Finite Group Databasebeta

← #27307489

Subgroups — #27307489

Order 13568.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C2×#16810525C211yesmaximal, characteristic
3C2×#16810525C211yesmaximal, characteristic
4C2×#16810521C211yesmaximal, characteristic, complemented
5C2×#16810494C212yesmaximal, complemented
6#20272959C212yesmaximal, complemented
7#20272957C212yesmaximal, complemented
8#20272945C211yesmaximal, characteristic, complemented
9#20272945C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal, complemented
11C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2212yes—
14C2×C4×D212—24no—
15C2×C4×D212—24no—
16C2×C4×D212—24no—
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26#16810525—24no—
27#16810525C418yescomplemented
28#16810521—24no—
29#16810494—28no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C4×C4⋊C4×C53—24no—
41C2×#95×C53C2211yescharacteristic
42C2×#95×C53C2211yescharacteristic
43C24×D53C2312yes—
44C22×D212—22no—
45C22×D212—22no—
46C22×D212—22no—
47C22×D212—22no—
48C22×D212C2×C414yes—
49C22×D212D414yes—
50C22×D212Q814yes—
51C23×Dic53C2312yes—
52C23×Dic53C2312yes—
53C23×Dic53C2312yes—
54C22×C4×D53—24no—
55C22×C4×D53—24no—
56C22×C4×D53—24no—
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—42no—
60C22×C4×D53—42no—
61C4×D212—232no—
62C2×C4⋊Dic53—22no—
63C2×C4⋊Dic53—22no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53C2×C414yescomplemented
70C2×C4⋊Dic53D414yes—
71C2×#11719919—24no—
72C2×#11719919—24no—
73C2×#11719919—42no—
74C2×#11719921—24no—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—42no—
84C2×#11719921—42no—
85C2×#11719921—42no—
86C2×#11719921—42no—
87C2×#11719921C2×C418yescomplemented
88C2×#11719921C2×C418yescomplemented
89#13133124—24no—
90#13133124—24no—
91#13133124—24no—
92#13133124—42no—
93#13133124—42no—
94C23×C4×C53C2311yescharacteristic
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53D414yescomplemented
107C2×C42×C53—22no—
108C2×C42×C53—22no—
109C2×C42×C53—22no—
110C2×C42×C53—22no—
111C2×C42×C53—22no—
112C2×C42×C53—22no—
113C2×C42×C53—22no—
114C2×C42×C53C2×C414yescomplemented
115C2×C42×C53D414yes—
116#95×C53—22no—
117#95×C53—22no—
118C24×C53C2411yescharacteristic
119C23×D53—22no—
120C23×D53—22no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—22no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—22no—
129C23×D53—22no—
130C23×D53—22no—
131C23×D53C22×C414yes—
132C23×D53C2×D414yes—
133C23×D53C2×Q814yes—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
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×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
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×C53C22×C412yes—
167C22×C4×C53C22×C412yes—
168C22×C4×C53C22×C412yes—
169C22×C4×C53C2×D412yes—
170C22×C4×C53C2×D412yes—
171C22×C4×C53C2×D412yes—
172C22×C4×C53C2×D412yes—
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2×D412yes—
175C22×C4×C53C2×D412yes—
176C22×C4×C53C2×D412yes—
177C22×C4×C53C2×Q812yes—
178C22×C4×C53#4112yes—
179C22×C4×C53#4112yes—
180C22×C4×C53#4112yes—
181C22×C4×C53#4112yes—
182C22×C4×C53#4112yes—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53C22×C414yes—
203C22×Dic53C2×D414yes—
204C2×D212—28no—
205C2×D212—28no—
206C2×D212—28no—
207C2×D212—28no—
208C2×D212—28no—
209C2×D212—28no—
210C2×D212C4⋊C4116yescomplemented
211C2×C4×D53—216no—
212C2×C4×D53—48no—
213C2×C4×D53—48no—
214C2×C4×D53—48no—
215C2×C4×D53—48no—
216C2×C4×D53—48no—
217C2×C4×D53—48no—
218C4⋊C4×C53—28no—
219C4⋊C4×C53—28no—
220C42×C53—28no—
221C42×C53—28no—
222C42×C53—44no—
223#11719921—216no—
224#11719921—216no—
225#11719921—48no—
226#11719921—48no—
227#11719921—48no—
228C4⋊Dic53—28no—
229C4⋊Dic53—28no—
230C4⋊Dic53—44no—
231#11719919—48no—
232C23×C53C23×C411yescharacteristic
233C23×C53C22×D411yescharacteristic
234C23×C53C22×D411yescharacteristic
235C23×C53C22×D411yescharacteristic
236C23×C53C22×D411yescharacteristic
237C23×C53C22×Q811yescharacteristic
238C23×C53C2×#4111yescharacteristic
239C23×C53C2×#4111yescharacteristic
240C23×C53C2×#4111yescharacteristic
241C23×C53C2×#4111yescharacteristic
242C23×C53C2×#4111yescharacteristic
243C23×C53H(5,𝔽2)11yescharacteristic
244C23×C53H(5,𝔽2)11yescharacteristic
245C23×C53H(5,𝔽2)11yescharacteristic
246C23×C532−1+411yescharacteristic
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—24no—
258C22×D53—24no—
259C22×D53—24no—
260C22×D53—24no—
261C22×D53—24no—
262C22×D53—24no—
263C22×D53—24no—
264C22×D53—24no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53C2×C4⋊C418yes—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53C2×C4⋊C414yes—
323C2×C4×C53C4×D414yes—
324C2×C4×C53C4×D414yes—
325C2×C4×C53C4×D414yescomplemented
326C2×C4×C53#12014yes—
327C2×C4×C53#12114yes—
328C2×C4×C53C22⋊Q814yes—
329C2×C4×C53C22⋊Q814yes—
330C2×C4×C53#12314yes—
331C2×Dic53—24no—
332C2×Dic53—24no—
333C2×Dic53—24no—
334C2×Dic53—24no—
335C2×Dic53—24no—
336C2×Dic53—24no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352D212—232no—
353C4×D53—432no—
354#14018—531nomaximal, Sylow
355C22×C53C22×C4⋊C411yescharacteristic
356C22×C53C2×C4×D411yescharacteristic
357C22×C53C2×C4×D411yescharacteristic
358C22×C53C2×C4×D411yescharacteristic
359C22×C53C4×#4111yescharacteristic
360C22×C53#51811yescharacteristic
361C22×C53#52011yescharacteristic
362C22×C53C2×#12011yescharacteristic
363C22×C53C2×#12111yescharacteristic
364C22×C53C2×C22⋊Q811yescharacteristic
365C22×C53C2×C22⋊Q811yescharacteristic
366C22×C53C2×#12311yescharacteristic
367C22×C53#52511yescharacteristic
368C22×C53#52911yescharacteristic
369C22×C53#53211yescharacteristic
370C22×C53#53511yescharacteristic
371C22×C53#53711yescharacteristic
372C22×C53#54011yescharacteristic
373C22×C53#54211yescharacteristic
374C22×C53D4211yescharacteristic
375C22×C53D4211yescharacteristic
376C22×C53#54611yescharacteristic
377C22×C53#54611yescharacteristic
378C22×C53#54611yescharacteristic
379C22×C53#54711yescharacteristic
380C22×C53#54811yescharacteristic
381C22×C53D4×Q811yescharacteristic
382C22×C53#55011yescharacteristic
383C22×C53#55011yescharacteristic
384C22×C53#55411yescharacteristic
385C22×C53#55411yescharacteristic
386C22×C53#55411yescharacteristic
387C22×C53#55611yescharacteristic
388C22×C53#55911yescharacteristic
389C22×C53#55911yescharacteristic
390C2×D53—28no—
391C2×D53—28no—
392C2×D53—28no—
393C2×D53—44no—
394C2×D53—44no—
395C2×D53—44no—
396C2×D53—44no—
397C2×D53—44no—
398C2×D53—44no—
399C2×D53—44no—
400C2×D53—44no—
401C2×D53—44no—
402C2×D53—44no—
403C2×D53—44no—
404C2×D53—44no—
405C4×C53—24no—
406C4×C53—24no—
407C4×C53—42no—
408C4×C53—42no—
409C4×C53—42no—
410C4×C53—42no—
411C4×C53#38518yescomplemented
412Dic53—44no—
413Dic53—44no—
414Dic53—82no—
415C22×C4×D4—531no—
416C2×#390—531no—
417C2×#390—531no—
418C2×#389—531no—
419C2×#385—532no—
420C2×C4×C4⋊C4D5311yescharacteristic, complemented
421#1439—532no—
422#1439—532no—
423C4⋊#95—531no—
424C4⋊#95—531no—
425C22⋊#95—532no—
426C2×C53C2×#38511yescharacteristic
427C2×C53C4×#12111yescharacteristic
428C2×C53#232411yescharacteristic
429C2×C53D4×C4⋊C411yescharacteristic
430C2×C53#234911yescharacteristic
431C2×C53#236611yescharacteristic
432C2×C53#236711yescharacteristic
433C2×C53#240711yescharacteristic
434C2×C53#240811yescharacteristic
435C2×C53#244511yescharacteristic
436C2×C53#244711yescharacteristic
437C2×C53#245211yescharacteristic
438C2×C53#245411yescharacteristic
439C2×C53#253811yescharacteristic
440C2×C53#258011yescharacteristic
441D53—48no—
442C23×D4—531no—
443C24×C4—532no—
444C2×C4×D4—1064no—
445C2×C4×D4—1064no—
446C2×C4×D4—1064no—
447C22×C4⋊C4—531no—
448C22×C4⋊C4—531no—
449C22×C4⋊C4—531no—
450C22×C4⋊C4—532no—
451C22×C4⋊C4C2×D5311yescharacteristic
452C22×C4⋊C4C2×D5311yescharacteristic
453C22×C22⋊C4—532no—
454C22×C22⋊C4—532no—
455C22×C22⋊C4—532no—
456C22×C22⋊C4—532no—
457C22×C22⋊C4—532no—
458C22×C42C2×D5311yescharacteristic
459C22×C42C2×D5311yescharacteristic
460C22×C42C2×D5311yescharacteristic
461#390—538no—
462#390—1064no—
463#389—1064no—
464#385—1068no—
465C4×C4⋊C4—24no—
466C2×#95—532no—
467C2×#95—532no—
468C2×#95—532no—
469C2×#95—532no—
470C2×#95—532no—
471C2×#95C2×D5311yescharacteristic
472C2×#95C2×D5311yescharacteristic
473C53#1401811yescharacteristic, complemented, Sylow
474C25—532no—
475C22×D4—534no—
476C22×D4—534no—
477C22×D4—534no—
478C22×D4—1062no—
479C22×D4—1062no—
480C22×D4—1062no—
481C22×D4—1062no—
482C23×C4—532no—
483C23×C4—532no—
484C23×C4—532no—
485C23×C4—1064no—
486C23×C4—1064no—
487C23×C4—1064no—
488C23×C4—1064no—
489C23×C4—1064no—
490C23×C4—2122no—
491C23×C4—2122no—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C23×C4C22×D5311yescharacteristic
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5311yescharacteristic
499C4×D4—10632no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1062no—
510C2×C4⋊C4—1062no—
511C2×C4⋊C4—1064no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—1062no—
514C2×C4⋊C4—1062no—
515C2×C4⋊C4—1062no—
516C2×C4⋊C4—2122no—
517C2×C4⋊C4D21214yescomplemented
518C2×C22⋊C4—538no—
519C2×C22⋊C4—538no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—1064no—
524C2×C22⋊C4—1064no—
525C2×C22⋊C4—1064no—
526C2×C22⋊C4—1064no—
527C2×C22⋊C4—1064no—
528C2×C22⋊C4—1064no—
529C2×C22⋊C4—2122no—
530C2×C22⋊C4—2122no—
531C2×C22⋊C4—2122no—
532C2×C22⋊C4—2122no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42C4×D5314yescomplemented
541C2×C42C22⋊D5314yes—
542#95—22no—
543#95—22no—
544#95—1064no—
545#95—1064no—
546#95—1064no—
547#95—2122no—
548#95—2122no—
549C24—534no—
550C24—534no—
551C24—534no—
552C24—1062no—
553C24—1062no—
554C24—1062no—
555C24—1062no—
556C24—1062no—
557C24—1062no—
558C24—1062no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24—1062no—
563C24—1062no—
564C24C23×D5311yescharacteristic
565C2×D4—5316no—
566C2×D4—1068no—
567C2×D4—1068no—
568C2×D4—1068no—
569C2×D4—1068no—
570C2×D4—1068no—
571C2×D4—1068no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—534no—
605C22×C4—534no—
606C22×C4—10616no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
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—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—2128no—
627C22×C4—2128no—
628C22×C4—2128no—
629C22×C4—2128no—
630C22×C4—2128no—
631C22×C4—2128no—
632C22×C4C2×C4×D5312yes—
633C22×C4C2×C4×D5312yes—
634C22×C4C2×C4×D5312yes—
635C22×C4C2×D21212yes—
636C22×C4C2×D21212yes—
637C22×C4C2×D21212yes—
638C22×C4#1171994512yes—
639C22×C4#1171994512yes—
640C22×C4#1171994512yes—
641C22×C4#1171994512yes—
642C22×C4D4×D5312yes—
643C22×C4D4×D5312yes—
644C22×C4Q8×D5312yes—
645C22×C4#1171994912yes—
646C22×C4C2×C22⋊D5312yes—
647C22×C4C2×C22⋊D5312yes—
648C22×C4C2×C22⋊D5312yes—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—1068no—
652C4⋊C4—1068no—
653C4⋊C4—2128no—
654C4⋊C4—2124no—
655C22⋊C4—10616no—
656C22⋊C4—10616no—
657C22⋊C4—2128no—
658C22⋊C4—2128no—
659C22⋊C4—2128no—
660C42—28no—
661C42—28no—
662C42—44no—
663C23—538no—
664C23—1064no—
665C23—1064no—
666C23—1064no—
667C23—1064no—
668C23—1064no—
669C23—1064no—
670C23—1064no—
671C23—1064no—
672C23—1064no—
673C23—1064no—
674C23—1064no—
675C23—1064no—
676C23—1064no—
677C23—1064no—
678C23—1064no—
679C23—1064no—
680C23—1064no—
681C23—1064no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23—2122no—
688C23—2122no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23—2122no—
698C23C22×C4×D5311yescharacteristic
699C23C2×D4×D5311yescharacteristic
700C23C2×D4×D5311yescharacteristic
701C23C22×C22⋊D5311yescharacteristic
702C23C22×D21211yescharacteristic
703C23C2×Q8×D5311yescharacteristic
704C23C2×#1171994511yescharacteristic
705C23C2×#1171994511yescharacteristic
706C23C2×#1171994511yescharacteristic
707C23C2×#1171994511yescharacteristic
708C23C2×#1171994911yescharacteristic
709C23#1313326311yescharacteristic
710C23#1313326311yescharacteristic
711C23#1313326311yescharacteristic
712C23#1313326411yescharacteristic
713D4—10632no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—1064no—
755C2×C4—1064no—
756C2×C4—1064no—
757C2×C4—1064no—
758C2×C4—1064no—
759C2×C4—1064no—
760C2×C4—21232no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4—2122no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4—2122no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4—2122no—
774C2×C4—2122no—
775C2×C4—2122no—
776C2×C4C4⋊C4×D5314yes—
777C2×C4C4×C22⋊D5314yes—
778C2×C4#1313317914yes—
779C2×C4C4×D21214yescomplemented
780C2×C4#1313318514yes—
781C2×C4#1313319114yes—
782C2×C4#1313319314yes—
783C2×C4#1313319514yes—
784C2×C4#1313320214yes—
785C22—1068no—
786C22—1068no—
787C22—1068no—
788C22—2124no—
789C22—2124no—
790C22—2124no—
791C22—2124no—
792C22—2124no—
793C22—2124no—
794C22—2124no—
795C22—2124no—
796C22—2124no—
797C22—2124no—
798C22—2124no—
799C22—2124no—
800C22C2×C4⋊C4×D5311yescharacteristic
801C22C2×C4×C22⋊D5311yescharacteristic
802C22C2×#1313317911yescharacteristic
803C22C2×C4×D21211yescharacteristic
804C22C4×#1171994511yescharacteristic
805C22#1681109711yescharacteristic
806C22#1681110311yescharacteristic
807C22C2×#1313318511yescharacteristic
808C22C2×#1313319111yescharacteristic
809C22C2×#1313319311yescharacteristic
810C22C2×#1313319511yescharacteristic
811C22C2×#1313320211yescharacteristic
812C22#1681113411yescharacteristic
813C22#1681115711yescharacteristic
814C22#1681117311yescharacteristic
815C22#1681118711yescharacteristic
816C22#1681120111yescharacteristic
817C22#1681122811yescharacteristic
818C22#1681124411yescharacteristic
819C22D4×D21211yescharacteristic
820C22D4×D21211yescharacteristic
821C22#1681126911yescharacteristic
822C22#1681126911yescharacteristic
823C22#1681126911yescharacteristic
824C22#1681127811yescharacteristic
825C22#1681128211yescharacteristic
826C22Q8×D21211yescharacteristic
827C22#1681129411yescharacteristic
828C22#1681129511yescharacteristic
829C22#1681133311yescharacteristic
830C22#1681133311yescharacteristic
831C22#1681133311yescharacteristic
832C22#1681134611yescharacteristic
833C22#1681135811yescharacteristic
834C22#1681135811yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—4242no—
842C4—2124no—
843C4—2124no—
844C4#1681049418yescomplemented
845C2—2128no—
846C2C2×#1681049411yescharacteristic
847C2C4×#1313319111yescharacteristic
848C2#2027740811yescharacteristic
849C2C4⋊C4×D21211yescharacteristic
850C2#2027762611yescharacteristic
851C2#2027777911yescharacteristic
852C2#2027778411yescharacteristic
853C2#2027806011yescharacteristic
854C2#2027807111yescharacteristic
855C2#2027848011yescharacteristic
856C2#2027850211yescharacteristic
857C2#2027856511yescharacteristic
858C2#2027858711yescharacteristic
859C2#2027963311yescharacteristic
860C2#2028007311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C4⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC2×C4×C4⋊C4D53
hypocenterC53#14018
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#16810521C2semidirect
5. C2×#16810494C2semidirect
6. #20272959C2semidirect
7. #20272957C2semidirect
8. #20272945C2semidirect
9. #20272945C2semidirect
10. #20272936C2semidirect
11. C2×C4×C4⋊C4×C53C2semidirect
27. #16810525C4semidirect
69. C2×C4⋊Dic53C2×C4semidirect
87. C2×#11719921C2×C4semidirect
88. C2×#11719921C2×C4semidirect
106. C2×C4⋊C4×C53D4semidirect
114. C2×C42×C53C2×C4semidirect
210. C2×D212C4⋊C4semidirect
325. C2×C4×C53C4×D4semidirect
411. C4×C53#385semidirect
420. C2×C4×C4⋊C4D53semidirect
473. C53#14018semidirect
517. C2×C4⋊C4D212semidirect
540. C2×C42C4×D53semidirect
779. C2×C4C4×D212semidirect
844. C4#16810494semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C2×#168105252
C2×#168105212
C2×#168104942
#202729592
#202729572
#202729452
#202729362
C2×C4×C4⋊C4×C532
#1401853