Finite Group Databasebeta

← #27400832

Subgroups — #27400832

Order 13568.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811155C211yesmaximal, characteristic
2C2×#16810752C211yesmaximal, characteristic, complemented
3C2×#16810751C211yesmaximal, characteristic, complemented
4#20275514C211yesmaximal, characteristic, complemented
5#20275511C211yesmaximal, characteristic, complemented
6#20275511C211yesmaximal, characteristic, complemented
7#20275507C211yesmaximal, characteristic, complemented
8#20275507C211yesmaximal, characteristic, complemented
9#20274697C211yesmaximal, characteristic, complemented
10#20274697C211yesmaximal, characteristic, complemented
11#20274692C211yesmaximal, characteristic, complemented
12#20274483C211yesmaximal, characteristic, complemented
13#20274483C211yesmaximal, characteristic, complemented
14#20274478C211yesmaximal, characteristic, complemented
15C53×#1955C211yesmaximal, characteristic, complemented
16#16811155—24no—
17#16811155—24no—
18C2×#13133210C411yescharacteristic
19C2×#13133210C411yescharacteristic
20C2×#13133208C411yescharacteristic
21C2×#13133204C411yescharacteristic
22C2×#13133199C411yescharacteristic
23C2×#13133199C411yescharacteristic
24C2×#13133197C411yescharacteristic
25C2×#13133188C411yescharacteristic
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×C22⋊D53C2211yescharacteristic
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×#13133176C2211yescharacteristic
30C2×#13133176C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32#16810752—24no—
33#16810751—24no—
34C2×C4⋊#88322C2211yescharacteristic
35C2×#13133146C2211yescharacteristic
36C2×#13133146C2211yescharacteristic
37C2×#13133146C2211yescharacteristic
38C2×#13133146C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×C22⋊#88322C2211yescharacteristic
42C2×C22⋊#88322C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45C2×#13133129C2211yescharacteristic
46C2×#13133129C2211yescharacteristic
47C2×#13133128C2211yescharacteristic
48C2×#13133127C2211yescharacteristic
49C2×#13133127C2211yescharacteristic
50C2×C8×Dic53C2211yescharacteristic
51C2×C8×Dic53C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×#97×C53C2211yescharacteristic
63C22×Dic106C2×C411yescharacteristic
64C22×C22⋊D53C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C22×C4×D53C2×C411yescharacteristic
67C22×C4×D53C2×C411yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133210—24no—
74#13133210—24no—
75#13133208—24no—
76#13133204—24no—
77#13133199—24no—
78#13133199—24no—
79#13133197—24no—
80#13133188—24no—
81C4×Dic106D414yes—
82C4×Dic106D414yes—
83C4×C22⋊D53—22no—
84C4×C22⋊D53—22no—
85C4×C22⋊D53—22no—
86C4×C22⋊D53—22no—
87#13133176—22no—
88#13133176—22no—
89#13133176—22no—
90#13133176—22no—
91C2×C4⋊Dic53C2×C411yescharacteristic
92C2×C4⋊Dic53C2×C411yescharacteristic
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×C22⋊Dic53C2×C411yescharacteristic
101C2×C22⋊Dic53C2×C411yescharacteristic
102C2×C22⋊Dic53C2×C411yescharacteristic
103C2×C22⋊Dic53C2×C411yescharacteristic
104C2×C22⋊Dic53C2×C411yescharacteristic
105C2×C22⋊Dic53C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×C4×Dic53C2×C411yescharacteristic
109C2×C4×Dic53C2×C411yescharacteristic
110C2×C4×Dic53C2311yescharacteristic
111C2×C4×Dic53C2311yescharacteristic
112C2×C4×Dic53C2311yescharacteristic
113C42×D53—22no—
114C42×D53—22no—
115C4⋊#88322—22no—
116#13133146—22no—
117#13133146—22no—
118#13133146—22no—
119#13133146—22no—
120C22⋊#88322—22no—
121C22⋊#88322—22no—
122C22⋊#88322—41no—
123C22⋊#88322—41no—
124#13133129—22no—
125#13133129—22no—
126#13133129—41no—
127#13133129—41no—
128#13133128—22no—
129#13133127—22no—
130#13133127—22no—
131C8×Dic53—22no—
132C8×Dic53—22no—
133C22×D4×C53C2×C411yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C22×C8×C53C2311yescharacteristic
140C4×D4×C53—22no—
141C4×D4×C53—22no—
142C2×C4⋊C4×C53C2×C411yescharacteristic
143C2×C22⋊C4×C53C2×C411yescharacteristic
144C2×C22⋊C4×C53C2×C411yescharacteristic
145C2×C42×C53C2311yescharacteristic
146C4⋊C8×C53—22no—
147C22⋊C8×C53—22no—
148C22⋊C8×C53—22no—
149C22⋊C8×C53—41no—
150C22⋊C8×C53—41no—
151#97×C53—22no—
152C24×C53C22×C411yescharacteristic
153C24×C53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C2×D4×C53—22no—
156C2×D4×C53—41no—
157C2×D4×C53—41no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C2411yescharacteristic
175C2×C22⋊D53—22no—
176C2×C22⋊D53—22no—
177C2×C22⋊D53—22no—
178C2×C22⋊D53—22no—
179C2×C22⋊D53—41no—
180C2×C22⋊D53—41no—
181C22×Dic53C22×C411yescharacteristic
182C22×Dic53C22×C411yescharacteristic
183C22×Dic53C22×C411yescharacteristic
184C22×Dic53C22×C411yescharacteristic
185C22×Dic53C22×C411yescharacteristic
186C22×Dic53C22×C411yescharacteristic
187C22×Dic53C22×C411yescharacteristic
188C2×C4×D53—22no—
189C2×C4×D53—22no—
190C2×C4×D53—22no—
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—41no—
198C2×C4×D53—41no—
199C2×C4×D53—41no—
200C2×Dic106—41no—
201C2×Dic106—41no—
202C2×Dic106C22⋊C414yes—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—21no—
214C2×C8×C53#4112yes—
215C4⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C42×C53C2×D412yes—
219C42×C53C2×D412yes—
220C22⋊Dic53—22no—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225C22⋊Dic53—22no—
226#11719921—22no—
227#11719921—22no—
228C4⋊Dic53—22no—
229C4⋊Dic53—22no—
230C4⋊Dic53—22no—
231C4⋊Dic53—22no—
232C4⋊Dic53C22⋊C414yes—
233#11719919—22no—
234#11719919—22no—
235#11719919C22⋊C414yes—
236#11719919C22⋊C414yes—
237C4×Dic53—22no—
238C4×Dic53—22no—
239C4×Dic53—21no—
240C4×Dic53—21no—
241C4×Dic53C2×D412yes—
242C4×Dic53C2×D412yes—
243C4×Dic53C2×D412yes—
244C4×Dic53C2×D412yes—
245C2×#88322—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#4112yes—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53C23×C411yescharacteristic
272C22×D53—21no—
273C22×D53—21no—
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53#13112yes—
279D4×C53—44no—
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×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53C2×C22⋊C412yes—
299C2×C4×C53C2×C22⋊C412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4111yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C2×C4×C53H(5,𝔽2)11yescharacteristic
305C2×C4×C532−1+411yescharacteristic
306C22⋊D53—44no—
307C22⋊D53—44no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323C2×Dic53—21no—
324C2×Dic53—21no—
325C2×Dic53C2×C22⋊C412yes—
326C2×Dic53C2×C22⋊C412yes—
327C2×Dic53C2×C22⋊C412yes—
328C2×Dic53C2×C22⋊C412yes—
329C4×D53—44no—
330C4×D53—44no—
331C4×D53—41no—
332C4×D53—41no—
333C4×D53—41no—
334C4×D53—41no—
335Dic106—44no—
336C8×C53—22no—
337C8×C53—41no—
338C8×C53—41no—
339C8×C53—41no—
340#88322—22no—
341#88322—41no—
342#88322—41no—
343#88322—41no—
344#22533—531nomaximal, Sylow
345C22×C53—41no—
346C22×C53—41no—
347C22×C53—41no—
348C22×C53—41no—
349C22×C53—41no—
350C22×C53—41no—
351C22×C53—41no—
352C22×C53—41no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53C22×C22⋊C411yescharacteristic
360C22×C53C4×#4111yescharacteristic
361C22×C53#52011yescharacteristic
362C22×C53C2×#13111yescharacteristic
363C22×C53#56811yescharacteristic
364C22×C53#56811yescharacteristic
365C22×C53#56811yescharacteristic
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—41no—
372C2×D53—41no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—41no—
376C4×C53—41no—
377C4×C53#54811yescharacteristic
378C4×C53#54811yescharacteristic
379C4×C53#55011yescharacteristic
380C4×C53#55011yescharacteristic
381Dic53—22no—
382Dic53—22no—
383Dic53—22no—
384Dic53—22no—
385Dic53—41no—
386Dic53—41no—
387Dic53—41no—
388C2×#529—531no—
389C2×#446—531no—
390C2×#446—531no—
391#1955—531no—
392#1955—531no—
393#1955—531no—
394#1955D5311yescharacteristic, complemented
395#1954—531no—
396#1954—531no—
397#1798—531no—
398#1798—531no—
399#1797—531no—
400#1750—531no—
401#1750—531no—
402#1749—531no—
403C2×C53—81no—
404C2×C53—81no—
405C2×C53#234111yescharacteristic
406C2×C53#287911yescharacteristic
407C2×C53#288011yescharacteristic
408C2×C53#296711yescharacteristic
409C2×C53#296811yescharacteristic
410C2×C53#299211yescharacteristic
411C2×C53#299511yescharacteristic
412D53—42no—
413#529—1064no—
414#529—1064no—
415C2×#126—531no—
416C2×#126—531no—
417C2×#125—531no—
418C2×#124—531no—
419C2×#123—531no—
420C2×#123—531no—
421C2×C22⋊Q8—531no—
422C2×#121—531no—
423C2×C4×Q8—531no—
424C2×C4×D4—531no—
425C2×C4×D4—531no—
426C2×C4×D4C2×D5311yescharacteristic
427C2×#117—531no—
428C2×#117—531no—
429C22×C42—531no—
430#446—1064no—
431#446—1064no—
432C2×C4⋊C8—531no—
433C2×C4⋊C8—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8C2×D5311yescharacteristic
438C2×C22⋊C8—531no—
439C2×C22⋊C8—531no—
440C2×C22⋊C8—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C22⋊C8—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8C2×D5311yescharacteristic
447C2×C22⋊C8C2×D5311yescharacteristic
448C2×C22⋊C8C2×D5311yescharacteristic
449C2×C22⋊C8C2×D5311yescharacteristic
450C2×#97—531no—
451C2×#97—531no—
452C2×#97—531no—
453C2×#97C2×D5311yescharacteristic
454C2×C4×C8—531no—
455C2×C4×C8—531no—
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460C53#2253311yescharacteristic, complemented, Sylow
461C22×Q8—531no—
462C22×D4—531no—
463C22×D4—531no—
464C22×D4C4×D5311yescharacteristic
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8C22×D5311yescharacteristic
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5311yescharacteristic
477C22×C8C22×D5311yescharacteristic
478#126—1064no—
479#126—1064no—
480#125—1064no—
481#124—1064no—
482#123—1064no—
483#123—1064no—
484C22⋊Q8—1064no—
485#121—1064no—
486C4×Q8—534no—
487C4×Q8—534no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494#117—1062no—
495#117—1062no—
496#117—1062no—
497#117—1062no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4C4×D5311yescharacteristic
508C2×C22⋊C4—531no—
509C2×C22⋊C4—531no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—531no—
513C2×C22⋊C4—531no—
514C2×C22⋊C4—531no—
515C2×C22⋊C4—531no—
516C2×C22⋊C4C4×D5311yescharacteristic
517C2×C22⋊C4C4×D5311yescharacteristic
518C2×C42—531no—
519C2×C42—531no—
520C2×C42—531no—
521C2×C42—531no—
522C2×C42—531no—
523C2×C42—1062no—
524C2×C42—1062no—
525C2×C42C22×D5311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—1062no—
528C4⋊C8—1062no—
529C4⋊C8—1062no—
530C4⋊C8—1062no—
531C4⋊C8—1062no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—1062no—
539C22⋊C8—1062no—
540C22⋊C8—2121no—
541C22⋊C8—2121no—
542C22⋊C8—2121no—
543C22⋊C8—2121no—
544#97—22no—
545#97—1062no—
546#97—1062no—
547#97—1062no—
548C4×C8—1062no—
549C4×C8—1062no—
550C24—531no—
551C24C2×C4×D5311yescharacteristic
552C24C2×C4×D5311yescharacteristic
553C2×Q8—534no—
554C2×Q8—2121no—
555C2×Q8—2121no—
556C2×D4—22no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—2121no—
564C2×D4—2121no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—531no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—531no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—2121no—
594C22×C4—2121no—
595C22×C4—2121no—
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4C23×D5311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—532no—
613C2×C8—1061no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1061no—
617C2×C8—1061no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8#1171994712yes—
625C4⋊C4—22no—
626C4⋊C4—534no—
627C4⋊C4—534no—
628C4⋊C4—534no—
629C4⋊C4—1062no—
630C4⋊C4—1062no—
631C4⋊C4—1062no—
632C4⋊C4—1062no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—1062no—
638C22⋊C4—1062no—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C42—532no—
646C42—532no—
647C42—532no—
648C42—532no—
649C42—1062no—
650C42—1062no—
651C42—1061no—
652C42—1061no—
653C42D4×D5312yes—
654C42D4×D5312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—532no—
670C23—1061no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—1061no—
675C23—1061no—
676C23C22×C4×D5311yescharacteristic
677Q8—2124no—
678D4—44no—
679D4—2124no—
680D4—2124no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—532no—
700C2×C4—532no—
701C2×C4—532no—
702C2×C4—532no—
703C2×C4—1061no—
704C2×C4—1061no—
705C2×C4—1061no—
706C2×C4—1061no—
707C2×C4—1061no—
708C2×C4—1061no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—2124no—
721C2×C4—2124no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4C22⋊C4×D5312yes—
727C2×C4C22⋊C4×D5312yes—
728C2×C4C2×D4×D5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4C2×#1171994711yescharacteristic
732C2×C4#1313326211yescharacteristic
733C2×C4#1313326411yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—1062no—
739C8—2121no—
740C8—2121no—
741C8—2121no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—1062no—
757C22—1062no—
758C22—1062no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22C2×C22⋊C4×D5311yescharacteristic
764C22C4×#1171994711yescharacteristic
765C22#1681110211yescharacteristic
766C22#131×D5311yescharacteristic
767C22#1681138811yescharacteristic
768C22#1681138911yescharacteristic
769C22#1681138911yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—1062no—
775C4—1062no—
776C4—1062no—
777C4—1062no—
778C4—2121no—
779C4—2121no—
780C4—2121no—
781C4#1681127911yescharacteristic
782C4#1681128111yescharacteristic
783C4#1681129111yescharacteristic
784C4#1681129311yescharacteristic
785C2—81no—
786C2—81no—
787C2—2122no—
788C2#2027755411yescharacteristic
789C2#2028315811yescharacteristic
790C2#2028316311yescharacteristic
791C2#2028369711yescharacteristic
792C2#2028370611yescharacteristic
793C2#2028385011yescharacteristic
794C2#2028388111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1955C2
prime radicalC2×#13133188C4
cosocleC22×C4×C53C24
hypercenter#1955D53
hypocenterC53#22533
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#16810752C2semidirect
3. C2×#16810751C2semidirect
4. #20275514C2semidirect
5. #20275511C2semidirect
6. #20275511C2semidirect
7. #20275507C2semidirect
8. #20275507C2semidirect
9. #20274697C2semidirect
10. #20274697C2semidirect
11. #20274692C2semidirect
12. #20274483C2semidirect
13. #20274483C2semidirect
14. #20274478C2semidirect
15. C53×#1955C2semidirect
394. #1955D53semidirect
460. C53#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168111552
C2×#168107522
C2×#168107512
#202755142
#202755112
#202755072
#202746972
#202746922
#202744832
#202744782
C53×#19552
#2253353