Finite Group Databasebeta

← C2×#20287370 #28263671

Subgroups — C2×#20287370 #28263671

Order 13568.

1970 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811355C211yesmaximal, characteristic, complemented
2C2×#16811332C211yesmaximal, characteristic, complemented
3#20287370C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810977C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810925C211yesmaximal, characteristic, complemented
9C2×#16810924C211yesmaximal, characteristic, complemented
10C2×#16810840C211yesmaximal, characteristic, complemented
11C2×#16810816C211yesmaximal, characteristic
12C2×#16810747C211yesmaximal, characteristic, complemented
13C2×SD16×Dic53C211yesmaximal, characteristic, complemented
14C2×D8×Dic53C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719922C2211yescharacteristic
18#16811355—24no—
19#16811355C2218yescomplemented
20#16811332—24no—
21#16811332C2218yescomplemented
22C2×#13133216C2211yescharacteristic
23C2×#13133213C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133206C2211yescharacteristic
27C2×#13133203—21no—
28C2×#13133201—21no—
29C2×#13133199—21no—
30C2×#13133196—21no—
31C2×#13133194—21no—
32C2×#13133194—21no—
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×D4×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133177—21no—
40C22×#11719919—21no—
41#16810979C2218yescomplemented
42#16810977C2218yescomplemented
43#16810968C2218yescomplemented
44#16810925C2218yescomplemented
45#16810924C2218yescomplemented
46#16810916C2218yescomplemented
47#16810840C2218yescomplemented
48#16810816C2218yes—
49#16810747C2218yescomplemented
50SD16×Dic53C2218yescomplemented
51D8×Dic53C2218yescomplemented
52C4×#11719922C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C4×#88322C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C23×Dic53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719922—24no—
87C2×#11719922C2314yes—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90#13133216—22no—
91#13133216C2314yes—
92#13133213—22no—
93#13133213C2314yes—
94#13133209—22no—
95#13133209C2314yes—
96#13133208—22no—
97#13133208C2314yes—
98#13133206—22no—
99#13133206C2314yes—
100#13133203—28no—
101#13133201—28no—
102#13133199—28no—
103#13133196—28no—
104#13133194—28no—
105#13133194—28no—
106Q8×Dic53—22no—
107Q8×Dic53C2314yes—
108C4×Dic106D414yes—
109C4×Dic106C2314yes—
110C4×D212—22no—
111C4×D212C2314yes—
112D4×Dic53—22no—
113D4×Dic53—22no—
114D4×Dic53—22no—
115D4×Dic53C2314yes—
116D4×Dic53C2314yes—
117D4×Dic53C2314yes—
118#13133177—28no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—28no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53C2311yescharacteristic
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133150C2314yes—
143#13133149C2314yes—
144#13133146C2314yes—
145#13133146C2314yes—
146#13133141C2314yes—
147#13133141C2314yes—
148#13133139C2314yes—
149#13133139C2314yes—
150#13133138C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133137C2314yes—
154C4×#88322C2314yes—
155C8×Dic53C2314yes—
156C8×Dic53C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×D4×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C2×SD16×C53—24no—
162C2×SD16×C53C2314yes—
163C2×D8×C53—24no—
164C2×D8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167#124×C53—22no—
168#124×C53C2314yes—
169C4×D4×C53—22no—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53C2311yescharacteristic
176C4⋊C8×C53C2314yes—
177#103×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C24×C53—21no—
181C23×D53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53#4114yes—
192C2×D4×C53C2412yes—
193C2×D4×C53C2412yes—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—24no—
197C22×C4×C53—82no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C2×C22⋊D53—82no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—24no—
210C22×Dic53—24no—
211C22×Dic53—44no—
212C22×Dic53—82no—
213C22×Dic53—82no—
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—21no—
221C2×D212C2412yes—
222C2×C4×D53—24no—
223C2×C4×D53—82no—
224C2×Dic106—24no—
225C2×Dic106—24no—
226C2×Dic106—82no—
227C2×Dic106C2×D414yes—
228SD16×C53—28no—
229D8×C53—28no—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53C2412yes—
233C2×C8×C53C2412yes—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719922—28no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2×D414yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919C2×D414yes—
262#11719919C2×D414yes—
263C4×Dic53—24no—
264C4×Dic53C2×D412yes—
265C4×Dic53C2×D412yes—
266C4×Dic53C2412yes—
267C4×Dic53C2412yes—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C23×C53—24no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—42no—
288D4×C53—24no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—42no—
293D4×C53C2×#4114yes—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
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—22no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—48no—
319C2×Dic53—84no—
320C2×Dic53—84no—
321C2×Dic53#13514yes—
322C2×Dic53C22×D412yes—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325C2×Dic53C22×D412yes—
326D212—22no—
327D212—22no—
328D212—42no—
329C4×D53—84no—
330Dic106—28no—
331Dic106—84no—
332C8×C53—22no—
333C8×C53—22no—
334#88322—22no—
335#88322—22no—
336C2×#3361—531nomaximal, Sylow
337C22×C53—24no—
338C22×C53—48no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—84no—
345C22×C53#54812yes—
346C22×C53C2×#13512yes—
347C22×C53#57612yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—84no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#54812yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C2×2−1+411yescharacteristic
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—42no—
366Dic53C2×#13514yes—
367C2×#559—531no—
368C2×#554—531no—
369#3361—5316no—
370C2×#488—531no—
371C2×#488—531no—
372C2×#486—531no—
373C2×#477—531no—
374C2×#478—531no—
375C2×#478—531no—
376C2×#463—531no—
377C2×#463D5311yescharacteristic, complemented
378C2×#459—531no—
379C2×C8×Q8—531no—
380C2×C4×SD16—531no—
381C2×C4×D8—531no—
382C2×C4×D8—531no—
383C2×C53—44no—
384C2×C53—82no—
385C2×C53#336114yescomplemented
386C2×C53C2×#54811yescharacteristic
387C2×C53C22×#13511yescharacteristic
388C2×C53C2×#57611yescharacteristic
389D53—82no—
390C22×SD16C2×D5311yescharacteristic
391C22×D8—531no—
392C22×D8C2×D5311yescharacteristic
393#559—538no—
394#559—1064no—
395#554—538no—
396#554—1064no—
397C2×C4⋊Q8—531no—
398C2×#127—531no—
399C2×#125—531no—
400C2×#125—531no—
401C2×#124—531no—
402C2×#124—1061no—
403C2×#124C2×D5311yescharacteristic
404C2×#123—1061no—
405C2×#123—1061no—
406C2×C22⋊Q8—1061no—
407C2×C22⋊Q8—1061no—
408C2×C22⋊Q8—1061no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×D4—531no—
412C2×C4×D4—531no—
413C2×C4×D4—531no—
414C2×C4×D4—531no—
415C2×C4×D4—1061no—
416C2×C4×D4C2×D5311yescharacteristic
417C22×C4⋊C4—1061no—
418#488—538no—
419#488—538no—
420#486—538no—
421#478—538no—
422#478—538no—
423#477—538no—
424#463—538no—
425#463C2×D5318yescomplemented
426#459—538no—
427C8×Q8—538no—
428C4×SD16—538no—
429C4×D8—538no—
430C4×D8—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8C2×D5311yescharacteristic
437C2×#103—531no—
438C2×#103—531no—
439C2×#103C2×D5311yescharacteristic
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102C2×D5311yescharacteristic
447C2×C4×C8—531no—
448C2×C4×C8—531no—
449C2×C4×C8—531no—
450C53C2×#336111yescharacteristic, complemented, Sylow
451C22×Q8—531no—
452C22×Q8—1061no—
453C22×Q8C22×D5311yescharacteristic
454C22×D4—531no—
455C22×D4—1061no—
456C22×D4—1061no—
457C22×D4C22×D5311yescharacteristic
458C22×D4C22×D5311yescharacteristic
459C23×C4—21no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4—1061no—
464C2×SD16—24no—
465C2×SD16C22×D5314yes—
466C2×D8—24no—
467C2×D8—534no—
468C2×D8—1064no—
469C2×D8C22×D5314yes—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—1062no—
476#127—534no—
477#127—1062no—
478#125—534no—
479#125—534no—
480#125—1062no—
481#125—1062no—
482#124—22no—
483#124—534no—
484#124—1062no—
485#124—1068no—
486#124C22×D5314yes—
487#123—1068no—
488#123—1068no—
489C22⋊Q8—1068no—
490C22⋊Q8—1068no—
491C22⋊Q8—1068no—
492C4×Q8—534no—
493C4×Q8—534no—
494C4×Q8—534no—
495C4×Q8—1062no—
496C4×D4—22no—
497C4×D4—534no—
498C4×D4—534no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—1062no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4—1068no—
505C4×D4—1062no—
506C4×D4C22×D5314yes—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—1068no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—1061no—
533C2×C42C22×D5311yescharacteristic
534#107—534no—
535#107—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8C22×D5314yes—
540#103—534no—
541#103—534no—
542#103C22×D5314yes—
543#102—534no—
544#102—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548#102—534no—
549#102C22×D5314yes—
550C4×C8—534no—
551C4×C8—534no—
552C4×C8—534no—
553C24—21no—
554C24—21no—
555C24—1061no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—534no—
560C2×Q8—1064no—
561C2×Q8—1064no—
562C2×Q8—4242no—
563C2×Q8C23×D5312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—532no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—1061no—
573C2×D4—1062no—
574C2×D4—1062no—
575C2×D4—4242no—
576C2×D4—2124no—
577C2×D4#1171994714yes—
578C2×D4C23×D5312yes—
579C2×D4C23×D5312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—1064no—
589C22×C4—1064no—
590C22×C4—1064no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1064no—
595C22×C4—4242no—
596C22×C4—4242no—
597C22×C4—4242no—
598C22×C4—2124no—
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602SD16—28no—
603D8—28no—
604D8—1068no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1062no—
610C2×C8—1062no—
611C2×C8C23×D5312yes—
612C2×C8C23×D5312yes—
613C4⋊C4—21no—
614C4⋊C4—534no—
615C4⋊C4—534no—
616C4⋊C4—534no—
617C4⋊C4—532no—
618C4⋊C4—532no—
619C4⋊C4—532no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4C23×D5312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—532no—
640C42—532no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42D4×D5312yes—
645C42C23×D5312yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1062no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23C2×D4×D5311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—1068no—
663Q8—4244no—
664D4—24no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—1062no—
670D4—1062no—
671D4—4244no—
672D4—2128no—
673D4—2122no—
674D4C2×#1171994714yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—534no—
683C2×C4—532no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—532no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—4244no—
694C2×C4—4244no—
695C2×C4—4244no—
696C2×C4—2128no—
697C2×C4—2122no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4C2×#1171994712yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—24no—
711C22—48no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—4244no—
719C22—2122no—
720C22—2122no—
721C22—2122no—
722C22#1681127912yes—
723C22#135×D5312yes—
724C22#1681142712yes—
725C22C22×D4×D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—534no—
731C4—1062no—
732C4—1062no—
733C4—1062no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127912yes—
738C4C22×#1171994711yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—44no—
741C2—82no—
742C2—4242no—
743C2#2028737014yesdirect product factor
744C2C2×#1681127911yescharacteristic
745C2C2×#135×D5311yescharacteristic
746C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC2×#16810816C2
hypercenterC2×#463D53
hypocenterC53C2×#3361
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811355C2semidirect
2. C2×#16811332C2semidirect
3. #20287370C2direct (N × H)
4. C2×#16810979C2semidirect
5. C2×#16810977C2semidirect
6. C2×#16810968C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810925C2semidirect
9. C2×#16810924C2semidirect
10. C2×#16810840C2semidirect
12. C2×#16810747C2semidirect
13. C2×SD16×Dic53C2semidirect
14. C2×D8×Dic53C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#463C2semidirect
19. #16811355C22semidirect
21. #16811332C22semidirect
41. #16810979C22semidirect
42. #16810977C22semidirect
43. #16810968C22semidirect
44. #16810925C22semidirect
45. #16810924C22semidirect
46. #16810916C22semidirect
47. #16810840C22semidirect
49. #16810747C22semidirect
50. SD16×Dic53C22semidirect
51. D8×Dic53C22semidirect
52. C4×#11719922C22semidirect
73. C53×#463C22semidirect
377. C2×#463D53semidirect
385. C2×C53#3361semidirect
425. #463C2×D53semidirect
450. C53C2×#3361semidirect
743. C2#20287370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113552
C2×#168113322
#202873702
C2×#168109792
C2×#168109772
C2×#168109682
C2×#168109162
C2×#168109252
C2×#168109242
C2×#168108402
C2×#168108162
C2×#168107472
C2×SD16×Dic532
C2×D8×Dic532
C2×C4×#117199222
C2×C53×#4632
C2×#336153