Finite Group Databasebeta

← #28325732

Subgroups — #28325732

Order 13568.

1396 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811651C211yesmaximal, characteristic, complemented
2C2×#16811650C211yesmaximal, characteristic, complemented
3C22×#13133274C211yesmaximal, characteristic, complemented
4C2×D53⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
5#20290837C211yesmaximal, characteristic, complemented
6#20290787C211yesmaximal, characteristic, complemented
7#20290786C211yesmaximal, characteristic, complemented
8#20290691C211yesmaximal, characteristic, complemented
9#20290691C211yesmaximal, characteristic, complemented
10#20290690C211yesmaximal, characteristic, complemented
11#20290660C211yesmaximal, characteristic, complemented
12#20290658C211yesmaximal, characteristic, complemented
13#20290449C211yesmaximal, characteristic, complemented
14C22⋊C4×#88324C211yesmaximal, characteristic, complemented
15#20277216C211yesmaximal, characteristic
16C22×D53⋊C8C2211yescharacteristic
17C22×D53⋊C8C2211yescharacteristic
18C22×D53⋊C8C2211yescharacteristic, complemented
19C23×#88324C2211yescharacteristic
20C23×#88324C2211yescharacteristic
21#16811651—24no—
22#16811650—24no—
23C2×#13133284C2211yescharacteristic, complemented
24C2×C4⋊#88324C2211yescharacteristic, complemented
25C2×C4⋊#88324C2211yescharacteristic, complemented
26C2×#13133274—24no—
27C2×#13133274C2211yescharacteristic
28C2×#13133274C2211yescharacteristic
29C2×#13133274C2211yescharacteristic
30C2×#13133274C2211yescharacteristic
31C2×#13133274C2211yescharacteristic
32C2×#13133274C2211yescharacteristic
33C2×#13133274C2211yescharacteristic, complemented
34C2×#13133274C2211yescharacteristic, complemented
35C2×#13133274C2211yescharacteristic, complemented
36D53⋊(C22⋊C8)—24no—
37C2×C22⋊#88324C2211yescharacteristic
38C2×C22⋊#88324C2211yescharacteristic
39C2×C4×#88324C2211yescharacteristic, complemented
40C2×C4×#88324C2211yescharacteristic, complemented
41C2×C4×#88324C2211yescharacteristic, complemented
42#16811489C2211yescharacteristic, complemented
43#16811489C2211yescharacteristic, complemented
44#16811489C2211yescharacteristic, complemented
45#16811489C2211yescharacteristic, complemented
46#16811489C2211yescharacteristic, complemented
47#16811489C2211yescharacteristic, complemented
48C23×C4×D53C2211yescharacteristic
49C2×#13133187C411yescharacteristic
50C2×#13133179C2211yescharacteristic
51C2×#13133179C2211yescharacteristic
52C2×#13133177C2211yescharacteristic
53#16810502C411yescharacteristic
54#16810501C411yescharacteristic
55#16810501C411yescharacteristic
56#16810494C411yescharacteristic
57#16810494C411yescharacteristic
58#16810478C411yescharacteristic
59C22⋊C4×Dic53C2211yescharacteristic
60#16810470C2211yescharacteristic
61#16810470C2211yescharacteristic
62C53×#385C411yescharacteristic
63C2×D53⋊C8—22no—
64C2×D53⋊C8—22no—
65C2×D53⋊C8—22no—
66C2×D53⋊C8—22no—
67C2×D53⋊C8—22no—
68C2×D53⋊C8—22no—
69C2×D53⋊C8—41no—
70C2×D53⋊C8—41no—
71C2×D53⋊C8—41no—
72C22×#88324—22no—
73C22×#88324—22no—
74C22×#88324—22no—
75C22×#88324—22no—
76C22×#88324—41no—
77C22×#88324—41no—
78C22×#88324C2311yescharacteristic
79C22×#88324C2311yescharacteristic
80C22×#88324C2311yescharacteristic
81C22×#88324C2311yescharacteristic
82C22×#88324C2311yescharacteristic
83C22×#88324C2311yescharacteristic
84C22×#88324C2311yescharacteristic
85C22×#88324C2311yescharacteristic
86#13133284—22no—
87C4⋊#88324—22no—
88C4⋊#88324—41no—
89#13133274—22no—
90#13133274—22no—
91#13133274—22no—
92#13133274—22no—
93#13133274—22no—
94#13133274—22no—
95#13133274—22no—
96#13133274—41no—
97#13133274D414yescomplemented
98C22⋊#88324—22no—
99C22⋊#88324D414yescomplemented
100C4×#88324—22no—
101C4×#88324—22no—
102C4×#88324—41no—
103C24×D53C2×C411yescharacteristic
104C22×D212C2×C411yescharacteristic
105C22×D212C2×C411yescharacteristic
106C22×C22⋊D53C2×C411yescharacteristic
107C23×Dic53C2311yescharacteristic
108C22×C4×D53—22no—
109C22×C4×D53—22no—
110C22×C4×D53—22no—
111C22×C4×D53—22no—
112C22×C4×D53—41no—
113C22×C4×D53—41no—
114C22×C4×D53C2×C411yescharacteristic
115C22×C4×D53C2×C411yescharacteristic
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2311yescharacteristic
119#13133187C818yescomplemented
120#13133179—22no—
121#13133179—22no—
122#13133179—41no—
123#13133179—41no—
124#13133177—22no—
125#13133177—22no—
126C2×#11719919C2×C411yescharacteristic
127C2×C22⋊Dic53C2×C411yescharacteristic
128C2×#11719921C2×C411yescharacteristic
129C2×#11719921C2×C411yescharacteristic
130C2×#11719921C2×C411yescharacteristic
131C2×#11719921C2×C411yescharacteristic
132C2×#11719921C2×C411yescharacteristic
133C2×#11719921C2×C411yescharacteristic
134C2×#11719921C2×C411yescharacteristic
135C2×#11719921C2×C411yescharacteristic
136C2×#11719921C2×C411yescharacteristic
137C2×C4×Dic53C2311yescharacteristic
138C2×C4×Dic53C2311yescharacteristic
139C2×C4×Dic53C2311yescharacteristic
140#13133124C2×C411yescharacteristic
141#13133124C2×C411yescharacteristic
142#13133124C2×C411yescharacteristic
143#13133124C2×C411yescharacteristic
144C23×C4×C53C2×C411yescharacteristic
145C2×C4⋊C4×C53C2×C411yescharacteristic
146C2×C4⋊C4×C53C2×C411yescharacteristic
147C2×C22⋊C4×C53C2×C411yescharacteristic
148C2×C22⋊C4×C53C2×C411yescharacteristic
149#95×C53C2×C411yescharacteristic
150#95×C53C2×C411yescharacteristic
151C24×C53C22×C411yescharacteristic
152C23×D53—22no—
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—41no—
157C23×D53—41no—
158C23×D53C2×C814yescomplemented
159C23×D53C22×C411yescharacteristic
160C23×D53C22×C411yescharacteristic
161C23×D53C22×C411yescharacteristic
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—41no—
165C22×C4×C53C22×C411yescharacteristic
166C22×C4×C53C22×C411yescharacteristic
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C2×C22⋊D53—22no—
172C2×C22⋊D53—22no—
173C2×C22⋊D53C2×C814yescomplemented
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53C22×C411yescharacteristic
179C22×Dic53C22×C411yescharacteristic
180C22×Dic53C22×C411yescharacteristic
181C22×Dic53C22×C411yescharacteristic
182C22×Dic53C2×D412yes—
183C22×Dic53#4112yes—
184C22×Dic53C2411yescharacteristic
185C2×D212—22no—
186C2×D212—22no—
187C2×D212—41no—
188C2×D212—41no—
189C2×D212C2×C814yescomplemented
190C2×D212C2×C814yescomplemented
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—22no—
196C2×C4×D53—22no—
197C2×C4×D53—22no—
198C2×C4×D53—22no—
199C2×C4×D53—21no—
200C2×C4×D53—21no—
201C2×C4×D53—21no—
202C2×C4×D53—21no—
203C2×C4×D53—21no—
204C2×C4×D53—21no—
205C2×C4×D53—21no—
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53—21no—
210C2×C4×D53—21no—
211C2×C4×D53—44no—
212C2×C4×D53—44no—
213C2×C4×D53—44no—
214C2×C4×D53—44no—
215C2×C4×D53—41no—
216C2×C4×D53—41no—
217C2×C4×D53C2×D412yes—
218C2×C4×D53#4112yes—
219C2×#88324—21no—
220C2×#88324—21no—
221C2×#88324—21no—
222C2×#88324—21no—
223C2×#88324—21no—
224C2×#88324—21no—
225C2×#88324—21no—
226C2×#88324—21no—
227C2×#88324—21no—
228C2×#88324—21no—
229C2×#88324—21no—
230C2×#88324—21no—
231C2×#88324—21no—
232C2×#88324—21no—
233C2×#88324—21no—
234C2×#88324—21no—
235C2×#88324—21no—
236C2×#88324—21no—
237C2×#88324—21no—
238C2×#88324—21no—
239C2×#88324—44no—
240C2×#88324—44no—
241C2×#88324C2×D412yes—
242C2×#88324C2×D412yes—
243C2×#88324C2×D412yes—
244C2×#88324C2×D412yes—
245D53⋊C8—44no—
246D53⋊C8—44no—
247D53⋊C8—44no—
248C4⋊C4×C53—22no—
249C4⋊C4×C53—41no—
250C22⋊C4×C53—22no—
251C22⋊C4×C53C2×C814yescomplemented
252C22⋊Dic53—22no—
253#11719921—22no—
254#11719921—22no—
255#11719921—22no—
256#11719921—22no—
257#11719921—41no—
258#11719921—41no—
259#11719921—41no—
260#11719921C2×C814yescomplemented
261#11719921C2×C814yescomplemented
262#11719919—22no—
263C4×Dic53—21no—
264C4×Dic53—21no—
265C4×Dic53—21no—
266C4×Dic53—21no—
267C4×Dic53—21no—
268C4×Dic53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53C4×D412yes—
274C23×C53C22×C812yes—
275C23×C53#13112yes—
276C23×C53C23×C411yescharacteristic
277C22×D53—21no—
278C22×D53—21no—
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—21no—
282C22×D53—21no—
283C22×D53—21no—
284C22×D53—21no—
285C22×D53—21no—
286C22×D53—21no—
287C22×D53—21no—
288C22×D53—21no—
289C22×D53—21no—
290C22×D53—21no—
291C22×D53—21no—
292C22×D53—21no—
293C22×D53—28no—
294C22×D53—28no—
295C22×D53—44no—
296C22×D53—44no—
297C22×D53—44no—
298C22×D53—44no—
299C22×D53—44no—
300C22×D53C4×D412yes—
301C22×D53C22×C812yes—
302C22×D53C22×C812yes—
303C22×D53C22×C812yes—
304C22×D53#13112yes—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—44no—
321C2×C4×C53C4×D412yes—
322C2×C4×C53C22×C812yes—
323C2×C4×C53C22×C812yes—
324C22⋊D53—28no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—21no—
328C2×Dic53—21no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—21no—
337C2×Dic53—21no—
338C2×Dic53—21no—
339C2×Dic53C4×D412yes—
340C2×Dic53C22×C812yes—
341C2×Dic53C22×D411yescharacteristic
342C2×Dic53C22×D411yescharacteristic
343C2×Dic53C2×#4111yescharacteristic
344C2×Dic53C2×#4111yescharacteristic
345C2×Dic53H(5,𝔽2)11yescharacteristic
346C2×Dic53H(5,𝔽2)11yescharacteristic
347D212—28no—
348D212—44no—
349C4×D53—22no—
350C4×D53—22no—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—44no—
354C4×D53—44no—
355C4×D53—41no—
356C4×D53—41no—
357C4×D53—41no—
358C4×D53—41no—
359C4×D53—41no—
360C4×D53—41no—
361C4×D53—41no—
362C4×D53—41no—
363#88324—22no—
364#88324—22no—
365#88324—22no—
366#88324—22no—
367#88324—41no—
368#88324—41no—
369#88324—41no—
370#88324—41no—
371#22842—531nomaximal, Sylow
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53C8×D414yescomplemented
379C22×C53C2×C4×D411yescharacteristic
380C22×C53C2×C4×D411yescharacteristic
381C22×C53#51811yescharacteristic
382C22×C53C23×C811yescharacteristic
383C22×C53C2×#13111yescharacteristic
384C22×C53C2×#13111yescharacteristic
385C22×C53#56811yescharacteristic
386C2×D53—22no—
387C2×D53—22no—
388C2×D53—22no—
389C2×D53—22no—
390C2×D53—22no—
391C2×D53—22no—
392C2×D53—22no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—22no—
398C2×D53—416no—
399C2×D53—41no—
400C2×D53—41no—
401C2×D53—41no—
402C2×D53—41no—
403C2×D53—41no—
404C2×D53—41no—
405C2×D53—41no—
406C2×D53—41no—
407C2×D53C8×D414yescomplemented
408C4×C53—22no—
409C4×C53—22no—
410C4×C53—22no—
411C4×C53—41no—
412C4×C53—41no—
413C4×C53—41no—
414Dic53—22no—
415Dic53—22no—
416Dic53—41no—
417Dic53—41no—
418Dic53D4211yescharacteristic
419Dic53#54611yescharacteristic
420Dic53#54611yescharacteristic
421Dic53#55111yescharacteristic
422C2×C8×D4—531no—
423C2×C8×D4—531no—
424C22×C22⋊C8—531no—
425C22×C22⋊C8—531no—
426C4×#120—531no—
427#1954—531no—
428#1923—531no—
429#1923—531no—
430#1869—531no—
431#1869—531no—
432#1869—531no—
433#1850—531no—
434#1850—531no—
435C8×C22⋊C4—531no—
436C8×C22⋊C4—531no—
437C2×C53—24no—
438C2×C53#235811yescharacteristic
439C2×C53C2×C8×D411yescharacteristic
440C2×C53C2×C8×D411yescharacteristic
441C2×C53#293311yescharacteristic
442C2×C53#293311yescharacteristic
443C2×C53#297211yescharacteristic
444C2×C53#297711yescharacteristic
445D53—24no—
446D53—42no—
447D53—42no—
448C24×C4—531no—
449C23×C8—531no—
450C23×C8—531no—
451C23×C8—531no—
452C23×C8—531no—
453C23×C8—531no—
454C2×#120—531no—
455C2×C4×D4—531no—
456C2×C4×D4—531no—
457C2×C4×D4—531no—
458C8×D4—1064no—
459C8×D4—1064no—
460C2×C4⋊C8—531no—
461C2×C4⋊C8—531no—
462C2×C4⋊C8—531no—
463C2×C22⋊C8—531no—
464C2×C22⋊C8—531no—
465C2×C22⋊C8—531no—
466C2×C22⋊C8—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×C22⋊C8—531no—
470C2×C22⋊C8—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×C22⋊C8—531no—
474C2×C22⋊C8—1064no—
475C2×C22⋊C8—1064no—
476C2×C4×C8—531no—
477C2×C4×C8—531no—
478C2×C4×C8—531no—
479#386—531no—
480#386—531no—
481#386—531no—
482#385—531no—
483#385—531no—
484#385#615711yescharacteristic
485#379—531no—
486C4×C22⋊C4—531no—
487C4×C22⋊C4—531no—
488C4×C22⋊C4—531no—
489#336—531no—
490#336—531no—
491#336—531no—
492#336—531no—
493#336—531no—
494#336—531no—
495C53#2284211yescharacteristic, complemented, Sylow
496C25—531no—
497C22×D4—531no—
498C22×D4—531no—
499C22×D4—531no—
500C23×C4—531no—
501C23×C4—531no—
502C23×C4—531no—
503C23×C4—531no—
504C23×C4—531no—
505C23×C4—531no—
506C23×C4—1062no—
507C23×C4—1062no—
508C23×C4—1062no—
509C23×C4—1062no—
510C23×C4—2121no—
511C23×C4—2121no—
512C23×C4C2×#615711yescharacteristic
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8—531no—
520C22×C8—531no—
521C22×C8—1062no—
522C22×C8—1062no—
523C22×C8—1062no—
524C22×C8—1062no—
525C22×C8—1062no—
526C22×C8—1062no—
527C22×C8—1062no—
528C22×C8—1062no—
529C22×C8—1062no—
530C22×C8—1062no—
531C22×C8—2121no—
532C22×C8—2121no—
533C22×C8—2121no—
534C22×C8—2121no—
535C22×C8—2121no—
536#120—538no—
537C4×D4—1062no—
538C4×D4—1062no—
539C4×D4—1062no—
540C4×D4—1062no—
541C4×D4—2121no—
542C4×D4—2121no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4C2×#615711yescharacteristic
545C2×C4⋊C4C2×#615711yescharacteristic
546C2×C22⋊C4—531no—
547C2×C22⋊C4—531no—
548C2×C22⋊C4—531no—
549C2×C22⋊C4—531no—
550C2×C22⋊C4—531no—
551C2×C22⋊C4—531no—
552C2×C22⋊C4—531no—
553C2×C22⋊C4—531no—
554C2×C22⋊C4—531no—
555C2×C22⋊C4—531no—
556C2×C22⋊C4C2×#615711yescharacteristic
557C2×C22⋊C4C2×#615711yescharacteristic
558C2×C42—531no—
559C2×C42—531no—
560C2×C42—531no—
561C4⋊C8—1062no—
562C4⋊C8—1062no—
563C4⋊C8—2121no—
564C22⋊C8—534no—
565C22⋊C8—534no—
566C22⋊C8—1062no—
567C22⋊C8—1062no—
568C22⋊C8—1062no—
569C22⋊C8—1062no—
570C22⋊C8—1062no—
571C22⋊C8—1062no—
572C22⋊C8—1062no—
573C22⋊C8—1062no—
574C22⋊C8—2121no—
575C4×C8—1062no—
576C4×C8—1062no—
577C4×C8—2121no—
578#95—531no—
579#95—531no—
580#95—531no—
581#95—531no—
582#95C2×#615711yescharacteristic
583#95C2×#615711yescharacteristic
584C24—531no—
585C24—531no—
586C24—531no—
587C24—534no—
588C24—1062no—
589C24—1062no—
590C24—1062no—
591C24—1062no—
592C24—2121no—
593C24—2121no—
594C24C22×#615711yescharacteristic
595C2×D4—534no—
596C2×D4—534no—
597C2×D4—534no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—1062no—
601C2×D4—1062no—
602C2×D4—2121no—
603C2×D4—2121no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—531no—
608C22×C4—532no—
609C22×C4—532no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—531no—
615C22×C4—531no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1062no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1062no—
640C22×C4—2121no—
641C22×C4—2121no—
642C22×C4—2124no—
643C22×C4—2124no—
644C22×C4—2124no—
645C22×C4—2124no—
646C22×C4C22×#615711yescharacteristic
647C22×C4C22×#615711yescharacteristic
648C22×C4C22×#615711yescharacteristic
649C22×C4C22×#615711yescharacteristic
650C22×C4C22×#615711yescharacteristic
651C22×C4C22×#615711yescharacteristic
652C2×C8—532no—
653C2×C8—532no—
654C2×C8—532no—
655C2×C8—532no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—1061no—
667C2×C8—1061no—
668C2×C8—1061no—
669C2×C8—1061no—
670C2×C8—1061no—
671C2×C8—1061no—
672C2×C8—1061no—
673C2×C8—1061no—
674C2×C8—1061no—
675C2×C8—1061no—
676C2×C8—2124no—
677C2×C8—2124no—
678C2×C8—2124no—
679C2×C8—2124no—
680C2×C8—2124no—
681C4⋊C4—22no—
682C4⋊C4—41no—
683C4⋊C4—1062no—
684C22⋊C4—22no—
685C22⋊C4—534no—
686C22⋊C4—534no—
687C22⋊C4—1062no—
688C22⋊C4—1062no—
689C22⋊C4—1062no—
690C22⋊C4—1062no—
691C22⋊C4—1062no—
692C22⋊C4—2121no—
693C22⋊C4—2121no—
694C22⋊C4—2121no—
695C22⋊C4D53⋊C814yescomplemented
696C42—1061no—
697C42—1061no—
698C42—1061no—
699C42—1061no—
700C42—1061no—
701C42—1061no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—532no—
707C23—532no—
708C23—532no—
709C23—532no—
710C23—532no—
711C23—1068no—
712C23—1061no—
713C23—1061no—
714C23—1061no—
715C23—1061no—
716C23—1068no—
717C23—1061no—
718C23—1061no—
719C23—1061no—
720C23—1061no—
721C23—1061no—
722C23—1061no—
723C23—1061no—
724C23—1061no—
725C23—1061no—
726C23—1061no—
727C23—1061no—
728C23—1061no—
729C23—2124no—
730C23—2124no—
731C23—2124no—
732C23—2124no—
733C23—2124no—
734C23D4×#615712yes—
735C23C2×D53⋊C812yes—
736C23#1313330512yes—
737C23C23×#615711yescharacteristic
738D4—1068no—
739D4—1068no—
740D4—2124no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—44no—
757C2×C4—531no—
758C2×C4—531no—
759C2×C4—531no—
760C2×C4—531no—
761C2×C4—531no—
762C2×C4—531no—
763C2×C4—532no—
764C2×C4—532no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1061no—
774C2×C4—1061no—
775C2×C4—1061no—
776C2×C4—1061no—
777C2×C4—1061no—
778C2×C4—1061no—
779C2×C4—1061no—
780C2×C4—1061no—
781C2×C4—1061no—
782C2×C4—1061no—
783C2×C4—2124no—
784C2×C4—2121no—
785C2×C4—2121no—
786C2×C4—2121no—
787C2×C4—2121no—
788C2×C4—2121no—
789C2×C4—2121no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2124no—
793C2×C4D4×#615712yes—
794C2×C4C2×D53⋊C812yes—
795C2×C4C2×D53⋊C812yes—
796C8—1062no—
797C8—1062no—
798C8—1062no—
799C8—1062no—
800C8—2121no—
801C8—2121no—
802C8—2121no—
803C8—2121no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—534no—
811C22—1062no—
812C22—1062no—
813C22—1062no—
814C22—1062no—
815C22—1062no—
816C22—1062no—
817C22—1062no—
818C22—1062no—
819C22—1062no—
820C22—1062no—
821C22—1062no—
822C22—1062no—
823C22—21216no—
824C22—2121no—
825C22—2121no—
826C22—2121no—
827C22—2121no—
828C22—2121no—
829C22—2121no—
830C22—2121no—
831C22—2121no—
832C22#1681165114yescomplemented
833C22C2×D4×#615711yescharacteristic
834C22C2×D4×#615711yescharacteristic
835C22#1681169011yescharacteristic
836C22C22×D53⋊C811yescharacteristic
837C22D53⋊#13111yescharacteristic
838C22C2×#1313330511yescharacteristic
839C22#1681170211yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—531no—
847C4—531no—
848C4—531no—
849C4—531no—
850C4—1062no—
851C4—1062no—
852C4—2121no—
853C4—2121no—
854C2—24no—
855C2—1064no—
856C2—2122no—
857C2—2122no—
858C2#2029123711yescharacteristic
859C2D4×D53⋊C811yescharacteristic
860C2C2×#1681165111yescharacteristic
861C2#2029144811yescharacteristic
862C2#2029144911yescharacteristic
863C2#2029156311yescharacteristic
864C2#2029159011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C23×C8
FittingC53×#385C4
socleC23×C53C23×C4
prime radicalC2×#13133187C4
cosocleC22×Dic53C24
hypercenter#385#6157
hypocenterC53#22842
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#16811651C2semidirect
2. C2×#16811650C2semidirect
3. C22×#13133274C2semidirect
4. C2×D53⋊(C22⋊C8)C2semidirect
5. #20290837C2semidirect
6. #20290787C2semidirect
7. #20290786C2semidirect
8. #20290691C2semidirect
9. #20290691C2semidirect
10. #20290690C2semidirect
11. #20290660C2semidirect
12. #20290658C2semidirect
13. #20290449C2semidirect
14. C22⋊C4×#88324C2semidirect
18. C22×D53⋊C8C22semidirect
23. C2×#13133284C22semidirect
24. C2×C4⋊#88324C22semidirect
25. C2×C4⋊#88324C22semidirect
33. C2×#13133274C22semidirect
34. C2×#13133274C22semidirect
35. C2×#13133274C22semidirect
39. C2×C4×#88324C22semidirect
40. C2×C4×#88324C22semidirect
41. C2×C4×#88324C22semidirect
42. #16811489C22semidirect
43. #16811489C22semidirect
44. #16811489C22semidirect
45. #16811489C22semidirect
46. #16811489C22semidirect
47. #16811489C22semidirect
97. #13133274D4semidirect
99. C22⋊#88324D4semidirect
119. #13133187C8semidirect
158. C23×D53C2×C8semidirect
173. C2×C22⋊D53C2×C8semidirect
189. C2×D212C2×C8semidirect
190. C2×D212C2×C8semidirect
251. C22⋊C4×C53C2×C8semidirect
260. #11719921C2×C8semidirect
261. #11719921C2×C8semidirect
378. C22×C53C8×D4semidirect
407. C2×D53C8×D4semidirect
495. C53#22842semidirect
695. C22⋊C4D53⋊C8semidirect
832. C22#16811651semidirect

Maximal subgroups

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

subgroupindex
C2×#168116512
C2×#168116502
C22×#131332742
C2×D53⋊(C22⋊C8)2
#202908372
#202907872
#202907862
#202906912
#202906902
#202906602
#202906582
#202904492
C22⋊C4×#883242
#202772162
#2284253