Finite Group Databasebeta

← #27390181

Subgroups — #27390181

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×#16810702C211yesmaximal, characteristic, complemented
2C2×#16810696C211yesmaximal, characteristic, complemented
3C2×#16810696C211yesmaximal, characteristic, complemented
4C2×#16810575C211yesmaximal, characteristic, complemented
5C4×#13133192C211yesmaximal, characteristic
6#20275512C211yesmaximal, characteristic, complemented
7#20275439C211yesmaximal, characteristic, complemented
8#20275322C211yesmaximal, characteristic, complemented
9#20275322C211yesmaximal, characteristic, complemented
10#20275011C211yesmaximal, characteristic, complemented
11#20275011C211yesmaximal, characteristic, complemented
12#20274692C211yesmaximal, characteristic, complemented
13#20274500C211yesmaximal, characteristic, complemented
14C8×#11719921C211yesmaximal, characteristic, complemented
15C53×#1771C211yesmaximal, 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#16810702—24no—
26#16810696—24no—
27#16810696—24no—
28C2×C4⋊#88322C2211yescharacteristic
29C2×C4⋊#88322C2211yescharacteristic
30C2×C4⋊#88322C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39#16810575—24no—
40C2×#13133128C2211yescharacteristic
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×#97×C53C2211yescharacteristic
58C2×#97×C53C2211yescharacteristic
59C2×C4×C8×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—
113C4⋊#88322—22no—
114C4⋊#88322—22no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—22no—
120#13133129—22no—
121#13133129—22no—
122#13133129—22no—
123#13133128—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—
140#97×C53—22no—
141#97×C53D414yescomplemented
142C4×C8×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×C53C2×D412yes—
202C2×C8×C53C2×D412yes—
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×#88322—21no—
239C2×#88322—21no—
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—41no—
326C8×C53—41no—
327C8×C53#12114yescomplemented
328#88322—22no—
329#88322—22no—
330#88322—41no—
331#88322—41no—
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#1940—531no—
383#1923—531no—
384#1923—531no—
385#1870—531no—
386#1870—531no—
387#1797—531no—
388#1771D5311yescharacteristic, complemented
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⋊C8—531no—
415C2×C4⋊C8—531no—
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×#97C2×D5311yescharacteristic
428C2×#97C2×D5311yescharacteristic
429C2×C4×C8—531no—
430C2×C4×C8—531no—
431C2×C4×C8C2×D5311yescharacteristic
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—1062no—
509C4⋊C8—1062no—
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—1062no—
521#97D21214yescomplemented
522C4×C8—22no—
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—532no—
591C2×C8—532no—
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×C8—2124no—
603C2×C8C2×D21212yes—
604C2×C8C2×D21212yes—
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—
630C42C2×D21212yes—
631C42#1171994512yes—
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×C4C4×D21212yes—
702C2×C4C4×D21212yes—
703C2×C4M16×D5312yes—
704C2×C4C2×D4×D5311yescharacteristic
705C2×C4C22×D21211yescharacteristic
706C2×C4#41×D5311yescharacteristic
707C2×C4#41×D5311yescharacteristic
708C2×C4C2×#1171994511yescharacteristic
709C2×C4C2×#1171994911yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—1062no—
714C8—1062no—
715C8—2121no—
716C8—2121no—
717C8#1313319214yescomplemented
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×C4×D21211yescharacteristic
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—
757C4C2×#1313319211yescharacteristic
758C4#1681113511yescharacteristic
759C4#1681116011yescharacteristic
760C4#1681117011yescharacteristic
761C2—4241no—
762C2—2122no—
763C2—2122no—
764C2C4×#1313319211yescharacteristic
765C2#2028344311yescharacteristic
766C2#2028344811yescharacteristic
767C2M16×D21211yescharacteristic
768C2#2028345611yescharacteristic
769C2#2028368011yescharacteristic
770C2#2028369911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1771C2
prime radicalC2×#13133192C4
cosocleC22×C4×C53C24
hypercenter#1771D53
hypocenterC53#21490
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#16810702C2semidirect
2. C2×#16810696C2semidirect
3. C2×#16810696C2semidirect
4. C2×#16810575C2semidirect
6. #20275512C2semidirect
7. #20275439C2semidirect
8. #20275322C2semidirect
9. #20275322C2semidirect
10. #20275011C2semidirect
11. #20275011C2semidirect
12. #20274692C2semidirect
13. #20274500C2semidirect
14. C8×#11719921C2semidirect
15. C53×#1771C2semidirect
79. C2×#11719912D4semidirect
141. #97×C53D4semidirect
222. #11719921M16semidirect
327. C8×C53#121semidirect
388. #1771D53semidirect
448. C53#21490semidirect
521. #97D212semidirect
717. C8#13133192semidirect

Maximal subgroups

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

subgroupindex
C2×#168107022
C2×#168106962
C2×#168105752
C4×#131331922
#202755122
#202754392
#202753222
#202750112
#202746922
#202745002
C8×#117199212
C53×#17712
#2149053