Finite Group Databasebeta

← #27389811

Subgroups — #27389811

Order 13568.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810757C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×C4×#11719922C211yesmaximal, characteristic, complemented
4#20277408C211yesmaximal, characteristic, complemented
5#20275063C211yesmaximal, characteristic, complemented
6#20275063C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic, complemented
8#20274976C211yesmaximal, characteristic, complemented
9#20274962C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic, complemented
11#20274646C211yesmaximal, characteristic, complemented
12#20274540C211yesmaximal, characteristic, complemented
13C4×#13133138C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C2×C53×#518C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic, complemented
20#16810757C418yescomplemented
21#16810733—24no—
22C4×#11719922—24no—
23C2×#13133150C2211yescharacteristic, complemented
24C2×#13133148C2211yescharacteristic, complemented
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133137C2211yescharacteristic, complemented
32C2×#13133137C2211yescharacteristic, complemented
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×#13133128C2211yescharacteristic, complemented
36C2×C4×#88322C2211yescharacteristic, complemented
37#16810525C2211yescharacteristic, complemented
38#16810523—21no—
39#16810521C2211yescharacteristic, complemented
40#16810513—21no—
41#16810499—21no—
42#16810494—21no—
43#16810483C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50#16810378C2211yescharacteristic, complemented
51C23×D4×C53C2211yescharacteristic
52C53×#518—24no—
53C53×#518—24no—
54C2×C4×D4×C53—21no—
55C2×C4×D4×C53—21no—
56C2×C4×D4×C53C2211yescharacteristic
57C2×C4×D4×C53C2211yescharacteristic
58C2×C4×D4×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×#117×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C22⋊C4×C53—21no—
63C22×C22⋊C4×C53—21no—
64C22×D212C2311yescharacteristic
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C2×#11719922—22no—
68C2×#11719922—22no—
69C2×#11719922—22no—
70C2×#11719922—22no—
71C2×#11719922C2×C414yescomplemented
72C2×#11719922C2×C414yescomplemented
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133191—22no—
78#13133191C2×C414yescomplemented
79C4×D212—22no—
80C4×D212—22no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×C4×Dic53—21no—
91#13133150—22no—
92#13133148—22no—
93#13133138—22no—
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138C2×C414yescomplemented
98#13133138C2×C414yescomplemented
99#13133137—22no—
100#13133137—22no—
101C22⋊#88322—22no—
102C22⋊#88322C2×C414yescomplemented
103#13133128—22no—
104C4×#88322—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108C25×C53—21no—
109C22×D4×C53—22no—
110C22×D4×C53—22no—
111C22×D4×C53—22no—
112C22×D4×C53—22no—
113C22×D4×C53—21no—
114C22×D4×C53—22no—
115C22×D4×C53C2×C414yescomplemented
116C22×D4×C53C2311yescharacteristic
117C22×D4×C53C2311yescharacteristic
118C23×C4×C53—21no—
119C23×C4×C53—21no—
120C23×C4×C53—21no—
121C23×C4×C53—21no—
122C23×C4×C53C2311yescharacteristic
123C4×D4×C53—28no—
124C4×D4×C53—28no—
125C4×D4×C53—22no—
126C4×D4×C53—22no—
127C4×D4×C53—22no—
128C4×D4×C53—22no—
129C4×D4×C53—22no—
130C4×D4×C53—22no—
131C4×D4×C53D414yescomplemented
132C4×D4×C53D414yescomplemented
133#117×C53—22no—
134#117×C53—22no—
135#117×C53—22no—
136#117×C53—22no—
137C2×C4⋊C4×C53D411yescharacteristic
138C2×C4⋊C4×C53D411yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C22⋊C4×C53—28no—
142C2×C22⋊C4×C53—28no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C22⋊C4×C53D411yescharacteristic
150C2×C42×C53—21no—
151C2×C42×C53C2311yescharacteristic
152C2×C42×C53C2311yescharacteristic
153C24×C53—24no—
154C24×C53—24no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—24no—
158C24×C53—81no—
159C24×C53—81no—
160C24×C53—81no—
161C24×C53—81no—
162C24×C53C2×D411yescharacteristic
163C23×D53—21no—
164C2×D4×C53—24no—
165C2×D4×C53—24no—
166C2×D4×C53—28no—
167C2×D4×C53—28no—
168C2×D4×C53—28no—
169C2×D4×C53—28no—
170C2×D4×C53—24no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53C22×C412yes—
178C2×D4×C53C22×C412yes—
179C2×D4×C53C2×D412yes—
180C2×D4×C53C2×D412yes—
181C2×D4×C53#4112yes—
182C2×D4×C53#4112yes—
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—24no—
190C22×C4×C53—24no—
191C22×C4×C53—24no—
192C22×C4×C53—24no—
193C22×C4×C53—81no—
194C22×C4×C53—81no—
195C22×C4×C53—81no—
196C22×C4×C53—81no—
197C22×C4×C53—81no—
198C22×C4×C53—81no—
199C22×C4×C53—81no—
200C22×C4×C53—81no—
201C22×C4×C53C22×C412yes—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53#4112yes—
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—24no—
210C2×C22⋊D53—81no—
211C2×C22⋊D53—81no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212C22×C412yes—
221C2×C4×D53—42no—
222C2×C4×D53—81no—
223C2×C4×D53—81no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53C2×D412yes—
229C4⋊C4×C53C2×D412yes—
230C22⋊C4×C53—24no—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—22no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—24no—
236C22⋊C4×C53—24no—
237C42×C53—24no—
238C42×C53—21no—
239C42×C53—21no—
240C42×C53C2×D412yes—
241C42×C53C2×D412yes—
242C22⋊Dic53—81no—
243#11719922—28no—
244#11719922—28no—
245#11719921—24no—
246#11719921—42no—
247#11719921—81no—
248#11719921—81no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53C22×C412yes—
255#11719919—81no—
256C4×Dic53—81no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322C22×C412yes—
268C2×#88322C22×C412yes—
269C23×C53—216no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53—41no—
286C23×C53—41no—
287C23×C53—41no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—84no—
291C23×C53—84no—
292C23×C53—84no—
293C23×C53—84no—
294C23×C53—84no—
295C23×C53—84no—
296C23×C53C4×D412yes—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305D4×C53—216no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53C4×D414yes—
313D4×C53C4×D414yes—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—84no—
337C2×C4×C53—84no—
338C2×C4×C53—84no—
339C2×C4×C53—84no—
340C2×C4×C53C4×D412yes—
341C2×C4×C53#12012yes—
342C2×C4×C53#12012yes—
343C2×C4×C53C23×C411yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C2×#4111yescharacteristic
347C2×C4×C53C2×#4111yescharacteristic
348C2×C4×C53C2×#4111yescharacteristic
349C22⋊D53—84no—
350C2×Dic53—22no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359D212—22no—
360D212—22no—
361D212—41no—
362D212—41no—
363C4×D53—84no—
364#88322—22no—
365#88322—22no—
366#88322—41no—
367#88322—41no—
368#21458—531nomaximal, Sylow
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—24no—
373C22×C53—24no—
374C22×C53—41no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—41no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—42no—
382C22×C53—42no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—41no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—41no—
390C22×C53—816no—
391C22×C53C2×C4×D411yescharacteristic
392C22×C53C2×#12011yescharacteristic
393C22×C53#52511yescharacteristic
394C22×C53#57611yescharacteristic
395C22×C53#57611yescharacteristic
396C22×C53#57611yescharacteristic
397C22×C53#57711yescharacteristic
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—81no—
402C2×D53—81no—
403C2×D53—81no—
404C2×D53—81no—
405C4×C53—22no—
406C4×C53—22no—
407C4×C53—22no—
408C4×C53—41no—
409C4×C53—42no—
410C4×C53—41no—
411C4×C53—42no—
412C4×C53C2×C4×D411yescharacteristic
413C4×C53C2×C4×D411yescharacteristic
414C4×C53#52511yescharacteristic
415C4×C53#52511yescharacteristic
416Dic53—42no—
417Dic53—81no—
418Dic53—81no—
419C2×#518D5311yescharacteristic, complemented
420C2×#447—531no—
421C2×#442—531no—
422C2×C4×D8—531no—
423#2324—531no—
424#1879—531no—
425#1879—531no—
426#1875—531no—
427#1864—531no—
428#1862—531no—
429#1854—531no—
430#1786—531no—
431#1762—531no—
432C4×#102—531no—
433#1750—531no—
434C2×C53—42no—
435C2×C53—44no—
436C2×C53—44no—
437C2×C53C4×#12011yescharacteristic
438C2×C53#294611yescharacteristic
439C2×C53#294811yescharacteristic
440C2×C53#300811yescharacteristic
441C2×C53#301211yescharacteristic
442C2×C53#311811yescharacteristic
443C2×C53#312211yescharacteristic
444D53—82no—
445C23×D4C2×D5311yescharacteristic
446C22×D8—531no—
447C22×D8—531no—
448C2×#121—531no—
449#518—24no—
450#518—24no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×C4×D4—531no—
454C2×C4×D4C2×D5311yescharacteristic
455C2×C4×D4C2×D5311yescharacteristic
456C2×C4×D4C2×D5311yescharacteristic
457C2×C4×D4C2×D5311yescharacteristic
458C2×#117C2×D5311yescharacteristic
459C2×#117C2×D5311yescharacteristic
460C22×C22⋊C4—21no—
461C22×C22⋊C4—21no—
462#447—538no—
463#442—1064no—
464C4×D8—1064no—
465C2×#107—531no—
466C2×#106—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×C22⋊C8—531no—
476C2×C22⋊C8—531no—
477C2×#97—531no—
478C2×C4×C8—531no—
479#390—531no—
480#390—1061no—
481#389—531no—
482#388—1061no—
483#386—1061no—
484#385—1061no—
485#380—531no—
486C4×C4⋊C4—531no—
487#340—531no—
488#340—531no—
489#340—531no—
490#340—531no—
491#336—531no—
492#336—531no—
493C53#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—531no—
502C22×D4—1061no—
503C22×D4C4×D5314yescomplemented
504C22×D4C22×D5311yescharacteristic
505C22×D4C22×D5311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—1061no—
511C23×C4C22×D5311yescharacteristic
512C2×D8—534no—
513C2×D8—534no—
514C2×D8—1062no—
515C2×D8—1062no—
516C2×D8—1062no—
517C2×D8—1062no—
518C22×C8—531no—
519C22×C8—531no—
520C22×C8—531no—
521C22×C8—531no—
522#121—534no—
523#121—1062no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—1062no—
533C4×D4—1062no—
534C4×D4C22⋊D5314yescomplemented
535C4×D4C22⋊D5314yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4C22⋊D5311yescharacteristic
545C2×C4⋊C4C22⋊D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4C22⋊D5311yescharacteristic
561C2×C22⋊C4C22⋊D5311yescharacteristic
562C2×C42—21no—
563C2×C42—1061no—
564C2×C42C22×D5311yescharacteristic
565C2×C42C22×D5311yescharacteristic
566#107—1062no—
567#106—1062no—
568#102—534no—
569#102—534no—
570#102—1062no—
571#102—1062no—
572#102—1062no—
573#102—1062no—
574#102—1062no—
575#102—1062no—
576C22⋊C8—534no—
577C22⋊C8—1062no—
578#97—1062no—
579C4×C8—1062no—
580#95—1061no—
581#95—1061no—
582#95—1061no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—1061no—
593C24C2×C22⋊D5311yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—532no—
608C2×D4—1064no—
609C2×D4—1061no—
610C2×D4—1061no—
611C2×D4—1061no—
612C2×D4—1061no—
613C2×D4—1061no—
614C2×D4—4241no—
615C2×D4—4241no—
616C2×D4C2×C4×D5312yes—
617C2×D4C2×C4×D5312yes—
618C2×D4#1171994512yes—
619C2×D4#1171994512yes—
620C2×D4C2×C22⋊D5312yes—
621C2×D4C2×C22⋊D5312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—4241no—
644C22×C4—4241no—
645C22×C4—2122no—
646C22×C4C2×C4×D5312yes—
647C22×C4#1171994512yes—
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5311yescharacteristic
654D8—1068no—
655D8—1068no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—1061no—
667C2×C8—1061no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—532no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4—4241no—
679C4⋊C4C2×C22⋊D5312yes—
680C4⋊C4C2×C22⋊D5312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1064no—
689C22⋊C4—4241no—
690C22⋊C4—4241no—
691C22⋊C4—4241no—
692C22⋊C4—2122no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—4241no—
697C42C2×C22⋊D5312yes—
698C42C2×C22⋊D5312yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—1062no—
727C23—2121no—
728C23—2121no—
729C23—2121no—
730C23—2121no—
731C23—2121no—
732C23—2121no—
733C23C4×C22⋊D5312yes—
734C23C22×C22⋊D5311yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—1062no—
743D4—1062no—
744D4—4244no—
745D4—2121no—
746D4—2121no—
747D4C4×C22⋊D5314yes—
748D4C4×C22⋊D5314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—1062no—
776C2×C4—4244no—
777C2×C4—2121no—
778C2×C4—2121no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4—2121no—
782C2×C4—2121no—
783C2×C4—2121no—
784C2×C4—2121no—
785C2×C4C4×C22⋊D5312yes—
786C2×C4#1313318612yes—
787C2×C4#1313318612yes—
788C2×C4C22×C4×D5311yescharacteristic
789C2×C4C22×C22⋊D5311yescharacteristic
790C2×C4C22×C22⋊D5311yescharacteristic
791C2×C4C2×#1171994511yescharacteristic
792C2×C4C2×#1171994511yescharacteristic
793C2×C4C2×#1171994511yescharacteristic
794C8—1062no—
795C8—1062no—
796C8—2121no—
797C8—2121no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—816no—
820C22—4241no—
821C22—4241no—
822C22—4241no—
823C22—4241no—
824C22—2122no—
825C22—2122no—
826C22—2122no—
827C22C2×C4×C22⋊D5311yescharacteristic
828C22C2×#1313318611yescharacteristic
829C22#1681113411yescharacteristic
830C22#1681142611yescharacteristic
831C22#1681142611yescharacteristic
832C22#1681142611yescharacteristic
833C22#1681143411yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—42no—
841C4—4241no—
842C4—4241no—
843C4—2122no—
844C4C2×C4×C22⋊D5311yescharacteristic
845C4C2×C4×C22⋊D5311yescharacteristic
846C4#1681113411yescharacteristic
847C4#1681113411yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—4242no—
852C2C4×#1313318611yescharacteristic
853C2#2028354711yescharacteristic
854C2#2028356511yescharacteristic
855C2#2028398311yescharacteristic
856C2#2028401911yescharacteristic
857C2#2028489911yescharacteristic
858C2#2028495811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#518C2
socleC23×C53C22×D4
prime radicalC2×#16810757C2
cosocleC22×C4×C53C24
hypercenterC2×#518D53
hypocenterC53#21458
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×C4×#11719922C2semidirect
4. #20277408C2semidirect
5. #20275063C2semidirect
6. #20275063C2semidirect
7. #20275037C2semidirect
8. #20274976C2semidirect
9. #20274962C2semidirect
10. #20274914C2semidirect
11. #20274646C2semidirect
12. #20274540C2semidirect
13. C4×#13133138C2semidirect
14. #20274481C2semidirect
15. C2×C53×#518C2semidirect
19. C2×C4×D212C22semidirect
20. #16810757C4semidirect
23. C2×#13133150C22semidirect
24. C2×#13133148C22semidirect
31. C2×#13133137C22semidirect
32. C2×#13133137C22semidirect
35. C2×#13133128C22semidirect
36. C2×C4×#88322C22semidirect
37. #16810525C22semidirect
39. #16810521C22semidirect
44. C4×C4⋊Dic53C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810378C22semidirect
50. #16810378C22semidirect
71. C2×#11719922C2×C4semidirect
72. C2×#11719922C2×C4semidirect
78. #13133191C2×C4semidirect
97. #13133138C2×C4semidirect
98. #13133138C2×C4semidirect
102. C22⋊#88322C2×C4semidirect
115. C22×D4×C53C2×C4semidirect
131. C4×D4×C53D4semidirect
132. C4×D4×C53D4semidirect
419. C2×#518D53semidirect
493. C53#21458semidirect
503. C22×D4C4×D53semidirect
534. C4×D4C22⋊D53semidirect
535. C4×D4C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107572
C2×#168107332
C2×C4×#117199222
#202774082
#202750632
#202750372
#202749762
#202749622
#202749142
#202746462
#202745402
C4×#131331382
#202744812
C2×C53×#5182
#2145853