Finite Group Databasebeta

← #27400235

Subgroups — #27400235

Order 13568.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811299C211yesmaximal, characteristic
2#20277566C212yesmaximal, complemented
3#20275698C212yesmaximal, complemented
4#20275172C212yesmaximal, complemented
5#20275166C212yesmaximal
6#20274791C211yesmaximal, characteristic, complemented
7#20274702C211yesmaximal, characteristic, complemented
8#20274502C211yesmaximal, characteristic, complemented
9#20274446C211yesmaximal, characteristic, complemented
10C2×#16810390C211yesmaximal, characteristic, complemented
11C53×#1819C211yesmaximal, characteristic, complemented
12#16811299—22no—
13#16811299—22no—
14#16811299—22no—
15#16811299—22no—
16C2×#13133210C411yescharacteristic, complemented
17C2×#13133210C411yescharacteristic, complemented
18C2×#13133203C411yescharacteristic, complemented
19C2×#13133201C2211yescharacteristic
20C2×#13133200C411yescharacteristic, complemented
21C2×#13133199C411yescharacteristic, complemented
22C2×#13133196C411yescharacteristic, complemented
23C2×#13133194C2211yescharacteristic
24C2×#13133186C2211yescharacteristic
25C2×C4×C22⋊D53C411yescharacteristic, complemented
26C2×#13133177C2211yescharacteristic
27C2×#13133176C411yescharacteristic, complemented
28C2×#13133173C2212yes—
29C2×#13133173C2211yescharacteristic
30C22×C22⋊Dic53C2212yes—
31C22×C22⋊Dic53C2211yescharacteristic
32C2×#13133131C2212yes—
33C2×#13133131C2212yes—
34#16810517—22no—
35#16810511—22no—
36#16810495—22no—
37#16810484C2212yes—
38#16810481C2212yes—
39C22⋊C4×Dic53—22no—
40C22⋊C4×Dic53C2212yes—
41#16810390C2211yescharacteristic
42#16810390C2211yescharacteristic
43#16810390C2212yes—
44#16810389C2212yes—
45#16810389C2212yes—
46C22×C22⋊C4×C53C2211yescharacteristic
47C53×#379C2212yes—
48C53×#342C2211yescharacteristic
49C53×#342C2211yescharacteristic
50C53×#342C2212yes—
51C22×Dic106C2×C411yescharacteristic, complemented
52C22×C22⋊D53C2×C411yescharacteristic
53C22×C22⋊D53C2×C411yescharacteristic
54C22×C22⋊D53C2311yescharacteristic
55C23×Dic53—22no—
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C22×C4×D53C2×C411yescharacteristic, complemented
59#13133210—22no—
60#13133210—22no—
61#13133210—22no—
62#13133210—22no—
63#13133203—22no—
64#13133203—22no—
65#13133201—22no—
66#13133201—22no—
67#13133200—22no—
68#13133200—22no—
69#13133199—22no—
70#13133199—22no—
71#13133196—22no—
72#13133196—22no—
73#13133194—22no—
74#13133194—22no—
75#13133186—22no—
76#13133186—22no—
77C4×C22⋊D53—21no—
78C4×C22⋊D53—21no—
79C4×C22⋊D53—21no—
80C4×C22⋊D53—21no—
81#13133177—22no—
82#13133177—22no—
83#13133176—21no—
84#13133176—21no—
85#13133176—21no—
86#13133176—21no—
87#13133173—24no—
88#13133173—22no—
89#13133173—22no—
90#13133173—42no—
91C2×C4⋊Dic53C2×C411yescharacteristic, complemented
92C2×C4⋊Dic53C2×C411yescharacteristic, complemented
93C2×C4⋊Dic53C2×C411yescharacteristic, complemented
94C2×#11719919—22no—
95C2×#11719919—22no—
96C2×#11719919C2×C411yescharacteristic, complemented
97C2×#11719919C2×C411yescharacteristic, complemented
98C2×#11719919C2×C411yescharacteristic, complemented
99C2×#11719919C2×C411yescharacteristic, complemented
100C2×#11719919C2×C411yescharacteristic, complemented
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53—24no—
103C2×C22⋊Dic53—42no—
104C2×C22⋊Dic53C2×C411yescharacteristic
105C2×C22⋊Dic53C2×C411yescharacteristic
106C2×C22⋊Dic53C2×C411yescharacteristic
107C2×C22⋊Dic53C2×C411yescharacteristic
108C2×C22⋊Dic53C2×C411yescharacteristic
109C2×C22⋊Dic53C2×C411yescharacteristic
110C2×C22⋊Dic53D412yes—
111C2×C22⋊Dic53D412yes—
112C2×C22⋊Dic53D412yes—
113C2×C22⋊Dic53D412yes—
114C2×C22⋊Dic53C2312yes—
115C2×C22⋊Dic53C2312yes—
116C2×C22⋊Dic53C2311yescharacteristic
117C2×#11719921C2×C411yescharacteristic, complemented
118C2×#11719921C2×C411yescharacteristic, complemented
119C2×#11719921C2×C411yescharacteristic, complemented
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53C2×C411yescharacteristic, complemented
123C2×C4×Dic53C2×C411yescharacteristic, complemented
124C2×C4×Dic53C2×C411yescharacteristic, complemented
125#13133131—24no—
126#13133131—42no—
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—22no—
131C25×C53C2311yescharacteristic
132C23×C4×C53C2×C411yescharacteristic
133C23×C4×C53C2×C411yescharacteristic
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53C2×C411yescharacteristic
139C2×C22⋊C4×C53C2×C411yescharacteristic
140C2×C22⋊C4×C53C2312yes—
141C2×C22⋊C4×C53C2312yes—
142C2×C22⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53C2311yescharacteristic
144C24×C53—22no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—42no—
148C24×C53—81no—
149C24×C53C22×C411yescharacteristic
150C24×C53C22×C411yescharacteristic
151C24×C53C2×D412yes—
152C24×C53C2×D412yes—
153C24×C53C2411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—42no—
162C22×C4×C53—81no—
163C22×C4×C53C22×C411yescharacteristic
164C22×C4×C53C22×C411yescharacteristic
165C22×C4×C53C22×C411yescharacteristic
166C22×C4×C53C22×C411yescharacteristic
167C2×C22⋊D53—21no—
168C2×C22⋊D53—21no—
169C2×C22⋊D53—22no—
170C2×C22⋊D53—22no—
171C2×C22⋊D53—21no—
172C2×C22⋊D53—21no—
173C2×C22⋊D53—22no—
174C2×C22⋊D53—42no—
175C2×C22⋊D53—81no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—44no—
182C22×Dic53—44no—
183C22×Dic53—81no—
184C22×Dic53—82no—
185C22×Dic53C22×C411yescharacteristic
186C22×Dic53C22×C411yescharacteristic
187C22×Dic53C22×C411yescharacteristic
188C22×Dic53C22×C411yescharacteristic
189C22×Dic53C22×C411yescharacteristic
190C22×Dic53C22×C411yescharacteristic
191C22×Dic53C22×C411yescharacteristic
192C22×Dic53C2×D412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C2×C4×D53—21no—
197C2×C4×D53—21no—
198C2×C4×D53—81no—
199C2×Dic106—22no—
200C2×Dic106—81no—
201C22⋊C4×C53—22no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—22no—
204C22⋊C4×C53—22no—
205C22⋊C4×C53—22no—
206C22⋊C4×C53—22no—
207C22⋊C4×C53—22no—
208C22⋊C4×C53—22no—
209C22⋊C4×C53—44no—
210C22⋊C4×C53—82no—
211C22⋊Dic53—21no—
212C22⋊Dic53—21no—
213C22⋊Dic53—22no—
214C22⋊Dic53—22no—
215C22⋊Dic53—22no—
216C22⋊Dic53—22no—
217C22⋊Dic53—22no—
218C22⋊Dic53—44no—
219C22⋊Dic53C22⋊C411yescharacteristic
220C22⋊Dic53C22⋊C411yescharacteristic
221C22⋊Dic53C22⋊C411yescharacteristic
222C22⋊Dic53C22⋊C411yescharacteristic
223C22⋊Dic53C22⋊C412yes—
224C22⋊Dic53C22⋊C412yes—
225C22⋊Dic53C22⋊C412yes—
226C22⋊Dic53C22⋊C412yes—
227C22⋊Dic53C22⋊C412yes—
228C22⋊Dic53C22⋊C412yes—
229C22⋊Dic53#4114yes—
230#11719921—22no—
231#11719921—21no—
232#11719921—21no—
233#11719921—22no—
234C4⋊Dic53—21no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—22no—
239#11719919—22no—
240#11719919—22no—
241#11719919—22no—
242#11719919—21no—
243#11719919—21no—
244#11719919—22no—
245#11719919—44no—
246#11719919—82no—
247C4×Dic53—21no—
248C4×Dic53—21no—
249C4×Dic53—21no—
250C4×Dic53—21no—
251C4×Dic53—21no—
252C4×Dic53—21no—
253C4×Dic53—44no—
254C4×Dic53—82no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—24no—
260C23×C53—22no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—42no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53—84no—
274C23×C53—82no—
275C23×C53—82no—
276C23×C53C2×C22⋊C411yescharacteristic
277C23×C53C2×C22⋊C412yes—
278C23×C53C2×C22⋊C411yescharacteristic
279C23×C53C23×C411yescharacteristic
280C23×C53C22×D412yes—
281C23×C53C2×#4112yes—
282C23×C53H(5,𝔽2)11yescharacteristic
283C23×C532−1+411yescharacteristic
284C22×D53—21no—
285C22×D53—21no—
286C22×D53—21no—
287C22×D53—41no—
288C22×D53—41no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—81no—
306C2×C4×C53—81no—
307C22⋊D53—42no—
308C22⋊D53—42no—
309C22⋊D53—42no—
310C22⋊D53—42no—
311C22⋊D53—82no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323C2×Dic53—21no—
324C2×Dic53—21no—
325C2×Dic53—24no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—88no—
338C2×Dic53C2×C22⋊C412yes—
339C2×Dic53C2×C22⋊C411yescharacteristic
340C2×Dic53C2×C22⋊C411yescharacteristic
341C2×Dic53C2×C22⋊C411yescharacteristic
342C2×Dic53C2×C22⋊C411yescharacteristic
343C2×Dic53C2×C22⋊C412yes—
344C4×D53—81no—
345C4×D53—81no—
346Dic106—82no—
347#22477—531nomaximal, Sylow
348C22×C53—21no—
349C22×C53—22no—
350C22×C53—21no—
351C22×C53—22no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—22no—
356C22×C53—21no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—21no—
360C22×C53—42no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—82no—
368C22×C53—82no—
369C22×C53—81no—
370C22×C53—81no—
371C22×C53#41012yes—
372C22×C53C22×C22⋊C411yescharacteristic
373C22×C53C4×#4111yescharacteristic
374C22×C53#52011yescharacteristic
375C22×C53#54612yes—
376C22×C53#54712yes—
377C2×D53—41no—
378C2×D53—41no—
379C2×D53—41no—
380C2×D53—81no—
381C2×D53—81no—
382C4×C53—41no—
383C4×C53—41no—
384C4×C53—41no—
385C4×C53—41no—
386C4×C53—82no—
387C4×C53—82no—
388Dic53—21no—
389Dic53—22no—
390Dic53—21no—
391Dic53—22no—
392Dic53—21no—
393Dic53—21no—
394Dic53—44no—
395Dic53—41no—
396Dic53—41no—
397Dic53—41no—
398Dic53—82no—
399C2×#551—531no—
400#2342—532no—
401#1996—532no—
402#1899—532no—
403#1898—532no—
404#1820—531no—
405#1819D5311yescharacteristic, complemented
406#1799—531no—
407C4×#99—531no—
408#1740—531no—
409C2×#342—531no—
410C2×C53—22no—
411C2×C53—22no—
412C2×C53—21no—
413C2×C53—21no—
414C2×C53—22no—
415C2×C53—41no—
416C2×C53—42no—
417C2×C53#233911yescharacteristic
418C2×C53C2×#41011yescharacteristic
419C2×C53#288311yescharacteristic
420D53—81no—
421#551—1062no—
422#551—1062no—
423#551—1062no—
424#551—1062no—
425C2×#126—531no—
426C2×#126—531no—
427C2×#124—531no—
428C2×#123—531no—
429C2×#123—531no—
430C2×#123—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—531no—
433C2×#120—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×#117—531no—
437C2×#117—531no—
438C2×#117—532no—
439C22×C22⋊C4—531no—
440C22×C22⋊C4—532no—
441C22×C22⋊C4C2×D5311yescharacteristic
442C2×#99—532no—
443C2×#99—532no—
444#388—1062no—
445#388—1062no—
446#385—1062no—
447#381—532no—
448#380—532no—
449#379C2×D5312yes—
450C4×C22⋊C4—532no—
451C4×C22⋊C4—1062no—
452#342—531no—
453#342—532no—
454#342—532no—
455#342—532no—
456#342—531no—
457#342C2×D5311yescharacteristic
458#342C2×D5311yescharacteristic
459#342C2×D5312yes—
460C53#2247711yescharacteristic, complemented, Sylow
461C25C22×D5311yescharacteristic
462C22×Q8—531no—
463C22×D4—531no—
464C22×D4—531no—
465C22×D4—531no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—1062no—
470C23×C4C4×D5311yescharacteristic
471C23×C4C4×D5311yescharacteristic
472#126—1062no—
473#126—1062no—
474#126—1062no—
475#126—1062no—
476#124—1062no—
477#124—1062no—
478#123—1062no—
479#123—1062no—
480#123—1062no—
481#123—1062no—
482#123—1062no—
483#123—1062no—
484C22⋊Q8—1062no—
485C22⋊Q8—1062no—
486C22⋊Q8—1062no—
487C22⋊Q8—1062no—
488#120—1062no—
489#120—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1061no—
493C4×D4—1061no—
494C4×D4—1061no—
495C4×D4—1061no—
496#117—1062no—
497#117—1062no—
498#117—1061no—
499#117—1061no—
500#117—1061no—
501#117—1061no—
502#117—1064no—
503#117—2122no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1062no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—531no—
519C2×C22⋊C4—531no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—532no—
523C2×C22⋊C4—532no—
524C2×C22⋊C4—532no—
525C2×C22⋊C4—532no—
526C2×C22⋊C4—532no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4—531no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—531no—
533C2×C22⋊C4—532no—
534C2×C22⋊C4—1064no—
535C2×C22⋊C4—1062no—
536C2×C22⋊C4—2122no—
537C2×C22⋊C4C4×D5311yescharacteristic
538C2×C22⋊C4C4×D5311yescharacteristic
539C2×C22⋊C4C22×D5312yes—
540C2×C22⋊C4C22×D5312yes—
541C2×C22⋊C4C22×D5311yescharacteristic
542C2×C22⋊C4C22×D5311yescharacteristic
543C2×C42—531no—
544C2×C42—531no—
545C2×C42—531no—
546C2×C42—1062no—
547C2×C42—1062no—
548#99—1064no—
549#99—2122no—
550#95—1062no—
551#95—1062no—
552#95—1062no—
553#95—1062no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24—531no—
560C24C2×C4×D5311yescharacteristic
561C24C2×C4×D5311yescharacteristic
562C24D4×D5312yes—
563C24D4×D5312yes—
564C24C23×D5311yescharacteristic
565C2×Q8—1062no—
566C2×Q8—4241no—
567C2×D4—1062no—
568C2×D4—1061no—
569C2×D4—1061no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—1061no—
573C2×D4—1061no—
574C2×D4—4241no—
575C2×D4—2122no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—531no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1062no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—4241no—
603C22×C4—4242no—
604C22×C4—4241no—
605C22×C4—2124no—
606C22×C4—2124no—
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4C2×C4×D5311yescharacteristic
609C22×C4C2×C4×D5311yescharacteristic
610C22×C4C2×C4×D5311yescharacteristic
611C4⋊C4—1062no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1062no—
615C4⋊C4—1061no—
616C4⋊C4—1061no—
617C4⋊C4—1062no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1062no—
621C4⋊C4—1062no—
622C4⋊C4—4242no—
623C4⋊C4—2124no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—44no—
633C22⋊C4—82no—
634C22⋊C4—531no—
635C22⋊C4—531no—
636C22⋊C4—531no—
637C22⋊C4—531no—
638C22⋊C4—532no—
639C22⋊C4—532no—
640C22⋊C4—532no—
641C22⋊C4—532no—
642C22⋊C4—532no—
643C22⋊C4—532no—
644C22⋊C4—534no—
645C22⋊C4—1062no—
646C22⋊C4—1061no—
647C22⋊C4—1061no—
648C22⋊C4—1062no—
649C22⋊C4—1061no—
650C22⋊C4—1061no—
651C22⋊C4—1062no—
652C22⋊C4—1062no—
653C22⋊C4—1062no—
654C22⋊C4—1062no—
655C22⋊C4—1062no—
656C22⋊C4—2124no—
657C42—1061no—
658C42—1061no—
659C42—1061no—
660C42—1061no—
661C42—1061no—
662C42—1061no—
663C42—4242no—
664C42—2124no—
665C23—22no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—84no—
684C23—82no—
685C23—82no—
686C23—1061no—
687C23—1061no—
688C23—1061no—
689C23—2121no—
690C23—2121no—
691C23C22⋊C4×D5312yes—
692C23C22⋊C4×D5311yescharacteristic
693C23C22⋊C4×D5311yescharacteristic
694C23C22×C4×D5311yescharacteristic
695C23C2×D4×D5312yes—
696C23#41×D5312yes—
697C23#1313326311yescharacteristic
698C23#1313326411yescharacteristic
699Q8—4242no—
700D4—4242no—
701D4—2122no—
702D4—2122no—
703D4—2122no—
704D4—2122no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—531no—
724C2×C4—531no—
725C2×C4—531no—
726C2×C4—531no—
727C2×C4—532no—
728C2×C4—532no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1061no—
734C2×C4—1061no—
735C2×C4—1061no—
736C2×C4—1061no—
737C2×C4—1064no—
738C2×C4—1061no—
739C2×C4—1061no—
740C2×C4—1061no—
741C2×C4—1061no—
742C2×C4—1061no—
743C2×C4—4241no—
744C2×C4—4241no—
745C2×C4—4248no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2121no—
756C2×C4—2121no—
757C22—22no—
758C22—21no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—22no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—81no—
779C22—81no—
780C22—4241no—
781C22—4241no—
782C22—2121no—
783C22—2121no—
784C22—2121no—
785C22#1681059512yes—
786C22C2×C22⋊C4×D5311yescharacteristic
787C22#1681109111yescharacteristic
788C22#1681110311yescharacteristic
789C22#1681126512yes—
790C22#1681127112yes—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—82no—
796C4—82no—
797C4—1061no—
798C4—1061no—
799C4—1062no—
800C4—1061no—
801C4—1061no—
802C4—1062no—
803C4—4242no—
804C4—2124no—
805C4—2121no—
806C4—2121no—
807C4—2121no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—4241no—
816C2#2027753911yescharacteristic
817C2C2×#1681059511yescharacteristic
818C2#2028317311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC53×#1819C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#13133186C22
cosocleC24×C53C24
hypercenter#1819D53
hypocenterC53#22477
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #20277566C2semidirect
3. #20275698C2semidirect
4. #20275172C2semidirect
6. #20274791C2semidirect
7. #20274702C2semidirect
8. #20274502C2semidirect
9. #20274446C2semidirect
10. C2×#16810390C2semidirect
11. C53×#1819C2semidirect
16. C2×#13133210C4semidirect
17. C2×#13133210C4semidirect
18. C2×#13133203C4semidirect
20. C2×#13133200C4semidirect
21. C2×#13133199C4semidirect
22. C2×#13133196C4semidirect
25. C2×C4×C22⋊D53C4semidirect
27. C2×#13133176C4semidirect
51. C22×Dic106C2×C4semidirect
58. C22×C4×D53C2×C4semidirect
91. C2×C4⋊Dic53C2×C4semidirect
92. C2×C4⋊Dic53C2×C4semidirect
93. C2×C4⋊Dic53C2×C4semidirect
96. C2×#11719919C2×C4semidirect
97. C2×#11719919C2×C4semidirect
98. C2×#11719919C2×C4semidirect
99. C2×#11719919C2×C4semidirect
100. C2×#11719919C2×C4semidirect
117. C2×#11719921C2×C4semidirect
118. C2×#11719921C2×C4semidirect
119. C2×#11719921C2×C4semidirect
122. C2×C4×Dic53C2×C4semidirect
123. C2×C4×Dic53C2×C4semidirect
124. C2×C4×Dic53C2×C4semidirect
405. #1819D53semidirect
460. C53#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#168112992
#202775662
#202756982
#202751722
#202751662
#202747912
#202747022
#202745022
#202744462
C2×#168103902
C53×#18192
#2247753