Finite Group Databasebeta

← #27312034

Subgroups — #27312034

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810516C211yesmaximal, characteristic
2C2×#16810498C211yesmaximal, characteristic
3C2×#16810498C211yesmaximal, characteristic
4C2×#16810489C211yesmaximal, characteristic, complemented
5#20272980C211yesmaximal, characteristic, complemented
6#20272980C211yesmaximal, characteristic, complemented
7#20272972C211yesmaximal, characteristic, complemented
8#20272968C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic
10#20272960C211yesmaximal, characteristic
11#20272949C211yesmaximal, characteristic, complemented
12#20272945C211yesmaximal, characteristic, complemented
13#20272944C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic
15C2×C53×#388C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810516—24no—
29#16810498—24no—
30#16810498—24no—
31#16810489—24no—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C22×C4⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C42×C53C2211yescharacteristic
53C53×#388C418yescomplemented
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—41no—
60C23×Dic53—41no—
61C23×Dic53—41no—
62C23×Dic53—41no—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53—22no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—22no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—41no—
83C2×C4⋊Dic53—41no—
84C2×C4⋊Dic53—41no—
85C2×C4⋊Dic53—41no—
86C2×C4⋊Dic53—41no—
87C2×C4⋊Dic53—41no—
88C2×C4⋊Dic53—41no—
89C2×C4⋊Dic53—41no—
90C2×C4⋊Dic53—41no—
91C2×C4⋊Dic53—41no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—41no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—41no—
104#13133124—22no—
105#13133124—22no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—41no—
113#13133124—41no—
114#13133124—41no—
115#13133124—41no—
116#13133124—41no—
117#13133124—41no—
118#13133124—41no—
119#13133124D414yes—
120C25×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53—41no—
128C2×C4⋊C4×C53—41no—
129C2×C4⋊C4×C53C2×C414yescomplemented
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—41no—
133C2×C22⋊C4×C53—41no—
134C2×C22⋊C4×C53C2×C414yes—
135C2×C22⋊C4×C53C2×C414yes—
136C2×C22⋊C4×C53C2×C414yes—
137C2×C22⋊C4×C53D414yes—
138C2×C22⋊C4×C53Q814yes—
139C2×C42×C53—22no—
140C2×C42×C53—22no—
141C2×C42×C53C2×C414yescomplemented
142#95×C53C2×C414yescomplemented
143#95×C53C2×C414yescomplemented
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53C22×C412yes—
157C24×C53C2×D412yes—
158C24×C53C2×Q812yes—
159C24×C53C2411yescharacteristic
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×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C22×C412yes—
191C22×C4×C53C22×C412yes—
192C22×C4×C53C22×C412yes—
193C22×C4×C53C22×C412yes—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×Q812yes—
200C22×C4×C53C2×Q812yes—
201C22×C4×C53#4112yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—44no—
255C22×Dic53—44no—
256C22×Dic53—44no—
257C22×Dic53—44no—
258C22×Dic53—44no—
259C22×Dic53—44no—
260C22×Dic53—44no—
261C22×Dic53C2×D412yes—
262C22×Dic53C2×D412yes—
263C22×Dic53#4112yes—
264C22×Dic53#4112yes—
265C4⋊C4×C53—44no—
266C22⋊C4×C53—28no—
267C22⋊C4×C53—44no—
268C22⋊C4×C53C4⋊C4116yescomplemented
269C42×C53—28no—
270C22⋊Dic53—44no—
271C22⋊Dic53—44no—
272C22⋊Dic53—44no—
273C4⋊Dic53—44no—
274C4⋊Dic53—44no—
275C4⋊Dic53—44no—
276C4⋊Dic53—44no—
277C4⋊Dic53—44no—
278C4⋊Dic53—44no—
279C4⋊Dic53—44no—
280C4×Dic53—44no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53C2×C4⋊C414yes—
316C23×C53C23×C411yescharacteristic
317C23×C53C22×D411yescharacteristic
318C23×C53C22×D411yescharacteristic
319C23×C53C22×Q811yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53C2×#4111yescharacteristic
322C23×C53C2×#4111yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C53H(5,𝔽2)11yescharacteristic
325C23×C53H(5,𝔽2)11yescharacteristic
326C23×C53H(5,𝔽2)11yescharacteristic
327C23×C53H(5,𝔽2)11yescharacteristic
328C23×C532−1+411yescharacteristic
329C23×C532−1+411yescharacteristic
330C23×C532−1+411yescharacteristic
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53C2×C4⋊C414yes—
371C2×C4×C53C2×C4⋊C414yes—
372C2×C4×C53C4×D414yes—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—416no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430#14403—531nomaximal, Sylow
431C22×C53—24no—
432C22×C53—24no—
433C22×C53—24no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—42no—
438C22×C53—42no—
439C22×C53—42no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53C22×C4⋊C411yescharacteristic
447C22×C53C2×C4×D411yescharacteristic
448C22×C53C4×#4111yescharacteristic
449C22×C53#51811yescharacteristic
450C22×C53#52011yescharacteristic
451C22×C53#52011yescharacteristic
452C22×C53#52011yescharacteristic
453C22×C53#53511yescharacteristic
454C22×C53#53511yescharacteristic
455C22×C53#53611yescharacteristic
456C22×C53#53711yescharacteristic
457C22×C53#53811yescharacteristic
458C22×C53#53911yescharacteristic
459C22×C53#54011yescharacteristic
460C22×C53#54111yescharacteristic
461C22×C53#54211yescharacteristic
462C22×C53#54211yescharacteristic
463C22×C53#54411yescharacteristic
464C22×C53#54411yescharacteristic
465C22×C53D4211yescharacteristic
466C22×C53#54611yescharacteristic
467C22×C53#54611yescharacteristic
468C22×C53#54611yescharacteristic
469C22×C53#54711yescharacteristic
470C22×C53#54711yescharacteristic
471C22×C53D4×Q811yescharacteristic
472C22×C53#55111yescharacteristic
473C22×C53#55211yescharacteristic
474C22×C53#55411yescharacteristic
475C22×C53#55411yescharacteristic
476C22×C53#55411yescharacteristic
477C22×C53H(3,𝔽4)11yescharacteristic
478C22×C53#56211yescharacteristic
479C22×C53#56211yescharacteristic
480C22×C53#56311yescharacteristic
481C4×C53—24no—
482C4×C53—24no—
483C4×C53—24no—
484C4×C53—42no—
485C4×C53—42no—
486C4×C53—42no—
487Dic53—42no—
488Dic53—42no—
489Dic53—42no—
490Dic53—42no—
491Dic53—81no—
492Dic53—81no—
493Dic53—81no—
494Dic53—81no—
495C2×#388—531no—
496C2×#388D5311yescharacteristic
497C2×#385—531no—
498C2×#385—531no—
499C2×#382—531no—
500#1444—531no—
501#1444—531no—
502#1442—531no—
503#1441—531no—
504#1439—531no—
505#1439—531no—
506#1436—531no—
507C4⋊#95—531no—
508C4⋊#95—531no—
509C22⋊#95—531no—
510C2×C53—44no—
511C2×C53#231711yescharacteristic
512C2×C53#232411yescharacteristic
513C2×C53#233411yescharacteristic
514C2×C53D4×C4⋊C411yescharacteristic
515C2×C53#234911yescharacteristic
516C2×C53#235911yescharacteristic
517C2×C53#237911yescharacteristic
518C2×C53#267011yescharacteristic
519C2×C53#267211yescharacteristic
520C2×C53#269811yescharacteristic
521C2×C53#270411yescharacteristic
522C2×C53#270611yescharacteristic
523C2×C53#272011yescharacteristic
524C2×C53#276311yescharacteristic
525C2×C53#276811yescharacteristic
526C24×C4—531no—
527C22×C4⋊C4—531no—
528C22×C4⋊C4—531no—
529C22×C4⋊C4—531no—
530C22×C4⋊C4—531no—
531C22×C4⋊C4—531no—
532C22×C4⋊C4—531no—
533C22×C4⋊C4—531no—
534C22×C4⋊C4C2×D5311yescharacteristic
535C22×C22⋊C4—531no—
536C22×C22⋊C4—531no—
537C22×C22⋊C4—531no—
538C22×C22⋊C4C2×D5311yescharacteristic
539C22×C22⋊C4C2×D5311yescharacteristic
540C22×C22⋊C4C2×D5311yescharacteristic
541C22×C42—531no—
542C22×C42C2×D5311yescharacteristic
543#388—1064no—
544#388Dic5318yescomplemented
545#385—1064no—
546#385—1064no—
547#382—1064no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95C2×D5311yescharacteristic
565C2×#95C2×D5311yescharacteristic
566C53#1440311yescharacteristic, complemented, Sylow
567C25C22×D5311yescharacteristic
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4—531no—
574C23×C4—531no—
575C23×C4—531no—
576C23×C4—1062no—
577C23×C4—1062no—
578C23×C4—1062no—
579C23×C4—2121no—
580C23×C4—2121no—
581C23×C4—2121no—
582C23×C4—2121no—
583C23×C4C22×D5311yescharacteristic
584C23×C4C22×D5311yescharacteristic
585C23×C4C22×D5311yescharacteristic
586C23×C4C22×D5311yescharacteristic
587C23×C4C22×D5311yescharacteristic
588C23×C4C22×D5311yescharacteristic
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—1062no—
592C2×C4⋊C4—1062no—
593C2×C4⋊C4—1062no—
594C2×C4⋊C4—1062no—
595C2×C4⋊C4—1062no—
596C2×C4⋊C4—1062no—
597C2×C4⋊C4—1062no—
598C2×C4⋊C4—1062no—
599C2×C4⋊C4—1062no—
600C2×C4⋊C4—1062no—
601C2×C4⋊C4—1062no—
602C2×C4⋊C4—2121no—
603C2×C4⋊C4—2121no—
604C2×C4⋊C4—2121no—
605C2×C4⋊C4—2121no—
606C2×C4⋊C4—2121no—
607C2×C4⋊C4—2121no—
608C2×C4⋊C4—2121no—
609C2×C4⋊C4—2121no—
610C2×C4⋊C4—2121no—
611C2×C4⋊C4—2121no—
612C2×C4⋊C4C2×Dic5314yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—1062no—
618C2×C22⋊C4—1062no—
619C2×C22⋊C4—1062no—
620C2×C22⋊C4—1062no—
621C2×C22⋊C4—1062no—
622C2×C22⋊C4—2121no—
623C2×C22⋊C4—2121no—
624C2×C22⋊C4—2121no—
625C2×C22⋊C4—2121no—
626C2×C22⋊C4Dic10614yes—
627C2×C22⋊C4D21214yes—
628C2×C22⋊C4C2×Dic5314yes—
629C2×C22⋊C4C2×Dic5314yes—
630C2×C22⋊C4C2×Dic5314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—1062no—
634C2×C42—1062no—
635C2×C42—2121no—
636C2×C42C2×Dic5314yescomplemented
637#95—534no—
638#95—1062no—
639#95—1062no—
640#95—1062no—
641#95—1062no—
642#95—1062no—
643#95—1062no—
644#95—1062no—
645#95—1062no—
646#95—2121no—
647#95—2121no—
648#95—2121no—
649#95—2121no—
650#95—2121no—
651#95—2121no—
652#95—2121no—
653#95C2×Dic5314yescomplemented
654#95C2×Dic5314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic10612yes—
668C24C2×D21212yes—
669C24C22×Dic5312yes—
670C24C23×D5311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—2124no—
758C22×C4—2124no—
759C22×C4—2124no—
760C22×C4—2124no—
761C22×C4—2124no—
762C22×C4—2124no—
763C22×C4—2124no—
764C22×C4C2×Dic10612yes—
765C22×C4C2×Dic10612yes—
766C22×C4C2×D21212yes—
767C22×C4C2×D21212yes—
768C22×C4D4×D5312yes—
769C22×C4#1171994712yes—
770C22×C4C22×Dic5312yes—
771C22×C4C22×Dic5312yes—
772C22×C4C22×Dic5312yes—
773C22×C4C22×Dic5312yes—
774C22×C4C22×Dic5312yes—
775C22×C4C22×Dic5312yes—
776C4⋊C4—44no—
777C4⋊C4—2124no—
778C4⋊C4—2124no—
779C4⋊C4—2124no—
780C4⋊C4—2124no—
781C4⋊C4—2124no—
782C4⋊C4—2124no—
783C4⋊C4—2124no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—2124no—
787C22⋊C4—2124no—
788C22⋊C4—2124no—
789C22⋊C4C4⋊Dic53116yescomplemented
790C42—28no—
791C42—2124no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic5314yes—
827C23C23×Dic5311yescharacteristic
828C23C2×D4×D5311yescharacteristic
829C23C22×D21211yescharacteristic
830C23C22×Dic10611yescharacteristic
831C23#41×D5311yescharacteristic
832C23#41×D5311yescharacteristic
833C23C2×#1171994711yescharacteristic
834C23#1313326211yescharacteristic
835C23#1313326211yescharacteristic
836C23#1313326311yescharacteristic
837C23#1313326311yescharacteristic
838C23#1313326311yescharacteristic
839C23#1313326411yescharacteristic
840C23#1313326411yescharacteristic
841C23#1313326411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—1062no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—2121no—
894C2×C4—2121no—
895C2×C4—2121no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4—2121no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—21216no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4C2×C4⋊Dic5314yes—
939C2×C4C2×C4⋊Dic5314yes—
940C2×C4D4×Dic5314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic5311yescharacteristic
957C22C2×D4×Dic5311yescharacteristic
958C22#41×Dic5311yescharacteristic
959C22#1681109811yescharacteristic
960C22#1681110611yescharacteristic
961C22#1681110611yescharacteristic
962C22#1681110611yescharacteristic
963C22#1681118911yescharacteristic
964C22#1681119211yescharacteristic
965C22#1681119911yescharacteristic
966C22#1681120211yescharacteristic
967C22#1681121211yescharacteristic
968C22#1681121411yescharacteristic
969C22#1681122611yescharacteristic
970C22#1681123011yescharacteristic
971C22#1681123911yescharacteristic
972C22#1681124011yescharacteristic
973C22#1681125111yescharacteristic
974C22#1681125111yescharacteristic
975C22D4×D21211yescharacteristic
976C22#1681126511yescharacteristic
977C22#1681126811yescharacteristic
978C22#1681126811yescharacteristic
979C22#1681127111yescharacteristic
980C22#1681127711yescharacteristic
981C22D4×Dic10611yescharacteristic
982C22#1681129611yescharacteristic
983C22#1681131011yescharacteristic
984C22#1681133011yescharacteristic
985C22#1681133211yescharacteristic
986C22#1681133211yescharacteristic
987C22#1681136511yescharacteristic
988C22#1681136711yescharacteristic
989C22#1681136711yescharacteristic
990C22#1681137311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—4241no—
998C4—4241no—
999C4—4241no—
1000C4—4241no—
1001C4—2122no—
1002C4—2122no—
1003C4—2122no—
1004C4—2122no—
1005C2—44no—
1006C2#2027733811yescharacteristic
1007C2#2027741011yescharacteristic
1008C2#2027749411yescharacteristic
1009C2D4×C4⋊Dic5311yescharacteristic
1010C2#2027762511yescharacteristic
1011C2#2027771111yescharacteristic
1012C2#2027788911yescharacteristic
1013C2#2028093911yescharacteristic
1014C2#2028096411yescharacteristic
1015C2#2028128711yescharacteristic
1016C2#2028137411yescharacteristic
1017C2#2028140111yescharacteristic
1018C2#2028159911yescharacteristic
1019C2#2028213111yescharacteristic
1020C2#2028219911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53#14403
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#16810489C2semidirect
5. #20272980C2semidirect
6. #20272980C2semidirect
7. #20272972C2semidirect
8. #20272968C2semidirect
11. #20272949C2semidirect
12. #20272945C2semidirect
13. #20272944C2semidirect
53. C53×#388C4semidirect
129. C2×C4⋊C4×C53C2×C4semidirect
141. C2×C42×C53C2×C4semidirect
142. #95×C53C2×C4semidirect
143. #95×C53C2×C4semidirect
268. C22⋊C4×C53C4⋊C4semidirect
544. #388Dic53semidirect
566. C53#14403semidirect
612. C2×C4⋊C4C2×Dic53semidirect
636. C2×C42C2×Dic53semidirect
653. #95C2×Dic53semidirect
654. #95C2×Dic53semidirect
789. C22⋊C4C4⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105162
C2×#168104982
C2×#168104892
#202729802
#202729722
#202729682
#202729602
#202729492
#202729452
#202729442
#202729372
C2×C53×#3882
#1440353