Finite Group Databasebeta

← C2×#20284862 #28252214

Subgroups — C2×#20284862 #28252214

Order 13568.

2430 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic, complemented
2C2×C4×#11719947C211yesmaximal, characteristic, complemented
3#20284862C2116yesmaximal, direct product factor
4C2×#16810949C211yesmaximal, characteristic, complemented
5C2×#16810945C211yesmaximal, characteristic, complemented
6C2×#16810907C211yesmaximal, characteristic, complemented
7C2×#16810901C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810816C211yesmaximal, characteristic, complemented
10C2×#16810769C211yesmaximal, characteristic, complemented
11C2×#16810765C211yesmaximal, characteristic, complemented
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×#16810678C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719947C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811170—24no—
23#16811170C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26C2×#13133203—21no—
27C2×#13133192C2211yescharacteristic
28C2×#13133190—21no—
29C2×#13133188C2211yescharacteristic
30C4×#11719947—24no—
31C4×#11719947C2218yescomplemented
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133182C2211yescharacteristic
34C2×C4×D212C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×C4×C22⋊D53—21no—
37C2×C4×C22⋊D53—21no—
38C2×#13133177—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133173—21no—
41C22×C4×Dic53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810949C2218yescomplemented
44#16810945C2218yescomplemented
45#16810907C2218yescomplemented
46#16810901C2218yescomplemented
47#16810822C2218yescomplemented
48#16810816C2218yescomplemented
49#16810769C2218yescomplemented
50#16810765C2218yescomplemented
51#16810733C2218yescomplemented
52#16810725C2218yescomplemented
53#16810723C2218yescomplemented
54#16810678C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C2×#11719947—24no—
80C2×#11719947—22no—
81C2×#11719947—24no—
82C2×#11719947C2314yes—
83C22×Dic106—21no—
84C22×Dic106C2311yescharacteristic
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53D411yescharacteristic
95C22×C4×D53D411yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C2×#11719913—24no—
98C2×#11719913C2314yes—
99C2×#11719923—24no—
100C2×#11719923C2314yes—
101C2×#11719922—24no—
102C2×#11719922C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133213—22no—
108#13133213C2314yes—
109#13133203—28no—
110#13133192—22no—
111#13133192C2314yes—
112#13133190—28no—
113#13133188—22no—
114#13133188C2314yes—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117#13133182—22no—
118#13133182C2314yes—
119C4×D212—22no—
120C4×D212C2314yes—
121D4×Dic53—22no—
122D4×Dic53C2314yes—
123C4×C22⋊D53—28no—
124C4×C22⋊D53—28no—
125#13133177—28no—
126#13133175—22no—
127#13133175C2314yes—
128#13133173—28no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—28no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53D411yescharacteristic
145C2×C4×Dic53C2311yescharacteristic
146C42×D53D414yes—
147C42×D53C2314yes—
148#13133151C2314yes—
149#13133150C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160#13133129C2314yes—
161#13133128C2314yes—
162C22×D4×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C23×C4×C53—21no—
166C2×D8×C53—24no—
167C2×D8×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4×D4×C53—22no—
171C4×D4×C53—22no—
172C4×D4×C53C2314yes—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C42×C53C2311yescharacteristic
179#106×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182#97×C53C2314yes—
183C24×C53—21no—
184C24×C53—21no—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53#4114yescomplemented
193C2×D4×C53C2412yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53—44no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—28no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C22×Dic53—28no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—24no—
218C22×Dic53—44no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222#11719947—216no—
223#11719947—28no—
224#11719947—28no—
225#11719945—432no—
226C2×D212—22no—
227C2×D212—22no—
228C2×D212—24no—
229C2×D212—21no—
230C2×D212—44no—
231C2×D212C2412yes—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—42no—
237C2×C4×D53—44no—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2×D414yes—
240C2×C4×D53C2×D414yes—
241C2×C4×D53C2412yes—
242C2×Dic106—21no—
243C2×Dic106—22no—
244C2×Dic106—24no—
245C2×Dic106—44no—
246C2×Dic106#4114yescomplemented
247C2×Dic106C2412yes—
248D8×C53—28no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53C2412yes—
252C2×C8×C53C2412yes—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C22⋊C4×C53—24no—
258C22⋊C4×C53—24no—
259C42×C53C2×D412yes—
260C42×C53C2412yes—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263#11719923—28no—
264#11719922—28no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2×D414yes—
280C4×Dic53C2×D414yes—
281C4×Dic53C2412yes—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286#11719913—28no—
287C23×C53—24no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53C22×D412yes—
304D4×C53—24no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—42no—
309D4×C53C2×#4114yescomplemented
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—48no—
315C2×C4×C53—48no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53C2×#4112yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—216no—
325C22⋊D53—48no—
326C22⋊D53—48no—
327C22⋊D53—48no—
328C2×Dic53—216no—
329C2×Dic53—24no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—48no—
338C2×Dic53AGL(1,ℤ/8)14yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342D212—22no—
343D212—22no—
344D212—48no—
345D212—42no—
346C4×D53—24no—
347C4×D53—22no—
348C4×D53—22no—
349C4×D53—28no—
350C4×D53—44no—
351C4×D53—48no—
352Dic106—24no—
353Dic106—22no—
354Dic106—48no—
355Dic106C2×#4114yescomplemented
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3115—531nomaximal, Sylow
361C22×C53—24no—
362C22×C53—48no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—84no—
369C22×C53#52512yes—
370C22×C53C2×AGL(1,ℤ/8)12yes—
371C22×C53#57512yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—44no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—84no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53#52512yes—
386C4×C53C22×#4111yescharacteristic
387C4×C53C22×#4111yescharacteristic
388Dic53—24no—
389Dic53—22no—
390Dic53—22no—
391Dic53—42no—
392Dic53—42no—
393Dic53C2×AGL(1,ℤ/8)14yes—
394C2×#532—531no—
395C2×C4×#41—531no—
396#3115—5316no—
397C2×#482—531no—
398C2×#482—531no—
399C2×#475—531no—
400C2×#474—531no—
401C2×#460—531no—
402C2×#459—531no—
403C2×#449—531no—
404C2×#449—531no—
405C2×#442—531no—
406C2×#442D5311yescharacteristic, complemented
407C2×#440—531no—
408C2×#440—531no—
409C2×#432—531no—
410C2×C53—44no—
411C2×C53—82no—
412C2×C53#311514yescomplemented
413C2×C53C2×#52511yescharacteristic
414C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
415C2×C53C2×#57511yescharacteristic
416D53—42no—
417D53—82no—
418C22×#41—531no—
419C22×#41—1061no—
420C22×SD16—531no—
421C22×SD16—531no—
422C22×D8—531no—
423C22×D8C2×D5311yescharacteristic
424#532—538no—
425#532—1064no—
426C2×C4⋊Q8—531no—
427C2×#127—531no—
428C2×#124—1061no—
429C2×#121—531no—
430C2×#121—531no—
431C2×#121—1061no—
432C4×#41—538no—
433C4×#41—1064no—
434C2×C4×Q8—531no—
435C2×C4×Q8—531no—
436C2×C4×D4—531no—
437C2×C4×D4—531no—
438C2×C4×D4—1061no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×C4×D4C2×D5311yescharacteristic
443C2×#117—531no—
444C2×#117—1061no—
445C22×C42—531no—
446C22×C42—1061no—
447#482—538no—
448#482—538no—
449#475—538no—
450#474—538no—
451#460—538no—
452#459—538no—
453#449—538no—
454#449—538no—
455#442—538no—
456#442C2×D5318yescomplemented
457#440—538no—
458#440—538no—
459#432—538no—
460C2×#107—531no—
461C2×#107—531no—
462C2×#106—531no—
463C2×#106C2×D5311yescharacteristic
464C2×C4⋊C8—531no—
465C2×C4⋊C8—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102C2×D5311yescharacteristic
473C2×#102C2×D5311yescharacteristic
474C2×C22⋊C8—531no—
475C2×C22⋊C8—531no—
476C2×#97—531no—
477C2×#97C2×D5311yescharacteristic
478C53C2×#311511yescharacteristic, complemented, Sylow
479C2×#41—534no—
480C2×#41—1068no—
481C2×#41—1062no—
482C2×#41—1064no—
483C2×#41—1064no—
484C2×#41—2128no—
485C22×Q8—531no—
486C22×Q8—1061no—
487C22×D4—531no—
488C22×D4—1061no—
489C22×D4—1061no—
490C22×D4—1061no—
491C22×D4—1061no—
492C22×D4—1061no—
493C22×D4C22×D5311yescharacteristic
494C22×D4C22×D5311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—531no—
498C23×C4—531no—
499C23×C4—531no—
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4—1061no—
503C2×SD16—534no—
504C2×SD16—534no—
505C2×SD16—1064no—
506C2×SD16—1064no—
507C2×D8—24no—
508C2×D8—534no—
509C2×D8—1064no—
510C2×D8C22×D5314yes—
511C22×C8—531no—
512C22×C8—531no—
513C22×C8C22×D5311yescharacteristic
514C22×C8C22×D5311yescharacteristic
515C4⋊Q8—534no—
516C4⋊Q8—1062no—
517#127—534no—
518#127—1062no—
519#124—1068no—
520#121—534no—
521#121—534no—
522#121—1068no—
523#121—1062no—
524#121—1062no—
525C4×Q8—534no—
526C4×Q8—534no—
527C4×Q8—1062no—
528C4×Q8—1062no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—534no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1062no—
535C4×D4—1068no—
536C4×D4—1068no—
537C4×D4—1062no—
538C4×D4C22×D5314yes—
539C4×D4C22×D5314yes—
540#117—534no—
541#117—1068no—
542#117—1062no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C4⋊C4C22×D5311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—531no—
558C2×C42—531no—
559C2×C42—531no—
560C2×C42—534no—
561C2×C42—534no—
562C2×C42—1068no—
563C2×C42—1061no—
564C2×C42—1061no—
565C2×C42—1061no—
566C2×C42C22×D5311yescharacteristic
567#107—534no—
568#107—534no—
569#106—534no—
570#106C22×D5314yes—
571C4⋊C8—534no—
572C4⋊C8—534no—
573#103—534no—
574#103—534no—
575#102—534no—
576#102—534no—
577#102—534no—
578#102—534no—
579#102C22×D5314yes—
580#102C22×D5314yes—
581C22⋊C8—534no—
582C22⋊C8—534no—
583#97—534no—
584#97C22×D5314yes—
585C24—21no—
586C24—21no—
587C24—531no—
588C24—1061no—
589#41—1068no—
590#41—10616no—
591#41—1068no—
592#41—21232no—
593C2×Q8—534no—
594C2×Q8—532no—
595C2×Q8—1064no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—2124no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—532no—
605C2×D4—1064no—
606C2×D4—1064no—
607C2×D4—1064no—
608C2×D4—1064no—
609C2×D4—1068no—
610C2×D4—1064no—
611C2×D4—1061no—
612C2×D4—1062no—
613C2×D4—1062no—
614C2×D4—2124no—
615C2×D4—2124no—
616C2×D4—2124no—
617C2×D4—2124no—
618C2×D4#1171994514yescomplemented
619C2×D4C23×D5312yes—
620C2×D4C23×D5312yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—531no—
628C22×C4—531no—
629C22×C4—531no—
630C22×C4—532no—
631C22×C4—534no—
632C22×C4—532no—
633C22×C4—534no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1064no—
637C22×C4—1068no—
638C22×C4—1061no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—1064no—
644C22×C4—2122no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4D4×D5311yescharacteristic
648C22×C4D4×D5311yescharacteristic
649C22×C4C23×D5311yescharacteristic
650SD16—1068no—
651SD16—1068no—
652D8—28no—
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—21no—
663C4⋊C4—21no—
664C4⋊C4—532no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1061no—
669C4⋊C4—1061no—
670C4⋊C4—1064no—
671C4⋊C4C23×D5312yes—
672C4⋊C4C23×D5312yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C42—534no—
681C42—534no—
682C42—532no—
683C42—532no—
684C42—1064no—
685C42—1064no—
686C42—1064no—
687C42D4×D5312yes—
688C42C23×D5312yes—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—532no—
698C23—1062no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—2122no—
703C23—2122no—
704C23—2122no—
705C23C2×D4×D5311yescharacteristic
706Q8—534no—
707Q8—1064no—
708Q8—1062no—
709Q8—2128no—
710D4—24no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—10616no—
716D4—1062no—
717D4—1062no—
718D4—2128no—
719D4—2128no—
720D4—2128no—
721D4—2128no—
722D4—2122no—
723D4C2×#1171994514yescomplemented
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—534no—
733C2×C4—532no—
734C2×C4—532no—
735C2×C4—532no—
736C2×C4—1068no—
737C2×C4—10616no—
738C2×C4—1062no—
739C2×C4—1064no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1064no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—2124no—
748C2×C4—2128no—
749C2×C4—2128no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4C2×D4×D5312yes—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4#41×D5312yes—
756C2×C4C2×#1171994512yes—
757C2×C4C24×D5311yescharacteristic
758C8—22no—
759C8—22no—
760C8—1062no—
761C8—1062no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—48no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—1062no—
771C22—1062no—
772C22—1062no—
773C22—4244no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2124no—
778C22#1681113212yes—
779C22AGL(1,ℤ/8)×D5312yes—
780C22#1681141912yes—
781C22C22×D4×D5311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—534no—
787C4—1062no—
788C4—1062no—
789C4—1064no—
790C4—2122no—
791C4—2122no—
792C4#1681113212yes—
793C4C2×#41×D5311yescharacteristic
794C4C22×#1171994511yescharacteristic
795C2—44no—
796C2—82no—
797C2—4242no—
798C2—2122no—
799C2#2028486214yesdirect product factor
800C2C2×#1681113211yescharacteristic
801C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
802C2C2×#1681141911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
hypercenterC2×#442D53
hypocenterC53C2×#3115
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811170C2semidirect
2. C2×C4×#11719947C2semidirect
3. #20284862C2direct (N × H)
4. C2×#16810949C2semidirect
5. C2×#16810945C2semidirect
6. C2×#16810907C2semidirect
7. C2×#16810901C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810816C2semidirect
10. C2×#16810769C2semidirect
11. C2×#16810765C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810723C2semidirect
15. C2×#16810678C2semidirect
16. C2×C53×#442C2semidirect
23. #16811170C22semidirect
31. C4×#11719947C22semidirect
43. #16810949C22semidirect
44. #16810945C22semidirect
45. #16810907C22semidirect
46. #16810901C22semidirect
47. #16810822C22semidirect
48. #16810816C22semidirect
49. #16810769C22semidirect
50. #16810765C22semidirect
51. #16810733C22semidirect
52. #16810725C22semidirect
53. #16810723C22semidirect
54. #16810678C22semidirect
72. C53×#442C22semidirect
192. C2×D4×C53#41semidirect
246. C2×Dic106#41semidirect
309. D4×C53C2×#41semidirect
355. Dic106C2×#41semidirect
406. C2×#442D53semidirect
412. C2×C53#3115semidirect
456. #442C2×D53semidirect
478. C53C2×#3115semidirect
618. C2×D4#11719945semidirect
723. D4C2×#11719945semidirect
799. C2#20284862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111702
C2×C4×#117199472
#202848622
C2×#168109492
C2×#168109452
C2×#168109072
C2×#168109012
C2×#168108222
C2×#168108162
C2×#168107692
C2×#168107652
C2×#168107332
C2×#168107252
C2×#168107232
C2×#168106782
C2×C53×#4422
C2×#311553