Finite Group Databasebeta

← #27401105

Subgroups — #27401105

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810681C211yesmaximal, characteristic, complemented
2C2×#16810585C211yesmaximal, characteristic
3#20277094C211yesmaximal, characteristic
4#20275329C211yesmaximal, characteristic, complemented
5#20275328C211yesmaximal, characteristic, complemented
6#20275322C211yesmaximal, characteristic, complemented
7#20275321C211yesmaximal, characteristic, complemented
8#20274899C211yesmaximal, characteristic, complemented
9#20274899C211yesmaximal, characteristic, complemented
10#20274784C211yesmaximal, characteristic, complemented
11#20274699C211yesmaximal, characteristic, complemented
12#20274624C211yesmaximal, characteristic
13#20274500C211yesmaximal, characteristic, complemented
14#20274498C211yesmaximal, characteristic, complemented
15C53×#1750C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810681—24no—
21C2×C4⋊#88322C2211yescharacteristic, complemented
22C2×C4⋊#88322C2211yescharacteristic, complemented
23C2×#13133146C2211yescharacteristic, complemented
24C2×#13133146C2211yescharacteristic, complemented
25#16810585—24no—
26C2×C22⋊#88322C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133127C2211yescharacteristic, complemented
35C2×C8×Dic53C2211yescharacteristic, complemented
36#16810484C411yescharacteristic
37#16810484C411yescharacteristic
38#16810480C411yescharacteristic
39#16810480C411yescharacteristic
40#16810480C411yescharacteristic
41#16810480C411yescharacteristic
42#16810478C411yescharacteristic
43#16810478C411yescharacteristic
44C4×#11719921C2211yescharacteristic
45C4×#11719921C2211yescharacteristic
46C4×#11719921C2211yescharacteristic
47C4×#11719921C2211yescharacteristic
48#16810378C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50#16810377C2211yescharacteristic, complemented
51#16810377C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C2×#117×C53C2211yescharacteristic
55C2×C22⋊C8×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C2×#97×C53C2211yescharacteristic, complemented
58C2×C4×C8×C53C2211yescharacteristic, complemented
59C53×#336C2211yescharacteristic, complemented
60C53×#336C2211yescharacteristic, complemented
61C24×D53C2×C411yescharacteristic
62C23×Dic53C2×C411yescharacteristic
63C22×C4×D53—22no—
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—22no—
67C22×C4×D53—41no—
68C22×C4×D53—41no—
69C22×C4×D53C2×C411yescharacteristic
70C22×C4×D53C2×C411yescharacteristic
71C22×C4×D53C2311yescharacteristic
72C22×C4×D53C2311yescharacteristic
73C2×#11719912—22no—
74C2×#11719912—22no—
75C2×#11719912—22no—
76C2×#11719912—22no—
77C2×#11719912—41no—
78C2×#11719912—41no—
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83#13133176—22no—
84#13133176—22no—
85C2×C4⋊Dic53C2×C411yescharacteristic
86C2×C4⋊Dic53C2×C411yescharacteristic
87C2×C22⋊Dic53C2×C411yescharacteristic
88C2×C22⋊Dic53C2×C411yescharacteristic
89C2×#11719921C2×C411yescharacteristic
90C2×#11719921C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×#11719921C2×C411yescharacteristic
94C2×#11719921C2×C411yescharacteristic
95C2×#11719921C2×C411yescharacteristic
96C2×#11719921C2×C411yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98C2×C4×Dic53C2311yescharacteristic
99C4⋊#88322—41no—
100C4⋊#88322—41no—
101#13133146—22no—
102#13133146—22no—
103C22⋊#88322—22no—
104C22⋊#88322—22no—
105#13133129—22no—
106#13133129—22no—
107#13133129—22no—
108#13133129—22no—
109#13133129—41no—
110#13133129—41no—
111#13133127—22no—
112C8×Dic53—22no—
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118#13133124C2×C411yescharacteristic
119#13133124C2×C411yescharacteristic
120#13133124C2×C411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126#117×C53—41no—
127#117×C53—41no—
128C2×C4⋊C4×C53C2×C411yescharacteristic
129C2×C4⋊C4×C53C2×C411yescharacteristic
130C2×C22⋊C4×C53C2×C411yescharacteristic
131C2×C22⋊C4×C53C2×C411yescharacteristic
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134C22⋊C8×C53—22no—
135C22⋊C8×C53D414yes—
136#97×C53—41no—
137C4×C8×C53—41no—
138C24×C53C22×C411yescharacteristic
139C23×D53—22no—
140C23×D53—22no—
141C23×D53—22no—
142C23×D53—41no—
143C23×D53—41no—
144C23×D53—41no—
145C23×D53—41no—
146C23×D53C22×C411yescharacteristic
147C23×D53C22×C411yescharacteristic
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C22×C411yescharacteristic
157C22×C4×C53C2×D412yes—
158C22×C4×C53#4112yes—
159C22×C4×C53C2411yescharacteristic
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—41no—
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—22no—
174C2×C4×D53—22no—
175C2×C4×D53—22no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—22no—
183C2×C4×D53—44no—
184C2×C4×D53—44no—
185C2×C4×D53—44no—
186C2×C4×D53—44no—
187C2×C4×D53—41no—
188C2×C4×D53—41no—
189C2×C4×D53#4112yes—
190C2×C4×D53#4112yes—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53C2×D412yes—
202C2×C8×C53C2×D412yes—
203C4⋊C4×C53—41no—
204C4⋊C4×C53—41no—
205C22⋊C4×C53—41no—
206C22⋊C4×C53—41no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C22⋊Dic53—22no—
212C22⋊Dic53—22no—
213#11719921—22no—
214#11719921—22no—
215#11719921—41no—
216#11719921—41no—
217#11719921—41no—
218#11719921—41no—
219#11719921—41no—
220#11719921—41no—
221C4⋊Dic53—22no—
222C4⋊Dic53—22no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239#11719912—44no—
240#11719912—44no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53C4×D412yes—
248C23×C53C23×C411yescharacteristic
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—44no—
262C22×D53—44no—
263C22×D53—44no—
264C22×D53—44no—
265C22×D53—44no—
266C22×D53—44no—
267C22×D53—44no—
268C22×D53#11712yes—
269C22×D53#13112yes—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53C4×D412yes—
289C2×C4×C53C22×D411yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C53H(5,𝔽2)11yescharacteristic
294C2×C4×C53H(5,𝔽2)11yescharacteristic
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—44no—
313C2×Dic53#11712yes—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—22no—
318C4×D53—44no—
319C4×D53—44no—
320C4×D53—41no—
321C4×D53—41no—
322C4×D53—41no—
323C4×D53—41no—
324C8×C53—22no—
325C8×C53—22no—
326C8×C53—41no—
327C8×C53—41no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#88322—41no—
332#22559—531nomaximal, Sylow
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53C2×#11711yescharacteristic
341C22×C53C2×C4×D411yescharacteristic
342C22×C53#51811yescharacteristic
343C22×C53C2×#13111yescharacteristic
344C22×C53#56811yescharacteristic
345C22×C53#56811yescharacteristic
346C22×C53#56811yescharacteristic
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—416no—
354C2×D53—41no—
355C2×D53—41no—
356C2×D53—41no—
357C2×D53—41no—
358C2×D53—41no—
359C2×D53—41no—
360C2×D53—41no—
361C2×D53—41no—
362C4×C53—22no—
363C4×C53—41no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53#54611yescharacteristic
368C4×C53#54611yescharacteristic
369C4×C53#55111yescharacteristic
370C4×C53#55111yescharacteristic
371Dic53—22no—
372Dic53—41no—
373Dic53—41no—
374Dic53—41no—
375Dic53—41no—
376Dic53—41no—
377C2×#433—531no—
378C2×#407—531no—
379#2280—531no—
380#1924—531no—
381#1924—531no—
382#1923—531no—
383#1923—531no—
384#1851—531no—
385#1851—531no—
386#1818—531no—
387#1798—531no—
388#1779—531no—
389#1753—531no—
390#1753—531no—
391#1750D5311yescharacteristic, complemented
392C2×C53—42no—
393C2×C53#234211yescharacteristic
394C2×C53#292111yescharacteristic
395C2×C53#292411yescharacteristic
396C2×C53#293011yescharacteristic
397C2×C53#293311yescharacteristic
398C2×C53#297611yescharacteristic
399C2×C53#297811yescharacteristic
400D53—42no—
401D53—42no—
402C24×C4—531no—
403C22×M16—531no—
404C22×M16—531no—
405C2×#117—531no—
406C2×#117C2×D5311yescharacteristic
407#433—1064no—
408C2×C4⋊C8—531no—
409C2×C4⋊C8—531no—
410C2×C4⋊C8—531no—
411C2×C4⋊C8—531no—
412#407—1064no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419C2×C22⋊C8—531no—
420C2×C22⋊C8—531no—
421C2×C22⋊C8C2×D5311yescharacteristic
422C2×C22⋊C8C2×D5311yescharacteristic
423C2×#97—531no—
424C2×#97C2×D5311yescharacteristic, complemented
425C2×C4×C8—531no—
426C2×C4×C8C2×D5311yescharacteristic, complemented
427#381—531no—
428#381—531no—
429#380—531no—
430#380—531no—
431#380—531no—
432#380—531no—
433#379—531no—
434#379—531no—
435C4×C22⋊C4—531no—
436C4×C22⋊C4—531no—
437C4×C22⋊C4—531no—
438C4×C22⋊C4—531no—
439#336—531no—
440#336—531no—
441#336—531no—
442#336—531no—
443#336—531no—
444#336—531no—
445#336C2×D5311yescharacteristic, complemented
446#336C2×D5311yescharacteristic, complemented
447C53#2255911yescharacteristic, complemented, Sylow
448C25—531no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—531no—
454C23×C4—1062no—
455C23×C4—1062no—
456C23×C4—1062no—
457C23×C4—1062no—
458C23×C4—2121no—
459C23×C4—2121no—
460C23×C4C22×D5311yescharacteristic
461C2×M16—1062no—
462C2×M16—1062no—
463C2×M16—1062no—
464C2×M16—1062no—
465C2×M16—2121no—
466C2×M16—2121no—
467C22×C8—531no—
468C22×C8—531no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8C22×D5311yescharacteristic
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475#117—41no—
476#117—41no—
477#117—1062no—
478#117—1062no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4C4×D5311yescharacteristic
482C2×C4⋊C4C4×D5311yescharacteristic
483C2×C22⋊C4—531no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C22⋊C4—531no—
487C2×C22⋊C4—531no—
488C2×C22⋊C4—531no—
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4C4×D5311yescharacteristic
494C2×C22⋊C4C4×D5311yescharacteristic
495C2×C42—531no—
496C2×C42—531no—
497C2×C42C22×D5311yescharacteristic
498C2×C42C22×D5311yescharacteristic
499C4⋊C8—1062no—
500C4⋊C8—1062no—
501C4⋊C8—2121no—
502C4⋊C8—2121no—
503C22⋊C8—22no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—1062no—
508C22⋊C8—1062no—
509C22⋊C8—1062no—
510C22⋊C8—2121no—
511C22⋊C8—2121no—
512C22⋊C8D21214yes—
513#97—41no—
514#97—1062no—
515C4×C8—41no—
516C4×C8—1062no—
517#95—531no—
518#95—531no—
519#95—531no—
520#95—531no—
521#95—531no—
522#95—531no—
523#95—531no—
524#95—531no—
525C24—531no—
526C24—531no—
527C24—1062no—
528C24—1062no—
529C24—1062no—
530C24—2121no—
531C24—2121no—
532C24—2121no—
533C24—2121no—
534C24C2×C4×D5311yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—531no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—531no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—531no—
546C22×C4—531no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—2121no—
564C22×C4—2121no—
565C22×C4—2124no—
566C22×C4—2124no—
567C22×C4—2124no—
568C22×C4—2124no—
569C22×C4—2121no—
570C22×C4C2×C4×D5311yescharacteristic
571C22×C4C2×C4×D5311yescharacteristic
572C22×C4C2×C4×D5311yescharacteristic
573C22×C4C2×C4×D5311yescharacteristic
574C22×C4C2×C4×D5311yescharacteristic
575C22×C4C2×D21212yes—
576C22×C4#1171994512yes—
577C22×C4C23×D5311yescharacteristic
578M16—2124no—
579M16—2124no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8C2×D21212yes—
603C2×C8C2×D21212yes—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—1062no—
607C4⋊C4—1062no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—1062no—
611C22⋊C4—1062no—
612C22⋊C4—1062no—
613C22⋊C4—1062no—
614C22⋊C4—2121no—
615C22⋊C4—2121no—
616C22⋊C4—2121no—
617C22⋊C4—2121no—
618C22⋊C4—2121no—
619C22⋊C4—2121no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—1061no—
625C42—1061no—
626C42—1061no—
627C42—1061no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—532no—
635C23—532no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1061no—
642C23—1061no—
643C23—1061no—
644C23—1061no—
645C23—1061no—
646C23—1061no—
647C23—1061no—
648C23—2124no—
649C23—2124no—
650C23—2124no—
651C23—2124no—
652C23—2124no—
653C23—2124no—
654C23—2124no—
655C23C4×D21212yes—
656C23C22×C4×D5311yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—532no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—1061no—
691C2×C4—1061no—
692C2×C4—1061no—
693C2×C4—1061no—
694C2×C4—1061no—
695C2×C4—1061no—
696C2×C4—1061no—
697C2×C4—2124no—
698C2×C4—2124no—
699C2×C4—2124no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4C4×D21212yes—
705C2×C4C22×D21211yescharacteristic
706C2×C4#41×D5311yescharacteristic
707C2×C4#41×D5311yescharacteristic
708C2×C4C2×#1171994511yescharacteristic
709C2×C4#1313326211yescharacteristic
710C2×C4#1313326211yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—2121no—
716C8—2121no—
717C8—2121no—
718C8—2121no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—1062no—
727C22—1062no—
728C22—1062no—
729C22—1062no—
730C22—1062no—
731C22—1062no—
732C22—21216no—
733C22—2121no—
734C22—2121no—
735C22—2121no—
736C22—2121no—
737C22—2121no—
738C22—2121no—
739C22—2121no—
740C22—2121no—
741C22#117×D5311yescharacteristic
742C22C2×C4×D21211yescharacteristic
743C22#1681109611yescharacteristic
744C22#131×D5311yescharacteristic
745C22#1681138811yescharacteristic
746C22#1681138811yescharacteristic
747C22#1681138811yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—1062no—
754C4—2121no—
755C4—2121no—
756C4—2121no—
757C4—2121no—
758C4—2121no—
759C4#1681126811yescharacteristic
760C4#1681126811yescharacteristic
761C4#1681130211yescharacteristic
762C4#1681130211yescharacteristic
763C2—42no—
764C2—2122no—
765C2—2122no—
766C2#2027756711yescharacteristic
767C2#2028334911yescharacteristic
768C2#2028337111yescharacteristic
769C2#2028342011yescharacteristic
770C2#2028344311yescharacteristic
771C2#2028375811yescharacteristic
772C2#2028377311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1750C2
prime radicalC24×D53C2×C4
cosocleC22×C4×C53C24
hypercenter#1750D53
hypocenterC53#22559
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#16810681C2semidirect
4. #20275329C2semidirect
5. #20275328C2semidirect
6. #20275322C2semidirect
7. #20275321C2semidirect
8. #20274899C2semidirect
9. #20274899C2semidirect
10. #20274784C2semidirect
11. #20274699C2semidirect
13. #20274500C2semidirect
14. #20274498C2semidirect
15. C53×#1750C2semidirect
21. C2×C4⋊#88322C22semidirect
22. C2×C4⋊#88322C22semidirect
23. C2×#13133146C22semidirect
24. C2×#13133146C22semidirect
34. C2×#13133127C22semidirect
35. C2×C8×Dic53C22semidirect
48. #16810378C22semidirect
49. #16810378C22semidirect
50. #16810377C22semidirect
51. #16810377C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
57. C2×#97×C53C22semidirect
58. C2×C4×C8×C53C22semidirect
59. C53×#336C22semidirect
60. C53×#336C22semidirect
391. #1750D53semidirect
424. C2×#97C2×D53semidirect
426. C2×C4×C8C2×D53semidirect
445. #336C2×D53semidirect
446. #336C2×D53semidirect
447. C53#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#168106812
C2×#168105852
#202770942
#202753292
#202753282
#202753222
#202753212
#202748992
#202747842
#202746992
#202746242
#202745002
#202744982
C53×#17502
#2255953