Finite Group Databasebeta

← #27312938

Subgroups — #27312938

Order 13568.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810512C211yesmaximal, characteristic
2#20272981C211yesmaximal, characteristic, complemented
3#20272976C211yesmaximal, characteristic, complemented
4#20272972C211yesmaximal, characteristic, complemented
5#20272969C211yesmaximal, characteristic, complemented
6#20272963C211yesmaximal, characteristic
7#20272961C211yesmaximal, characteristic
8#20272953C211yesmaximal, characteristic
9#20272942C211yesmaximal, characteristic, complemented
10#20272940C211yesmaximal, characteristic, complemented
11#20272939C211yesmaximal, characteristic, complemented
12#20272936C211yesmaximal, characteristic
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810512C418yescomplemented
27C2×#13133124C2211yescharacteristic
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
45C22×C42×C53C2211yescharacteristic
46C2×#95×C53C2211yescharacteristic
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C24×D53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C22×C4×D53—22no—
61C22×C4×D53—22no—
62C22×C4×D53—22no—
63C22×C4×D53—41no—
64C22×C4×D53—41no—
65C22×C4×D53—41no—
66C22×C4×D53—41no—
67C2×C4⋊Dic53—41no—
68C2×C4⋊Dic53—41no—
69C2×C4⋊Dic53—41no—
70C2×#11719919—41no—
71C2×#11719919—41no—
72C2×#11719919C2×C414yescomplemented
73C2×#11719921—22no—
74C2×#11719921—22no—
75C2×#11719921—22no—
76C2×#11719921—22no—
77C2×#11719921—22no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—41no—
81C2×#11719921—41no—
82C2×#11719921—41no—
83C2×#11719921—41no—
84C2×#11719921—41no—
85C2×#11719921—41no—
86C2×#11719921—41no—
87C2×#11719921—41no—
88C2×#11719921C2×C414yes—
89C2×#11719921C2×C414yes—
90C2×#11719921C2×C414yes—
91C2×C4×Dic53—41no—
92C2×C4×Dic53—41no—
93C2×C4×Dic53C2×C414yescomplemented
94#13133124—22no—
95#13133124—22no—
96#13133124—22no—
97#13133124—22no—
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#13133124—41no—
109#13133124—41no—
110#13133124—41no—
111#13133124C2×C414yescomplemented
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C23×C4×C53C2311yescharacteristic
119C2×C42×C53—22no—
120C2×C42×C53—22no—
121C2×C42×C53—41no—
122#95×C53—22no—
123#95×C53—22no—
124#95×C53—41no—
125#95×C53—41no—
126#95×C53—41no—
127#95×C53C2×C414yescomplemented
128C24×C53C2411yescharacteristic
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—21no—
134C23×D53—21no—
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53C22×C412yes—
142C23×D53#4112yes—
143C23×D53#4112yes—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
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×C53C22×C412yes—
188C22×C4×C53C22×C412yes—
189C22×C4×C53C22×C412yes—
190C22×C4×C53#4112yes—
191C22×C4×C53#4112yes—
192C22×C4×C53#4112yes—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
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×Dic53C22×C412yes—
239C22×Dic53C22×C412yes—
240C22×Dic53C22×C412yes—
241C22×Dic53#4112yes—
242C2×C4×D53—44no—
243C2×C4×D53—44no—
244C2×C4×D53—44no—
245C2×C4×D53—44no—
246C2×C4×D53—44no—
247C2×C4×D53—44no—
248C2×C4×D53—44no—
249C42×C53—44no—
250#11719921—28no—
251#11719921—44no—
252#11719921—44no—
253#11719921—44no—
254#11719921—44no—
255#11719921—44no—
256C4⋊Dic53—44no—
257#11719919—44no—
258C4×Dic53—44no—
259C23×C53C23×C411yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53C2×#4111yescharacteristic
262C23×C53C2×#4111yescharacteristic
263C23×C53C2×#4111yescharacteristic
264C23×C53C2×#4111yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C23×C53H(5,𝔽2)11yescharacteristic
267C23×C53H(5,𝔽2)11yescharacteristic
268C23×C53H(5,𝔽2)11yescharacteristic
269C23×C53H(5,𝔽2)11yescharacteristic
270C23×C53H(5,𝔽2)11yescharacteristic
271C23×C53H(5,𝔽2)11yescharacteristic
272C23×C532−1+411yescharacteristic
273C23×C532−1+411yescharacteristic
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
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#11714yes—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
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—41no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
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×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
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—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
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—
407C4×D53—416no—
408#14479—531nomaximal, Sylow
409C22×C53C2×#11711yescharacteristic
410C22×C53C4×#4111yescharacteristic
411C22×C53C4×#4111yescharacteristic
412C22×C53#51811yescharacteristic
413C22×C53#51811yescharacteristic
414C22×C53#52011yescharacteristic
415C22×C53#52011yescharacteristic
416C22×C53#53811yescharacteristic
417C22×C53#53811yescharacteristic
418C22×C53#53811yescharacteristic
419C22×C53#53811yescharacteristic
420C22×C53#53911yescharacteristic
421C22×C53#53911yescharacteristic
422C22×C53#53911yescharacteristic
423C22×C53#53911yescharacteristic
424C22×C53#54011yescharacteristic
425C22×C53#54111yescharacteristic
426C22×C53#54211yescharacteristic
427C22×C53#54211yescharacteristic
428C22×C53#55111yescharacteristic
429C22×C53#55111yescharacteristic
430C22×C53#55111yescharacteristic
431C22×C53#55111yescharacteristic
432C22×C53#55111yescharacteristic
433C22×C53#55111yescharacteristic
434C22×C53#55211yescharacteristic
435C22×C53#55211yescharacteristic
436C22×C53#55311yescharacteristic
437C22×C53#55311yescharacteristic
438C22×C53#55511yescharacteristic
439C22×C53#55511yescharacteristic
440C22×C53#56011yescharacteristic
441C22×C53#56011yescharacteristic
442C22×C53#56211yescharacteristic
443C22×C53#56211yescharacteristic
444C2×D53—24no—
445C2×D53—24no—
446C2×D53—24no—
447C2×D53—42no—
448C2×D53—42no—
449C2×D53—42no—
450C2×D53—42no—
451C2×D53—42no—
452C2×D53—42no—
453C2×D53—42no—
454C2×D53—42no—
455C2×D53—42no—
456C2×D53—42no—
457C2×D53—42no—
458C2×D53—42no—
459C4×C53—42no—
460C4×C53—42no—
461C4×C53—42no—
462C4×C53—42no—
463C4×C53—42no—
464C4×C53—42no—
465C4×C53—81no—
466Dic53—42no—
467Dic53—42no—
468Dic53—42no—
469Dic53—42no—
470Dic53—81no—
471Dic53—81no—
472Dic53—81no—
473C2×#388—531no—
474#1445—531no—
475#1443—531no—
476#1442—531no—
477#1441—531no—
478#1440—531no—
479#1439—531no—
480#1437—531no—
481#1434—531no—
482#1434—531no—
483#1434—531no—
484#1434D5311yescharacteristic, complemented
485C22⋊#95—531no—
486C22⋊#95—531no—
487C22⋊#95—531no—
488C2×C53#231811yescharacteristic
489C2×C53#233411yescharacteristic
490C2×C53#233511yescharacteristic
491C2×C53#234311yescharacteristic
492C2×C53#235311yescharacteristic
493C2×C53#237211yescharacteristic
494C2×C53#237711yescharacteristic
495C2×C53#273511yescharacteristic
496C2×C53#273711yescharacteristic
497C2×C53#274311yescharacteristic
498C2×C53#274411yescharacteristic
499C2×C53#274611yescharacteristic
500C2×C53#274711yescharacteristic
501C2×C53#275611yescharacteristic
502C2×C53#278111yescharacteristic
503D53—44no—
504C24×C4—531no—
505C22×C4⋊C4—531no—
506C22×C4⋊C4—531no—
507C22×C22⋊C4—531no—
508C22×C22⋊C4—531no—
509C22×C22⋊C4—531no—
510C22×C22⋊C4—531no—
511C22×C22⋊C4—531no—
512C22×C22⋊C4—531no—
513C22×C42—531no—
514C22×C42C2×D5311yescharacteristic
515#388—538no—
516C2×#95—531no—
517C2×#95—531no—
518C2×#95—531no—
519C2×#95—531no—
520C2×#95—531no—
521C2×#95—531no—
522C2×#95—531no—
523C2×#95—531no—
524C2×#95—531no—
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×#95C2×D5311yescharacteristic
535C2×#95C2×D5311yescharacteristic
536C2×#95C2×D5311yescharacteristic
537C2×#95C2×D5311yescharacteristic
538C2×#95C2×D5311yescharacteristic
539C2×#95C2×D5311yescharacteristic
540C53#1447911yescharacteristic, complemented, Sylow
541C25—531no—
542C23×C4—531no—
543C23×C4—531no—
544C23×C4—531no—
545C23×C4—531no—
546C23×C4—531no—
547C23×C4—531no—
548C23×C4—531no—
549C23×C4—1062no—
550C23×C4—1062no—
551C23×C4—1062no—
552C23×C4—2121no—
553C23×C4—2121no—
554C23×C4—2121no—
555C23×C4—2121no—
556C23×C4C22×D5311yescharacteristic
557C23×C4C22×D5311yescharacteristic
558C23×C4C22×D5311yescharacteristic
559C23×C4C22×D5311yescharacteristic
560C23×C4C22×D5311yescharacteristic
561C23×C4C22×D5311yescharacteristic
562C23×C4C22×D5311yescharacteristic
563C2×C4⋊C4—534no—
564C2×C4⋊C4—2121no—
565C2×C4⋊C4—2121no—
566C2×C4⋊C4—2121no—
567C2×C4⋊C4—2121no—
568C2×C4⋊C4—2121no—
569C2×C22⋊C4—534no—
570C2×C22⋊C4—534no—
571C2×C22⋊C4—534no—
572C2×C22⋊C4—1062no—
573C2×C22⋊C4—1062no—
574C2×C22⋊C4—1062no—
575C2×C22⋊C4—1062no—
576C2×C22⋊C4—1062no—
577C2×C22⋊C4—1062no—
578C2×C22⋊C4—1062no—
579C2×C22⋊C4—2121no—
580C2×C22⋊C4—2121no—
581C2×C22⋊C4—2121no—
582C2×C22⋊C4—2121no—
583C2×C22⋊C4—2121no—
584C2×C22⋊C4—2121no—
585C2×C22⋊C4—2121no—
586C2×C22⋊C4—2121no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—41no—
590C2×C42—534no—
591C2×C42—2121no—
592C2×C42—2121no—
593#95—22no—
594#95—22no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—534no—
599#95—1062no—
600#95—1062no—
601#95—1062no—
602#95—1062no—
603#95—2121no—
604#95—2121no—
605#95—2121no—
606#95—2121no—
607#95—2121no—
608#95—2121no—
609#95—2121no—
610#95—2121no—
611#95—2121no—
612#95—2121no—
613#95—2121no—
614#95—2121no—
615#95—2121no—
616#95C4×D5314yescomplemented
617C24—532no—
618C24—532no—
619C24—532no—
620C24—1061no—
621C24—1061no—
622C24—1061no—
623C24—1061no—
624C24—1061no—
625C24—1061no—
626C24—1061no—
627C24—1061no—
628C24—1061no—
629C24—1061no—
630C24—1061no—
631C24—1061no—
632C24C23×D5311yescharacteristic
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
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—532no—
677C22×C4—532no—
678C22×C4—532no—
679C22×C4—532no—
680C22×C4—1061no—
681C22×C4—1061no—
682C22×C4—1061no—
683C22×C4—1061no—
684C22×C4—1061no—
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—2124no—
726C22×C4—2124no—
727C22×C4—2124no—
728C22×C4—2124no—
729C22×C4—2124no—
730C22×C4—2124no—
731C22×C4—2124no—
732C22×C4C2×C4×D5312yes—
733C22×C4C2×C4×D5312yes—
734C22×C4C2×C4×D5312yes—
735C22×C4#1171994512yes—
736C22×C4#1171994512yes—
737C22×C4#1171994712yes—
738C4⋊C4—2124no—
739C4⋊C4—2124no—
740C22⋊C4—1068no—
741C22⋊C4—2124no—
742C22⋊C4—2124no—
743C22⋊C4—2124no—
744C22⋊C4—2124no—
745C22⋊C4—2124no—
746C42—44no—
747C42—2124no—
748C23—534no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—1062no—
755C23—1062no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
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—
783C23C22×C4×D5311yescharacteristic
784C23#41×D5311yescharacteristic
785C23#41×D5311yescharacteristic
786C23#41×D5311yescharacteristic
787C23C2×#1171994711yescharacteristic
788C23C2×#1171994511yescharacteristic
789C23C2×#1171994511yescharacteristic
790C23#1313326211yescharacteristic
791C23#1313326211yescharacteristic
792C23#1313326311yescharacteristic
793C23#1313326311yescharacteristic
794C23#1313326311yescharacteristic
795C23#1313326311yescharacteristic
796C23#1313326411yescharacteristic
797C23#1313326511yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
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—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—1062no—
848C2×C4—1062no—
849C2×C4—1062no—
850C2×C4—1062no—
851C2×C4—1062no—
852C2×C4—1062no—
853C2×C4—1062no—
854C2×C4—1062no—
855C2×C4—1062no—
856C2×C4—1062no—
857C2×C4—1062no—
858C2×C4—1062no—
859C2×C4—21216no—
860C2×C4—2121no—
861C2×C4—2121no—
862C2×C4—2121no—
863C2×C4—2121no—
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—
897C22—1064no—
898C22—1064no—
899C22—1064no—
900C22—2122no—
901C22—2122no—
902C22—2122no—
903C22—2122no—
904C22—2122no—
905C22—2122no—
906C22—2122no—
907C22—2122no—
908C22—2122no—
909C22—2122no—
910C22—2122no—
911C22—2122no—
912C22#117×D5311yescharacteristic
913C22C4×#1171994711yescharacteristic
914C22C4×#1171994511yescharacteristic
915C22#1681109511yescharacteristic
916C22#1681109511yescharacteristic
917C22#1681110311yescharacteristic
918C22#1681110511yescharacteristic
919C22#1681120611yescharacteristic
920C22#1681120911yescharacteristic
921C22#1681121211yescharacteristic
922C22#1681121211yescharacteristic
923C22#1681121711yescharacteristic
924C22#1681121911yescharacteristic
925C22#1681122011yescharacteristic
926C22#1681122111yescharacteristic
927C22#1681122811yescharacteristic
928C22#1681123211yescharacteristic
929C22#1681124511yescharacteristic
930C22#1681124611yescharacteristic
931C22#1681129611yescharacteristic
932C22#1681129711yescharacteristic
933C22#1681129711yescharacteristic
934C22#1681129911yescharacteristic
935C22#1681130211yescharacteristic
936C22#1681130311yescharacteristic
937C22#1681131211yescharacteristic
938C22#1681131211yescharacteristic
939C22#1681132011yescharacteristic
940C22#1681132411yescharacteristic
941C22#1681133611yescharacteristic
942C22#1681133811yescharacteristic
943C22#1681136111yescharacteristic
944C22#1681136411yescharacteristic
945C22#1681136711yescharacteristic
946C22#1681137011yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—81no—
954C4—4241no—
955C4—4241no—
956C4—4241no—
957C4—2122no—
958C4—2122no—
959C4—2122no—
960C4—2122no—
961C2—2124no—
962C2#2027734711yescharacteristic
963C2#2027749511yescharacteristic
964C2#2027749911yescharacteristic
965C2#2027757611yescharacteristic
966C2#2027765011yescharacteristic
967C2#2027782311yescharacteristic
968C2#2027786811yescharacteristic
969C2#2028175111yescharacteristic
970C2#2028176511yescharacteristic
971C2#2028185411yescharacteristic
972C2#2028187011yescharacteristic
973C2#2028189511yescharacteristic
974C2#2028190911yescharacteristic
975C2#2028203311yescharacteristic
976C2#2028238211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1434C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1434D53
hypocenterC53#14479
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #20272981C2semidirect
3. #20272976C2semidirect
4. #20272972C2semidirect
5. #20272969C2semidirect
9. #20272942C2semidirect
10. #20272940C2semidirect
11. #20272939C2semidirect
15. C53×#1434C2semidirect
26. #16810512C4semidirect
72. C2×#11719919C2×C4semidirect
93. C2×C4×Dic53C2×C4semidirect
111. #13133124C2×C4semidirect
127. #95×C53C2×C4semidirect
484. #1434D53semidirect
540. C53#14479semidirect
616. #95C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105122
#202729812
#202729762
#202729722
#202729692
#202729632
#202729612
#202729532
#202729422
#202729402
#202729392
#202729362
C53×#14342
#1447953