Finite Group Databasebeta

← C2×#20286153 #28257031

Subgroups — C2×#20286153 #28257031

Order 13568.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811229C211yesmaximal, characteristic, complemented
2C2×#16811224C211yesmaximal, characteristic, complemented
3#20286153C2116yesmaximal, direct product factor
4C2×#16810926C211yesmaximal, characteristic, complemented
5C2×#16810922C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810877C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810860C211yesmaximal, characteristic, complemented
10C2×#16810858C211yesmaximal, characteristic, complemented
11C2×#16810819C211yesmaximal, characteristic, complemented
12C2×#16810818C211yesmaximal, characteristic, complemented
13C2×#16810817C211yesmaximal, characteristic, complemented
14C2×#16810817C211yesmaximal, characteristic, complemented
15C2×#16810648C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×D424C2211yescharacteristic
18C22×D424C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811229—24no—
24#16811229C2218yescomplemented
25#16811224—24no—
26#16811224C2218yescomplemented
27C2×#13133214C2211yescharacteristic
28C2×#13133213C2211yescharacteristic
29C2×#13133208C2211yescharacteristic
30C2×#13133202—21no—
31C2×#13133202—21no—
32C2×#13133200—21no—
33C2×#13133199—21no—
34C2×#13133192—21no—
35C2×#13133192—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133192C2211yescharacteristic
39C2×#13133191—21no—
40C2×#13133190—21no—
41C2×#13133188C2211yescharacteristic
42C2×C4×D212C2211yescharacteristic
43C2×#13133179C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133174C2211yescharacteristic
46#16810926C2218yescomplemented
47#16810922C2218yescomplemented
48#16810920C2218yescomplemented
49#16810877C2218yescomplemented
50#16810875C2218yescomplemented
51#16810860C2218yescomplemented
52#16810858C2218yescomplemented
53#16810819C2218yescomplemented
54#16810818C2218yescomplemented
55#16810817C2218yescomplemented
56#16810817C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
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
77C22×D212—21no—
78C22×D212—21no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
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×D53—21no—
91C22×C4×D53C2311yescharacteristic
92C2×D424—42no—
93C2×D424—42no—
94C2×D424C2314yes—
95C2×D424C2314yes—
96C2×#11719922—42no—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C2×#11719922C2314yes—
100C2×#11719912—42no—
101C2×#11719912C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C2×C8×D53—42no—
105C2×C8×D53C2314yes—
106#13133214—22no—
107#13133214C2314yes—
108#13133213—22no—
109#13133213C2314yes—
110#13133208—22no—
111#13133208C2314yes—
112#13133202—28no—
113#13133202—28no—
114#13133200—28no—
115#13133199—28no—
116#13133192—28no—
117#13133192—28no—
118#13133192—22no—
119#13133192—22no—
120#13133192—22no—
121#13133192C2314yes—
122#13133192C2314yes—
123#13133192C2314yes—
124#13133191—28no—
125#13133190—28no—
126#13133188—22no—
127#13133188C2314yes—
128C4×D212—22no—
129C4×D212C2314yes—
130#13133179—22no—
131#13133179—22no—
132#13133179C2314yes—
133#13133179C2314yes—
134#13133174D414yes—
135#13133174C2314yes—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53C2311yescharacteristic
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133137C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#125×C53—22no—
167#125×C53C2314yes—
168C4×D4×C53—22no—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182C24×C53—21no—
183C23×D53—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—82no—
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—82no—
203C2×C22⋊D53—82no—
204C2×C22⋊D53—82no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—22no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—24no—
219C2×D212—24no—
220C2×D212—24no—
221C2×D212—24no—
222C2×D212—24no—
223C2×D212—82no—
224C2×D212—82no—
225C2×D212—82no—
226C2×D212—82no—
227C2×D212—82no—
228C2×D212C2412yes—
229C2×D212C2412yes—
230C2×D212C2412yes—
231C2×C4×D53—22no—
232C2×C4×D53—22no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—82no—
237C2×C4×D53—82no—
238C2×C4×D53—82no—
239C2×C4×D53C2×D412yes—
240C2×C4×D53C2412yes—
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#11719922—44no—
258#11719922—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921C2×D414yes—
266#11719921C2×D414yes—
267C4⋊Dic53—21no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919C2×D414yes—
272#11719919C2×D414yes—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279D424—44no—
280D424—44no—
281#11719912—44no—
282C8×D53—44no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D411yescharacteristic
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53C22×D412yes—
304D4×C53—22no—
305D4×C53—22no—
306D4×C53—42no—
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×C53C22×D412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53H(5,𝔽2)12yes—
320C2×C4×C532−1+412yes—
321C2×C4×C53C2511yescharacteristic
322C22⋊D53—84no—
323C22⋊D53—84no—
324C22⋊D53—84no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—42no—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333D212—22no—
334D212—22no—
335D212—22no—
336D212—22no—
337D212—22no—
338D212—22no—
339D212—42no—
340D212—42no—
341D212—42no—
342D212—84no—
343D212—84no—
344D212—84no—
345D212—84no—
346D212—84no—
347C4×D53—24no—
348C4×D53—22no—
349C4×D53—22no—
350C4×D53—84no—
351C4×D53—84no—
352C4×D53—84no—
353C8×C53—22no—
354C8×C53—22no—
355#88322—22no—
356#88322—22no—
357C2×#3259—531nomaximal, Sylow
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—84no—
362C22×C53#53712yes—
363C22×C53#57612yes—
364C22×C53#57612yes—
365C22×C53C23×D411yescharacteristic
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—44no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—84no—
380C2×D53—84no—
381C2×D53—84no—
382C4×C53—22no—
383C4×C53—22no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53#53712yes—
388C4×C53C2×H(5,𝔽2)11yescharacteristic
389C4×C53C2×2−1+411yescharacteristic
390Dic53—22no—
391Dic53—22no—
392Dic53—22no—
393Dic53—42no—
394C2×#540—531no—
395C2×#540—531no—
396#3259—5316no—
397C2×#478—531no—
398C2×#478—531no—
399C2×#478—531no—
400C2×#478D5311yescharacteristic, complemented
401C2×#469—531no—
402C2×#469—531no—
403C2×#466—531no—
404C2×#466—531no—
405C2×#459—531no—
406C2×#459—531no—
407C2×#459—531no—
408C2×#459—531no—
409C2×#424—531no—
410C2×C53—82no—
411C2×C53#325914yescomplemented
412C2×C53C2×#53711yescharacteristic
413C2×C53C2×#57611yescharacteristic
414C2×C53C2×#57611yescharacteristic
415D53—42no—
416D53—82no—
417D53—82no—
418D53—82no—
419C22×D8—531no—
420C22×D8—531no—
421C22×D8—531no—
422C22×D8—531no—
423C22×M16—531no—
424C23×C8—531no—
425#540—538no—
426#540—538no—
427#540—1064no—
428#540—1064no—
429C2×#127—531no—
430C2×#127—531no—
431C2×#125—531no—
432C2×#125C2×D5311yescharacteristic
433C2×#123—1061no—
434C2×#123—1061no—
435C2×#123—1061no—
436C2×#123—1061no—
437C2×#121—531no—
438C2×#121—531no—
439C2×#121—531no—
440C2×#121—531no—
441C2×#121—1061no—
442C2×#121—1061no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4C2×D5311yescharacteristic
449C2×#117—531no—
450#478—538no—
451#478—538no—
452#478—538no—
453#478C2×D5318yescomplemented
454#469—538no—
455#469—538no—
456#466—538no—
457#466—538no—
458#459—538no—
459#459—538no—
460#459—538no—
461#459—538no—
462C2×#107—531no—
463C2×#107C2×D5311yescharacteristic
464C2×#106—531no—
465C2×#106C2×D5311yescharacteristic
466#424—538no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
469C2×C4⋊C8—531no—
470C2×C4⋊C8C2×D5311yescharacteristic
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102C2×D5311yescharacteristic
478C2×#102C2×D5311yescharacteristic
479C53C2×#325911yescharacteristic, complemented, Sylow
480C22×D4—531no—
481C22×D4—531no—
482C22×D4—531no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4—1061no—
488C22×D4—1061no—
489C22×D4—1061no—
490C22×D4—1061no—
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—531no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C2×D8—534no—
498C2×D8—534no—
499C2×D8—534no—
500C2×D8—534no—
501C2×D8—2122no—
502C2×D8—2122no—
503C2×D8—2122no—
504C2×D8—2122no—
505C2×M16—534no—
506C2×M16—2122no—
507C22×C8—531no—
508C22×C8—531no—
509C22×C8—534no—
510C22×C8—2122no—
511C22×C8C22×D5311yescharacteristic
512C22×C8C22×D5311yescharacteristic
513#127—534no—
514#127—534no—
515#127—1062no—
516#127—1062no—
517#125—22no—
518#125—534no—
519#125—1062no—
520#125C22×D5314yes—
521#123—1068no—
522#123—1068no—
523#123—1068no—
524#123—1068no—
525#121—534no—
526#121—534no—
527#121—534no—
528#121—534no—
529#121—1068no—
530#121—1068no—
531#121—1068no—
532#121—1068no—
533#121—1062no—
534#121—1062no—
535#121—1062no—
536#121—1062no—
537C4×D4—22no—
538C4×D4—534no—
539C4×D4—534no—
540C4×D4—534no—
541C4×D4—1062no—
542C4×D4—1062no—
543C4×D4—1062no—
544C4×D4C22×D5314yes—
545#117—534no—
546#117—534no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—531no—
559C2×C22⋊C4—531no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C42—531no—
568C2×C42C22×D5311yescharacteristic
569#107—534no—
570#107C22×D5314yes—
571#106—534no—
572#106C22×D5314yes—
573C4⋊C8—534no—
574C4⋊C8—534no—
575C4⋊C8—534no—
576C4⋊C8C22×D5314yes—
577#102—534no—
578#102—534no—
579#102—534no—
580#102—534no—
581#102—534no—
582#102—534no—
583#102C22×D5314yes—
584#102C22×D5314yes—
585C24—21no—
586C24—531no—
587C24—1061no—
588C24—1061no—
589C24—1061no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—532no—
594C2×D4—532no—
595C2×D4—532no—
596C2×D4—1064no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1064no—
603C2×D4—1064no—
604C2×D4—1061no—
605C2×D4—1061no—
606C2×D4—1061no—
607C2×D4—1062no—
608C2×D4—1062no—
609C2×D4—1062no—
610C2×D4—1062no—
611C2×D4—1062no—
612C2×D4—1062no—
613C2×D4—4242no—
614C2×D4—4242no—
615C2×D4—4242no—
616C2×D4—4242no—
617C2×D4—4242no—
618C2×D4—4242no—
619C2×D4—4242no—
620C2×D4—4242no—
621C2×D4C23×D5312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—531no—
628C22×C4—531no—
629C22×C4—531no—
630C22×C4—532no—
631C22×C4—532no—
632C22×C4—1064no—
633C22×C4—1064no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1061no—
637C22×C4—1064no—
638C22×C4—4242no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4D4×D5311yescharacteristic
642C22×C4D4×D5311yescharacteristic
643C22×C4C23×D5311yescharacteristic
644D8—2124no—
645D8—2124no—
646D8—2124no—
647D8—2124no—
648M16—2124no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—532no—
652C2×C8—532no—
653C2×C8—1062no—
654C2×C8—1062no—
655C2×C8—2124no—
656C2×C8C23×D5312yes—
657C2×C8C23×D5312yes—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—534no—
664C4⋊C4—534no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1061no—
669C4⋊C4C23×D5312yes—
670C4⋊C4C23×D5312yes—
671C4⋊C4C23×D5312yes—
672C22⋊C4—24no—
673C22⋊C4—534no—
674C22⋊C4—534no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C42—532no—
683C42—532no—
684C42D4×D5312yes—
685C42C23×D5312yes—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—532no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—1062no—
697C23—2122no—
698C23—2122no—
699C23—2122no—
700C23—2122no—
701C23—2122no—
702C23—2122no—
703C23—2122no—
704C23—2122no—
705C23—2122no—
706C23C2×D4×D5311yescharacteristic
707D4—22no—
708D4—22no—
709D4—42no—
710D4—1062no—
711D4—1062no—
712D4—1062no—
713D4—1062no—
714D4—1062no—
715D4—1062no—
716D4—4244no—
717D4—4244no—
718D4—4244no—
719D4—4244no—
720D4—4244no—
721D4—4244no—
722D4—4244no—
723D4—4244no—
724D4—2122no—
725D4—2122no—
726D4—2122no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—532no—
737C2×C4—532no—
738C2×C4—532no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1064no—
745C2×C4—1062no—
746C2×C4—4244no—
747C2×C4—4244no—
748C2×C4—4244no—
749C2×C4—2122no—
750C2×C4C2×D4×D5312yes—
751C2×C4C2×D4×D5312yes—
752C2×C4C2×D4×D5311yescharacteristic
753C2×C4#1313326312yes—
754C2×C4#1313326512yes—
755C2×C4C24×D5311yescharacteristic
756C8—22no—
757C8—22no—
758C8—1062no—
759C8—1062no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—1062no—
765C22—1062no—
766C22—1062no—
767C22—4244no—
768C22—4244no—
769C22—4244no—
770C22—2122no—
771C22—2122no—
772C22—2122no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22—2122no—
779C22—2124no—
780C22#1681120312yes—
781C22#1681142512yes—
782C22#1681142712yes—
783C22C22×D4×D5311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—1062no—
790C4—1062no—
791C4—1062no—
792C4—2122no—
793C4#1681120312yes—
794C4C2×#1313326311yescharacteristic
795C4C2×#1313326511yescharacteristic
796C2—82no—
797C2—4242no—
798C2—4242no—
799C2—4242no—
800C2—2122no—
801C2#2028615314yesdirect product factor
802C2C2×#1681120311yescharacteristic
803C2C2×#1681142511yescharacteristic
804C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3259
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×#16811229C2semidirect
2. C2×#16811224C2semidirect
3. #20286153C2direct (N × H)
4. C2×#16810926C2semidirect
5. C2×#16810922C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810877C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810860C2semidirect
10. C2×#16810858C2semidirect
11. C2×#16810819C2semidirect
12. C2×#16810818C2semidirect
13. C2×#16810817C2semidirect
14. C2×#16810817C2semidirect
15. C2×#16810648C2semidirect
16. C2×C53×#478C2semidirect
24. #16811229C22semidirect
26. #16811224C22semidirect
46. #16810926C22semidirect
47. #16810922C22semidirect
48. #16810920C22semidirect
49. #16810877C22semidirect
50. #16810875C22semidirect
51. #16810860C22semidirect
52. #16810858C22semidirect
53. #16810819C22semidirect
54. #16810818C22semidirect
55. #16810817C22semidirect
56. #16810817C22semidirect
59. #16810648C22semidirect
71. C53×#478C22semidirect
400. C2×#478D53semidirect
411. C2×C53#3259semidirect
453. #478C2×D53semidirect
479. C53C2×#3259semidirect
801. C2#20286153direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112292
C2×#168112242
#202861532
C2×#168109262
C2×#168109222
C2×#168109202
C2×#168108772
C2×#168108752
C2×#168108602
C2×#168108582
C2×#168108192
C2×#168108182
C2×#168108172
C2×#168106482
C2×C53×#4782
C2×#325953