Finite Group Databasebeta

← C2×#20284731 #28252105

Subgroups — C2×#20284731 #28252105

Order 13568.

2202 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×#16811155C211yesmaximal, characteristic, complemented
2C2×C4×#11719949C211yesmaximal, characteristic, complemented
3#20284731C2116yesmaximal, direct product factor
4C2×#16810967C211yesmaximal, characteristic, complemented
5C2×#16810946C211yesmaximal, characteristic, complemented
6C2×#16810928C211yesmaximal, characteristic, complemented
7C2×#16810922C211yesmaximal, characteristic, complemented
8C2×#16810843C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic
12C2×C4×#11719925C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810674C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811155—24no—
22#16811155C2218yescomplemented
23C2×#13133210—21no—
24C2×#13133208C2211yescharacteristic
25C2×#13133204C2211yescharacteristic
26C2×#13133199—21no—
27C2×#13133197C2211yescharacteristic
28C2×#13133188C2211yescharacteristic
29C4×#11719949—24no—
30C4×#11719949C2218yescomplemented
31C2×Q8×Dic53C2211yescharacteristic
32C2×C4×Dic106C2211yescharacteristic
33C2×C4×D212—21no—
34C2×C4×D212C2211yescharacteristic
35C2×#13133179—21no—
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×#13133176—21no—
39C2×#13133175—21no—
40C2×#13133175C2211yescharacteristic
41C2×C42×D53—21no—
42C2×C42×D53C2211yescharacteristic
43#16810967C2218yescomplemented
44#16810946C2218yescomplemented
45#16810928C2218yescomplemented
46#16810922C2218yescomplemented
47#16810843C2218yescomplemented
48#16810837C2218yescomplemented
49#16810788C2218yescomplemented
50#16810767C2218yes—
51C4×#11719925C2218yescomplemented
52C4×#11719913C2218yescomplemented
53C4×#11719922C2218yescomplemented
54#16810674C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
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
72C4×SD16×C53C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719949—24no—
78C2×#11719949—24no—
79C2×#11719949—22no—
80C2×#11719949C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91C2×#11719925—24no—
92C2×#11719925C2314yes—
93C2×#11719913—24no—
94C2×#11719913C2314yes—
95C2×#11719922—24no—
96C2×#11719922C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99#13133210—28no—
100#13133208—22no—
101#13133208C2314yes—
102#13133204—22no—
103#13133204C2314yes—
104#13133199—28no—
105#13133197—22no—
106#13133197C2314yes—
107#13133188—22no—
108#13133188C2314yes—
109Q8×Dic53—22no—
110Q8×Dic53C2314yes—
111C4×Dic106—22no—
112C4×Dic106C2314yes—
113C4×D212—22no—
114C4×D212—28no—
115C4×D212C2314yes—
116#13133179—22no—
117#13133179—28no—
118#13133179C2314yes—
119C4×C22⋊D53—28no—
120#13133176—28no—
121#13133175—28no—
122#13133175—22no—
123#13133175C2314yes—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53D411yescharacteristic
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144C42×D53—28no—
145C42×D53D414yes—
146C42×D53C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
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#106×C53C2314yes—
179#103×C53C2314yes—
180#102×C53C2314yes—
181C4×C8×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—44no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—44no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209#11719949—216no—
210#11719949—28no—
211#11719949—28no—
212C2×D212—28no—
213C2×D212—24no—
214C2×D212—21no—
215C2×D212—22no—
216C2×D212#4114yes—
217C2×D212C2412yes—
218C2×C4×D53—28no—
219C2×C4×D53—24no—
220C2×C4×D53—22no—
221C2×C4×D53—22no—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—42no—
226C2×C4×D53—44no—
227C2×C4×D53—44no—
228C2×C4×D53C2×D412yes—
229C2×C4×D53C2×D414yes—
230C2×C4×D53C2×D414yes—
231C2×C4×D53C2412yes—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—21no—
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—
251C22⋊Dic53—24no—
252C22⋊Dic53—24no—
253#11719925—28no—
254#11719922—28no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—24no—
262C4⋊Dic53—24no—
263C4⋊Dic53—24no—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266#11719919—24no—
267#11719919—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271C4×Dic53C2×D414yes—
272C4×Dic53C2×D412yes—
273C4×Dic53C2×D414yes—
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—24no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
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—42no—
305C2×C4×C53—42no—
306C2×C4×C53—48no—
307C2×C4×C53#13514yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C22×D412yes—
311C2×C4×C53C2×#4112yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C22⋊D53—48no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326C2×Dic53C22×D412yes—
327D212—216no—
328D212—24no—
329D212—22no—
330D212C2×#4114yes—
331C4×D53—216no—
332C4×D53—24no—
333C4×D53—28no—
334C4×D53—22no—
335C4×D53—22no—
336C4×D53—44no—
337C4×D53—48no—
338C4×D53—48no—
339Dic106—22no—
340Dic106—22no—
341Dic106—42no—
342C8×C53—22no—
343C8×C53—22no—
344#88322—22no—
345#88322—22no—
346C2×#3102—531nomaximal, Sylow
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—84no—
351C22×C53#52512yes—
352C22×C53C2×#13512yes—
353C22×C53#57512yes—
354C22×C53C23×D411yescharacteristic
355C2×D53—22no—
356C2×D53—24no—
357C2×D53—22no—
358C2×D53—22no—
359C2×D53—44no—
360C2×D53—48no—
361C2×D53—42no—
362C2×D53—42no—
363C4×C53—24no—
364C4×C53—22no—
365C4×C53—42no—
366C4×C53—42no—
367C4×C53#52512yes—
368C4×C53C2×#13514yes—
369C4×C53C22×#4111yescharacteristic
370C4×C53C22×#4111yescharacteristic
371Dic53—22no—
372Dic53—22no—
373Dic53—22no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C2×#529—531no—
378C2×C4×#41—531no—
379#3102—5316no—
380C2×#485—531no—
381C2×#482—531no—
382C2×#479—531no—
383C2×#478—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#452—531no—
387C2×#449—531no—
388C2×C4×Q16—531no—
389C2×C4×SD16—531no—
390C2×C4×SD16D5311yescharacteristic, complemented
391C2×C4×D8—531no—
392C2×#431—531no—
393C2×C53—82no—
394C2×C53#310214yescomplemented
395C2×C53C2×#52511yescharacteristic
396C2×C53C22×#13511yescharacteristic
397C2×C53C2×#57511yescharacteristic
398D53—42no—
399D53—44no—
400C22×#41—531no—
401C22×Q16—531no—
402C22×SD16—531no—
403C22×SD16C2×D5311yescharacteristic
404C22×D8—531no—
405#529—538no—
406#529—1064no—
407C2×#126—1061no—
408C2×#125—531no—
409C2×#124—531no—
410C2×#123—1061no—
411C2×C22⋊Q8—531no—
412C2×#121—531no—
413C4×#41—538no—
414C4×#41—1064no—
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8C2×D5311yescharacteristic
418C2×C4×D4—531no—
419C2×C4×D4—531no—
420C2×C4×D4—1061no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×C4×D4C2×D5311yescharacteristic
424C2×#117—531no—
425C2×#117—1061no—
426C2×#117—1061no—
427C22×C42—531no—
428C22×C42—1061no—
429#485—538no—
430#482—538no—
431#479—538no—
432#478—538no—
433#464—538no—
434#463—538no—
435#452—538no—
436#449—538no—
437C4×Q16—538no—
438C4×SD16—538no—
439C4×SD16C2×D5318yescomplemented
440C4×D8—538no—
441#431—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
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×C4×C8—531no—
459C2×C4×C8C2×D5311yescharacteristic
460C53C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—534no—
462C2×#41—1062no—
463C2×#41—1064no—
464C2×#41—1064no—
465C22×Q8—531no—
466C22×Q8C22×D5311yescharacteristic
467C22×D4—531no—
468C22×D4—1061no—
469C22×D4—1061no—
470C22×D4C22×D5311yescharacteristic
471C23×C4—21no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C2×Q16—534no—
479C2×Q16—1064no—
480C2×SD16—24no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16C22×D5314yes—
484C2×D8—534no—
485C2×D8—1064no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490#126—1068no—
491#125—534no—
492#125—1062no—
493#124—534no—
494#124—1062no—
495#123—1068no—
496C22⋊Q8—534no—
497C22⋊Q8—1062no—
498#121—534no—
499#121—1062no—
500C4×Q8—22no—
501C4×Q8—534no—
502C4×Q8—534no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8C22×D5314yes—
506C4×D4—22no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—1068no—
510C4×D4—1062no—
511C4×D4—1068no—
512C4×D4—1068no—
513C4×D4—1062no—
514C4×D4C22×D5314yes—
515#117—534no—
516#117—1068no—
517#117—1068no—
518#117—1062no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—21no—
538C2×C42—531no—
539C2×C42—531no—
540C2×C42—531no—
541C2×C42—534no—
542C2×C42—534no—
543C2×C42—1068no—
544C2×C42—1061no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107—534no—
550#106—534no—
551#106C22×D5314yes—
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—
564C4×C8—534no—
565C4×C8C22×D5314yes—
566C24—21no—
567C24—531no—
568C24—1061no—
569#41—1068no—
570#41—10616no—
571#41—1068no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—532no—
575C2×Q8—1061no—
576C2×Q8—1062no—
577C2×Q8—1062no—
578C2×Q8#1171994514yes—
579C2×Q8C23×D5312yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—534no—
584C2×D4—532no—
585C2×D4—1064no—
586C2×D4—1068no—
587C2×D4—1064no—
588C2×D4—1061no—
589C2×D4—1062no—
590C2×D4—2124no—
591C2×D4C23×D5312yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—532no—
601C22×C4—534no—
602C22×C4—532no—
603C22×C4—534no—
604C22×C4—1064no—
605C22×C4—1064no—
606C22×C4—1068no—
607C22×C4—1064no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1064no—
614C22×C4—2122no—
615C22×C4—2124no—
616C22×C4—2124no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620Q16—1068no—
621SD16—28no—
622SD16—1068no—
623D8—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—532no—
636C4⋊C4—532no—
637C4⋊C4—1064no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1064no—
644C4⋊C4C23×D5312yes—
645C4⋊C4C23×D5312yes—
646C22⋊C4—24no—
647C22⋊C4—1064no—
648C22⋊C4—1064no—
649C22⋊C4—1064no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C42—24no—
655C42—534no—
656C42—534no—
657C42—532no—
658C42—532no—
659C42—1064no—
660C42—1064no—
661C42—1064no—
662C42D4×D5312yes—
663C42C23×D5312yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—532no—
669C23—1064no—
670C23—1062no—
671C23—1062no—
672C23—1062no—
673C23—1062no—
674C23—2122no—
675C23—2122no—
676C23C2×D4×D5311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—1062no—
680Q8—1062no—
681Q8—2122no—
682Q8C2×#1171994514yes—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—534no—
687D4—10616no—
688D4—1064no—
689D4—1062no—
690D4—2128no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—48no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—532no—
702C2×C4—10616no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1064no—
707C2×C4—1068no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—2124no—
714C2×C4—2128no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2128no—
719C2×C4#1313323814yes—
720C2×C4C2×D4×D5312yes—
721C2×C4C2×D4×D5311yescharacteristic
722C2×C4C2×D4×D5312yes—
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—1064no—
737C22—1062no—
738C22—2124no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22#1681113212yes—
743C22C2×#1313323812yes—
744C22#1681142012yes—
745C22C22×D4×D5311yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—1062no—
751C4—1062no—
752C4—1062no—
753C4—2122no—
754C4—2122no—
755C4—2122no—
756C4#1681113212yes—
757C4C2×#1313323814yes—
758C4C2×#41×D5311yescharacteristic
759C4C22×#1171994511yescharacteristic
760C2—82no—
761C2—2122no—
762C2—2124no—
763C2#2028473114yesdirect product factor
764C2C2×#1681113211yescharacteristic
765C2C22×#1313323811yescharacteristic
766C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810767C2
hypercenterC2×C4×SD16D53
hypocenterC53C2×#3102
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16811155C2semidirect
2. C2×C4×#11719949C2semidirect
3. #20284731C2direct (N × H)
4. C2×#16810967C2semidirect
5. C2×#16810946C2semidirect
6. C2×#16810928C2semidirect
7. C2×#16810922C2semidirect
8. C2×#16810843C2semidirect
9. C2×#16810837C2semidirect
10. C2×#16810788C2semidirect
12. C2×C4×#11719925C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810674C2semidirect
16. C2×C4×SD16×C53C2semidirect
22. #16811155C22semidirect
30. C4×#11719949C22semidirect
43. #16810967C22semidirect
44. #16810946C22semidirect
45. #16810928C22semidirect
46. #16810922C22semidirect
47. #16810843C22semidirect
48. #16810837C22semidirect
49. #16810788C22semidirect
51. C4×#11719925C22semidirect
52. C4×#11719913C22semidirect
53. C4×#11719922C22semidirect
54. #16810674C22semidirect
72. C4×SD16×C53C22semidirect
390. C2×C4×SD16D53semidirect
394. C2×C53#3102semidirect
439. C4×SD16C2×D53semidirect
460. C53C2×#3102semidirect
763. C2#20284731direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111552
C2×C4×#117199492
#202847312
C2×#168109672
C2×#168109462
C2×#168109282
C2×#168109222
C2×#168108432
C2×#168108372
C2×#168107882
C2×#168107672
C2×C4×#117199252
C2×C4×#117199132
C2×C4×#117199222
C2×#168106742
C2×C4×SD16×C532
C2×#310253