Finite Group Databasebeta

← #27305586

Subgroups — #27305586

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810499C211yesmaximal, characteristic
3C2×#16810499C211yesmaximal, characteristic
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic, complemented
6C2×#16810470C211yesmaximal, characteristic, complemented
7C2×#95×D53C211yesmaximal, characteristic, complemented
8#20272952C211yesmaximal, characteristic, complemented
9#20272946C211yesmaximal, characteristic, complemented
10#20272946C211yesmaximal, characteristic, complemented
11#20272939C211yesmaximal, characteristic, complemented
12#20272937C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic, complemented
14C4×#13133124C211yesmaximal, characteristic, complemented
15C53×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C2×#13133177—24no—
22C2×#13133177—24no—
23C2×#13133177C418yescomplemented
24C22×#11719919C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34#16810499C418yescomplemented
35#16810499C418yescomplemented
36C22⋊C4×Dic53—24no—
37C4×#11719921—24no—
38#16810470—24no—
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52#95×D53—24no—
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—22no—
64C22×C22⋊D53—22no—
65C22×C22⋊D53C2×C414yes—
66C22×C22⋊D53C2×C414yes—
67C22×C22⋊D53C2×C414yes—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—41no—
73C23×Dic53—41no—
74C23×Dic53C2×C414yescomplemented
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—22no—
87C22×C4×D53—22no—
88C22×C4×D53—22no—
89C22×C4×D53—22no—
90C22×C4×D53—22no—
91C22×C4×D53—22no—
92C22×C4×D53—22no—
93C22×C4×D53—22no—
94C22×C4×D53—41no—
95C22×C4×D53—41no—
96C22×C4×D53—41no—
97C22×C4×D53—41no—
98C22×C4×D53—41no—
99C22×C4×D53—41no—
100C22×C4×D53C2×C414yes—
101C22×C4×D53C2×C414yescomplemented
102C22×C4×D53C2×C414yescomplemented
103#13133177—232no—
104C2×#11719919—22no—
105C2×#11719919—22no—
106C2×#11719919C2×C414yescomplemented
107C2×C22⋊Dic53—22no—
108C2×C22⋊Dic53—22no—
109C2×C22⋊Dic53—41no—
110C2×C22⋊Dic53—41no—
111C2×C22⋊Dic53C2×C414yescomplemented
112C2×C22⋊Dic53C2×C414yescomplemented
113C2×#11719921—22no—
114C2×#11719921—22no—
115C2×#11719921—22no—
116C2×#11719921—22no—
117C2×#11719921C2×C414yes—
118C2×#11719921C2×C414yescomplemented
119C2×#11719921C2×C414yescomplemented
120C2×#11719921D414yes—
121C2×#11719921D414yes—
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53—41no—
131C2×C4×Dic53—41no—
132C2×C4×Dic53—41no—
133C2×C4×Dic53C2×C414yescomplemented
134#13133124—22no—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124—22no—
140#13133124—22no—
141#13133124—41no—
142#13133124C2×C414yescomplemented
143#13133124C2×C414yescomplemented
144#13133124C2×C414yescomplemented
145#13133124C2×C414yescomplemented
146#13133124D414yescomplemented
147C25×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—41no—
159C2×C22⋊C4×C53—41no—
160C2×C22⋊C4×C53C2×C414yescomplemented
161C2×C22⋊C4×C53C2×C414yescomplemented
162C2×C22⋊C4×C53C2×C414yescomplemented
163C2×C42×C53—22no—
164C2×C42×C53—22no—
165C2×C42×C53—41no—
166#95×C53—22no—
167#95×C53—22no—
168#95×C53—41no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53C22×C412yes—
182C24×C53C22×C412yes—
183C24×C53C22×C412yes—
184C24×C53C2411yescharacteristic
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53C22×C412yes—
194C23×D53C22×C412yes—
195C23×D53C22×C412yes—
196C23×D53C2×D412yes—
197C23×D53C2×D412yes—
198C23×D53#4112yes—
199C23×D53#4112yes—
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—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53C22×C412yes—
233C22×C4×C53C22×C412yes—
234C22×C4×C53C22×C412yes—
235C22×C4×C53C22×C412yes—
236C22×C4×C53C22×C412yes—
237C22×C4×C53C22×C412yes—
238C22×C4×C53C2×D412yes—
239C22×C4×C53C2×D412yes—
240C22×C4×C53C2×D412yes—
241C22×C4×C53#4112yes—
242C2×C22⋊D53—28no—
243C2×C22⋊D53—28no—
244C2×C22⋊D53—28no—
245C2×C22⋊D53—28no—
246C2×C22⋊D53—28no—
247C2×C22⋊D53—28no—
248C2×C22⋊D53C42116yescomplemented
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—28no—
284C22×Dic53—28no—
285C22×Dic53—44no—
286C22×Dic53—44no—
287C22×Dic53—44no—
288C22×Dic53—44no—
289C22×Dic53—44no—
290C22×Dic53C22×C412yes—
291C22×Dic53C22×C412yes—
292C22×Dic53C22×C412yes—
293C22×Dic53C22×C412yes—
294C22×Dic53C22×C412yes—
295C22×Dic53C22×C412yes—
296C22×Dic53C22×C412yes—
297C22×Dic53C22×C412yes—
298C22×Dic53C22×C412yes—
299C22×Dic53C2×D412yes—
300C22×Dic53C2×D412yes—
301C22×Dic53C2×D412yes—
302C22×Dic53C2×D412yes—
303C22×Dic53#4112yes—
304C22×Dic53#4112yes—
305C2×C4×D53—28no—
306C2×C4×D53—28no—
307C2×C4×D53—28no—
308C2×C4×D53—28no—
309C2×C4×D53—28no—
310C2×C4×D53—28no—
311C2×C4×D53—44no—
312C2×C4×D53—44no—
313C2×C4×D53—44no—
314C2×C4×D53—44no—
315C2×C4×D53—44no—
316C2×C4×D53—44no—
317C2×C4×D53—44no—
318C2×C4×D53—44no—
319C2×C4×D53—44no—
320C2×C4×D53—44no—
321C2×C4×D53—44no—
322C2×C4×D53—44no—
323C2×C4×D53—44no—
324C2×C4×D53—44no—
325C2×C4×D53—44no—
326C22⋊C4×C53—28no—
327C22⋊C4×C53—28no—
328C22⋊C4×C53—44no—
329C42×C53—44no—
330C22⋊Dic53—28no—
331C22⋊Dic53—44no—
332#11719921—28no—
333#11719921—28no—
334#11719921C22⋊C4116yescomplemented
335#11719919—28no—
336C4×Dic53—28no—
337C4×Dic53—44no—
338C4×Dic53—44no—
339C4×Dic53—44no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53C2×C4214yes—
375C23×C53C23×C411yescharacteristic
376C23×C53C23×C411yescharacteristic
377C23×C53C23×C411yescharacteristic
378C23×C53C22×D411yescharacteristic
379C23×C53C22×D411yescharacteristic
380C23×C53C22×D411yescharacteristic
381C23×C53C2×#4111yescharacteristic
382C23×C53C2×#4111yescharacteristic
383C23×C53C2×#4111yescharacteristic
384C23×C53C2×#4111yescharacteristic
385C23×C53C2×#4111yescharacteristic
386C23×C53H(5,𝔽2)11yescharacteristic
387C23×C53H(5,𝔽2)11yescharacteristic
388C23×C53H(5,𝔽2)11yescharacteristic
389C23×C532−1+411yescharacteristic
390C22×D53—22no—
391C22×D53—22no—
392C22×D53—22no—
393C22×D53—22no—
394C22×D53—22no—
395C22×D53—22no—
396C22×D53—22no—
397C22×D53—22no—
398C22×D53—22no—
399C22×D53—22no—
400C22×D53—22no—
401C22×D53—22no—
402C22×D53—22no—
403C22×D53—22no—
404C22×D53—22no—
405C22×D53—22no—
406C22×D53—22no—
407C22×D53—22no—
408C22×D53—22no—
409C22×D53—22no—
410C22×D53—22no—
411C22×D53—22no—
412C22×D53—22no—
413C22×D53—22no—
414C22×D53—22no—
415C22×D53—22no—
416C22×D53—22no—
417C22×D53—22no—
418C22×D53C2×C4214yes—
419C22×D53C2×C22⋊C414yes—
420C22×D53#11714yes—
421C22×D53C4×D414yes—
422C22×D53C4×D414yes—
423C22×D53C4×D414yes—
424C22×D53C4×D414yes—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—22no—
448C2×C4×C53—22no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—41no—
465C2×C4×C53C2×C22⋊C414yes—
466C2×C4×C53C4×D414yescomplemented
467C22⋊D53—232no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—22no—
472C2×Dic53—22no—
473C2×Dic53—22no—
474C2×Dic53—22no—
475C2×Dic53—22no—
476C2×Dic53—22no—
477C2×Dic53—22no—
478C2×Dic53—22no—
479C2×Dic53—22no—
480C2×Dic53—22no—
481C2×Dic53—22no—
482C2×Dic53—22no—
483C2×Dic53—22no—
484C2×Dic53—22no—
485C2×Dic53—22no—
486C2×Dic53—22no—
487C2×Dic53—22no—
488C2×Dic53—22no—
489C2×Dic53—22no—
490C2×Dic53—22no—
491C2×Dic53—22no—
492C2×Dic53—22no—
493C2×Dic53—22no—
494C2×Dic53—22no—
495C2×Dic53—22no—
496C2×Dic53—22no—
497C2×Dic53—22no—
498C2×Dic53—22no—
499C2×Dic53—22no—
500C2×Dic53—22no—
501C2×Dic53—416no—
502C2×Dic53—41no—
503C2×Dic53—41no—
504C2×Dic53—41no—
505C2×Dic53—41no—
506C2×Dic53—41no—
507C2×Dic53—41no—
508C2×Dic53—41no—
509C2×Dic53—41no—
510C2×Dic53—41no—
511C2×Dic53—41no—
512C2×Dic53—41no—
513C2×Dic53—41no—
514C2×Dic53C2×C4214yes—
515C2×Dic53C2×C22⋊C414yes—
516C2×Dic53C4×D414yes—
517C2×Dic53C4×D414yescomplemented
518C4×D53—416no—
519C4×D53—416no—
520C4×D53—416no—
521#13813—531nomaximal, Sylow
522C22×C53—24no—
523C22×C53—24no—
524C22×C53—24no—
525C22×C53—42no—
526C22×C53—42no—
527C22×C53—42no—
528C22×C53—42no—
529C22×C53—42no—
530C22×C53—42no—
531C22×C53—42no—
532C22×C53—42no—
533C22×C53—42no—
534C22×C53—42no—
535C22×C53—42no—
536C22×C53—42no—
537C22×C53C22×C4211yescharacteristic
538C22×C53C22×C22⋊C411yescharacteristic
539C22×C53C2×#11711yescharacteristic
540C22×C53C2×C4×D411yescharacteristic
541C22×C53C2×C4×D411yescharacteristic
542C22×C53C2×C4×D411yescharacteristic
543C22×C53C2×C4×D411yescharacteristic
544C22×C53C2×C4×D411yescharacteristic
545C22×C53C2×C4×D411yescharacteristic
546C22×C53C2×C4×D411yescharacteristic
547C22×C53C4×#4111yescharacteristic
548C22×C53C4×#4111yescharacteristic
549C22×C53C4×#4111yescharacteristic
550C22×C53#51811yescharacteristic
551C22×C53#51811yescharacteristic
552C22×C53#51811yescharacteristic
553C22×C53#52011yescharacteristic
554C22×C53#52011yescharacteristic
555C22×C53#52011yescharacteristic
556C22×C53D4211yescharacteristic
557C22×C53D4211yescharacteristic
558C22×C53#54611yescharacteristic
559C22×C53#54611yescharacteristic
560C22×C53#54611yescharacteristic
561C22×C53#54611yescharacteristic
562C22×C53#54611yescharacteristic
563C22×C53#54711yescharacteristic
564C22×C53#54711yescharacteristic
565C22×C53#54811yescharacteristic
566C22×C53#55111yescharacteristic
567C22×C53#55111yescharacteristic
568C22×C53#55211yescharacteristic
569C22×C53#55311yescharacteristic
570C22×C53#55311yescharacteristic
571C22×C53#55311yescharacteristic
572C2×D53—24no—
573C2×D53—24no—
574C2×D53—24no—
575C2×D53—24no—
576C2×D53—24no—
577C2×D53—24no—
578C2×D53—24no—
579C2×D53—24no—
580C2×D53—24no—
581C2×D53—24no—
582C2×D53—24no—
583C2×D53—24no—
584C2×D53—24no—
585C2×D53—24no—
586C2×D53C4×C22⋊C418yescomplemented
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—42no—
590C4×C53—42no—
591C4×C53—42no—
592C4×C53—42no—
593Dic53—24no—
594Dic53—24no—
595Dic53—24no—
596Dic53—24no—
597Dic53—42no—
598Dic53—42no—
599Dic53—42no—
600C22×C4×D4—531no—
601C2×#386—531no—
602C2×#386—531no—
603C2×C4×C22⋊C4—531no—
604C2×C4×C22⋊C4—531no—
605C2×C4×C22⋊C4—531no—
606C22×#95—531no—
607#1437—531no—
608#1437D5311yescharacteristic, complemented
609#1436—531no—
610#1436—531no—
611#1434—531no—
612C22⋊#95—531no—
613C22⋊#95—531no—
614C4×#95—531no—
615C2×C53—44no—
616C2×C53C2×C4×C22⋊C411yescharacteristic
617C2×C53C42×D411yescharacteristic
618C2×C53#227511yescharacteristic
619C2×C53D4×C22⋊C411yescharacteristic
620C2×C53#233911yescharacteristic
621C2×C53#235211yescharacteristic
622C2×C53#235311yescharacteristic
623C2×C53#235811yescharacteristic
624C2×C53#235811yescharacteristic
625C2×C53#235911yescharacteristic
626C2×C53#235911yescharacteristic
627C2×C53#236111yescharacteristic
628C2×C53#236111yescharacteristic
629C2×C53#236411yescharacteristic
630C2×C53#236411yescharacteristic
631D53—28no—
632C23×D4—531no—
633C24×C4—531no—
634C24×C4—531no—
635C24×C4—531no—
636C24×C4—531no—
637C2×C4×D4—538no—
638C2×C4×D4—1064no—
639C2×C4×D4—1064no—
640C22×C4⋊C4—531no—
641C22×C22⋊C4—531no—
642C22×C22⋊C4—531no—
643C22×C22⋊C4—531no—
644C22×C22⋊C4—531no—
645C22×C22⋊C4—531no—
646C22×C22⋊C4C2×D5311yescharacteristic
647C22×C22⋊C4C2×D5311yescharacteristic
648C22×C22⋊C4C2×D5311yescharacteristic
649C22×C42—531no—
650C22×C42—531no—
651C22×C42—531no—
652C22×C42—531no—
653C22×C42C2×D5311yescharacteristic
654#386—538no—
655#386—538no—
656C4×C22⋊C4—1064no—
657C4×C22⋊C4—1064no—
658C4×C22⋊C4—1064no—
659C2×#95—531no—
660C2×#95—531no—
661C2×#95—531no—
662C2×#95—531no—
663C2×#95—531no—
664C2×#95—531no—
665C2×#95—531no—
666C2×#95—531no—
667C2×#95—531no—
668C2×#95—531no—
669C2×#95—531no—
670C2×#95—531no—
671C2×#95—531no—
672C2×#95—1064no—
673C2×#95C2×D5311yescharacteristic
674C2×#95C2×D5311yescharacteristic
675C2×#95C2×D5311yescharacteristic
676C53#1381311yescharacteristic, complemented, Sylow
677C25—531no—
678C25C22×D5311yescharacteristic
679C22×D4—534no—
680C22×D4—534no—
681C22×D4—534no—
682C22×D4—1062no—
683C22×D4—1062no—
684C22×D4—1062no—
685C22×D4—1062no—
686C23×C4—531no—
687C23×C4—531no—
688C23×C4—531no—
689C23×C4—531no—
690C23×C4—531no—
691C23×C4—531no—
692C23×C4—531no—
693C23×C4—534no—
694C23×C4—534no—
695C23×C4—534no—
696C23×C4—534no—
697C23×C4—1062no—
698C23×C4—1062no—
699C23×C4—1062no—
700C23×C4—1062no—
701C23×C4—1062no—
702C23×C4—1062no—
703C23×C4—1062no—
704C23×C4—1062no—
705C23×C4—1062no—
706C23×C4—1062no—
707C23×C4—1062no—
708C23×C4—1062no—
709C23×C4—1062no—
710C23×C4—1062no—
711C23×C4—1062no—
712C23×C4—1062no—
713C23×C4—2121no—
714C23×C4—2121no—
715C23×C4—2121no—
716C23×C4—2121no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4—2121no—
721C23×C4C22×D5311yescharacteristic
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C4×D4—10632no—
728C2×C4⋊C4—534no—
729C2×C4⋊C4—1062no—
730C2×C4⋊C4—1062no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—534no—
738C2×C22⋊C4—534no—
739C2×C22⋊C4—534no—
740C2×C22⋊C4—534no—
741C2×C22⋊C4—534no—
742C2×C22⋊C4—534no—
743C2×C22⋊C4—534no—
744C2×C22⋊C4—1062no—
745C2×C22⋊C4—1062no—
746C2×C22⋊C4—1062no—
747C2×C22⋊C4—1062no—
748C2×C22⋊C4—1062no—
749C2×C22⋊C4—1062no—
750C2×C22⋊C4—2121no—
751C2×C22⋊C4—2121no—
752C2×C22⋊C4C4×D5314yescomplemented
753C2×C22⋊C4C4×D5314yescomplemented
754C2×C22⋊C4C4×D5314yescomplemented
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—41no—
758C2×C42—534no—
759C2×C42—1062no—
760C2×C42—1062no—
761C2×C42—1062no—
762C2×C42—1062no—
763C2×C42—1062no—
764C2×C42—1062no—
765C2×C42—1062no—
766C2×C42—1062no—
767C2×C42—2121no—
768C2×C42—2121no—
769C2×C42—2121no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—534no—
774#95—534no—
775#95—534no—
776#95—534no—
777#95—534no—
778#95—1062no—
779#95—1062no—
780#95—1062no—
781#95—1062no—
782#95—1062no—
783#95—1062no—
784#95—1062no—
785#95—2121no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—532no—
799C24—532no—
800C24—532no—
801C24—532no—
802C24—532no—
803C24—532no—
804C24—532no—
805C24—1061no—
806C24—1061no—
807C24—1061no—
808C24—1061no—
809C24—1061no—
810C24—1061no—
811C24—1061no—
812C24—1061no—
813C24C2×C4×D5312yes—
814C24C2×C4×D5312yes—
815C24C2×C4×D5312yes—
816C24C23×D5311yescharacteristic
817C2×D4—5316no—
818C2×D4—1068no—
819C2×D4—1068no—
820C2×D4—1068no—
821C2×D4—1068no—
822C2×D4—1068no—
823C2×D4—1068no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—532no—
857C22×C4—532no—
858C22×C4—532no—
859C22×C4—532no—
860C22×C4—532no—
861C22×C4—532no—
862C22×C4—532no—
863C22×C4—532no—
864C22×C4—532no—
865C22×C4—532no—
866C22×C4—532no—
867C22×C4—532no—
868C22×C4—532no—
869C22×C4—532no—
870C22×C4—532no—
871C22×C4—1068no—
872C22×C4—1068no—
873C22×C4—1068no—
874C22×C4—1068no—
875C22×C4—1068no—
876C22×C4—1068no—
877C22×C4—1068no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—1061no—
890C22×C4—1061no—
891C22×C4—1061no—
892C22×C4—1061no—
893C22×C4—1061no—
894C22×C4—1061no—
895C22×C4—1061no—
896C22×C4—1061no—
897C22×C4—1061no—
898C22×C4—1061no—
899C22×C4—1061no—
900C22×C4—1061no—
901C22×C4—1061no—
902C22×C4—1061no—
903C22×C4—1061no—
904C22×C4—1061no—
905C22×C4—1061no—
906C22×C4—1061no—
907C22×C4—1061no—
908C22×C4—1061no—
909C22×C4—1061no—
910C22×C4—1061no—
911C22×C4—1061no—
912C22×C4—1068no—
913C22×C4—2124no—
914C22×C4—2124no—
915C22×C4—2124no—
916C22×C4—2124no—
917C22×C4—2124no—
918C22×C4—2124no—
919C22×C4—2124no—
920C22×C4—2124no—
921C22×C4—2124no—
922C22×C4—2124no—
923C22×C4—2124no—
924C22×C4—2124no—
925C22×C4—2124no—
926C22×C4—2124no—
927C22×C4—2124no—
928C22×C4—2124no—
929C22×C4—2124no—
930C22×C4—2124no—
931C22×C4—2124no—
932C22×C4—2124no—
933C22×C4C2×C4×D5312yes—
934C22×C4C2×C4×D5312yes—
935C22×C4C2×C4×D5312yes—
936C22×C4C2×C4×D5312yes—
937C22×C4C2×C4×D5312yes—
938C22×C4C2×C4×D5312yes—
939C22×C4D4×D5312yes—
940C22×C4D4×D5312yes—
941C22×C4D4×D5312yes—
942C22×C4#1171994712yes—
943C4⋊C4—1068no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—5316no—
948C22⋊C4—1068no—
949C22⋊C4—1068no—
950C22⋊C4—1068no—
951C22⋊C4—2124no—
952C42—44no—
953C42—1068no—
954C42—2124no—
955C42—2124no—
956C42—2124no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—534no—
992C23—534no—
993C23—534no—
994C23—534no—
995C23—534no—
996C23—534no—
997C23—534no—
998C23—1062no—
999C23—1062no—
1000C23—1062no—
1001C23—1062no—
1002C23—1062no—
1003C23—1062no—
1004C23—1062no—
1005C23—1062no—
1006C23—1062no—
1007C23—1062no—
1008C23—1062no—
1009C23—1062no—
1010C23—1062no—
1011C23—1062no—
1012C23—1062no—
1013C23—1062no—
1014C23—1062no—
1015C23—1062no—
1016C23—1062no—
1017C23—1062no—
1018C23—1062no—
1019C23—1062no—
1020C23—1062no—
1021C23—1062no—
1022C23—1062no—
1023C23—1062no—
1024C23—1062no—
1025C23—1062no—
1026C23C42×D5314yes—
1027C23C22×C4×D5311yescharacteristic
1028C23C22×C4×D5311yescharacteristic
1029C23C22×C4×D5311yescharacteristic
1030C23C2×D4×D5311yescharacteristic
1031C23C2×D4×D5311yescharacteristic
1032C23C2×D4×D5311yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23#41×D5311yescharacteristic
1036C23#41×D5311yescharacteristic
1037C23C2×#1171994711yescharacteristic
1038C23#1313326211yescharacteristic
1039C23#1313326211yescharacteristic
1040C23#1313326311yescharacteristic
1041C23#1313326411yescharacteristic
1042D4—10632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—534no—
1084C2×C4—534no—
1085C2×C4—534no—
1086C2×C4—534no—
1087C2×C4—1062no—
1088C2×C4—1062no—
1089C2×C4—1062no—
1090C2×C4—1062no—
1091C2×C4—1062no—
1092C2×C4—1062no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1062no—
1096C2×C4—1062no—
1097C2×C4—1062no—
1098C2×C4—1062no—
1099C2×C4—1062no—
1100C2×C4—1062no—
1101C2×C4—1062no—
1102C2×C4—1062no—
1103C2×C4—1062no—
1104C2×C4—1062no—
1105C2×C4—1062no—
1106C2×C4—1062no—
1107C2×C4—1062no—
1108C2×C4—1062no—
1109C2×C4—1062no—
1110C2×C4—1062no—
1111C2×C4—1062no—
1112C2×C4—1062no—
1113C2×C4—1062no—
1114C2×C4—1062no—
1115C2×C4—1062no—
1116C2×C4—1062no—
1117C2×C4—1062no—
1118C2×C4—1062no—
1119C2×C4—1062no—
1120C2×C4—21216no—
1121C2×C4—21216no—
1122C2×C4—21216no—
1123C2×C4—21216no—
1124C2×C4—2121no—
1125C2×C4—2121no—
1126C2×C4—2121no—
1127C2×C4—2121no—
1128C2×C4—2121no—
1129C2×C4—2121no—
1130C2×C4—2121no—
1131C2×C4—2121no—
1132C2×C4—2121no—
1133C2×C4—2121no—
1134C2×C4—2121no—
1135C2×C4—2121no—
1136C2×C4C22⋊C4×D5314yes—
1137C2×C4#1313317714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—538no—
1154C22—1064no—
1155C22—1064no—
1156C22—1064no—
1157C22—1064no—
1158C22—1064no—
1159C22—1064no—
1160C22—1064no—
1161C22—1064no—
1162C22—1064no—
1163C22—1064no—
1164C22—1064no—
1165C22—1064no—
1166C22—1064no—
1167C22—1064no—
1168C22C2×C42×D5311yescharacteristic
1169C22C2×C22⋊C4×D5311yescharacteristic
1170C22#117×D5311yescharacteristic
1171C22C4×D4×D5311yescharacteristic
1172C22C4×D4×D5311yescharacteristic
1173C22C4×D4×D5311yescharacteristic
1174C22C4×D4×D5311yescharacteristic
1175C22C4×D4×D5311yescharacteristic
1176C22C4×D4×D5311yescharacteristic
1177C22C2×#1313317711yescharacteristic
1178C22C4×#1171994711yescharacteristic
1179C22C4×#1171994711yescharacteristic
1180C22#1681109111yescharacteristic
1181C22#1681109511yescharacteristic
1182C22#1681109511yescharacteristic
1183C22#1681109611yescharacteristic
1184C22#1681110211yescharacteristic
1185C22#1681110211yescharacteristic
1186C22#1681110311yescharacteristic
1187C22#1681125711yescharacteristic
1188C22#1681125811yescharacteristic
1189C22#1681126011yescharacteristic
1190C22#1681126211yescharacteristic
1191C22#1681126211yescharacteristic
1192C22#1681126611yescharacteristic
1193C22#1681127011yescharacteristic
1194C22#1681127111yescharacteristic
1195C22#1681127311yescharacteristic
1196C22#1681128111yescharacteristic
1197C22#1681129611yescharacteristic
1198C22#1681130311yescharacteristic
1199C22#1681130911yescharacteristic
1200C22#1681131811yescharacteristic
1201C22#1681132011yescharacteristic
1202C22#1681132411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—1064no—
1210C4—1064no—
1211C4—1064no—
1212C4—1064no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—44no—
1217C2—1068no—
1218C2C4×C22⋊C4×D5311yescharacteristic
1219C2C4×#1313317711yescharacteristic
1220C2#2027707411yescharacteristic
1221C2#2027753611yescharacteristic
1222C2#2027754111yescharacteristic
1223C2#2027764311yescharacteristic
1224C2#2027765011yescharacteristic
1225C2#2027769511yescharacteristic
1226C2#2027769611yescharacteristic
1227C2#2027770411yescharacteristic
1228C2#2027770611yescharacteristic
1229C2#2027772811yescharacteristic
1230C2#2027773611yescharacteristic
1231C2#2027775911yescharacteristic
1232C2#2027776411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53#13813
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic53C2semidirect
5. C2×C4×#11719921C2semidirect
6. C2×#16810470C2semidirect
7. C2×#95×D53C2semidirect
8. #20272952C2semidirect
9. #20272946C2semidirect
10. #20272946C2semidirect
11. #20272939C2semidirect
12. #20272937C2semidirect
13. #20272936C2semidirect
14. C4×#13133124C2semidirect
15. C53×#1437C2semidirect
23. C2×#13133177C4semidirect
34. #16810499C4semidirect
35. #16810499C4semidirect
74. C23×Dic53C2×C4semidirect
101. C22×C4×D53C2×C4semidirect
102. C22×C4×D53C2×C4semidirect
106. C2×#11719919C2×C4semidirect
111. C2×C22⋊Dic53C2×C4semidirect
112. C2×C22⋊Dic53C2×C4semidirect
118. C2×#11719921C2×C4semidirect
119. C2×#11719921C2×C4semidirect
133. C2×C4×Dic53C2×C4semidirect
142. #13133124C2×C4semidirect
143. #13133124C2×C4semidirect
144. #13133124C2×C4semidirect
145. #13133124C2×C4semidirect
146. #13133124D4semidirect
160. C2×C22⋊C4×C53C2×C4semidirect
161. C2×C22⋊C4×C53C2×C4semidirect
162. C2×C22⋊C4×C53C2×C4semidirect
248. C2×C22⋊D53C42semidirect
334. #11719921C22⋊C4semidirect
466. C2×C4×C53C4×D4semidirect
517. C2×Dic53C4×D4semidirect
586. C2×D53C4×C22⋊C4semidirect
608. #1437D53semidirect
676. C53#13813semidirect
752. C2×C22⋊C4C4×D53semidirect
753. C2×C22⋊C4C4×D53semidirect
754. C2×C22⋊C4C4×D53semidirect
1137. C2×C4#13133177semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168104992
C2×C22⋊C4×Dic532
C2×C4×#117199212
C2×#168104702
C2×#95×D532
#202729522
#202729462
#202729392
#202729372
#202729362
C4×#131331242
C53×#14372
#1381353