Finite Group Databasebeta

← C2×#20287804 #28265123

Subgroups — C2×#20287804 #28265123

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×#16811358C211yesmaximal, characteristic, complemented
2C2×#16811356C211yesmaximal, characteristic, complemented
3#20287804C2116yesmaximal, direct product factor
4C2×#16811012C211yesmaximal, characteristic, complemented
5C2×#16811009C211yesmaximal, characteristic, complemented
6C2×#16811004C211yesmaximal, characteristic, complemented
7C2×#16810848C211yesmaximal, characteristic, complemented
8C2×#16810845C211yesmaximal, characteristic, complemented
9C2×#16810841C211yesmaximal, characteristic, complemented
10C2×#16810837C211yesmaximal, characteristic, complemented
11C2×#16810818C211yesmaximal, characteristic, complemented
12C2×#16810817C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810722C211yesmaximal, characteristic, complemented
15C2×#16810705C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×D424C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719922C2211yescharacteristic
25#16811358—24no—
26#16811358C2218yescomplemented
27#16811356—24no—
28#16811356C2218yescomplemented
29C2×#13133214C2211yescharacteristic
30C2×#13133213C2211yescharacteristic
31C2×#13133206C2211yescharacteristic
32C2×#13133206C2211yescharacteristic
33C2×#13133205—21no—
34C2×#13133205C2211yescharacteristic
35C2×#13133204C2211yescharacteristic
36C2×#13133203—21no—
37C2×#13133202—21no—
38C2×#13133202—21no—
39C2×#13133200—21no—
40C2×#13133199—21no—
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×C4×D212—21no—
44C2×#13133179C2211yescharacteristic
45C2×#13133179C2211yescharacteristic
46C2×#13133179C2211yescharacteristic
47C2×C4×C22⋊D53—21no—
48#16811012C2218yescomplemented
49#16811009C2218yescomplemented
50#16811004C2218yescomplemented
51#16810848C2218yescomplemented
52#16810845C2218yescomplemented
53#16810841C2218yescomplemented
54#16810837C2218yescomplemented
55#16810818C2218yescomplemented
56#16810817C2218yescomplemented
57#16810751C2218yescomplemented
58#16810722C2218yescomplemented
59#16810705C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212—21no—
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C2×#11719913—24no—
92C2×#11719913—42no—
93C2×#11719913C2314yes—
94C2×#11719913C2314yes—
95C2×#11719924—42no—
96C2×#11719924C2314yes—
97C2×D424—24no—
98C2×D424—42no—
99C2×D424C2314yes—
100C2×D424C2314yes—
101C2×#11719922—42no—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C2×#11719922C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133214—22no—
108#13133214C2314yes—
109#13133213—22no—
110#13133213C2314yes—
111#13133206—22no—
112#13133206—22no—
113#13133206C2314yes—
114#13133206C2314yes—
115#13133205—22no—
116#13133205—28no—
117#13133205C2314yes—
118#13133204—22no—
119#13133204C2314yes—
120#13133203—28no—
121#13133202—28no—
122#13133202—28no—
123#13133200—28no—
124#13133199—28no—
125C4×Dic106D414yes—
126C4×Dic106C2314yes—
127#13133182—22no—
128#13133182C2314yes—
129C4×D212—28no—
130#13133179—22no—
131#13133179—22no—
132#13133179—22no—
133#13133179C2314yes—
134#13133179C2314yes—
135#13133179C2314yes—
136C4×C22⋊D53—28no—
137C2×C4⋊Dic53D411yescharacteristic
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yes—
156#13133146C2314yes—
157#13133146C2314yes—
158#13133140C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—24no—
168C2×SD16×C53C2314yes—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#107×C53C2314yes—
182#103×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C23×D53—21no—
187C23×D53—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—22no—
195C2×D4×C53—22no—
196C2×D4×C53C2412yes—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—24no—
201C22×C4×C53—82no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—82no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—24no—
224C2×D212—24no—
225C2×D212—44no—
226C2×D212—82no—
227C2×D212C2412yes—
228C2×D212C2412yes—
229C2×D212C2412yes—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—82no—
234C2×C4×D53—82no—
235C2×C4×D53—82no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—21no—
239C2×Dic106—42no—
240C2×Dic106C2×D414yes—
241C2×Dic106C2412yes—
242SD16×C53—28no—
243C2×C8×C53—22no—
244C2×C8×C53#4114yes—
245C2×C8×C53C2412yes—
246C2×C8×C53C2412yes—
247C4⋊C4×C53—24no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C22⋊C4×C53—24no—
253C42×C53—24no—
254C42×C53C2×D412yes—
255C42×C53C2412yes—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258#11719925—44no—
259#11719924—44no—
260#11719922—44no—
261#11719922—44no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271C4⋊Dic53C2×D414yes—
272#11719919—24no—
273#11719919C2×D414yes—
274#11719919C2×D414yes—
275C4×Dic53—24no—
276C4×Dic53C2×D412yes—
277C4×Dic53C2×D412yes—
278C4×Dic53C2412yes—
279C4×Dic53C2412yes—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284D424—28no—
285D424—44no—
286#11719913—28no—
287#11719913—44no—
288C23×C53—22no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
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—42no—
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—84no—
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
326C22⋊D53—48no—
327C22⋊D53—84no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—22no—
339D212—22no—
340D212—22no—
341D212—22no—
342D212—22no—
343D212—22no—
344D212—48no—
345D212—42no—
346D212—42no—
347D212—42no—
348D212—84no—
349C4×D53—84no—
350C4×D53—84no—
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—84no—
365C22×C53#55012yes—
366C22×C53#57512yes—
367C22×C53#57612yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—42no—
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—84no—
379C2×D53—84no—
380C2×D53—84no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53#55012yes—
387C4×C53C22×#4111yescharacteristic
388C4×C53C2×H(5,𝔽2)11yescharacteristic
389Dic53—22no—
390Dic53—22no—
391Dic53—22no—
392Dic53—22no—
393Dic53—42no—
394C2×#559—531no—
395C2×#559—531no—
396#3403—5316no—
397C2×#496—531no—
398C2×#496—531no—
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×#440D5311yescharacteristic, complemented
409C2×C4×D8—531no—
410C2×C53—82no—
411C2×C53#340314yescomplemented
412C2×C53C2×#55011yescharacteristic
413C2×C53C2×#57511yescharacteristic
414C2×C53C2×#57611yescharacteristic
415D53—82no—
416D53—82no—
417D53—82no—
418C22×Q16—531no—
419C22×SD16—531no—
420C22×SD16—531no—
421C22×SD16—531no—
422C22×SD16C2×D5311yescharacteristic
423C22×D8—531no—
424C22×D8—531no—
425C22×D8—531no—
426C22×D8—531no—
427#559—538no—
428#559—538no—
429#559—1064no—
430#559—1064no—
431C2×#127—531no—
432C2×#127—531no—
433C2×#124—531no—
434C2×#124—531no—
435C2×#124—531no—
436C2×#124—531no—
437C2×#124—1061no—
438C2×#124—1061no—
439C2×#123—1061no—
440C2×#123—1061no—
441C2×#123—1061no—
442C2×#123—1061no—
443C2×C4×Q8—531no—
444C2×C4×Q8—531no—
445C2×C4×Q8C2×D5311yescharacteristic
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—1061no—
450C2×C4×D4—1061no—
451C2×C4×D4C2×D5311yescharacteristic
452#496—538no—
453#496—538no—
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#440C2×D5318yescomplemented
464C4×D8—538no—
465C2×#107C2×D5311yescharacteristic
466C2×C4⋊C8—531no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
469C2×#103—531no—
470C2×#103C2×D5311yescharacteristic
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102C2×D5311yescharacteristic
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—531no—
483C22×D4—531no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4—1061no—
488C22×D4—1061no—
489C22×D4C22×D5311yescharacteristic
490C23×C4—21no—
491C23×C4—1061no—
492C23×C4—1061no—
493C23×C4—1061no—
494C2×Q16—534no—
495C2×Q16—2122no—
496C2×SD16—24no—
497C2×SD16—534no—
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—1064no—
501C2×SD16—2122no—
502C2×SD16—2122no—
503C2×SD16C22×D5314yes—
504C2×D8—534no—
505C2×D8—534no—
506C2×D8—534no—
507C2×D8—534no—
508C2×D8—1064no—
509C2×D8—2122no—
510C2×D8—2122no—
511C2×D8—2122no—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8C22×D5311yescharacteristic
515C22×C8C22×D5311yescharacteristic
516#127—534no—
517#127—534no—
518#127—1062no—
519#127—1062no—
520#124—534no—
521#124—534no—
522#124—534no—
523#124—534no—
524#124—1068no—
525#124—1062no—
526#124—1062no—
527#124—1062no—
528#124—1068no—
529#124—1062no—
530#123—1068no—
531#123—1068no—
532#123—1068no—
533#123—1068no—
534C4×Q8—22no—
535C4×Q8—534no—
536C4×Q8—534no—
537C4×Q8—534no—
538C4×Q8—1062no—
539C4×Q8C22×D5314yes—
540C4×D4—22no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1068no—
545C4×D4—1062no—
546C4×D4—1062no—
547C4×D4—1062no—
548C4×D4—1068no—
549C4×D4C22×D5314yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—1061no—
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—21no—
570C2×C42—531no—
571C2×C42—531no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107C22×D5314yes—
575C4⋊C8—534no—
576C4⋊C8—534no—
577C4⋊C8—534no—
578#103—534no—
579#103C22×D5314yes—
580#102—534no—
581#102—534no—
582#102—534no—
583#102C22×D5314yes—
584#97—534no—
585#97C22×D5314yes—
586C4×C8—534no—
587C24—21no—
588C24—1061no—
589C24—1061no—
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—22no—
603C2×D4—22no—
604C2×D4—532no—
605C2×D4—532no—
606C2×D4—532no—
607C2×D4—1064no—
608C2×D4—1064no—
609C2×D4—1064no—
610C2×D4—1064no—
611C2×D4—1061no—
612C2×D4—1061no—
613C2×D4—1061no—
614C2×D4—1062no—
615C2×D4—1062no—
616C2×D4—1062no—
617C2×D4—1062no—
618C2×D4—1062no—
619C2×D4—1062no—
620C2×D4—4242no—
621C2×D4—4242no—
622C2×D4—2124no—
623C2×D4—2124no—
624C2×D4C23×D5312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—531no—
631C22×C4—531no—
632C22×C4—531no—
633C22×C4—531no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1064no—
637C22×C4—1061no—
638C22×C4—4242no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4D4×D5311yescharacteristic
642C22×C4D4×D5311yescharacteristic
643C22×C4C23×D5311yescharacteristic
644Q16—2124no—
645SD16—28no—
646SD16—1068no—
647SD16—2124no—
648SD16—2124no—
649D8—1068no—
650D8—2124no—
651D8—2124no—
652D8—2124no—
653C2×C8—22no—
654C2×C8—532no—
655C2×C8—532no—
656C2×C8—1062no—
657C2×C8—1062no—
658C2×C8#1171994514yes—
659C2×C8C23×D5312yes—
660C2×C8C23×D5312yes—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—534no—
665C4⋊C4—534no—
666C4⋊C4—534no—
667C4⋊C4—1064no—
668C4⋊C4C23×D5312yes—
669C4⋊C4C23×D5312yes—
670C22⋊C4—24no—
671C22⋊C4—1064no—
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—24no—
683C42—532no—
684C42—532no—
685C42—532no—
686C42—532no—
687C42—1064no—
688C42D4×D5312yes—
689C42C23×D5312yes—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
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
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—1062no—
711Q8—1062no—
712Q8—2124no—
713Q8—2122no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—1062no—
718D4—1062no—
719D4—1062no—
720D4—1062no—
721D4—1062no—
722D4—1062no—
723D4—4244no—
724D4—4244no—
725D4—2128no—
726D4—2128no—
727D4—2122no—
728D4—2122no—
729D4—2122no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—84no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—532no—
742C2×C4—532no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—4244no—
749C2×C4—4244no—
750C2×C4—4244no—
751C2×C4—2122no—
752C2×C4C2×D4×D5312yes—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4C2×#1171994512yes—
756C2×C4#1313326312yes—
757C2×C4C24×D5311yescharacteristic
758C8—22no—
759C8—1062no—
760C8—1062no—
761C8C2×#1171994514yes—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—4244no—
767C22—4244no—
768C22—4244no—
769C22—2122no—
770C22—2122no—
771C22—2122no—
772C22—2122no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22#1681129412yes—
779C22#1681142212yes—
780C22#1681142712yes—
781C22C22×D4×D5311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—1062no—
788C4—1062no—
789C4—1062no—
790C4—1062no—
791C4—2122no—
792C4#1681129412yes—
793C4C22×#1171994511yescharacteristic
794C4C2×#1313326311yescharacteristic
795C2—82no—
796C2—4242no—
797C2—4242no—
798C2—4242no—
799C2#2028780414yesdirect product factor
800C2C2×#1681129411yescharacteristic
801C2C2×#1681142211yescharacteristic
802C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3403
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811358C2semidirect
2. C2×#16811356C2semidirect
3. #20287804C2direct (N × H)
4. C2×#16811012C2semidirect
5. C2×#16811009C2semidirect
6. C2×#16811004C2semidirect
7. C2×#16810848C2semidirect
8. C2×#16810845C2semidirect
9. C2×#16810841C2semidirect
10. C2×#16810837C2semidirect
11. C2×#16810818C2semidirect
12. C2×#16810817C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810722C2semidirect
15. C2×#16810705C2semidirect
16. C2×C53×#440C2semidirect
26. #16811358C22semidirect
28. #16811356C22semidirect
48. #16811012C22semidirect
49. #16811009C22semidirect
50. #16811004C22semidirect
51. #16810848C22semidirect
52. #16810845C22semidirect
53. #16810841C22semidirect
54. #16810837C22semidirect
55. #16810818C22semidirect
56. #16810817C22semidirect
57. #16810751C22semidirect
58. #16810722C22semidirect
59. #16810705C22semidirect
72. C53×#440C22semidirect
408. C2×#440D53semidirect
411. C2×C53#3403semidirect
463. #440C2×D53semidirect
478. C53C2×#3403semidirect
799. C2#20287804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113582
C2×#168113562
#202878042
C2×#168110122
C2×#168110092
C2×#168110042
C2×#168108482
C2×#168108452
C2×#168108412
C2×#168108372
C2×#168108182
C2×#168108172
C2×#168107512
C2×#168107222
C2×#168107052
C2×C53×#4402
C2×#340353