Finite Group Databasebeta

← C2×#20284728 #28252102

Subgroups — C2×#20284728 #28252102

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×#16811154C211yesmaximal, characteristic, complemented
2C2×#16811091C211yesmaximal, characteristic, complemented
3#20284728C2116yesmaximal, direct product factor
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810933C211yesmaximal, characteristic, complemented
6C2×#16810926C211yesmaximal, characteristic, complemented
7C2×#16810844C211yesmaximal, characteristic, complemented
8C2×#16810837C211yesmaximal, characteristic, complemented
9C2×#16810787C211yesmaximal, characteristic, complemented
10C2×#16810766C211yesmaximal, characteristic
11C2×#16810717C211yesmaximal, characteristic, complemented
12C2×#16810714C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×#16810703C211yesmaximal, characteristic, complemented
15C2×#16810673C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22#16811154—24no—
23#16811154C2218yescomplemented
24C2×#13133210—21no—
25C2×#13133208C2211yescharacteristic
26C2×#13133204C2211yescharacteristic
27C2×#13133198—21no—
28C2×#13133196C2211yescharacteristic
29#16811091—24no—
30#16811091C2218yescomplemented
31C2×#13133182C2211yescharacteristic
32C2×#13133182C2211yescharacteristic
33C2×#13133182C2211yescharacteristic
34C2×D4×Dic53—21no—
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×#13133177—21no—
39C2×#13133177—21no—
40C2×#13133174—21no—
41C2×#13133173—21no—
42C22×C4×Dic53C2211yescharacteristic
43C2×C42×D53—21no—
44#16810964C2218yescomplemented
45#16810933C2218yescomplemented
46#16810926C2218yescomplemented
47#16810844C2218yescomplemented
48#16810837C2218yescomplemented
49#16810787C2218yescomplemented
50#16810766C2218yes—
51#16810717C2218yescomplemented
52#16810714C2218yescomplemented
53#16810710C2218yescomplemented
54#16810703C2218yescomplemented
55#16810673C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—24no—
80C2×#11719945C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×Dic106C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C23×Dic53—21no—
86C23×Dic53D411yescharacteristic
87C23×Dic53D411yescharacteristic
88C22×C4×D53—21no—
89C22×C4×D53—21no—
90C22×C4×D53—21no—
91C2×Dic212—24no—
92C2×Dic212C2314yes—
93C2×#11719913—24no—
94C2×#11719913C2314yes—
95C2×#11719923—24no—
96C2×#11719923C2314yes—
97C2×#11719922—24no—
98C2×#11719922C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133210—28no—
102#13133208—22no—
103#13133208C2314yes—
104#13133204—22no—
105#13133204C2314yes—
106#13133198—28no—
107#13133196—22no—
108#13133196C2314yes—
109#13133182—22no—
110#13133182—22no—
111#13133182—22no—
112#13133182C2314yes—
113#13133182C2314yes—
114#13133182C2314yes—
115D4×Dic53—22no—
116D4×Dic53—28no—
117D4×Dic53C2314yes—
118#13133179—22no—
119#13133179—22no—
120#13133179C2314yes—
121#13133179C2314yes—
122#13133177—28no—
123#13133177—28no—
124#13133174—28no—
125#13133173—28no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53D411yescharacteristic
143C2×C4×Dic53D411yescharacteristic
144C2×C4×Dic53D414yes—
145C2×C4×Dic53C2311yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147C2×C4×Dic53C2314yes—
148C42×D53—28no—
149#13133150C2314yes—
150#13133148C2314yes—
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133139C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160C8×Dic53C2314yes—
161C8×Dic53C2314yes—
162C22×D4×C53—21no—
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#121×C53—22no—
168#121×C53C2314yes—
169#117×C53—22no—
170#117×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177#107×C53C2314yes—
178#106×C53C2314yes—
179#102×C53C2314yes—
180#102×C53C2314yes—
181C22⋊C8×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C2×D4×C53—24no—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—44no—
190C2×D4×C53C2412yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—28no—
201C2×C22⋊D53—24no—
202C22×Dic53—21no—
203C22×Dic53—24no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—24no—
207C22×Dic53—42no—
208C22×Dic53—44no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D414yes—
213C22×Dic53C2×D414yes—
214C22×Dic53C2×D411yescharacteristic
215#11719945—216no—
216#11719945—28no—
217#11719945—28no—
218C2×D212—21no—
219C2×D212—22no—
220C2×D212#4114yes—
221C2×D212C2412yes—
222C2×C4×D53—28no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—44no—
227C2×C4×D53—44no—
228C2×Dic106—21no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106#4114yes—
234C2×Dic106C2412yes—
235C2×Dic106C2412yes—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C4⋊C4×C53C2412yes—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C42×C53—24no—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252C22⋊Dic53—24no—
253#11719923—28no—
254#11719922—28no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—24no—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53C2×D414yes—
269C4×Dic53C2×D414yes—
270C4×Dic53C2×D412yes—
271C4×Dic53C2×D412yes—
272C4×Dic53C2412yes—
273C4×Dic53C2412yes—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278Dic212—28no—
279#11719913—28no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—24no—
290C22×D53—22no—
291C22×D53—42no—
292C22×D53—42no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—48no—
296D4×C53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—24no—
299C2×C4×C53—22no—
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—42no—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4112yes—
310C2×C4×C53C2×#4112yes—
311C2×C4×C53C2511yescharacteristic
312C22⋊D53—216no—
313C2×Dic53—24no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—28no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—44no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—48no—
325C2×Dic53#13514yes—
326C2×Dic53C22×D412yes—
327C2×Dic53C22×D412yes—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330D212—24no—
331D212—22no—
332D212C2×#4114yes—
333C4×D53—216no—
334C4×D53—48no—
335C4×D53—48no—
336Dic106—24no—
337Dic106—22no—
338Dic106—22no—
339Dic106—22no—
340Dic106—42no—
341Dic106C2×#4114yes—
342C8×C53—22no—
343C8×C53—22no—
344#88322—22no—
345#88322—22no—
346C2×#3102—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—44no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—84no—
355C22×C53#52512yes—
356C22×C53C2×#13512yes—
357C22×C53#57512yes—
358C22×C53C23×D411yescharacteristic
359C2×D53—24no—
360C2×D53—48no—
361C2×D53—42no—
362C2×D53—42no—
363C4×C53—22no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53—42no—
367C4×C53#52512yes—
368C4×C53C22×#4111yescharacteristic
369C4×C53C22×#4111yescharacteristic
370Dic53—24no—
371Dic53—22no—
372Dic53—22no—
373Dic53—22no—
374Dic53—42no—
375Dic53—42no—
376Dic53C2×#13514yes—
377C2×#529—531no—
378C2×C4×#41—531no—
379#3102—5316no—
380C2×#485—531no—
381C2×#482D5311yescharacteristic, complemented
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×SD16—531no—
391C2×C4×D8—531no—
392C2×#431—531no—
393C2×C53—42no—
394C2×C53—82no—
395C2×C53#310214yescomplemented
396C2×C53C2×#52511yescharacteristic
397C2×C53C22×#13511yescharacteristic
398C2×C53C2×#57511yescharacteristic
399D53—44no—
400C22×#41—531no—
401C22×Q16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
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×#121C2×D5311yescharacteristic
413C4×#41—538no—
414C4×#41—1064no—
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×D4—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×C4×D4—1061no—
424C2×#117—1061no—
425C2×#117—1061no—
426C2×#117C2×D5311yescharacteristic
427C22×C42—531no—
428C22×C42—1061no—
429#485—538no—
430#482C2×D5318yescomplemented
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×SD16—538no—
440C4×D8—538no—
441#431—538no—
442C2×#107—531no—
443C2×#107C2×D5311yescharacteristic
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102C2×D5311yescharacteristic
455C2×#102C2×D5311yescharacteristic
456C2×C22⋊C8—531no—
457C2×C22⋊C8C2×D5311yescharacteristic
458C2×C4×C8—531no—
459C2×C4×C8—531no—
460C53C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—534no—
462C2×#41—1064no—
463C2×#41—1064no—
464C2×#41—1062no—
465C22×Q8—531no—
466C22×Q8—531no—
467C22×D4—21no—
468C22×D4—531no—
469C22×D4—1061no—
470C22×D4C22×D5311yescharacteristic
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—1061no—
474C23×C4—1061no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C2×Q16—534no—
479C2×Q16—1064no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
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—22no—
499#121C22×D5314yes—
500C4×Q8—534no—
501C4×Q8—534no—
502C4×Q8—534no—
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×D4—534no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—1062no—
510C4×D4—1062no—
511C4×D4—1062no—
512C4×D4—1068no—
513C4×D4—1068no—
514C4×D4—1068no—
515#117—22no—
516#117—1068no—
517#117—1068no—
518#117C22×D5314yes—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
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—534no—
541C2×C42—531no—
542C2×C42—531no—
543C2×C42—534no—
544C2×C42—1068no—
545C2×C42—1061no—
546C2×C42—1061no—
547C2×C42—1061no—
548#107—534no—
549#107C22×D5314yes—
550#106—534no—
551#106C22×D5314yes—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103—534no—
558#102—534no—
559#102—534no—
560#102C22×D5314yes—
561#102C22×D5314yes—
562C22⋊C8—534no—
563C22⋊C8C22×D5314yes—
564C4×C8—534no—
565C4×C8—534no—
566C24—21no—
567C24—1061no—
568C24D4×D5311yescharacteristic
569#41—1068no—
570#41—1068no—
571#41—10616no—
572C2×Q8—534no—
573C2×Q8—532no—
574C2×Q8—532no—
575C2×Q8—1061no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—1062no—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—44no—
585C2×D4—534no—
586C2×D4—532no—
587C2×D4—1068no—
588C2×D4—1064no—
589C2×D4—1061no—
590C2×D4—1062no—
591C2×D4C23×D5312yes—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—531no—
598C22×C4—534no—
599C22×C4—531no—
600C22×C4—531no—
601C22×C4—531no—
602C22×C4—534no—
603C22×C4—1064no—
604C22×C4—1064no—
605C22×C4—1068no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1061no—
609C22×C4—1064no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—2124no—
613C22×C4—2124no—
614C22×C4—2124no—
615C22×C4—2122no—
616C22×C4D4×D5312yes—
617C22×C4D4×D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620Q16—1068no—
621SD16—1068no—
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—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—532no—
636C4⋊C4—1064no—
637C4⋊C4—1064no—
638C4⋊C4—1064no—
639C4⋊C4—1064no—
640C4⋊C4—1064no—
641C4⋊C4—1061no—
642C4⋊C4—1064no—
643C4⋊C4C23×D5312yes—
644C4⋊C4C23×D5312yes—
645C4⋊C4C23×D5312yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
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—532no—
660C42—532no—
661C42—1064no—
662C42—1064no—
663C42—1064no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—1064no—
672C23—1062no—
673C23—2122no—
674C23—2122no—
675C23C2×D4×D5312yes—
676C23C2×D4×D5311yescharacteristic
677Q8—534no—
678Q8—1064no—
679Q8—1062no—
680Q8—1062no—
681Q8—1062no—
682Q8—2122no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—534no—
688D4—10616no—
689D4—1064no—
690D4—1062no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—534no—
702C2×C4—532no—
703C2×C4—532no—
704C2×C4—532no—
705C2×C4—532no—
706C2×C4—10616no—
707C2×C4—1068no—
708C2×C4—1064no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—2128no—
716C2×C4—2128no—
717C2×C4—2128no—
718C2×C4—2124no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4C2×D4×D5312yes—
722C2×C4C2×D4×D5311yescharacteristic
723C2×C4#41×D5312yes—
724C2×C4#41×D5312yes—
725C2×C4C24×D5311yescharacteristic
726C8—22no—
727C8—22no—
728C8—1062no—
729C8—1062no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—1064no—
739C22—2128no—
740C22—2122no—
741C22—2122no—
742C22#1681113112yes—
743C22#135×D5312yes—
744C22#1681141912yes—
745C22C22×D4×D5311yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—534no—
751C4—1062no—
752C4—1062no—
753C4—1062no—
754C4—1064no—
755C4—2122no—
756C4—2122no—
757C4#1681113112yes—
758C4C2×#41×D5311yescharacteristic
759C4C2×#41×D5311yescharacteristic
760C2—42no—
761C2—82no—
762C2—2124no—
763C2#2028472814yesdirect product factor
764C2C2×#1681113111yescharacteristic
765C2C2×#135×D5311yescharacteristic
766C2C2×#1681141911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
hypercenterC2×#482D53
hypocenterC53C2×#3102
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811154C2semidirect
2. C2×#16811091C2semidirect
3. #20284728C2direct (N × H)
4. C2×#16810964C2semidirect
5. C2×#16810933C2semidirect
6. C2×#16810926C2semidirect
7. C2×#16810844C2semidirect
8. C2×#16810837C2semidirect
9. C2×#16810787C2semidirect
11. C2×#16810717C2semidirect
12. C2×#16810714C2semidirect
13. C2×#16810710C2semidirect
14. C2×#16810703C2semidirect
15. C2×#16810673C2semidirect
16. C2×C53×#482C2semidirect
23. #16811154C22semidirect
30. #16811091C22semidirect
44. #16810964C22semidirect
45. #16810933C22semidirect
46. #16810926C22semidirect
47. #16810844C22semidirect
48. #16810837C22semidirect
49. #16810787C22semidirect
51. #16810717C22semidirect
52. #16810714C22semidirect
53. #16810710C22semidirect
54. #16810703C22semidirect
55. #16810673C22semidirect
71. C53×#482C22semidirect
381. C2×#482D53semidirect
395. C2×C53#3102semidirect
430. #482C2×D53semidirect
460. C53C2×#3102semidirect
763. C2#20284728direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111542
C2×#168110912
#202847282
C2×#168109642
C2×#168109332
C2×#168109262
C2×#168108442
C2×#168108372
C2×#168107872
C2×#168107662
C2×#168107172
C2×#168107142
C2×#168107102
C2×#168107032
C2×#168106732
C2×C53×#4822
C2×#310253