Finite Group Databasebeta

← C2×#20287524 #28263822

Subgroups — C2×#20287524 #28263822

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811355C211yesmaximal, characteristic
2C2×Q8×Dic106C211yesmaximal, characteristic, complemented
3#20287524C2116yesmaximal, direct product factor
4C2×#16810984C211yesmaximal, characteristic, complemented
5C2×#16810982C211yesmaximal, characteristic, complemented
6C2×#16810968C211yesmaximal, characteristic
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810904C211yesmaximal, characteristic, complemented
9C2×#16810901C211yesmaximal, characteristic, complemented
10C2×#16810847C211yesmaximal, characteristic, complemented
11C2×#16810821C211yesmaximal, characteristic
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810724C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×Q16×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18#16811355—24no—
19#16811355C2218yes—
20Q8×Dic106—24no—
21Q8×Dic106C2218yescomplemented
22C2×#13133217—21no—
23C2×#13133217C2211yescharacteristic
24C2×#13133216—21no—
25C2×#13133216—21no—
26C2×#13133216C2211yescharacteristic
27C2×#13133216C2211yescharacteristic
28C2×#13133213C2211yescharacteristic
29C2×#13133206C2211yescharacteristic
30C2×#13133203—21no—
31C2×#13133201—21no—
32C2×#13133199—21no—
33C2×Q8×Dic53C2211yescharacteristic
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×C4×Dic106—21no—
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×D4×Dic53C2211yescharacteristic
40C2×#13133177—21no—
41#16810984C2218yescomplemented
42#16810982C2218yescomplemented
43#16810968C2218yes—
44#16810916C2218yescomplemented
45#16810904C2218yescomplemented
46#16810901C2218yescomplemented
47#16810847C2218yescomplemented
48#16810821C2218yes—
49#16810752C2218yescomplemented
50#16810724C2218yescomplemented
51#16810721C2218yescomplemented
52Q16×Dic53C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106D411yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90#13133217—22no—
91#13133217—28no—
92#13133217C2314yes—
93#13133216—28no—
94#13133216—28no—
95#13133216—22no—
96#13133216—22no—
97#13133216C2314yes—
98#13133216C2314yes—
99#13133213—22no—
100#13133213C2314yes—
101#13133206—22no—
102#13133206C2314yes—
103#13133203—28no—
104#13133201—28no—
105#13133199—28no—
106Q8×Dic53—22no—
107Q8×Dic53—22no—
108Q8×Dic53—22no—
109Q8×Dic53C2314yes—
110Q8×Dic53C2314yes—
111Q8×Dic53C2314yes—
112C4×Dic106—28no—
113C4×Dic106D414yes—
114C4×Dic106C2314yes—
115C4×D212—22no—
116C4×D212C2314yes—
117D4×Dic53—22no—
118D4×Dic53C2314yes—
119#13133177—28no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C2×C22⋊Dic53—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53C2311yescharacteristic
140C2×C4×Dic53C2311yescharacteristic
141#13133151C2314yes—
142#13133151C2314yes—
143#13133150C2314yes—
144#13133146C2314yes—
145#13133146C2314yes—
146#13133141C2314yes—
147#13133141C2314yes—
148#13133141C2314yes—
149#13133139C2314yes—
150#13133139C2314yes—
151#13133138C2314yes—
152#13133138C2314yes—
153#13133137C2314yes—
154#13133128C2314yes—
155#13133127C2314yes—
156C8×Dic53C2314yes—
157C22×Q8×C53C2311yescharacteristic
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C2×Q16×C53—24no—
161C2×Q16×C53C2314yes—
162C2×SD16×C53—24no—
163C2×SD16×C53C2314yes—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#124×C53—22no—
167#124×C53C2314yes—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C42×C53—21no—
175C2×C42×C53C2311yescharacteristic
176C4⋊C8×C53C2314yes—
177#103×C53C2314yes—
178#102×C53C2314yes—
179C24×C53—21no—
180C23×D53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53#4114yes—
187C2×Q8×C53C2412yes—
188C2×Q8×C53C2412yes—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53C2412yes—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—24no—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—44no—
202C2×C22⋊D53—82no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—24no—
207C22×Dic53—82no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—21no—
215C2×D212C2412yes—
216C2×C4×D53—24no—
217C2×C4×D53—82no—
218C2×Dic106—24no—
219C2×Dic106—24no—
220C2×Dic106—24no—
221C2×Dic106—24no—
222C2×Dic106—82no—
223C2×Dic106—82no—
224C2×Dic106—82no—
225C2×Dic106C2×D414yes—
226Q16×C53—28no—
227SD16×C53—28no—
228C2×C8×C53—22no—
229C2×C8×C53—22no—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53C2412yes—
235C22⋊C4×C53—24no—
236C22⋊C4×C53—24no—
237C42×C53—24no—
238C42×C53C2×D412yes—
239C42×C53C2412yes—
240C22⋊Dic53—24no—
241#11719924—28no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53C2×D414yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919C2×D414yes—
259#11719919C2×D414yes—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53C2×D412yes—
264C4×Dic53C2×D412yes—
265C4×Dic53C2412yes—
266C4×Dic53C2412yes—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C23×C53—22no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53C22×D411yescharacteristic
276C22×D53—22no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280Q8×C53—24no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—22no—
284Q8×C53—42no—
285Q8×C53C2×#4114yes—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—42no—
289C2×C4×C53—24no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4112yes—
301C2×C4×C532−1+412yes—
302C2×C4×C53C2511yescharacteristic
303C22⋊D53—48no—
304C22⋊D53—84no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—84no—
315C2×Dic53#13714yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320D212—22no—
321D212—22no—
322D212—42no—
323C4×D53—84no—
324Dic106—28no—
325Dic106—84no—
326Dic106—84no—
327Dic106—84no—
328C8×C53—22no—
329C8×C53—22no—
330#88322—22no—
331#88322—22no—
332C2×#3375—531nomaximal, Sylow
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—84no—
337C22×C53#54812yes—
338C22×C53C2×#13712yes—
339C22×C53#57612yes—
340C22×C53C23×D411yescharacteristic
341C2×D53—42no—
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—84no—
345C4×C53—24no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53#54812yes—
351C4×C53C22×#4111yescharacteristic
352C4×C53C2×2−1+411yescharacteristic
353Dic53—22no—
354Dic53—22no—
355Dic53—22no—
356Dic53—42no—
357Dic53—42no—
358Dic53—42no—
359Dic53C2×#13714yes—
360C2×#559—531no—
361C2×Q82—531no—
362#3375—5316no—
363C2×#489—531no—
364C2×#489—531no—
365C2×#486—531no—
366C2×#477—531no—
367C2×#474—531no—
368C2×#474—531no—
369C2×#464—531no—
370C2×#464D5311yescharacteristic, complemented
371C2×#460—531no—
372C2×#446—531no—
373C2×#440—531no—
374C2×#440—531no—
375C2×C4×Q16—531no—
376C2×C53—82no—
377C2×C53#337514yescomplemented
378C2×C53C2×#54811yescharacteristic
379C2×C53C22×#13711yescharacteristic
380C2×C53C2×#57611yescharacteristic
381D53—82no—
382C22×Q16C2×D5311yescharacteristic
383C22×SD16—531no—
384C22×SD16C2×D5311yescharacteristic
385#559—538no—
386#559—1064no—
387Q82—538no—
388Q82—1064no—
389C2×C4⋊Q8—531no—
390C2×C4⋊Q8—531no—
391C2×C4⋊Q8—531no—
392C2×C4⋊Q8—1061no—
393C2×C4⋊Q8—1061no—
394C2×C4⋊Q8—1061no—
395C2×#127—531no—
396C2×#124—531no—
397C2×#124—1061no—
398C2×#124C2×D5311yescharacteristic
399C2×#123—1061no—
400C2×#123—1061no—
401C2×C4×Q8—531no—
402C2×C4×Q8—531no—
403C2×C4×Q8—531no—
404C2×C4×Q8—531no—
405C2×C4×Q8—1061no—
406C2×C4×Q8C2×D5311yescharacteristic
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C2×C4×D4—1061no—
410#489—538no—
411#489—538no—
412#486—538no—
413#477—538no—
414#474—538no—
415#474—538no—
416#464—538no—
417#464C2×D5318yescomplemented
418#460—538no—
419#446—538no—
420#440—538no—
421#440—538no—
422C4×Q16—538no—
423C2×#107—531no—
424C2×#107—531no—
425C2×#107—531no—
426C2×C4⋊C8—531no—
427C2×C4⋊C8—531no—
428C2×C4⋊C8C2×D5311yescharacteristic
429C2×#103—531no—
430C2×#103—531no—
431C2×#103—531no—
432C2×#103C2×D5311yescharacteristic
433C2×#102—531no—
434C2×#102—531no—
435C2×#102—531no—
436C2×#102—531no—
437C2×#102—531no—
438C2×#102C2×D5311yescharacteristic
439C2×#97—531no—
440C2×#97—531no—
441C2×C4×C8—531no—
442C53C2×#337511yescharacteristic, complemented, Sylow
443C22×Q8—531no—
444C22×Q8—1061no—
445C22×Q8—1061no—
446C22×Q8—1061no—
447C22×Q8C22×D5311yescharacteristic
448C22×Q8C22×D5311yescharacteristic
449C22×D4—531no—
450C22×D4—1061no—
451C22×D4—1061no—
452C22×D4C22×D5311yescharacteristic
453C23×C4—1061no—
454C23×C4—1061no—
455C2×Q16—24no—
456C2×Q16C22×D5314yes—
457C2×SD16—24no—
458C2×SD16—534no—
459C2×SD16—1064no—
460C2×SD16C22×D5314yes—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8C22×D5311yescharacteristic
464C22×C8C22×D5311yescharacteristic
465C4⋊Q8—534no—
466C4⋊Q8—534no—
467C4⋊Q8—534no—
468C4⋊Q8—1068no—
469C4⋊Q8—1062no—
470C4⋊Q8—1062no—
471C4⋊Q8—1068no—
472C4⋊Q8—1068no—
473C4⋊Q8—1062no—
474#127—534no—
475#127—1062no—
476#124—22no—
477#124—534no—
478#124—1062no—
479#124—1068no—
480#124C22×D5314yes—
481#123—1068no—
482#123—1068no—
483C4×Q8—22no—
484C4×Q8—534no—
485C4×Q8—534no—
486C4×Q8—534no—
487C4×Q8—534no—
488C4×Q8—534no—
489C4×Q8—1068no—
490C4×Q8—1062no—
491C4×Q8—1062no—
492C4×Q8—1062no—
493C4×Q8C22×D5314yes—
494C4×D4—534no—
495C4×D4—534no—
496C4×D4—1062no—
497C4×D4—1068no—
498C4×D4—1062no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C42—21no—
520C2×C42—531no—
521C2×C42—531no—
522C2×C42—1061no—
523C2×C42—1061no—
524C2×C42—1061no—
525C2×C42C22×D5311yescharacteristic
526#107—534no—
527#107—534no—
528#107—534no—
529C4⋊C8—534no—
530C4⋊C8—534no—
531C4⋊C8C22×D5314yes—
532#103—534no—
533#103—534no—
534#103—534no—
535#103C22×D5314yes—
536#102—534no—
537#102—534no—
538#102—534no—
539#102—534no—
540#102—534no—
541#102C22×D5314yes—
542#97—534no—
543#97—534no—
544C4×C8—534no—
545C24—21no—
546C24—1061no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—534no—
553C2×Q8—1064no—
554C2×Q8—1064no—
555C2×Q8—1064no—
556C2×Q8—1064no—
557C2×Q8—4242no—
558C2×Q8—4242no—
559C2×Q8—4242no—
560C2×Q8#1171994714yes—
561C2×Q8C23×D5312yes—
562C2×Q8C23×D5312yes—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—532no—
567C2×D4—1064no—
568C2×D4—1064no—
569C2×D4—1061no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—4242no—
573C2×D4—2124no—
574C2×D4C23×D5312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—1064no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1064no—
587C22×C4—4242no—
588C22×C4—4242no—
589C22×C4D4×D5311yescharacteristic
590C22×C4D4×D5311yescharacteristic
591C22×C4C23×D5311yescharacteristic
592Q16—28no—
593SD16—28no—
594SD16—1068no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—532no—
598C2×C8—532no—
599C2×C8—1062no—
600C2×C8—1062no—
601C2×C8C23×D5312yes—
602C2×C8C23×D5312yes—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—534no—
606C4⋊C4—534no—
607C4⋊C4—534no—
608C4⋊C4—532no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1064no—
620C4⋊C4C23×D5312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—1064no—
624C22⋊C4—1064no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C42—24no—
628C42—532no—
629C42—532no—
630C42—532no—
631C42—532no—
632C42—1064no—
633C42—1064no—
634C42—1064no—
635C42D4×D5312yes—
636C42C23×D5312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—1062no—
642C23—2122no—
643C23—2122no—
644C23—2122no—
645C23C2×D4×D5311yescharacteristic
646Q8—24no—
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—42no—
651Q8—1068no—
652Q8—4244no—
653Q8—4244no—
654Q8—4244no—
655Q8C2×#1171994714yes—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—1062no—
660D4—1062no—
661D4—4244no—
662D4—2128no—
663D4—2122no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—534no—
673C2×C4—532no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—4244no—
684C2×C4—4244no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4C2×D4×D5312yes—
689C2×C4C2×D4×D5312yes—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×#1171994712yes—
692C2×C4#1313326412yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—22no—
696C8—1062no—
697C8—1062no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—4244no—
703C22—2122no—
704C22—2122no—
705C22—2122no—
706C22#1681127912yes—
707C22#137×D5312yes—
708C22#1681142512yes—
709C22C22×D4×D5311yescharacteristic
710C4—22no—
711C4—24no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—534no—
716C4—1062no—
717C4—1062no—
718C4—1062no—
719C4—2122no—
720C4—2122no—
721C4—2122no—
722C4#1681127912yes—
723C4C22×#1171994711yescharacteristic
724C4C2×#1313326411yescharacteristic
725C2—82no—
726C2—4242no—
727C2#2028752414yesdirect product factor
728C2C2×#1681127911yescharacteristic
729C2C2×#137×D5311yescharacteristic
730C2C2×#1681142511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#13133213C22
hypercenterC2×#464D53
hypocenterC53C2×#3375
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic106C2semidirect
3. #20287524C2direct (N × H)
4. C2×#16810984C2semidirect
5. C2×#16810982C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810904C2semidirect
9. C2×#16810901C2semidirect
10. C2×#16810847C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810724C2semidirect
14. C2×#16810721C2semidirect
15. C2×Q16×Dic53C2semidirect
16. C2×C53×#464C2semidirect
21. Q8×Dic106C22semidirect
41. #16810984C22semidirect
42. #16810982C22semidirect
44. #16810916C22semidirect
45. #16810904C22semidirect
46. #16810901C22semidirect
47. #16810847C22semidirect
49. #16810752C22semidirect
50. #16810724C22semidirect
51. #16810721C22semidirect
52. Q16×Dic53C22semidirect
73. C53×#464C22semidirect
370. C2×#464D53semidirect
377. C2×C53#3375semidirect
417. #464C2×D53semidirect
442. C53C2×#3375semidirect
727. C2#20287524direct (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×Q8×Dic1062
#202875242
C2×#168109842
C2×#168109822
C2×#168109682
C2×#168109162
C2×#168109042
C2×#168109012
C2×#168108472
C2×#168108212
C2×#168107522
C2×#168107242
C2×#168107212
C2×Q16×Dic532
C2×C53×#4642
C2×#337553