Finite Group Databasebeta

← C2×#20286040 #28256884

Subgroups — C2×#20286040 #28256884

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic, complemented
2C2×#16811158C211yesmaximal, characteristic, complemented
3#20286040C2116yesmaximal, direct product factor
4C2×#16810917C211yesmaximal, characteristic, complemented
5C2×#16810920C211yesmaximal, characteristic, complemented
6C2×#16810912C211yesmaximal, characteristic, complemented
7C2×#16810860C211yesmaximal, characteristic, complemented
8C2×#16810858C211yesmaximal, characteristic, complemented
9C2×#16810853C211yesmaximal, characteristic, complemented
10C2×#16810851C211yesmaximal, characteristic, complemented
11C2×#16810822C211yesmaximal, characteristic, complemented
12C2×#16810839C211yesmaximal, characteristic, complemented
13C2×#16810838C211yesmaximal, characteristic, complemented
14C2×#16810817C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811170—24no—
25#16811170C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133213C2211yescharacteristic
28#16811158—24no—
29#16811158C2218yescomplemented
30C2×#13133212—21no—
31C2×#13133205C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133202—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133188C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×#13133179—21no—
42C2×#13133179C2211yescharacteristic
43C2×C4×C22⋊D53—21no—
44C2×#13133175—21no—
45C2×C42×D53C2211yescharacteristic
46#16810920C2218yescomplemented
47#16810917C2218yescomplemented
48#16810912C2218yescomplemented
49#16810860C2218yescomplemented
50#16810858C2218yescomplemented
51#16810853C2218yescomplemented
52#16810851C2218yescomplemented
53#16810839C2218yescomplemented
54#16810838C2218yescomplemented
55#16810822C2218yescomplemented
56#16810817C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×C4⋊#88322C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C4⋊C8×D53C2218yescomplemented
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53D411yescharacteristic
91C22×C4×D53D411yescharacteristic
92C22×C4×D53C2311yescharacteristic
93C2×#11719913—42no—
94C2×#11719913C2314yes—
95C2×#11719923—42no—
96C2×#11719923C2314yes—
97C2×D424—42no—
98C2×D424C2314yes—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103C2×C8×D53—42no—
104C2×C8×D53—42no—
105C2×C8×D53C2314yes—
106C2×C8×D53C2314yes—
107#13133216—22no—
108#13133216C2314yes—
109#13133213—22no—
110#13133213C2314yes—
111#13133212—28no—
112#13133205—22no—
113#13133205C2314yes—
114#13133203—28no—
115#13133202—28no—
116#13133197—22no—
117#13133197C2314yes—
118#13133192—22no—
119#13133192—22no—
120#13133192C2314yes—
121#13133192C2314yes—
122#13133190—28no—
123#13133188—22no—
124#13133188C2314yes—
125#13133182—22no—
126#13133182C2314yes—
127C4×D212—22no—
128C4×D212C2314yes—
129#13133179—22no—
130#13133179—28no—
131#13133179C2314yes—
132C4×C22⋊D53—28no—
133#13133175—28no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53D411yescharacteristic
148C2×C4×Dic53D411yescharacteristic
149C2×C4×Dic53C2311yescharacteristic
150C42×D53D414yes—
151C42×D53C2314yes—
152#13133150C2314yes—
153#13133148C2314yes—
154C4⋊#88322C2314yes—
155#13133146C2314yes—
156#13133146C2314yes—
157#13133142C2314yes—
158#13133140C2314yes—
159#13133139C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#125×C53—22no—
168#125×C53C2314yes—
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×C53C2314yes—
179#106×C53C2314yes—
180C4⋊C8×C53C2314yes—
181#102×C53C2314yes—
182#102×C53C2314yes—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—24no—
195C22×C4×C53—44no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—24no—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—44no—
203C2×C22⋊D53—44no—
204C2×C22⋊D53—44no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210#11719945—432no—
211C2×D212—22no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—24no—
216C2×D212—24no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—44no—
220C2×D212—44no—
221C2×D212C2412yes—
222C2×D212C2412yes—
223C2×C4×D53—24no—
224C2×C4×D53—22no—
225C2×C4×D53—22no—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—44no—
230C2×C4×D53—44no—
231C2×C4×D53C2×D412yes—
232C2×C4×D53C2×D414yes—
233C2×C4×D53C2×D414yes—
234C2×C4×D53C2412yes—
235C2×Dic106—22no—
236C2×Dic106—22no—
237C2×Dic106—21no—
238C2×Dic106—24no—
239C2×Dic106—44no—
240C2×Dic106C2412yes—
241C2×C8×C53—22no—
242C2×C8×C53—22no—
243C2×C8×C53C2412yes—
244C2×C8×C53C2412yes—
245C4⋊C4×C53—24no—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C22⋊C4×C53—24no—
254C42×C53C2×D412yes—
255C42×C53C2412yes—
256C22⋊Dic53—24no—
257#11719923—44no—
258#11719922—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271C4×Dic53—24no—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D414yes—
274C4×Dic53C2×D414yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280D424—44no—
281#11719913—44no—
282C8×D53—44no—
283C8×D53—44no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53AGL(1,ℤ/8)14yes—
300C22×D53C22×D412yes—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53—42no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—48no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53H(5,𝔽2)12yes—
317C2×C4×C532−1+412yes—
318C2×C4×C53C2511yescharacteristic
319C22⋊D53—48no—
320C22⋊D53—48no—
321C22⋊D53—48no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53#13514yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332D212—22no—
333D212—22no—
334D212—22no—
335D212—22no—
336D212—48no—
337D212—48no—
338D212—42no—
339D212—42no—
340C4×D53—28no—
341C4×D53—24no—
342C4×D53—22no—
343C4×D53—22no—
344C4×D53—28no—
345C4×D53—48no—
346C4×D53—48no—
347Dic106—22no—
348Dic106—22no—
349Dic106—48no—
350Dic106—42no—
351C8×C53—22no—
352C8×C53—22no—
353#88322—22no—
354#88322—22no—
355C2×#3247—531nomaximal, Sylow
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—84no—
360C22×C53#53712yes—
361C22×C53C2×#13512yes—
362C22×C53C2×AGL(1,ℤ/8)12yes—
363C22×C53C23×D411yescharacteristic
364C2×D53—22no—
365C2×D53—28no—
366C2×D53—22no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—84no—
374C2×D53—84no—
375C2×D53C2×AGL(1,ℤ/8)14yes—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#53712yes—
382C4×C53C2×H(5,𝔽2)11yescharacteristic
383C4×C53C2×2−1+411yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—42no—
387Dic53—42no—
388Dic53C2×#13514yes—
389C2×#532—531no—
390C2×#529—531no—
391#3247—5316no—
392C2×#477—531no—
393C2×#478—531no—
394C2×#478D5311yescharacteristic, complemented
395C2×#476—531no—
396C2×#466—531no—
397C2×#466—531no—
398C2×#465—531no—
399C2×#465—531no—
400C2×#460—531no—
401C2×#463—531no—
402C2×#463—531no—
403C2×#459—531no—
404C22×C4⋊C8—531no—
405C2×C53—82no—
406C2×C53#324714yescomplemented
407C2×C53C2×#53711yescharacteristic
408C2×C53C22×#13511yescharacteristic
409C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
410D53—24no—
411D53—82no—
412D53—82no—
413C22×#41—1061no—
414C22×SD16—531no—
415C22×SD16—531no—
416C22×D8—531no—
417C22×D8—531no—
418C23×C8—531no—
419C23×C8—531no—
420#532—538no—
421#532—1064no—
422C2×C4⋊Q8—531no—
423C2×#127—531no—
424#529—538no—
425#529—1064no—
426C2×#126—1061no—
427C2×#125C2×D5311yescharacteristic
428C2×#124—531no—
429C2×#124—1061no—
430C2×#123—1061no—
431C2×C22⋊Q8—531no—
432C2×#121—531no—
433C2×#121—531no—
434C2×#121—531no—
435C2×#121—1061no—
436C2×C4×Q8—531no—
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×#117—1061no—
443C22×C42—531no—
444#478—538no—
445#478C2×D5318yescomplemented
446#477—538no—
447#476—538no—
448#466—538no—
449#466—538no—
450#465—538no—
451#465—538no—
452#463—538no—
453#463—538no—
454#460—538no—
455#459—538no—
456C2×#107—531no—
457C2×#107C2×D5311yescharacteristic
458C2×#106—531no—
459C2×#106C2×D5311yescharacteristic
460C2×C4⋊C8—531no—
461C2×C4⋊C8—531no—
462C2×C4⋊C8—531no—
463C2×C4⋊C8—538no—
464C2×C4⋊C8C2×D5311yescharacteristic
465C2×#103—531no—
466C2×#103—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102C2×D5311yescharacteristic
472C2×#102C2×D5311yescharacteristic
473C53C2×#324711yescharacteristic, complemented, Sylow
474C2×#41—1068no—
475C2×#41—2128no—
476C22×Q8—531no—
477C22×Q8—1061no—
478C22×D4—531no—
479C22×D4—531no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4—1061no—
492C2×SD16—534no—
493C2×SD16—534no—
494C2×SD16—2122no—
495C2×SD16—2122no—
496C2×D8—534no—
497C2×D8—534no—
498C2×D8—2122no—
499C2×D8—2122no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—534no—
504C22×C8—2122no—
505C22×C8—2122no—
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C4⋊Q8—534no—
509C4⋊Q8—1062no—
510#127—534no—
511#127—1062no—
512#126—1068no—
513#125—22no—
514#125C22×D5314yes—
515#124—534no—
516#124—1068no—
517#124—1062no—
518#123—1068no—
519C22⋊Q8—534no—
520C22⋊Q8—1062no—
521#121—534no—
522#121—534no—
523#121—534no—
524#121—1068no—
525#121—1062no—
526#121—1062no—
527#121—1062no—
528C4×Q8—534no—
529C4×Q8—1062no—
530C4×D4—22no—
531C4×D4—534no—
532C4×D4—534no—
533C4×D4—1062no—
534C4×D4—1068no—
535C4×D4—1068no—
536C4×D4—1062no—
537C4×D4C22×D5314yes—
538#117—1068no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
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—1061no—
563C2×C42C22×D5311yescharacteristic
564#107—534no—
565#107C22×D5314yes—
566#106—534no—
567#106C22×D5314yes—
568C4⋊C8—534no—
569C4⋊C8—534no—
570C4⋊C8—534no—
571C4⋊C8C22×D5314yes—
572#103—534no—
573#103—534no—
574#102—534no—
575#102—534no—
576#102—534no—
577#102—534no—
578#102C22×D5314yes—
579#102C22×D5314yes—
580C24—21no—
581C24—531no—
582C24—1061no—
583C24—1061no—
584#41—21232no—
585C2×Q8—532no—
586C2×Q8—1064no—
587C2×Q8—1061no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—2124no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—532no—
595C2×D4—532no—
596C2×D4—1064no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1061no—
602C2×D4—1061no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4—2124no—
610C2×D4—2124no—
611C2×D4—2124no—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—534no—
622C22×C4—532no—
623C22×C4—534no—
624C22×C4—532no—
625C22×C4—1064no—
626C22×C4—1064no—
627C22×C4—1064no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1064no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—2124no—
639SD16—2124no—
640D8—2124no—
641D8—2124no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—2124no—
649C2×C8—2124no—
650C2×C8C23×D5312yes—
651C2×C8C23×D5312yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—532no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4C23×D5312yes—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C42—534no—
675C42—532no—
676C42—534no—
677C42—532no—
678C42—1064no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—534no—
686C23—532no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23C2×D4×D5311yescharacteristic
698Q8—1062no—
699Q8—1062no—
700Q8—2128no—
701Q8—2122no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—1062no—
706D4—1062no—
707D4—1062no—
708D4—1062no—
709D4—2128no—
710D4—2128no—
711D4—2128no—
712D4—2128no—
713D4—2128no—
714D4—2122no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—534no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—532no—
729C2×C4—1068no—
730C2×C4—1068no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1064no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—2128no—
739C2×C4—2128no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4C2×D4×D5312yes—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4#1313326312yes—
746C2×C4#1313326512yes—
747C2×C4C24×D5311yescharacteristic
748C8—22no—
749C8—22no—
750C8—1062no—
751C8—1062no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—534no—
757C22—1062no—
758C22—1068no—
759C22—1062no—
760C22—4244no—
761C22—4244no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22#1681120312yes—
769C22#135×D5312yes—
770C22AGL(1,ℤ/8)×D5312yes—
771C22C22×D4×D5311yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—534no—
778C4—1062no—
779C4—1062no—
780C4—2122no—
781C4—2122no—
782C4#1681120312yes—
783C4C2×#1313326311yescharacteristic
784C4C2×#1313326511yescharacteristic
785C2—82no—
786C2—1064no—
787C2—4242no—
788C2—4242no—
789C2#2028604014yesdirect product factor
790C2C2×#1681120311yescharacteristic
791C2C2×#135×D5311yescharacteristic
792C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3247
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×#16811170C2semidirect
2. C2×#16811158C2semidirect
3. #20286040C2direct (N × H)
4. C2×#16810917C2semidirect
5. C2×#16810920C2semidirect
6. C2×#16810912C2semidirect
7. C2×#16810860C2semidirect
8. C2×#16810858C2semidirect
9. C2×#16810853C2semidirect
10. C2×#16810851C2semidirect
11. C2×#16810822C2semidirect
12. C2×#16810839C2semidirect
13. C2×#16810838C2semidirect
14. C2×#16810817C2semidirect
15. C2×C4⋊C8×D53C2semidirect
16. C2×C53×#478C2semidirect
25. #16811170C22semidirect
29. #16811158C22semidirect
46. #16810920C22semidirect
47. #16810917C22semidirect
48. #16810912C22semidirect
49. #16810860C22semidirect
50. #16810858C22semidirect
51. #16810853C22semidirect
52. #16810851C22semidirect
53. #16810839C22semidirect
54. #16810838C22semidirect
55. #16810822C22semidirect
56. #16810817C22semidirect
62. C4⋊C8×D53C22semidirect
71. C53×#478C22semidirect
394. C2×#478D53semidirect
406. C2×C53#3247semidirect
445. #478C2×D53semidirect
473. C53C2×#3247semidirect
789. C2#20286040direct (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×#168111582
#202860402
C2×#168109172
C2×#168109202
C2×#168109122
C2×#168108602
C2×#168108582
C2×#168108532
C2×#168108512
C2×#168108222
C2×#168108392
C2×#168108382
C2×#168108172
C2×C4⋊C8×D532
C2×C53×#4782
C2×#324753