Finite Group Databasebeta

← #27305590

Subgroups — #27305590

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×#16810502C211yesmaximal, characteristic
3C2×#16810500C211yesmaximal, characteristic
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272953C211yesmaximal, characteristic, complemented
8#20272951C211yesmaximal, characteristic, complemented
9#20272950C211yesmaximal, characteristic, complemented
10#20272948C211yesmaximal, characteristic, complemented
11#20272939C211yesmaximal, characteristic, complemented
12#20272937C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic, complemented
14C4×#13133124C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133177—24no—
21C2×#13133177—24no—
22C2×#13133177C418yescomplemented
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810502C418yescomplemented
34#16810500C418yescomplemented
35C22⋊C4×Dic53—24no—
36C4×#11719921—24no—
37C2×#13133124—24no—
38C2×#13133124C2211yescharacteristic
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
52C24×C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C42×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C4×C22⋊C4×C53—24no—
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—22no—
73C23×Dic53—22no—
74C23×Dic53—22no—
75C23×Dic53—22no—
76C23×Dic53—41no—
77C23×Dic53—41no—
78C23×Dic53—41no—
79C23×Dic53—41no—
80C23×Dic53C2×C414yes—
81C23×Dic53C2×C414yescomplemented
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C22×C4×D53—22no—
90C22×C4×D53—22no—
91C22×C4×D53—22no—
92C22×C4×D53—22no—
93C22×C4×D53—41no—
94C22×C4×D53—41no—
95C22×C4×D53C2×C414yescomplemented
96#13133177—232no—
97C2×#11719919—22no—
98C2×#11719919—22no—
99C2×#11719919C2×C414yescomplemented
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53C2×C414yescomplemented
103C2×#11719921—22no—
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—41no—
110C2×#11719921—41no—
111C2×#11719921—41no—
112C2×#11719921—41no—
113C2×#11719921C2×C414yescomplemented
114C2×#11719921C2×C414yescomplemented
115C2×#11719921C2×C414yescomplemented
116C2×#11719921C2×C414yescomplemented
117C2×#11719921C2×C414yescomplemented
118C2×C4×Dic53—22no—
119C2×C4×Dic53—22no—
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—41no—
125C2×C4×Dic53—41no—
126C2×C4×Dic53C2×C414yescomplemented
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—22no—
131#13133124—22no—
132#13133124—22no—
133#13133124—22no—
134#13133124—41no—
135#13133124—41no—
136#13133124C2×C414yescomplemented
137#13133124C2×C414yescomplemented
138#13133124C2×C414yescomplemented
139#13133124C2×C414yescomplemented
140#13133124D414yescomplemented
141C25×C53C2311yescharacteristic
142C23×C4×C53—22no—
143C23×C4×C53—22no—
144C23×C4×C53—22no—
145C23×C4×C53—22no—
146C23×C4×C53—41no—
147C23×C4×C53—41no—
148C23×C4×C53C2×C414yescomplemented
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53C2×C414yes—
158C2×C22⋊C4×C53C2×C414yescomplemented
159C2×C22⋊C4×C53D414yes—
160C2×C22⋊C4×C53D414yes—
161C2×C42×C53—22no—
162C2×C42×C53—22no—
163C2×C42×C53—22no—
164C2×C42×C53—22no—
165C2×C42×C53—41no—
166C2×C42×C53—41no—
167#95×C53—22no—
168#95×C53—22no—
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×C53C22×C412yes—
178C24×C53C22×C412yes—
179C24×C53C22×C412yes—
180C24×C53C2×D412yes—
181C24×C53C2×D412yes—
182C24×C53#4112yes—
183C24×C53#4112yes—
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×D53—21no—
194C23×D53—21no—
195C23×D53—21no—
196C23×D53—21no—
197C23×D53C22×C412yes—
198C23×D53C22×C412yes—
199C23×D53C22×C412yes—
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—28no—
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—28no—
232C22×C4×C53—44no—
233C22×C4×C53—44no—
234C22×C4×C53—44no—
235C22×C4×C53—44no—
236C22×C4×C53—44no—
237C22×C4×C53C22×C412yes—
238C22×C4×C53C22×C412yes—
239C22×C4×C53C22×C412yes—
240C22×C4×C53C22×C412yes—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C2×D412yes—
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×D412yes—
248C22×C4×C53#4112yes—
249C2×C22⋊D53—28no—
250C2×C22⋊D53—28no—
251C2×C22⋊D53—28no—
252C2×C22⋊D53—28no—
253C2×C22⋊D53—28no—
254C2×C22⋊D53—28no—
255C2×C22⋊D53C42116yescomplemented
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—28no—
269C22×Dic53—28no—
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—21no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—21no—
292C22×Dic53—21no—
293C22×Dic53—21no—
294C22×Dic53—28no—
295C22×Dic53—28no—
296C22×Dic53—44no—
297C22×Dic53—44no—
298C22×Dic53—44no—
299C22×Dic53—44no—
300C22×Dic53—44no—
301C22×Dic53—44no—
302C22×Dic53—44no—
303C22×Dic53—44no—
304C22×Dic53—44no—
305C22×Dic53—44no—
306C22×Dic53C22×C412yes—
307C22×Dic53C22×C412yes—
308C22×Dic53C22×C412yes—
309C22×Dic53C22×C412yes—
310C22×Dic53C22×C412yes—
311C22×Dic53C22×C412yes—
312C22×Dic53C22×C412yes—
313C22×Dic53C22×C412yes—
314C22×Dic53C22×C412yes—
315C22×Dic53C2×D412yes—
316C22×Dic53C2×D412yes—
317C22×Dic53#4112yes—
318C22×Dic53#4112yes—
319C2×C4×D53—28no—
320C2×C4×D53—28no—
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×C53C22⋊C4116yescomplemented
328C42×C53—44no—
329C42×C53—44no—
330C22⋊Dic53—28no—
331#11719921—28no—
332#11719921—28no—
333#11719921—28no—
334#11719921—44no—
335#11719921—44no—
336#11719919—28no—
337C4×Dic53—28no—
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—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53C2×C4214yes—
369C23×C53C2×C22⋊C414yes—
370C23×C53#11714yes—
371C23×C53C4×D414yes—
372C23×C53C4×D414yes—
373C23×C53C4×D414yes—
374C23×C53C4×D414yes—
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—41no—
409C22×D53—41no—
410C22×D53—41no—
411C22×D53—41no—
412C22×D53—41no—
413C22×D53—41no—
414C22×D53—41no—
415C22×D53—41no—
416C22×D53—41no—
417C22×D53—41no—
418C22×D53—41no—
419C22×D53—41no—
420C22×D53—41no—
421C22×D53—41no—
422C22×D53—41no—
423C22×D53—41no—
424C22×D53C2×C4214yes—
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—22no—
450C2×C4×C53—22no—
451C2×C4×C53—22no—
452C2×C4×C53—416no—
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×C53C2×C22⋊C414yes—
467C2×C4×C53C4×D414yescomplemented
468C22⋊D53—232no—
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—416no—
500C2×Dic53—416no—
501C2×Dic53—41no—
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×Dic53—41no—
515C2×Dic53—41no—
516C2×Dic53—41no—
517C2×Dic53C2×C4214yes—
518C2×Dic53C4×D414yes—
519C2×Dic53C4×D414yescomplemented
520C4×D53—416no—
521#13813—531nomaximal, Sylow
522C22×C53—24no—
523C22×C53—24no—
524C22×C53—24no—
525C22×C53—24no—
526C22×C53—24no—
527C22×C53—24no—
528C22×C53—24no—
529C22×C53—24no—
530C22×C53—24no—
531C22×C53—24no—
532C22×C53—24no—
533C22×C53—24no—
534C22×C53—24no—
535C22×C53—24no—
536C22×C53C4×C22⋊C418yescomplemented
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—42no—
576C2×D53—42no—
577C2×D53—42no—
578C2×D53—42no—
579C2×D53—42no—
580C2×D53—42no—
581C2×D53—42no—
582C2×D53—42no—
583C2×D53—42no—
584C2×D53—42no—
585C2×D53—42no—
586C2×D53—42no—
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—24no—
590C4×C53—42no—
591C4×C53—42no—
592C4×C53—42no—
593Dic53—24no—
594Dic53—24no—
595Dic53—24no—
596Dic53—42no—
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⋊C4D5311yescharacteristic, complemented
606C22×#95—531no—
607#1437—531no—
608#1437—531no—
609#1436—531no—
610#1436—531no—
611#1434—531no—
612C22⋊#95—531no—
613C22⋊#95—531no—
614C4×#95—531no—
615C2×C53—28no—
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—44no—
632C23×D4—531no—
633C24×C4—531no—
634C24×C4—531no—
635C24×C4—531no—
636C24×C4C2×D5311yescharacteristic
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⋊C4—531no—
647C22×C22⋊C4C2×D5311yescharacteristic
648C22×C22⋊C4C2×D5311yescharacteristic
649C22×C42—531no—
650C22×C42—531no—
651C22×C42—531no—
652C22×C42C2×D5311yescharacteristic
653C22×C42C2×D5311yescharacteristic
654#386—538no—
655#386—538no—
656C4×C22⋊C4—24no—
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—531no—
673C2×#95—1064no—
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—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—531no—
693C23×C4—531no—
694C23×C4—531no—
695C23×C4—531no—
696C23×C4—531no—
697C23×C4—531no—
698C23×C4—531no—
699C23×C4—534no—
700C23×C4—534no—
701C23×C4—534no—
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—1062no—
714C23×C4—2121no—
715C23×C4—2121no—
716C23×C4—2121no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4C4×D5314yescomplemented
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—534no—
734C2×C22⋊C4—534no—
735C2×C22⋊C4—534no—
736C2×C22⋊C4—534no—
737C2×C22⋊C4—534no—
738C2×C22⋊C4—534no—
739C2×C22⋊C4—1062no—
740C2×C22⋊C4—1062no—
741C2×C22⋊C4—1062no—
742C2×C22⋊C4—1062no—
743C2×C22⋊C4—1062no—
744C2×C22⋊C4—1062no—
745C2×C22⋊C4—1062no—
746C2×C22⋊C4—1062no—
747C2×C22⋊C4—2121no—
748C2×C22⋊C4—2121no—
749C2×C22⋊C4—2121no—
750C2×C22⋊C4—2121no—
751C2×C22⋊C4C4×D5314yes—
752C2×C22⋊C4C4×D5314yescomplemented
753C2×C22⋊C4D21214yes—
754C2×C22⋊C4C22⋊D5314yes—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42—534no—
762C2×C42—1062no—
763C2×C42—1062no—
764C2×C42—1062no—
765C2×C42—1062no—
766C2×C42—1062no—
767C2×C42—1062no—
768C2×C42—2121no—
769C2×C42—2121no—
770#95—22no—
771#95—22no—
772#95—534no—
773#95—534no—
774#95—534no—
775#95—534no—
776#95—534no—
777#95—1062no—
778#95—1062no—
779#95—1062no—
780#95—1062no—
781#95—1062no—
782#95—1062no—
783#95—1062no—
784#95—2121no—
785#95—2121no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—532no—
795C24—532no—
796C24—532no—
797C24—1061no—
798C24—1061no—
799C24—1061no—
800C24—1061no—
801C24—1061no—
802C24—1061no—
803C24—1061no—
804C24—1061no—
805C24—1061no—
806C24—1061no—
807C24—1061no—
808C24—1061no—
809C24C2×C4×D5312yes—
810C24C2×C4×D5312yes—
811C24C2×C4×D5312yes—
812C24C2×D21212yes—
813C24#1171994512yes—
814C24#1171994512yes—
815C24C2×C22⋊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—28no—
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—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
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—532no—
872C22×C4—532no—
873C22×C4—532no—
874C22×C4—1068no—
875C22×C4—1068no—
876C22×C4—1068no—
877C22×C4—1061no—
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—1068no—
890C22×C4—1068no—
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—1061no—
913C22×C4—1061no—
914C22×C4—1061no—
915C22×C4—1068no—
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×C4C2×C4×D5312yes—
932C22×C4C2×C4×D5312yes—
933C22×C4C2×C4×D5312yes—
934C22×C4C2×C4×D5312yes—
935C22×C4C2×C4×D5312yes—
936C22×C4C2×C4×D5312yes—
937C22×C4C2×D21212yes—
938C22×C4C2×D21212yes—
939C22×C4D4×D5312yes—
940C22×C4#1171994712yes—
941C22×C4C2×C22⋊D5312yes—
942C22×C4C2×C22⋊D5312yes—
943C4⋊C4—1068no—
944C22⋊C4—28no—
945C22⋊C4—1068no—
946C22⋊C4—1068no—
947C22⋊C4—1068no—
948C22⋊C4—1068no—
949C22⋊C4—2124no—
950C22⋊C4—2124no—
951C22⋊C4#11719921116yescomplemented
952C42—44no—
953C42—44no—
954C42—1068no—
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—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—534no—
986C23—1062no—
987C23—1062no—
988C23—1062no—
989C23—1062no—
990C23—1062no—
991C23—1062no—
992C23—1062no—
993C23—1062no—
994C23—1062no—
995C23—1062no—
996C23—1062no—
997C23—1062no—
998C23—1062no—
999C23—1062no—
1000C23—1062no—
1001C23—1062no—
1002C23—1062no—
1003C23—1062no—
1004C23—2121no—
1005C23—2121no—
1006C23—2121no—
1007C23—2121no—
1008C23—2121no—
1009C23—2121no—
1010C23—2121no—
1011C23—2121no—
1012C23—2121no—
1013C23—2121no—
1014C23—2121no—
1015C23—2121no—
1016C23—2121no—
1017C23—2121no—
1018C23—2121no—
1019C23—2121no—
1020C23C42×D5314yes—
1021C23C2×#1171992114yes—
1022C23#1313317414yes—
1023C23C4×C22⋊D5314yes—
1024C23C4×C22⋊D5314yes—
1025C23C4×D21214yes—
1026C23C4×D21214yes—
1027C23C22×C4×D5311yescharacteristic
1028C23C22×C4×D5311yescharacteristic
1029C23C22×C4×D5311yescharacteristic
1030C23C2×D4×D5311yescharacteristic
1031C23C22×C22⋊D5311yescharacteristic
1032C23C22×D21211yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23C2×#1171994711yescharacteristic
1036C23C2×#1171994511yescharacteristic
1037C23C2×#1171994511yescharacteristic
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—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
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—1062no—
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—21216no—
1117C2×C4—21216no—
1118C2×C4—21216no—
1119C2×C4—2121no—
1120C2×C4—2121no—
1121C2×C4—2121no—
1122C2×C4—2121no—
1123C2×C4—2121no—
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×C4C2×#1171992114yes—
1136C2×C4C2×#1171992114yes—
1137C2×C4#1313317714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—1064no—
1153C22—1064no—
1154C22—1064no—
1155C22—2122no—
1156C22—2122no—
1157C22—2122no—
1158C22—2122no—
1159C22—2122no—
1160C22—2122no—
1161C22—2122no—
1162C22—2122no—
1163C22—2122no—
1164C22—2122no—
1165C22—2122no—
1166C22—2122no—
1167C22C4×#1171992118yescomplemented
1168C22C2×C42×D5311yescharacteristic
1169C22C22×#1171992111yescharacteristic
1170C22C2×#1313317411yescharacteristic
1171C22C4×D4×D5311yescharacteristic
1172C22C4×D4×D5311yescharacteristic
1173C22C2×#1313317711yescharacteristic
1174C22C2×C4×C22⋊D5311yescharacteristic
1175C22C2×C4×C22⋊D5311yescharacteristic
1176C22C2×C4×D21211yescharacteristic
1177C22C2×C4×D21211yescharacteristic
1178C22C4×#1171994711yescharacteristic
1179C22C4×#1171994711yescharacteristic
1180C22#1681109111yescharacteristic
1181C22#1681109511yescharacteristic
1182C22#1681109511yescharacteristic
1183C22#1681109611yescharacteristic
1184C22#1681110211yescharacteristic
1185C22#1681110211yescharacteristic
1186C22#1681110311yescharacteristic
1187C22D4×C22⋊D5311yescharacteristic
1188C22D4×D21211yescharacteristic
1189C22#1681126111yescharacteristic
1190C22#1681126311yescharacteristic
1191C22#1681126711yescharacteristic
1192C22#1681126811yescharacteristic
1193C22#1681126811yescharacteristic
1194C22#1681127211yescharacteristic
1195C22#1681127711yescharacteristic
1196C22#1681128211yescharacteristic
1197C22#1681129711yescharacteristic
1198C22#1681129911yescharacteristic
1199C22#1681130611yescharacteristic
1200C22#1681131911yescharacteristic
1201C22#1681132211yescharacteristic
1202C22#1681132211yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—1064no—
1210C4—1064no—
1211C4—1064no—
1212C4—2122no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—28no—
1217C2—2124no—
1218C2C2×C4×#1171992111yescharacteristic
1219C2C4×#1313317711yescharacteristic
1220C2#2027707411yescharacteristic
1221C2D4×#1171992111yescharacteristic
1222C2#2027754011yescharacteristic
1223C2#2027763811yescharacteristic
1224C2#2027764911yescharacteristic
1225C2#2027769411yescharacteristic
1226C2#2027769711yescharacteristic
1227C2#2027770711yescharacteristic
1228C2#2027770911yescharacteristic
1229C2#2027772911yescharacteristic
1230C2#2027773211yescharacteristic
1231C2#2027776011yescharacteristic
1232C2#2027776511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13813
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic53C2semidirect
5. C2×C4×#11719921C2semidirect
6. C22×#13133124C2semidirect
7. #20272953C2semidirect
8. #20272951C2semidirect
9. #20272950C2semidirect
10. #20272948C2semidirect
11. #20272939C2semidirect
12. #20272937C2semidirect
13. #20272936C2semidirect
14. C4×#13133124C2semidirect
15. C2×C4×C22⋊C4×C53C2semidirect
22. C2×#13133177C4semidirect
33. #16810502C4semidirect
34. #16810500C4semidirect
81. C23×Dic53C2×C4semidirect
95. C22×C4×D53C2×C4semidirect
99. C2×#11719919C2×C4semidirect
102. C2×C22⋊Dic53C2×C4semidirect
113. C2×#11719921C2×C4semidirect
114. C2×#11719921C2×C4semidirect
115. C2×#11719921C2×C4semidirect
116. C2×#11719921C2×C4semidirect
117. C2×#11719921C2×C4semidirect
126. C2×C4×Dic53C2×C4semidirect
136. #13133124C2×C4semidirect
137. #13133124C2×C4semidirect
138. #13133124C2×C4semidirect
139. #13133124C2×C4semidirect
140. #13133124D4semidirect
148. C23×C4×C53C2×C4semidirect
158. C2×C22⋊C4×C53C2×C4semidirect
255. C2×C22⋊D53C42semidirect
327. C22⋊C4×C53C22⋊C4semidirect
467. C2×C4×C53C4×D4semidirect
519. C2×Dic53C4×D4semidirect
536. C22×C53C4×C22⋊C4semidirect
605. C2×C4×C22⋊C4D53semidirect
676. C53#13813semidirect
720. C23×C4C4×D53semidirect
752. C2×C22⋊C4C4×D53semidirect
951. C22⋊C4#11719921semidirect
1137. C2×C4#13133177semidirect
1167. C22C4×#11719921semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105022
C2×#168105002
C2×C22⋊C4×Dic532
C2×C4×#117199212
C22×#131331242
#202729532
#202729512
#202729502
#202729482
#202729392
#202729372
#202729362
C4×#131331242
C2×C4×C22⋊C4×C532
#1381353