Finite Group Databasebeta

← C2×#20287318 #28262817

Subgroups — C2×#20287318 #28262817

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811326C211yesmaximal, characteristic, complemented
2C2×#16811323C211yesmaximal, characteristic, complemented
3#20287318C2116yesmaximal, direct product factor
4C2×#16811022C211yesmaximal, characteristic, complemented
5C2×#16810949C211yesmaximal, characteristic, complemented
6C2×#16810946C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810935C211yesmaximal, characteristic, complemented
9C2×#16810924C211yesmaximal, characteristic, complemented
10C2×#16810875C211yesmaximal, characteristic, complemented
11C2×#16810875C211yesmaximal, characteristic, complemented
12C2×C4×#11719922C211yesmaximal, characteristic, complemented
13C2×#16810700C211yesmaximal, characteristic, complemented
14C2×#16810664C211yesmaximal, characteristic, complemented
15C2×#16810662C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719922C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20#16811326—24no—
21#16811326C2218yescomplemented
22#16811323—24no—
23#16811323C2218yescomplemented
24C2×#13133212—21no—
25C2×#13133210—21no—
26C2×#13133209C2211yescharacteristic
27C2×#13133202—21no—
28C2×#13133200—21no—
29C2×#13133192—21no—
30C2×#13133192C2211yescharacteristic
31C2×#13133192C2211yescharacteristic
32C2×#13133190—21no—
33C2×#13133188C2211yescharacteristic
34C2×#13133188C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133179—21no—
38C2×C4×C22⋊D53—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811022C2218yescomplemented
44#16810949C2218yescomplemented
45#16810946C2218yescomplemented
46#16810938C2218yescomplemented
47#16810935C2218yescomplemented
48#16810924C2218yescomplemented
49#16810875C2218yescomplemented
50#16810875C2218yescomplemented
51C4×#11719922C2218yescomplemented
52#16810700C2218yescomplemented
53#16810664C2218yescomplemented
54#16810662C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C53×#478C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×D212—21no—
78C22×D212—21no—
79C22×D212D411yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C22×C4×D53C2311yescharacteristic
88C2×#11719922—24no—
89C2×#11719922C2314yes—
90C2×#11719912—24no—
91C2×#11719912—24no—
92C2×#11719912C2314yes—
93C2×#11719912C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133212—28no—
97#13133210—28no—
98#13133209—22no—
99#13133209C2314yes—
100#13133202—28no—
101#13133200—28no—
102#13133192—28no—
103#13133192—22no—
104#13133192—22no—
105#13133192C2314yes—
106#13133192C2314yes—
107#13133190—28no—
108#13133188—22no—
109#13133188—22no—
110#13133188C2314yes—
111#13133188C2314yes—
112C4×D212—22no—
113C4×D212D414yes—
114C4×D212C2314yes—
115C4×D212C2314yes—
116#13133179—28no—
117C4×C22⋊D53—28no—
118#13133175—22no—
119#13133175—22no—
120#13133175C2314yes—
121#13133175C2314yes—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C4⋊C4×D53—22no—
131C4⋊C4×D53—22no—
132C4⋊C4×D53C2314yes—
133C4⋊C4×D53C2314yes—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145#13133151C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133139C2314yes—
153#13133139C2314yes—
154#13133138C2314yes—
155#13133137C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158C4×#88322C2314yes—
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#125×C53—22no—
164#125×C53C2314yes—
165C4×D4×C53—22no—
166C4×D4×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#107×C53C2314yes—
175#106×C53C2314yes—
176C4⋊C8×C53C2314yes—
177#102×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C23×D53—21no—
181C23×D53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×D4×C53—21no—
184C2×D4×C53—22no—
185C2×D4×C53—22no—
186C2×D4×C53C2412yes—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—24no—
191C22×C4×C53—82no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53—24no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53—82no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×D212—22no—
205C2×D212—22no—
206C2×D212—24no—
207C2×D212—21no—
208C2×D212—24no—
209C2×D212—42no—
210C2×D212—44no—
211C2×D212—82no—
212C2×D212C2×D414yes—
213C2×D212C2412yes—
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C2×C4×D53—82no—
223C2×C4×D53—82no—
224C2×C4×D53C2×D412yes—
225C2×C4×D53C2×D412yes—
226C2×C4×D53C2412yes—
227C2×C4×D53C2412yes—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C22⋊C4×C53—24no—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245#11719922—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921C2×D414yes—
252#11719921C2×D414yes—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53C2×D414yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C2×#88322—22no—
267C2×#88322#4114yes—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719912—28no—
271#11719912—28no—
272C23×C53—22no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53C22×D412yes—
288C22×D53C22×D412yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—42no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—84no—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4112yes—
305C2×C4×C532−1+412yes—
306C2×C4×C53C2511yescharacteristic
307C22⋊D53—48no—
308C22⋊D53—84no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319D212—22no—
320D212—22no—
321D212—44no—
322D212—48no—
323D212—42no—
324D212—84no—
325C4×D53—24no—
326C4×D53—24no—
327C4×D53—22no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—84no—
332C4×D53—84no—
333C4×D53—84no—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322C2×#4114yes—
338C2×#3355—531nomaximal, Sylow
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—84no—
343C22×C53#54712yes—
344C22×C53#57512yes—
345C22×C53#57612yes—
346C22×C53C23×D411yescharacteristic
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—44no—
354C2×D53—44no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53#54712yes—
365C4×C53C22×#4111yescharacteristic
366C4×C53C2×2−1+411yescharacteristic
367Dic53—22no—
368Dic53—22no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#553—531no—
373C2×#553—531no—
374#3355—5316no—
375C2×#499—531no—
376C2×#482—531no—
377C2×#482—531no—
378C2×#480—531no—
379C2×#480—531no—
380C2×#478—531no—
381C2×#478D5311yescharacteristic, complemented
382C2×#469—531no—
383C2×#469—531no—
384C2×C4×D8—531no—
385C2×#436—531no—
386C2×#428—531no—
387C2×#428—531no—
388C2×C53—82no—
389C2×C53#335514yescomplemented
390C2×C53C2×#54711yescharacteristic
391C2×C53C2×#57511yescharacteristic
392C2×C53C2×#57611yescharacteristic
393D53—42no—
394D53—42no—
395D53—82no—
396C22×D8—531no—
397C22×M16—531no—
398C22×M16—531no—
399#553—538no—
400#553—538no—
401#553—1064no—
402#553—1064no—
403C2×#126—1061no—
404C2×#126—1061no—
405C2×#125—531no—
406C2×#125C2×D5311yescharacteristic
407C2×#123—1061no—
408C2×#123—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#121—531no—
412C2×#121—531no—
413C2×#121—1061no—
414C2×#121—1061no—
415C2×C4×D4—531no—
416C2×C4×D4—531no—
417C2×C4×D4—1061no—
418C2×C4×D4—1061no—
419C2×C4×D4C2×D5311yescharacteristic
420C2×#117—531no—
421C2×#117—531no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424#499—538no—
425#482—538no—
426#482—538no—
427#480—538no—
428#480—538no—
429#478—538no—
430#478C2×D5318yescomplemented
431#469—538no—
432#469—538no—
433C4×D8—538no—
434#436—538no—
435#428—538no—
436#428—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107—531no—
441C2×#107C2×D5311yescharacteristic
442C2×#106—531no—
443C2×#106—531no—
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×C4×C8—531no—
456C53C2×#335511yescharacteristic, complemented, Sylow
457C22×D4—531no—
458C22×D4—531no—
459C22×D4—1061no—
460C22×D4—1061no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—21no—
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4—1061no—
470C2×D8—534no—
471C2×D8—1064no—
472C2×M16—534no—
473C2×M16—534no—
474C2×M16—1064no—
475C2×M16—1064no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5311yescharacteristic
480#126—1068no—
481#126—1068no—
482#125—22no—
483#125—534no—
484#125—1062no—
485#125C22×D5314yes—
486#123—1068no—
487#123—1068no—
488#121—534no—
489#121—534no—
490#121—534no—
491#121—534no—
492#121—1068no—
493#121—1062no—
494#121—1062no—
495#121—1068no—
496#121—1062no—
497#121—1062no—
498C4×D4—22no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1068no—
503C4×D4—1068no—
504C4×D4—1062no—
505C4×D4C22×D5314yes—
506#117—534no—
507#117—534no—
508#117—1062no—
509#117—1062no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—534no—
517C2×C4⋊C4—534no—
518C2×C4⋊C4—1062no—
519C2×C4⋊C4—1062no—
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—21no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4—531no—
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—1061no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540#107—534no—
541#107—534no—
542#107—534no—
543#107—534no—
544#107C22×D5314yes—
545#106—534no—
546#106—534no—
547#106—534no—
548#106C22×D5314yes—
549C4⋊C8C22×D5314yes—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102C22×D5314yes—
555#102C22×D5314yes—
556C22⋊C8—534no—
557C22⋊C8—534no—
558C4×C8—534no—
559C24—21no—
560C24—531no—
561C24—531no—
562C24—1061no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—534no—
567C2×D4—532no—
568C2×D4—1064no—
569C2×D4—1064no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—1061no—
573C2×D4—1062no—
574C2×D4—1062no—
575C2×D4—4242no—
576C2×D4—4242no—
577C2×D4—2122no—
578C2×D4—2124no—
579C2×D4—2124no—
580C2×D4C23×D5312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—1064no—
593C22×C4—1064no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1064no—
602C22×C4—4242no—
603C22×C4—4242no—
604C22×C4—4242no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608D8—1068no—
609M16—1068no—
610M16—1068no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—534no—
614C2×C8—532no—
615C2×C8—532no—
616C2×C8—1062no—
617C2×C8C23×D5312yes—
618C2×C8C23×D5312yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—534no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—532no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1061no—
631C4⋊C4—1061no—
632C4⋊C4—1061no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4C23×D5312yes—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—24no—
639C22⋊C4—534no—
640C22⋊C4—534no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C42—1064no—
649C42—1064no—
650C42D4×D5312yes—
651C42C23×D5312yes—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—532no—
657C23—532no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23C2×D4×D5311yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—1062no—
673D4—1062no—
674D4—4244no—
675D4—4244no—
676D4—2124no—
677D4—2128no—
678D4—2128no—
679D4—2122no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—532no—
690C2×C4—532no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1064no—
694C2×C4—1064no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—4244no—
703C2×C4—4244no—
704C2×C4—4244no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4C2×D4×D5312yes—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4#41×D5312yes—
712C2×C4#1313326512yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—22no—
716C8—534no—
717C8—1062no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—1062no—
723C22—1062no—
724C22—1062no—
725C22—1062no—
726C22—1062no—
727C22—1062no—
728C22—4244no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2124no—
733C22—2124no—
734C22#1681127512yes—
735C22#1681142012yes—
736C22#1681142712yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—1062no—
744C4—1062no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127512yes—
749C4C2×#41×D5311yescharacteristic
750C4C2×#1313326511yescharacteristic
751C2—82no—
752C2—4242no—
753C2—2122no—
754C2—2122no—
755C2#2028731814yesdirect product factor
756C2C2×#1681127511yescharacteristic
757C2C2×#1681142011yescharacteristic
758C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
hypercenterC2×#478D53
hypocenterC53C2×#3355
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16811326C2semidirect
2. C2×#16811323C2semidirect
3. #20287318C2direct (N × H)
4. C2×#16811022C2semidirect
5. C2×#16810949C2semidirect
6. C2×#16810946C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810935C2semidirect
9. C2×#16810924C2semidirect
10. C2×#16810875C2semidirect
11. C2×#16810875C2semidirect
12. C2×C4×#11719922C2semidirect
13. C2×#16810700C2semidirect
14. C2×#16810664C2semidirect
15. C2×#16810662C2semidirect
16. C2×C53×#478C2semidirect
21. #16811326C22semidirect
23. #16811323C22semidirect
43. #16811022C22semidirect
44. #16810949C22semidirect
45. #16810946C22semidirect
46. #16810938C22semidirect
47. #16810935C22semidirect
48. #16810924C22semidirect
49. #16810875C22semidirect
50. #16810875C22semidirect
51. C4×#11719922C22semidirect
52. #16810700C22semidirect
53. #16810664C22semidirect
54. #16810662C22semidirect
71. C53×#478C22semidirect
381. C2×#478D53semidirect
389. C2×C53#3355semidirect
430. #478C2×D53semidirect
456. C53C2×#3355semidirect
755. C2#20287318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113262
C2×#168113232
#202873182
C2×#168110222
C2×#168109492
C2×#168109462
C2×#168109382
C2×#168109352
C2×#168109242
C2×#168108752
C2×C4×#117199222
C2×#168107002
C2×#168106642
C2×#168106622
C2×C53×#4782
C2×#335553