Finite Group Databasebeta

← #27393209

Subgroups — #27393209

Order 13568.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810590C211yesmaximal, characteristic, complemented
2#20277307C211yesmaximal, characteristic, complemented
3#20275154C211yesmaximal, characteristic, complemented
4#20275149C211yesmaximal, characteristic, complemented
5#20275144C211yesmaximal, characteristic, complemented
6#20275139C211yesmaximal, characteristic, complemented
7#20275038C211yesmaximal, characteristic, complemented
8#20275033C211yesmaximal, characteristic, complemented
9#20275028C211yesmaximal, characteristic, complemented
10#20275023C211yesmaximal, characteristic, complemented
11#20274805C211yesmaximal, characteristic, complemented
12#20274801C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274655C211yesmaximal, characteristic, complemented
15C2×C53×#537C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C2×#13133141C2211yescharacteristic
21C2×#13133141C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28#16810590—24no—
29C2×C22⋊#88322C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33#16810530—21no—
34#16810526—21no—
35#16810503—21no—
36#16810503—21no—
37#16810483C2211yescharacteristic
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49C22×#41×C53C2211yescharacteristic
50C22×#41×C53C2211yescharacteristic
51C53×#537—24no—
52C53×#537C418yescomplemented
53C2×C22⋊Q8×C53—21no—
54C2×C22⋊Q8×C53C2211yescharacteristic
55C2×C22⋊Q8×C53C2211yescharacteristic
56C2×#121×C53—21no—
57C2×#121×C53—21no—
58C2×#121×C53—21no—
59C2×#121×C53C2211yescharacteristic
60C2×#121×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C23×Dic53—21no—
63C2×#11719917—22no—
64C2×#11719917—41no—
65C2×#11719917—41no—
66C22×#88322—22no—
67C22×#88322—41no—
68C22×#88322—41no—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133176—41no—
74#13133176—41no—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53—41no—
77C2×C4⋊Dic53—41no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88#13133141—41no—
89#13133141—41no—
90#13133141—41no—
91#13133141—41no—
92#13133138—41no—
93#13133138—41no—
94#13133138—41no—
95#13133138—41no—
96C22⋊#88322—22no—
97C22⋊#88322—22no—
98C22⋊#88322—22no—
99C22⋊#88322—22no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104C2×#41×C53—22no—
105C2×#41×C53—41no—
106C2×#41×C53—41no—
107C2×#41×C53—41no—
108C2×#41×C53—41no—
109C2×#41×C53—41no—
110C2×#41×C53—41no—
111C2×#41×C53—41no—
112C2×#41×C53—41no—
113C2×#41×C53C2×C414yes—
114C2×#41×C53C2×C414yescomplemented
115C2×#41×C53D414yes—
116C22×Q8×C53D411yescharacteristic
117C22×Q8×C53C2311yescharacteristic
118C22×D4×C53—21no—
119C22×D4×C53—21no—
120C22×D4×C53—21no—
121C22×D4×C53D411yescharacteristic
122C22×D4×C53D411yescharacteristic
123C22×D4×C53D411yescharacteristic
124C22×D4×C53C2311yescharacteristic
125C23×C4×C53—21no—
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C22⋊Q8×C53—28no—
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53—22no—
133C22⋊Q8×C53C2×C414yes—
134C22⋊Q8×C53C2×C414yescomplemented
135#121×C53—28no—
136#121×C53—28no—
137#121×C53—28no—
138#121×C53—22no—
139#121×C53—22no—
140#121×C53C2×C414yes—
141#121×C53C2×C414yescomplemented
142C2×C4⋊C4×C53—21no—
143C2×C4⋊C4×C53—22no—
144C2×C4⋊C4×C53—21no—
145C2×C4⋊C4×C53—21no—
146C2×C4⋊C4×C53C2×C414yescomplemented
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C22⋊C4×C53—21no—
150C2×C22⋊C4×C53—21no—
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C24×C53—21no—
154C24×C53C2×D411yescharacteristic
155C24×C53C2×D411yescharacteristic
156C24×C53C2×D411yescharacteristic
157#41×C53—44no—
158#41×C53—44no—
159#41×C53—44no—
160#41×C53—44no—
161#41×C53—44no—
162#41×C53—44no—
163#41×C53—44no—
164#41×C53—44no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—41no—
171C2×Q8×C53—41no—
172C2×Q8×C53C22⋊C414yes—
173C2×Q8×C53C22×C412yes—
174C2×D4×C53—24no—
175C2×D4×C53—24no—
176C2×D4×C53—24no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—41no—
183C2×D4×C53—41no—
184C2×D4×C53—41no—
185C2×D4×C53—41no—
186C2×D4×C53—41no—
187C2×D4×C53—41no—
188C2×D4×C53—42no—
189C2×D4×C53—42no—
190C2×D4×C53—81no—
191C2×D4×C53—81no—
192C2×D4×C53—81no—
193C2×D4×C53—81no—
194C2×D4×C53C22⋊C414yes—
195C2×D4×C53C22⋊C414yes—
196C2×D4×C53C22⋊C414yes—
197C2×D4×C53C22×C412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—24no—
215C22×C4×C53—42no—
216C22×C4×C53—42no—
217C22×C4×C53—81no—
218C22×C4×C53—81no—
219C22×C4×C53C22×C412yes—
220C22×C4×C53C22×C412yes—
221C22×C4×C53C22×C412yes—
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2411yescharacteristic
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—42no—
234C22×Dic53—81no—
235C22×Dic53—81no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C22×C412yes—
242C4⋊C4×C53C22×C412yes—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊Dic53—42no—
248C22⋊Dic53—81no—
249C22⋊Dic53—81no—
250C22⋊Dic53—81no—
251C22⋊Dic53—81no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—42no—
261C4×Dic53—42no—
262#11719917—44no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—44no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—22no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53C2×C22⋊C412yes—
302C23×C53C2×C22⋊C412yes—
303C23×C53C2×C22⋊C412yes—
304C23×C53C22×D411yescharacteristic
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—44no—
308Q8×C53—41no—
309Q8×C53—41no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—44no—
313D4×C53—44no—
314D4×C53—44no—
315D4×C53—48no—
316D4×C53—41no—
317D4×C53—41no—
318D4×C53—84no—
319D4×C53—84no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—48no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—84no—
349C2×C4×C53C2×C22⋊C412yes—
350C2×C4×C53C2×C22⋊C412yes—
351C2×C4×C53C2×C22⋊C412yes—
352C2×C4×C53C23×C411yescharacteristic
353C2×C4×C53C22×D411yescharacteristic
354C2×C4×C53H(5,𝔽2)11yescharacteristic
355C2×C4×C53H(5,𝔽2)11yescharacteristic
356C2×C4×C53H(5,𝔽2)11yescharacteristic
357C2×C4×C53H(5,𝔽2)11yescharacteristic
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—84no—
371#88322—41no—
372#88322—41no—
373#88322—41no—
374#88322—41no—
375#21772—531nomaximal, Sylow
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—42no—
400C22×C53—81no—
401C22×C53—81no—
402C22×C53—81no—
403C22×C53—81no—
404C22×C53C22×C22⋊C411yescharacteristic
405C22×C53#53411yescharacteristic
406C22×C53#53411yescharacteristic
407C22×C53#57611yescharacteristic
408C22×C53#57711yescharacteristic
409C22×C53#57711yescharacteristic
410C22×C53#57811yescharacteristic
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53—42no—
417C4×C53#51811yescharacteristic
418C4×C53#51811yescharacteristic
419C4×C53#53411yescharacteristic
420C4×C53#53411yescharacteristic
421Dic53—81no—
422Dic53—81no—
423Dic53—81no—
424Dic53—81no—
425C2×#537D5311yescharacteristic
426C2×#408—531no—
427#2311—531no—
428#1895—531no—
429#1894—531no—
430#1893—531no—
431#1892—531no—
432#1875—531no—
433#1874—531no—
434#1873—531no—
435#1872—531no—
436#1824—531no—
437#1823—531no—
438#1788—531no—
439#1788—531no—
440C2×C53—42no—
441C2×C53—42no—
442C2×C53—42no—
443C2×C53—82no—
444C2×C53#230811yescharacteristic
445C2×C53#289711yescharacteristic
446C2×C53#289811yescharacteristic
447C2×C53#319811yescharacteristic
448C2×C53#320111yescharacteristic
449C2×C53#320311yescharacteristic
450C2×C53#320411yescharacteristic
451C22×#41C2×D5311yescharacteristic
452C22×#41C2×D5311yescharacteristic
453C22×M16—531no—
454C23×C8—531no—
455#537—24no—
456#537Dic5318yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C2×D5311yescharacteristic
459C2×C22⋊Q8C2×D5311yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D5311yescharacteristic
464C2×#121C2×D5311yescharacteristic
465C2×#117—531no—
466C22×C4⋊C4—531no—
467C22×C4⋊C4C2×D5311yescharacteristic
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476#408—1064no—
477C2×C22⋊C8—531no—
478C2×C22⋊C8—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481#391—1061no—
482#390—1061no—
483#386—1061no—
484#386—1061no—
485#380—531no—
486#380—531no—
487#380—531no—
488#380—531no—
489#340—531no—
490#340—531no—
491#340—531no—
492#340—531no—
493#340—531no—
494#340—531no—
495#340—531no—
496#340—531no—
497C53#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic5314yes—
508C2×#41C2×Dic5314yescomplemented
509C2×#41C22⋊D5314yes—
510C22×Q8C22⋊D5311yescharacteristic
511C22×Q8C22×D5311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D5311yescharacteristic
516C22×D4C22⋊D5311yescharacteristic
517C22×D4C22⋊D5311yescharacteristic
518C22×D4C22×D5311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1061no—
522C23×C4C22×D5311yescharacteristic
523C23×C4C22×D5311yescharacteristic
524C23×C4C22×D5311yescharacteristic
525C2×M16—1062no—
526C2×M16—2121no—
527C2×M16—2121no—
528C22×C8—531no—
529C22×C8—531no—
530C22×C8—531no—
531C22×C8—531no—
532C22×C8—1062no—
533C22×C8—2121no—
534C22×C8—2121no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic5314yes—
539C22⋊Q8C2×Dic5314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic5314yes—
546#121C2×Dic5314yescomplemented
547#117—2121no—
548#117—2121no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—2121no—
559C2×C4⋊C4—2121no—
560C2×C4⋊C4C2×Dic5314yescomplemented
561C2×C4⋊C4C22×D5311yescharacteristic
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C42—1061no—
573#103—2121no—
574#103—2121no—
575#103—2121no—
576#103—2121no—
577#102—2121no—
578#102—2121no—
579#102—2121no—
580#102—2121no—
581C22⋊C8—1062no—
582C22⋊C8—1062no—
583C22⋊C8—1062no—
584C22⋊C8—1062no—
585#95—1061no—
586#95—1061no—
587#95—1061no—
588#95—1061no—
589C24—21no—
590C24C2×C22⋊D5311yescharacteristic
591C24C2×C22⋊D5311yescharacteristic
592C24C2×C22⋊D5311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic5314yes—
609C2×Q8C22×Dic5312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic5314yes—
631C2×D4C22⋊Dic5314yes—
632C2×D4C22⋊Dic5314yes—
633C2×D4C22×Dic5312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—4241no—
660C22×C4—4241no—
661C22×C4—2122no—
662C22×C4C22×Dic5312yes—
663C22×C4C22×Dic5312yes—
664C22×C4C22×Dic5312yes—
665C22×C4C2×C22⋊D5311yescharacteristic
666C22×C4C2×C22⋊D5311yescharacteristic
667C22×C4C2×C22⋊D5311yescharacteristic
668C22×C4C2×C22⋊D5312yes—
669C22×C4C2×C22⋊D5312yes—
670C22×C4C2×C22⋊D5312yes—
671C22×C4C23×D5311yescharacteristic
672M16—2124no—
673C2×C8—1061no—
674C2×C8—1061no—
675C2×C8—1061no—
676C2×C8—1061no—
677C2×C8—1061no—
678C2×C8—1061no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—1061no—
684C2×C8—1061no—
685C2×C8—2124no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—1061no—
698C4⋊C4—1061no—
699C4⋊C4—2122no—
700C4⋊C4C22×Dic5312yes—
701C4⋊C4C22×Dic5312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—4241no—
707C22⋊C4—4241no—
708C22⋊C4—4241no—
709C22⋊C4—4241no—
710C22⋊C4—2122no—
711C42—2122no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic5312yes—
738C23C2×C22⋊Dic5312yes—
739C23C2×C22⋊Dic5312yes—
740C23C22×C22⋊D5311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—4244no—
786C2×C4—2121no—
787C2×C4—2121no—
788C2×C4—2121no—
789C2×C4—2121no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4C2×C22⋊Dic5312yes—
799C2×C4C2×C22⋊Dic5312yes—
800C2×C4C2×C22⋊Dic5312yes—
801C2×C4C23×Dic5311yescharacteristic
802C2×C4C22×C22⋊D5311yescharacteristic
803C2×C4#1313326211yescharacteristic
804C2×C4#1313326211yescharacteristic
805C2×C4#1313326211yescharacteristic
806C2×C4#1313326211yescharacteristic
807C8—2121no—
808C8—2121no—
809C8—2121no—
810C8—2121no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic5311yescharacteristic
840C22#1681118211yescharacteristic
841C22#1681118211yescharacteristic
842C22#1681142611yescharacteristic
843C22#1681143111yescharacteristic
844C22#1681143411yescharacteristic
845C22#1681143811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—4241no—
853C4—4241no—
854C4—4241no—
855C4—4241no—
856C4#1681109811yescharacteristic
857C4#1681109811yescharacteristic
858C4#1681118211yescharacteristic
859C4#1681118211yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2027729311yescharacteristic
865C2#2028324111yescharacteristic
866C2#2028324811yescharacteristic
867C2#2028556111yescharacteristic
868C2#2028559111yescharacteristic
869C2#2028561211yescharacteristic
870C2#2028562111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#537C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#537D53
hypocenterC53#21772
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16810590C2semidirect
2. #20277307C2semidirect
3. #20275154C2semidirect
4. #20275149C2semidirect
5. #20275144C2semidirect
6. #20275139C2semidirect
7. #20275038C2semidirect
8. #20275033C2semidirect
9. #20275028C2semidirect
10. #20275023C2semidirect
11. #20274805C2semidirect
12. #20274801C2semidirect
13. #20274655C2semidirect
14. #20274655C2semidirect
52. C53×#537C4semidirect
114. C2×#41×C53C2×C4semidirect
134. C22⋊Q8×C53C2×C4semidirect
141. #121×C53C2×C4semidirect
146. C2×C4⋊C4×C53C2×C4semidirect
456. #537Dic53semidirect
497. C53#21772semidirect
508. C2×#41C2×Dic53semidirect
539. C22⋊Q8C2×Dic53semidirect
546. #121C2×Dic53semidirect
560. C2×C4⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105902
#202773072
#202751542
#202751492
#202751442
#202751392
#202750382
#202750332
#202750282
#202750232
#202748052
#202748012
#202746552
C2×C53×#5372
#2177253