Finite Group Databasebeta

← #27306956

Subgroups — #27306956

Order 13568.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810498C211yesmaximal, characteristic, complemented
4C2×#16810498C211yesmaximal, characteristic, complemented
5C2×#16810483C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272980C211yesmaximal, characteristic, complemented
8#20272972C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic, complemented
10#20272960C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272949C211yesmaximal, characteristic, complemented
13#20272937C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C2×C53×#386C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×D4×Dic53—24no—
20C2×D4×Dic53—24no—
21C2×D4×Dic53—24no—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4⋊Dic53C2211yescharacteristic
26C22×C4⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810503—24no—
34#16810498—24no—
35#16810498—24no—
36#16810483—24no—
37C2×#13133124—24no—
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C23×D4×C53C2211yescharacteristic
53C24×C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C53×#386C418yescomplemented
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—22no—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—22no—
74C23×Dic53—41no—
75C23×Dic53—41no—
76C23×Dic53—41no—
77C23×Dic53—41no—
78C23×Dic53—41no—
79C23×Dic53—41no—
80C23×Dic53D414yes—
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89D4×Dic53—232no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—22no—
94C2×C4⋊Dic53—22no—
95C2×C4⋊Dic53—22no—
96C2×C4⋊Dic53—22no—
97C2×C4⋊Dic53—22no—
98C2×C4⋊Dic53—22no—
99C2×C4⋊Dic53—22no—
100C2×C4⋊Dic53—22no—
101C2×C4⋊Dic53—41no—
102C2×C4⋊Dic53—41no—
103C2×C4⋊Dic53—41no—
104C2×C4⋊Dic53—41no—
105C2×C22⋊Dic53—22no—
106C2×C22⋊Dic53—22no—
107C2×C22⋊Dic53—22no—
108C2×C22⋊Dic53—22no—
109C2×C22⋊Dic53—22no—
110C2×C22⋊Dic53—22no—
111C2×C22⋊Dic53—22no—
112C2×C22⋊Dic53—22no—
113C2×C22⋊Dic53—22no—
114C2×C22⋊Dic53—22no—
115C2×C22⋊Dic53—22no—
116C2×C22⋊Dic53—22no—
117C2×C22⋊Dic53—41no—
118C2×C22⋊Dic53—41no—
119C2×C22⋊Dic53D414yes—
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—22no—
126#13133124—22no—
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—22no—
131#13133124—22no—
132#13133124—22no—
133#13133124—22no—
134#13133124—41no—
135#13133124—41no—
136#13133124D414yescomplemented
137C25×C53C2311yescharacteristic
138C25×C53C2311yescharacteristic
139C22×D4×C53—22no—
140C22×D4×C53—22no—
141C22×D4×C53—22no—
142C22×D4×C53—22no—
143C22×D4×C53C2×C414yes—
144C22×D4×C53D414yes—
145C22×D4×C53Q814yes—
146C23×C4×C53—22no—
147C23×C4×C53—22no—
148C23×C4×C53—22no—
149C23×C4×C53—22no—
150C23×C4×C53—41no—
151C23×C4×C53—41no—
152C23×C4×C53C2×C414yescomplemented
153C23×C4×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C23×C4×C53C2311yescharacteristic
156C23×C4×C53C2311yescharacteristic
157C23×C4×C53C2311yescharacteristic
158C2×C22⋊C4×C53—22no—
159C2×C22⋊C4×C53—22no—
160C2×C22⋊C4×C53—22no—
161C2×C22⋊C4×C53—22no—
162C2×C22⋊C4×C53—41no—
163C2×C22⋊C4×C53—41no—
164C2×C22⋊C4×C53C2×C414yescomplemented
165C2×C22⋊C4×C53C2×C414yescomplemented
166C2×C22⋊C4×C53C2×C414yescomplemented
167#95×C53C2×C414yescomplemented
168#95×C53C2×C414yescomplemented
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53C22×C412yes—
190C24×C53C22×C412yes—
191C24×C53C2×D412yes—
192C24×C53C2×D412yes—
193C24×C53C2×D412yes—
194C24×C53C2×D412yes—
195C24×C53C2×Q812yes—
196C24×C53C2×Q812yes—
197C24×C53#4112yes—
198C24×C53#4112yes—
199C24×C53C2411yescharacteristic
200C2×D4×C53—28no—
201C2×D4×C53—28no—
202C2×D4×C53—28no—
203C2×D4×C53—28no—
204C2×D4×C53—28no—
205C2×D4×C53—28no—
206C2×D4×C53C4⋊C4116yescomplemented
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—28no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—28no—
235C22×C4×C53—44no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53—44no—
240C22×C4×C53C22×C412yes—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C22×C412yes—
244C22×C4×C53C22×C412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×Q812yes—
248C22×C4×C53#4112yes—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—28no—
254C22×Dic53—28no—
255C22×Dic53—28no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—28no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—21no—
292C22×Dic53—21no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295C22×Dic53—21no—
296C22×Dic53—21no—
297C22×Dic53—21no—
298C22×Dic53—21no—
299C22×Dic53—21no—
300C22×Dic53—21no—
301C22×Dic53—44no—
302C22×Dic53—44no—
303C22×Dic53—44no—
304C22×Dic53—44no—
305C22×Dic53—44no—
306C22×Dic53—44no—
307C22×Dic53—44no—
308C22×Dic53—44no—
309C22×Dic53—44no—
310C22×Dic53—44no—
311C22×Dic53—44no—
312C22×Dic53—44no—
313C22×Dic53—44no—
314C22×Dic53—44no—
315C22×Dic53—44no—
316C22×Dic53—44no—
317C22×Dic53—44no—
318C22×Dic53C2×D412yes—
319C22×Dic53C2×D412yes—
320C22×Dic53C2×D412yes—
321C22×Dic53C2×D412yes—
322C22×Dic53C2×D412yes—
323C22×Dic53C2×D412yes—
324C22×Dic53#4112yes—
325C22×Dic53#4112yes—
326C22⋊C4×C53—28no—
327C22⋊C4×C53—28no—
328C22⋊C4×C53—44no—
329C22⋊Dic53—28no—
330C22⋊Dic53—28no—
331C22⋊Dic53—44no—
332C22⋊Dic53—44no—
333C22⋊Dic53—44no—
334C4⋊Dic53—28no—
335C4⋊Dic53—44no—
336C4⋊Dic53—44no—
337C4⋊Dic53—44no—
338C4⋊Dic53—44no—
339C4×Dic53—28no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53—41no—
395C23×C53—41no—
396C23×C53—41no—
397C23×C53—41no—
398C23×C53—41no—
399C23×C53—41no—
400C23×C53—41no—
401C23×C53—41no—
402C23×C53C2×C4⋊C414yes—
403C23×C53C2×C4⋊C414yes—
404C23×C53C4×D414yes—
405C23×C53C4×D414yes—
406C23×C53#12014yes—
407C23×C53C22⋊Q814yes—
408C23×C53C22⋊Q814yes—
409C23×C53#12314yes—
410C23×C53C23×C411yescharacteristic
411C23×C53C22×D411yescharacteristic
412C23×C53C22×D411yescharacteristic
413C23×C53C22×D411yescharacteristic
414C23×C53C22×D411yescharacteristic
415C23×C53C22×Q811yescharacteristic
416C23×C53C2×#4111yescharacteristic
417C23×C53C2×#4111yescharacteristic
418C23×C53C2×#4111yescharacteristic
419C23×C53C2×#4111yescharacteristic
420C23×C53C2×#4111yescharacteristic
421C23×C53H(5,𝔽2)11yescharacteristic
422C23×C53H(5,𝔽2)11yescharacteristic
423C23×C53H(5,𝔽2)11yescharacteristic
424C23×C532−1+411yescharacteristic
425D4×C53—232no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—416no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53C2×C4⋊C414yes—
461C2×C4×C53C4×D414yescomplemented
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—22no—
472C2×Dic53—22no—
473C2×Dic53—22no—
474C2×Dic53—22no—
475C2×Dic53—22no—
476C2×Dic53—22no—
477C2×Dic53—22no—
478C2×Dic53—22no—
479C2×Dic53—22no—
480C2×Dic53—22no—
481C2×Dic53—22no—
482C2×Dic53—22no—
483C2×Dic53—416no—
484C2×Dic53—416no—
485C2×Dic53—416no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C2×Dic53—41no—
496C2×Dic53—41no—
497C2×Dic53—41no—
498C2×Dic53—41no—
499C2×Dic53—41no—
500C2×Dic53—41no—
501C2×Dic53—41no—
502C2×Dic53—41no—
503C2×Dic53—41no—
504C2×Dic53—41no—
505C2×Dic53—41no—
506C2×Dic53—41no—
507C2×Dic53—41no—
508C2×Dic53—41no—
509C2×Dic53—41no—
510C2×Dic53—41no—
511C2×Dic53—41no—
512C2×Dic53—41no—
513C2×Dic53—41no—
514C2×Dic53—41no—
515C2×Dic53—41no—
516C2×Dic53—41no—
517C2×Dic53—41no—
518C2×Dic53—41no—
519C2×Dic53—41no—
520C2×Dic53#12114yes—
521#13975—531nomaximal, Sylow
522C22×C53—24no—
523C22×C53—24no—
524C22×C53—24no—
525C22×C53—24no—
526C22×C53—24no—
527C22×C53—24no—
528C22×C53—24no—
529C22×C53—24no—
530C22×C53—24no—
531C22×C53—24no—
532C22×C53—24no—
533C22×C53—24no—
534C22×C53—24no—
535C22×C53—24no—
536C22×C53—24no—
537C22×C53—24no—
538C22×C53—24no—
539C22×C53—42no—
540C22×C53—42no—
541C22×C53—42no—
542C22×C53—42no—
543C22×C53—42no—
544C22×C53—42no—
545C22×C53—42no—
546C22×C53—42no—
547C22×C53—42no—
548C22×C53—42no—
549C22×C53—42no—
550C22×C53—42no—
551C22×C53#38518yescomplemented
552C22×C53C22×C4⋊C411yescharacteristic
553C22×C53C2×C4×D411yescharacteristic
554C22×C53C2×C4×D411yescharacteristic
555C22×C53C2×C4×D411yescharacteristic
556C22×C53C4×#4111yescharacteristic
557C22×C53#51811yescharacteristic
558C22×C53#52011yescharacteristic
559C22×C53C2×#12011yescharacteristic
560C22×C53C2×#12111yescharacteristic
561C22×C53C2×C22⋊Q811yescharacteristic
562C22×C53C2×C22⋊Q811yescharacteristic
563C22×C53C2×#12311yescharacteristic
564C22×C53#52511yescharacteristic
565C22×C53#52911yescharacteristic
566C22×C53#53211yescharacteristic
567C22×C53#53411yescharacteristic
568C22×C53#53711yescharacteristic
569C22×C53#53811yescharacteristic
570C22×C53#53911yescharacteristic
571C22×C53D4211yescharacteristic
572C22×C53D4211yescharacteristic
573C22×C53#54611yescharacteristic
574C22×C53#54611yescharacteristic
575C22×C53#54611yescharacteristic
576C22×C53#54611yescharacteristic
577C22×C53#54611yescharacteristic
578C22×C53#54711yescharacteristic
579C22×C53#54711yescharacteristic
580C22×C53D4×Q811yescharacteristic
581C22×C53#55111yescharacteristic
582C22×C53#55111yescharacteristic
583C22×C53#55211yescharacteristic
584C22×C53#55411yescharacteristic
585C22×C53#55411yescharacteristic
586C22×C53#55411yescharacteristic
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—42no—
590C4×C53—42no—
591C4×C53—42no—
592Dic53—24no—
593Dic53—42no—
594Dic53—42no—
595Dic53—42no—
596Dic53—42no—
597Dic53—42no—
598Dic53—81no—
599Dic53—81no—
600C22×C4×D4—531no—
601C2×#386—531no—
602C2×#386D5311yescharacteristic
603C2×#385—531no—
604C2×#385—531no—
605C2×#380—531no—
606C22×#95—531no—
607#1444—531no—
608#1442—531no—
609#1439—531no—
610#1439—531no—
611#1436—531no—
612#1436—531no—
613C22⋊#95—531no—
614C22⋊#95—531no—
615C2×C53—28no—
616C2×C53—44no—
617C2×C53C2×#38511yescharacteristic
618C2×C53C4×#12111yescharacteristic
619C2×C53#232511yescharacteristic
620C2×C53D4×C4⋊C411yescharacteristic
621C2×C53#234911yescharacteristic
622C2×C53#235811yescharacteristic
623C2×C53#235911yescharacteristic
624C2×C53#241011yescharacteristic
625C2×C53#241711yescharacteristic
626C2×C53#241811yescharacteristic
627C2×C53#241911yescharacteristic
628C2×C53#243011yescharacteristic
629C2×C53#244911yescharacteristic
630C2×C53#245011yescharacteristic
631C2×C53#256411yescharacteristic
632C23×D4C2×D5311yescharacteristic
633C24×C4—531no—
634C24×C4—531no—
635C24×C4—531no—
636C24×C4C2×D5311yescharacteristic
637C2×C4×D4—1064no—
638C2×C4×D4—1064no—
639C2×C4×D4—1064no—
640C22×C4⋊C4—531no—
641C22×C4⋊C4—531no—
642C22×C4⋊C4—531no—
643C22×C4⋊C4—531no—
644C22×C4⋊C4—531no—
645C22×C22⋊C4—531no—
646C22×C22⋊C4—531no—
647C22×C22⋊C4—531no—
648C22×C22⋊C4—531no—
649C22×C22⋊C4—531no—
650C22×C22⋊C4C2×D5311yescharacteristic
651C22×C22⋊C4C2×D5311yescharacteristic
652C22×C22⋊C4C2×D5311yescharacteristic
653C22×C42—531no—
654#386—1064no—
655#386Dic5318yescomplemented
656#385—1064no—
657#385—1064no—
658#380—1064no—
659C2×#95—531no—
660C2×#95—531no—
661C2×#95—531no—
662C2×#95—531no—
663C2×#95—531no—
664C2×#95—531no—
665C2×#95—531no—
666C2×#95—531no—
667C2×#95—531no—
668C2×#95—531no—
669C2×#95—531no—
670C2×#95—531no—
671C2×#95—531no—
672C2×#95—531no—
673C2×#95—1064no—
674C2×#95C2×D5311yescharacteristic
675C2×#95C2×D5311yescharacteristic
676C53#1397511yescharacteristic, complemented, Sylow
677C25C22×D5311yescharacteristic
678C25C22×D5311yescharacteristic
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4Dic10614yes—
684C22×D4D21214yes—
685C22×D4C2×Dic5314yes—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—531no—
693C23×C4—531no—
694C23×C4—531no—
695C23×C4—531no—
696C23×C4—531no—
697C23×C4—531no—
698C23×C4—534no—
699C23×C4—531no—
700C23×C4—531no—
701C23×C4—1062no—
702C23×C4—1062no—
703C23×C4—1062no—
704C23×C4—1062no—
705C23×C4—1062no—
706C23×C4—1062no—
707C23×C4—1062no—
708C23×C4—1062no—
709C23×C4—1062no—
710C23×C4—1062no—
711C23×C4—1062no—
712C23×C4—1062no—
713C23×C4—1062no—
714C23×C4—1062no—
715C23×C4—2121no—
716C23×C4—2121no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4—2121no—
721C23×C4C2×Dic5314yescomplemented
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C4×D4—10632no—
728C2×C4⋊C4—1062no—
729C2×C4⋊C4—1062no—
730C2×C4⋊C4—1062no—
731C2×C4⋊C4—1062no—
732C2×C4⋊C4—1062no—
733C2×C4⋊C4—1062no—
734C2×C4⋊C4—1062no—
735C2×C4⋊C4—1062no—
736C2×C4⋊C4—1062no—
737C2×C4⋊C4—1062no—
738C2×C4⋊C4—1062no—
739C2×C4⋊C4—2121no—
740C2×C4⋊C4—2121no—
741C2×C4⋊C4—2121no—
742C2×C4⋊C4—2121no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—534no—
750C2×C22⋊C4—1062no—
751C2×C22⋊C4—1062no—
752C2×C22⋊C4—1062no—
753C2×C22⋊C4—1062no—
754C2×C22⋊C4—1062no—
755C2×C22⋊C4—1062no—
756C2×C22⋊C4—1062no—
757C2×C22⋊C4—1062no—
758C2×C22⋊C4—1062no—
759C2×C22⋊C4—1062no—
760C2×C22⋊C4—1062no—
761C2×C22⋊C4—1062no—
762C2×C22⋊C4—2121no—
763C2×C22⋊C4—2121no—
764C2×C22⋊C4C2×Dic5314yescomplemented
765C2×C22⋊C4C2×Dic5314yescomplemented
766C2×C22⋊C4C2×Dic5314yescomplemented
767C2×C42—1062no—
768C2×C42—1062no—
769C2×C42—1062no—
770#95—534no—
771#95—1062no—
772#95—1062no—
773#95—1062no—
774#95—1062no—
775#95—1062no—
776#95—1062no—
777#95—1062no—
778#95—1062no—
779#95—1062no—
780#95—1062no—
781#95—1062no—
782#95—2121no—
783#95—2121no—
784#95C2×Dic5314yescomplemented
785#95C2×Dic5314yescomplemented
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×Dic10612yes—
807C24C2×Dic10612yes—
808C24C2×D21212yes—
809C24C2×D21212yes—
810C24D4×D5312yes—
811C24D4×D5312yes—
812C24#1171994712yes—
813C24#1171994712yes—
814C24C22×Dic5312yes—
815C24C22×Dic5312yes—
816C24C23×D5311yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4⋊Dic53116yescomplemented
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—532no—
858C22×C4—532no—
859C22×C4—532no—
860C22×C4—532no—
861C22×C4—532no—
862C22×C4—532no—
863C22×C4—532no—
864C22×C4—532no—
865C22×C4—1068no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1068no—
871C22×C4—1068no—
872C22×C4—1068no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—1061no—
890C22×C4—1061no—
891C22×C4—1061no—
892C22×C4—1061no—
893C22×C4—1061no—
894C22×C4—1061no—
895C22×C4—1061no—
896C22×C4—1061no—
897C22×C4—1061no—
898C22×C4—1061no—
899C22×C4—1061no—
900C22×C4—1061no—
901C22×C4—1061no—
902C22×C4—1061no—
903C22×C4—1061no—
904C22×C4—1061no—
905C22×C4—1061no—
906C22×C4—1061no—
907C22×C4—1061no—
908C22×C4—1061no—
909C22×C4—1061no—
910C22×C4—1061no—
911C22×C4—1061no—
912C22×C4—1061no—
913C22×C4—1061no—
914C22×C4—1061no—
915C22×C4—1061no—
916C22×C4—1061no—
917C22×C4—2124no—
918C22×C4—2124no—
919C22×C4—2124no—
920C22×C4—2124no—
921C22×C4—2124no—
922C22×C4—2124no—
923C22×C4—2124no—
924C22×C4—2124no—
925C22×C4—2124no—
926C22×C4—2124no—
927C22×C4—2124no—
928C22×C4—2124no—
929C22×C4—2124no—
930C22×C4—2124no—
931C22×C4—2124no—
932C22×C4—2124no—
933C22×C4—2124no—
934C22×C4C2×Dic10612yes—
935C22×C4C2×D21212yes—
936C22×C4D4×D5312yes—
937C22×C4#1171994712yes—
938C22×C4C22×Dic5312yes—
939C22×C4C22×Dic5312yes—
940C22×C4C22×Dic5312yes—
941C22×C4C22×Dic5312yes—
942C22×C4C22×Dic5312yes—
943C4⋊C4—1068no—
944C4⋊C4—2124no—
945C4⋊C4—2124no—
946C4⋊C4—2124no—
947C4⋊C4—2124no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—1068no—
952C22⋊C4—1068no—
953C22⋊C4—2124no—
954C22⋊C4—2124no—
955C22⋊C4—2124no—
956C42—1068no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C4⋊Dic5314yes—
1020C23C2×C4⋊Dic5314yes—
1021C23D4×Dic5314yes—
1022C23D4×Dic5314yes—
1023C23#1313318714yes—
1024C23#1313319414yes—
1025C23#1313319414yes—
1026C23#1313320114yes—
1027C23C23×Dic5311yescharacteristic
1028C23C2×D4×D5311yescharacteristic
1029C23C2×D4×D5311yescharacteristic
1030C23C2×D4×D5311yescharacteristic
1031C23C22×D21211yescharacteristic
1032C23C22×Dic10611yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23C2×#1171994711yescharacteristic
1036C23C2×#1171994711yescharacteristic
1037C23C2×#1171994711yescharacteristic
1038C23#1313326211yescharacteristic
1039C23#1313326211yescharacteristic
1040C23#1313326311yescharacteristic
1041C23#1313326411yescharacteristic
1042D4—232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—416no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—534no—
1078C2×C4—1062no—
1079C2×C4—1062no—
1080C2×C4—1062no—
1081C2×C4—1062no—
1082C2×C4—1062no—
1083C2×C4—1062no—
1084C2×C4—1062no—
1085C2×C4—1062no—
1086C2×C4—1062no—
1087C2×C4—1062no—
1088C2×C4—1062no—
1089C2×C4—1062no—
1090C2×C4—1062no—
1091C2×C4—1062no—
1092C2×C4—1062no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1062no—
1096C2×C4—1062no—
1097C2×C4—1062no—
1098C2×C4—1062no—
1099C2×C4—21216no—
1100C2×C4—21216no—
1101C2×C4—2121no—
1102C2×C4—2121no—
1103C2×C4—2121no—
1104C2×C4—2121no—
1105C2×C4—2121no—
1106C2×C4—2121no—
1107C2×C4—2121no—
1108C2×C4—2121no—
1109C2×C4—2121no—
1110C2×C4—2121no—
1111C2×C4—2121no—
1112C2×C4—2121no—
1113C2×C4—2121no—
1114C2×C4—2121no—
1115C2×C4—21216no—
1116C2×C4—2121no—
1117C2×C4—2121no—
1118C2×C4—2121no—
1119C2×C4—2121no—
1120C2×C4—2121no—
1121C2×C4—2121no—
1122C2×C4—2121no—
1123C2×C4—2121no—
1124C2×C4—2121no—
1125C2×C4—2121no—
1126C2×C4—2121no—
1127C2×C4—2121no—
1128C2×C4—2121no—
1129C2×C4—2121no—
1130C2×C4—2121no—
1131C2×C4—2121no—
1132C2×C4—2121no—
1133C2×C4—2121no—
1134C2×C4—2121no—
1135C2×C4—2121no—
1136C2×C4C2×C4⋊Dic5314yes—
1137C2×C4D4×Dic5314yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1681049818yescomplemented
1168C22C22×C4⋊Dic5311yescharacteristic
1169C22C2×D4×Dic5311yescharacteristic
1170C22C2×D4×Dic5311yescharacteristic
1171C22C2×D4×Dic5311yescharacteristic
1172C22#41×Dic5311yescharacteristic
1173C22#1681109811yescharacteristic
1174C22#1681110611yescharacteristic
1175C22C2×#1313318711yescharacteristic
1176C22#121×D5311yescharacteristic
1177C22C2×#1313319411yescharacteristic
1178C22C2×#1313319411yescharacteristic
1179C22C2×#1313320111yescharacteristic
1180C22#1681113311yescharacteristic
1181C22#1681115411yescharacteristic
1182C22#1681116811yescharacteristic
1183C22#1681118111yescharacteristic
1184C22#1681120011yescharacteristic
1185C22#1681121011yescharacteristic
1186C22#1681121811yescharacteristic
1187C22#1681125511yescharacteristic
1188C22D4×D21211yescharacteristic
1189C22#1681126011yescharacteristic
1190C22#1681126011yescharacteristic
1191C22#1681126511yescharacteristic
1192C22#1681126811yescharacteristic
1193C22#1681126811yescharacteristic
1194C22#1681127111yescharacteristic
1195C22#1681127711yescharacteristic
1196C22D4×Dic10611yescharacteristic
1197C22#1681129611yescharacteristic
1198C22#1681130411yescharacteristic
1199C22#1681131011yescharacteristic
1200C22#1681133011yescharacteristic
1201C22#1681133211yescharacteristic
1202C22#1681133211yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—1064no—
1209C4—4241no—
1210C4—4241no—
1211C4—2122no—
1212C4—2122no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1681049811yescharacteristic
1219C2#121×Dic5311yescharacteristic
1220C2#2027742011yescharacteristic
1221C2D4×C4⋊Dic5311yescharacteristic
1222C2#2027762511yescharacteristic
1223C2#2027769911yescharacteristic
1224C2#2027771111yescharacteristic
1225C2#2027808811yescharacteristic
1226C2#2027816311yescharacteristic
1227C2#2027817511yescharacteristic
1228C2#2027819011yescharacteristic
1229C2#2027832311yescharacteristic
1230C2#2027852811yescharacteristic
1231C2#2027854311yescharacteristic
1232C2#2027989911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#13975
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16810498C2semidirect
4. C2×#16810498C2semidirect
5. C2×#16810483C2semidirect
6. C22×#13133124C2semidirect
7. #20272980C2semidirect
8. #20272972C2semidirect
9. #20272960C2semidirect
10. #20272960C2semidirect
11. #20272949C2semidirect
12. #20272949C2semidirect
13. #20272937C2semidirect
14. #20272937C2semidirect
57. C53×#386C4semidirect
136. #13133124D4semidirect
152. C23×C4×C53C2×C4semidirect
164. C2×C22⋊C4×C53C2×C4semidirect
165. C2×C22⋊C4×C53C2×C4semidirect
166. C2×C22⋊C4×C53C2×C4semidirect
167. #95×C53C2×C4semidirect
168. #95×C53C2×C4semidirect
206. C2×D4×C53C4⋊C4semidirect
461. C2×C4×C53C4×D4semidirect
551. C22×C53#385semidirect
655. #386Dic53semidirect
676. C53#13975semidirect
721. C23×C4C2×Dic53semidirect
764. C2×C22⋊C4C2×Dic53semidirect
765. C2×C22⋊C4C2×Dic53semidirect
766. C2×C22⋊C4C2×Dic53semidirect
784. #95C2×Dic53semidirect
785. #95C2×Dic53semidirect
823. C2×D4C4⋊Dic53semidirect
1137. C2×C4D4×Dic53semidirect
1167. 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
C2×#168105032
C2×#168104982
C2×#168104832
C22×#131331242
#202729802
#202729722
#202729602
#202729492
#202729372
C2×C53×#3862
#1397553