Finite Group Databasebeta

← #27306878

Subgroups — #27306878

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133198C211yesmaximal, characteristic
2C22×D4×Dic53C211yesmaximal, characteristic
3C2×#16810484C211yesmaximal, characteristic, complemented
4C22×#13133124C211yesmaximal, characteristic, complemented
5#20272969C212yesmaximal, complemented
6#20272962C212yesmaximal, complemented
7#20272950C212yesmaximal, complemented
8#20272938C211yesmaximal, characteristic, complemented
9#20272937C211yesmaximal, characteristic, complemented
10#20272937C212yesmaximal, complemented
11C2×C53×#386C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×#13133198—24no—
16C2×#13133198—24no—
17C2×#13133198C418yescomplemented
18C2×D4×Dic53—24no—
19C2×D4×Dic53—24no—
20C2×D4×Dic53—24no—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×#11719919C2212yes—
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2212yes—
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810484—24no—
29C2×#13133124—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C23×D4×C53C2211yescharacteristic
39C24×C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2212yes—
42C53×#386—24no—
43C2×#95×C53C2212yes—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—22no—
47C23×Dic53—22no—
48C23×Dic53—22no—
49C23×Dic53—22no—
50C23×Dic53—22no—
51C23×Dic53—22no—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—22no—
55C23×Dic53—24no—
56C23×Dic53—24no—
57C23×Dic53—42no—
58C23×Dic53—42no—
59C23×Dic53C2×C414yescomplemented
60C23×Dic53D414yes—
61C23×Dic53C2312yes—
62C23×Dic53C2312yes—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67#13133198—232no—
68D4×Dic53—232no—
69C2×C4⋊Dic53—22no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53—22no—
72C2×#11719919—24no—
73C2×#11719919—24no—
74C2×#11719919C2×C418yescomplemented
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—22no—
78C2×C22⋊Dic53—22no—
79C2×C22⋊Dic53—22no—
80C2×C22⋊Dic53—24no—
81C2×C22⋊Dic53—24no—
82C2×C22⋊Dic53—22no—
83C2×C22⋊Dic53—22no—
84C2×C22⋊Dic53C2×C414yescomplemented
85C2×C22⋊Dic53C2×C418yescomplemented
86C2×C22⋊Dic53D414yes—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—22no—
89C2×C4×Dic53—22no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—42no—
97#13133124—42no—
98C25×C53C2311yescharacteristic
99C25×C53C2311yescharacteristic
100C22×D4×C53—22no—
101C22×D4×C53—22no—
102C22×D4×C53—22no—
103C22×D4×C53—22no—
104C22×D4×C53C2×C414yes—
105C22×D4×C53D414yes—
106C22×D4×C53D414yes—
107C23×C4×C53—22no—
108C23×C4×C53—24no—
109C23×C4×C53—22no—
110C23×C4×C53—22no—
111C23×C4×C53—42no—
112C23×C4×C53C2312yes—
113C23×C4×C53C2312yes—
114C23×C4×C53C2311yescharacteristic
115C2×C22⋊C4×C53—24no—
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—24no—
120C2×C22⋊C4×C53—42no—
121#95×C53—24no—
122C24×C53—22no—
123C24×C53—22no—
124C24×C53—22no—
125C24×C53—22no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—22no—
129C24×C53—21no—
130C24×C53—21no—
131C24×C53—22no—
132C24×C53—22no—
133C24×C53—22no—
134C24×C53C22×C412yes—
135C24×C53C22×C412yes—
136C24×C53C2×D412yes—
137C24×C53C2×D412yes—
138C24×C53C2×D412yes—
139C24×C53C2×D412yes—
140C24×C53C2×D412yes—
141C24×C53C2×D412yes—
142C24×C53#4112yes—
143C24×C53#4112yes—
144C24×C53C2411yescharacteristic
145C2×D4×C53—28no—
146C2×D4×C53—28no—
147C2×D4×C53—28no—
148C2×D4×C53—28no—
149C2×D4×C53—28no—
150C2×D4×C53—28no—
151C2×D4×C53C22⋊C4116yes—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—28no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—48no—
171C22×C4×C53—48no—
172C22×C4×C53—44no—
173C22×C4×C53—44no—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C2×D412yes—
176C22×C4×C53C2×D412yes—
177C22×C4×C53#4114yes—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—22no—
181C22×Dic53—28no—
182C22×Dic53—28no—
183C22×Dic53—28no—
184C22×Dic53—28no—
185C22×Dic53—28no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—28no—
211C22×Dic53—44no—
212C22×Dic53—48no—
213C22×Dic53—48no—
214C22×Dic53—48no—
215C22×Dic53—48no—
216C22×Dic53—44no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C22×Dic53—44no—
221C22×Dic53—44no—
222C22×Dic53C22×C414yes—
223C22×Dic53C22×C414yes—
224C22×Dic53C2×D412yes—
225C22×Dic53C2×D412yes—
226C22×Dic53C2×D412yes—
227C22×Dic53C2×D412yes—
228C22×Dic53#4114yes—
229C22⋊C4×C53—48no—
230C22⋊C4×C53—44no—
231C22⋊Dic53—28no—
232C22⋊Dic53—216no—
233C22⋊Dic53—28no—
234C22⋊Dic53—28no—
235C4⋊Dic53—28no—
236#11719919—216no—
237C4×Dic53—28no—
238C23×C53—24no—
239C23×C53—24no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—24no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—24no—
246C23×C53—24no—
247C23×C53—24no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—24no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—24no—
257C23×C53—24no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—24no—
263C23×C53—24no—
264C23×C53—24no—
265C23×C53—24no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—42no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C2×C22⋊C414yes—
277C23×C53C2×C22⋊C414yes—
278C23×C53C4×D414yes—
279C23×C53C4×D414yes—
280C23×C53#12014yes—
281C23×C53#12114yes—
282C23×C53#12114yes—
283C23×C53#12314yes—
284C23×C53C23×C411yescharacteristic
285C23×C53C22×D411yescharacteristic
286C23×C53C22×D411yescharacteristic
287C23×C53C22×D411yescharacteristic
288C23×C53C22×D411yescharacteristic
289C23×C53C2×#4112yes—
290C23×C53C2×#4111yescharacteristic
291C23×C53C2×#4111yescharacteristic
292C23×C53C2×#4112yes—
293C23×C53H(5,𝔽2)12yes—
294C23×C532−1+412yes—
295D4×C53—232no—
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—24no—
303C2×C4×C53—24no—
304C2×C4×C53—24no—
305C2×C4×C53—416no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53C2×C22⋊C414yes—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—24no—
321C2×Dic53—24no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—24no—
326C2×Dic53—24no—
327C2×Dic53—24no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—24no—
334C2×Dic53—24no—
335C2×Dic53—416no—
336C2×Dic53—416no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53—416no—
354C2×Dic53#12314yescomplemented
355#13968—531nomaximal, Sylow
356C22×C53—24no—
357C22×C53—28no—
358C22×C53—28no—
359C22×C53—24no—
360C22×C53—24no—
361C22×C53—28no—
362C22×C53—28no—
363C22×C53—24no—
364C22×C53—24no—
365C22×C53—24no—
366C22×C53—28no—
367C22×C53—24no—
368C22×C53—42no—
369C22×C53—44no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—44no—
373C22×C53—44no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53#38618yes—
378C22×C53C22×C22⋊C411yescharacteristic
379C22×C53C2×C4×D411yescharacteristic
380C22×C53C2×C4×D411yescharacteristic
381C22×C53C4×#4112yes—
382C22×C53#52012yes—
383C22×C53C2×#12011yescharacteristic
384C22×C53C2×#12111yescharacteristic
385C22×C53C2×#12111yescharacteristic
386C22×C53C2×#12311yescharacteristic
387C22×C53C2×#12311yescharacteristic
388C22×C53#52511yescharacteristic
389C22×C53#52912yes—
390C22×C53#53411yescharacteristic
391C22×C53#53611yescharacteristic
392C22×C53#53912yes—
393C22×C53#54612yes—
394C22×C53#54612yes—
395C22×C53#54612yes—
396C22×C53#54712yes—
397C22×C53#54712yes—
398C22×C53#54712yes—
399C22×C53#55112yes—
400C22×C53#55212yes—
401C4×C53—24no—
402C4×C53—44no—
403C4×C53—82no—
404Dic53—24no—
405Dic53—44no—
406Dic53—42no—
407Dic53—42no—
408Dic53—42no—
409Dic53—44no—
410C22×#123—531no—
411C22×C4×D4—531no—
412C2×#386D5311yescharacteristic
413C2×#381—531no—
414C22×#95—531no—
415#1441—532no—
416#1440—532no—
417#1436—532no—
418C22⋊#95—531no—
419C22⋊#95—531no—
420C22⋊#95—532no—
421C2×C53—28no—
422C2×C53—44no—
423C2×C53C2×#38611yescharacteristic
424C2×C53C4×#12311yescharacteristic
425C2×C53#232211yescharacteristic
426C2×C53#233912yes—
427C2×C53#235912yes—
428C2×C53#240511yescharacteristic
429C2×C53#240611yescharacteristic
430C2×C53#241912yes—
431C2×C53#242512yes—
432C2×C53#248611yescharacteristic
433C2×C53#253411yescharacteristic
434C23×D4C2×D5311yescharacteristic
435C24×C4—531no—
436C24×C4—531no—
437C24×C4—531no—
438C24×C4C2×D5311yescharacteristic
439C2×#123—538no—
440C2×#123—1064no—
441C2×#123—1064no—
442C2×C4×D4—1064no—
443C2×C4×D4—1064no—
444C2×C4×D4—1064no—
445C22×C4⋊C4—532no—
446C22×C4⋊C4—531no—
447C22×C22⋊C4—531no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—532no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4C2×D5311yescharacteristic
452C22×C22⋊C4C2×D5312yes—
453C22×C42—531no—
454#386—24no—
455#381—1064no—
456C2×#95—532no—
457C2×#95—532no—
458C2×#95—532no—
459C2×#95—532no—
460C2×#95—532no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95—1064no—
465C2×#95C2×D5312yes—
466C53#1396811yescharacteristic, complemented, Sylow
467C25C22×D5311yescharacteristic
468C25C22×D5311yescharacteristic
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4C4×D5314yes—
474C22×D4D21214yes—
475C22×D4C22⋊D5314yes—
476C23×C4—22no—
477C23×C4—24no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—42no—
481C23×C4—531no—
482C23×C4—534no—
483C23×C4—532no—
484C23×C4—531no—
485C23×C4—532no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—534no—
489C23×C4—1062no—
490C23×C4—1062no—
491C23×C4—1064no—
492C23×C4—1064no—
493C23×C4—1062no—
494C23×C4—1062no—
495C23×C4—1062no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—1062no—
499C23×C4—1062no—
500C23×C4—1062no—
501C23×C4—1062no—
502C23×C4—2122no—
503C23×C4—2122no—
504C23×C4C22×D5312yes—
505C23×C4C22×D5312yes—
506C23×C4C22×D5311yescharacteristic
507#123—10632no—
508C4×D4—10632no—
509C2×C4⋊C4—538no—
510C2×C4⋊C4—1062no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1064no—
514C2×C4⋊C4—1064no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—534no—
522C2×C22⋊C4—538no—
523C2×C22⋊C4—534no—
524C2×C22⋊C4—1062no—
525C2×C22⋊C4—1062no—
526C2×C22⋊C4—1062no—
527C2×C22⋊C4—1062no—
528C2×C22⋊C4—1062no—
529C2×C22⋊C4—1064no—
530C2×C22⋊C4—1062no—
531C2×C22⋊C4—1062no—
532C2×C22⋊C4—1064no—
533C2×C42—1062no—
534C2×C42—1062no—
535C2×C42—1062no—
536#95—24no—
537#95—1064no—
538#95—1064no—
539#95—1064no—
540#95—1064no—
541#95—1064no—
542#95—1064no—
543#95—2122no—
544#95—2122no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24C2×C4×D5312yes—
558C24C2×C4×D5312yes—
559C24C2×D21212yes—
560C24C2×D21212yes—
561C24D4×D5312yes—
562C24D4×D5312yes—
563C24#1171994712yes—
564C24#1171994712yes—
565C24C2×C22⋊D5312yes—
566C24C2×C22⋊D5312yes—
567C24C23×D5311yescharacteristic
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4#11719921116yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—532no—
598C22×C4—534no—
599C22×C4—534no—
600C22×C4—534no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—532no—
604C22×C4—1068no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1062no—
608C22×C4—1068no—
609C22×C4—1068no—
610C22×C4—1068no—
611C22×C4—1068no—
612C22×C4—1068no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1062no—
637C22×C4—2124no—
638C22×C4—2124no—
639C22×C4—2128no—
640C22×C4—2128no—
641C22×C4—2128no—
642C22×C4—2128no—
643C22×C4—2124no—
644C22×C4—2124no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4—2124no—
648C22×C4C2×C4×D5312yes—
649C22×C4C2×D21212yes—
650C22×C4#1171994714yes—
651C22×C4C2×C22⋊D5312yes—
652C4⋊C4—1068no—
653C4⋊C4—10616no—
654C22⋊C4—48no—
655C22⋊C4—44no—
656C22⋊C4—1068no—
657C22⋊C4—1068no—
658C22⋊C4—10616no—
659C22⋊C4—1068no—
660C42—1068no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23C2×#1171992114yes—
700C23C2×#1171992114yes—
701C23#1313317714yes—
702C23#1313317714yes—
703C23#1313318714yes—
704C23#1313318914yes—
705C23#1313318914yes—
706C23#1313320114yes—
707C23C22×C4×D5311yescharacteristic
708C23C2×D4×D5311yescharacteristic
709C23C2×D4×D5311yescharacteristic
710C23C22×C22⋊D5311yescharacteristic
711C23C22×D21211yescharacteristic
712C23#41×D5312yes—
713C23C2×#1171994712yes—
714C23C2×#1171994711yescharacteristic
715C23C2×#1171994711yescharacteristic
716C23#1313326212yes—
717C23#1313326412yes—
718D4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—534no—
741C2×C4—1064no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1064no—
745C2×C4—1064no—
746C2×C4—1064no—
747C2×C4—1064no—
748C2×C4—1064no—
749C2×C4—1064no—
750C2×C4—1064no—
751C2×C4—1064no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1064no—
758C2×C4—21216no—
759C2×C4—21216no—
760C2×C4—2122no—
761C2×C4—21216no—
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—2121no—
772C2×C4—2122no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2121no—
776C2×C4—2122no—
777C2×C4C2×#1171992114yes—
778C22—28no—
779C22—24no—
780C22—24no—
781C22—28no—
782C22—24no—
783C22—24no—
784C22—28no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—24no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22#1681050018yes—
800C22C22×#1171992111yescharacteristic
801C22C2×#1313317711yescharacteristic
802C22C2×#1313317711yescharacteristic
803C22C4×#1171994712yes—
804C22#1681110212yes—
805C22C2×#1313318711yescharacteristic
806C22C2×#1313318911yescharacteristic
807C22C2×#1313318911yescharacteristic
808C22#123×D5311yescharacteristic
809C22C2×#1313320111yescharacteristic
810C22#1681112911yescharacteristic
811C22#1681115412yes—
812C22#1681118311yescharacteristic
813C22#1681119511yescharacteristic
814C22#1681121812yes—
815C22#1681126212yes—
816C22#1681126712yes—
817C22#1681126812yes—
818C22#1681127212yes—
819C22#1681127312yes—
820C22#1681127712yes—
821C22#1681130412yes—
822C22#1681131012yes—
823C4—24no—
824C4—44no—
825C4—82no—
826C4—1064no—
827C4—2122no—
828C4—2122no—
829C4—2122no—
830C4—2124no—
831C4—2124no—
832C2—28no—
833C2—44no—
834C2C2×#1681050011yescharacteristic
835C2#2027724011yescharacteristic
836C2#2027738911yescharacteristic
837C2#2027754012yes—
838C2#2027771312yes—
839C2#2027804111yescharacteristic
840C2#2027804911yescharacteristic
841C2#2027819012yes—
842C2#2027827212yes—
843C2#2027902011yescharacteristic
844C2#2027960211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#13968
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16810484C2semidirect
4. C22×#13133124C2semidirect
5. #20272969C2semidirect
6. #20272962C2semidirect
7. #20272950C2semidirect
8. #20272938C2semidirect
9. #20272937C2semidirect
10. #20272937C2semidirect
17. C2×#13133198C4semidirect
59. C23×Dic53C2×C4semidirect
74. C2×#11719919C2×C4semidirect
84. C2×C22⋊Dic53C2×C4semidirect
85. C2×C22⋊Dic53C2×C4semidirect
354. C2×Dic53#123semidirect
466. C53#13968semidirect

Maximal subgroups

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

subgroupindex
C22×#131331982
C22×D4×Dic532
C2×#168104842
C22×#131331242
#202729692
#202729622
#202729502
#202729382
#202729372
C2×C53×#3862
#1396853