Finite Group Databasebeta

← #27399626

Subgroups — #27399626

Order 13568.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D212C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3C2×#16810627C211yesmaximal, characteristic, complemented
4C22×#13133137C211yesmaximal, characteristic, complemented
5#20275642C211yesmaximal, characteristic, complemented
6#20275538C211yesmaximal, characteristic, complemented
7#20275151C211yesmaximal, characteristic, complemented
8#20275141C211yesmaximal, characteristic, complemented
9#20275037C211yesmaximal, characteristic, complemented
10#20275032C211yesmaximal, characteristic, complemented
11#20274722C211yesmaximal, characteristic, complemented
12#20274645C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14#20274543C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C23×D212C2211yescharacteristic
18C22×D4×D53—21no—
19C22×#11719917C2211yescharacteristic, complemented
20C23×#88322C2211yescharacteristic, complemented
21D4×D212—24no—
22D4×D212C418yescomplemented
23C2×#13133214C2211yescharacteristic
24C2×#13133192—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133191C2211yescharacteristic
27C2×#13133187—21no—
28C2×#13133187—21no—
29C2×C4×D212C2211yescharacteristic
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic, complemented
32#16810627—24no—
33C2×#13133137—24no—
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic, complemented
39C2×#13133137C2211yescharacteristic, complemented
40C2×#13133137C2211yescharacteristic, complemented
41C2×#13133137C2211yescharacteristic, complemented
42C2×#13133137C2211yescharacteristic, complemented
43C2×#13133137C2211yescharacteristic, complemented
44C2×#13133137C2211yescharacteristic, complemented
45C2×#13133137C2211yescharacteristic, complemented
46C2×C22⋊#88322C2211yescharacteristic, complemented
47C2×C22⋊#88322C2211yescharacteristic, complemented
48C2×#13133128C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53C2×C4×D4×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic, complemented
55C22×C4⋊C4×C53C2211yescharacteristic, complemented
56C53×#388—21no—
57C53×#387—21no—
58C53×#386—21no—
59C53×#382C2211yescharacteristic, complemented
60C53×#380C2211yescharacteristic, complemented
61C53×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C53C2211yescharacteristic, complemented
63C4×C22⋊C4×C53—21no—
64C24×D53—21no—
65C24×D53—21no—
66C22×D212—22no—
67C22×D212—22no—
68C22×D212—22no—
69C22×D212—22no—
70C22×D212—21no—
71C22×D212—21no—
72C22×D212—21no—
73C22×D212—22no—
74C22×D212—22no—
75C22×D212—21no—
76C22×D212—41no—
77C22×D212—41no—
78C22×D212—41no—
79C22×D212—41no—
80C22×D212C2×C414yes—
81C22×D212C2×C414yescomplemented
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C2×D4×D53—28no—
88C2×D4×D53—44no—
89C2×D4×D53—44no—
90C22×C4×D53—21no—
91C2×#11719917—22no—
92C2×#11719917—22no—
93C2×#11719917—41no—
94C22×#88322—22no—
95C22×#88322—22no—
96C22×#88322—41no—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133214—22no—
102#13133214C2×C414yescomplemented
103#13133192—28no—
104#13133191—22no—
105#13133191—22no—
106#13133191C2×C414yes—
107#13133191C2×C414yescomplemented
108#13133187—28no—
109#13133187—28no—
110C4×D212—22no—
111C4×D212C2×C414yescomplemented
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C4⋊#88322—22no—
117#13133137—22no—
118#13133137—22no—
119#13133137—22no—
120#13133137—22no—
121#13133137—22no—
122#13133137—22no—
123#13133137—22no—
124#13133137—41no—
125#13133137—41no—
126#13133137—41no—
127#13133137—41no—
128#13133137D414yescomplemented
129C22⋊#88322—22no—
130C22⋊#88322—22no—
131#13133128—22no—
132C22×D4×C53D411yescharacteristic
133C23×C4×C53—21no—
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C4×D4×C53C2×C414yes—
137C4×D4×C53D414yes—
138#117×C53—22no—
139#117×C53—41no—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53—22no—
142C2×C4⋊C4×C53—41no—
143C2×C4⋊C4×C53D411yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C4⋊C4×C53C2311yescharacteristic
146C2×C4⋊C4×C53C2311yescharacteristic
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53—21no—
150C2×C22⋊C4×C53—21no—
151C2×C22⋊C4×C53D411yescharacteristic
152C2×C22⋊C4×C53D411yescharacteristic
153C2×C42×C53—21no—
154C2×C42×C53—21no—
155C2×C42×C53C2311yescharacteristic
156#95×C53—21no—
157#95×C53—21no—
158#95×C53—21no—
159#95×C53—21no—
160#95×C53—21no—
161C24×C53C2×D411yescharacteristic
162C24×C53C2×D411yescharacteristic
163C23×D53—21no—
164C23×D53—21no—
165C23×D53—21no—
166C23×D53—24no—
167C23×D53—24no—
168C23×D53—42no—
169C23×D53—42no—
170C23×D53—42no—
171C23×D53—42no—
172C23×D53—42no—
173C23×D53—42no—
174C23×D53—42no—
175C23×D53—42no—
176C23×D53—81no—
177C23×D53—81no—
178C23×D53—81no—
179C23×D53—81no—
180C2×D4×C53—22no—
181C2×D4×C53—22no—
182C2×D4×C53C22⋊C414yes—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—42no—
196C22×C4×C53—42no—
197C22×C4×C53—81no—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C22×C412yes—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—42no—
210C2×C22⋊D53—42no—
211C2×C22⋊D53—42no—
212C2×C22⋊D53—42no—
213C22×Dic53—21no—
214D4×D53—432no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—21no—
226C2×D212—28no—
227C2×D212—28no—
228C2×D212—24no—
229C2×D212—24no—
230C2×D212—24no—
231C2×D212—21no—
232C2×D212—21no—
233C2×D212—24no—
234C2×D212—44no—
235C2×D212—44no—
236C2×D212—44no—
237C2×D212—44no—
238C2×D212—44no—
239C2×D212—44no—
240C2×D212—42no—
241C2×D212—42no—
242C2×D212—42no—
243C2×D212—42no—
244C2×D212—42no—
245C2×D212—42no—
246C2×D212—81no—
247C2×D212—81no—
248C2×D212C22×C412yes—
249C2×D212C22×C412yes—
250C2×D212C22×C412yes—
251C2×D212C2×D412yes—
252C2×D212#4112yes—
253C2×C4×D53—24no—
254C2×C4×D53—42no—
255C2×C4×D53—42no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—42no—
264C4⋊C4×C53C22⋊C414yes—
265C4⋊C4×C53C2×D412yescomplemented
266C22⋊C4×C53—42no—
267C22⋊C4×C53—42no—
268C22⋊C4×C53—81no—
269C22⋊C4×C53C22⋊C414yes—
270C22⋊C4×C53C22⋊C414yes—
271C42×C53—42no—
272C42×C53—81no—
273C42×C53C22×C412yes—
274C42×C53C2×D412yes—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278C4⋊Dic53—21no—
279C4⋊Dic53C22×C412yes—
280#11719917—44no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—21no—
291C2×#88322—21no—
292C2×#88322—44no—
293C2×#88322C2×D412yescomplemented
294C23×C53—21no—
295C23×C53—21no—
296C23×C53—21no—
297C23×C53—21no—
298C23×C53—21no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—21no—
302C23×C53—21no—
303C23×C53—21no—
304C23×C53C2×C22⋊C412yes—
305C23×C53C2×C22⋊C412yes—
306C23×C53AGL(1,ℤ/8)12yes—
307C23×C53AGL(1,ℤ/8)12yes—
308C23×C53C22×D411yescharacteristic
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—48no—
315C22×D53—48no—
316C22×D53—41no—
317C22×D53—41no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—48no—
321C22×D53—41no—
322C22×D53—41no—
323C22×D53—41no—
324C22×D53—41no—
325C22×D53—41no—
326C22×D53—41no—
327C22×D53—41no—
328C22×D53—41no—
329C22×D53—41no—
330C22×D53—41no—
331C22×D53—41no—
332C22×D53—41no—
333C22×D53—48no—
334C22×D53—84no—
335C22×D53—84no—
336C22×D53—84no—
337C22×D53—84no—
338C22×D53—84no—
339C22×D53—84no—
340C22×D53—84no—
341C22×D53—84no—
342C22×D53—84no—
343C22×D53—84no—
344D4×C53—28no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—84no—
374C2×C4×C53C2×C22⋊C412yes—
375C2×C4×C53C2×C22⋊C412yes—
376C2×C4×C53C2×C22⋊C412yes—
377C2×C4×C53C2×C22⋊C412yes—
378C2×C4×C53C23×C411yescharacteristic
379C2×C4×C53C22×D411yescharacteristic
380C2×C4×C53C22×D411yescharacteristic
381C2×C4×C53C2×#4111yescharacteristic
382C2×C4×C53H(5,𝔽2)11yescharacteristic
383C2×C4×C53H(5,𝔽2)11yescharacteristic
384C22⋊D53—48no—
385C22⋊D53—48no—
386C2×Dic53—22no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389D212—22no—
390D212—22no—
391D212—22no—
392D212—22no—
393D212—22no—
394D212—22no—
395D212—22no—
396D212—48no—
397D212—48no—
398D212—48no—
399D212—41no—
400D212—41no—
401D212—41no—
402D212—41no—
403D212—84no—
404D212C4×D414yes—
405C4×D53—48no—
406#88322—22no—
407#88322—41no—
408#88322—41no—
409#88322—41no—
410#22423—531nomaximal, Sylow
411C22×C53—22no—
412C22×C53—22no—
413C22×C53—22no—
414C22×C53—22no—
415C22×C53—22no—
416C22×C53—22no—
417C22×C53—22no—
418C22×C53—22no—
419C22×C53—22no—
420C22×C53—41no—
421C22×C53—41no—
422C22×C53—41no—
423C22×C53—41no—
424C22×C53#41814yescomplemented
425C22×C53C22×C22⋊C411yescharacteristic
426C22×C53D4211yescharacteristic
427C22×C53#54611yescharacteristic
428C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C53#57611yescharacteristic
431C22×C53#57711yescharacteristic
432C2×D53—24no—
433C2×D53—42no—
434C2×D53—42no—
435C2×D53—42no—
436C2×D53—42no—
437C2×D53—42no—
438C2×D53—42no—
439C2×D53—42no—
440C2×D53—42no—
441C2×D53—42no—
442C2×D53—42no—
443C2×D53—42no—
444C2×D53—42no—
445C2×D53—816no—
446C2×D53—816no—
447C2×D53—81no—
448C2×D53—81no—
449C2×D53—81no—
450C2×D53—81no—
451C2×D53—81no—
452C2×D53—81no—
453C2×D53—81no—
454C2×D53—81no—
455C4×C53—22no—
456C4×C53—22no—
457C4×C53—22no—
458C4×C53—22no—
459C4×C53—42no—
460C4×C53—81no—
461C4×C53—81no—
462C4×C53—81no—
463C4×C53C2×C4×D411yescharacteristic
464C4×C53#51811yescharacteristic
465C4×C53D4211yescharacteristic
466C4×C53#54611yescharacteristic
467Dic53—42no—
468C2×D42—531no—
469C2×#435—531no—
470C2×#418—531no—
471C22×#102—531no—
472#2352D5311yescharacteristic, complemented
473#1982—531no—
474#1961—531no—
475#1895—531no—
476#1893—531no—
477#1875—531no—
478#1874—531no—
479#1804—531no—
480#1786—531no—
481#1786—531no—
482#1762—531no—
483C2×C53—24no—
484C2×C53—42no—
485C2×C53D4×C22⋊C411yescharacteristic
486C2×C53C2×#41811yescharacteristic
487C2×C53#289711yescharacteristic
488C2×C53#326411yescharacteristic
489C2×C53#326511yescharacteristic
490C2×C53#331011yescharacteristic
491C2×C53#331811yescharacteristic
492D53—44no—
493D53—82no—
494D53—82no—
495C23×D4—531no—
496C23×D4—531no—
497C23×D4—1061no—
498C22×M16—531no—
499C23×C8—531no—
500D42—538no—
501D42—1064no—
502C2×#127—531no—
503C2×#121—531no—
504C2×#121—531no—
505C2×#121—1061no—
506C2×#120—1061no—
507C2×#120—1061no—
508C2×C4×D4—531no—
509C2×C4×D4C2×D5311yescharacteristic
510C2×#117C2×D5311yescharacteristic, complemented
511C22×C4⋊C4C2×D5311yescharacteristic, complemented
512#435—1064no—
513C2×C4⋊C8—531no—
514#418—1064no—
515C2×#102—531no—
516C2×#102—531no—
517C2×#102—531no—
518C2×#102—531no—
519C2×#102—531no—
520C2×#102—531no—
521C2×#102—531no—
522C2×#102—531no—
523C2×#102—531no—
524C2×#102—531no—
525C2×#102—531no—
526C2×#102—531no—
527C2×#102—1064no—
528C2×C22⋊C8—531no—
529C2×C22⋊C8—531no—
530C2×#97—531no—
531#388—21no—
532#387—21no—
533#386—21no—
534#382C2×D5311yescharacteristic, complemented
535#380C2×D5311yescharacteristic, complemented
536#380C2×D5311yescharacteristic, complemented
537C4×C4⋊C4C2×D5311yescharacteristic, complemented
538C4×C22⋊C4—21no—
539#340—531no—
540#340—531no—
541#340—531no—
542#340—531no—
543C53#2242311yescharacteristic, complemented, Sylow
544C25—1061no—
545C25—1061no—
546C22×D4—534no—
547C22×D4—534no—
548C22×D4—531no—
549C22×D4—531no—
550C22×D4—531no—
551C22×D4—1062no—
552C22×D4—1062no—
553C22×D4—1062no—
554C22×D4—1062no—
555C22×D4—1061no—
556C22×D4—1061no—
557C22×D4—1068no—
558C22×D4—1062no—
559C22×D4—1062no—
560C22×D4—1061no—
561C22×D4—1061no—
562C22×D4—1061no—
563C22×D4—1061no—
564C22×D4—2121no—
565C22×D4—2121no—
566C22×D4—2121no—
567C22×D4—2121no—
568C22×D4—2124no—
569C22×D4—2124no—
570C22×D4C22⋊D5311yescharacteristic
571C23×C4—21no—
572C23×C4—1061no—
573C23×C4C22×D5311yescharacteristic
574C23×C4C22×D5311yescharacteristic
575C2×M16—1062no—
576C2×M16—1062no—
577C2×M16—2121no—
578C22×C8—531no—
579C22×C8—531no—
580C22×C8—531no—
581C22×C8—531no—
582C22×C8—1062no—
583C22×C8—1062no—
584C22×C8—2121no—
585#127—534no—
586#127—1062no—
587#121—534no—
588#121—534no—
589#121—1062no—
590#121—1062no—
591#121—1068no—
592#120—1068no—
593#120—1068no—
594C4×D4—534no—
595C4×D4—1062no—
596C4×D4C4×D5314yes—
597C4×D4D21214yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4C22⋊D5311yescharacteristic
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C4⋊C4C22×D5311yescharacteristic
608C2×C4⋊C4C22×D5311yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4C22⋊D5311yescharacteristic
616C2×C22⋊C4C22⋊D5311yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C22×D5311yescharacteristic
620C4⋊C8—1062no—
621#102—534no—
622#102—1062no—
623#102—1062no—
624#102—1062no—
625#102—1062no—
626#102—1062no—
627#102—1062no—
628#102—1062no—
629#102—2121no—
630#102—2121no—
631#102—2121no—
632#102—2121no—
633C22⋊C8—1062no—
634C22⋊C8—1062no—
635#97—1062no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—1061no—
642C24—1064no—
643C24—1064no—
644C24—1061no—
645C24—1061no—
646C24—4241no—
647C24—4241no—
648C24—4241no—
649C24—4241no—
650C24—2122no—
651C24—2122no—
652C24—2122no—
653C24—2122no—
654C24—2122no—
655C24—2122no—
656C24—2122no—
657C24—2122no—
658C24C2×C22⋊D5311yescharacteristic
659C24C2×C22⋊D5311yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—532no—
663C2×D4—532no—
664C2×D4—532no—
665C2×D4—532no—
666C2×D4—532no—
667C2×D4—1068no—
668C2×D4—1068no—
669C2×D4—1064no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1064no—
674C2×D4—1064no—
675C2×D4—1061no—
676C2×D4—1061no—
677C2×D4—1061no—
678C2×D4—1061no—
679C2×D4—1061no—
680C2×D4—1061no—
681C2×D4—1061no—
682C2×D4—1061no—
683C2×D4—1061no—
684C2×D4—1061no—
685C2×D4—1061no—
686C2×D4—1061no—
687C2×D4—1061no—
688C2×D4—4241no—
689C2×D4—4241no—
690C2×D4—2124no—
691C2×D4—2124no—
692C2×D4—2124no—
693C2×D4—2124no—
694C2×D4—2124no—
695C2×D4—2124no—
696C2×D4—2122no—
697C2×D4—2122no—
698C2×D4—2122no—
699C2×D4—2122no—
700C2×D4—2122no—
701C2×D4—2122no—
702C2×D4—21232no—
703C2×D4—2122no—
704C2×D4—2122no—
705C2×D4—2122no—
706C2×D4—2122no—
707C2×D4#1171992114yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—1061no—
724C22×C4—1064no—
725C22×C4—2122no—
726C22×C4—2122no—
727C22×C4C2×C4×D5312yes—
728C22×C4C2×C4×D5312yes—
729C22×C4C2×D21212yes—
730C22×C4C2×D21212yes—
731C22×C4C2×C22⋊D5311yescharacteristic
732C22×C4C2×C22⋊D5311yescharacteristic
733C22×C4C2×C22⋊D5311yescharacteristic
734C22×C4C2×C22⋊D5311yescharacteristic
735C22×C4C23×D5311yescharacteristic
736M16—2124no—
737C2×C8—532no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—1061no—
741C2×C8—1061no—
742C2×C8—1061no—
743C2×C8—1061no—
744C2×C8—1061no—
745C2×C8—1061no—
746C2×C8—1061no—
747C2×C8—1061no—
748C2×C8—1061no—
749C2×C8—2124no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—42no—
758C4⋊C4—532no—
759C4⋊C4—1061no—
760C4⋊C4#1171992114yes—
761C4⋊C4D4×D5312yescomplemented
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—1064no—
766C22⋊C4—1064no—
767C22⋊C4—1064no—
768C22⋊C4#1171992114yes—
769C22⋊C4#1171992114yes—
770C42—42no—
771C42—81no—
772C42C2×C4×D5312yes—
773C42C2×D21212yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—1062no—
785C23—1062no—
786C23—1062no—
787C23—1062no—
788C23—1062no—
789C23—4244no—
790C23—4244no—
791C23—4244no—
792C23—4244no—
793C23—4244no—
794C23—4244no—
795C23—4244no—
796C23—4244no—
797C23—4244no—
798C23—4244no—
799C23—2128no—
800C23—2128no—
801C23—2128no—
802C23—2128no—
803C23—2121no—
804C23—2121no—
805C23—2121no—
806C23—2121no—
807C23—2121no—
808C23—2121no—
809C23—2121no—
810C23—2121no—
811C23—2121no—
812C23—2121no—
813C23—2121no—
814C23—2121no—
815C23—2121no—
816C23—2121no—
817C23—2121no—
818C23—2121no—
819C23C2×#1171992112yes—
820C23C2×#1171992112yes—
821C23#1313324212yes—
822C23#1313324212yes—
823C23C22×C22⋊D5311yescharacteristic
824D4—28no—
825D4—534no—
826D4—1062no—
827D4—1062no—
828D4—1062no—
829D4—1062no—
830D4—1062no—
831D4—1062no—
832D4—1062no—
833D4—4244no—
834D4—2128no—
835D4—2128no—
836D4—2128no—
837D4—2128no—
838D4—2128no—
839D4—2121no—
840D4—2121no—
841D4—2121no—
842D4—2121no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—84no—
872C2×C4—1062no—
873C2×C4—2128no—
874C2×C4—2121no—
875C2×C4—2121no—
876C2×C4C2×#1171992112yes—
877C2×C4C2×#1171992112yes—
878C2×C4C2×#1171992112yes—
879C2×C4C2×#1171992112yes—
880C2×C4C22×C4×D5311yescharacteristic
881C2×C4C2×D4×D5311yescharacteristic
882C2×C4C22×D21211yescharacteristic
883C2×C4#41×D5311yescharacteristic
884C2×C4#1313326211yescharacteristic
885C2×C4#1313326311yescharacteristic
886C8—1062no—
887C8—2121no—
888C8—2121no—
889C8—2121no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—1064no—
904C22—42416no—
905C22—42416no—
906C22—4241no—
907C22—4241no—
908C22—4241no—
909C22—4241no—
910C22—4241no—
911C22—4241no—
912C22—4241no—
913C22—4241no—
914C22—2122no—
915C22—2122no—
916C22—2122no—
917C22—2122no—
918C22—2122no—
919C22—2122no—
920C22—2122no—
921C22—2122no—
922C22—2122no—
923C22—2122no—
924C22—2122no—
925C22—2122no—
926C22#1681062714yescomplemented
927C22C22×#1171992111yescharacteristic
928C22D4×C22⋊D5311yescharacteristic
929C22#1681126111yescharacteristic
930C22C2×#1313324211yescharacteristic
931C22C2×#1313324211yescharacteristic
932C22#1681142611yescharacteristic
933C22#1681143111yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—2122no—
943C4C4×D4×D5311yescharacteristic
944C4#1681109511yescharacteristic
945C4D4×D21211yescharacteristic
946C4#1681126811yescharacteristic
947C2—24no—
948C2—42no—
949C2—4242no—
950C2—4242no—
951C2—2124no—
952C2D4×#1171992111yescharacteristic
953C2C2×#1681062711yescharacteristic
954C2#2028323811yescharacteristic
955C2#2028619611yescharacteristic
956C2#2028621111yescharacteristic
957C2#2028673011yescharacteristic
958C2#2028685011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC2×D4×D212C2
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22423
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. C2×#16810627C2semidirect
4. C22×#13133137C2semidirect
5. #20275642C2semidirect
6. #20275538C2semidirect
7. #20275151C2semidirect
8. #20275141C2semidirect
9. #20275037C2semidirect
10. #20275032C2semidirect
11. #20274722C2semidirect
12. #20274645C2semidirect
13. #20274645C2semidirect
14. #20274543C2semidirect
15. C53×#2352C2semidirect
19. C22×#11719917C22semidirect
20. C23×#88322C22semidirect
22. D4×D212C4semidirect
31. C2×C4⋊#88322C22semidirect
38. C2×#13133137C22semidirect
39. C2×#13133137C22semidirect
40. C2×#13133137C22semidirect
41. C2×#13133137C22semidirect
42. C2×#13133137C22semidirect
43. C2×#13133137C22semidirect
44. C2×#13133137C22semidirect
45. C2×#13133137C22semidirect
46. C2×C22⋊#88322C22semidirect
47. C2×C22⋊#88322C22semidirect
48. C2×#13133128C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
54. C2×#117×C53C22semidirect
55. C22×C4⋊C4×C53C22semidirect
59. C53×#382C22semidirect
60. C53×#380C22semidirect
61. C53×#380C22semidirect
62. C4×C4⋊C4×C53C22semidirect
81. C22×D212C2×C4semidirect
102. #13133214C2×C4semidirect
107. #13133191C2×C4semidirect
111. C4×D212C2×C4semidirect
128. #13133137D4semidirect
265. C4⋊C4×C53C2×D4semidirect
293. C2×#88322C2×D4semidirect
424. C22×C53#418semidirect
472. #2352D53semidirect
510. C2×#117C2×D53semidirect
511. C22×C4⋊C4C2×D53semidirect
534. #382C2×D53semidirect
535. #380C2×D53semidirect
536. #380C2×D53semidirect
537. C4×C4⋊C4C2×D53semidirect
543. C53#22423semidirect
761. C4⋊C4D4×D53semidirect
926. C22#16810627semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2122
C2×#168106952
C2×#168106272
C22×#131331372
#202756422
#202755382
#202751512
#202751412
#202750372
#202750322
#202747222
#202746452
#202745432
C53×#23522
#2242353