Finite Group Databasebeta

← #27312427

Subgroups — #27312427

Order 13568.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810515C211yesmaximal, characteristic
2C2×#16810513C211yesmaximal, characteristic
3#20272975C211yesmaximal, characteristic, complemented
4#20272968C211yesmaximal, characteristic, complemented
5#20272963C211yesmaximal, characteristic
6#20272957C211yesmaximal, characteristic
7#20272957C211yesmaximal, characteristic
8#20272957C211yesmaximal, characteristic
9#20272953C211yesmaximal, characteristic
10#20272947C211yesmaximal, characteristic, complemented
11#20272947C211yesmaximal, characteristic, complemented
12#20272944C211yesmaximal, characteristic, complemented
13#20272942C211yesmaximal, characteristic, complemented
14#20272940C211yesmaximal, characteristic, complemented
15C2×C53×#389C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719921C2211yescharacteristic
18C22×#11719921C2211yescharacteristic
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810515—24no—
27#16810513C418yescomplemented
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C22×C4⋊C4×C53C2211yescharacteristic
47C22×C4⋊C4×C53C2211yescharacteristic
48C22×C4⋊C4×C53C2211yescharacteristic
49C22×C4⋊C4×C53C2211yescharacteristic
50C22×C42×C53C2211yescharacteristic
51C53×#389—24no—
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C24×D53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C2×C4⋊Dic53—22no—
63C2×C4⋊Dic53—22no—
64C2×C4⋊Dic53—41no—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—22no—
68C2×#11719921—22no—
69C2×#11719921—22no—
70C2×#11719921—22no—
71C2×#11719921—22no—
72C2×#11719921—22no—
73C2×#11719921—41no—
74C2×#11719921—41no—
75C2×#11719921—41no—
76C2×#11719921—41no—
77C2×#11719921—41no—
78C2×#11719921—41no—
79C2×#11719921—41no—
80C2×#11719921—41no—
81C2×#11719921—41no—
82C2×#11719921—41no—
83C2×#11719921C2×C414yes—
84C2×#11719921C2×C414yes—
85C2×#11719921C2×C414yes—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—41no—
88C2×C4×Dic53—41no—
89C2×C4×Dic53—41no—
90C2×C4×Dic53—41no—
91C2×C4×Dic53C2×C414yes—
92#13133124—22no—
93#13133124—22no—
94#13133124—22no—
95#13133124—22no—
96#13133124—22no—
97#13133124—41no—
98#13133124—41no—
99#13133124—41no—
100#13133124—41no—
101#13133124—41no—
102#13133124—41no—
103#13133124—41no—
104#13133124—41no—
105#13133124—41no—
106#13133124—41no—
107#13133124—41no—
108#13133124C2×C414yes—
109#13133124C2×C414yes—
110C23×C4×C53C2311yescharacteristic
111C23×C4×C53C2311yescharacteristic
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2311yescharacteristic
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53—22no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53—22no—
121C2×C4⋊C4×C53—22no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—22no—
125C2×C4⋊C4×C53—41no—
126C2×C4⋊C4×C53—41no—
127C2×C4⋊C4×C53—41no—
128C2×C4⋊C4×C53C2×C414yes—
129C2×C42×C53—22no—
130C2×C42×C53—22no—
131C2×C42×C53—41no—
132#95×C53—22no—
133#95×C53D414yes—
134C24×C53C2411yescharacteristic
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—21no—
148C23×D53—21no—
149C23×D53C22×C412yes—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
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×C53C22×C412yes—
190C22×C4×C53C22×C412yes—
191C22×C4×C53C22×C412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2×D412yes—
195C22×C4×C53#4112yes—
196C22×C4×C53#4112yes—
197C22×C4×C53#4112yes—
198C22×C4×C53#4112yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
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×Dic53C22×C412yes—
245C22×Dic53C22×C412yes—
246C22×Dic53C22×C412yes—
247C22×Dic53#4112yes—
248C4⋊C4×C53—28no—
249C4⋊C4×C53—44no—
250C4⋊C4×C53—44no—
251C4⋊C4×C53—44no—
252C42×C53—44no—
253#11719921—28no—
254#11719921—28no—
255#11719921—44no—
256#11719921—44no—
257#11719921—44no—
258#11719921—44no—
259#11719921—44no—
260C4⋊Dic53—44no—
261C4×Dic53—44no—
262C4×Dic53—44no—
263C23×C53C23×C411yescharacteristic
264C23×C53C22×D411yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C23×C53C2×#4111yescharacteristic
267C23×C53C2×#4111yescharacteristic
268C23×C53C2×#4111yescharacteristic
269C23×C53C2×#4111yescharacteristic
270C23×C53H(5,𝔽2)11yescharacteristic
271C23×C53H(5,𝔽2)11yescharacteristic
272C23×C53H(5,𝔽2)11yescharacteristic
273C23×C53H(5,𝔽2)11yescharacteristic
274C23×C53H(5,𝔽2)11yescharacteristic
275C23×C532−1+411yescharacteristic
276C23×C532−1+411yescharacteristic
277C23×C532−1+411yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—41no—
286C22×D53—41no—
287C22×D53—41no—
288C22×D53—41no—
289C22×D53—41no—
290C22×D53—41no—
291C22×D53—41no—
292C22×D53—41no—
293C22×D53—41no—
294C22×D53—41no—
295C22×D53—41no—
296C22×D53—41no—
297C22×D53—41no—
298C22×D53—41no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
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—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53#11714yes—
361C2×C4×C53C4×D414yes—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—41no—
379C2×Dic53—41no—
380C2×Dic53—41no—
381C2×Dic53—41no—
382C2×Dic53—41no—
383C2×Dic53—41no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411#14434—531nomaximal, Sylow
412C22×C53C2×#11711yescharacteristic
413C22×C53C2×C4×D411yescharacteristic
414C22×C53C4×#4111yescharacteristic
415C22×C53#51811yescharacteristic
416C22×C53#52011yescharacteristic
417C22×C53#52011yescharacteristic
418C22×C53#52011yescharacteristic
419C22×C53#53511yescharacteristic
420C22×C53#53611yescharacteristic
421C22×C53#53811yescharacteristic
422C22×C53#53911yescharacteristic
423C22×C53#54011yescharacteristic
424C22×C53#54011yescharacteristic
425C22×C53#54111yescharacteristic
426C22×C53#54211yescharacteristic
427C22×C53#54211yescharacteristic
428C22×C53#54211yescharacteristic
429C22×C53#54211yescharacteristic
430C22×C53#54211yescharacteristic
431C22×C53#54611yescharacteristic
432C22×C53#54611yescharacteristic
433C22×C53#54611yescharacteristic
434C22×C53#54811yescharacteristic
435C22×C53#55211yescharacteristic
436C22×C53#55311yescharacteristic
437C22×C53#55311yescharacteristic
438C22×C53#55311yescharacteristic
439C22×C53#55311yescharacteristic
440C22×C53#55311yescharacteristic
441C22×C53#55611yescharacteristic
442C22×C53#55611yescharacteristic
443C22×C53#56011yescharacteristic
444C22×C53#56211yescharacteristic
445C22×C53#56211yescharacteristic
446C22×C53#56311yescharacteristic
447C2×D53—42no—
448C2×D53—42no—
449C2×D53—42no—
450C2×D53—42no—
451C2×D53—42no—
452C2×D53—42no—
453C2×D53—42no—
454C2×D53—81no—
455C2×D53—81no—
456C2×D53—81no—
457C2×D53—81no—
458C2×D53—81no—
459C2×D53—81no—
460C2×D53—81no—
461C2×D53—81no—
462C4×C53—24no—
463C4×C53—24no—
464C4×C53—42no—
465C4×C53—42no—
466C4×C53—42no—
467C4×C53—42no—
468C4×C53—81no—
469Dic53—42no—
470Dic53—42no—
471Dic53—42no—
472Dic53—42no—
473Dic53—81no—
474Dic53—81no—
475Dic53—81no—
476C2×#389D5311yescharacteristic, complemented
477C2×#388—531no—
478C2×#388—531no—
479#1443—531no—
480#1441—531no—
481#1440—531no—
482#1439—531no—
483#1439—531no—
484#1439—531no—
485#1437—531no—
486#1436—531no—
487#1436—531no—
488C4⋊#95—531no—
489#1434—531no—
490#1434—531no—
491C2×C53#231911yescharacteristic
492C2×C53#232611yescharacteristic
493C2×C53#233411yescharacteristic
494C2×C53#234711yescharacteristic
495C2×C53#235211yescharacteristic
496C2×C53#236411yescharacteristic
497C2×C53#237611yescharacteristic
498C2×C53#270011yescharacteristic
499C2×C53#270311yescharacteristic
500C2×C53#271111yescharacteristic
501C2×C53#271611yescharacteristic
502C2×C53#277211yescharacteristic
503C2×C53#277711yescharacteristic
504C2×C53#280011yescharacteristic
505C2×C53#280111yescharacteristic
506D53—82no—
507C22×C4⋊C4—531no—
508C22×C4⋊C4C2×D5311yescharacteristic
509C22×C4⋊C4C2×D5311yescharacteristic
510C22×C4⋊C4C2×D5311yescharacteristic
511C22×C4⋊C4C2×D5311yescharacteristic
512C22×C22⋊C4—531no—
513C22×C22⋊C4—531no—
514C22×C22⋊C4—531no—
515C22×C22⋊C4—531no—
516C22×C22⋊C4—531no—
517C22×C22⋊C4—531no—
518C22×C22⋊C4—531no—
519C22×C42—531no—
520C22×C42—531no—
521C22×C42C2×D5311yescharacteristic
522#389—24no—
523#388—538no—
524#388—1064no—
525C2×#95—531no—
526C2×#95—531no—
527C2×#95—531no—
528C2×#95—531no—
529C2×#95—531no—
530C2×#95—531no—
531C2×#95—531no—
532C2×#95—531no—
533C2×#95—531no—
534C2×#95—531no—
535C2×#95—531no—
536C2×#95—531no—
537C2×#95—531no—
538C2×#95—531no—
539C2×#95—531no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95C2×D5311yescharacteristic
544C2×#95C2×D5311yescharacteristic
545C53#1443411yescharacteristic, complemented, Sylow
546C25—531no—
547C23×C4—531no—
548C23×C4—531no—
549C23×C4—531no—
550C23×C4—531no—
551C23×C4—531no—
552C23×C4—531no—
553C23×C4—531no—
554C23×C4C22×D5311yescharacteristic
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5311yescharacteristic
557C23×C4C22×D5311yescharacteristic
558C23×C4C22×D5311yescharacteristic
559C23×C4C22×D5311yescharacteristic
560C23×C4C22×D5311yescharacteristic
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—1062no—
573C2×C4⋊C4—1062no—
574C2×C4⋊C4—2121no—
575C2×C4⋊C4C4×D5314yes—
576C2×C22⋊C4—534no—
577C2×C22⋊C4—534no—
578C2×C22⋊C4—534no—
579C2×C22⋊C4—1062no—
580C2×C22⋊C4—1062no—
581C2×C22⋊C4—1062no—
582C2×C22⋊C4—1062no—
583C2×C22⋊C4—1062no—
584C2×C22⋊C4—1062no—
585C2×C22⋊C4—1062no—
586C2×C22⋊C4—1062no—
587C2×C22⋊C4—2121no—
588C2×C22⋊C4—2121no—
589C2×C22⋊C4—2121no—
590C2×C22⋊C4—2121no—
591C2×C22⋊C4—2121no—
592C2×C22⋊C4—2121no—
593C2×C22⋊C4—2121no—
594C2×C22⋊C4—2121no—
595C2×C22⋊C4—2121no—
596C2×C22⋊C4—2121no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—41no—
600C2×C42—534no—
601C2×C42—1062no—
602C2×C42—2121no—
603C2×C42—2121no—
604C2×C42—2121no—
605C2×C42—2121no—
606#95—22no—
607#95—534no—
608#95—534no—
609#95—1062no—
610#95—1062no—
611#95—1062no—
612#95—1062no—
613#95—1062no—
614#95—2121no—
615#95—2121no—
616#95—2121no—
617#95—2121no—
618#95—2121no—
619#95—2121no—
620#95—2121no—
621#95—2121no—
622#95—2121no—
623#95—2121no—
624#95—2121no—
625#95C22⋊D5314yes—
626C24—532no—
627C24—1061no—
628C24—1061no—
629C24—1061no—
630C24—1061no—
631C24—1061no—
632C24—1061no—
633C24—1061no—
634C24—1061no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—1061no—
639C24—1061no—
640C24—1061no—
641C24C23×D5311yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—532no—
682C22×C4—532no—
683C22×C4—532no—
684C22×C4—532no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—1061no—
690C22×C4—1061no—
691C22×C4—1061no—
692C22×C4—1061no—
693C22×C4—1061no—
694C22×C4—1061no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—1061no—
698C22×C4—1061no—
699C22×C4—1061no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—1061no—
704C22×C4—1061no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4C2×C4×D5312yes—
731C22×C4C2×C4×D5312yes—
732C22×C4C2×C4×D5312yes—
733C22×C4#1171994512yes—
734C22×C4#1171994712yes—
735C22×C4#1171994712yes—
736C22×C4#1171994912yes—
737C22×C4C2×C22⋊D5312yes—
738C22×C4C2×C22⋊D5312yes—
739C22×C4C2×C22⋊D5312yes—
740C4⋊C4—28no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—2124no—
745C22⋊C4—1068no—
746C22⋊C4—1068no—
747C22⋊C4—2124no—
748C22⋊C4—2124no—
749C22⋊C4—2124no—
750C22⋊C4—2124no—
751C22⋊C4—2124no—
752C42—44no—
753C42—2124no—
754C42—2124no—
755C23—1062no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—2121no—
763C23—2121no—
764C23—2121no—
765C23—2121no—
766C23—2121no—
767C23—2121no—
768C23—2121no—
769C23—2121no—
770C23—2121no—
771C23—2121no—
772C23—2121no—
773C23—2121no—
774C23—2121no—
775C23—2121no—
776C23—2121no—
777C23—2121no—
778C23—2121no—
779C23—2121no—
780C23—2121no—
781C23—2121no—
782C23—2121no—
783C23—2121no—
784C23—2121no—
785C23—2121no—
786C23—2121no—
787C23—2121no—
788C23—2121no—
789C23—2121no—
790C23C22×C4×D5311yescharacteristic
791C23C22×C22⋊D5311yescharacteristic
792C23#41×D5311yescharacteristic
793C23C2×#1171994711yescharacteristic
794C23C2×#1171994711yescharacteristic
795C23C2×#1171994511yescharacteristic
796C23C2×#1171994911yescharacteristic
797C23#1313326211yescharacteristic
798C23#1313326211yescharacteristic
799C23#1313326311yescharacteristic
800C23#1313326311yescharacteristic
801C23#1313326311yescharacteristic
802C23#1313326511yescharacteristic
803C23#1313326511yescharacteristic
804C23#1313326511yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—1062no—
853C2×C4—1062no—
854C2×C4—1062no—
855C2×C4—1062no—
856C2×C4—1062no—
857C2×C4—1062no—
858C2×C4—1062no—
859C2×C4—1062no—
860C2×C4—1062no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—2121no—
865C2×C4—2121no—
866C2×C4—2121no—
867C2×C4—2121no—
868C2×C4—2121no—
869C2×C4—2121no—
870C2×C4—2121no—
871C2×C4—2121no—
872C2×C4—2121no—
873C2×C4—2121no—
874C2×C4—2121no—
875C2×C4—2121no—
876C2×C4—2121no—
877C2×C4—2121no—
878C2×C4—2121no—
879C2×C4—2121no—
880C2×C4—2121no—
881C2×C4—2121no—
882C2×C4—2121no—
883C2×C4—2121no—
884C2×C4—2121no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4—2121no—
888C2×C4—2121no—
889C2×C4—2121no—
890C2×C4—2121no—
891C2×C4—2121no—
892C2×C4—2121no—
893C2×C4—2121no—
894C2×C4—2121no—
895C2×C4—2121no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4#1313317514yes—
902C2×C4C4×C22⋊D5314yes—
903C22—4241no—
904C22—4241no—
905C22—4241no—
906C22—4241no—
907C22—4241no—
908C22—4241no—
909C22—4241no—
910C22—4241no—
911C22—2122no—
912C22—2122no—
913C22—2122no—
914C22—2122no—
915C22—2122no—
916C22—2122no—
917C22—2122no—
918C22C2×#1313317511yescharacteristic
919C22C2×C4×C22⋊D5311yescharacteristic
920C22C4×#1171994711yescharacteristic
921C22#1681109511yescharacteristic
922C22#1681110411yescharacteristic
923C22#1681110511yescharacteristic
924C22#1681110511yescharacteristic
925C22#1681118711yescharacteristic
926C22#1681119711yescharacteristic
927C22#1681121011yescharacteristic
928C22#1681122111yescharacteristic
929C22#1681122611yescharacteristic
930C22#1681122911yescharacteristic
931C22#1681123411yescharacteristic
932C22#1681124311yescharacteristic
933C22#1681124511yescharacteristic
934C22#1681124511yescharacteristic
935C22#1681124611yescharacteristic
936C22#1681124711yescharacteristic
937C22#1681126111yescharacteristic
938C22#1681126711yescharacteristic
939C22#1681126711yescharacteristic
940C22#1681128411yescharacteristic
941C22#1681130811yescharacteristic
942C22#1681131911yescharacteristic
943C22#1681132111yescharacteristic
944C22#1681132211yescharacteristic
945C22#1681132511yescharacteristic
946C22#1681132611yescharacteristic
947C22#1681134411yescharacteristic
948C22#1681134711yescharacteristic
949C22#1681136111yescharacteristic
950C22#1681136911yescharacteristic
951C22#1681137111yescharacteristic
952C22#1681137211yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—81no—
960C4—4241no—
961C4—4241no—
962C4—4241no—
963C4—2122no—
964C4—2122no—
965C4—2122no—
966C4—2122no—
967C2—4242no—
968C2#2027735411yescharacteristic
969C2#2027742211yescharacteristic
970C2#2027748311yescharacteristic
971C2#2027760711yescharacteristic
972C2#2027764011yescharacteristic
973C2#2027776011yescharacteristic
974C2#2027786011yescharacteristic
975C2#2028130911yescharacteristic
976C2#2028135411yescharacteristic
977C2#2028146811yescharacteristic
978C2#2028153511yescharacteristic
979C2#2028224311yescharacteristic
980C2#2028231811yescharacteristic
981C2#2028260511yescharacteristic
982C2#2028262011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53#14434
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #20272975C2semidirect
4. #20272968C2semidirect
10. #20272947C2semidirect
11. #20272947C2semidirect
12. #20272944C2semidirect
13. #20272942C2semidirect
14. #20272940C2semidirect
15. C2×C53×#389C2semidirect
27. #16810513C4semidirect
476. C2×#389D53semidirect
545. C53#14434semidirect

Maximal subgroups

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

subgroupindex
C2×#168105152
C2×#168105132
#202729752
#202729682
#202729632
#202729572
#202729532
#202729472
#202729442
#202729422
#202729402
C2×C53×#3892
#1443453