Finite Group Databasebeta

← C2×#20286818 #28260753

Subgroups — C2×#20286818 #28260753

Order 13568.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811314C211yesmaximal, characteristic, complemented
2C2×#16811276C211yesmaximal, characteristic
3#20286818C2116yesmaximal, direct product factor
4C2×#16810991C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810924C211yesmaximal, characteristic, complemented
8C2×#16810878C211yesmaximal, characteristic, complemented
9C2×#16810861C211yesmaximal, characteristic, complemented
10C2×#16810784C211yesmaximal, characteristic, complemented
11C2×#16810784C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810693C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#462C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719949C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811314—24no—
23#16811314C2218yescomplemented
24#16811276—24no—
25#16811276C2218yes—
26C2×#13133211—21no—
27C2×#13133209C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133202—21no—
30C2×#13133202—21no—
31C2×#13133202—21no—
32C2×#13133193C2211yescharacteristic
33C2×#13133193C2211yescharacteristic
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×#13133192—21no—
37C2×C4×D212C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133175C2211yescharacteristic
40C2×#13133174—21no—
41C2×C4⋊C4×D53—21no—
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810991C2218yescomplemented
44#16810962C2218yescomplemented
45#16810957C2218yescomplemented
46#16810924C2218yescomplemented
47#16810878C2218yescomplemented
48#16810861C2218yescomplemented
49#16810784C2218yescomplemented
50#16810784C2218yescomplemented
51#16810721C2218yescomplemented
52#16810693C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56#16810623C2218yescomplemented
57#16810618C2218yescomplemented
58C2×#13133141C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#462C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949—24no—
81C2×#11719949—42no—
82C2×#11719949—42no—
83C2×#11719949C2314yes—
84C2×#11719949C2314yes—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212D411yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C2×#11719924—24no—
96C2×#11719924C2314yes—
97C2×#11719912—42no—
98C2×#11719912C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C2×C8×D53—42no—
102C2×C8×D53C2314yes—
103#13133211—28no—
104#13133209—22no—
105#13133209C2314yes—
106#13133207—28no—
107#13133202—28no—
108#13133202—28no—
109#13133202—28no—
110#13133193—22no—
111#13133193—22no—
112#13133193—22no—
113#13133193—22no—
114#13133193C2314yes—
115#13133193C2314yes—
116#13133193C2314yes—
117#13133193C2314yes—
118#13133192—28no—
119C4×D212—22no—
120C4×D212D414yes—
121C4×D212C2314yes—
122C4×D212C2314yes—
123#13133175—22no—
124#13133175C2314yes—
125#13133174—28no—
126C2×C4⋊Dic53D411yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C4⋊C4×D53—28no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×#11719921D411yescharacteristic
148C2×C4×Dic53—21no—
149#13133151C2314yes—
150#13133150C2314yes—
151#13133149C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162#13133128C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C2×Q16×C53—42no—
167C2×Q16×C53—42no—
168C2×Q16×C53C2314yes—
169C2×Q16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C4⋊Q8×C53—22no—
173C4⋊Q8×C53C2314yes—
174C4×Q8×C53—22no—
175C4×Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53C2412yes—
198C2×Q8×C53C2412yes—
199C2×Q8×C53C2412yes—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2411yescharacteristic
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212#11719949—28no—
213#11719949—28no—
214#11719949—44no—
215#11719949—44no—
216#11719949—48no—
217#11719949—48no—
218C2×D212—21no—
219C2×D212—22no—
220C2×D212—24no—
221C2×D212—24no—
222C2×D212—42no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212C2×D414yes—
226C2×D212#4114yes—
227C2×D212C2412yes—
228C2×C4×D53—22no—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53—44no—
240C2×C4×D53C2×D412yes—
241C2×C4×D53C2×D412yes—
242C2×C4×D53C2412yes—
243C2×C4×D53C2412yes—
244Q16×C53—44no—
245Q16×C53—44no—
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—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2412yes—
255C42×C53—24no—
256C42×C53C2×D412yes—
257C42×C53C2412yes—
258#11719924—28no—
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—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53C2×D414yes—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273C4⋊Dic53C2412yes—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286#11719912—44no—
287C8×D53—44no—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—24no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53C22×D412yes—
300C22×D53C22×D412yes—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—42no—
308Q8×C53—42no—
309Q8×C53—42no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—42no—
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×C53H(5,𝔽2)12yes—
325C2×C4×C53C2511yescharacteristic
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336D212—24no—
337D212—22no—
338D212—44no—
339D212—48no—
340D212—48no—
341D212C2×#4114yes—
342C4×D53—24no—
343C4×D53—24no—
344C4×D53—22no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—22no—
348C4×D53—48no—
349C4×D53—48no—
350C4×D53—48no—
351C4×D53—48no—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3315—531nomaximal, Sylow
357C22×C53#54612yes—
358C22×C53#57512yes—
359C22×C53#57812yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—24no—
364C2×D53—22no—
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—44no—
369C2×D53—44no—
370C2×D53—48no—
371C2×D53—42no—
372C2×D53—42no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53#54612yes—
380C4×C53C22×#4111yescharacteristic
381C4×C53C2×H(5,𝔽2)11yescharacteristic
382Dic53—22no—
383Dic53—22no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552—531no—
388C2×#547—531no—
389#3315—5316no—
390C2×#491—531no—
391C2×#484—531no—
392C2×#485—531no—
393C2×#478—531no—
394C2×#470—531no—
395C2×#467—531no—
396C2×#462D5311yescharacteristic, complemented
397C2×#452—531no—
398C2×#452—531no—
399C2×#440—531no—
400C2×#435—531no—
401C2×#417—531no—
402C2×#416—531no—
403C2×C53#331514yescomplemented
404C2×C53C2×#54611yescharacteristic
405C2×C53C2×#57511yescharacteristic
406C2×C53C2×#57811yescharacteristic
407D53—42no—
408D53—42no—
409D53—44no—
410C22×#41—531no—
411C22×#41—531no—
412C22×Q16C2×D5311yescharacteristic
413C22×Q16C2×D5311yescharacteristic
414C22×SD16—531no—
415C22×M16—531no—
416C23×C8—531no—
417#552—538no—
418#552—1064no—
419#547—538no—
420#547—1064no—
421C2×C4⋊Q8C2×D5311yescharacteristic
422C2×#126—1061no—
423C2×#125—531no—
424C2×#125—1061no—
425C2×#123—1061no—
426C2×#123—1061no—
427C2×#123—1061no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×#121—1061no—
433C2×C4×Q8C2×D5311yescharacteristic
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×#117—531no—
437C2×#117—1061no—
438C22×C4⋊C4—531no—
439C22×C4⋊C4—1061no—
440#491—538no—
441#485—538no—
442#484—538no—
443#478—538no—
444#470—538no—
445#467—538no—
446#462C2×D5318yescomplemented
447#452—538no—
448#452—538no—
449#440—538no—
450#435—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8C2×D5311yescharacteristic
455#417—538no—
456#416—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103C2×D5311yescharacteristic
463C2×#103C2×D5311yescharacteristic
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×#97—531no—
470C53C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—534no—
473C2×#41—1062no—
474C2×#41—1062no—
475C2×#41—1064no—
476C2×#41—1064no—
477C2×#41—2122no—
478C2×#41—2122no—
479C22×Q8C22×D5311yescharacteristic
480C22×Q8C22×D5311yescharacteristic
481C22×Q8C22×D5311yescharacteristic
482C22×D4—531no—
483C22×D4—531no—
484C22×D4—1061no—
485C22×D4—1061no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C2×Q16—42no—
493C2×Q16—42no—
494C2×Q16C22×D5314yes—
495C2×Q16C22×D5314yes—
496C2×SD16—534no—
497C2×SD16—1064no—
498C2×M16—534no—
499C2×M16—2122no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—2122no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8C22×D5314yes—
508#126—1068no—
509#125—534no—
510#125—1068no—
511#125—1062no—
512#123—1068no—
513#123—1068no—
514#123—1068no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—534no—
518C22⋊Q8—534no—
519C22⋊Q8—1062no—
520C22⋊Q8—1062no—
521C22⋊Q8—1062no—
522C22⋊Q8—1062no—
523#121—1068no—
524C4×Q8—22no—
525C4×Q8C22×D5314yes—
526C4×D4—534no—
527C4×D4—534no—
528C4×D4—534no—
529C4×D4—1062no—
530#117—534no—
531#117—1068no—
532#117—1062no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—534no—
541C2×C4⋊C4—1068no—
542C2×C4⋊C4—1062no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4C22×D5311yescharacteristic
551C2×C22⋊C4—531no—
552C2×C22⋊C4—531no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C42—21no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107—534no—
564#106—534no—
565C4⋊C8C22×D5314yes—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103C22×D5314yes—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8—534no—
577C22⋊C8—534no—
578#97—534no—
579C24—531no—
580C24—531no—
581C24—1061no—
582#41—1068no—
583#41—1068no—
584#41—2124no—
585#41—2124no—
586#41—2128no—
587#41—2128no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D5312yes—
598C2×Q8C23×D5312yes—
599C2×Q8C23×D5312yes—
600C2×D4—534no—
601C2×D4—534no—
602C2×D4—532no—
603C2×D4—1064no—
604C2×D4—1064no—
605C2×D4—1061no—
606C2×D4—1062no—
607C2×D4—2122no—
608C2×D4—2124no—
609C2×D4—2124no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—531no—
615C22×C4—531no—
616C22×C4—532no—
617C22×C4—532no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—1064no—
621C22×C4—1064no—
622C22×C4—1064no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1064no—
631C22×C4—2124no—
632C22×C4—2124no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638Q16—44no—
639Q16—44no—
640SD16—1068no—
641M16—2124no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—2124no—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—534no—
656C4⋊C4—532no—
657C4⋊C4—532no—
658C4⋊C4—532no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1061no—
665C4⋊C4—1061no—
666C4⋊C4—1061no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4C23×D5312yes—
670C22⋊C4—534no—
671C22⋊C4—534no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C42—24no—
679C42—1064no—
680C42D4×D5312yes—
681C42C23×D5312yes—
682C23—532no—
683C23—532no—
684C23—1062no—
685C23—1062no—
686C23—1064no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—2122no—
693C23—2122no—
694C23C2×D4×D5311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704D4—534no—
705D4—1064no—
706D4—1062no—
707D4—2124no—
708D4—2128no—
709D4—2128no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—532no—
721C2×C4—532no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1064no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—2128no—
734C2×C4—2128no—
735C2×C4—2128no—
736C2×C4—2128no—
737C2×C4—2122no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4C2×D4×D5312yes—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4#41×D5312yes—
744C2×C4#1313326212yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—1062no—
751C22—1062no—
752C22—1064no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—1062no—
757C22—2124no—
758C22—2124no—
759C22—2128no—
760C22—2122no—
761C22—2122no—
762C22#1681127012yes—
763C22#1681142212yes—
764C22#1681143612yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—1062no—
773C4—1062no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681127012yes—
778C4C2×#41×D5311yescharacteristic
779C4C2×#1313326211yescharacteristic
780C2—2122no—
781C2—2122no—
782C2—2124no—
783C2#2028681814yesdirect product factor
784C2C2×#1681127011yescharacteristic
785C2C2×#1681142211yescharacteristic
786C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#462C2
socleC23×C53C22×D4
prime radicalC2×#16811276C2
hypercenterC2×#462D53
hypocenterC53C2×#3315
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16811314C2semidirect
3. #20286818C2direct (N × H)
4. C2×#16810991C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810924C2semidirect
8. C2×#16810878C2semidirect
9. C2×#16810861C2semidirect
10. C2×#16810784C2semidirect
11. C2×#16810784C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810693C2semidirect
14. C2×#16810623C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#462C2semidirect
23. #16811314C22semidirect
43. #16810991C22semidirect
44. #16810962C22semidirect
45. #16810957C22semidirect
46. #16810924C22semidirect
47. #16810878C22semidirect
48. #16810861C22semidirect
49. #16810784C22semidirect
50. #16810784C22semidirect
51. #16810721C22semidirect
52. #16810693C22semidirect
56. #16810623C22semidirect
57. #16810618C22semidirect
73. C53×#462C22semidirect
396. C2×#462D53semidirect
403. C2×C53#3315semidirect
446. #462C2×D53semidirect
470. C53C2×#3315semidirect
783. C2#20286818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113142
C2×#168112762
#202868182
C2×#168109912
C2×#168109572
C2×#168109622
C2×#168109242
C2×#168108782
C2×#168108612
C2×#168107842
C2×#168107212
C2×#168106932
C2×#168106232
C2×#168106182
C2×C53×#4622
C2×#331553