Finite Group Databasebeta

← C2×#20287051 #28261035

Subgroups — C2×#20287051 #28261035

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic, complemented
2C2×#16811291C211yesmaximal, characteristic
3#20287051C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810938C211yesmaximal, characteristic, complemented
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810867C211yesmaximal, characteristic, complemented
9C2×#16810822C211yesmaximal, characteristic, complemented
10C2×#16810787C211yesmaximal, characteristic, complemented
11C2×#16810786C211yesmaximal, characteristic, complemented
12C2×#16810717C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810621C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×#11719912C2211yescharacteristic
24#16811328—24no—
25#16811328C2218yescomplemented
26#16811291—24no—
27#16811291C2218yes—
28C2×#13133216C2211yescharacteristic
29C2×#13133213—21no—
30C2×#13133213C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133196—21no—
34C2×#13133196C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133189—21no—
39C2×#13133182C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133177—21no—
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810968C2218yescomplemented
46#16810938C2218yescomplemented
47#16810917C2218yescomplemented
48#16810870C2218yescomplemented
49#16810867C2218yescomplemented
50#16810822C2218yescomplemented
51#16810787C2218yescomplemented
52#16810786C2218yescomplemented
53#16810717C2218yescomplemented
54#16810698C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810622C2218yescomplemented
58#16810621C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#480C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C2×#11719947—22no—
82C2×#11719947—24no—
83C2×#11719947—42no—
84C2×#11719947C2314yes—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53D411yescharacteristic
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C22×C4×D53C2311yescharacteristic
99C2×Dic212—24no—
100C2×Dic212C2314yes—
101C2×#11719913—42no—
102C2×#11719913C2314yes—
103C2×#11719923—42no—
104C2×#11719923C2314yes—
105C2×#11719917—42no—
106C2×#11719917C2314yes—
107C2×#11719912—42no—
108C2×#11719912C2314yes—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111#13133216—22no—
112#13133216C2314yes—
113#13133213—22no—
114#13133213—28no—
115#13133213C2314yes—
116#13133207—28no—
117#13133197—22no—
118#13133197C2314yes—
119#13133196—28no—
120#13133196—22no—
121#13133196C2314yes—
122#13133195—28no—
123#13133192—22no—
124#13133192C2314yes—
125#13133190—28no—
126#13133189—28no—
127#13133182—22no—
128#13133182—22no—
129#13133182C2314yes—
130#13133182C2314yes—
131C4×C22⋊D53—28no—
132C4×C22⋊D53D414yes—
133C4×C22⋊D53C2314yes—
134#13133177—28no—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919D411yescharacteristic
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yes—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133139C2314yes—
160#13133138C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171#121×C53—22no—
172#121×C53C2314yes—
173C2×C4⋊C4×C53—22no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180#107×C53C2314yes—
181#107×C53C2314yes—
182#102×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C2×D4×C53—24no—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—82no—
194C2×D4×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
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×D412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53—44no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—82no—
215C2×C22⋊D53C2×D414yes—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—24no—
220C22×Dic53—44no—
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224#11719947—28no—
225#11719947—44no—
226#11719947—48no—
227#11719945—28no—
228#11719945—44no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212—24no—
234C2×D212—82no—
235C2×D212C2412yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—44no—
241C2×C4×D53—82no—
242C2×C4×D53C2×D412yes—
243C2×C4×D53C2412yes—
244C2×Dic106—21no—
245C2×Dic106—22no—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106—24no—
250C2×Dic106—82no—
251C2×Dic106#4114yes—
252C2×Dic106C2412yes—
253C2×Dic106C2412yes—
254C2×C8×C53—22no—
255C2×C8×C53—22no—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53C2412yes—
263C4⋊C4×C53C2412yes—
264C4⋊C4×C53C2412yes—
265C22⋊C4×C53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53C2×D414yes—
268#11719923—44no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919C2×D414yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285#11719917—44no—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290Dic212—28no—
291#11719913—44no—
292#11719912—44no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53C22×D412yes—
301C23×C53C22×D411yescharacteristic
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53C22×D412yes—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—42no—
313D4×C53—84no—
314C2×C4×C53—22no—
315C2×C4×C53—24no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—84no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4112yes—
328C2×C4×C53H(5,𝔽2)12yes—
329C2×C4×C53C2511yescharacteristic
330C22⋊D53—28no—
331C22⋊D53—48no—
332C22⋊D53—48no—
333C22⋊D53—48no—
334C22⋊D53—84no—
335C2×Dic53—24no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—48no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53#13714yes—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348D212—22no—
349D212—22no—
350D212—42no—
351D212—84no—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—48no—
356C4×D53—84no—
357Dic106—24no—
358Dic106—22no—
359Dic106—22no—
360Dic106—22no—
361Dic106—42no—
362Dic106—84no—
363Dic106C2×#4114yes—
364C8×C53—22no—
365C8×C53—22no—
366#88322—22no—
367#88322—22no—
368C2×#3333—531nomaximal, Sylow
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—44no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—84no—
377C22×C53#54612yes—
378C22×C53C2×#13712yes—
379C22×C53#57612yes—
380C22×C53C23×D411yescharacteristic
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—44no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—84no—
389C4×C53—22no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53#54612yes—
394C4×C53C22×#4111yescharacteristic
395C4×C53C2×H(5,𝔽2)11yescharacteristic
396Dic53—24no—
397Dic53—22no—
398Dic53—22no—
399Dic53—42no—
400Dic53—42no—
401Dic53C2×#13714yes—
402C2×#554—531no—
403C2×#550—531no—
404#3333—5316no—
405C2×#486—531no—
406C2×#480—531no—
407C2×#480D5311yescharacteristic, complemented
408C2×#477—531no—
409C2×#468—531no—
410C2×#468—531no—
411C2×#460—531no—
412C2×#452—531no—
413C2×#452—531no—
414C2×C4×Q16—531no—
415C2×#436—531no—
416C2×#417—531no—
417C2×#417—531no—
418C2×C53—42no—
419C2×C53—82no—
420C2×C53#333314yescomplemented
421C2×C53C2×#54611yescharacteristic
422C2×C53C22×#13711yescharacteristic
423C2×C53C2×#57611yescharacteristic
424D53—42no—
425D53—82no—
426C22×#41—531no—
427C22×#41—531no—
428C22×Q16—531no—
429C22×SD16—531no—
430C22×SD16—531no—
431C22×M16—531no—
432C22×M16—531no—
433#554—538no—
434#554—1064no—
435#550—538no—
436#550—1064no—
437C2×C4⋊Q8—531no—
438C2×#127—531no—
439C2×#127—1061no—
440C2×#125—1061no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8—1061no—
444C2×C22⋊Q8—1061no—
445C2×#121—531no—
446C2×#121—1061no—
447C2×#121—1061no—
448C2×#121C2×D5311yescharacteristic
449C2×C4×Q8—531no—
450C2×C4×Q8—531no—
451C2×C4×D4—531no—
452C2×C4×D4—1061no—
453C2×C4×D4—1061no—
454C22×C4⋊C4—531no—
455C22×C4⋊C4C2×D5311yescharacteristic
456#486—538no—
457#480—538no—
458#480C2×D5318yescomplemented
459#477—538no—
460#468—538no—
461#468—538no—
462#460—538no—
463#452—538no—
464#452—538no—
465C4×Q16—538no—
466#436—538no—
467C2×#107—531no—
468C2×#107C2×D5311yescharacteristic
469C2×#107C2×D5311yescharacteristic
470C2×C4⋊C8—531no—
471#417—538no—
472#417—538no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#102C2×D5311yescharacteristic
482C2×#102C2×D5311yescharacteristic
483C2×C22⋊C8—531no—
484C2×C22⋊C8C2×D5311yescharacteristic
485C2×C4×C8—531no—
486C53C2×#333311yescharacteristic, complemented, Sylow
487C2×#41—534no—
488C2×#41—534no—
489C2×#41—1064no—
490C2×#41—1062no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2122no—
494C2×#41—2122no—
495C22×Q8—531no—
496C22×Q8—531no—
497C22×Q8—1061no—
498C22×D4—21no—
499C22×D4—531no—
500C22×D4—531no—
501C22×D4—1061no—
502C22×D4—1061no—
503C22×D4—1061no—
504C22×D4—1061no—
505C22×D4—1061no—
506C22×D4C22×D5311yescharacteristic
507C23×C4—21no—
508C23×C4—531no—
509C23×C4—1061no—
510C23×C4—1061no—
511C23×C4—1061no—
512C23×C4C22×D5311yescharacteristic
513C2×Q16—534no—
514C2×Q16—1064no—
515C2×SD16—534no—
516C2×SD16—534no—
517C2×SD16—2122no—
518C2×SD16—2122no—
519C2×M16—534no—
520C2×M16—534no—
521C2×M16—2122no—
522C2×M16—2122no—
523C22×C8—531no—
524C22×C8—531no—
525C22×C8C22×D5311yescharacteristic
526C22×C8C22×D5311yescharacteristic
527C4⋊Q8—534no—
528C4⋊Q8—1062no—
529#127—534no—
530#127—1062no—
531#127—1068no—
532#125—1068no—
533C22⋊Q8—534no—
534C22⋊Q8—534no—
535C22⋊Q8—1068no—
536C22⋊Q8—1068no—
537C22⋊Q8—1062no—
538C22⋊Q8—1062no—
539#121—22no—
540#121—534no—
541#121—1068no—
542#121—1068no—
543#121—1062no—
544#121C22×D5314yes—
545C4×Q8—534no—
546C4×Q8—534no—
547C4×Q8—1062no—
548C4×Q8—1062no—
549C4×D4—534no—
550C4×D4—534no—
551C4×D4—1068no—
552C4×D4—1068no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—534no—
558C2×C4⋊C4—1062no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5314yes—
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—531no—
571C2×C22⋊C4—531no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C42—531no—
576C2×C42—1061no—
577C2×C42—1061no—
578#107—534no—
579#107C22×D5314yes—
580#107C22×D5314yes—
581C4⋊C8—534no—
582#103—534no—
583#103—534no—
584#103—534no—
585#103—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102—534no—
590#102C22×D5314yes—
591#102C22×D5314yes—
592C22⋊C8—534no—
593C22⋊C8C22×D5314yes—
594C4×C8—534no—
595C24—21no—
596C24—531no—
597C24—1061no—
598C24D4×D5311yescharacteristic
599#41—1068no—
600#41—1068no—
601#41—2124no—
602#41—2128no—
603#41—2124no—
604#41—2128no—
605C2×Q8—534no—
606C2×Q8—532no—
607C2×Q8—532no—
608C2×Q8—1064no—
609C2×Q8—1061no—
610C2×Q8—1061no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8—1062no—
614C2×Q8—4242no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—82no—
620C2×D4—534no—
621C2×D4—532no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1061no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—4242no—
632C2×D4—4242no—
633C2×D4—2124no—
634C2×D4—2124no—
635C2×D4—2124no—
636C2×D4C23×D5312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—82no—
644C22×C4—531no—
645C22×C4—531no—
646C22×C4—531no—
647C22×C4—532no—
648C22×C4—532no—
649C22×C4—1064no—
650C22×C4—1064no—
651C22×C4—1061no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1064no—
657C22×C4—4242no—
658C22×C4—2124no—
659C22×C4—2124no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—1068no—
665SD16—2124no—
666SD16—2124no—
667M16—2124no—
668M16—2124no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—532no—
672C2×C8—532no—
673C2×C8—1062no—
674C2×C8—1062no—
675C2×C8C23×D5312yes—
676C2×C8C23×D5312yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—534no—
682C4⋊C4—532no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1061no—
689C4⋊C4—1064no—
690C4⋊C4C23×D5312yes—
691C4⋊C4C23×D5312yes—
692C4⋊C4C23×D5312yes—
693C22⋊C4—24no—
694C22⋊C4—534no—
695C22⋊C4—534no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C42—532no—
700C42—532no—
701C42—1064no—
702C42—1064no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—532no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23C2×D4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720Q8—534no—
721Q8—1064no—
722Q8—1062no—
723Q8—1062no—
724Q8—1062no—
725Q8—4244no—
726Q8—2122no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—1068no—
732D4—1062no—
733D4—1062no—
734D4—4244no—
735D4—4244no—
736D4—2128no—
737D4—2128no—
738D4—2128no—
739D4—2122no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—534no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—532no—
755C2×C4—1062no—
756C2×C4—1064no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1064no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—4244no—
765C2×C4—2128no—
766C2×C4—2128no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4C2×D4×D5312yes—
770C2×C4C2×D4×D5311yescharacteristic
771C2×C4#41×D5312yes—
772C2×C4#1313326312yes—
773C2×C4C24×D5311yescharacteristic
774C8—22no—
775C8—22no—
776C8—1062no—
777C8—1062no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—1062no—
787C22—1062no—
788C22—1062no—
789C22—4244no—
790C22—2122no—
791C22—2122no—
792C22—2122no—
793C22—2124no—
794C22#1681126512yes—
795C22#137×D5312yes—
796C22#1681142412yes—
797C22C22×D4×D5311yescharacteristic
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—534no—
803C4—1062no—
804C4—1064no—
805C4—1062no—
806C4—2122no—
807C4—2122no—
808C4#1681126512yes—
809C4C2×#41×D5311yescharacteristic
810C4C2×#1313326311yescharacteristic
811C2—42no—
812C2—82no—
813C2—4242no—
814C2—2122no—
815C2#2028705114yesdirect product factor
816C2C2×#1681126511yescharacteristic
817C2C2×#137×D5311yescharacteristic
818C2C2×#1681142411yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
prime radicalC2×#16811291C2
hypercenterC2×#480D53
hypocenterC53C2×#3333
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16811328C2semidirect
3. #20287051C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810938C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810867C2semidirect
9. C2×#16810822C2semidirect
10. C2×#16810787C2semidirect
11. C2×#16810786C2semidirect
12. C2×#16810717C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810621C2semidirect
16. C2×C53×#480C2semidirect
25. #16811328C22semidirect
45. #16810968C22semidirect
46. #16810938C22semidirect
47. #16810917C22semidirect
48. #16810870C22semidirect
49. #16810867C22semidirect
50. #16810822C22semidirect
51. #16810787C22semidirect
52. #16810786C22semidirect
53. #16810717C22semidirect
54. #16810698C22semidirect
57. #16810622C22semidirect
58. #16810621C22semidirect
71. C53×#480C22semidirect
407. C2×#480D53semidirect
420. C2×C53#3333semidirect
458. #480C2×D53semidirect
486. C53C2×#3333semidirect
815. C2#20287051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112912
#202870512
C2×#168109682
C2×#168109382
C2×#168109172
C2×#168108702
C2×#168108672
C2×#168108222
C2×#168107872
C2×#168107862
C2×#168107172
C2×#168106982
C2×#168106222
C2×#168106212
C2×C53×#4802
C2×#333353