Finite Group Databasebeta

← #27395202

Subgroups — #27395202

Order 13568.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810702C211yesmaximal, characteristic, complemented
2C2×#16810585C211yesmaximal, characteristic, complemented
3C4×#13133187C211yesmaximal, characteristic
4#20275512C211yesmaximal, characteristic, complemented
5#20275507C211yesmaximal, characteristic, complemented
6#20275330C211yesmaximal, characteristic, complemented
7#20275322C211yesmaximal, characteristic, complemented
8#20275321C211yesmaximal, characteristic, complemented
9#20275011C211yesmaximal, characteristic, complemented
10#20275011C211yesmaximal, characteristic, complemented
11#20275009C211yesmaximal, characteristic, complemented
12#20274896C211yesmaximal, characteristic, complemented
13#20274624C211yesmaximal, characteristic, complemented
14#20274497C211yesmaximal, characteristic, complemented
15C53×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×#11719912C2211yescharacteristic, complemented
20C2×#13133187C411yescharacteristic
21C2×C4×D212C2211yescharacteristic
22C2×C4×D212C2211yescharacteristic
23C2×C4×C22⋊D53C2211yescharacteristic
24#16810702—24no—
25C2×C4⋊#88322C2211yescharacteristic, complemented
26C2×#13133146C2211yescharacteristic, complemented
27#16810585—24no—
28C2×C22⋊#88322C2211yescharacteristic
29C2×C22⋊#88322C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic, complemented
37C2×#13133129C2211yescharacteristic, complemented
38C2×#13133129C2211yescharacteristic, complemented
39C2×#13133128C2211yescharacteristic, complemented
40C2×C8×Dic53C2211yescharacteristic, complemented
41#16810501C411yescharacteristic
42#16810501C411yescharacteristic
43#16810500C411yescharacteristic
44#16810498C411yescharacteristic
45#16810497C411yescharacteristic
46#16810497C411yescharacteristic
47#16810478C411yescharacteristic
48C4×#11719921C2211yescharacteristic
49C4×#11719921C2211yescharacteristic
50#16810378C2211yescharacteristic, complemented
51#16810378C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C2×C4⋊C8×C53C2211yescharacteristic, complemented
55C2×C22⋊C8×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C2×C4×C8×C53C2211yescharacteristic, complemented
58C4×C22⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic, complemented
60C53×#336C2211yescharacteristic, complemented
61C24×D53C2×C411yescharacteristic
62C22×D212C2×C411yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×C22⋊D53C2×C411yescharacteristic
65C23×Dic53C2×C411yescharacteristic
66C22×C4×D53—22no—
67C22×C4×D53—22no—
68C22×C4×D53—41no—
69C22×C4×D53—41no—
70C22×C4×D53—41no—
71C22×C4×D53—41no—
72C22×C4×D53C2×C411yescharacteristic
73C22×C4×D53C2×C411yescharacteristic
74C22×C4×D53C2311yescharacteristic
75C22×C4×D53C2311yescharacteristic
76C22×C4×D53C2311yescharacteristic
77C2×#11719912—22no—
78C2×#11719912—22no—
79C2×#11719912—41no—
80C2×#11719912—41no—
81C2×#11719912—41no—
82C2×#11719912—41no—
83C2×#11719912—41no—
84C2×#11719912—41no—
85C2×#11719912D414yescomplemented
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90#13133187—24no—
91C4×D212—22no—
92C4×D212—22no—
93C4×D212—41no—
94C4×D212—41no—
95C4×C22⋊D53—41no—
96C4×C22⋊D53—41no—
97C2×C4⋊Dic53C2×C411yescharacteristic
98C2×C4⋊Dic53C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×C22⋊Dic53C2×C411yescharacteristic
101C2×#11719921C2×C411yescharacteristic
102C2×#11719921C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×C4×Dic53C2311yescharacteristic
111C4⋊#88322—22no—
112#13133146—41no—
113C22⋊#88322—22no—
114C22⋊#88322—41no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—22no—
120#13133129—41no—
121#13133129—41no—
122#13133129—41no—
123#13133129—41no—
124#13133128—41no—
125C8×Dic53—41no—
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129#13133124C2×C411yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C22⋊C4×C53C2×C411yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C2×C42×C53C2311yescharacteristic
139C4⋊C8×C53—41no—
140C22⋊C8×C53—22no—
141C22⋊C8×C53—41no—
142C4×C8×C53—22no—
143#95×C53C2×C411yescharacteristic
144#95×C53C2×C411yescharacteristic
145C24×C53C22×C411yescharacteristic
146C23×D53—22no—
147C23×D53—22no—
148C23×D53—22no—
149C23×D53—41no—
150C23×D53—41no—
151C23×D53—41no—
152C23×D53—41no—
153C23×D53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C23×D53C22×C411yescharacteristic
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×C53C22×C411yescharacteristic
163C22×C4×C53C22×C411yescharacteristic
164C22×C4×C53C22×C411yescharacteristic
165C22×C4×C53C22×C411yescharacteristic
166C22×C4×C53C22×C411yescharacteristic
167C22×C4×C53C2411yescharacteristic
168C2×C22⋊D53—22no—
169C2×C22⋊D53—22no—
170C2×C22⋊D53—41no—
171C22×Dic53—22no—
172C22×Dic53—41no—
173C22×Dic53—41no—
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C22×Dic53C22×C411yescharacteristic
178C22×Dic53C22×C411yescharacteristic
179C2×D212—22no—
180C2×D212—22no—
181C2×D212—22no—
182C2×D212—41no—
183C2×D212—41no—
184C2×D212—41no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—22no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—21no—
196C2×C4×D53—21no—
197C2×C4×D53—21no—
198C2×C4×D53—21no—
199C2×C4×D53—21no—
200C2×C4×D53—21no—
201C2×C4×D53—21no—
202C2×C4×D53—22no—
203C2×C4×D53—44no—
204C2×C4×D53—44no—
205C2×C4×D53—44no—
206C2×C4×D53—44no—
207C2×C4×D53—41no—
208C2×C4×D53—41no—
209C2×C4×D53—41no—
210C2×C4×D53—41no—
211C2×C4×D53C2×D412yes—
212C2×C4×D53#4112yes—
213C2×C8×C53—21no—
214C2×C8×C53—21no—
215C2×C8×C53—21no—
216C2×C8×C53—21no—
217C2×C8×C53—21no—
218C2×C8×C53—21no—
219C2×C8×C53—21no—
220C2×C8×C53—21no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53C2×D412yes—
225C22⋊C4×C53—22no—
226C22⋊C4×C53—22no—
227C42×C53—21no—
228C42×C53—21no—
229C42×C53—21no—
230C42×C53—21no—
231C22⋊Dic53—41no—
232#11719921—22no—
233#11719921—22no—
234#11719921—22no—
235#11719921—41no—
236#11719921—41no—
237#11719921—41no—
238#11719921—41no—
239#11719921—41no—
240#11719921M1614yescomplemented
241C4⋊Dic53—22no—
242C4⋊Dic53—41no—
243#11719919—41no—
244C4×Dic53—21no—
245C4×Dic53—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322C2×D412yes—
258#11719912—44no—
259#11719912—44no—
260#11719912—44no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53#13112yes—
268C23×C53C23×C411yescharacteristic
269C22×D53—21no—
270C22×D53—21no—
271C22×D53—21no—
272C22×D53—21no—
273C22×D53—21no—
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53—21no—
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—21no—
282C22×D53—21no—
283C22×D53—21no—
284C22×D53—21no—
285C22×D53—21no—
286C22×D53—21no—
287C22×D53—21no—
288C22×D53—44no—
289C22×D53—44no—
290C22×D53—44no—
291C22×D53—44no—
292C22×D53—44no—
293C22×D53—44no—
294C22×D53—44no—
295C22×D53C4×D412yes—
296C22×D53C2×M1612yes—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53C2×M1612yes—
316C2×C4×C53C22×D411yescharacteristic
317C2×C4×C53C2×#4111yescharacteristic
318C2×C4×C53H(5,𝔽2)11yescharacteristic
319C2×C4×C53H(5,𝔽2)11yescharacteristic
320C2×C4×C53H(5,𝔽2)11yescharacteristic
321C2×C4×C53H(5,𝔽2)11yescharacteristic
322C22⋊D53—44no—
323C2×Dic53—21no—
324C2×Dic53—21no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—21no—
328C2×Dic53—21no—
329C2×Dic53—21no—
330C2×Dic53—21no—
331C2×Dic53—21no—
332C2×Dic53—21no—
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—44no—
337C2×Dic53C4×D412yes—
338C2×Dic53C2×M1612yes—
339D212—44no—
340D212—44no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—44no—
346C4×D53—44no—
347C4×D53—41no—
348C4×D53—41no—
349C4×D53—41no—
350C4×D53—41no—
351C4×D53—41no—
352C4×D53—41no—
353C4×D53—41no—
354C4×D53—41no—
355C8×C53—22no—
356C8×C53—41no—
357C8×C53—41no—
358C8×C53—41no—
359#88322—22no—
360#88322—41no—
361#88322—41no—
362#88322—41no—
363#22038—531nomaximal, Sylow
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—41no—
370C22×C53—41no—
371C22×C53C2×C4×D411yescharacteristic
372C22×C53#51811yescharacteristic
373C22×C53#51811yescharacteristic
374C22×C53C22×M1611yescharacteristic
375C22×C53C2×#13111yescharacteristic
376C22×C53#56811yescharacteristic
377C22×C53#56811yescharacteristic
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—416no—
385C2×D53—41no—
386C2×D53—41no—
387C2×D53—41no—
388C2×D53—41no—
389C2×D53—41no—
390C2×D53—41no—
391C2×D53—41no—
392C2×D53—41no—
393C2×D53—41no—
394C2×D53—41no—
395C2×D53—41no—
396C2×D53—41no—
397C2×D53—41no—
398C2×D53—41no—
399C2×D53—41no—
400C4×C53—22no—
401C4×C53—41no—
402C4×C53—41no—
403C4×C53—41no—
404C4×C53—41no—
405C4×C53#53411yescharacteristic
406C4×C53#53511yescharacteristic
407C4×C53#53811yescharacteristic
408C4×C53#53811yescharacteristic
409Dic53—22no—
410Dic53—22no—
411Dic53—41no—
412Dic53—41no—
413Dic53—41no—
414C2×#436—531no—
415C2×#407—531no—
416C4×#120—531no—
417#1955—531no—
418#1954—531no—
419#1924—531no—
420#1923—531no—
421#1923—531no—
422#1923D5311yescharacteristic, complemented
423#1870—531no—
424#1870—531no—
425#1870—531no—
426#1851—531no—
427#1779—531no—
428#1753—531no—
429C2×C53—42no—
430C2×C53#232111yescharacteristic
431C2×C53#293311yescharacteristic
432C2×C53D4×M1611yescharacteristic
433C2×C53#297411yescharacteristic
434C2×C53#297511yescharacteristic
435C2×C53#297611yescharacteristic
436C2×C53#297811yescharacteristic
437D53—42no—
438D53—42no—
439D53—81no—
440C24×C4—531no—
441C22×M16—531no—
442C22×M16—531no—
443C22×M16—531no—
444C2×#120—531no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448#436—1064no—
449C2×C4⋊C8—531no—
450C2×C4⋊C8—531no—
451C2×C4⋊C8C2×D5311yescharacteristic, complemented
452#407—1064no—
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×C22⋊C8—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×C22⋊C8—531no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×C22⋊C8—531no—
462C2×C22⋊C8—531no—
463C2×C22⋊C8—531no—
464C2×C22⋊C8C2×D5311yescharacteristic
465C2×C22⋊C8C2×D5311yescharacteristic
466C2×#97—531no—
467C2×C4×C8—531no—
468C2×C4×C8C2×D5311yescharacteristic, complemented
469#386—531no—
470#386—531no—
471#386—531no—
472#385—531no—
473#385—531no—
474#385—531no—
475#379—531no—
476C4×C22⋊C4—531no—
477C4×C22⋊C4—531no—
478C4×C22⋊C4C2×D5311yescharacteristic
479#336—531no—
480#336—531no—
481#336—531no—
482#336—531no—
483#336C2×D5311yescharacteristic, complemented
484#336C2×D5311yescharacteristic, complemented
485C53#2203811yescharacteristic, complemented, Sylow
486C25—531no—
487C22×D4—531no—
488C22×D4—531no—
489C22×D4—531no—
490C23×C4—531no—
491C23×C4—531no—
492C23×C4—531no—
493C23×C4—531no—
494C23×C4—531no—
495C23×C4—531no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—2121no—
499C23×C4—2121no—
500C23×C4—2121no—
501C23×C4—2121no—
502C23×C4C22×D5311yescharacteristic
503C2×M16—534no—
504C2×M16—1062no—
505C2×M16—1062no—
506C2×M16—2121no—
507C2×M16—2121no—
508C2×M16—2121no—
509C2×M16—2121no—
510C2×M16—2121no—
511C2×M16—2121no—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8C22×D5311yescharacteristic
517C22×C8C22×D5311yescharacteristic
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5311yescharacteristic
520#120—1064no—
521C4×D4—1062no—
522C4×D4—1062no—
523C4×D4—2121no—
524C4×D4—2121no—
525C4×D4—2121no—
526C4×D4—2121no—
527C2×C4⋊C4—531no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—531no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—531no—
533C2×C22⋊C4—531no—
534C2×C22⋊C4—531no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—531no—
538C2×C22⋊C4—531no—
539C2×C22⋊C4—531no—
540C2×C22⋊C4C4×D5311yescharacteristic
541C2×C22⋊C4C4×D5311yescharacteristic
542C2×C42—531no—
543C2×C42C22×D5311yescharacteristic
544C2×C42C22×D5311yescharacteristic
545C4⋊C8—41no—
546C4⋊C8—1062no—
547C4⋊C8—2121no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—1062no—
551C22⋊C8—1062no—
552C22⋊C8—1062no—
553C22⋊C8—1062no—
554C22⋊C8—1062no—
555C22⋊C8—1062no—
556C22⋊C8—2121no—
557C22⋊C8—2121no—
558C22⋊C8—2121no—
559C22⋊C8—2121no—
560C22⋊C8—2121no—
561#97—2121no—
562C4×C8—22no—
563C4×C8—2121no—
564#95—531no—
565#95—531no—
566#95—531no—
567#95—531no—
568#95C4×D5311yescharacteristic
569#95C4×D5311yescharacteristic
570C24—531no—
571C24—531no—
572C24—531no—
573C24—1062no—
574C24—1062no—
575C24—1062no—
576C24—2121no—
577C24—2121no—
578C24—2121no—
579C24—2121no—
580C24C2×C4×D5311yescharacteristic
581C2×D4—1062no—
582C2×D4—1062no—
583C2×D4—1062no—
584C2×D4—1062no—
585C2×D4—1062no—
586C2×D4—2121no—
587C2×D4—2121no—
588C2×D4—2121no—
589C2×D4—2121no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—532no—
599C22×C4—532no—
600C22×C4—531no—
601C22×C4—531no—
602C22×C4—531no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—2121no—
623C22×C4—2121no—
624C22×C4—2121no—
625C22×C4—2121no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—2124no—
629C22×C4—2124no—
630C22×C4—2121no—
631C22×C4—2121no—
632C22×C4C2×C4×D5311yescharacteristic
633C22×C4C2×C4×D5311yescharacteristic
634C22×C4C2×C4×D5311yescharacteristic
635C22×C4C2×C4×D5311yescharacteristic
636C22×C4C2×C4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638M16—2124no—
639M16—2124no—
640M16—2124no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—532no—
653C2×C8—1061no—
654C2×C8—1061no—
655C2×C8—1061no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8D4×D5312yes—
665C4⋊C4—1062no—
666C4⋊C4—2121no—
667C4⋊C4—2121no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—534no—
671C22⋊C4—1062no—
672C22⋊C4—1062no—
673C22⋊C4—1062no—
674C22⋊C4—2121no—
675C22⋊C4—2121no—
676C22⋊C4—2121no—
677C22⋊C4—2121no—
678C22⋊C4—2121no—
679C22⋊C4—2121no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—1061no—
685C42—1061no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—532no—
693C23—532no—
694C23—1061no—
695C23—1061no—
696C23—1061no—
697C23—1061no—
698C23—1061no—
699C23—1061no—
700C23—1061no—
701C23—1061no—
702C23—1061no—
703C23—1061no—
704C23—1061no—
705C23—1061no—
706C23—1061no—
707C23—1061no—
708C23—1061no—
709C23—1061no—
710C23—1061no—
711C23—1061no—
712C23—1061no—
713C23—2124no—
714C23—2124no—
715C23—2124no—
716C23—2124no—
717C23—2124no—
718C23—2124no—
719C23—2124no—
720C23#1313322312yes—
721C23C22×C4×D5311yescharacteristic
722D4—2124no—
723D4—2124no—
724D4—2124no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—1061no—
746C2×C4—1061no—
747C2×C4—1061no—
748C2×C4—1061no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1061no—
754C2×C4—1061no—
755C2×C4—1061no—
756C2×C4—1061no—
757C2×C4—1061no—
758C2×C4—1061no—
759C2×C4—1061no—
760C2×C4—1061no—
761C2×C4—1061no—
762C2×C4—2124no—
763C2×C4—2124no—
764C2×C4—2124no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4—2121no—
769C2×C4—2121no—
770C2×C4—2121no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4M16×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4#41×D5311yescharacteristic
776C2×C4#1313326211yescharacteristic
777C2×C4#1313326311yescharacteristic
778C2×C4#1313326311yescharacteristic
779C2×C4#1313326311yescharacteristic
780C8—22no—
781C8—41no—
782C8—41no—
783C8—41no—
784C8—1062no—
785C8—2121no—
786C8—2121no—
787C8—2121no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1062no—
796C22—1062no—
797C22—1062no—
798C22—1062no—
799C22—1062no—
800C22—1062no—
801C22—21216no—
802C22—2121no—
803C22—2121no—
804C22—2121no—
805C22—2121no—
806C22—2121no—
807C22—2121no—
808C22—2121no—
809C22—2121no—
810C22—2121no—
811C22—2121no—
812C22—2121no—
813C22—2121no—
814C22—2121no—
815C22—2121no—
816C22—2121no—
817C22C4×D4×D5311yescharacteristic
818C22#1681109511yescharacteristic
819C22#1681109711yescharacteristic
820C22C2×M16×D5311yescharacteristic
821C22C2×#1313322311yescharacteristic
822C22#1681138811yescharacteristic
823C22#1681138811yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—1062no—
830C4—1062no—
831C4—2121no—
832C4—2121no—
833C4—2121no—
834C4#1681118411yescharacteristic
835C4#1681118911yescharacteristic
836C4#1681120711yescharacteristic
837C4#1681121211yescharacteristic
838C2—42no—
839C2—4241no—
840C2—2122no—
841C2—2122no—
842C2#2027737711yescharacteristic
843C2#2028343511yescharacteristic
844C2#2028344811yescharacteristic
845C2#2028374911yescharacteristic
846C2#2028375311yescharacteristic
847C2#2028375711yescharacteristic
848C2#2028377611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1923C2
prime radicalC2×#13133187C4
cosocleC22×C4×C53C24
hypercenter#1923D53
hypocenterC53#22038
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16810702C2semidirect
2. C2×#16810585C2semidirect
4. #20275512C2semidirect
5. #20275507C2semidirect
6. #20275330C2semidirect
7. #20275322C2semidirect
8. #20275321C2semidirect
9. #20275011C2semidirect
10. #20275011C2semidirect
11. #20275009C2semidirect
12. #20274896C2semidirect
13. #20274624C2semidirect
14. #20274497C2semidirect
15. C53×#1923C2semidirect
19. C22×#11719912C22semidirect
25. C2×C4⋊#88322C22semidirect
26. C2×#13133146C22semidirect
36. C2×#13133129C22semidirect
37. C2×#13133129C22semidirect
38. C2×#13133129C22semidirect
39. C2×#13133128C22semidirect
40. C2×C8×Dic53C22semidirect
50. #16810378C22semidirect
51. #16810378C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
54. C2×C4⋊C8×C53C22semidirect
57. C2×C4×C8×C53C22semidirect
59. C53×#336C22semidirect
60. C53×#336C22semidirect
85. C2×#11719912D4semidirect
240. #11719921M16semidirect
422. #1923D53semidirect
451. C2×C4⋊C8C2×D53semidirect
468. C2×C4×C8C2×D53semidirect
483. #336C2×D53semidirect
484. #336C2×D53semidirect
485. C53#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#168107022
C2×#168105852
C4×#131331872
#202755122
#202755072
#202753302
#202753222
#202753212
#202750112
#202750092
#202748962
#202746242
#202744972
C53×#19232
#2203853