22⋊Q8—534no—
522C22⋊Q8—1062no—
523#121—534no—
524#121—1062no—
525C4×Q8—534no—
526C4×Q8—1062no—
527C4×D4—22no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—534no—
531C4×D4—534no—
532C4×D4—1068no—
533C4×D4—1062no—
534C4×D4—1062no—
535C4×D4—1068no—
536C4×D4—1062no—
537C4×D4—1068no—
538C4×D4—1062no—
539C4×D4C22×D5314yes—
540#117—1068no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—534no—
545C2×C4⋊C4—1062no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4C22×D5311yescharacteristic
550C2×C4⋊C4C22×D5311yescharacteristic
551C2×C4⋊C4C22×D5311yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1068no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C42—531no—
563C2×C42—531no—
564C2×C42—531no—
565C2×C42—534no—
566C2×C42—534no—
567C2×C42—1061no—
568C2×C42C22×D5311yescharacteristic
569#107—534no—
570#107C22×D5314yescomplemented
571#106—534no—
572#106C22×D5314yescomplemented
573C4⋊C8—534no—
574C4⋊C8C22×D5314yescomplemented
575#103—534no—
576#103—534no—
577#102—534no—
578#102—534no—
579#102—534no—
580#102—534no—
581#102C22×D5314yes—
582#102C22×D5314yes—
583C22⋊C8—534no—
584C22⋊C8—534no—
585C4×C8—534no—
586C4×C8—534no—
587C24—21no—
588C24—531no—
589C24—1064no—
590C24—1068no—
591C24—1061no—
592C24—1061no—
593C24—2124no—
594C24—2124no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—534no—
602C2×D4—532no—
603C2×D4—532no—
604C2×D4—1064no—
605C2×D4—1064no—
606C2×D4—1068no—
607C2×D4—10616no—
608C2×D4—1068no—
609C2×D4—1068no—
610C2×D4—1061no—
611C2×D4—1061no—
612C2×D4—1062no—
613C2×D4—1062no—
614C2×D4—1062no—
615C2×D4—2124no—
616C2×D4#1171994914yes—
617C2×D4C23×D5312yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—531no—
624C22×C4—531no—
625C22×C4—531no—
626C22×C4—534no—
627C22×C4—532no—
628C22×C4—534no—
629C22×C4—532no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1064no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1062no—
637C22×C4—1062no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1064no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4—2124no—
644C22×C4—21232no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4D4×D5311yescharacteristic
648C22×C4D4×D5311yescharacteristic
649C22×C4C23×D5311yescharacteristic
650SD16—1068no—
651SD16—1068no—
652D8—1068no—
653D8—1068no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1062no—
659C2×C8—1062no—
660C2×C8C23×D5312yes—
661C2×C8C23×D5312yes—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—532no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1061no—
672C4⋊C4C23×D5312yes—
673C4⋊C4C23×D5312yes—
674C4⋊C4C23×D5312yes—
675C22⋊C4—24no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—534no—
685C42—532no—
686C42—534no—
687C42—532no—
688C42—1064no—
689C42D4×D5312yes—
690C42C23×D5312yes—
691C23—24no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—534no—
696C23—532no—
697C23—10616no—
698C23—1062no—
699C23—1062no—
700C23—1064no—
701C23—1062no—
702C23—1062no—
703C23—2128no—
704C23—2128no—
705C23—21232no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23C2×D4×D5311yescharacteristic
712Q8—1062no—
713Q8—1062no—
714Q8—2122no—
715D4—24no—
716D4—22no—
717D4—534no—
718D4—10616no—
719D4—1064no—
720D4—1062no—
721D4—1062no—
722D4—1062no—
723D4—2128no—
724D4—2122no—
725D4C2×#1171994914yes—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—534no—
736C2×C4—532no—
737C2×C4—532no—
738C2×C4—532no—
739C2×C4—1068no—
740C2×C4—1068no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1064no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—2128no—
749C2×C4—2128no—
750C2×C4—2128no—
751C2×C4—2128no—
752C2×C4—2128no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4C2×D4×D5312yes—
756C2×C4C2×D4×D5312yes—
757C2×C4C2×D4×D5311yescharacteristic
758C2×C4#41×D5312yes—
759C2×C4C2×#1171994912yes—
760C2×C4C24×D5311yescharacteristic
761C8—22no—
762C8—22no—
763C8—1062no—
764C8—1062no—
765C22—24no—
766C22—48no—
767C22—42no—
768C22—42no—
769C22—534no—
770C22—1068no—
771C22—1062no—
772C22—1062no—
773C22—1064no—
774C22—4244no—
775C22—21232no—
776C22—2122no—
777C22—2122no—
778C22—2122no—
779C22—2128no—
780C22—2122no—
781C22—2122no—
782C22#1681113612yes—
783C22#135×D5312yes—
784C22AGL(1,ℤ/8)×D5312yes—
785C22C22×D4×D5311yescharacteristic
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—534no—
792C4—1062no—
793C4—1062no—
794C4—2122no—
795C4—2122no—
796C4#1681113612yes—
797C4C2×#41×D5311yescharacteristic
798C4C22×#1171994911yescharacteristic
799C2—44no—
800C2—1064no—
801C2—4242no—
802C2—2124no—
803C2#2028476714yesdirect product factor
804C2C2×#1681113611yescharacteristic
805C2C2×#135×D5311yescharacteristic
806C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC2×#16810758C2
hypercenterC2×#478D53
hypocenterC53C2×#3105
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811158C2semidirect
2. C2×C4×D4×D53C2semidirect
3. #20284767C2direct (N × H)
4. C2×#16810960C2semidirect
5. C2×#16810943C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810839C2semidirect
8. C2×#16810838C2semidirect
9. C2×#16810775C2semidirect
11. C2×#16810714C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810705C2semidirect
14. C2×#16810703C2semidirect
15. C2×#16810675C2semidirect
16. C2×C53×#478C2semidirect
24. #16811158C22semidirect
26. C2×#13133205C22semidirect
30. C2×#13133182C22semidirect
35. C2×#13133179C22semidirect
39. C4×D4×D53C22semidirect
44. #16810960C22semidirect
45. #16810943C22semidirect
46. #16810920C22semidirect
47. #16810839C22semidirect
48. #16810838C22semidirect
49. #16810775C22semidirect
51. #16810714C22semidirect
52. #16810710C22semidirect
53. #16810705C22semidirect
54. #16810703C22semidirect
55. #16810675C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133148C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
67. C2×C8×Dic53C22semidirect
68. C2×C8×Dic53C22semidirect
69. C2×#125×C53C22semidirect
71. C53×#478C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×C4⋊C8×C53C22semidirect
109. #13133205C23semidirect
116. #13133182C23semidirect
125. #13133179C23semidirect
150. #13133150C23semidirect
151. #13133148C23semidirect
152. C4⋊#88322C23semidirect
153. #13133142C23semidirect
154. #13133140C23semidirect
155. #13133139C23semidirect
158. #13133137C23semidirect
161. C8×Dic53C23semidirect
162. C8×Dic53C23semidirect
168. #125×C53C23semidirect
178. #107×C53C23semidirect
179. #106×C53C23semidirect
180. C4⋊C8×C53C23semidirect
402. C2×#478D53semidirect
413. C2×C53#3105semidirect
429. C2×#125C2×D53semidirect
452. #478C2×D53semidirect
463. C2×#107C2×D53semidirect
465. C2×#106C2×D53semidirect
467. C2×C4⋊C8C2×D53semidirect
480. C53C2×#3105semidirect
517. #125C22×D53semidirect
570. #107C22×D53semidirect
572. #106C22×D53semidirect
574. C4⋊C8C22×D53semidirect
803. C2#20284767direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111582
C2×C4×D4×D532
#202847672
C2×#168109602
C2×#168109432
C2×#168109202
C2×#168108392
C2×#168108382
C2×#168107752
C2×#168107582
C2×#168107142
C2×#168107102
C2×#168107052
C2×#168107032
C2×#168106752
C2×C53×#4782
C2×#310553