Finite Group Databasebeta

← D53×#1441 #27305761

Subgroups — D53×#1441 #27305761

Order 13568.

3246 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D53C211yesmaximal, characteristic
2C22×C4⋊C4×D53C211yesmaximal, characteristic
3C2×#95×D53C212yesmaximal
4C2×#95×D53C212yesmaximal
5C2×#95×D53C211yesmaximal, characteristic
6#20272969C211yesmaximal, characteristic, complemented
7#20272968C211yesmaximal, characteristic, complemented
8#20272967C212yesmaximal, complemented
9#20272966C212yesmaximal, complemented
10#20272965C211yesmaximal, characteristic, complemented
11C53×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C23×C4×D53C2212yes—
14C23×C4×D53C2212yes—
15C23×C4×D53C2211yescharacteristic
16C23×C4×D53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C2×C4⋊C4×D53—28no—
23C2×C4⋊C4×D53—24no—
24C2×C4⋊C4×D53—24no—
25C2×C4⋊C4×D53—24no—
26C2×C4⋊C4×D53C418yescomplemented
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35#95×D53—28no—
36#95×D53—24no—
37#95×D53—28no—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C2×#95×C53C2211yescharacteristic
43C24×D53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2312yes—
46C23×Dic53C2312yes—
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—24no—
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—24no—
55C22×C4×D53—22no—
56C22×C4×D53—22no—
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—24no—
60C22×C4×D53—24no—
61C22×C4×D53—24no—
62C22×C4×D53—24no—
63C22×C4×D53—24no—
64C22×C4×D53—24no—
65C22×C4×D53—24no—
66C22×C4×D53—24no—
67C22×C4×D53—24no—
68C22×C4×D53—24no—
69C22×C4×D53—24no—
70C22×C4×D53—24no—
71C22×C4×D53C2×C414yes—
72C22×C4×D53C2×C414yes—
73C22×C4×D53C2×C414yes—
74C22×C4×D53D418yes—
75C22×C4×D53D414yes—
76C22×C4×D53D414yes—
77C22×C4×D53D414yes—
78C22×C4×D53Q818yes—
79C22×C4×D53Q814yes—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—24no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53C2×C414yescomplemented
85C2×#11719919—24no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—24no—
89C2×#11719919—22no—
90C2×#11719919—22no—
91C2×#11719919—24no—
92C2×#11719919C2×C414yescomplemented
93C2×#11719919C2×C414yescomplemented
94C4⋊C4×D53—232no—
95C4⋊C4×D53—232no—
96#13133124—24no—
97#13133124—22no—
98#13133124—24no—
99#13133124—24no—
100#13133124—24no—
101#13133124—24no—
102#13133124—24no—
103#13133124—24no—
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C23×C4×C53C2312yes—
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109C2×C4⋊C4×C53—24no—
110C2×C4⋊C4×C53—22no—
111C2×C4⋊C4×C53—22no—
112C2×C4⋊C4×C53—22no—
113C2×C4⋊C4×C53C2×C414yescomplemented
114#95×C53—24no—
115#95×C53—22no—
116#95×C53—24no—
117C24×C53C2411yescharacteristic
118C23×D53C22×C412yes—
119C23×D53C2×D412yes—
120C23×D53C2×D412yes—
121C23×D53C2×D412yes—
122C23×D53C2×D414yes—
123C23×D53C2×Q812yes—
124C23×D53C2×Q814yes—
125C23×D53#4112yes—
126C23×D53#4112yes—
127C23×D53#4114yes—
128C23×D53#4114yes—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C22×C412yes—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C2×D414yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×Q814yes—
159C22×C4×C53C2×Q812yes—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53C22×C412yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C2×D414yes—
186C22×Dic53C2×D412yes—
187C22×Dic53C2×D412yes—
188C22×Dic53C2×D412yes—
189C22×Dic53C2×Q814yes—
190C22×Dic53C2×Q812yes—
191C2×C4×D53—28no—
192C2×C4×D53—28no—
193C2×C4×D53—216no—
194C2×C4×D53—28no—
195C2×C4×D53—28no—
196C2×C4×D53—28no—
197C2×C4×D53—216no—
198C2×C4×D53—28no—
199C2×C4×D53—28no—
200C2×C4×D53—28no—
201C2×C4×D53—28no—
202C2×C4×D53—216no—
203C2×C4×D53—216no—
204C2×C4×D53—216no—
205C2×C4×D53—216no—
206C2×C4×D53—216no—
207C2×C4×D53—216no—
208C2×C4×D53—216no—
209C2×C4×D53—44no—
210C2×C4×D53—48no—
211C2×C4×D53—48no—
212C2×C4×D53—48no—
213C2×C4×D53—48no—
214C2×C4×D53—48no—
215C2×C4×D53—48no—
216C2×C4×D53—44no—
217C2×C4×D53—48no—
218C2×C4×D53—48no—
219C2×C4×D53—48no—
220C2×C4×D53C22⋊C4116yes—
221C2×C4×D53C4⋊C4116yescomplemented
222C4⋊C4×C53—28no—
223C4⋊C4×C53—28no—
224C4⋊Dic53—28no—
225C4⋊Dic53—28no—
226#11719919—216no—
227#11719919—28no—
228#11719919—28no—
229C23×C53C23×C411yescharacteristic
230C23×C53C22×D411yescharacteristic
231C23×C53C22×D411yescharacteristic
232C23×C53C22×D411yescharacteristic
233C23×C53C22×D412yes—
234C23×C53C22×Q811yescharacteristic
235C23×C53C22×Q812yes—
236C23×C53C2×#4111yescharacteristic
237C23×C53C2×#4111yescharacteristic
238C23×C53C2×#4112yes—
239C23×C53C2×#4112yes—
240C22×D53C2×C22⋊C414yes—
241C22×D53C2×C4⋊C414yes—
242C22×D53#11714yes—
243C22×D53C4×D418yes—
244C22×D53C4×Q818yes—
245C22×D53#12014yes—
246C22×D53#12114yes—
247C22×D53#12114yes—
248C22×D53#12118yes—
249C22×D53#12118yes—
250C22×D53C22⋊Q814yes—
251C22×D53C22⋊Q814yes—
252C22×D53C22⋊Q818yes—
253C22×D53C22⋊Q818yes—
254C22×D53C22⋊Q818yes—
255C22×D53#12314yes—
256C22×D53#12318yes—
257C22×D53#12414yes—
258C22×D53#12518yes—
259C22×D53#12518yes—
260C22×D53#12618yes—
261C22×D53C4⋊Q818yes—
262C22×D53C4⋊Q814yes—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—24no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—24no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—41no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—41no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53C2×C22⋊C414yes—
293C2×C4×C53C2×C4⋊C414yescomplemented
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—24no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—24no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—24no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—24no—
312C2×Dic53—41no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—41no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53C2×C22⋊C414yes—
324C2×Dic53C2×C4⋊C414yescomplemented
325C4×D53—232no—
326C4×D53—232no—
327C4×D53—416no—
328C4×D53—432no—
329C4×D53—432no—
330C2×#1441—531nomaximal, Sylow
331C22×C53C22×C22⋊C411yescharacteristic
332C22×C53C22×C4⋊C411yescharacteristic
333C22×C53C2×#11711yescharacteristic
334C22×C53C2×C4×D412yes—
335C22×C53C2×C4×Q812yes—
336C22×C53C2×#12011yescharacteristic
337C22×C53C2×#12112yes—
338C22×C53C2×#12111yescharacteristic
339C22×C53C2×#12111yescharacteristic
340C22×C53C2×#12112yes—
341C22×C53C2×C22⋊Q812yes—
342C22×C53C2×C22⋊Q811yescharacteristic
343C22×C53C2×C22⋊Q812yes—
344C22×C53C2×C22⋊Q812yes—
345C22×C53C2×C22⋊Q811yescharacteristic
346C22×C53C2×#12312yes—
347C22×C53C2×#12311yescharacteristic
348C22×C53C2×#12411yescharacteristic
349C22×C53C2×#12512yes—
350C22×C53C2×#12512yes—
351C22×C53C2×#12612yes—
352C22×C53C2×C4⋊Q812yes—
353C22×C53C2×C4⋊Q811yescharacteristic
354C2×D53#38018yes—
355C2×D53#38618yes—
356C2×D53#387116yes—
357C2×D53#389116yes—
358C2×D53#39118yes—
359C2×D53#39418yes—
360C2×D53#39518yes—
361C2×D53#396116yes—
362C2×D53#39818yes—
363C2×D53#398116yes—
364C2×D53#40018yes—
365C4×C53—24no—
366C4×C53—24no—
367C4×C53—44no—
368C4×C53—44no—
369C4×C53—42no—
370Dic53—24no—
371Dic53—24no—
372Dic53—44no—
373Dic53—44no—
374Dic53—42no—
375C23×C4⋊C4—531no—
376C23×C4⋊C4—531no—
377C22×#95—531no—
378C22×#95—532no—
379C22×#95—532no—
380#1441—532no—
381#1441—532no—
382#1441—531no—
383#1441—531no—
384#1441—531no—
385#1441D5311yescharacteristic, direct product factor
386C2×C53C2×#38011yescharacteristic
387C2×C53C2×#38611yescharacteristic
388C2×C53C2×#38712yes—
389C2×C53C2×#38912yes—
390C2×C53C2×#39111yescharacteristic
391C2×C53C2×#39411yescharacteristic
392C2×C53C2×#39511yescharacteristic
393C2×C53C2×#39612yes—
394C2×C53C2×#39811yescharacteristic
395C2×C53C2×#39812yes—
396C2×C53C2×#40011yescharacteristic
397D53#1441116yesdirect product factor
398C24×C4—531no—
399C24×C4—531no—
400C24×C4—531no—
401C24×C4—532no—
402C24×C4—532no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—538no—
407C22×C4⋊C4—532no—
408C22×C4⋊C4—531no—
409C22×C4⋊C4—1064no—
410C22×C4⋊C4—1064no—
411C22×C4⋊C4—1064no—
412C22×C4⋊C4—1068no—
413C22×C4⋊C4C2×D5311yescharacteristic
414C22×C4⋊C4C2×D5311yescharacteristic
415C2×#95—532no—
416C2×#95—532no—
417C2×#95—532no—
418C2×#95—532no—
419C2×#95—532no—
420C2×#95—532no—
421C2×#95—532no—
422C2×#95—531no—
423C2×#95—1064no—
424C2×#95—1068no—
425C2×#95—1068no—
426C2×#95C2×D5312yes—
427C2×#95C2×D5312yes—
428C2×#95C2×D5311yescharacteristic
429C53C2×#144111yescharacteristic, complemented, Sylow
430C25—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—534no—
434C23×C4—534no—
435C23×C4—534no—
436C23×C4—534no—
437C23×C4—534no—
438C23×C4—534no—
439C23×C4—531no—
440C23×C4—532no—
441C23×C4—532no—
442C23×C4—534no—
443C23×C4—538no—
444C23×C4—538no—
445C23×C4—1064no—
446C23×C4—1062no—
447C23×C4—1062no—
448C23×C4—1064no—
449C23×C4—1062no—
450C23×C4—1062no—
451C23×C4—1062no—
452C23×C4—1062no—
453C23×C4—1064no—
454C23×C4—1064no—
455C23×C4—1064no—
456C23×C4—1064no—
457C23×C4—1064no—
458C23×C4—1064no—
459C23×C4—1064no—
460C23×C4—1064no—
461C23×C4—1064no—
462C23×C4—1064no—
463C23×C4—1064no—
464C23×C4—1064no—
465C23×C4—1064no—
466C23×C4—1064no—
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5312yes—
469C23×C4C22×D5312yes—
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—10632no—
480C2×C4⋊C4—10632no—
481C2×C4⋊C4—1062no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1062no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1064no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1062no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1062no—
492C2×C4⋊C4C4×D5314yescomplemented
493#95—24no—
494#95—22no—
495#95—24no—
496#95—1064no—
497#95—1064no—
498#95—1064no—
499#95—1064no—
500#95—1064no—
501#95—1064no—
502#95—1062no—
503#95—1064no—
504C24—532no—
505C24—532no—
506C24—532no—
507C24—532no—
508C24—534no—
509C24—532no—
510C24—534no—
511C24—532no—
512C24—532no—
513C24—534no—
514C24—534no—
515C24C23×D5311yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—532no—
543C22×C4—532no—
544C22×C4—5316no—
545C22×C4—5316no—
546C22×C4—532no—
547C22×C4—534no—
548C22×C4—534no—
549C22×C4—1068no—
550C22×C4—1068no—
551C22×C4—1068no—
552C22×C4—10616no—
553C22×C4—10616no—
554C22×C4—1068no—
555C22×C4—1068no—
556C22×C4—1068no—
557C22×C4—1068no—
558C22×C4—1068no—
559C22×C4—1068no—
560C22×C4—10616no—
561C22×C4—10616no—
562C22×C4—10616no—
563C22×C4—10616no—
564C22×C4—10616no—
565C22×C4—10616no—
566C22×C4—10616no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1062no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—2124no—
590C22×C4—2128no—
591C22×C4—2128no—
592C22×C4—2128no—
593C22×C4—2128no—
594C22×C4—2128no—
595C22×C4—2128no—
596C22×C4—2124no—
597C22×C4—2128no—
598C22×C4—2128no—
599C22×C4—2128no—
600C22×C4C2×C4×D5312yes—
601C22×C4C2×C4×D5312yes—
602C22×C4C2×C4×D5312yes—
603C22×C4D4×D5314yes—
604C22×C4D4×D5312yes—
605C22×C4D4×D5312yes—
606C22×C4D4×D5312yes—
607C22×C4Q8×D5314yes—
608C22×C4Q8×D5312yes—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—1068no—
612C4⋊C4—1068no—
613C4⋊C4—10616no—
614C4⋊C4—1068no—
615C4⋊C4—1068no—
616C23—534no—
617C23—534no—
618C23—534no—
619C23—538no—
620C23—538no—
621C23—534no—
622C23—534no—
623C23—534no—
624C23—538no—
625C23—538no—
626C23—534no—
627C23—534no—
628C23—538no—
629C23—538no—
630C23—538no—
631C23—534no—
632C23—538no—
633C23—534no—
634C23—538no—
635C23—538no—
636C23—538no—
637C23—538no—
638C23—534no—
639C23C22×C4×D5311yescharacteristic
640C23C2×D4×D5311yescharacteristic
641C23C2×D4×D5311yescharacteristic
642C23C2×D4×D5311yescharacteristic
643C23C2×D4×D5312yes—
644C23C2×Q8×D5311yescharacteristic
645C23C2×Q8×D5312yes—
646C23#41×D5311yescharacteristic
647C23#41×D5311yescharacteristic
648C23#41×D5312yes—
649C23#41×D5312yes—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—534no—
680C2×C4—534no—
681C2×C4—10632no—
682C2×C4—10632no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1064no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1064no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1064no—
695C2×C4—1064no—
696C2×C4—1064no—
697C2×C4—1064no—
698C2×C4—1064no—
699C2×C4—1064no—
700C2×C4—1064no—
701C2×C4—21216no—
702C2×C4—21232no—
703C2×C4—21232no—
704C2×C4—2121no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2121no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4C22⋊C4×D5314yes—
716C2×C4C4⋊C4×D5314yescomplemented
717C22—538no—
718C22—538no—
719C22—5316no—
720C22—538no—
721C22—538no—
722C22—5316no—
723C22—5316no—
724C22—538no—
725C22—5316no—
726C22—538no—
727C22—538no—
728C22C2×C22⋊C4×D5311yescharacteristic
729C22C2×C4⋊C4×D5311yescharacteristic
730C22#117×D5311yescharacteristic
731C22C4×D4×D5312yes—
732C22C4×Q8×D5312yes—
733C22#120×D5311yescharacteristic
734C22#121×D5311yescharacteristic
735C22#121×D5311yescharacteristic
736C22#121×D5312yes—
737C22#121×D5312yes—
738C22C22⋊Q8×D5311yescharacteristic
739C22C22⋊Q8×D5311yescharacteristic
740C22C22⋊Q8×D5312yes—
741C22C22⋊Q8×D5312yes—
742C22C22⋊Q8×D5312yes—
743C22#123×D5311yescharacteristic
744C22#123×D5312yes—
745C22#124×D5311yescharacteristic
746C22#125×D5312yes—
747C22#125×D5312yes—
748C22#126×D5312yes—
749C22C4⋊Q8×D5312yes—
750C22C4⋊Q8×D5311yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—1064no—
757C4—1064no—
758C4—2122no—
759C4—2124no—
760C4—2124no—
761C2—5316no—
762C2#380×D5311yescharacteristic
763C2#386×D5311yescharacteristic
764C2#387×D5312yes—
765C2#389×D5312yes—
766C2#391×D5311yescharacteristic
767C2#394×D5311yescharacteristic
768C2#395×D5311yescharacteristic
769C2#396×D5312yes—
770C2#398×D5311yescharacteristic
771C2#398×D5312yes—
772C2#400×D5311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1441C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1441D53
hypocenterC53C2×#1441
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #20272969C2semidirect
7. #20272968C2semidirect
8. #20272967C2semidirect
9. #20272966C2semidirect
10. #20272965C2semidirect
11. C53×#1441C2semidirect
26. C2×C4⋊C4×D53C4semidirect
84. C2×C4⋊Dic53C2×C4semidirect
92. C2×#11719919C2×C4semidirect
93. C2×#11719919C2×C4semidirect
113. C2×C4⋊C4×C53C2×C4semidirect
221. C2×C4×D53C4⋊C4semidirect
293. C2×C4×C53C2×C4⋊C4semidirect
324. C2×Dic53C2×C4⋊C4semidirect
385. #1441D53direct (N × H)
397. D53#1441direct (N × H)
429. C53C2×#1441semidirect
492. C2×C4⋊C4C4×D53semidirect
716. C2×C4C4⋊C4×D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D532
C2×#95×D532
#202729692
#202729682
#202729672
#202729662
#202729652
C53×#14412
C2×#144153