Finite Group Databasebeta

← #27390174

Subgroups — #27390174

Order 13568.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810700C211yesmaximal, characteristic, complemented
2C2×#16810693C211yesmaximal, characteristic, complemented
3C2×#16810693C211yesmaximal, characteristic, complemented
4C2×#16810575C211yesmaximal, characteristic, complemented
5C4×#13133192C211yesmaximal, characteristic
6#20275513C211yesmaximal, characteristic, complemented
7#20275320C211yesmaximal, characteristic, complemented
8#20275320C211yesmaximal, characteristic, complemented
9#20275011C211yesmaximal, characteristic, complemented
10#20275011C211yesmaximal, characteristic, complemented
11#20274692C211yesmaximal, characteristic, complemented
12#20274590C211yesmaximal, characteristic, complemented
13#20274497C211yesmaximal, characteristic, complemented
14#20274485C211yesmaximal, characteristic, complemented
15C53×#1940C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C2×#13133192C411yescharacteristic
21C2×C4×D212C2211yescharacteristic
22C2×C4×D212C2211yescharacteristic
23C2×C4×D212C2211yescharacteristic
24C2×C42×D53C2211yescharacteristic
25#16810700—24no—
26#16810693—24no—
27#16810693—24no—
28C2×C4⋊#88322C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37#16810575—24no—
38C2×#13133128C2211yescharacteristic
39C2×#13133128C2211yescharacteristic
40C2×C4×#88322C2211yescharacteristic
41C2×C8×Dic53C2211yescharacteristic
42C2×C8×Dic53C2211yescharacteristic
43#16810524C411yescharacteristic
44#16810522C411yescharacteristic
45#16810515C411yescharacteristic
46#16810515C411yescharacteristic
47#16810501C411yescharacteristic
48#16810501C411yescharacteristic
49#16810480C411yescharacteristic
50C4×#11719921C2211yescharacteristic
51C4×#11719921C2211yescharacteristic
52#16810378C2211yescharacteristic
53#16810378C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×#97×C53C2211yescharacteristic
60C4×C4⋊C4×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×D212C2×C411yescharacteristic
65C22×D212C2×C411yescharacteristic
66C22×C4×D53C2×C411yescharacteristic
67C22×C4×D53C2×C411yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C22×C4×D53C2311yescharacteristic
70C22×C4×D53C2311yescharacteristic
71C2×#11719912—22no—
72C2×#11719912—22no—
73C2×#11719912—22no—
74C2×#11719912—22no—
75C2×#11719912—22no—
76C2×#11719912—22no—
77C2×#11719912—22no—
78C2×#11719912—22no—
79C2×#11719912D414yescomplemented
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C2×C8×D53—22no—
85C2×C8×D53—22no—
86C2×C8×D53—22no—
87#13133192—24no—
88C4×D212—22no—
89C4×D212—22no—
90C4×D212—22no—
91C4×D212—22no—
92C4×D212—22no—
93C4×D212—22no—
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×C4⋊Dic53C2×C411yescharacteristic
97C2×#11719921C2×C411yescharacteristic
98C2×#11719921C2×C411yescharacteristic
99C2×#11719921C2×C411yescharacteristic
100C2×#11719921C2×C411yescharacteristic
101C2×#11719921C2×C411yescharacteristic
102C2×#11719921C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×C4×Dic53C2×C411yescharacteristic
108C2×C4×Dic53C2×C411yescharacteristic
109C2×C4×Dic53C2311yescharacteristic
110C42×D53—22no—
111C42×D53—22no—
112C4⋊#88322—22no—
113#13133129—22no—
114#13133129—22no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—22no—
120#13133129—22no—
121#13133128—22no—
122#13133128D414yescomplemented
123C4×#88322—22no—
124C8×Dic53—22no—
125C8×Dic53—22no—
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129#13133124C2×C411yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134C2×C4⋊C4×C53C2×C411yescharacteristic
135C2×C4⋊C4×C53C2×C411yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C2×C42×C53C2311yescharacteristic
139C4⋊C8×C53—22no—
140C4⋊C8×C53—22no—
141C4⋊C8×C53—22no—
142#97×C53—22no—
143#95×C53C2×C411yescharacteristic
144#95×C53C2×C411yescharacteristic
145C23×D53C22×C411yescharacteristic
146C23×D53C22×C411yescharacteristic
147C23×D53C22×C411yescharacteristic
148C22×C4×C53C22×C411yescharacteristic
149C22×C4×C53C22×C411yescharacteristic
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C2411yescharacteristic
155C22×Dic53C22×C411yescharacteristic
156C22×Dic53C22×C411yescharacteristic
157C22×Dic53C22×C411yescharacteristic
158C22×Dic53C22×C411yescharacteristic
159C22×Dic53C22×C411yescharacteristic
160C2×D212—22no—
161C2×D212—22no—
162C2×D212—22no—
163C2×D212—22no—
164C2×D212—22no—
165C2×D212—22no—
166C2×D212—41no—
167C2×D212—41no—
168C2×D212—41no—
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—21no—
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—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—22no—
188C2×C4×D53—22no—
189C2×C4×D53—41no—
190C2×C4×D53—41no—
191C2×C4×D53C2×D412yes—
192C2×C4×D53#4112yes—
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×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53C2×D412yes—
204C2×C8×C53#4112yes—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—41no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53C2×D412yes—
212C42×C53#4112yes—
213#11719921—22no—
214#11719921—22no—
215#11719921—22no—
216#11719921—22no—
217#11719921—22no—
218#11719921—22no—
219#11719921—22no—
220#11719921—22no—
221#11719921—22no—
222#11719921M1614yescomplemented
223C4⋊Dic53—22no—
224C4⋊Dic53—22no—
225C4⋊Dic53—22no—
226C4×Dic53—22no—
227C4×Dic53—22no—
228C4×Dic53—21no—
229C4×Dic53—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×#88322C2×D412yes—
239C2×#88322C2×D412yes—
240C2×#88322C2×D412yes—
241C2×#88322#4112yes—
242#11719912—28no—
243#11719912—28no—
244#11719912—44no—
245C8×D53—44no—
246C23×C53C23×C411yescharacteristic
247C22×D53—21no—
248C22×D53—21no—
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—21no—
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53—21no—
266C22×D53C4×D412yes—
267C22×D53C2×M1612yes—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
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×C53C4×D412yes—
284C2×C4×C53C4×D412yes—
285C2×C4×C53C2×M1612yes—
286C2×C4×C53C22×D411yescharacteristic
287C2×C4×C53C22×D411yescharacteristic
288C2×C4×C53C2×#4111yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53C2×#4111yescharacteristic
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
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×Dic53C4×D412yes—
305C2×Dic53C2×M1612yes—
306C2×Dic53#13112yes—
307D212—44no—
308D212—44no—
309D212—44no—
310C4×D53—22no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—44no—
315C4×D53—44no—
316C4×D53—41no—
317C4×D53—41no—
318C4×D53—41no—
319C4×D53—41no—
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—22no—
329#88322—41no—
330#88322—41no—
331#88322#12114yescomplemented
332#21490—531nomaximal, Sylow
333C22×C53C2×C4×D411yescharacteristic
334C22×C53C2×C4×D411yescharacteristic
335C22×C53C4×#4111yescharacteristic
336C22×C53C22×M1611yescharacteristic
337C22×C53C2×#13111yescharacteristic
338C22×C53#56811yescharacteristic
339C22×C53#56811yescharacteristic
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C2×D53—41no—
355C2×D53—41no—
356C2×D53—41no—
357C2×D53—41no—
358C2×D53—41no—
359C2×D53—41no—
360C2×D53—41no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—22no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53C2×#12111yescharacteristic
368C4×C53#52511yescharacteristic
369C4×C53#52911yescharacteristic
370C4×C53#53211yescharacteristic
371Dic53—22no—
372Dic53—22no—
373Dic53—22no—
374Dic53—41no—
375Dic53—41no—
376C2×#436—531no—
377C2×#435—531no—
378C2×#435—531no—
379C2×C4×M16—531no—
380C4×#121—531no—
381#1955—531no—
382#1940D5311yescharacteristic, complemented
383#1923—531no—
384#1923—531no—
385#1870—531no—
386#1870—531no—
387#1797—531no—
388#1771—531no—
389#1753—531no—
390C8×C22⋊C4—531no—
391C2×C53C4×#12111yescharacteristic
392C2×C53#293311yescharacteristic
393C2×C53D4×M1611yescharacteristic
394C2×C53D4×M1611yescharacteristic
395C2×C53#293511yescharacteristic
396C2×C53#296511yescharacteristic
397C2×C53#296711yescharacteristic
398D53—42no—
399D53—42no—
400D53—81no—
401C22×M16—531no—
402C22×M16—531no—
403C22×M16—531no—
404C23×C8—531no—
405C2×#121—531no—
406C2×C4×D4—531no—
407C2×C4×D4—531no—
408C2×C4×D4—531no—
409C22×C42—531no—
410#436—1064no—
411#435—1064no—
412#435—1064no—
413C2×C4⋊C8—531no—
414C2×C4⋊C8C2×D5311yescharacteristic
415C2×C4⋊C8C2×D5311yescharacteristic
416C2×C4⋊C8C2×D5311yescharacteristic
417C2×C22⋊C8—531no—
418C2×C22⋊C8—531no—
419C2×C22⋊C8—531no—
420C2×C22⋊C8—531no—
421C2×C22⋊C8—531no—
422C2×C22⋊C8—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C4×M16—1064no—
426C2×#97—531no—
427C2×#97—531no—
428C2×#97C2×D5311yescharacteristic
429C2×C4×C8—531no—
430C2×C4×C8—531no—
431C2×C4×C8—531no—
432#390—531no—
433#389—531no—
434#388—531no—
435#388—531no—
436#386—531no—
437#386—531no—
438#380—531no—
439C4×C4⋊C4C2×D5311yescharacteristic
440C4×C22⋊C4—531no—
441C4×C22⋊C4—531no—
442#336—531no—
443#336—531no—
444#336—531no—
445#336—531no—
446#336C2×D5311yescharacteristic
447#336C2×D5311yescharacteristic
448C53#2149011yescharacteristic, complemented, Sylow
449C22×D4—531no—
450C22×D4—531no—
451C22×D4—531no—
452C23×C4—531no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—531no—
457C2×M16—534no—
458C2×M16—1062no—
459C2×M16—1062no—
460C2×M16—1062no—
461C2×M16—1062no—
462C2×M16—1062no—
463C2×M16—1062no—
464C2×M16—1062no—
465C2×M16—1062no—
466C22×C8—531no—
467C22×C8—531no—
468C22×C8—531no—
469C22×C8—531no—
470C22×C8—1062no—
471C22×C8—1062no—
472C22×C8—1062no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5311yescharacteristic
477#121—1064no—
478C4×D4—1062no—
479C4×D4—1062no—
480C4×D4—1062no—
481C4×D4—1062no—
482C4×D4—1062no—
483C4×D4—1062no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4C4×D5311yescharacteristic
488C2×C4⋊C4C4×D5311yescharacteristic
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—531no—
495C2×C22⋊C4—531no—
496C2×C22⋊C4—531no—
497C2×C22⋊C4—531no—
498C2×C22⋊C4—531no—
499C2×C42—531no—
500C2×C42—531no—
501C2×C42—531no—
502C2×C42—1062no—
503C2×C42—1062no—
504C2×C42C22×D5311yescharacteristic
505C2×C42C22×D5311yescharacteristic
506C2×C42C22×D5311yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—1062no—
511C22⋊C8—1062no—
512C22⋊C8—1062no—
513C22⋊C8—1062no—
514C22⋊C8—1062no—
515C22⋊C8—1062no—
516C22⋊C8—1062no—
517C22⋊C8—1062no—
518C22⋊C8—1062no—
519#97—22no—
520#97—534no—
521#97—1062no—
522C4×C8—1062no—
523C4×C8—1062no—
524C4×C8—1062no—
525#95—531no—
526#95—531no—
527#95—531no—
528#95—531no—
529#95C4×D5311yescharacteristic
530#95C4×D5311yescharacteristic
531C24—531no—
532C24—531no—
533C24—531no—
534C2×D4—1062no—
535C2×D4—1062no—
536C2×D4—1062no—
537C2×D4—1062no—
538C2×D4—1062no—
539C2×D4—1062no—
540C2×D4—2121no—
541C2×D4—2121no—
542C2×D4—2121no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—531no—
546C22×C4—532no—
547C22×C4—532no—
548C22×C4—531no—
549C22×C4—531no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—2121no—
571C22×C4—2121no—
572C22×C4C2×C4×D5311yescharacteristic
573C22×C4C2×C4×D5311yescharacteristic
574C22×C4C2×C4×D5311yescharacteristic
575C22×C4C2×C4×D5311yescharacteristic
576C22×C4C2×C4×D5311yescharacteristic
577C22×C4C2×C4×D5311yescharacteristic
578C22×C4C23×D5311yescharacteristic
579M16—1068no—
580M16—1068no—
581M16—2124no—
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—21no—
591C2×C8—21no—
592C2×C8—532no—
593C2×C8—532no—
594C2×C8—532no—
595C2×C8—532no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—2124no—
605C2×C8D4×D5312yes—
606C2×C8#1171994912yes—
607C4⋊C4—22no—
608C4⋊C4—41no—
609C4⋊C4—1062no—
610C4⋊C4—1062no—
611C4⋊C4—1062no—
612C22⋊C4—534no—
613C22⋊C4—1062no—
614C22⋊C4—1062no—
615C22⋊C4—1062no—
616C22⋊C4—1062no—
617C22⋊C4—1062no—
618C22⋊C4—1062no—
619C22⋊C4—1062no—
620C22⋊C4—1062no—
621C22⋊C4—1062no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—1062no—
627C42—1062no—
628C42—1061no—
629C42—1061no—
630C42D4×D5312yes—
631C42#1171994912yes—
632C23—532no—
633C23—532no—
634C23—1061no—
635C23—1061no—
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—1061no—
649C23—1061no—
650C23—1061no—
651C23—1061no—
652C23—1061no—
653C23C22×C4×D5311yescharacteristic
654D4—2124no—
655D4—2124no—
656D4—2124no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
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—532no—
673C2×C4—532no—
674C2×C4—532no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—1061no—
680C2×C4—1061no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—1061no—
691C2×C4—2124no—
692C2×C4—2124no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4#1313317912yes—
702C2×C4#1313317912yes—
703C2×C4M16×D5312yes—
704C2×C4C2×D4×D5311yescharacteristic
705C2×C4C2×D4×D5311yescharacteristic
706C2×C4#41×D5311yescharacteristic
707C2×C4#41×D5311yescharacteristic
708C2×C4C2×#1171994911yescharacteristic
709C2×C4C2×#1171994911yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—534no—
715C8—1062no—
716C8—2121no—
717C8—2121no—
718C22—1062no—
719C22—1062no—
720C22—1062no—
721C22—1062no—
722C22—1062no—
723C22—1062no—
724C22—2121no—
725C22—2121no—
726C22—2121no—
727C22—2121no—
728C22—2121no—
729C22—2121no—
730C22—2121no—
731C22—2121no—
732C22—2121no—
733C22—2121no—
734C22—2121no—
735C22—2121no—
736C22—2121no—
737C22—2121no—
738C22—2121no—
739C22C4×D4×D5311yescharacteristic
740C22C2×#1313317911yescharacteristic
741C22C4×#1171994911yescharacteristic
742C22C2×M16×D5311yescharacteristic
743C22#131×D5311yescharacteristic
744C22#1681138811yescharacteristic
745C22#1681138911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—1062no—
753C4—1062no—
754C4—1062no—
755C4—2121no—
756C4—2121no—
757C4#121×D5311yescharacteristic
758C4#1681113611yescharacteristic
759C4#1681115811yescharacteristic
760C4#1681117411yescharacteristic
761C2—4241no—
762C2—2122no—
763C2—2122no—
764C2#2027722311yescharacteristic
765C2#2028343911yescharacteristic
766C2#2028344811yescharacteristic
767C2#2028345011yescharacteristic
768C2#2028345611yescharacteristic
769C2#2028368011yescharacteristic
770C2#2028369911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1940C2
prime radicalC2×#13133192C4
cosocleC22×C4×C53C24
hypercenter#1940D53
hypocenterC53#21490
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. C2×#16810700C2semidirect
2. C2×#16810693C2semidirect
3. C2×#16810693C2semidirect
4. C2×#16810575C2semidirect
6. #20275513C2semidirect
7. #20275320C2semidirect
8. #20275320C2semidirect
9. #20275011C2semidirect
10. #20275011C2semidirect
11. #20274692C2semidirect
12. #20274590C2semidirect
13. #20274497C2semidirect
14. #20274485C2semidirect
15. C53×#1940C2semidirect
79. C2×#11719912D4semidirect
122. #13133128D4semidirect
222. #11719921M16semidirect
331. #88322#121semidirect
382. #1940D53semidirect
448. C53#21490semidirect

Maximal subgroups

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

subgroupindex
C2×#168107002
C2×#168106932
C2×#168105752
C4×#131331922
#202755132
#202753202
#202750112
#202746922
#202745902
#202744972
#202744852
C53×#19402
#2149053