Finite Group Databasebeta

← C2×#20285903 #28256195

Subgroups — C2×#20285903 #28256195

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic
2C2×#125×D53C211yesmaximal, characteristic, complemented
3#20285903C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811030C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810986C211yesmaximal, characteristic, complemented
8C2×#16810943C211yesmaximal, characteristic, complemented
9C2×#16810940C211yesmaximal, characteristic, complemented
10C2×#16810938C211yesmaximal, characteristic, complemented
11C2×#16810935C211yesmaximal, characteristic, complemented
12C2×#16810924C211yesmaximal, characteristic, complemented
13C2×#16810923C211yesmaximal, characteristic, complemented
14C2×#16810920C211yesmaximal, characteristic, complemented
15C2×#16810679C211yesmaximal, characteristic, complemented
16C2×C53×#478C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18#16811170—24no—
19#16811170C2218yes—
20C2×#13133216C2211yescharacteristic
21C2×#13133213C2211yescharacteristic
22C2×#13133209C2211yescharacteristic
23C2×#13133208C2211yescharacteristic
24C2×#13133208C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133207—21no—
27#125×D53—24no—
28#125×D53C2218yescomplemented
29C2×#13133203—21no—
30C2×#13133192C2211yescharacteristic
31C2×#13133190—21no—
32C2×#13133188C2211yescharacteristic
33C2×C4×D212C2211yescharacteristic
34C2×C4×C22⋊D53—21no—
35C2×C4⋊C4×D53—21no—
36C2×C4⋊C4×D53—21no—
37C2×C4⋊C4×D53C2211yescharacteristic
38C2×C4⋊C4×D53C2211yescharacteristic
39C2×C42×D53C2211yescharacteristic
40#16811031C2218yescomplemented
41#16811030C2218yescomplemented
42#16810986C2218yescomplemented
43#16810986C2218yescomplemented
44#16810943C2218yescomplemented
45#16810940C2218yescomplemented
46#16810938C2218yescomplemented
47#16810935C2218yescomplemented
48#16810924C2218yescomplemented
49#16810923C2218yescomplemented
50#16810920C2218yescomplemented
51#16810679C2218yescomplemented
52C2×#13133151C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133139C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
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
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133216—22no—
94#13133216C2314yes—
95#13133213—22no—
96#13133213C2314yes—
97#13133209—22no—
98#13133209C2314yes—
99#13133208—22no—
100#13133208—22no—
101#13133208C2314yes—
102#13133208C2314yes—
103#13133207—28no—
104#13133207—28no—
105#13133203—28no—
106#13133192—22no—
107#13133192C2314yes—
108#13133190—28no—
109#13133188—22no—
110#13133188C2314yes—
111C4×D212—22no—
112C4×D212C2314yes—
113C4×C22⋊D53—28no—
114C2×C4⋊Dic53—21no—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53C2311yescharacteristic
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2311yescharacteristic
119C2×#11719919—21no—
120C2×#11719919—21no—
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C4⋊C4×D53—28no—
127C4⋊C4×D53—28no—
128C4⋊C4×D53—22no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53C2314yes—
131C4⋊C4×D53C2314yes—
132C2×C22⋊Dic53—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×C4×Dic53D411yescharacteristic
136C2×C4×Dic53D411yescharacteristic
137C2×C4×Dic53C2311yescharacteristic
138C42×D53D414yes—
139C42×D53C2314yes—
140#13133151C2314yes—
141#13133150C2314yes—
142#13133150C2314yes—
143#13133149C2314yes—
144#13133148C2314yes—
145#13133148C2314yes—
146C4⋊#88322C2314yes—
147#13133139C2314yes—
148#13133139C2314yes—
149#13133138C2314yes—
150#13133138C2314yes—
151#13133137C2314yes—
152#13133137C2314yes—
153#13133129C2314yes—
154#13133129C2314yes—
155#13133127C2314yes—
156#13133127C2314yes—
157C22×D4×C53C2311yescharacteristic
158C23×C4×C53—21no—
159C22×C8×C53C2311yescharacteristic
160C22×C8×C53C2311yescharacteristic
161#125×C53—22no—
162#125×C53C2314yes—
163C4×D4×C53—22no—
164C4×D4×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C22⋊C4×C53—21no—
171C2×C42×C53C2311yescharacteristic
172#107×C53C2314yes—
173#106×C53C2314yes—
174C4⋊C8×C53C2314yes—
175#102×C53C2314yes—
176#102×C53C2314yes—
177C24×C53—21no—
178C23×D53—21no—
179C23×D53C2×D411yescharacteristic
180C2×D4×C53—21no—
181C2×D4×C53—22no—
182C2×D4×C53—22no—
183C2×D4×C53C2412yes—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—24no—
188C22×C4×C53—44no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C2×C22⋊D53—24no—
193C2×C22⋊D53—24no—
194C2×C22⋊D53—24no—
195C2×C22⋊D53—44no—
196C2×C22⋊D53—44no—
197C2×C22⋊D53—44no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204#11719945—432no—
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—24no—
208C2×D212—21no—
209C2×D212—44no—
210C2×D212C2412yes—
211C2×C4×D53—24no—
212C2×C4×D53—22no—
213C2×C4×D53—22no—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—24no—
217C2×C4×D53—42no—
218C2×C4×D53—44no—
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—24no—
226C2×Dic106—44no—
227C2×C8×C53—22no—
228C2×C8×C53—22no—
229C2×C8×C53C2412yes—
230C2×C8×C53C2412yes—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C4⋊C4×C53C2412yes—
239C22⋊C4×C53—24no—
240C42×C53C2×D412yes—
241C42×C53C2412yes—
242C22⋊Dic53—24no—
243#11719921—24no—
244#11719921—24no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260C4×Dic53C2×D412yes—
261C4×Dic53C2×D414yes—
262C4×Dic53C2×D414yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C23×C53—22no—
269C23×C53—42no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53C22×D411yescharacteristic
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53AGL(1,ℤ/8)14yes—
280C22×D53C22×D412yes—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—42no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—48no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C532−1+412yes—
297C2×C4×C532−1+412yes—
298C2×C4×C53C2511yescharacteristic
299C22⋊D53—48no—
300C22⋊D53—48no—
301C22⋊D53—48no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314D212—22no—
315D212—22no—
316D212—48no—
317D212—42no—
318C4×D53—28no—
319C4×D53—24no—
320C4×D53—22no—
321C4×D53—22no—
322C4×D53—44no—
323C4×D53—48no—
324C4×D53—48no—
325C4×D53—48no—
326Dic106—48no—
327C8×C53—22no—
328C8×C53—22no—
329#88322—22no—
330#88322—22no—
331C2×#3234—531nomaximal, Sylow
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—84no—
336C22×C53#53612yes—
337C22×C53C2×AGL(1,ℤ/8)12yes—
338C22×C53#57512yes—
339C22×C53C23×D411yescharacteristic
340C2×D53—22no—
341C2×D53—28no—
342C2×D53—22no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C2×D53C2×AGL(1,ℤ/8)14yes—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53#53612yes—
354C4×C53C2×2−1+411yescharacteristic
355C4×C53C2×2−1+411yescharacteristic
356Dic53—22no—
357Dic53—22no—
358Dic53—22no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362C2×#532—531no—
363C22×#125—531no—
364#3234—5316no—
365C2×#501—531no—
366C2×#501—531no—
367C2×#490—531no—
368C2×#490—531no—
369C2×#481—531no—
370C2×#481—531no—
371C2×#480—531no—
372C2×#480—531no—
373C2×#478—531no—
374C2×#478—531no—
375C2×#478—531no—
376C2×#478D5311yescharacteristic, complemented
377C2×#432—531no—
378C2×C53—82no—
379C2×C53#323414yescomplemented
380C2×C53C2×#53611yescharacteristic
381C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C53C2×#57511yescharacteristic
383D53—24no—
384D53—82no—
385C22×#41—1061no—
386#532—538no—
387#532—1064no—
388C2×C4⋊Q8—531no—
389C2×#127—531no—
390C2×#125—538no—
391C2×#125—531no—
392C2×#125—531no—
393C2×#125—531no—
394C2×#125—1061no—
395C2×#125—1061no—
396C2×#125—1064no—
397C2×#125C2×D5311yescharacteristic
398C2×#124—1061no—
399C2×#121—531no—
400C2×#121—531no—
401C2×#121—1061no—
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×C4×D4C2×D5311yescharacteristic
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—1061no—
408C22×C4⋊C4—1061no—
409C22×C42—531no—
410#501—538no—
411#501—538no—
412#490—538no—
413#490—538no—
414#481—538no—
415#481—538no—
416#480—538no—
417#480—538no—
418#478—538no—
419#478—538no—
420#478—538no—
421#478C2×D5318yescomplemented
422#432—538no—
423C2×#107—531no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107C2×D5311yescharacteristic
427C2×#106—531no—
428C2×#106—531no—
429C2×#106—531no—
430C2×#106C2×D5311yescharacteristic
431C2×C4⋊C8—531no—
432C2×C4⋊C8C2×D5311yescharacteristic
433C2×#102—531no—
434C2×#102—531no—
435C2×#102—531no—
436C2×#102—531no—
437C2×#102—531no—
438C2×#102—531no—
439C2×#102C2×D5311yescharacteristic
440C2×#102C2×D5311yescharacteristic
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×#97—531no—
444C2×#97—531no—
445C53C2×#323411yescharacteristic, complemented, Sylow
446C2×#41—1068no—
447C2×#41—2128no—
448C22×Q8—1061no—
449C22×D4—531no—
450C22×D4—1061no—
451C22×D4—1061no—
452C22×D4—1061no—
453C22×D4—1061no—
454C22×D4C22×D5311yescharacteristic
455C23×C4—21no—
456C23×C4—531no—
457C23×C4—531no—
458C23×C4—531no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4—1061no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8C22×D5311yescharacteristic
465C22×C8C22×D5311yescharacteristic
466C4⋊Q8—534no—
467C4⋊Q8—1062no—
468#127—534no—
469#127—1062no—
470#125—22no—
471#125—534no—
472#125—534no—
473#125—534no—
474#125—1068no—
475#125—1068no—
476#125—1062no—
477#125—1062no—
478#125—1062no—
479#125C22×D5314yes—
480#124—1068no—
481#121—534no—
482#121—534no—
483#121—1068no—
484#121—1062no—
485#121—1062no—
486C4×D4—22no—
487C4×D4—534no—
488C4×D4—1068no—
489C4×D4—1062no—
490C4×D4C22×D5314yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1068no—
501C2×C4⋊C4—1068no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—1061no—
518C2×C42—531no—
519C2×C42—531no—
520C2×C42—531no—
521C2×C42—534no—
522C2×C42—534no—
523C2×C42C22×D5311yescharacteristic
524#107—534no—
525#107—534no—
526#107—534no—
527#107C22×D5314yes—
528#106—534no—
529#106—534no—
530#106—534no—
531#106C22×D5314yes—
532C4⋊C8—534no—
533C4⋊C8C22×D5314yes—
534#102—534no—
535#102—534no—
536#102—534no—
537#102—534no—
538#102—534no—
539#102—534no—
540#102C22×D5314yes—
541#102C22×D5314yes—
542C22⋊C8—534no—
543C22⋊C8—534no—
544#97—534no—
545#97—534no—
546C24—21no—
547C24—531no—
548C24—1061no—
549#41—21232no—
550C2×Q8—1064no—
551C2×Q8—2124no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—532no—
556C2×D4—1064no—
557C2×D4—1064no—
558C2×D4—1064no—
559C2×D4—1064no—
560C2×D4—1061no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—2124no—
564C2×D4—2124no—
565C2×D4—2124no—
566C2×D4—2124no—
567C2×D4C23×D5312yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—532no—
577C22×C4—534no—
578C22×C4—532no—
579C22×C4—534no—
580C22×C4—1064no—
581C22×C4—1064no—
582C22×C4—1064no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1064no—
589C22×C4—2122no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4D4×D5311yescharacteristic
594C22×C4D4×D5311yescharacteristic
595C22×C4C23×D5311yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—532no—
599C2×C8—532no—
600C2×C8—1062no—
601C2×C8—1062no—
602C2×C8C23×D5312yes—
603C2×C8C23×D5312yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—532no—
610C4⋊C4—532no—
611C4⋊C4—532no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4C23×D5312yes—
625C4⋊C4C23×D5312yes—
626C4⋊C4C23×D5312yes—
627C22⋊C4—24no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4—1064no—
631C42—534no—
632C42—534no—
633C42—532no—
634C42—532no—
635C42D4×D5312yes—
636C42C23×D5312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—534no—
642C23—532no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—2122no—
647C23—2122no—
648C23—2122no—
649C23C2×D4×D5311yescharacteristic
650Q8—2128no—
651D4—22no—
652D4—22no—
653D4—42no—
654D4—1062no—
655D4—1062no—
656D4—2128no—
657D4—2128no—
658D4—2128no—
659D4—2128no—
660D4—2122no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—532no—
671C2×C4—532no—
672C2×C4—532no—
673C2×C4—1068no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1064no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—2124no—
684C2×C4—2128no—
685C2×C4—2128no—
686C2×C4—2128no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4C2×D4×D5312yes—
691C2×C4C2×D4×D5312yes—
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#1313326412yes—
694C2×C4#1313326512yes—
695C2×C4C24×D5311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1062no—
699C8—1062no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—534no—
705C22—1062no—
706C22—1062no—
707C22—1068no—
708C22—4244no—
709C22—2122no—
710C22—2122no—
711C22—2122no—
712C22#1681119612yes—
713C22AGL(1,ℤ/8)×D5312yes—
714C22#1681142012yes—
715C22C22×D4×D5311yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—1062no—
722C4—1062no—
723C4—1062no—
724C4—2122no—
725C4—2122no—
726C4—2122no—
727C4#1681119612yes—
728C4C2×#1313326411yescharacteristic
729C4C2×#1313326511yescharacteristic
730C2—82no—
731C2—1064no—
732C2—4242no—
733C2#2028590314yesdirect product factor
734C2C2×#1681119611yescharacteristic
735C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
736C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#478C2
socleC23×C53C22×D4
prime radicalC2×#16811170C2
hypercenterC2×#478D53
hypocenterC53C2×#3234
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
2. C2×#125×D53C2semidirect
3. #20285903C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811030C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810986C2semidirect
8. C2×#16810943C2semidirect
9. C2×#16810940C2semidirect
10. C2×#16810938C2semidirect
11. C2×#16810935C2semidirect
12. C2×#16810924C2semidirect
13. C2×#16810923C2semidirect
14. C2×#16810920C2semidirect
15. C2×#16810679C2semidirect
16. C2×C53×#478C2semidirect
28. #125×D53C22semidirect
40. #16811031C22semidirect
41. #16811030C22semidirect
42. #16810986C22semidirect
43. #16810986C22semidirect
44. #16810943C22semidirect
45. #16810940C22semidirect
46. #16810938C22semidirect
47. #16810935C22semidirect
48. #16810924C22semidirect
49. #16810923C22semidirect
50. #16810920C22semidirect
51. #16810679C22semidirect
71. C53×#478C22semidirect
376. C2×#478D53semidirect
379. C2×C53#3234semidirect
421. #478C2×D53semidirect
445. C53C2×#3234semidirect
733. C2#20285903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111702
C2×#125×D532
#202859032
C2×#168110312
C2×#168110302
C2×#168109862
C2×#168109432
C2×#168109402
C2×#168109382
C2×#168109352
C2×#168109242
C2×#168109232
C2×#168109202
C2×#168106792
C2×C53×#4782
C2×#323453