Finite Group Databasebeta

← #27390245

Subgroups — #27390245

Order 13568.

1052 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810693C211yesmaximal, characteristic, complemented
2C2×#16810691C211yesmaximal, characteristic, complemented
3C2×#16810686C211yesmaximal, characteristic, complemented
4C2×#16810577C211yesmaximal, characteristic, complemented
5#20277959C211yesmaximal, characteristic
6#20275507C211yesmaximal, characteristic, complemented
7#20275430C211yesmaximal, characteristic, complemented
8#20275321C211yesmaximal, characteristic, complemented
9#20275011C211yesmaximal, characteristic, complemented
10#20275009C211yesmaximal, characteristic, complemented
11#20274698C211yesmaximal, characteristic, complemented
12#20274588C211yesmaximal, characteristic, complemented
13#20274497C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15C53×#1923C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×C22⋊D53C2211yescharacteristic
22C2×C4×C22⋊D53C2211yescharacteristic
23C2×#13133174C2211yescharacteristic
24#16810693—24no—
25#16810691—24no—
26#16810686—24no—
27C2×#13133146C2211yescharacteristic
28C2×#13133146C2211yescharacteristic
29C2×#13133146C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36#16810577—24no—
37C2×#13133128C2211yescharacteristic
38C2×#13133128C2211yescharacteristic
39C2×#13133127C2211yescharacteristic
40C2×C8×Dic53C2211yescharacteristic
41C2×C8×Dic53C2211yescharacteristic
42#16810557C411yescharacteristic
43#16810552C411yescharacteristic
44#16810547C411yescharacteristic
45#16810546C411yescharacteristic
46#16810541C411yescharacteristic
47#16810538C411yescharacteristic
48#16810538C411yescharacteristic
49#16810532C411yescharacteristic
50C4×#11719919C2211yescharacteristic
51C4×#11719921C2211yescharacteristic
52#16810378C2211yescharacteristic
53#16810378C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C22⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C4×C8×C53C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×C22⋊D53C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C22×C4×D53C2311yescharacteristic
68C2×#11719912—22no—
69C2×#11719912—22no—
70C2×#11719912—22no—
71C2×#11719912—22no—
72C2×#11719912—22no—
73C2×#11719912—22no—
74C22×#88322—22no—
75C22×#88322—22no—
76C22×#88322—22no—
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C2×C8×D53—22no—
82C2×C8×D53—22no—
83C2×C8×D53D414yescomplemented
84C4×D212—22no—
85C4×D212—22no—
86C4×C22⋊D53—22no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90#13133174—22no—
91#13133174—22no—
92C2×C4⋊Dic53C2×C411yescharacteristic
93C2×#11719919C2×C411yescharacteristic
94C2×#11719919C2×C411yescharacteristic
95C2×#11719919C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×C22⋊Dic53C2×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×C4×Dic53C2311yescharacteristic
110C2×C4×Dic53C2311yescharacteristic
111#13133146—22no—
112#13133146—22no—
113#13133146—22no—
114C22⋊#88322—22no—
115#13133129—22no—
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—22no—
120#13133128—22no—
121#13133128—22no—
122#13133127D414yescomplemented
123C8×Dic53—22no—
124C8×Dic53—22no—
125#13133124C2×C411yescharacteristic
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134C2×C22⋊C4×C53C2×C411yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C4⋊C8×C53—22no—
139C22⋊C8×C53—22no—
140C22⋊C8×C53—22no—
141C4×C8×C53—22no—
142#95×C53C2×C411yescharacteristic
143#95×C53C2×C411yescharacteristic
144C24×C53C22×C411yescharacteristic
145C23×D53C22×C411yescharacteristic
146C23×D53C22×C411yescharacteristic
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×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C22×C411yescharacteristic
157C22×C4×C53C22×C411yescharacteristic
158C22×C4×C53C2411yescharacteristic
159C2×C22⋊D53—22no—
160C2×C22⋊D53—22no—
161C2×C22⋊D53—22no—
162C2×C22⋊D53—22no—
163C2×C22⋊D53—22no—
164C2×C22⋊D53—41no—
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169C22×Dic53C22×C411yescharacteristic
170C22×Dic53C22×C411yescharacteristic
171C2×D212—22no—
172C2×D212—41no—
173C2×D212—41no—
174C2×C4×D53—21no—
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×D53C2×D412yes—
185C2×C4×D53#4112yes—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53C2×D412yes—
197C2×C8×C53C2×D412yes—
198C22⋊C4×C53—22no—
199C22⋊C4×C53—41no—
200C42×C53—21no—
201C42×C53—21no—
202C42×C53—21no—
203C42×C53—21no—
204C22⋊Dic53—22no—
205C22⋊Dic53—22no—
206#11719921—22no—
207#11719921—22no—
208#11719921—22no—
209#11719921—22no—
210#11719921—22no—
211#11719921—22no—
212#11719921—22no—
213#11719921—41no—
214C4⋊Dic53—22no—
215#11719919—22no—
216#11719919—22no—
217#11719919—22no—
218#11719919—22no—
219#11719919—22no—
220#11719919—41no—
221C4×Dic53—21no—
222C4×Dic53—21no—
223C4×Dic53C2×D412yes—
224C4×Dic53#4112yes—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—44no—
234C2×#88322C2×D412yes—
235C2×#88322C2×D412yes—
236C2×#88322#4112yes—
237C2×#88322#4112yes—
238#11719912—28no—
239#11719912—44no—
240C8×D53—28no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53#13112yes—
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—21no—
262C22×D53C4×D412yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
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—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C22×D411yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C22⋊D53—28no—
289C22⋊D53—44no—
290C2×Dic53—21no—
291C2×Dic53—21no—
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×Dic53C4×D412yes—
306C2×Dic53C4×D412yes—
307C2×Dic53#13112yes—
308D212—44no—
309C4×D53—22no—
310C4×D53—22no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—41no—
314C4×D53—41no—
315C4×D53—41no—
316C4×D53—41no—
317C8×C53—22no—
318C8×C53—22no—
319C8×C53—41no—
320C8×C53—41no—
321#88322—22no—
322#88322—41no—
323#88322—41no—
324#88322#12114yes—
325#21495—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53C2×C4×D411yescharacteristic
334C22×C53C2×C4×D411yescharacteristic
335C22×C53C4×#4111yescharacteristic
336C22×C53C2×#13111yescharacteristic
337C22×C53C2×#13111yescharacteristic
338C22×C53#56811yescharacteristic
339C22×C53#56811yescharacteristic
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53—41no—
357C4×C53—41no—
358C4×C53—41no—
359C4×C53C2×#12111yescharacteristic
360C4×C53#52511yescharacteristic
361C4×C53#52911yescharacteristic
362C4×C53#53211yescharacteristic
363Dic53—22no—
364Dic53—22no—
365Dic53—22no—
366Dic53—22no—
367Dic53—41no—
368Dic53—41no—
369C2×#435—531no—
370C2×#435—531no—
371C2×C8×D4—531no—
372C2×#405—531no—
373#2392—531no—
374#1954—531no—
375#1939—531no—
376#1923—531no—
377#1923D5311yescharacteristic, complemented
378#1870—531no—
379#1870—531no—
380#1798—531no—
381#1771—531no—
382#1753—531no—
383#1752—531no—
384C2×C53—42no—
385C2×C53C4×#12111yescharacteristic
386C2×C53#292911yescharacteristic
387C2×C53#293011yescharacteristic
388C2×C53#293311yescharacteristic
389C2×C53#293511yescharacteristic
390C2×C53#296811yescharacteristic
391C2×C53#296911yescharacteristic
392D53—42no—
393D53—81no—
394C22×M16—531no—
395C22×M16—531no—
396C23×C8—531no—
397C23×C8—531no—
398C2×C4×D4—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117—531no—
402#435—1064no—
403#435—1064no—
404C8×D4—1064no—
405C2×C4⋊C8—531no—
406C2×C4⋊C8—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8C2×D5311yescharacteristic
409C2×C22⋊C8—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8C2×D5311yescharacteristic
416C2×C22⋊C8C2×D5311yescharacteristic
417#405—1064no—
418C2×#97—531no—
419C2×#97—531no—
420C2×#97—531no—
421C2×C4×C8—531no—
422C2×C4×C8—531no—
423C2×C4×C8C2×D5311yescharacteristic
424#398—531no—
425#397—531no—
426#396—531no—
427#396—531no—
428#394—531no—
429#394—531no—
430#394—531no—
431#392—531no—
432C4×C4⋊C4—531no—
433C4×C22⋊C4—531no—
434C4×C22⋊C4C2×D5311yescharacteristic
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336C2×D5311yescharacteristic
440#336C2×D5311yescharacteristic
441C53#2149511yescharacteristic, complemented, Sylow
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4C22×D5311yescharacteristic
448C2×M16—1062no—
449C2×M16—1062no—
450C2×M16—1062no—
451C2×M16—1062no—
452C2×M16—1062no—
453C2×M16—1062no—
454C22×C8—531no—
455C22×C8—531no—
456C22×C8—534no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—1062no—
460C22×C8—1062no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—1062no—
464C22×C8C22×D5311yescharacteristic
465C22×C8C22×D5311yescharacteristic
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C4×D4—1062no—
469C4×D4—1062no—
470C4×D4—1062no—
471C4×D4—1062no—
472C4×D4—1062no—
473C4×D4—1062no—
474#117—1062no—
475#117—1062no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
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—22no—
500C4⋊C8—1062no—
501C4⋊C8—1062no—
502C4⋊C8—1062no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—1062no—
508C22⋊C8—1062no—
509C22⋊C8—1062no—
510C22⋊C8—1062no—
511#97—534no—
512#97—1062no—
513#97—1062no—
514C4×C8—22no—
515C4×C8—1062no—
516C4×C8—1062no—
517#95—531no—
518#95—531no—
519#95—531no—
520#95—531no—
521#95C4×D5311yescharacteristic
522#95C4×D5311yescharacteristic
523C24—531no—
524C24—531no—
525C24C2×C4×D5311yescharacteristic
526C2×D4—1062no—
527C2×D4—1062no—
528C2×D4—1062no—
529C2×D4—1062no—
530C2×D4—1062no—
531C2×D4—1062no—
532C2×D4—2121no—
533C2×D4—2121no—
534C2×D4—2121no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—531no—
542C22×C4—531no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—532no—
546C22×C4—532no—
547C22×C4—531no—
548C22×C4—531no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4C2×C4×D5311yescharacteristic
560C22×C4C2×C4×D5311yescharacteristic
561C22×C4C2×C4×D5311yescharacteristic
562C22×C4C2×C4×D5311yescharacteristic
563C22×C4C2×C4×D5311yescharacteristic
564C22×C4C23×D5311yescharacteristic
565M16—1068no—
566M16—2124no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—532no—
578C2×C8—532no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—1068no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—2124no—
591C2×C8D4×D5312yes—
592C2×C8D4×D5312yes—
593C4⋊C4—1062no—
594C4⋊C4—1062no—
595C4⋊C4—1062no—
596C4⋊C4—1062no—
597C4⋊C4—1062no—
598C4⋊C4—1062no—
599C4⋊C4—2121no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—1062no—
608C22⋊C4—1062no—
609C22⋊C4—1062no—
610C22⋊C4—1062no—
611C22⋊C4—2121no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—532no—
617C42—532no—
618C42—1061no—
619C42—1061no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—532no—
627C23—1061no—
628C23—1061no—
629C23—1061no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23#1313322312yes—
641C23C22×C4×D5311yescharacteristic
642D4—1068no—
643D4—2124no—
644D4—2124no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—532no—
665C2×C4—532no—
666C2×C4—532no—
667C2×C4—532no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1061no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4C2×D4×D5311yescharacteristic
691C2×C4C2×D4×D5311yescharacteristic
692C2×C4#41×D5311yescharacteristic
693C2×C4#41×D5311yescharacteristic
694C2×C4#41×D5311yescharacteristic
695C2×C4#41×D5311yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—534no—
701C8—1062no—
702C8—2121no—
703C8—2121no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1062no—
712C22—1062no—
713C22—1062no—
714C22—2121no—
715C22—2121no—
716C22—2121no—
717C22—2121no—
718C22—2121no—
719C22—2121no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22—2121no—
724C22—2121no—
725C22C4×D4×D5311yescharacteristic
726C22C4×D4×D5311yescharacteristic
727C22#1681109111yescharacteristic
728C22#131×D5311yescharacteristic
729C22C2×#1313322311yescharacteristic
730C22#1681138811yescharacteristic
731C22#1681138911yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—1062no—
738C4—1062no—
739C4—1062no—
740C4—1062no—
741C4—2121no—
742C4—2121no—
743C4#121×D5311yescharacteristic
744C4#1681113111yescharacteristic
745C4#1681115611yescharacteristic
746C4#1681117211yescharacteristic
747C2—42no—
748C2—4241no—
749C2—2122no—
750C2#2027722711yescharacteristic
751C2#2028340411yescharacteristic
752C2#2028341511yescharacteristic
753C2#2028343511yescharacteristic
754C2#2028345611yescharacteristic
755C2#2028370411yescharacteristic
756C2#2028371711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1923C2
prime radical#16810532C4
cosocleC22×C4×C53C24
hypercenter#1923D53
hypocenterC53#21495
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16810693C2semidirect
2. C2×#16810691C2semidirect
3. C2×#16810686C2semidirect
4. C2×#16810577C2semidirect
6. #20275507C2semidirect
7. #20275430C2semidirect
8. #20275321C2semidirect
9. #20275011C2semidirect
10. #20275009C2semidirect
11. #20274698C2semidirect
12. #20274588C2semidirect
13. #20274497C2semidirect
14. #20274493C2semidirect
15. C53×#1923C2semidirect
83. C2×C8×D53D4semidirect
122. #13133127D4semidirect
377. #1923D53semidirect
441. C53#21495semidirect

Maximal subgroups

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

subgroupindex
C2×#168106932
C2×#168106912
C2×#168106862
C2×#168105772
#202779592
#202755072
#202754302
#202753212
#202750112
#202750092
#202746982
#202745882
#202744972
#202744932
C53×#19232
#2149553