Finite Group Databasebeta

← C2×#20286069 #28256916

Subgroups — C2×#20286069 #28256916

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811160C211yesmaximal, characteristic, complemented
2C2×#16811158C211yesmaximal, characteristic, complemented
3#20286069C2116yesmaximal, direct product factor
4C2×#16810929C211yesmaximal, characteristic, complemented
5C2×#16810922C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810863C211yesmaximal, characteristic, complemented
8C2×#16810860C211yesmaximal, characteristic
9C2×#16810855C211yesmaximal, characteristic, complemented
10C2×#16810853C211yesmaximal, characteristic, complemented
11C2×#16810848C211yesmaximal, characteristic, complemented
12C2×#16810845C211yesmaximal, characteristic, complemented
13C2×#16810841C211yesmaximal, characteristic, complemented
14C2×#16810839C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#479C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811160—24no—
24#16811160C2218yescomplemented
25#16811158—24no—
26#16811158C2218yescomplemented
27C2×#13133212—21no—
28C2×#13133212—21no—
29C2×#13133208C2211yescharacteristic
30C2×#13133206C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133202—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133182C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×#13133179—21no—
42C2×#13133179C2211yescharacteristic
43C2×#13133175—21no—
44C2×#13133174—21no—
45C2×C42×D53C2211yescharacteristic
46#16810929C2218yescomplemented
47#16810922C2218yescomplemented
48#16810920C2218yescomplemented
49#16810863C2218yescomplemented
50#16810860C2218yes—
51#16810855C2218yescomplemented
52#16810853C2218yescomplemented
53#16810848C2218yescomplemented
54#16810845C2218yescomplemented
55#16810841C2218yescomplemented
56#16810839C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×C4⋊#88322C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C4⋊C8×D53C2218yescomplemented
63C2×#13133142C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133137C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#479C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53D411yescharacteristic
85C22×C4×D53D411yescharacteristic
86C22×C4×D53C2311yescharacteristic
87C2×#11719925—42no—
88C2×#11719925C2314yes—
89C2×#11719913—42no—
90C2×#11719913C2314yes—
91C2×#11719924—42no—
92C2×#11719924C2314yes—
93C2×D424—42no—
94C2×D424C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C2×C8×D53—42no—
98C2×C8×D53—42no—
99C2×C8×D53C2314yes—
100C2×C8×D53C2314yes—
101#13133212—28no—
102#13133212—28no—
103#13133208—22no—
104#13133208C2314yes—
105#13133206—22no—
106#13133206C2314yes—
107#13133205—22no—
108#13133205C2314yes—
109#13133202—28no—
110#13133202—28no—
111#13133197—22no—
112#13133197C2314yes—
113#13133193—22no—
114#13133193C2314yes—
115#13133192—22no—
116#13133192—22no—
117#13133192C2314yes—
118#13133192C2314yes—
119#13133182—22no—
120#13133182C2314yes—
121C4×D212—22no—
122C4×D212—28no—
123C4×D212C2314yes—
124#13133179—22no—
125#13133179—28no—
126#13133179C2314yes—
127#13133175—28no—
128#13133174—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53D411yescharacteristic
148C2×C4×Dic53C2311yescharacteristic
149C42×D53D414yes—
150C42×D53C2314yes—
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133140C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#125×C53—22no—
166#125×C53C2314yes—
167C4×Q8×C53—22no—
168C4×Q8×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×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53C2×D411yescharacteristic
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2411yescharacteristic
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—24no—
206C2×D212—24no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212—44no—
210C2×D212—44no—
211C2×D212C2412yes—
212C2×D212C2412yes—
213C2×C4×D53—24no—
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53—24no—
217C2×C4×D53—24no—
218C2×C4×D53—42no—
219C2×C4×D53—44no—
220C2×C4×D53—44no—
221C2×C4×D53C2×D412yes—
222C2×C4×D53C2×D414yes—
223C2×C4×D53C2×D414yes—
224C2×C4×D53C2412yes—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106C2412yes—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C4⋊C4×C53C2412yes—
242C42×C53—24no—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245#11719925—44no—
246#11719924—44no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257C4⋊Dic53—21no—
258C4⋊Dic53—24no—
259C4⋊Dic53—24no—
260C4⋊Dic53C2412yes—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53C2×D412yes—
266C4×Dic53C2×D414yes—
267C4×Dic53C2×D414yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273D424—44no—
274#11719913—44no—
275C8×D53—44no—
276C8×D53—44no—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53#13514yes—
289C22×D53C22×D412yes—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53H(5,𝔽2)12yes—
307C2×C4×C532−1+412yes—
308C2×C4×C53C2511yescharacteristic
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319D212—22no—
320D212—22no—
321D212—22no—
322D212—22no—
323D212—48no—
324D212—48no—
325D212—42no—
326D212—42no—
327C4×D53—28no—
328C4×D53—24no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—44no—
332C4×D53—48no—
333C4×D53—48no—
334Dic106—22no—
335Dic106—22no—
336Dic106—42no—
337C8×C53—22no—
338C8×C53—22no—
339#88322—22no—
340#88322—22no—
341C2×#3250—531nomaximal, Sylow
342C22×C53#53712yes—
343C22×C53C2×#13512yes—
344C22×C53#57512yes—
345C22×C53C23×D411yescharacteristic
346C2×D53—22no—
347C2×D53—28no—
348C2×D53—22no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—84no—
356C2×D53—84no—
357C2×D53C2×#13514yes—
358C4×C53—22no—
359C4×C53—22no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53#53712yes—
365C4×C53C2×H(5,𝔽2)11yescharacteristic
366C4×C53C2×2−1+411yescharacteristic
367Dic53—22no—
368Dic53—22no—
369Dic53—22no—
370Dic53—42no—
371Dic53—42no—
372C2×#529—531no—
373C2×#529—531no—
374#3250—5316no—
375C2×#479—531no—
376C2×#479D5311yescharacteristic, complemented
377C2×#478—531no—
378C2×#478—531no—
379C2×#467—531no—
380C2×#466—531no—
381C2×#465—531no—
382C2×#465—531no—
383C2×#464—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#463—531no—
387C22×C4⋊C8—531no—
388C2×C53#325014yescomplemented
389C2×C53C2×#53711yescharacteristic
390C2×C53C22×#13511yescharacteristic
391C2×C53C2×#57511yescharacteristic
392D53—24no—
393D53—82no—
394D53—82no—
395C22×Q16—531no—
396C22×SD16—531no—
397C22×SD16—531no—
398C22×D8—531no—
399C23×C8—531no—
400C23×C8—531no—
401#529—538no—
402#529—538no—
403#529—1064no—
404#529—1064no—
405C2×#126—1061no—
406C2×#126—1061no—
407C2×#125—531no—
408C2×#125C2×D5311yescharacteristic
409C2×#124—531no—
410C2×#124—531no—
411C2×#123—1061no—
412C2×#123—1061no—
413C2×C22⋊Q8—531no—
414C2×C22⋊Q8—531no—
415C2×#121—531no—
416C2×#121—531no—
417C2×C4×Q8—531no—
418C2×C4×Q8C2×D5311yescharacteristic
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4—1061no—
423C2×#117—1061no—
424C2×#117—1061no—
425C22×C42—531no—
426#479—538no—
427#479C2×D5318yescomplemented
428#478—538no—
429#478—538no—
430#467—538no—
431#466—538no—
432#465—538no—
433#465—538no—
434#464—538no—
435#464—538no—
436#463—538no—
437#463—538no—
438C2×#107—531no—
439C2×#107C2×D5311yescharacteristic
440C2×#106—531no—
441C2×#106C2×D5311yescharacteristic
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×C4⋊C8—538no—
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×#103—531no—
448C2×#103—531no—
449C2×#103C2×D5311yescharacteristic
450C2×#103C2×D5311yescharacteristic
451C2×#102—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C53C2×#325011yescharacteristic, complemented, Sylow
456C22×Q8—531no—
457C22×Q8C22×D5311yescharacteristic
458C22×D4—531no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4—1061no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4—1061no—
466C23×C4—1061no—
467C2×Q16—534no—
468C2×Q16—2122no—
469C2×SD16—534no—
470C2×SD16—534no—
471C2×SD16—2122no—
472C2×SD16—2122no—
473C2×D8—534no—
474C2×D8—2122no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—534no—
478C22×C8—534no—
479C22×C8—2122no—
480C22×C8—2122no—
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483#126—1068no—
484#126—1068no—
485#125—22no—
486#125—534no—
487#125—1062no—
488#125C22×D5314yes—
489#124—534no—
490#124—534no—
491#124—1062no—
492#124—1062no—
493#123—1068no—
494#123—1068no—
495C22⋊Q8—534no—
496C22⋊Q8—534no—
497C22⋊Q8—1062no—
498C22⋊Q8—1062no—
499#121—534no—
500#121—534no—
501#121—1062no—
502#121—1062no—
503C4×Q8—22no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×Q8C22×D5314yes—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—1068no—
510C4×D4—1062no—
511C4×D4—1068no—
512C4×D4—1062no—
513#117—1068no—
514#117—1068no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
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—1061no—
544C2×C42C22×D5311yescharacteristic
545#107—534no—
546#107C22×D5314yes—
547#106—534no—
548#106C22×D5314yes—
549C4⋊C8—534no—
550C4⋊C8—534no—
551C4⋊C8—534no—
552C4⋊C8C22×D5314yes—
553#103—534no—
554#103—534no—
555#103C22×D5314yes—
556#103C22×D5314yes—
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561C24—531no—
562C24—1061no—
563C24—1061no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—532no—
568C2×Q8—1061no—
569C2×Q8—1062no—
570C2×Q8—1062no—
571C2×Q8C23×D5312yes—
572C2×D4—532no—
573C2×D4—532no—
574C2×D4—1064no—
575C2×D4—1064no—
576C2×D4—1061no—
577C2×D4—1061no—
578C2×D4—1062no—
579C2×D4—1062no—
580C2×D4—1062no—
581C2×D4—1062no—
582C2×D4—2124no—
583C2×D4—2124no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—532no—
592C22×C4—534no—
593C22×C4—532no—
594C22×C4—534no—
595C22×C4—1064no—
596C22×C4—1064no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1064no—
602C22×C4—2122no—
603C22×C4—2124no—
604C22×C4—2124no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608Q16—2124no—
609SD16—2124no—
610SD16—2124no—
611D8—2124no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—532no—
615C2×C8—532no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—2124no—
619C2×C8—2124no—
620C2×C8C23×D5312yes—
621C2×C8C23×D5312yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—532no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1061no—
635C4⋊C4C23×D5312yes—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C42—24no—
649C42—534no—
650C42—534no—
651C42—532no—
652C42—532no—
653C42—1064no—
654C42D4×D5312yes—
655C42C23×D5312yes—
656C23—534no—
657C23—532no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1062no—
662C23—2122no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1062no—
673Q8—1062no—
674Q8—2122no—
675D4—1062no—
676D4—1062no—
677D4—1062no—
678D4—1062no—
679D4—2128no—
680D4—2128no—
681D4—2122no—
682D4—2122no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—1068no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—2124no—
706C2×C4—2128no—
707C2×C4—2128no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4C2×D4×D5312yes—
711C2×C4C2×D4×D5312yes—
712C2×C4C2×D4×D5311yescharacteristic
713C2×C4#1313326312yes—
714C2×C4#1313326512yes—
715C2×C4C24×D5311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1062no—
719C8—1062no—
720C22—534no—
721C22—1062no—
722C22—1068no—
723C22—1062no—
724C22—4244no—
725C22—4244no—
726C22—2122no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22#1681120312yes—
733C22#135×D5312yes—
734C22#1681142212yes—
735C22C22×D4×D5311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—1062no—
743C4—1062no—
744C4—1062no—
745C4—2122no—
746C4—2122no—
747C4#1681120312yes—
748C4C2×#1313326311yescharacteristic
749C4C2×#1313326511yescharacteristic
750C2—1064no—
751C2—4242no—
752C2—4242no—
753C2#2028606914yesdirect product factor
754C2C2×#1681120311yescharacteristic
755C2C2×#135×D5311yescharacteristic
756C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#479C2
socleC23×C53C22×D4
prime radicalC2×#16810860C2
hypercenterC2×#479D53
hypocenterC53C2×#3250
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#16811160C2semidirect
2. C2×#16811158C2semidirect
3. #20286069C2direct (N × H)
4. C2×#16810929C2semidirect
5. C2×#16810922C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810863C2semidirect
9. C2×#16810855C2semidirect
10. C2×#16810853C2semidirect
11. C2×#16810848C2semidirect
12. C2×#16810845C2semidirect
13. C2×#16810841C2semidirect
14. C2×#16810839C2semidirect
15. C2×C4⋊C8×D53C2semidirect
16. C2×C53×#479C2semidirect
24. #16811160C22semidirect
26. #16811158C22semidirect
46. #16810929C22semidirect
47. #16810922C22semidirect
48. #16810920C22semidirect
49. #16810863C22semidirect
51. #16810855C22semidirect
52. #16810853C22semidirect
53. #16810848C22semidirect
54. #16810845C22semidirect
55. #16810841C22semidirect
56. #16810839C22semidirect
62. C4⋊C8×D53C22semidirect
71. C53×#479C22semidirect
376. C2×#479D53semidirect
388. C2×C53#3250semidirect
427. #479C2×D53semidirect
455. C53C2×#3250semidirect
753. C2#20286069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111602
C2×#168111582
#202860692
C2×#168109292
C2×#168109222
C2×#168109202
C2×#168108632
C2×#168108602
C2×#168108552
C2×#168108532
C2×#168108482
C2×#168108452
C2×#168108412
C2×#168108392
C2×C4⋊C8×D532
C2×C53×#4792
C2×#325053