Finite Group Databasebeta

← #28254867

Subgroups — #28254867

Order 13568.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic, complemented
2C2×#16811134C211yesmaximal, characteristic, complemented
3#20285557C214yesmaximal, complemented
4#20285547C212yesmaximal, complemented
5#20285531C212yesmaximal, complemented
6#20285508C214yesmaximal, complemented
7#20285498C212yesmaximal, complemented
8#20285482C212yesmaximal, complemented
9#20284664C211yesmaximal, characteristic, complemented
10#20284656C211yesmaximal, characteristic, complemented
11#20284648C212yesmaximal, complemented
12#20284345C212yesmaximal, complemented
13#20284334C212yesmaximal, complemented
14#20283977C211yesmaximal, characteristic, complemented
15#20283969C211yesmaximal, characteristic, complemented
16#20283960C212yesmaximal, complemented
17C2×C53×#407C211yesmaximal, characteristic, complemented
18C22×#11719945C2211yescharacteristic
19C22×#11719945C2211yescharacteristic, complemented
20C2×#13133250C2212yescomplemented
21C2×#13133245C2212yescomplemented
22#16811134—21no—
23#16811134—21no—
24#16811134—21no—
25#16811134—21no—
26#16811134—21no—
27#16811134—21no—
28#16811134—21no—
29#16811134—21no—
30#16811134C2212yes—
31#16811134C2212yes—
32#16811134C2212yes—
33#16811134C2212yes—
34#16811134C2212yescomplemented
35#16811134C2212yescomplemented
36#16811134C2212yescomplemented
37#16811134C2212yescomplemented
38C2×#13133200—21no—
39C2×#13133200—21no—
40C2×#13133196C2211yescharacteristic
41C2×#13133196C2211yescharacteristic, complemented
42C2×#13133196C2211yescharacteristic, complemented
43C2×#13133196C2211yescharacteristic, complemented
44C2×#13133191C2211yescharacteristic
45C2×#13133191C2211yescharacteristic, complemented
46C2×#13133191C2211yescharacteristic, complemented
47C2×#13133191C2211yescharacteristic, complemented
48C2×#13133186—21no—
49C2×#13133186—21no—
50C2×C4×C22⋊D53—21no—
51C2×C4×C22⋊D53—21no—
52C2×C4×C22⋊D53—21no—
53C2×C4×C22⋊D53—21no—
54C2×#13133176C2211yescharacteristic
55C2×#13133176C2211yescharacteristic, complemented
56#16810965C2214yescomplemented
57#16810965C2214yescomplemented
58#16810965C2214yescomplemented
59#16810959C2212yescomplemented
60#16810954C2212yescomplemented
61#16810948C2214yescomplemented
62#16810948C2214yescomplemented
63#16810948C2214yescomplemented
64#16810942C2212yescomplemented
65#16810937C2212yescomplemented
66#16810881C2214yescomplemented
67#16810876C2214yescomplemented
68#16810869C2214yescomplemented
69#16810869C2214yescomplemented
70#16810864C2214yescomplemented
71#16810859C2214yescomplemented
72#16810852C2214yescomplemented
73#16810852C2214yescomplemented
74#16810787C2214yescomplemented
75#16810787C2214yescomplemented
76#16810787C2214yescomplemented
77#16810781C2212yescomplemented
78#16810776C2212yescomplemented
79#16810770C2214yescomplemented
80#16810770C2214yescomplemented
81#16810770C2214yescomplemented
82#16810764C2212yescomplemented
83#16810759C2212yescomplemented
84#16810665C2212yescomplemented
85#16810665C2212yescomplemented
86#16810633C2212yescomplemented
87#16810629C2212yescomplemented
88#16810625C2212yescomplemented
89#16810625C2212yescomplemented
90C24×C4×C53C2211yescharacteristic
91C22×M16×C53C2212yescomplemented
92C53×#407C2211yescharacteristic
93C53×#407C2211yescharacteristic
94C53×#407C2212yescomplemented
95C53×#407C2212yescomplemented
96C53×#407C2212yescomplemented
97C2×C22⋊C8×C53C2212yescomplemented
98C2×C22⋊C8×C53C2212yescomplemented
99C2×#11719945—21no—
100C2×#11719945—21no—
101C2×#11719945—21no—
102C2×#11719945—21no—
103C2×#11719945—44no—
104C2×#11719945—44no—
105C2×#11719945C2312yes—
106C2×#11719945C2312yes—
107C2×#11719945C2312yes—
108C2×#11719945C2312yes—
109C22×Dic106C2311yescharacteristic
110C22×Dic106C2311yescharacteristic
111C22×D212C2311yescharacteristic
112C22×D212C2311yescharacteristic
113C22×C22⋊D53—21no—
114C22×C22⋊D53—21no—
115C22×C22⋊D53—21no—
116C22×C22⋊D53—21no—
117C22×C22⋊D53—21no—
118C22×C22⋊D53—21no—
119C22×C4×D53—21no—
120C22×C4×D53—21no—
121#13133250—44no—
122#13133245—44no—
123C2×Dic212C2314yescomplemented
124C2×#11719913C2314yescomplemented
125C2×#11719913C2314yescomplemented
126C2×D424C2314yescomplemented
127#13133200—22no—
128#13133200—22no—
129#13133200—22no—
130#13133200—22no—
131#13133200—22no—
132#13133200—22no—
133#13133200—22no—
134#13133200—22no—
135#13133196—21no—
136#13133196—21no—
137#13133196—21no—
138#13133196—21no—
139#13133196—21no—
140#13133196—21no—
141#13133196—21no—
142#13133196—21no—
143#13133196C2312yes—
144#13133196C2312yes—
145#13133196C2312yes—
146#13133196C2312yes—
147#13133196C2312yes—
148#13133196C2312yes—
149#13133196C2312yes—
150#13133196C2312yes—
151#13133191—21no—
152#13133191—21no—
153#13133191—21no—
154#13133191—21no—
155#13133191—21no—
156#13133191—21no—
157#13133191—21no—
158#13133191—21no—
159#13133191C2312yes—
160#13133191C2312yes—
161#13133191C2312yes—
162#13133191C2312yes—
163#13133191C2312yes—
164#13133191C2312yes—
165#13133191C2312yes—
166#13133191C2312yes—
167#13133186—22no—
168#13133186—22no—
169#13133186—22no—
170#13133186—22no—
171#13133186—22no—
172#13133186—22no—
173#13133186—22no—
174#13133186—22no—
175C4×C22⋊D53—22no—
176C4×C22⋊D53—22no—
177C4×C22⋊D53—22no—
178C4×C22⋊D53—22no—
179C4×C22⋊D53—22no—
180C4×C22⋊D53—22no—
181C4×C22⋊D53—22no—
182C4×C22⋊D53—22no—
183C4×C22⋊D53—22no—
184C4×C22⋊D53—22no—
185C4×C22⋊D53—22no—
186C4×C22⋊D53—22no—
187C4×C22⋊D53—22no—
188C4×C22⋊D53—22no—
189C4×C22⋊D53—22no—
190C4×C22⋊D53—22no—
191#13133176—21no—
192#13133176—21no—
193#13133176—21no—
194#13133176—21no—
195#13133176C2312yes—
196#13133176C2312yes—
197#13133176C2312yes—
198#13133176C2312yes—
199C2×C4⋊Dic53C2311yescharacteristic
200C2×C4⋊Dic53C2311yescharacteristic
201C2×C4⋊Dic53C2311yescharacteristic
202C2×C4⋊Dic53C2311yescharacteristic
203C2×#11719919—21no—
204C2×#11719919—21no—
205C2×#11719919—21no—
206C2×#11719919—21no—
207C2×C22⋊Dic53—21no—
208C2×C22⋊Dic53—21no—
209C2×C22⋊Dic53—21no—
210C2×C22⋊Dic53—21no—
211C2×C22⋊Dic53—21no—
212C2×C22⋊Dic53—21no—
213C2×#11719921—21no—
214C2×#11719921—21no—
215C2×#11719921—21no—
216C2×#11719921—21no—
217C2×C4×Dic53—21no—
218C2×C4×Dic53—21no—
219#13133151C2314yescomplemented
220#13133151C2314yescomplemented
221#13133149C2314yescomplemented
222#13133149C2314yescomplemented
223#13133142C2314yescomplemented
224#13133142C2314yescomplemented
225#13133142C2314yescomplemented
226#13133142C2314yescomplemented
227#13133139C2314yescomplemented
228#13133139C2314yescomplemented
229#13133139C2314yescomplemented
230#13133139C2314yescomplemented
231C25×C53D411yescharacteristic
232C23×C4×C53—44no—
233C23×C4×C53D411yescharacteristic
234C23×C4×C53D411yescharacteristic
235C23×C4×C53D411yescharacteristic
236C23×C4×C53D411yescharacteristic
237C23×C4×C53D411yescharacteristic
238C23×C4×C53D411yescharacteristic
239C23×C4×C53D411yescharacteristic
240C23×C4×C53C2311yescharacteristic
241C23×C4×C53C2311yescharacteristic
242C23×C4×C53C2311yescharacteristic
243C23×C4×C53C2311yescharacteristic
244C23×C4×C53C2311yescharacteristic
245C23×C4×C53C2311yescharacteristic
246C23×C4×C53C2311yescharacteristic
247C2×M16×C53—44no—
248C2×M16×C53C2312yes—
249C2×M16×C53C2312yes—
250C2×M16×C53C2314yes—
251C22×C8×C53C2314yes—
252C22⋊C8×C53C2312yes—
253C22⋊C8×C53C2312yes—
254C22⋊C8×C53C2314yes—
255C22⋊C8×C53C2314yes—
256C22⋊C8×C53C2312yes—
257C22⋊C8×C53C2312yes—
258C24×C53—42no—
259C24×C53—42no—
260C24×C53—42no—
261C24×C53C2×D411yescharacteristic
262C24×C53C2×D411yescharacteristic
263C24×C53C2×D411yescharacteristic
264C24×C53C2×D411yescharacteristic
265C24×C53C2×D411yescharacteristic
266C24×C53C2×D411yescharacteristic
267C24×C53C2×D411yescharacteristic
268C23×D53—21no—
269C23×D53—21no—
270C22×C4×C53—24no—
271C22×C4×C53—24no—
272C22×C4×C53—24no—
273C22×C4×C53—42no—
274C22×C4×C53—42no—
275C22×C4×C53—42no—
276C22×C4×C53—42no—
277C22×C4×C53—42no—
278C22×C4×C53—42no—
279C22×C4×C53—42no—
280C22×C4×C53—42no—
281C22×C4×C53—42no—
282C22×C4×C53—42no—
283C22×C4×C53—42no—
284C22×C4×C53C2×D411yescharacteristic
285C22×C4×C53C2×D411yescharacteristic
286C22×C4×C53C2×D411yescharacteristic
287C22×C4×C53C2×D411yescharacteristic
288C22×C4×C53C2×D411yescharacteristic
289C22×C4×C53C2×D411yescharacteristic
290C22×C4×C53C2×D411yescharacteristic
291C22×C4×C53C2×D411yescharacteristic
292C22×C4×C53C2×D411yescharacteristic
293C22×C4×C53C2×D411yescharacteristic
294C22×C4×C53C2×D411yescharacteristic
295C22×C4×C53C2×D411yescharacteristic
296C22×C4×C53C2×D411yescharacteristic
297C22×C4×C53C2×D411yescharacteristic
298C22×C4×C53C2×D411yescharacteristic
299C22×C4×C53C2×D411yescharacteristic
300C22×C4×C53C2×D411yescharacteristic
301C22×C4×C53C2×D411yescharacteristic
302C22×C4×C53C2×D411yescharacteristic
303C22×C4×C53C2×D411yescharacteristic
304C22×C4×C53C2×D411yescharacteristic
305C22×C4×C53C2411yescharacteristic
306C22×C4×C53C2411yescharacteristic
307C22×C4×C53C2411yescharacteristic
308C22×C4×C53C2411yescharacteristic
309C22×C4×C53C2411yescharacteristic
310C22×C4×C53C2411yescharacteristic
311C22×C4×C53C2411yescharacteristic
312C2×C22⋊D53—22no—
313C2×C22⋊D53—22no—
314C2×C22⋊D53—22no—
315C2×C22⋊D53—22no—
316C2×C22⋊D53—22no—
317C2×C22⋊D53—22no—
318C2×C22⋊D53—22no—
319C2×C22⋊D53—22no—
320C2×C22⋊D53—22no—
321C2×C22⋊D53—22no—
322C2×C22⋊D53—22no—
323C2×C22⋊D53—22no—
324C2×C22⋊D53—44no—
325C2×C22⋊D53—44no—
326C2×C22⋊D53—44no—
327C2×C22⋊D53—44no—
328C2×C22⋊D53—44no—
329C2×C22⋊D53—44no—
330C22×Dic53—21no—
331C22×Dic53—21no—
332C22×Dic53—21no—
333C22×Dic53—21no—
334C22×Dic53—21no—
335C22×Dic53—21no—
336#11719945—24no—
337#11719945—24no—
338#11719945—44no—
339#11719945—44no—
340#11719945—42no—
341#11719945—42no—
342#11719945—44no—
343#11719945—44no—
344#11719945—44no—
345#11719945—44no—
346C2×D212—24no—
347C2×D212—21no—
348C2×D212—21no—
349C2×D212—42no—
350C2×D212C2412yes—
351C2×D212C2412yes—
352C2×C4×D53—22no—
353C2×C4×D53—22no—
354C2×C4×D53—22no—
355C2×C4×D53—22no—
356C2×C4×D53—44no—
357C2×C4×D53—44no—
358C2×Dic106—24no—
359C2×Dic106—21no—
360C2×Dic106—21no—
361C2×Dic106—42no—
362C2×Dic106C2412yes—
363C2×Dic106C2412yes—
364M16×C53—24no—
365M16×C53—24no—
366M16×C53—44no—
367C2×C8×C53—44no—
368C2×C8×C53C2414yes—
369C2×C8×C53C2414yes—
370C22⋊Dic53—22no—
371C22⋊Dic53—22no—
372C22⋊Dic53—22no—
373C22⋊Dic53—22no—
374C22⋊Dic53—22no—
375C22⋊Dic53—22no—
376C22⋊Dic53—22no—
377C22⋊Dic53—22no—
378C22⋊Dic53—22no—
379C22⋊Dic53—22no—
380C22⋊Dic53—22no—
381C22⋊Dic53—22no—
382#11719921—22no—
383#11719921—22no—
384#11719921—22no—
385#11719921—22no—
386#11719921—22no—
387#11719921—22no—
388#11719921—22no—
389#11719921—22no—
390C4⋊Dic53—21no—
391C4⋊Dic53—21no—
392C4⋊Dic53—21no—
393C4⋊Dic53—21no—
394C4⋊Dic53C2412yes—
395C4⋊Dic53C2412yes—
396C4⋊Dic53C2412yes—
397C4⋊Dic53C2412yes—
398#11719919—22no—
399#11719919—22no—
400#11719919—22no—
401#11719919—22no—
402#11719919—22no—
403#11719919—22no—
404#11719919—22no—
405#11719919—22no—
406C4×Dic53—22no—
407C4×Dic53—22no—
408C4×Dic53—22no—
409C4×Dic53—22no—
410Dic212—44no—
411D424—44no—
412#11719913—44no—
413#11719913—44no—
414C23×C53—22no—
415C23×C53—22no—
416C23×C53—22no—
417C23×C53—22no—
418C23×C53—22no—
419C23×C53—22no—
420C23×C53—22no—
421C23×C53—22no—
422C23×C53—22no—
423C23×C53—41no—
424C23×C53—41no—
425C23×C53—41no—
426C23×C53—41no—
427C23×C53—41no—
428C23×C53—41no—
429C23×C53—41no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53—41no—
434C23×C53—41no—
435C23×C53—416no—
436C23×C53C22×D411yescharacteristic
437C23×C53C22×D411yescharacteristic
438C23×C53C22×D411yescharacteristic
439C23×C53C22×D411yescharacteristic
440C23×C53C22×D411yescharacteristic
441C23×C53C22×D411yescharacteristic
442C23×C53C22×D411yescharacteristic
443C22×D53—22no—
444C22×D53—22no—
445C22×D53—42no—
446C22×D53—42no—
447C22×D53—42no—
448C22×D53—42no—
449C22×D53—42no—
450C22×D53—42no—
451C2×C4×C53—22no—
452C2×C4×C53—22no—
453C2×C4×C53—22no—
454C2×C4×C53—22no—
455C2×C4×C53—22no—
456C2×C4×C53—22no—
457C2×C4×C53—22no—
458C2×C4×C53—22no—
459C2×C4×C53—22no—
460C2×C4×C53—22no—
461C2×C4×C53—22no—
462C2×C4×C53—22no—
463C2×C4×C53—22no—
464C2×C4×C53—22no—
465C2×C4×C53—22no—
466C2×C4×C53—41no—
467C2×C4×C53—41no—
468C2×C4×C53—41no—
469C2×C4×C53—41no—
470C2×C4×C53—41no—
471C2×C4×C53—41no—
472C2×C4×C53—41no—
473C2×C4×C53—41no—
474C2×C4×C53—41no—
475C2×C4×C53—41no—
476C2×C4×C53—41no—
477C2×C4×C53—41no—
478C2×C4×C53C22×D411yescharacteristic
479C2×C4×C53C22×D411yescharacteristic
480C2×C4×C53C22×D411yescharacteristic
481C2×C4×C53C22×D411yescharacteristic
482C2×C4×C53C22×D411yescharacteristic
483C2×C4×C53C22×D411yescharacteristic
484C2×C4×C53C22×D411yescharacteristic
485C2×C4×C53H(5,𝔽2)14yes—
486C2×C4×C53C2511yescharacteristic
487C22⋊D53—44no—
488C22⋊D53—44no—
489C22⋊D53—44no—
490C22⋊D53—44no—
491C22⋊D53—44no—
492C22⋊D53—44no—
493C22⋊D53—44no—
494C22⋊D53—44no—
495C22⋊D53—44no—
496C22⋊D53—44no—
497C22⋊D53—44no—
498C22⋊D53—44no—
499C2×Dic53—22no—
500C2×Dic53—22no—
501C2×Dic53—22no—
502C2×Dic53—22no—
503C2×Dic53—22no—
504C2×Dic53—22no—
505C2×Dic53—42no—
506C2×Dic53—42no—
507C2×Dic53—42no—
508C2×Dic53—42no—
509C2×Dic53—42no—
510C2×Dic53—42no—
511D212—24no—
512D212—22no—
513D212—22no—
514D212—42no—
515D212—42no—
516C4×D53—44no—
517C4×D53—44no—
518C4×D53—44no—
519C4×D53—44no—
520Dic106—24no—
521Dic106—22no—
522Dic106—22no—
523Dic106—42no—
524Dic106—42no—
525C8×C53—24no—
526C8×C53—24no—
527#60752—531nomaximal, Sylow
528C22×C53—21no—
529C22×C53—21no—
530C22×C53—21no—
531C22×C53—21no—
532C22×C53—21no—
533C22×C53—21no—
534C22×C53—21no—
535C22×C53—21no—
536C22×C53—21no—
537C22×C53—21no—
538C22×C53—21no—
539C22×C53—21no—
540C22×C53—21no—
541C22×C53—21no—
542C22×C53—21no—
543C22×C53—21no—
544C22×C53—21no—
545C22×C53—21no—
546C22×C53—44no—
547C22×C53—44no—
548C22×C53—44no—
549C22×C53—44no—
550C22×C53—44no—
551C22×C53—44no—
552C22×C53—44no—
553C22×C53#53412yes—
554C22×C53#57512yes—
555C22×C53#57512yes—
556C22×C53C23×D411yescharacteristic
557C2×D53—42no—
558C2×D53—42no—
559C2×D53—42no—
560C2×D53—42no—
561C2×D53—42no—
562C2×D53—42no—
563C2×D53—84no—
564C2×D53—84no—
565C4×C53—21no—
566C4×C53—21no—
567C4×C53—21no—
568C4×C53—21no—
569C4×C53—21no—
570C4×C53—21no—
571C4×C53#53412yes—
572C4×C53C2×H(5,𝔽2)12yes—
573Dic53—42no—
574Dic53—42no—
575Dic53—42no—
576Dic53—42no—
577Dic53—42no—
578Dic53—42no—
579C2×#525—531no—
580C2×#525—531no—
581#3197—534no—
582#3196—532no—
583#3194—532no—
584#3191—534no—
585#3190—532no—
586#3188—532no—
587#3095—531no—
588#3094—531no—
589#3093—532no—
590#3056—532no—
591#3055—532no—
592#3007—531no—
593#3006—531no—
594#3005—532no—
595C2×#407D5311yescharacteristic, complemented
596C2×C53—22no—
597C2×C53—22no—
598C2×C53—22no—
599C2×C53—41no—
600C2×C53—41no—
601C2×C53—41no—
602C2×C53—41no—
603C2×C53C2×#53411yescharacteristic
604C2×C53C2×#57511yescharacteristic
605C2×C53C2×#57511yescharacteristic
606D53—82no—
607D53—82no—
608C22×#41—531no—
609C22×#41—531no—
610C24×C4C2×D5311yescharacteristic
611C2×#137—532no—
612C2×AGL(1,ℤ/8)—532no—
613C22×M16C2×D5312yescomplemented
614#525—532no—
615#525—532no—
616#525—532no—
617#525—532no—
618#525—532no—
619#525—532no—
620#525—532no—
621#525—532no—
622#525—1061no—
623#525—1061no—
624#525—1061no—
625#525—1061no—
626#525—1061no—
627#525—1061no—
628#525—1061no—
629#525—1061no—
630C2×#123—1061no—
631C2×#123—1061no—
632C2×C22⋊Q8—531no—
633C2×C22⋊Q8—531no—
634C2×C22⋊Q8—531no—
635C2×C22⋊Q8—531no—
636C2×#121—531no—
637C2×#121—531no—
638C2×#121—531no—
639C2×#121—531no—
640C2×#120—1061no—
641C2×#120—1061no—
642C2×C4×D4—1061no—
643C2×C4×D4—1061no—
644C2×C4×D4—1061no—
645C2×C4×D4—1061no—
646C2×#117—531no—
647C2×#117—531no—
648#485—534no—
649#485—534no—
650#485—534no—
651#484—532no—
652#483—532no—
653#482—534no—
654#482—534no—
655#482—534no—
656#481—532no—
657#480—532no—
658#470—534no—
659#469—534no—
660#468—534no—
661#468—534no—
662#467—534no—
663#466—534no—
664#465—534no—
665#465—534no—
666#452—534no—
667#452—534no—
668#452—534no—
669#451—532no—
670#450—532no—
671#449—534no—
672#449—534no—
673#449—534no—
674#448—532no—
675#447—532no—
676#428—532no—
677#428—532no—
678#419—532no—
679#418—532no—
680#417—532no—
681#417—532no—
682#407C2×D5311yescharacteristic
683#407C2×D5311yescharacteristic
684#407C2×D5312yescomplemented
685#407C2×D5312yescomplemented
686#407C2×D5312yescomplemented
687C2×C22⋊C8C2×D5312yescomplemented
688C2×C22⋊C8C2×D5312yescomplemented
689C53#6075211yescharacteristic, complemented, Sylow
690C25D21211yescharacteristic
691C2×#41—532no—
692C2×#41—532no—
693C2×#41—532no—
694C2×#41—532no—
695C2×#41—1061no—
696C2×#41—1061no—
697C2×#41—1061no—
698C2×#41—1061no—
699C2×#41—2124no—
700C2×#41—2124no—
701C22×Q8—531no—
702C22×Q8—531no—
703C22×D4—531no—
704C22×D4—531no—
705C22×D4—1061no—
706C22×D4—1061no—
707C22×D4—1061no—
708C22×D4—1061no—
709C22×D4—1061no—
710C22×D4—1061no—
711C23×C4—44no—
712C23×C4—1061no—
713C23×C4—1061no—
714C23×C4D21211yescharacteristic
715C23×C4D21211yescharacteristic
716C23×C4D21211yescharacteristic
717C23×C4D21211yescharacteristic
718C23×C4D21211yescharacteristic
719C23×C4D21211yescharacteristic
720C23×C4D21211yescharacteristic
721C23×C4C22×D5311yescharacteristic
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C23×C4C22×D5311yescharacteristic
728#137—2124no—
729AGL(1,ℤ/8)—2124no—
730C2×Q16—534no—
731C2×SD16—534no—
732C2×SD16—534no—
733C2×D8—534no—
734C2×M16—44no—
735C2×M16C22×D5312yes—
736C2×M16C22×D5312yes—
737C2×M16C22×D5314yes—
738C22×C8C22×D5314yes—
739#123—1062no—
740#123—1062no—
741#123—1062no—
742#123—1062no—
743#123—1062no—
744#123—1062no—
745#123—1062no—
746#123—1062no—
747C22⋊Q8—532no—
748C22⋊Q8—532no—
749C22⋊Q8—532no—
750C22⋊Q8—532no—
751C22⋊Q8—532no—
752C22⋊Q8—532no—
753C22⋊Q8—532no—
754C22⋊Q8—532no—
755C22⋊Q8—1061no—
756C22⋊Q8—1061no—
757C22⋊Q8—1061no—
758C22⋊Q8—1061no—
759C22⋊Q8—1061no—
760C22⋊Q8—1061no—
761C22⋊Q8—1061no—
762C22⋊Q8—1061no—
763#121—532no—
764#121—532no—
765#121—532no—
766#121—532no—
767#121—532no—
768#121—532no—
769#121—532no—
770#121—532no—
771#121—1061no—
772#121—1061no—
773#121—1061no—
774#121—1061no—
775#121—1061no—
776#121—1061no—
777#121—1061no—
778#121—1061no—
779#120—1062no—
780#120—1062no—
781#120—1062no—
782#120—1062no—
783#120—1062no—
784#120—1062no—
785#120—1062no—
786#120—1062no—
787C4×D4—1062no—
788C4×D4—1062no—
789C4×D4—1062no—
790C4×D4—1062no—
791C4×D4—1062no—
792C4×D4—1062no—
793C4×D4—1062no—
794C4×D4—1062no—
795C4×D4—1062no—
796C4×D4—1062no—
797C4×D4—1062no—
798C4×D4—1062no—
799C4×D4—1062no—
800C4×D4—1062no—
801C4×D4—1062no—
802C4×D4—1062no—
803#117—532no—
804#117—532no—
805#117—532no—
806#117—532no—
807#117—1061no—
808#117—1061no—
809#117—1061no—
810#117—1061no—
811C2×C4⋊C4—531no—
812C2×C4⋊C4—531no—
813C2×C4⋊C4—531no—
814C2×C4⋊C4—531no—
815C2×C4⋊C4—1061no—
816C2×C4⋊C4—1061no—
817C2×C4⋊C4—1061no—
818C2×C4⋊C4—1061no—
819C2×C22⋊C4—1061no—
820C2×C22⋊C4—1061no—
821C2×C22⋊C4—1061no—
822C2×C22⋊C4—1061no—
823C2×C22⋊C4—1061no—
824C2×C22⋊C4—1061no—
825C2×C22⋊C4—1061no—
826C2×C22⋊C4—1061no—
827C2×C22⋊C4—1061no—
828C2×C22⋊C4—1061no—
829C2×C42—1061no—
830C2×C42—1061no—
831#107—534no—
832#107—534no—
833#106—534no—
834#106—534no—
835#103—534no—
836#103—534no—
837#103—534no—
838#103—534no—
839#102—534no—
840#102—534no—
841#102—534no—
842#102—534no—
843C22⋊C8C22×D5312yes—
844C22⋊C8C22×D5312yes—
845C22⋊C8C22×D5312yes—
846C22⋊C8C22×D5312yes—
847C22⋊C8C22×D5314yes—
848C22⋊C8C22×D5314yes—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—1061no—
853C24—1061no—
854C24C2×D21211yescharacteristic
855C24C2×D21211yescharacteristic
856C24C2×D21211yescharacteristic
857C24C2×D21211yescharacteristic
858C24C2×D21211yescharacteristic
859C24C2×D21211yescharacteristic
860C24C2×D21211yescharacteristic
861#41—1064no—
862#41—1064no—
863#41—2122no—
864#41—2124no—
865#41—2124no—
866#41—2122no—
867#41—2124no—
868#41—2124no—
869#41—2124no—
870#41—2124no—
871C2×Q8—532no—
872C2×Q8—532no—
873C2×Q8—1061no—
874C2×Q8—1061no—
875C2×Q8—1064no—
876C2×Q8—2122no—
877C2×D4—532no—
878C2×D4—532no—
879C2×D4—1062no—
880C2×D4—1062no—
881C2×D4—1062no—
882C2×D4—1062no—
883C2×D4—1062no—
884C2×D4—1062no—
885C2×D4—1062no—
886C2×D4—1062no—
887C2×D4—1062no—
888C2×D4—1062no—
889C2×D4—1062no—
890C2×D4—1062no—
891C2×D4—1061no—
892C2×D4—1061no—
893C2×D4—1064no—
894C2×D4—2122no—
895C2×D4—2124no—
896C2×D4—2124no—
897C2×D4—2124no—
898C2×D4—2124no—
899C2×D4—2124no—
900C2×D4—2124no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—1061no—
916C22×C4—1061no—
917C22×C4—1061no—
918C22×C4—1061no—
919C22×C4—1061no—
920C22×C4—1061no—
921C22×C4—1062no—
922C22×C4—1062no—
923C22×C4—1062no—
924C22×C4—1062no—
925C22×C4—2124no—
926C22×C4—2124no—
927C22×C4C2×D21211yescharacteristic
928C22×C4C2×D21211yescharacteristic
929C22×C4C2×D21211yescharacteristic
930C22×C4C2×D21211yescharacteristic
931C22×C4C2×D21211yescharacteristic
932C22×C4C2×D21211yescharacteristic
933C22×C4C2×D21211yescharacteristic
934C22×C4C2×D21211yescharacteristic
935C22×C4C2×D21211yescharacteristic
936C22×C4C2×D21211yescharacteristic
937C22×C4C2×D21211yescharacteristic
938C22×C4C2×D21211yescharacteristic
939C22×C4C2×D21211yescharacteristic
940C22×C4C2×D21211yescharacteristic
941C22×C4C2×D21211yescharacteristic
942C22×C4C2×D21211yescharacteristic
943C22×C4C2×D21211yescharacteristic
944C22×C4C2×D21211yescharacteristic
945C22×C4C2×D21211yescharacteristic
946C22×C4C2×D21211yescharacteristic
947C22×C4C2×D21211yescharacteristic
948C22×C4C23×D5311yescharacteristic
949C22×C4C23×D5311yescharacteristic
950C22×C4C23×D5311yescharacteristic
951C22×C4C23×D5311yescharacteristic
952C22×C4C23×D5311yescharacteristic
953C22×C4C23×D5311yescharacteristic
954C22×C4C23×D5311yescharacteristic
955Q16—2124no—
956SD16—2124no—
957SD16—2124no—
958D8—2124no—
959M16—24no—
960M16—24no—
961M16—44no—
962C2×C8—44no—
963C2×C8C23×D5314yes—
964C2×C8C23×D5314yes—
965C4⋊C4—532no—
966C4⋊C4—532no—
967C4⋊C4—532no—
968C4⋊C4—532no—
969C4⋊C4—1061no—
970C4⋊C4—1061no—
971C4⋊C4—1061no—
972C4⋊C4—1061no—
973C4⋊C4—1062no—
974C4⋊C4—1062no—
975C4⋊C4—1062no—
976C4⋊C4—1062no—
977C4⋊C4—1062no—
978C4⋊C4—1062no—
979C4⋊C4—1062no—
980C4⋊C4—1062no—
981C22⋊C4—1062no—
982C22⋊C4—1062no—
983C22⋊C4—1062no—
984C22⋊C4—1062no—
985C22⋊C4—1062no—
986C22⋊C4—1062no—
987C22⋊C4—1062no—
988C22⋊C4—1062no—
989C22⋊C4—1062no—
990C22⋊C4—1062no—
991C22⋊C4—1062no—
992C22⋊C4—1062no—
993C22⋊C4—1062no—
994C22⋊C4—1062no—
995C22⋊C4—1062no—
996C22⋊C4—1062no—
997C22⋊C4—1062no—
998C22⋊C4—1062no—
999C22⋊C4—1062no—
1000C22⋊C4—1062no—
1001C42—1062no—
1002C42—1062no—
1003C42—1062no—
1004C42—1062no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—416no—
1027C23—1062no—
1028C23—1062no—
1029C23—2122no—
1030C23—2122no—
1031C23—2122no—
1032C23—2122no—
1033C23—2122no—
1034C23—2122no—
1035C23C22×D21211yescharacteristic
1036C23C22×D21211yescharacteristic
1037C23C22×D21211yescharacteristic
1038C23C22×D21211yescharacteristic
1039C23C22×D21211yescharacteristic
1040C23C22×D21211yescharacteristic
1041C23C22×D21211yescharacteristic
1042Q8—1062no—
1043Q8—1064no—
1044Q8—1062no—
1045Q8—2122no—
1046Q8—2122no—
1047D4—1062no—
1048D4—1064no—
1049D4—1062no—
1050D4—2122no—
1051D4—2124no—
1052D4—2124no—
1053D4—2124no—
1054D4—2124no—
1055D4—2124no—
1056D4—2124no—
1057D4—2124no—
1058D4—2124no—
1059D4—2124no—
1060D4—2124no—
1061D4—2124no—
1062D4—2124no—
1063D4—2122no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—1062no—
1092C2×C4—1062no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1062no—
1096C2×C4—1062no—
1097C2×C4—2124no—
1098C2×C4—2124no—
1099C2×C4—2124no—
1100C2×C4—2122no—
1101C2×C4—2122no—
1102C2×C4—2122no—
1103C2×C4—2122no—
1104C2×C4—2122no—
1105C2×C4—2122no—
1106C2×C4—2124no—
1107C2×C4C22×D21211yescharacteristic
1108C2×C4C22×D21211yescharacteristic
1109C2×C4C22×D21211yescharacteristic
1110C2×C4C22×D21211yescharacteristic
1111C2×C4C22×D21211yescharacteristic
1112C2×C4C22×D21211yescharacteristic
1113C2×C4C22×D21211yescharacteristic
1114C2×C4#1313326214yes—
1115C2×C4C24×D5311yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—4244no—
1144C22—4244no—
1145C22—2122no—
1146C22—2122no—
1147C22—2122no—
1148C22—2122no—
1149C22—2122no—
1150C22—2122no—
1151C22#1681118512yes—
1152C22#1681142312yes—
1153C22#1681142312yes—
1154C22C23×D21211yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—2122no—
1162C4—2122no—
1163C4—2122no—
1164C4—2122no—
1165C4—2122no—
1166C4—2122no—
1167C4#1681118512yes—
1168C4C2×#1313326212yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—4242no—
1177C2—4242no—
1178C2C2×#1681118511yescharacteristic
1179C2C2×#1681142311yescharacteristic
1180C2C2×#1681142311yescharacteristic
subgroupG/H
centerC22C23×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#407C2
socleC22×C53C23×D4
hypercenterC2×#407D53
hypocenterC53#60752
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16811134C2semidirect
2. C2×#16811134C2semidirect
3. #20285557C2semidirect
4. #20285547C2semidirect
5. #20285531C2semidirect
6. #20285508C2semidirect
7. #20285498C2semidirect
8. #20285482C2semidirect
9. #20284664C2semidirect
10. #20284656C2semidirect
11. #20284648C2semidirect
12. #20284345C2semidirect
13. #20284334C2semidirect
14. #20283977C2semidirect
15. #20283969C2semidirect
16. #20283960C2semidirect
17. C2×C53×#407C2semidirect
19. C22×#11719945C22semidirect
20. C2×#13133250C22semidirect
21. C2×#13133245C22semidirect
34. #16811134C22semidirect
35. #16811134C22semidirect
36. #16811134C22semidirect
37. #16811134C22semidirect
41. C2×#13133196C22semidirect
42. C2×#13133196C22semidirect
43. C2×#13133196C22semidirect
45. C2×#13133191C22semidirect
46. C2×#13133191C22semidirect
47. C2×#13133191C22semidirect
55. C2×#13133176C22semidirect
56. #16810965C22semidirect
57. #16810965C22semidirect
58. #16810965C22semidirect
59. #16810959C22semidirect
60. #16810954C22semidirect
61. #16810948C22semidirect
62. #16810948C22semidirect
63. #16810948C22semidirect
64. #16810942C22semidirect
65. #16810937C22semidirect
66. #16810881C22semidirect
67. #16810876C22semidirect
68. #16810869C22semidirect
69. #16810869C22semidirect
70. #16810864C22semidirect
71. #16810859C22semidirect
72. #16810852C22semidirect
73. #16810852C22semidirect
74. #16810787C22semidirect
75. #16810787C22semidirect
76. #16810787C22semidirect
77. #16810781C22semidirect
78. #16810776C22semidirect
79. #16810770C22semidirect
80. #16810770C22semidirect
81. #16810770C22semidirect
82. #16810764C22semidirect
83. #16810759C22semidirect
84. #16810665C22semidirect
85. #16810665C22semidirect
86. #16810633C22semidirect
87. #16810629C22semidirect
88. #16810625C22semidirect
89. #16810625C22semidirect
91. C22×M16×C53C22semidirect
94. C53×#407C22semidirect
95. C53×#407C22semidirect
96. C53×#407C22semidirect
97. C2×C22⋊C8×C53C22semidirect
98. C2×C22⋊C8×C53C22semidirect
123. C2×Dic212C23semidirect
124. C2×#11719913C23semidirect
125. C2×#11719913C23semidirect
126. C2×D424C23semidirect
219. #13133151C23semidirect
220. #13133151C23semidirect
221. #13133149C23semidirect
222. #13133149C23semidirect
223. #13133142C23semidirect
224. #13133142C23semidirect
225. #13133142C23semidirect
226. #13133142C23semidirect
227. #13133139C23semidirect
228. #13133139C23semidirect
229. #13133139C23semidirect
230. #13133139C23semidirect
595. C2×#407D53semidirect
613. C22×M16C2×D53semidirect
684. #407C2×D53semidirect
685. #407C2×D53semidirect
686. #407C2×D53semidirect
687. C2×C22⋊C8C2×D53semidirect
688. C2×C22⋊C8C2×D53semidirect
689. C53#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
#202855572
#202855472
#202855312
#202855082
#202854982
#202854822
#202846642
#202846562
#202846482
#202843452
#202843342
#202839772
#202839692
#202839602
C2×C53×#4072
#6075253