Finite Group Databasebeta

← C2×#20285005 #28252437

Subgroups — C2×#20285005 #28252437

Order 13568.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811224C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic, complemented
3#20285005C2116yesmaximal, direct product factor
4C2×#16810950C211yesmaximal, characteristic, complemented
5C2×#16810945C211yesmaximal, characteristic, complemented
6C2×#16810932C211yesmaximal, characteristic, complemented
7C2×#16810929C211yesmaximal, characteristic, complemented
8C2×#16810822C211yesmaximal, characteristic, complemented
9C2×#16810821C211yesmaximal, characteristic, complemented
10C2×#16810763C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×#16810725C211yesmaximal, characteristic, complemented
13C2×C4×#11719924C211yesmaximal, characteristic, complemented
14C2×C4×#11719923C211yesmaximal, characteristic, complemented
15C2×#16810685C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21#16811224—24no—
22#16811224C2218yes—
23C2×#13133213C2211yescharacteristic
24C2×#13133208C2211yescharacteristic
25C2×#13133200—21no—
26C2×#13133199—21no—
27C2×#13133192C2211yescharacteristic
28C2×#13133191—21no—
29C2×#13133190—21no—
30C2×#13133188C2211yescharacteristic
31#16811099—24no—
32#16811099C2218yescomplemented
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×#13133182—21no—
37C2×#13133182C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133175—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174—21no—
42C2×#13133174C2211yescharacteristic
43#16810950C2218yescomplemented
44#16810945C2218yescomplemented
45#16810932C2218yescomplemented
46#16810929C2218yescomplemented
47#16810822C2218yescomplemented
48#16810821C2218yescomplemented
49#16810763C2218yescomplemented
50#16810760C2218yescomplemented
51#16810725C2218yescomplemented
52C4×#11719924C2218yescomplemented
53C4×#11719923C2218yescomplemented
54#16810685C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
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×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×Q8×D53—24no—
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53C2314yes—
83C22×D212—21no—
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53C2311yescharacteristic
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719923—24no—
94C2×#11719923C2314yes—
95C2×#11719924—24no—
96C2×#11719924C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133213—22no—
100#13133213C2314yes—
101#13133208—22no—
102#13133208C2314yes—
103#13133200—28no—
104#13133199—28no—
105#13133192—22no—
106#13133192C2314yes—
107#13133191—28no—
108#13133190—28no—
109#13133188—22no—
110#13133188C2314yes—
111Q8×Dic53—22no—
112Q8×Dic53C2314yes—
113C4×Dic106—22no—
114C4×Dic106—28no—
115C4×Dic106C2314yes—
116#13133182—28no—
117#13133182—22no—
118#13133182C2314yes—
119C4×D212—22no—
120C4×D212C2314yes—
121#13133175—28no—
122#13133175—22no—
123#13133175C2314yes—
124#13133174—28no—
125#13133174D414yes—
126#13133174C2314yes—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×#11719919D411yescharacteristic
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921D411yescharacteristic
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160C4×#88322C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#102×C53C2314yes—
181#97×C53C2314yes—
182C24×C53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53#4114yes—
188C2×Q8×C53C2412yes—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—82no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—82no—
205C2×C22⋊D53—82no—
206C2×C22⋊D53—82no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213Q8×D53—216no—
214Q8×D53—28no—
215Q8×D53—28no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212—24no—
220C2×D212—82no—
221C2×D212C2412yes—
222C2×C4×D53—28no—
223C2×C4×D53—24no—
224C2×C4×D53—22no—
225C2×C4×D53—22no—
226C2×C4×D53—24no—
227C2×C4×D53—82no—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2412yes—
230C2×Dic106—28no—
231C2×Dic106—21no—
232C2×Dic106—22no—
233C2×Dic106—24no—
234C2×Dic106#4114yes—
235C2×Dic106C2412yes—
236SD16×C53—28no—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C2×C8×C53C2412yes—
240C2×C8×C53C2412yes—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53C2412yes—
245C4⋊C4×C53C2412yes—
246C22⋊C4×C53—24no—
247C42×C53—24no—
248C42×C53C2×D412yes—
249C42×C53C2412yes—
250C22⋊Dic53—24no—
251#11719924—28no—
252#11719923—28no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921C2×D414yes—
257#11719921C2×D414yes—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53—24no—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264#11719919—24no—
265#11719919—24no—
266#11719919—24no—
267#11719919C2×D414yes—
268#11719919C2×D414yes—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2412yes—
275C2×#88322—22no—
276C2×#88322—22no—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279#11719913—28no—
280C23×C53—22no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53C22×D412yes—
293Q8×C53—24no—
294Q8×C53—22no—
295Q8×C53C2×#4114yes—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—42no—
299C2×C4×C53—24no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—84no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—84no—
315C22⋊D53—84no—
316C22⋊D53—84no—
317C2×Dic53—22no—
318C2×Dic53—24no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329D212—22no—
330D212—22no—
331D212—42no—
332D212—84no—
333C4×D53—216no—
334C4×D53—24no—
335C4×D53—22no—
336C4×D53—22no—
337C4×D53—84no—
338Dic106—216no—
339Dic106—24no—
340Dic106—22no—
341Dic106C2×#4114yes—
342C8×C53—22no—
343C8×C53—22no—
344#88322—22no—
345#88322—22no—
346C2×#3126—531nomaximal, Sylow
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—84no—
351C22×C53#52512yes—
352C22×C53#57712yes—
353C22×C53#57712yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—22no—
358C2×D53—44no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C4×C53—24no—
364C4×C53—22no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53#52512yes—
369C4×C53C22×#4111yescharacteristic
370C4×C53C22×#4111yescharacteristic
371Dic53—22no—
372Dic53—24no—
373Dic53—22no—
374Dic53—22no—
375Dic53—42no—
376Dic53—42no—
377C2×#540—531no—
378C2×#519—531no—
379#3126—5316no—
380C2×#482—531no—
381C2×#482—531no—
382C2×#479—531no—
383C2×#479—531no—
384C2×#460—531no—
385C2×#460—531no—
386C2×#448—531no—
387C2×#448—531no—
388C2×#440—531no—
389C2×#440D5311yescharacteristic, complemented
390C2×C4×SD16—531no—
391C2×C4×SD16—531no—
392C2×#433—531no—
393C2×C53—82no—
394C2×C53#312614yescomplemented
395C2×C53C2×#52511yescharacteristic
396C2×C53C2×#57711yescharacteristic
397C2×C53C2×#57711yescharacteristic
398D53—42no—
399D53—82no—
400C23×Q8—531no—
401C22×SD16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
404C22×SD16C2×D5311yescharacteristic
405#540—538no—
406#540—1064no—
407C2×#127—531no—
408C2×#125—531no—
409C2×#123—1061no—
410C2×#123—1061no—
411C2×#121—531no—
412C2×#121—531no—
413C2×#121—1061no—
414C2×#121—1061no—
415#519—538no—
416#519—1064no—
417C2×C4×Q8—531no—
418C2×C4×Q8—531no—
419C2×C4×Q8—531no—
420C2×C4×Q8—1061no—
421C2×C4×Q8—1061no—
422C2×C4×Q8C2×D5311yescharacteristic
423C2×C4×D4—531no—
424C2×C4×D4C2×D5311yescharacteristic
425C2×#117—531no—
426C2×#117—531no—
427C2×#117—1061no—
428C2×#117—1061no—
429#482—538no—
430#482—538no—
431#479—538no—
432#479—538no—
433#460—538no—
434#460—538no—
435#448—538no—
436#448—538no—
437#440—538no—
438#440C2×D5318yescomplemented
439C4×SD16—538no—
440C4×SD16—538no—
441#433—538no—
442C2×#107—531no—
443C2×#107C2×D5311yescharacteristic
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103C2×D5311yescharacteristic
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102C2×D5311yescharacteristic
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×#97C2×D5311yescharacteristic
459C2×C4×C8—531no—
460C53C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—534no—
462C22×Q8—531no—
463C22×Q8—1061no—
464C22×Q8—1062no—
465C22×Q8—1064no—
466C22×Q8—1064no—
467C22×Q8C22×D5311yescharacteristic
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4C22×D5311yescharacteristic
474C23×C4—21no—
475C23×C4—531no—
476C23×C4—1061no—
477C23×C4—1061no—
478C2×SD16—24no—
479C2×SD16—534no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16—1064no—
485C2×SD16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490#127—534no—
491#127—1062no—
492#125—534no—
493#125—1062no—
494#123—1068no—
495#123—1068no—
496#121—534no—
497#121—534no—
498#121—1068no—
499#121—1068no—
500#121—1062no—
501#121—1062no—
502C4×Q8—22no—
503C4×Q8—534no—
504C4×Q8—534no—
505C4×Q8—534no—
506C4×Q8—1068no—
507C4×Q8—1062no—
508C4×Q8—1062no—
509C4×Q8—1068no—
510C4×Q8—1062no—
511C4×Q8C22×D5314yes—
512C4×D4—22no—
513C4×D4—534no—
514C4×D4—1062no—
515C4×D4C22×D5314yes—
516#117—534no—
517#117—534no—
518#117—534no—
519#117—1068no—
520#117—1068no—
521#117—1062no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C42—21no—
542C2×C42—531no—
543C2×C42—1061no—
544C2×C42—1061no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107C22×D5314yes—
550#106—534no—
551#106—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103C22×D5314yes—
558#102—534no—
559#102—534no—
560#102—534no—
561#102C22×D5314yes—
562C22⋊C8—534no—
563C22⋊C8—534no—
564#97C22×D5314yes—
565C4×C8—534no—
566C24—21no—
567C24—531no—
568C24—1061no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—534no—
572C2×Q8—532no—
573C2×Q8—1064no—
574C2×Q8—1068no—
575C2×Q8—1068no—
576C2×Q8—10616no—
577C2×Q8—1068no—
578C2×Q8—1061no—
579C2×Q8—1062no—
580C2×Q8#1171994514yes—
581C2×Q8C23×D5312yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—532no—
586C2×D4—1064no—
587C2×D4—1064no—
588C2×D4—1064no—
589C2×D4—1064no—
590C2×D4—1061no—
591C2×D4—1062no—
592C2×D4—1062no—
593C2×D4—4242no—
594C2×D4—4242no—
595C2×D4—4242no—
596C2×D4—4242no—
597C2×D4C23×D5312yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—531no—
604C22×C4—531no—
605C22×C4—531no—
606C22×C4—532no—
607C22×C4—532no—
608C22×C4—1064no—
609C22×C4—1068no—
610C22×C4—1061no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1064no—
616C22×C4—4242no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620SD16—28no—
621SD16—1068no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—534no—
636C4⋊C4—534no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1061no—
644C4⋊C4—1061no—
645C4⋊C4—1064no—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C22⋊C4—24no—
649C22⋊C4—534no—
650C22⋊C4—534no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C42—24no—
656C42—532no—
657C42—532no—
658C42—1064no—
659C42—1064no—
660C42—1064no—
661C42—1064no—
662C42D4×D5312yes—
663C42C23×D5312yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—532no—
669C23—1062no—
670C23—1062no—
671C23—1062no—
672C23—1062no—
673C23—2122no—
674C23—2122no—
675C23—2122no—
676C23C2×D4×D5311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—534no—
680Q8—10616no—
681Q8—1064no—
682Q8—1062no—
683Q8C2×#1171994514yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—1062no—
688D4—1062no—
689D4—4244no—
690D4—4244no—
691D4—4244no—
692D4—4244no—
693D4—2122no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—532no—
704C2×C4—532no—
705C2×C4—532no—
706C2×C4—10616no—
707C2×C4—1062no—
708C2×C4—1064no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1064no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—4244no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4#41×D5312yes—
724C2×C4C2×#1171994512yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1062no—
729C8—1062no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—1062no—
735C22—1062no—
736C22—1062no—
737C22—4244no—
738C22—2122no—
739C22—2122no—
740C22—2122no—
741C22—2124no—
742C22#1681113212yes—
743C22#1681143212yes—
744C22#1681143312yes—
745C22C22×D4×D5311yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—1062no—
752C4—1062no—
753C4—1062no—
754C4—1064no—
755C4—2122no—
756C4—2122no—
757C4#1681113212yes—
758C4C2×#41×D5311yescharacteristic
759C4C22×#1171994511yescharacteristic
760C2—82no—
761C2—4242no—
762C2—2122no—
763C2#2028500514yesdirect product factor
764C2C2×#1681113211yescharacteristic
765C2C2×#1681143211yescharacteristic
766C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#16811224C2
hypercenterC2×#440D53
hypocenterC53C2×#3126
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
2. C2×#16811099C2semidirect
3. #20285005C2direct (N × H)
4. C2×#16810950C2semidirect
5. C2×#16810945C2semidirect
6. C2×#16810932C2semidirect
7. C2×#16810929C2semidirect
8. C2×#16810822C2semidirect
9. C2×#16810821C2semidirect
10. C2×#16810763C2semidirect
11. C2×#16810760C2semidirect
12. C2×#16810725C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719923C2semidirect
15. C2×#16810685C2semidirect
16. C2×C53×#440C2semidirect
32. #16811099C22semidirect
43. #16810950C22semidirect
44. #16810945C22semidirect
45. #16810932C22semidirect
46. #16810929C22semidirect
47. #16810822C22semidirect
48. #16810821C22semidirect
49. #16810763C22semidirect
50. #16810760C22semidirect
51. #16810725C22semidirect
52. C4×#11719924C22semidirect
53. C4×#11719923C22semidirect
54. #16810685C22semidirect
72. C53×#440C22semidirect
389. C2×#440D53semidirect
394. C2×C53#3126semidirect
438. #440C2×D53semidirect
460. C53C2×#3126semidirect
763. C2#20285005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112242
C2×#168110992
#202850052
C2×#168109502
C2×#168109452
C2×#168109322
C2×#168109292
C2×#168108222
C2×#168108212
C2×#168107632
C2×#168107602
C2×#168107252
C2×C4×#117199242
C2×C4×#117199232
C2×#168106852
C2×C53×#4402
C2×#312653