Finite Group Databasebeta

← #27307457

Subgroups — #27307457

Order 13568.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic
2C23×C4⋊Dic53C211yesmaximal, characteristic, complemented
3C2×#16810503C211yesmaximal, characteristic
4C2×#16810498C212yesmaximal, complemented
5C2×#16810498C211yesmaximal, characteristic, complemented
6#20272980C212yesmaximal, complemented
7#20272960C212yesmaximal, complemented
8#20272949C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic, complemented
10#20272937C211yesmaximal, characteristic, complemented
11C2×C53×#386C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×D4×Dic53—24no—
16C2×D4×Dic53—24no—
17C2×D4×Dic53—24no—
18C22×C4⋊Dic53—24no—
19C22×C4⋊Dic53—28no—
20C22×C4⋊Dic53C2212yes—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2212yes—
23C22×C4⋊Dic53C2212yes—
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2212yes—
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29#16810503—24no—
30#16810498—28no—
31#16810498—24no—
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×#386C418yescomplemented
43C2×#95×C53C2212yes—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—22no—
47C23×Dic53—22no—
48C23×Dic53—24no—
49C23×Dic53—24no—
50C23×Dic53—22no—
51C23×Dic53—22no—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—24no—
55C23×Dic53—42no—
56C23×Dic53—42no—
57C23×Dic53—42no—
58C23×Dic53D414yes—
59C23×Dic53C2312yes—
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2312yes—
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65D4×Dic53—232no—
66C2×C4⋊Dic53—232no—
67C2×C4⋊Dic53—24no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—24no—
70C2×C4⋊Dic53—24no—
71C2×C4⋊Dic53—24no—
72C2×C4⋊Dic53—24no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—24no—
76C2×C4⋊Dic53—24no—
77C2×C4⋊Dic53—42no—
78C2×C4⋊Dic53D418yescomplemented
79C2×C22⋊Dic53—22no—
80C2×C22⋊Dic53—22no—
81C2×C22⋊Dic53—22no—
82C2×C22⋊Dic53—24no—
83C2×C22⋊Dic53—22no—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53—24no—
89C2×C22⋊Dic53—42no—
90C2×C22⋊Dic53D414yes—
91C2×C4×Dic53—22no—
92C2×C4×Dic53—22no—
93C2×C4×Dic53—22no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97#13133124—24no—
98#13133124—24no—
99#13133124—42no—
100C25×C53C2311yescharacteristic
101C25×C53C2311yescharacteristic
102C22×D4×C53—22no—
103C22×D4×C53—22no—
104C22×D4×C53—22no—
105C22×D4×C53—22no—
106C22×D4×C53C2×C414yes—
107C22×D4×C53D414yes—
108C22×D4×C53Q814yes—
109C23×C4×C53—22no—
110C23×C4×C53—22no—
111C23×C4×C53—24no—
112C23×C4×C53—24no—
113C23×C4×C53C2×C414yescomplemented
114C23×C4×C53C2312yes—
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2312yes—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—24no—
120C2×C22⋊C4×C53—24no—
121C2×C22⋊C4×C53C2×C414yescomplemented
122C2×C22⋊C4×C53C2×C418yescomplemented
123#95×C53C2×C418yescomplemented
124C24×C53—22no—
125C24×C53—22no—
126C24×C53—22no—
127C24×C53—22no—
128C24×C53—22no—
129C24×C53—21no—
130C24×C53—21no—
131C24×C53—22no—
132C24×C53—21no—
133C24×C53—21no—
134C24×C53—22no—
135C24×C53—22no—
136C24×C53C22×C412yes—
137C24×C53C22×C412yes—
138C24×C53C2×D412yes—
139C24×C53C2×D412yes—
140C24×C53C2×D412yes—
141C24×C53C2×D412yes—
142C24×C53C2×Q812yes—
143C24×C53C2×Q812yes—
144C24×C53#4112yes—
145C24×C53#4112yes—
146C24×C53C2411yescharacteristic
147C2×D4×C53—28no—
148C2×D4×C53—28no—
149C2×D4×C53—28no—
150C2×D4×C53—28no—
151C2×D4×C53—28no—
152C2×D4×C53—28no—
153C2×D4×C53C4⋊C4116yescomplemented
154C22×C4×C53—216no—
155C22×C4×C53—28no—
156C22×C4×C53—28no—
157C22×C4×C53—28no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—216no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53C22×C414yes—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C22×C414yes—
176C22×C4×C53C2×D412yes—
177C22×C4×C53C2×D414yes—
178C22×C4×C53C2×Q812yes—
179C22×C4×C53#4114yes—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—22no—
183C22×Dic53—28no—
184C22×Dic53—28no—
185C22×Dic53—28no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—28no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—44no—
213C22×Dic53—48no—
214C22×Dic53—48no—
215C22×Dic53—48no—
216C22×Dic53—48no—
217C22×Dic53—48no—
218C22×Dic53—48no—
219C22×Dic53—44no—
220C22×Dic53—44no—
221C22×Dic53—44no—
222C22×Dic53—44no—
223C22×Dic53C2×D412yes—
224C22×Dic53C2×D412yes—
225C22×Dic53C2×D414yes—
226C22×Dic53C2×D412yes—
227C22×Dic53C2×D414yes—
228C22×Dic53C2×D412yes—
229C22⋊C4×C53—28no—
230C22⋊C4×C53—216no—
231C22⋊Dic53—28no—
232C22⋊Dic53—28no—
233C22⋊Dic53—48no—
234C22⋊Dic53—44no—
235C4⋊Dic53—216no—
236C4⋊Dic53—28no—
237C4⋊Dic53—216no—
238C4⋊Dic53—48no—
239C4×Dic53—28no—
240C23×C53—24no—
241C23×C53—24no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—24no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—24no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—24no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—24no—
255C23×C53—24no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—24no—
259C23×C53—24no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—24no—
265C23×C53—24no—
266C23×C53—24no—
267C23×C53—24no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—42no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53C2×C4⋊C414yes—
279C23×C53C2×C4⋊C414yescomplemented
280C23×C53C4×D414yes—
281C23×C53C4×D414yes—
282C23×C53#12014yes—
283C23×C53C22⋊Q814yes—
284C23×C53C22⋊Q814yes—
285C23×C53#12314yes—
286C23×C53C23×C411yescharacteristic
287C23×C53C22×D411yescharacteristic
288C23×C53C22×D411yescharacteristic
289C23×C53C22×D412yes—
290C23×C53C22×D411yescharacteristic
291C23×C53C22×Q811yescharacteristic
292C23×C53C2×#4111yescharacteristic
293C23×C53C2×#4111yescharacteristic
294C23×C53C2×#4112yes—
295C23×C53H(5,𝔽2)12yes—
296C23×C532−1+412yes—
297D4×C53—232no—
298C2×C4×C53—232no—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—24no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—24no—
310C2×C4×C53—24no—
311C2×C4×C53—24no—
312C2×C4×C53—24no—
313C2×C4×C53—24no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53C2×C4⋊C414yescomplemented
319C2×C4×C53C4×D418yescomplemented
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—24no—
331C2×Dic53—24no—
332C2×Dic53—24no—
333C2×Dic53—24no—
334C2×Dic53—416no—
335C2×Dic53—416no—
336C2×Dic53—416no—
337C2×Dic53—41no—
338C2×Dic53—42no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—41no—
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—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—42no—
356C2×Dic53#12014yes—
357#14015—531nomaximal, Sylow
358C22×C53—24no—
359C22×C53—24no—
360C22×C53—28no—
361C22×C53—28no—
362C22×C53—24no—
363C22×C53—24no—
364C22×C53—24no—
365C22×C53—28no—
366C22×C53—28no—
367C22×C53—24no—
368C22×C53—28no—
369C22×C53—24no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—44no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—44no—
377C22×C53—44no—
378C22×C53—42no—
379C22×C53#38518yescomplemented
380C22×C53C22×C4⋊C411yescharacteristic
381C22×C53C2×C4×D411yescharacteristic
382C22×C53C2×C4×D412yes—
383C22×C53C2×C4×D411yescharacteristic
384C22×C53#52012yes—
385C22×C53C2×#12011yescharacteristic
386C22×C53C2×#12011yescharacteristic
387C22×C53C2×C22⋊Q811yescharacteristic
388C22×C53C2×C22⋊Q811yescharacteristic
389C22×C53C2×#12311yescharacteristic
390C22×C53#52511yescharacteristic
391C22×C53#52512yes—
392C22×C53#53411yescharacteristic
393C22×C53#53611yescharacteristic
394C22×C53#53912yes—
395C22×C53D4212yes—
396C22×C53D4212yes—
397C22×C53#54712yes—
398C22×C53#54712yes—
399C22×C53#54812yes—
400C22×C53D4×Q812yes—
401C22×C53#55312yes—
402C22×C53#55412yes—
403C4×C53—24no—
404C4×C53—28no—
405C4×C53—44no—
406Dic53—24no—
407Dic53—42no—
408Dic53—44no—
409Dic53—42no—
410Dic53—42no—
411Dic53—82no—
412C22×C4×D4—531no—
413C23×C4⋊C4—531no—
414C2×#386—531no—
415C2×#386D5311yescharacteristic
416C2×#385—531no—
417C2×#385—532no—
418#1444—532no—
419#1439—532no—
420#1436—532no—
421C22⋊#95—531no—
422C22⋊#95—531no—
423C2×C53—28no—
424C2×C53—44no—
425C2×C53C2×#38511yescharacteristic
426C2×C53C4×#12011yescharacteristic
427C2×C53#232211yescharacteristic
428C2×C53D4×C4⋊C412yes—
429C2×C53#236112yes—
430C2×C53#240311yescharacteristic
431C2×C53#240611yescharacteristic
432C2×C53#240911yescharacteristic
433C2×C53#244312yes—
434C2×C53#244912yes—
435C2×C53#257911yescharacteristic
436C23×D4C2×D5311yescharacteristic
437C24×C4—531no—
438C24×C4—531no—
439C24×C4—531no—
440C24×C4C2×D5311yescharacteristic
441C2×C4×D4—1064no—
442C2×C4×D4—1064no—
443C2×C4×D4—1064no—
444C22×C4⋊C4—532no—
445C22×C4⋊C4—532no—
446C22×C4⋊C4—531no—
447C22×C4⋊C4—532no—
448C22×C4⋊C4—1068no—
449C22×C4⋊C4—1064no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—531no—
452C22×C22⋊C4—531no—
453C22×C22⋊C4—532no—
454C22×C22⋊C4C2×D5311yescharacteristic
455C22×C22⋊C4C2×D5312yes—
456C22×C42—531no—
457#386—1064no—
458#386Dic5318yescomplemented
459#385—1064no—
460#385—1068no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95—532no—
465C2×#95—532no—
466C2×#95—532no—
467C2×#95C2×D5312yes—
468C53#1401511yescharacteristic, complemented, Sylow
469C25C22×D5311yescharacteristic
470C25C22×D5311yescharacteristic
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4Dic10614yes—
476C22×D4D21214yes—
477C22×D4C2×Dic5314yes—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—532no—
486C23×C4—531no—
487C23×C4—534no—
488C23×C4—532no—
489C23×C4—1064no—
490C23×C4—1064no—
491C23×C4—1062no—
492C23×C4—1062no—
493C23×C4—1064no—
494C23×C4—1062no—
495C23×C4—1062no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—1062no—
499C23×C4—1062no—
500C23×C4—2122no—
501C23×C4—2122no—
502C23×C4—2122no—
503C23×C4C2×Dic5314yescomplemented
504C23×C4C22×D5312yes—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5312yes—
507C4×D4—10632no—
508C2×C4⋊C4—538no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C4⋊C4—1064no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—1062no—
514C2×C4⋊C4—1062no—
515C2×C4⋊C4—10632no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1064no—
518C2×C4⋊C4—1064no—
519C2×C4⋊C4—1064no—
520C2×C4⋊C4—2122no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—534no—
526C2×C22⋊C4—1062no—
527C2×C22⋊C4—1062no—
528C2×C22⋊C4—1062no—
529C2×C22⋊C4—1062no—
530C2×C22⋊C4—1062no—
531C2×C22⋊C4—1064no—
532C2×C22⋊C4—1064no—
533C2×C22⋊C4—1062no—
534C2×C22⋊C4—1062no—
535C2×C22⋊C4—1062no—
536C2×C22⋊C4—2122no—
537C2×C22⋊C4C2×Dic5314yescomplemented
538C2×C22⋊C4C2×Dic5318yescomplemented
539C2×C42—1062no—
540C2×C42—1062no—
541C2×C42—1062no—
542#95—1064no—
543#95—1064no—
544#95—1064no—
545#95—1064no—
546#95—1064no—
547#95—2122no—
548#95C2×Dic5318yescomplemented
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—21no—
555C24—21no—
556C24—22no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24C2×Dic10612yes—
562C24C2×Dic10612yes—
563C24C2×D21212yes—
564C24C2×D21212yes—
565C24D4×D5312yes—
566C24D4×D5312yes—
567C24#1171994712yes—
568C24#1171994712yes—
569C24C22×Dic5312yes—
570C24C22×Dic5312yes—
571C24C23×D5311yescharacteristic
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4C4⋊Dic53116yescomplemented
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—216no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—534no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—534no—
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—1062no—
612C22×C4—1062no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1062no—
624C22×C4—1062no—
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—2124no—
637C22×C4—2124no—
638C22×C4—2128no—
639C22×C4—2128no—
640C22×C4—2128no—
641C22×C4—2128no—
642C22×C4—2128no—
643C22×C4—2128no—
644C22×C4—2124no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4C2×Dic10612yes—
648C22×C4C2×D21212yes—
649C22×C4D4×D5314yes—
650C22×C4#1171994714yes—
651C22×C4C22×Dic5314yes—
652C22×C4C22×Dic5312yes—
653C22×C4C22×Dic5314yes—
654C4⋊C4—10616no—
655C4⋊C4—10616no—
656C4⋊C4—1068no—
657C4⋊C4—2128no—
658C22⋊C4—28no—
659C22⋊C4—216no—
660C22⋊C4—1068no—
661C22⋊C4—1068no—
662C22⋊C4—2128no—
663C22⋊C4—2124no—
664C42—1068no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23C2×C4⋊Dic5314yes—
704C23C2×C4⋊Dic5314yescomplemented
705C23D4×Dic5314yes—
706C23D4×Dic5314yes—
707C23#1313318714yes—
708C23#1313319414yes—
709C23#1313319414yes—
710C23#1313320114yes—
711C23C23×Dic5311yescharacteristic
712C23C2×D4×D5311yescharacteristic
713C23C2×D4×D5312yes—
714C23C2×D4×D5311yescharacteristic
715C23C22×D21211yescharacteristic
716C23C22×Dic10611yescharacteristic
717C23C2×#1171994712yes—
718C23C2×#1171994711yescharacteristic
719C23C2×#1171994711yescharacteristic
720C23#1313326312yes—
721C23#1313326412yes—
722D4—232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—534no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1064no—
747C2×C4—1064no—
748C2×C4—1064no—
749C2×C4—1064no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1064no—
756C2×C4—1064no—
757C2×C4—1064no—
758C2×C4—21216no—
759C2×C4—21216no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4—2122no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—21216no—
768C2×C4—2122no—
769C2×C4—2121no—
770C2×C4—2122no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4—2122no—
774C2×C4—2121no—
775C2×C4—2122no—
776C2×C4—2122no—
777C2×C4—2122no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4C2×C4⋊Dic5314yescomplemented
781C2×C4D4×Dic5318yescomplemented
782C22—28no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—28no—
789C22—24no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22#1681049818yescomplemented
804C22C22×C4⋊Dic5311yescharacteristic
805C22C2×D4×Dic5312yes—
806C22C2×D4×Dic5311yescharacteristic
807C22C2×D4×Dic5311yescharacteristic
808C22#1681110612yes—
809C22#120×D5311yescharacteristic
810C22C2×#1313318711yescharacteristic
811C22C2×#1313319411yescharacteristic
812C22C2×#1313319411yescharacteristic
813C22C2×#1313320111yescharacteristic
814C22#1681112912yes—
815C22#1681112911yescharacteristic
816C22#1681118411yescharacteristic
817C22#1681119511yescharacteristic
818C22#1681121712yes—
819C22#1681125712yes—
820C22D4×D21212yes—
821C22#1681127312yes—
822C22#1681127712yes—
823C22#1681127912yes—
824C22D4×Dic10612yes—
825C22#1681132512yes—
826C22#1681133012yes—
827C4—24no—
828C4—28no—
829C4—44no—
830C4—1064no—
831C4—4242no—
832C4—2122no—
833C4—2124no—
834C4—2122no—
835C4—2122no—
836C2—28no—
837C2—44no—
838C2C2×#1681049811yescharacteristic
839C2#120×Dic5311yescharacteristic
840C2#2027738711yescharacteristic
841C2D4×C4⋊Dic5312yes—
842C2#2027773512yes—
843C2#2027802711yescharacteristic
844C2#2027804911yescharacteristic
845C2#2027807711yescharacteristic
846C2#2027844812yes—
847C2#2027853012yes—
848C2#2028005911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#14015
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic53C2semidirect
4. C2×#16810498C2semidirect
5. C2×#16810498C2semidirect
6. #20272980C2semidirect
7. #20272960C2semidirect
8. #20272949C2semidirect
9. #20272938C2semidirect
10. #20272937C2semidirect
42. C53×#386C4semidirect
78. C2×C4⋊Dic53D4semidirect
113. C23×C4×C53C2×C4semidirect
121. C2×C22⋊C4×C53C2×C4semidirect
122. C2×C22⋊C4×C53C2×C4semidirect
123. #95×C53C2×C4semidirect
153. C2×D4×C53C4⋊C4semidirect
279. C23×C53C2×C4⋊C4semidirect
318. C2×C4×C53C2×C4⋊C4semidirect
319. C2×C4×C53C4×D4semidirect
379. C22×C53#385semidirect
458. #386Dic53semidirect
468. C53#14015semidirect
503. C23×C4C2×Dic53semidirect
537. C2×C22⋊C4C2×Dic53semidirect
538. C2×C22⋊C4C2×Dic53semidirect
548. #95C2×Dic53semidirect
578. C2×D4C4⋊Dic53semidirect
704. C23C2×C4⋊Dic53semidirect
780. C2×C4C2×C4⋊Dic53semidirect
781. C2×C4D4×Dic53semidirect
803. C22#16810498semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic532
C23×C4⋊Dic532
C2×#168105032
C2×#168104982
#202729802
#202729602
#202729492
#202729382
#202729372
C2×C53×#3862
#1401553