Finite Group Databasebeta

← C2×#20285403 #28253981

Subgroups — C2×#20285403 #28253981

Order 13568.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811247C211yesmaximal, characteristic, complemented
2C2×#16811229C211yesmaximal, characteristic, complemented
3#20285403C2116yesmaximal, direct product factor
4C2×#16811012C211yesmaximal, characteristic, complemented
5C2×#16810980C211yesmaximal, characteristic, complemented
6C2×#16810971C211yesmaximal, characteristic, complemented
7C2×#16810877C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810860C211yesmaximal, characteristic, complemented
10C2×#16810853C211yesmaximal, characteristic, complemented
11C2×#16810734C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810710C211yesmaximal, characteristic, complemented
14C2×#16810705C211yesmaximal, characteristic, complemented
15C2×#16810580C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811247—24no—
24#16811247C2218yescomplemented
25#16811229—24no—
26#16811229C2218yescomplemented
27C2×#13133214C2211yescharacteristic
28C2×#13133212—21no—
29C2×#13133206—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133202—21no—
32C2×#13133202—21no—
33C2×#13133202—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133193—21no—
36C2×#13133192—21no—
37C2×#13133192—21no—
38C2×#13133192C2211yescharacteristic
39C2×#13133192C2211yescharacteristic
40C2×#13133192C2211yescharacteristic
41C2×#13133182C2211yescharacteristic
42C2×#13133179C2211yescharacteristic
43C2×#13133179C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133174C2211yescharacteristic
46#16811012C2218yescomplemented
47#16810980C2218yescomplemented
48#16810971C2218yescomplemented
49#16810877C2218yescomplemented
50#16810870C2218yescomplemented
51#16810860C2218yescomplemented
52#16810853C2218yescomplemented
53#16810734C2218yescomplemented
54#16810722C2218yescomplemented
55#16810710C2218yescomplemented
56#16810705C2218yescomplemented
57C2×#13133140C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133137C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65#16810580C2218yescomplemented
66C2×#13133127C2211yescharacteristic
67C2×C4×#88322C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53C2311yescharacteristic
90C2×#11719913—24no—
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719913C2314yes—
94C2×D424—24no—
95C2×D424—24no—
96C2×D424C2314yes—
97C2×D424C2314yes—
98C2×#11719912—24no—
99C2×#11719912C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—24no—
103C2×C8×D53C2314yes—
104#13133214—22no—
105#13133214C2314yes—
106#13133212—28no—
107#13133206—28no—
108#13133205—22no—
109#13133205C2314yes—
110#13133202—28no—
111#13133202—28no—
112#13133202—28no—
113#13133197—22no—
114#13133197C2314yes—
115#13133193—28no—
116#13133192—28no—
117#13133192—28no—
118#13133192—22no—
119#13133192—22no—
120#13133192—22no—
121#13133192C2314yes—
122#13133192C2314yes—
123#13133192C2314yes—
124#13133182—22no—
125#13133182C2314yes—
126#13133179—22no—
127#13133179—22no—
128#13133179—22no—
129#13133179C2314yes—
130#13133179C2314yes—
131#13133179C2314yes—
132#13133174D414yes—
133#13133174C2314yes—
134C2×C4⋊Dic53—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×#11719919D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921D411yescharacteristic
148C2×#11719921D411yescharacteristic
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133140C2314yes—
152#13133140C2314yes—
153#13133137C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133137C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159#13133127C2314yes—
160C4×#88322C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53—21no—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4⋊Q8×C53—22no—
166C4⋊Q8×C53C2314yes—
167#125×C53—22no—
168#125×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#107×C53C2314yes—
179#106×C53C2314yes—
180#106×C53C2314yes—
181#97×C53C2314yes—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53C2×D411yescharacteristic
186C2×Q8×C53—24no—
187C2×Q8×C53—82no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—21no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—24no—
209C2×D212—24no—
210C2×D212—24no—
211C2×D212—24no—
212C2×D212—24no—
213C2×D212—82no—
214C2×D212—82no—
215C2×D212—82no—
216C2×D212—82no—
217C2×D212—82no—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×D212C2412yes—
221C2×C4×D53—22no—
222C2×C4×D53—22no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—82no—
227C2×C4×D53—82no—
228C2×C4×D53—82no—
229C2×C4×D53C2×D412yes—
230C2×C4×D53C2412yes—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—21no—
234C2×Dic106C2412yes—
235C2×C8×C53#4114yes—
236C2×C8×C53#4114yes—
237C2×C8×C53C2412yes—
238C2×C8×C53C2412yes—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53C2412yes—
247C4⋊C4×C53C2412yes—
248C4⋊C4×C53C2412yes—
249C4⋊C4×C53C2412yes—
250C42×C53C2×D412yes—
251C42×C53C2412yes—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921C2×D414yes—
262#11719921C2×D414yes—
263C4⋊Dic53—24no—
264#11719919—24no—
265#11719919C2×D414yes—
266#11719919C2×D414yes—
267C4×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
274D424—28no—
275D424—28no—
276#11719913—28no—
277#11719913—28no—
278#11719912—28no—
279C8×D53—28no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53C22×D412yes—
297Q8×C53—84no—
298C2×C4×C53—22no—
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×C53—42no—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4112yes—
312C2×C4×C53C2×#4112yes—
313C2×C4×C53C2511yescharacteristic
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C2×Dic53C22×D412yes—
322D212—22no—
323D212—22no—
324D212—22no—
325D212—22no—
326D212—22no—
327D212—22no—
328D212—42no—
329D212—42no—
330D212—42no—
331D212—84no—
332D212—84no—
333D212—84no—
334D212—84no—
335D212—84no—
336C4×D53—24no—
337C4×D53—22no—
338C4×D53—22no—
339C4×D53—84no—
340C4×D53—84no—
341C4×D53—84no—
342Dic106—22no—
343Dic106—22no—
344Dic106—42no—
345C8×C53C2×#4114yes—
346C8×C53C2×#4114yes—
347#88322—22no—
348#88322—22no—
349C2×#3179—531nomaximal, Sylow
350C22×C53#53212yes—
351C22×C53#57612yes—
352C22×C53#57712yes—
353C22×C53C23×D411yescharacteristic
354C2×D53—22no—
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—44no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—84no—
368C2×D53—84no—
369C2×D53—84no—
370C4×C53—22no—
371C4×C53—22no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53#53212yes—
377C4×C53C22×#4111yescharacteristic
378C4×C53C22×#4111yescharacteristic
379Dic53—22no—
380Dic53—22no—
381Dic53—22no—
382Dic53—42no—
383C2×#542—531no—
384C2×#540—531no—
385#3179—5316no—
386C2×#501D5311yescharacteristic, complemented
387C2×#496—531no—
388C2×#488—531no—
389C2×#486—531no—
390C2×#469—531no—
391C2×#468—531no—
392C2×#466—531no—
393C2×#465—531no—
394C2×#442—531no—
395C2×#440—531no—
396C2×C4×SD16—531no—
397C2×C4×D8—531no—
398C2×#405—531no—
399C2×C53#317914yescomplemented
400C2×C53C2×#53211yescharacteristic
401C2×C53C2×#57611yescharacteristic
402C2×C53C2×#57711yescharacteristic
403D53—42no—
404D53—82no—
405D53—82no—
406D53—82no—
407C22×SD16—531no—
408C22×SD16—531no—
409C22×D8—531no—
410C22×D8—531no—
411C22×M16—531no—
412C23×C8—531no—
413#542—538no—
414#542—1064no—
415#540—538no—
416#540—1064no—
417C2×C4⋊Q8C2×D5311yescharacteristic
418C2×#127—531no—
419C2×#126—1061no—
420C2×#125C2×D5311yescharacteristic
421C2×#124—531no—
422C2×#124—1061no—
423C2×#123—1061no—
424C2×#123—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—531no—
427C2×C22⋊Q8—1061no—
428C2×#121—531no—
429C2×#121—531no—
430C2×#121—531no—
431C2×#121—1061no—
432C2×#121—1061no—
433C2×C4×Q8—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×#117—531no—
438#501C2×D5318yescomplemented
439#496—538no—
440#488—538no—
441#486—538no—
442#469—538no—
443#468—538no—
444#466—538no—
445#465—538no—
446#442—538no—
447#440—538no—
448C4×SD16—538no—
449C4×D8—538no—
450C2×#107C2×D5311yescharacteristic
451C2×#107C2×D5311yescharacteristic
452C2×#106C2×D5311yescharacteristic
453C2×#106C2×D5311yescharacteristic
454C2×#103—531no—
455C2×#103—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×#102—531no—
460C2×#102—531no—
461C2×#102—531no—
462#405—538no—
463C2×#97—531no—
464C2×#97C2×D5311yescharacteristic
465C2×C4×C8—531no—
466C2×C4×C8—531no—
467C53C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—531no—
470C22×D4—531no—
471C22×D4—531no—
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C22×D4—1061no—
478C23×C4—531no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4—1061no—
482C2×SD16—534no—
483C2×SD16—534no—
484C2×SD16—1064no—
485C2×SD16—1064no—
486C2×D8—534no—
487C2×D8—534no—
488C2×D8—1064no—
489C2×D8—1064no—
490C2×M16—534no—
491C2×M16—1064no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—534no—
495C22×C8—1064no—
496C22×C8C22×D5311yescharacteristic
497C22×C8C22×D5311yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D5314yes—
500#127—534no—
501#127—1062no—
502#126—1068no—
503#125—22no—
504#125C22×D5314yes—
505#124—534no—
506#124—1068no—
507#124—1062no—
508#123—1068no—
509#123—1068no—
510#123—1068no—
511C22⋊Q8—534no—
512C22⋊Q8—1062no—
513C22⋊Q8—1068no—
514#121—534no—
515#121—534no—
516#121—534no—
517#121—1068no—
518#121—1068no—
519#121—1062no—
520#121—1062no—
521#121—1062no—
522C4×Q8—534no—
523C4×Q8—1062no—
524C4×D4—534no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4—1062no—
530#117—534no—
531#117—534no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4C22×D5311yescharacteristic
540C2×C4⋊C4C22×D5311yescharacteristic
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C22⋊C4—531no—
544C2×C22⋊C4—531no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C42—531no—
555C2×C42—1061no—
556C2×C42C22×D5311yescharacteristic
557#107C22×D5314yes—
558#107C22×D5314yes—
559#106C22×D5314yes—
560#106C22×D5314yes—
561#103—534no—
562#103—534no—
563#102—534no—
564#102—534no—
565#102—534no—
566#102—534no—
567#102—534no—
568#102—534no—
569#97—534no—
570#97C22×D5314yes—
571C4×C8—534no—
572C4×C8—534no—
573C24—531no—
574C24—1061no—
575C24—1061no—
576C24—1061no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—532no—
580C2×Q8—1061no—
581C2×Q8—1062no—
582C2×Q8—1062no—
583C2×D4—532no—
584C2×D4—532no—
585C2×D4—532no—
586C2×D4—1064no—
587C2×D4—1064no—
588C2×D4—1064no—
589C2×D4—1064no—
590C2×D4—1064no—
591C2×D4—1061no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—1062no—
595C2×D4—1062no—
596C2×D4—1062no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—4242no—
601C2×D4—4242no—
602C2×D4—4242no—
603C2×D4—4242no—
604C2×D4—4242no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—1064no—
615C22×C4—1064no—
616C22×C4—1064no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1061no—
620C22×C4—4242no—
621C22×C4—4242no—
622C22×C4—4242no—
623C22×C4D4×D5311yescharacteristic
624C22×C4D4×D5311yescharacteristic
625C22×C4C23×D5311yescharacteristic
626SD16—1068no—
627SD16—1068no—
628D8—1068no—
629D8—1068no—
630M16—1068no—
631C2×C8—532no—
632C2×C8—532no—
633C2×C8—1062no—
634C2×C8—1062no—
635C2×C8—1068no—
636C2×C8#1171994914yes—
637C2×C8#1171994914yes—
638C2×C8C23×D5312yes—
639C2×C8C23×D5312yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—534no—
648C4⋊C4—534no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4C23×D5312yes—
652C4⋊C4C23×D5312yes—
653C4⋊C4C23×D5312yes—
654C4⋊C4C23×D5312yes—
655C22⋊C4—534no—
656C22⋊C4—534no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C42—532no—
667C42—532no—
668C42—1064no—
669C42D4×D5312yes—
670C42C23×D5312yes—
671C23—532no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—1062no—
678C23—2122no—
679C23—2122no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23C2×D4×D5311yescharacteristic
688Q8—84no—
689Q8—1062no—
690Q8—1062no—
691Q8—2122no—
692D4—1062no—
693D4—1062no—
694D4—1062no—
695D4—1062no—
696D4—1062no—
697D4—1062no—
698D4—4244no—
699D4—4244no—
700D4—4244no—
701D4—4244no—
702D4—4244no—
703D4—2122no—
704D4—2122no—
705D4—2122no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—532no—
717C2×C4—532no—
718C2×C4—532no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—4244no—
727C2×C4—4244no—
728C2×C4—4244no—
729C2×C4—2122no—
730C2×C4C2×D4×D5312yes—
731C2×C4C2×D4×D5312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4C2×#1171994912yes—
734C2×C4C2×#1171994912yes—
735C2×C4C24×D5311yescharacteristic
736C8—1062no—
737C8—1062no—
738C8C2×#1171994914yes—
739C8C2×#1171994914yes—
740C22—1062no—
741C22—1062no—
742C22—1062no—
743C22—4244no—
744C22—4244no—
745C22—4244no—
746C22—2122no—
747C22—2122no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22—2124no—
756C22#1681117412yes—
757C22#1681142712yes—
758C22#1681143212yes—
759C22C22×D4×D5311yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—1062no—
767C4—1062no—
768C4—1062no—
769C4—2122no—
770C4#1681117412yes—
771C4C22×#1171994911yescharacteristic
772C4C22×#1171994911yescharacteristic
773C2—4242no—
774C2—4242no—
775C2—4242no—
776C2—2122no—
777C2#2028540314yesdirect product factor
778C2C2×#1681117411yescharacteristic
779C2C2×#1681142711yescharacteristic
780C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
hypercenterC2×#501D53
hypocenterC53C2×#3179
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16811247C2semidirect
2. C2×#16811229C2semidirect
3. #20285403C2direct (N × H)
4. C2×#16811012C2semidirect
5. C2×#16810980C2semidirect
6. C2×#16810971C2semidirect
7. C2×#16810877C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810860C2semidirect
10. C2×#16810853C2semidirect
11. C2×#16810734C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810710C2semidirect
14. C2×#16810705C2semidirect
15. C2×#16810580C2semidirect
16. C2×C53×#501C2semidirect
24. #16811247C22semidirect
26. #16811229C22semidirect
46. #16811012C22semidirect
47. #16810980C22semidirect
48. #16810971C22semidirect
49. #16810877C22semidirect
50. #16810870C22semidirect
51. #16810860C22semidirect
52. #16810853C22semidirect
53. #16810734C22semidirect
54. #16810722C22semidirect
55. #16810710C22semidirect
56. #16810705C22semidirect
65. #16810580C22semidirect
71. C53×#501C22semidirect
386. C2×#501D53semidirect
399. C2×C53#3179semidirect
438. #501C2×D53semidirect
467. C53C2×#3179semidirect
777. C2#20285403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112472
C2×#168112292
#202854032
C2×#168110122
C2×#168109802
C2×#168109712
C2×#168108772
C2×#168108702
C2×#168108602
C2×#168108532
C2×#168107342
C2×#168107222
C2×#168107102
C2×#168107052
C2×#168105802
C2×C53×#5012
C2×#317953