Finite Group Databasebeta

← #27307209

Subgroups — #27307209

Order 13568.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133201C211yesmaximal, characteristic
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810500C211yesmaximal, characteristic
4C2×#16810498C211yesmaximal, characteristic, complemented
5C2×#16810484C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272982C212yesmaximal, complemented
8#20272961C212yesmaximal, complemented
9#20272953C212yesmaximal, complemented
10#20272945C212yesmaximal, complemented
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×#13133201—24no—
16C2×#13133201—24no—
17C2×#13133201C418yescomplemented
18C22×C4⋊Dic53C2212yes—
19C22×C4⋊Dic53C2212yes—
20C22×C22⋊Dic53C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2211yescharacteristic
25#16810502—24no—
26#16810500—24no—
27#16810498—24no—
28#16810484—24no—
29C2×#13133124—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2211yescharacteristic
38C24×C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C42×C53C2212yes—
42C4×C22⋊C4×C53—24no—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53—22no—
50C22×C22⋊D53—22no—
51C22×C22⋊D53C2×C414yes—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—22no—
55C23×Dic53—22no—
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—24no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—42no—
63C23×Dic53C2×C414yes—
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2312yes—
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2312yes—
69#13133201—232no—
70C2×C4⋊Dic53—24no—
71C2×C4⋊Dic53—24no—
72C2×C4⋊Dic53—24no—
73C2×C4⋊Dic53—24no—
74C2×C4⋊Dic53—42no—
75C2×C4⋊Dic53C2×C418yescomplemented
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—22no—
78C2×C22⋊Dic53—22no—
79C2×#11719921—24no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—22no—
83C2×#11719921—22no—
84C2×#11719921—24no—
85C2×#11719921—24no—
86C2×#11719921—42no—
87C2×#11719921—42no—
88C2×#11719921C2×C418yescomplemented
89#13133124—24no—
90#13133124—24no—
91#13133124—22no—
92#13133124—22no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97C25×C53C2311yescharacteristic
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53—24no—
101C23×C4×C53—42no—
102C23×C4×C53D414yes—
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C23×C4×C53C2311yescharacteristic
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
109C2×C22⋊C4×C53C2×C414yes—
110C2×C22⋊C4×C53D414yes—
111C2×C22⋊C4×C53D414yes—
112C2×C22⋊C4×C53D414yes—
113C2×C42×C53—24no—
114C2×C42×C53—24no—
115C2×C42×C53—42no—
116#95×C53—24no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53C22×C412yes—
122C24×C53C2×D412yes—
123C24×C53C2×D412yes—
124C24×C53C2×D412yes—
125C24×C53C2×D412yes—
126C24×C53#4112yes—
127C24×C53#4112yes—
128C24×C53C2411yescharacteristic
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—22no—
134C23×D53—22no—
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—22no—
138C23×D53—22no—
139C23×D53C22×C412yes—
140C22×C4×C53—21no—
141C22×C4×C53—22no—
142C22×C4×C53—21no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—28no—
148C22×C4×C53—21no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—21no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—28no—
159C22×C4×C53—44no—
160C22×C4×C53—48no—
161C22×C4×C53—48no—
162C22×C4×C53C22×C414yes—
163C22×C4×C53C2×D414yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×D414yes—
166C22×C4×C53C2×D414yes—
167C22×C4×C53C2×D412yes—
168C22×C4×C53#4114yes—
169C2×C22⋊D53—28no—
170C2×C22⋊D53—28no—
171C2×C22⋊D53—28no—
172C2×C22⋊D53—44no—
173C2×C22⋊D53—44no—
174C2×C22⋊D53—44no—
175C2×C22⋊D53—44no—
176C22×Dic53—28no—
177C22×Dic53—28no—
178C22×Dic53—28no—
179C22×Dic53—28no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—48no—
209C22×Dic53—48no—
210C22×Dic53—44no—
211C22×Dic53—44no—
212C22×Dic53—44no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53—44no—
216C22×Dic53C22×C414yes—
217C22×Dic53C22×C412yes—
218C22×Dic53#4114yes—
219C22⋊C4×C53—28no—
220C22⋊C4×C53C22⋊C4116yescomplemented
221C42×C53—48no—
222C22⋊Dic53—44no—
223#11719921—216no—
224#11719921—48no—
225#11719921—44no—
226#11719921—44no—
227C4⋊Dic53—216no—
228C4⋊Dic53—48no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—24no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—24no—
237C23×C53—24no—
238C23×C53—24no—
239C23×C53—24no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53C2×C22⋊C414yes—
246C23×C53C4×D414yes—
247C23×C53C4×D414yes—
248C23×C53#12114yes—
249C23×C53#12114yes—
250C23×C53#12414yes—
251C23×C53#12714yes—
252C23×C53C23×C411yescharacteristic
253C23×C53C22×D411yescharacteristic
254C23×C53C22×D411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C2×#4112yes—
258C23×C53C2×#4112yes—
259C23×C53C2×#4111yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53H(5,𝔽2)12yes—
262C23×C532−1+412yes—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—24no—
267C22×D53—24no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—42no—
274C22×D53—41no—
275C22×D53—41no—
276C22×D53—41no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C2×C4×C53—24no—
287C2×C4×C53—24no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—24no—
293C2×C4×C53—24no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—22no—
297C2×C4×C53—24no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—24no—
301C2×C4×C53—24no—
302C2×C4×C53—416no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C2×C22⋊C418yes—
310C2×C4×C53#12314yescomplemented
311C22⋊D53—416no—
312C2×Dic53—24no—
313C2×Dic53—22no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—24no—
321C2×Dic53—416no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—42no—
327C2×Dic53—41no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—41no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—416no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345#13996—531nomaximal, Sylow
346C22×C53—24no—
347C22×C53—28no—
348C22×C53—28no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—28no—
352C22×C53—28no—
353C22×C53—24no—
354C22×C53—24no—
355C22×C53—24no—
356C22×C53#39018yes—
357C22×C53C22×C22⋊C411yescharacteristic
358C22×C53C2×C4×D411yescharacteristic
359C22×C53C2×C4×D411yescharacteristic
360C22×C53C4×#4112yes—
361C22×C53#52012yes—
362C22×C53C2×#12111yescharacteristic
363C22×C53C2×#12111yescharacteristic
364C22×C53C2×#12311yescharacteristic
365C22×C53#52511yescharacteristic
366C22×C53C2×#12411yescharacteristic
367C22×C53#52912yes—
368C22×C53C2×#12711yescharacteristic
369C22×C53#53411yescharacteristic
370C22×C53#53611yescharacteristic
371C22×C53#53912yes—
372C22×C53#54612yes—
373C22×C53#54612yes—
374C22×C53#54612yes—
375C22×C53#54712yes—
376C22×C53#54712yes—
377C22×C53#54712yes—
378C22×C53#55112yes—
379C22×C53#55212yes—
380C2×D53—42no—
381C2×D53—44no—
382C2×D53—44no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—81no—
386C2×D53—81no—
387C2×D53—82no—
388C2×D53—82no—
389C2×D53—81no—
390C2×D53—81no—
391C4×C53—28no—
392C4×C53—24no—
393C4×C53—42no—
394C4×C53—44no—
395Dic53—44no—
396Dic53—44no—
397Dic53—42no—
398Dic53—81no—
399Dic53—81no—
400C22×#123—531no—
401C2×#386—531no—
402C2×#386—531no—
403C2×#385—531no—
404C2×#381—531no—
405C2×C4×C22⋊C4D5311yescharacteristic, complemented
406C22×#95—531no—
407#1445—532no—
408#1439—532no—
409#1437—532no—
410C4⋊#95—532no—
411C2×C53—28no—
412C2×C53C2×#39011yescharacteristic
413C2×C53C4×#12311yescharacteristic
414C2×C53#232211yescharacteristic
415C2×C53#233912yes—
416C2×C53#235912yes—
417C2×C53#241211yescharacteristic
418C2×C53#241311yescharacteristic
419C2×C53#242512yes—
420C2×C53#248812yes—
421C2×C53#250111yescharacteristic
422C2×C53#253911yescharacteristic
423D53—82no—
424C23×D4—531no—
425C24×C4—531no—
426C24×C4—531no—
427C24×C4C2×D5311yescharacteristic
428C2×#123—538no—
429C2×#123—1064no—
430C2×#123—1064no—
431C22×C4⋊C4—532no—
432C22×C4⋊C4—532no—
433C22×C22⋊C4—532no—
434C22×C22⋊C4—531no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—532no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4C2×D5311yescharacteristic
439C22×C22⋊C4C2×D5311yescharacteristic
440C22×C42C2×D5312yes—
441#386—1064no—
442#386—1064no—
443#385—1064no—
444#381—1064no—
445C4×C22⋊C4—24no—
446C2×#95—531no—
447C2×#95—532no—
448C2×#95—532no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—531no—
454C2×#95—1064no—
455C2×#95C2×D5312yes—
456C53#1399611yescharacteristic, complemented, Sylow
457C25—531no—
458C25C22×D5311yescharacteristic
459C22×D4—534no—
460C22×D4—1062no—
461C22×D4—1062no—
462C22×D4—1062no—
463C22×D4—1062no—
464C22×D4—1062no—
465C22×D4—1062no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—534no—
471C23×C4—532no—
472C23×C4—532no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4—1064no—
477C23×C4—1062no—
478C23×C4—1062no—
479C23×C4—1062no—
480C23×C4—1062no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—2122no—
487C23×C4D21214yes—
488C23×C4C22×D5312yes—
489C23×C4C22×D5311yescharacteristic
490C23×C4C22×D5312yes—
491C23×C4C22×D5311yescharacteristic
492#123—10632no—
493C2×C4⋊C4—538no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1064no—
497C2×C4⋊C4—1064no—
498C2×C4⋊C4—2122no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—538no—
502C2×C22⋊C4—1064no—
503C2×C22⋊C4—1064no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1062no—
507C2×C22⋊C4—1062no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1064no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4C4×D5314yes—
515C2×C22⋊C4D21214yes—
516C2×C22⋊C4D21214yes—
517C2×C22⋊C4C22⋊D5314yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—1064no—
523#95—1064no—
524#95—1064no—
525#95—1064no—
526#95—1064no—
527#95—1064no—
528#95—1062no—
529#95—1062no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—532no—
535C24—1061no—
536C24—1061no—
537C24—1061no—
538C24—1061no—
539C24—1062no—
540C24—1062no—
541C24—1061no—
542C24—1061no—
543C24—1062no—
544C24—1062no—
545C24C2×C4×D5312yes—
546C24C2×D21212yes—
547C24C2×D21212yes—
548C24C2×D21212yes—
549C24#1171994512yes—
550C24#1171994512yes—
551C24C2×C22⋊D5312yes—
552C24C23×D5311yescharacteristic
553C2×D4—1068no—
554C2×D4—1068no—
555C2×D4—1068no—
556C2×D4—2124no—
557C2×D4—2124no—
558C2×D4—2124no—
559C2×D4—2124no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—534no—
583C22×C4—532no—
584C22×C4—534no—
585C22×C4—1068no—
586C22×C4—1068no—
587C22×C4—1068no—
588C22×C4—1068no—
589C22×C4—1062no—
590C22×C4—1061no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—2128no—
618C22×C4—2128no—
619C22×C4—2124no—
620C22×C4—2124no—
621C22×C4—2124no—
622C22×C4—2124no—
623C22×C4—2124no—
624C22×C4—2124no—
625C22×C4C2×C4×D5314yes—
626C22×C4C2×D21214yes—
627C22×C4C2×D21212yes—
628C22×C4C2×D21214yes—
629C22×C4C2×D21212yes—
630C22×C4#1171994714yes—
631C22×C4C2×C22⋊D5314yes—
632C4⋊C4—10616no—
633C4⋊C4—2128no—
634C22⋊C4—28no—
635C22⋊C4—10616no—
636C22⋊C4—2128no—
637C22⋊C4—2124no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C22⋊C4#11719921116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1064no—
662C23—1064no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23—2122no—
669C23—2122no—
670C23—2122no—
671C23—2121no—
672C23—2121no—
673C23—2121no—
674C23—2121no—
675C23—2121no—
676C23—2122no—
677C23—2121no—
678C23—2121no—
679C23—2121no—
680C23—2122no—
681C23C2×#1171992114yes—
682C23C4×D21214yes—
683C23C4×D21214yes—
684C23#1313319114yes—
685C23#1313319114yes—
686C23#1313320514yes—
687C23#1313321414yes—
688C23C22×C4×D5311yescharacteristic
689C23C22×C22⋊D5311yescharacteristic
690C23C22×D21211yescharacteristic
691C23C22×D21211yescharacteristic
692C23C22×D21211yescharacteristic
693C23#41×D5312yes—
694C23C2×#1171994712yes—
695C23C2×#1171994511yescharacteristic
696C23C2×#1171994511yescharacteristic
697C23#1313326212yes—
698C23#1313326412yes—
699D4—21216no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—1064no—
724C2×C4—1064no—
725C2×C4—1064no—
726C2×C4—1062no—
727C2×C4—1064no—
728C2×C4—1064no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—21216no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—21216no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2122no—
751C2×C4—2121no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2121no—
755C2×C4—2122no—
756C2×C4C2×#1171992118yes—
757C2×C4#1313320114yescomplemented
758C22—28no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—28no—
768C22—4241no—
769C22—4241no—
770C22—4241no—
771C22—4241no—
772C22—4242no—
773C22—4242no—
774C22—2124no—
775C22—2122no—
776C22—2122no—
777C22—2124no—
778C22—2122no—
779C22#1681052518yes—
780C22C22×#1171992111yescharacteristic
781C22C2×C4×D21211yescharacteristic
782C22C2×C4×D21211yescharacteristic
783C22C4×#1171994712yes—
784C22#1681110212yes—
785C22C2×#1313319111yescharacteristic
786C22C2×#1313319111yescharacteristic
787C22C2×#1313320111yescharacteristic
788C22#1681113511yescharacteristic
789C22C2×#1313320511yescharacteristic
790C22#1681115312yes—
791C22C2×#1313321411yescharacteristic
792C22#1681118511yescharacteristic
793C22#1681119911yescharacteristic
794C22#1681121512yes—
795C22#1681126712yes—
796C22#1681126812yes—
797C22#1681126812yes—
798C22#1681127212yes—
799C22#1681127712yes—
800C22#1681127712yes—
801C22#1681129912yes—
802C22#1681130612yes—
803C4—28no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—4241no—
808C4—4241no—
809C4—2124no—
810C4—2124no—
811C4—2122no—
812C2—28no—
813C2—4242no—
814C2C2×#1681052511yescharacteristic
815C2C4×#1313320111yescharacteristic
816C2#2027738611yescharacteristic
817C2#2027754012yes—
818C2#2027770912yes—
819C2#2027810511yescharacteristic
820C2#2027811611yescharacteristic
821C2#2027826012yes—
822C2#2027903512yes—
823C2#2027918611yescharacteristic
824C2#2027964111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13996
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#16810498C2semidirect
5. C2×#16810484C2semidirect
6. C22×#13133124C2semidirect
7. #20272982C2semidirect
8. #20272961C2semidirect
9. #20272953C2semidirect
10. #20272945C2semidirect
11. C2×C4×C22⋊C4×C53C2semidirect
17. C2×#13133201C4semidirect
75. C2×C4⋊Dic53C2×C4semidirect
88. C2×#11719921C2×C4semidirect
220. C22⋊C4×C53C22⋊C4semidirect
310. C2×C4×C53#123semidirect
405. C2×C4×C22⋊C4D53semidirect
456. C53#13996semidirect
640. C22⋊C4#11719921semidirect
757. C2×C4#13133201semidirect

Maximal subgroups

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

subgroupindex
C22×#131332012
C2×#168105022
C2×#168105002
C2×#168104982
C2×#168104842
C22×#131331242
#202729822
#202729612
#202729532
#202729452
C2×C4×C22⋊C4×C532
#1399653