Finite Group Databasebeta

← C2×#20287800 #28265119

Subgroups — C2×#20287800 #28265119

Order 13568.

2066 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×#16811359C211yesmaximal, characteristic, complemented
2C2×#16811355C211yesmaximal, characteristic, complemented
3#20287800C2116yesmaximal, direct product factor
4C2×#16811011C211yesmaximal, characteristic, complemented
5C2×#16811004C211yesmaximal, characteristic, complemented
6C2×#16810843C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810840C211yesmaximal, characteristic, complemented
9C2×#16810836C211yesmaximal, characteristic, complemented
10C2×#16810816C211yesmaximal, characteristic, complemented
11C2×#16810815C211yesmaximal, characteristic, complemented
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810724C211yesmaximal, characteristic, complemented
15C2×D8×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#496C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811359—24no—
23#16811359C2218yescomplemented
24#16811355—24no—
25#16811355C2218yescomplemented
26C2×#13133213C2211yescharacteristic
27C2×#13133206C2211yescharacteristic
28C2×#13133204—21no—
29C2×#13133204C2211yescharacteristic
30C2×#13133204C2211yescharacteristic
31C2×#13133203—21no—
32C2×#13133201—21no—
33C2×#13133199—21no—
34C2×#13133198—21no—
35C2×#13133198—21no—
36C2×Q8×Dic53C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×D212C2211yescharacteristic
40C2×D4×Dic53—21no—
41C2×D4×Dic53C2211yescharacteristic
42C2×D4×Dic53C2211yescharacteristic
43C2×D4×Dic53C2211yescharacteristic
44C2×#13133177—21no—
45#16811011C2218yescomplemented
46#16811004C2218yescomplemented
47#16810843C2218yescomplemented
48#16810842C2218yescomplemented
49#16810840C2218yescomplemented
50#16810836C2218yescomplemented
51#16810816C2218yescomplemented
52#16810815C2218yescomplemented
53#16810751C2218yescomplemented
54#16810725C2218yescomplemented
55#16810724C2218yescomplemented
56D8×Dic53C2218yescomplemented
57C2×#13133151C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C22×D8×C53C2211yescharacteristic
73C2×#127×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic
75C53×#496C2218yescomplemented
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C23×Dic53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719925—42no—
87C2×#11719925C2314yes—
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90C2×#11719923—42no—
91C2×#11719923C2314yes—
92C2×#11719922—42no—
93C2×#11719922—42no—
94C2×#11719922C2314yes—
95C2×#11719922C2314yes—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98#13133213—22no—
99#13133213C2314yes—
100#13133206—22no—
101#13133206C2314yes—
102#13133204—22no—
103#13133204—22no—
104#13133204—28no—
105#13133204C2314yes—
106#13133204C2314yes—
107#13133203—28no—
108#13133201—28no—
109#13133199—28no—
110#13133198—28no—
111#13133198—28no—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114C4×Dic106—22no—
115C4×Dic106D414yes—
116C4×Dic106C2314yes—
117C4×Dic106C2314yes—
118C4×D212—22no—
119C4×D212C2314yes—
120D4×Dic53—28no—
121D4×Dic53—22no—
122D4×Dic53—22no—
123D4×Dic53—22no—
124D4×Dic53C2314yes—
125D4×Dic53C2314yes—
126D4×Dic53C2314yes—
127#13133177—28no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53D411yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919D411yescharacteristic
134C2×#11719919D411yescharacteristic
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149#13133151C2314yes—
150C4⋊#88322C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133127C2314yes—
160C8×Dic53C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53—21no—
163C22×D4×C53—21no—
164C22×D4×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C2×SD16×C53—24no—
168C2×SD16×C53—42no—
169C2×SD16×C53C2314yes—
170C2×SD16×C53C2314yes—
171C2×D8×C53—24no—
172C2×D8×C53—42no—
173C2×D8×C53C2314yes—
174C2×D8×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177#127×C53—22no—
178#127×C53C2314yes—
179#124×C53—22no—
180#124×C53C2314yes—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53C2311yescharacteristic
184#97×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C23×D53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—24no—
197C2×D4×C53—24no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—44no—
205C2×D4×C53—82no—
206C2×D4×C53C2412yes—
207C2×D4×C53C2412yes—
208C2×D4×C53C2412yes—
209C22×C4×C53—21no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—82no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—24no—
221C22×Dic53—24no—
222C22×Dic53—24no—
223C22×Dic53—82no—
224C22×Dic53—82no—
225C22×Dic53—82no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212C2412yes—
234C2×C4×D53—24no—
235C2×C4×D53—82no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—21no—
239C2×Dic106—42no—
240C2×Dic106C2×D414yes—
241C2×Dic106C2412yes—
242SD16×C53—28no—
243SD16×C53—44no—
244D8×C53—28no—
245D8×C53—44no—
246C2×C8×C53—22no—
247C2×C8×C53#4114yes—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C42×C53C2×D412yes—
253C42×C53C2412yes—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261#11719925—44no—
262#11719923—44no—
263#11719922—44no—
264#11719922—44no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—24no—
271C4⋊Dic53C2×D414yes—
272C4⋊Dic53C2412yes—
273C4⋊Dic53C2412yes—
274#11719919—24no—
275#11719919C2×D414yes—
276#11719919C2×D414yes—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53C2×D412yes—
280C4×Dic53C2×D412yes—
281C4×Dic53C2412yes—
282C4×Dic53C2412yes—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287#11719913—28no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53C22×D411yescharacteristic
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—42no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—48no—
315D4×C53—42no—
316D4×C53—42no—
317D4×C53—42no—
318D4×C53—84no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—42no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4112yes—
327C2×C4×C53H(5,𝔽2)12yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—48no—
330C22⋊D53—84no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—84no—
342C2×Dic53—84no—
343C2×Dic53—84no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348D212—22no—
349D212—22no—
350D212—42no—
351C4×D53—84no—
352Dic106—22no—
353Dic106—22no—
354Dic106—44no—
355Dic106—42no—
356C8×C53—22no—
357C8×C53C2×#4114yes—
358#88322—22no—
359#88322—22no—
360C2×#3403—531nomaximal, Sylow
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—84no—
371C22×C53—84no—
372C22×C53—84no—
373C22×C53#55012yes—
374C22×C53#57512yes—
375C22×C53#57612yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—84no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—42no—
384C4×C53#55012yes—
385C4×C53C22×#4111yescharacteristic
386C4×C53C2×H(5,𝔽2)11yescharacteristic
387Dic53—22no—
388Dic53—22no—
389Dic53—22no—
390Dic53—22no—
391Dic53—42no—
392Dic53—42no—
393Dic53—42no—
394C2×#559—531no—
395C2×#559—531no—
396#3403—5316no—
397C2×#496—531no—
398C2×#496D5311yescharacteristic, complemented
399C2×#495—531no—
400C2×#464—531no—
401C2×#464—531no—
402C2×#463—531no—
403C2×#463—531no—
404C2×#459—531no—
405C2×#459—531no—
406C2×#446—531no—
407C2×#440—531no—
408C2×#440—531no—
409C2×C4×D8—531no—
410C2×C53—82no—
411C2×C53—82no—
412C2×C53—82no—
413C2×C53#340314yescomplemented
414C2×C53C2×#55011yescharacteristic
415C2×C53C2×#57511yescharacteristic
416C2×C53C2×#57611yescharacteristic
417D53—82no—
418C22×Q16—531no—
419C22×SD16—531no—
420C22×SD16—531no—
421C22×SD16C2×D5311yescharacteristic
422C22×SD16C2×D5311yescharacteristic
423C22×D8—531no—
424C22×D8—531no—
425C22×D8C2×D5311yescharacteristic
426C22×D8C2×D5311yescharacteristic
427#559—538no—
428#559—538no—
429#559—1064no—
430#559—1064no—
431C2×#127—531no—
432C2×#127C2×D5311yescharacteristic
433C2×#124—531no—
434C2×#124—531no—
435C2×#124—531no—
436C2×#124—1061no—
437C2×#124—1061no—
438C2×#124C2×D5311yescharacteristic
439C2×#123—1061no—
440C2×#123—1061no—
441C2×#123—1061no—
442C2×#123—1061no—
443C2×C4×Q8—531no—
444C2×C4×Q8—531no—
445C2×C4×Q8—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—531no—
450C2×C4×D4—1061no—
451C2×C4×D4—1061no—
452#496—538no—
453#496C2×D5318yescomplemented
454#495—538no—
455#464—538no—
456#464—538no—
457#463—538no—
458#463—538no—
459#459—538no—
460#459—538no—
461#446—538no—
462#440—538no—
463#440—538no—
464C4×D8—538no—
465C2×#107—531no—
466C2×C4⋊C8—531no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#97—531no—
476C2×#97C2×D5311yescharacteristic
477C2×C4×C8—531no—
478C53C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—531no—
480C22×Q8—531no—
481C22×Q8C22×D5311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4C22×D5311yescharacteristic
488C22×D4C22×D5311yescharacteristic
489C22×D4C22×D5311yescharacteristic
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4—1061no—
493C23×C4—1061no—
494C2×Q16—534no—
495C2×Q16—2122no—
496C2×SD16—24no—
497C2×SD16—42no—
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—1064no—
501C2×SD16—2122no—
502C2×SD16C22×D5314yes—
503C2×SD16C22×D5314yes—
504C2×D8—24no—
505C2×D8—42no—
506C2×D8—534no—
507C2×D8—534no—
508C2×D8—2122no—
509C2×D8—2122no—
510C2×D8C22×D5314yes—
511C2×D8C22×D5314yes—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8C22×D5311yescharacteristic
515C22×C8C22×D5311yescharacteristic
516#127—22no—
517#127—534no—
518#127—1062no—
519#127C22×D5314yes—
520#124—22no—
521#124—534no—
522#124—534no—
523#124—534no—
524#124—1062no—
525#124—1062no—
526#124—1062no—
527#124—1068no—
528#124—1068no—
529#124C22×D5314yes—
530#123—1068no—
531#123—1068no—
532#123—1068no—
533#123—1068no—
534C4×Q8—534no—
535C4×Q8—534no—
536C4×Q8—534no—
537C4×Q8—534no—
538C4×Q8—1062no—
539C4×Q8—1062no—
540C4×D4—534no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1062no—
545C4×D4—1062no—
546C4×D4—1062no—
547C4×D4—1068no—
548C4×D4—1068no—
549C4×D4—1062no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1061no—
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×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C42—531no—
570C2×C42—531no—
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575C4⋊C8—534no—
576C4⋊C8—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#102—534no—
581#102—534no—
582#102—534no—
583#102—534no—
584#97—534no—
585#97C22×D5314yes—
586C4×C8—534no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—1061no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—534no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—2122no—
600C2×Q8C23×D5312yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—82no—
614C2×D4—532no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1061no—
618C2×D4—1062no—
619C2×D4—1062no—
620C2×D4—4242no—
621C2×D4—2124no—
622C2×D4C23×D5312yes—
623C2×D4C23×D5312yes—
624C2×D4C23×D5312yes—
625C22×C4—21no—
626C22×C4—531no—
627C22×C4—531no—
628C22×C4—531no—
629C22×C4—531no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1064no—
637C22×C4—4242no—
638C22×C4—4242no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4D4×D5311yescharacteristic
642C22×C4D4×D5311yescharacteristic
643C22×C4C23×D5311yescharacteristic
644Q16—2124no—
645SD16—28no—
646SD16—44no—
647SD16—1068no—
648SD16—2124no—
649D8—28no—
650D8—44no—
651D8—2124no—
652D8—2124no—
653C2×C8—22no—
654C2×C8—532no—
655C2×C8—532no—
656C2×C8—1062no—
657C2×C8—1062no—
658C2×C8#1171994714yes—
659C2×C8C23×D5312yes—
660C2×C8C23×D5312yes—
661C4⋊C4—534no—
662C4⋊C4—534no—
663C4⋊C4—534no—
664C4⋊C4—532no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1061no—
668C4⋊C4—1061no—
669C4⋊C4—1064no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
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—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C42D4×D5312yes—
689C42C23×D5312yes—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—1062no—
703C23—2122no—
704C23—2122no—
705C23—2122no—
706C23C2×D4×D5311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—1062no—
711Q8—1062no—
712Q8—2124no—
713Q8—2122no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—84no—
725D4—1062no—
726D4—1062no—
727D4—4244no—
728D4—2128no—
729D4—2122no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—532no—
735C2×C4—532no—
736C2×C4—532no—
737C2×C4—532no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—4244no—
746C2×C4—4244no—
747C2×C4—4244no—
748C2×C4—4244no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4C2×D4×D5312yes—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4C2×#1171994712yes—
756C2×C4#1313326212yes—
757C2×C4C24×D5311yescharacteristic
758C8—22no—
759C8—1062no—
760C8—1062no—
761C8C2×#1171994714yes—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—84no—
772C22—84no—
773C22—84no—
774C22—4244no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22#1681129312yes—
779C22#1681141912yes—
780C22#1681142712yes—
781C22C22×D4×D5311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—1062no—
786C4—1062no—
787C4—1062no—
788C4—1062no—
789C4—2122no—
790C4—2122no—
791C4—2122no—
792C4#1681129312yes—
793C4C22×#1171994711yescharacteristic
794C4C2×#1313326211yescharacteristic
795C2—82no—
796C2—82no—
797C2—82no—
798C2—4242no—
799C2#2028780014yesdirect product factor
800C2C2×#1681129311yescharacteristic
801C2C2×#1681141911yescharacteristic
802C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#496C2
socleC23×C53C22×D4
hypercenterC2×#496D53
hypocenterC53C2×#3403
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#16811359C2semidirect
2. C2×#16811355C2semidirect
3. #20287800C2direct (N × H)
4. C2×#16811011C2semidirect
5. C2×#16811004C2semidirect
6. C2×#16810843C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810840C2semidirect
9. C2×#16810836C2semidirect
10. C2×#16810816C2semidirect
11. C2×#16810815C2semidirect
12. C2×#16810751C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810724C2semidirect
15. C2×D8×Dic53C2semidirect
16. C2×C53×#496C2semidirect
23. #16811359C22semidirect
25. #16811355C22semidirect
45. #16811011C22semidirect
46. #16811004C22semidirect
47. #16810843C22semidirect
48. #16810842C22semidirect
49. #16810840C22semidirect
50. #16810836C22semidirect
51. #16810816C22semidirect
52. #16810815C22semidirect
53. #16810751C22semidirect
54. #16810725C22semidirect
55. #16810724C22semidirect
56. D8×Dic53C22semidirect
75. C53×#496C22semidirect
398. C2×#496D53semidirect
413. C2×C53#3403semidirect
453. #496C2×D53semidirect
478. C53C2×#3403semidirect
799. C2#20287800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113592
C2×#168113552
#202878002
C2×#168110112
C2×#168110042
C2×#168108432
C2×#168108422
C2×#168108402
C2×#168108362
C2×#168108162
C2×#168108152
C2×#168107512
C2×#168107252
C2×#168107242
C2×D8×Dic532
C2×C53×#4962
C2×#340353