Finite Group Databasebeta

← #27309750

Subgroups — #27309750

Order 13568.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810539C211yesmaximal, characteristic
2C2×#16810499C211yesmaximal, characteristic
3C2×C4×#11719921C211yesmaximal, characteristic, complemented
4C2×#16810470C211yesmaximal, characteristic, complemented
5#20272963C211yesmaximal, characteristic, complemented
6#20272957C211yesmaximal, characteristic, complemented
7#20272954C211yesmaximal, characteristic
8#20272952C211yesmaximal, characteristic, complemented
9#20272952C211yesmaximal, characteristic, complemented
10#20272952C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272944C211yesmaximal, characteristic, complemented
13#20272942C211yesmaximal, characteristic, complemented
14#20272939C211yesmaximal, characteristic, complemented
15C2×C53×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810539C418yescomplemented
31#16810499—24no—
32C4×#11719921—24no—
33#16810470—24no—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C22×C4⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C42×C53C2211yescharacteristic
53C53×#388—24no—
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C24×D53C2311yescharacteristic
57C22×C22⋊D53—22no—
58C22×C22⋊D53—22no—
59C22×C22⋊D53—41no—
60C22×C22⋊D53—41no—
61C22×C22⋊D53—41no—
62C22×C22⋊D53—41no—
63C22×C22⋊D53C2×C414yes—
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C22×C4×D53—22no—
72C22×C4×D53—22no—
73C22×C4×D53—22no—
74C22×C4×D53—22no—
75C22×C4×D53—41no—
76C22×C4×D53—41no—
77C22×C4×D53D414yes—
78C2×C4⋊Dic53—41no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2×C414yescomplemented
81C2×C22⋊Dic53—22no—
82C2×C22⋊Dic53—22no—
83C2×C22⋊Dic53—22no—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—41no—
87C2×C22⋊Dic53—41no—
88C2×C22⋊Dic53—41no—
89C2×C22⋊Dic53C2×C414yescomplemented
90C2×#11719921—22no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—22no—
97C2×#11719921—22no—
98C2×#11719921—22no—
99C2×#11719921—22no—
100C2×#11719921—22no—
101C2×#11719921—41no—
102C2×#11719921—41no—
103C2×#11719921C2×C414yes—
104C2×#11719921C2×C414yes—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53—22no—
110C2×C4×Dic53—41no—
111C2×C4×Dic53—41no—
112C2×C4×Dic53—41no—
113C2×C4×Dic53—41no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—41no—
123#13133124—41no—
124#13133124—41no—
125#13133124—41no—
126#13133124—41no—
127#13133124C2×C414yescomplemented
128C25×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53—22no—
136C2×C4⋊C4×C53—22no—
137C2×C4⋊C4×C53—41no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—22no—
140C2×C22⋊C4×C53—22no—
141C2×C22⋊C4×C53—22no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—22no—
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—41no—
146C2×C22⋊C4×C53C2×C414yescomplemented
147C2×C42×C53—22no—
148C2×C42×C53—22no—
149C2×C42×C53—22no—
150#95×C53—22no—
151#95×C53D414yescomplemented
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53C22×C412yes—
167C24×C53C2411yescharacteristic
168C23×D53—21no—
169C23×D53—21no—
170C23×D53—21no—
171C23×D53—21no—
172C23×D53—21no—
173C23×D53—21no—
174C23×D53—21no—
175C23×D53—21no—
176C23×D53—21no—
177C23×D53—21no—
178C23×D53—21no—
179C23×D53—21no—
180C23×D53C22×C412yes—
181C23×D53C2×D412yes—
182C23×D53#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—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53C22×C412yes—
217C22×C4×C53C22×C412yes—
218C22×C4×C53C2×D412yes—
219C22×C4×C53C2×D412yes—
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2×D412yes—
222C22×C4×C53#4112yes—
223C22×C4×C53#4112yes—
224C22×C4×C53#4112yes—
225C2×C22⋊D53—28no—
226C2×C22⋊D53—44no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—44no—
229C2×C22⋊D53—44no—
230C2×C22⋊D53—44no—
231C2×C22⋊D53—44no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
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×Dic53C22×C412yes—
274C22×Dic53C22×C412yes—
275C22×Dic53C22×C412yes—
276C22×Dic53C2×D412yes—
277C22×Dic53#4112yes—
278C22×Dic53#4112yes—
279C22×Dic53#4112yes—
280C22×Dic53#4112yes—
281C2×C4×D53—28no—
282C2×C4×D53—28no—
283C2×C4×D53—44no—
284C2×C4×D53—44no—
285C2×C4×D53—44no—
286C2×C4×D53—44no—
287C2×C4×D53—44no—
288C4⋊C4×C53—44no—
289C22⋊C4×C53—28no—
290C22⋊C4×C53—44no—
291C22⋊C4×C53—44no—
292C42×C53—44no—
293C22⋊Dic53—44no—
294C22⋊Dic53—44no—
295C22⋊Dic53—44no—
296#11719921—28no—
297#11719921—28no—
298#11719921—28no—
299#11719921—28no—
300#11719921—44no—
301C4⋊Dic53—44no—
302C4×Dic53—44no—
303C4×Dic53—44no—
304C4×Dic53—44no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53—41no—
324C23×C53—41no—
325C23×C53—41no—
326C23×C53—41no—
327C23×C53—41no—
328C23×C53—41no—
329C23×C53—41no—
330C23×C53—41no—
331C23×C53—41no—
332C23×C53—41no—
333C23×C53—41no—
334C23×C53—41no—
335C23×C53—41no—
336C23×C53—41no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53C23×C411yescharacteristic
341C23×C53C22×D411yescharacteristic
342C23×C53C22×D411yescharacteristic
343C23×C53C2×#4111yescharacteristic
344C23×C53C2×#4111yescharacteristic
345C23×C53C2×#4111yescharacteristic
346C23×C53C2×#4111yescharacteristic
347C23×C53C2×#4111yescharacteristic
348C23×C53C2×#4111yescharacteristic
349C23×C53C2×#4111yescharacteristic
350C23×C53C2×#4111yescharacteristic
351C23×C53H(5,𝔽2)11yescharacteristic
352C23×C53H(5,𝔽2)11yescharacteristic
353C23×C53H(5,𝔽2)11yescharacteristic
354C23×C53H(5,𝔽2)11yescharacteristic
355C22×D53—22no—
356C22×D53—22no—
357C22×D53—22no—
358C22×D53—22no—
359C22×D53—22no—
360C22×D53—22no—
361C22×D53—22no—
362C22×D53—22no—
363C22×D53—22no—
364C22×D53—22no—
365C22×D53—22no—
366C22×D53—22no—
367C22×D53—22no—
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—41no—
374C22×D53—41no—
375C22×D53—41no—
376C22×D53—41no—
377C22×D53—41no—
378C22×D53—41no—
379C22×D53—41no—
380C22×D53—41no—
381C22×D53—41no—
382C22×D53—41no—
383C22×D53—41no—
384C22×D53—41no—
385C22×D53—41no—
386C22×D53—41no—
387C22×D53—41no—
388C22×D53—41no—
389C22×D53C4×D414yes—
390C2×C4×C53—22no—
391C2×C4×C53—22no—
392C2×C4×C53—22no—
393C2×C4×C53—22no—
394C2×C4×C53—22no—
395C2×C4×C53—22no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53C4×D414yes—
431C2×C4×C53#12114yes—
432C22⋊D53—416no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—22no—
436C2×Dic53—22no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
440C2×Dic53—22no—
441C2×Dic53—22no—
442C2×Dic53—22no—
443C2×Dic53—22no—
444C2×Dic53—22no—
445C2×Dic53—22no—
446C2×Dic53—22no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—41no—
455C2×Dic53—41no—
456C2×Dic53—41no—
457C2×Dic53—41no—
458C2×Dic53—41no—
459C2×Dic53—41no—
460C2×Dic53—41no—
461C2×Dic53—41no—
462C2×Dic53—41no—
463C2×Dic53—41no—
464C2×Dic53—41no—
465C2×Dic53—41no—
466C2×Dic53—41no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53#12314yes—
482C4×D53—416no—
483#14199—531nomaximal, Sylow
484C22×C53—42no—
485C22×C53—42no—
486C22×C53—42no—
487C22×C53—42no—
488C22×C53—42no—
489C22×C53—42no—
490C22×C53—42no—
491C22×C53—81no—
492C22×C53—81no—
493C22×C53—81no—
494C22×C53—81no—
495C22×C53—81no—
496C22×C53—81no—
497C22×C53—81no—
498C22×C53—81no—
499C22×C53C2×C4×D411yescharacteristic
500C22×C53C2×C4×D411yescharacteristic
501C22×C53C4×#4111yescharacteristic
502C22×C53C4×#4111yescharacteristic
503C22×C53C4×#4111yescharacteristic
504C22×C53#51811yescharacteristic
505C22×C53#51811yescharacteristic
506C22×C53C2×#12111yescharacteristic
507C22×C53C2×#12311yescharacteristic
508C22×C53#52511yescharacteristic
509C22×C53#52511yescharacteristic
510C22×C53#52911yescharacteristic
511C22×C53#52911yescharacteristic
512C22×C53#52911yescharacteristic
513C22×C53#53211yescharacteristic
514C22×C53#53411yescharacteristic
515C22×C53#53511yescharacteristic
516C22×C53#53811yescharacteristic
517C22×C53#53811yescharacteristic
518C22×C53#54611yescharacteristic
519C22×C53#54611yescharacteristic
520C22×C53#54611yescharacteristic
521C22×C53#55011yescharacteristic
522C22×C53#55111yescharacteristic
523C22×C53#55111yescharacteristic
524C22×C53#55111yescharacteristic
525C22×C53#55311yescharacteristic
526C22×C53#55311yescharacteristic
527C22×C53#55311yescharacteristic
528C22×C53#55311yescharacteristic
529C22×C53#55311yescharacteristic
530C22×C53#55511yescharacteristic
531C22×C53#55511yescharacteristic
532C22×C53#55511yescharacteristic
533C22×C53#55911yescharacteristic
534C2×D53—24no—
535C2×D53—24no—
536C2×D53—24no—
537C2×D53—42no—
538C2×D53—42no—
539C2×D53—42no—
540C2×D53—42no—
541C2×D53—42no—
542C2×D53—42no—
543C2×D53—42no—
544C2×D53—42no—
545C2×D53—42no—
546C2×D53—42no—
547C2×D53—42no—
548C2×D53—42no—
549C4×C53—24no—
550C4×C53—24no—
551C4×C53—42no—
552C4×C53—42no—
553C4×C53—42no—
554C4×C53—81no—
555Dic53—24no—
556Dic53—42no—
557Dic53—42no—
558Dic53—42no—
559Dic53—42no—
560Dic53—42no—
561Dic53—81no—
562C2×#394—531no—
563C2×#388D5311yescharacteristic, complemented
564C2×#386—531no—
565C2×C4×C22⋊C4—531no—
566C2×C4×C22⋊C4—531no—
567#1440—531no—
568#1439—531no—
569#1438—531no—
570#1437—531no—
571#1437—531no—
572#1437—531no—
573#1436—531no—
574C4⋊#95—531no—
575#1434—531no—
576#1434—531no—
577C2×C53—82no—
578C2×C53C4×#12111yescharacteristic
579C2×C53C4×#12311yescharacteristic
580C2×C53#232111yescharacteristic
581C2×C53#236311yescharacteristic
582C2×C53#236411yescharacteristic
583C2×C53#237211yescharacteristic
584C2×C53#237411yescharacteristic
585C2×C53#241211yescharacteristic
586C2×C53#241411yescharacteristic
587C2×C53#245911yescharacteristic
588C2×C53#246711yescharacteristic
589C2×C53#250011yescharacteristic
590C2×C53#251811yescharacteristic
591C2×C53#251811yescharacteristic
592C2×C53#260211yescharacteristic
593D53—44no—
594C23×D4—531no—
595C24×C4—531no—
596C22×C4⋊C4—531no—
597C22×C4⋊C4C2×D5311yescharacteristic
598C22×C22⋊C4—531no—
599C22×C22⋊C4—531no—
600C22×C22⋊C4—531no—
601C22×C22⋊C4—531no—
602C22×C22⋊C4—531no—
603C22×C22⋊C4—531no—
604C22×C22⋊C4—531no—
605C22×C22⋊C4—531no—
606C22×C22⋊C4C2×D5311yescharacteristic
607C22×C22⋊C4C2×D5311yescharacteristic
608C22×C22⋊C4C2×D5311yescharacteristic
609C22×C42—531no—
610C22×C42—531no—
611C22×C42—531no—
612C22×C42C2×D5311yescharacteristic
613#394—538no—
614#388—24no—
615#386—1064no—
616C4×C22⋊C4—1064no—
617C4×C22⋊C4—1064no—
618C2×#95—531no—
619C2×#95—531no—
620C2×#95—531no—
621C2×#95—531no—
622C2×#95—531no—
623C2×#95—531no—
624C2×#95—531no—
625C2×#95—531no—
626C2×#95—531no—
627C2×#95—531no—
628C2×#95—531no—
629C2×#95—531no—
630C2×#95—531no—
631C2×#95—531no—
632C2×#95C2×D5311yescharacteristic
633C2×#95C2×D5311yescharacteristic
634C53#1419911yescharacteristic, complemented, Sylow
635C25—531no—
636C25C22×D5311yescharacteristic
637C22×D4—534no—
638C22×D4—1062no—
639C22×D4—1062no—
640C22×D4—2121no—
641C22×D4—2121no—
642C22×D4—2121no—
643C22×D4—2121no—
644C23×C4—531no—
645C23×C4—531no—
646C23×C4—531no—
647C23×C4—531no—
648C23×C4—531no—
649C23×C4—531no—
650C23×C4—534no—
651C23×C4—531no—
652C23×C4—1062no—
653C23×C4—1062no—
654C23×C4—1062no—
655C23×C4—1062no—
656C23×C4—2121no—
657C23×C4—2121no—
658C23×C4C22×D5311yescharacteristic
659C23×C4C22×D5311yescharacteristic
660C23×C4C22×D5311yescharacteristic
661C23×C4C22×D5311yescharacteristic
662C23×C4C22×D5311yescharacteristic
663C23×C4C22×D5311yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—534no—
668C2×C4⋊C4—2121no—
669C2×C4⋊C4—2121no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—534no—
679C2×C22⋊C4—534no—
680C2×C22⋊C4—534no—
681C2×C22⋊C4—1062no—
682C2×C22⋊C4—1062no—
683C2×C22⋊C4—1062no—
684C2×C22⋊C4—1062no—
685C2×C22⋊C4—1062no—
686C2×C22⋊C4—1062no—
687C2×C22⋊C4—1062no—
688C2×C22⋊C4—1062no—
689C2×C22⋊C4—1062no—
690C2×C22⋊C4—1062no—
691C2×C22⋊C4—1062no—
692C2×C22⋊C4—1062no—
693C2×C22⋊C4—1062no—
694C2×C22⋊C4—1062no—
695C2×C22⋊C4—1062no—
696C2×C22⋊C4—1062no—
697C2×C22⋊C4—2121no—
698C2×C22⋊C4—2121no—
699C2×C22⋊C4—2121no—
700C2×C22⋊C4—2121no—
701C2×C22⋊C4—2121no—
702C2×C22⋊C4C4×D5314yescomplemented
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—1062no—
707C2×C42—1062no—
708C2×C42—1062no—
709C2×C42—1062no—
710C2×C42—1062no—
711C2×C42—2121no—
712C2×C42—2121no—
713C2×C42—2121no—
714C2×C42—2121no—
715#95—22no—
716#95—534no—
717#95—1062no—
718#95—1062no—
719#95—1062no—
720#95—1062no—
721#95—1062no—
722#95—1062no—
723#95—1062no—
724#95—1062no—
725#95—2121no—
726#95—2121no—
727#95—2121no—
728#95—2121no—
729#95—2121no—
730#95C22⋊D5314yescomplemented
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—532no—
746C24—532no—
747C24—532no—
748C24—1061no—
749C24—1061no—
750C24—1061no—
751C24—1061no—
752C24—1061no—
753C24—1061no—
754C24—1061no—
755C24—1061no—
756C24—1061no—
757C24—1061no—
758C24—1061no—
759C24—1061no—
760C24C2×C4×D5312yes—
761C24C23×D5311yescharacteristic
762C2×D4—1068no—
763C2×D4—2124no—
764C2×D4—2124no—
765C2×D4—2124no—
766C2×D4—2124no—
767C2×D4—2124no—
768C2×D4—2124no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—532no—
803C22×C4—532no—
804C22×C4—532no—
805C22×C4—532no—
806C22×C4—532no—
807C22×C4—532no—
808C22×C4—532no—
809C22×C4—532no—
810C22×C4—1068no—
811C22×C4—1061no—
812C22×C4—1061no—
813C22×C4—1061no—
814C22×C4—1061no—
815C22×C4—1061no—
816C22×C4—1061no—
817C22×C4—1061no—
818C22×C4—1061no—
819C22×C4—1061no—
820C22×C4—1061no—
821C22×C4—1061no—
822C22×C4—1061no—
823C22×C4—1061no—
824C22×C4—1061no—
825C22×C4—1061no—
826C22×C4—1061no—
827C22×C4—1061no—
828C22×C4—1061no—
829C22×C4—1061no—
830C22×C4—1061no—
831C22×C4—1061no—
832C22×C4—1061no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
841C22×C4—1061no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1068no—
846C22×C4—1061no—
847C22×C4—1061no—
848C22×C4—1061no—
849C22×C4—1061no—
850C22×C4—1061no—
851C22×C4—1061no—
852C22×C4—1061no—
853C22×C4—2124no—
854C22×C4—2124no—
855C22×C4—2124no—
856C22×C4—2124no—
857C22×C4—2124no—
858C22×C4C2×C4×D5312yes—
859C22×C4C2×C4×D5312yes—
860C22×C4#1171994512yes—
861C22×C4D4×D5312yes—
862C22×C4#1171994712yes—
863C22×C4#1171994712yes—
864C22×C4C2×C22⋊D5312yes—
865C22×C4C2×C22⋊D5312yes—
866C22×C4C2×C22⋊D5312yes—
867C4⋊C4—44no—
868C4⋊C4—2124no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—1068no—
873C22⋊C4—1068no—
874C22⋊C4—1068no—
875C22⋊C4—1068no—
876C22⋊C4—2124no—
877C22⋊C4—2124no—
878C22⋊C4—2124no—
879C22⋊C4—2124no—
880C42—44no—
881C42—2124no—
882C42—2124no—
883C42—2124no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—534no—
920C23—1062no—
921C23—1062no—
922C23—1062no—
923C23—1062no—
924C23—1062no—
925C23—1062no—
926C23—1062no—
927C23—1062no—
928C23—1062no—
929C23—1062no—
930C23—1062no—
931C23—1062no—
932C23—1062no—
933C23—1062no—
934C23—1062no—
935C23—1062no—
936C23—1062no—
937C23—1062no—
938C23—2121no—
939C23—2121no—
940C23—2121no—
941C23—2121no—
942C23—2121no—
943C23—2121no—
944C23—2121no—
945C23—2121no—
946C23—2121no—
947C23—2121no—
948C23—2121no—
949C23—2121no—
950C23—2121no—
951C23—2121no—
952C23—2121no—
953C23—2121no—
954C23C22×C4×D5311yescharacteristic
955C23C2×D4×D5311yescharacteristic
956C23C22×C22⋊D5311yescharacteristic
957C23#41×D5311yescharacteristic
958C23#41×D5311yescharacteristic
959C23#41×D5311yescharacteristic
960C23#41×D5311yescharacteristic
961C23#41×D5311yescharacteristic
962C23C2×#1171994711yescharacteristic
963C23C2×#1171994711yescharacteristic
964C23C2×#1171994511yescharacteristic
965C23#1313326211yescharacteristic
966C23#1313326311yescharacteristic
967C23#1313326311yescharacteristic
968C23#1313326311yescharacteristic
969D4—21216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—534no—
1011C2×C4—1062no—
1012C2×C4—1062no—
1013C2×C4—1062no—
1014C2×C4—1062no—
1015C2×C4—1062no—
1016C2×C4—1062no—
1017C2×C4—1062no—
1018C2×C4—1062no—
1019C2×C4—1062no—
1020C2×C4—1062no—
1021C2×C4—1062no—
1022C2×C4—1062no—
1023C2×C4—1062no—
1024C2×C4—1062no—
1025C2×C4—1062no—
1026C2×C4—1062no—
1027C2×C4—1062no—
1028C2×C4—1062no—
1029C2×C4—1062no—
1030C2×C4—1062no—
1031C2×C4—1062no—
1032C2×C4—21216no—
1033C2×C4—2121no—
1034C2×C4—2121no—
1035C2×C4—2121no—
1036C2×C4—2121no—
1037C2×C4—2121no—
1038C2×C4—2121no—
1039C2×C4—2121no—
1040C2×C4—2121no—
1041C2×C4—2121no—
1042C2×C4—2121no—
1043C2×C4—2121no—
1044C2×C4—2121no—
1045C2×C4—2121no—
1046C2×C4—2121no—
1047C2×C4—2121no—
1048C2×C4—2121no—
1049C2×C4—2121no—
1050C2×C4—2121no—
1051C2×C4—2121no—
1052C2×C4—2121no—
1053C2×C4—2121no—
1054C2×C4—2121no—
1055C2×C4—2121no—
1056C2×C4—2121no—
1057C2×C4—2121no—
1058C2×C4—2121no—
1059C2×C4—2121no—
1060C2×C4C4×C22⋊D5314yes—
1061C2×C4#1313318814yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—1064no—
1078C22—1064no—
1079C22—1064no—
1080C22—2122no—
1081C22—2122no—
1082C22—2122no—
1083C22—2122no—
1084C22—2122no—
1085C22—2122no—
1086C22—2122no—
1087C22—2122no—
1088C22—2122no—
1089C22—2122no—
1090C22—2122no—
1091C22—2122no—
1092C22C4×D4×D5311yescharacteristic
1093C22C2×C4×C22⋊D5311yescharacteristic
1094C22C4×#1171994711yescharacteristic
1095C22C4×#1171994711yescharacteristic
1096C22#1681109111yescharacteristic
1097C22#1681109511yescharacteristic
1098C22#1681109711yescharacteristic
1099C22C2×#1313318811yescharacteristic
1100C22#123×D5311yescharacteristic
1101C22#1681113011yescharacteristic
1102C22#1681113311yescharacteristic
1103C22#1681115211yescharacteristic
1104C22#1681115511yescharacteristic
1105C22#1681115611yescharacteristic
1106C22#1681117011yescharacteristic
1107C22#1681118411yescharacteristic
1108C22#1681118911yescharacteristic
1109C22#1681120711yescharacteristic
1110C22#1681121211yescharacteristic
1111C22#1681126111yescharacteristic
1112C22#1681126111yescharacteristic
1113C22#1681126711yescharacteristic
1114C22#1681129211yescharacteristic
1115C22#1681129611yescharacteristic
1116C22#1681129611yescharacteristic
1117C22#1681129811yescharacteristic
1118C22#1681131711yescharacteristic
1119C22#1681131911yescharacteristic
1120C22#1681132211yescharacteristic
1121C22#1681132411yescharacteristic
1122C22#1681132511yescharacteristic
1123C22#1681133511yescharacteristic
1124C22#1681133611yescharacteristic
1125C22#1681133711yescharacteristic
1126C22#1681135511yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—1064no—
1134C4—4241no—
1135C4—2122no—
1136C4—2122no—
1137C4—2122no—
1138C4—2122no—
1139C4—2122no—
1140C2—82no—
1141C2—2124no—
1142C2C4×#1313318811yescharacteristic
1143C2#2027724211yescharacteristic
1144C2#2027737711yescharacteristic
1145C2#2027775311yescharacteristic
1146C2#2027776011yescharacteristic
1147C2#2027782211yescharacteristic
1148C2#2027784511yescharacteristic
1149C2#2027810711yescharacteristic
1150C2#2027812911yescharacteristic
1151C2#2027864811yescharacteristic
1152C2#2027876211yescharacteristic
1153C2#2027917511yescharacteristic
1154C2#2027937711yescharacteristic
1155C2#2027938011yescharacteristic
1156C2#2028033311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#388D53
hypocenterC53#14199
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11719921C2semidirect
4. C2×#16810470C2semidirect
5. #20272963C2semidirect
6. #20272957C2semidirect
8. #20272952C2semidirect
9. #20272952C2semidirect
10. #20272952C2semidirect
11. #20272949C2semidirect
12. #20272944C2semidirect
13. #20272942C2semidirect
14. #20272939C2semidirect
15. C2×C53×#388C2semidirect
30. #16810539C4semidirect
80. C2×C4⋊Dic53C2×C4semidirect
89. C2×C22⋊Dic53C2×C4semidirect
127. #13133124C2×C4semidirect
146. C2×C22⋊C4×C53C2×C4semidirect
151. #95×C53D4semidirect
563. C2×#388D53semidirect
634. C53#14199semidirect
702. C2×C22⋊C4C4×D53semidirect
730. #95C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105392
C2×#168104992
C2×C4×#117199212
C2×#168104702
#202729632
#202729572
#202729542
#202729522
#202729492
#202729442
#202729422
#202729392
C2×C53×#3882
#1419953