Finite Group Databasebeta

← #27307573

Subgroups — #27307573

Order 13568.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133203C211yesmaximal, characteristic
2C22×C4×Dic106C211yesmaximal, characteristic, complemented
3C2×#16810527C211yesmaximal, characteristic, complemented
4C2×#16810523C211yesmaximal, characteristic
5C2×#16810523C211yesmaximal, characteristic
6#20272961C211yesmaximal, characteristic, complemented
7#20272960C211yesmaximal, characteristic, complemented
8#20272959C211yesmaximal, characteristic, complemented
9#20272958C211yesmaximal, characteristic, complemented
10#20272953C211yesmaximal, characteristic, complemented
11#20272952C211yesmaximal, characteristic, complemented
12#20272951C211yesmaximal, characteristic, complemented
13#20272943C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×#1437C211yesmaximal, characteristic, complemented
16C23×Dic106C2211yescharacteristic
17C23×C22⋊D53C2211yescharacteristic
18C2×#13133203—24no—
19C2×#13133203—24no—
20C2×#13133203C418yescomplemented
21C2×C4×Dic106—24no—
22C2×C4×Dic106—24no—
23C2×C4×Dic106—24no—
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41#16810527—24no—
42#16810523—24no—
43#16810523—24no—
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C22×Dic106—22no—
62C22×Dic106—22no—
63C22×Dic106—22no—
64C22×Dic106—22no—
65C22×Dic106C2×C414yes—
66C22×Dic106D414yes—
67C22×Dic106D414yes—
68C22×C22⋊D53—22no—
69C22×C22⋊D53—22no—
70C22×C22⋊D53—22no—
71C22×C22⋊D53—22no—
72C22×C22⋊D53—22no—
73C22×C22⋊D53—22no—
74C22×C22⋊D53C2×C414yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82#13133203—232no—
83C4×Dic106—232no—
84C2×C4⋊Dic53—22no—
85C2×C4⋊Dic53—22no—
86C2×C4⋊Dic53—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—22no—
90C2×#11719919—22no—
91C2×#11719919—22no—
92C2×#11719919—22no—
93C2×#11719919—22no—
94C2×#11719919—22no—
95C2×#11719919D414yes—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—41no—
102C2×C22⋊Dic53—41no—
103C2×C22⋊Dic53—41no—
104C2×C22⋊Dic53C2×C414yes—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—22no—
112C2×#11719921—22no—
113C2×#11719921—22no—
114C2×#11719921—22no—
115C2×#11719921—22no—
116C2×#11719921—22no—
117C2×#11719921—41no—
118C2×#11719921—41no—
119C2×#11719921—41no—
120C2×#11719921—41no—
121C2×#11719921C2×C414yes—
122C2×#11719921C2×C414yes—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53—22no—
131C2×C4×Dic53—22no—
132C2×C4×Dic53—22no—
133C2×C4×Dic53C2×C414yes—
134C2×C4×Dic53D414yes—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124—22no—
140#13133124—22no—
141#13133124—41no—
142#13133124—41no—
143#13133124—41no—
144C25×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—41no—
159C2×C22⋊C4×C53C2×C414yes—
160C2×C42×C53—22no—
161C2×C42×C53—22no—
162C2×C42×C53—22no—
163#95×C53—22no—
164#95×C53—22no—
165#95×C53—41no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
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×C53C22×C412yes—
181C24×C53C2411yescharacteristic
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—21no—
195C23×D53—21no—
196C23×D53C22×C412yes—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
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—21no—
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×C53C22×C412yes—
231C22×C4×C53C22×C412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
238C22×C4×C53#4112yes—
239C2×C22⋊D53—28no—
240C2×C22⋊D53—28no—
241C2×C22⋊D53—28no—
242C2×C22⋊D53—44no—
243C2×C22⋊D53—44no—
244C2×C22⋊D53—44no—
245C2×C22⋊D53—44no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
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×Dic53C22×C412yes—
282C22×Dic53C22×C412yes—
283C22×Dic53C22×C412yes—
284C22×Dic53C2×D412yes—
285C22×Dic53C2×D412yes—
286C22×Dic53C2×D412yes—
287C22×Dic53C2×D412yes—
288C22×Dic53C2×D412yes—
289C22×Dic53C2×D412yes—
290C22×Dic53C2×D412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53#4112yes—
293C22×Dic53#4112yes—
294C22×Dic53#4112yes—
295C2×Dic106—28no—
296C2×Dic106—28no—
297C2×Dic106—28no—
298C2×Dic106—28no—
299C2×Dic106—28no—
300C2×Dic106—28no—
301C2×Dic106C22⋊C4116yescomplemented
302C22⋊C4×C53—28no—
303C22⋊C4×C53—44no—
304C22⋊C4×C53—44no—
305C42×C53—28no—
306C22⋊Dic53—28no—
307C22⋊Dic53—44no—
308C22⋊Dic53—44no—
309#11719921—28no—
310#11719921—28no—
311#11719921—44no—
312#11719921—44no—
313#11719921—44no—
314#11719921—44no—
315C4⋊Dic53—28no—
316#11719919—28no—
317#11719919—28no—
318#11719919—44no—
319C4×Dic53—28no—
320C4×Dic53—28no—
321C4×Dic53—28no—
322C4×Dic53—44no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—41no—
331C23×C53—41no—
332C23×C53—41no—
333C23×C53—41no—
334C23×C53—41no—
335C23×C53—41no—
336C23×C53—41no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53C23×C411yescharacteristic
359C23×C53C22×D411yescharacteristic
360C23×C53C22×D411yescharacteristic
361C23×C53C22×D411yescharacteristic
362C23×C53C22×D411yescharacteristic
363C23×C53C2×#4111yescharacteristic
364C23×C53C2×#4111yescharacteristic
365C23×C53C2×#4111yescharacteristic
366C23×C53C2×#4111yescharacteristic
367C23×C53C2×#4111yescharacteristic
368C23×C53C2×#4111yescharacteristic
369C23×C53H(5,𝔽2)11yescharacteristic
370C23×C53H(5,𝔽2)11yescharacteristic
371C23×C532−1+411yescharacteristic
372C23×C532−1+411yescharacteristic
373C22×D53—22no—
374C22×D53—22no—
375C22×D53—22no—
376C22×D53—22no—
377C22×D53—22no—
378C22×D53—22no—
379C22×D53—22no—
380C22×D53—41no—
381C22×D53—41no—
382C22×D53—41no—
383C22×D53—41no—
384C22×D53—41no—
385C22×D53—41no—
386C22×D53—41no—
387C22×D53—41no—
388C22×D53—41no—
389C22×D53—41no—
390C22×D53—41no—
391C22×D53—41no—
392C22×D53—41no—
393C22×D53—41no—
394C22×D53—41no—
395C22×D53—41no—
396C22×D53—41no—
397C22×D53—41no—
398C22×D53—41no—
399C22×D53—41no—
400C22×D53—41no—
401C22×D53—41no—
402C22×D53—41no—
403C22×D53—41no—
404C22×D53—41no—
405C22×D53—41no—
406C22×D53—41no—
407C22×D53—41no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
441C2×C4×C53—41no—
442C2×C4×C53—41no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53C2×C22⋊C414yes—
449C2×C4×C53#12414yescomplemented
450C22⋊D53—416no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53C2×C22⋊C414yes—
493C2×Dic53C2×C22⋊C414yes—
494C2×Dic53C4×D414yes—
495C2×Dic53C4×D414yes—
496C2×Dic53#12014yes—
497C2×Dic53#12114yes—
498C2×Dic53#12114yes—
499C2×Dic53#12314yes—
500Dic106—232no—
501#14026—531nomaximal, Sylow
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—81no—
510C22×C53—81no—
511C22×C53—81no—
512C22×C53—81no—
513C22×C53—81no—
514C22×C53—81no—
515C22×C53—81no—
516C22×C53—81no—
517C22×C53C22×C22⋊C411yescharacteristic
518C22×C53C2×C4×D411yescharacteristic
519C22×C53C2×C4×D411yescharacteristic
520C22×C53C4×#4111yescharacteristic
521C22×C53C4×#4111yescharacteristic
522C22×C53#52011yescharacteristic
523C22×C53#52011yescharacteristic
524C22×C53C2×#12011yescharacteristic
525C22×C53C2×#12111yescharacteristic
526C22×C53C2×#12111yescharacteristic
527C22×C53C2×#12311yescharacteristic
528C22×C53C2×#12411yescharacteristic
529C22×C53#52911yescharacteristic
530C22×C53#52911yescharacteristic
531C22×C53#53211yescharacteristic
532C22×C53#53511yescharacteristic
533C22×C53#53611yescharacteristic
534C22×C53#54211yescharacteristic
535C22×C53#54211yescharacteristic
536C22×C53#54611yescharacteristic
537C22×C53#54611yescharacteristic
538C22×C53#54811yescharacteristic
539C22×C53#54811yescharacteristic
540C22×C53#54811yescharacteristic
541C22×C53#54811yescharacteristic
542C22×C53#54811yescharacteristic
543C22×C53#54811yescharacteristic
544C22×C53#55011yescharacteristic
545C22×C53#55011yescharacteristic
546C22×C53#55011yescharacteristic
547C22×C53#55011yescharacteristic
548C22×C53#55611yescharacteristic
549C22×C53#55611yescharacteristic
550C22×C53#55911yescharacteristic
551C22×C53#55911yescharacteristic
552C2×D53—42no—
553C2×D53—42no—
554C2×D53—42no—
555C2×D53—42no—
556C2×D53—42no—
557C2×D53—42no—
558C2×D53—42no—
559C2×D53—81no—
560C2×D53—81no—
561C2×D53—81no—
562C2×D53—81no—
563C2×D53—81no—
564C2×D53—81no—
565C2×D53—81no—
566C2×D53—81no—
567C4×C53—24no—
568C4×C53—24no—
569C4×C53—42no—
570C4×C53—42no—
571C4×C53—42no—
572C4×C53—81no—
573Dic53—24no—
574Dic53—42no—
575Dic53—42no—
576Dic53—42no—
577Dic53—42no—
578Dic53—81no—
579Dic53#38618yes—
580C22×#124—531no—
581C22×C4×Q8—531no—
582C2×#391—531no—
583C2×#390—531no—
584C2×#390—531no—
585#1439—531no—
586#1439—531no—
587#1439—531no—
588#1439—531no—
589#1437—531no—
590#1437—531no—
591#1437—531no—
592#1437D5311yescharacteristic, complemented
593C4⋊#95—531no—
594C4×#95—531no—
595C2×C53—82no—
596C2×C53C2×#38611yescharacteristic
597C2×C53C4×#12411yescharacteristic
598C2×C53#232611yescharacteristic
599C2×C53#234111yescharacteristic
600C2×C53#234111yescharacteristic
601C2×C53#236711yescharacteristic
602C2×C53#236711yescharacteristic
603C2×C53#242611yescharacteristic
604C2×C53#242611yescharacteristic
605C2×C53#243111yescharacteristic
606C2×C53#243611yescharacteristic
607C2×C53#244811yescharacteristic
608C2×C53#244811yescharacteristic
609C2×C53#254511yescharacteristic
610C2×C53#254811yescharacteristic
611D53—82no—
612C23×Q8—531no—
613C23×D4—531no—
614C2×#124—538no—
615C2×#124—1064no—
616C2×#124—1064no—
617C2×C4×Q8—1064no—
618C2×C4×Q8—1064no—
619C2×C4×Q8—1064no—
620C22×C4⋊C4—531no—
621C22×C4⋊C4—531no—
622C22×C4⋊C4—531no—
623C22×C4⋊C4—531no—
624C22×C22⋊C4—531no—
625C22×C22⋊C4—531no—
626C22×C22⋊C4—531no—
627C22×C22⋊C4—531no—
628C22×C22⋊C4—531no—
629C22×C22⋊C4—531no—
630C22×C22⋊C4—531no—
631C22×C22⋊C4—531no—
632C22×C22⋊C4—531no—
633C22×C22⋊C4C2×D5311yescharacteristic
634C22×C22⋊C4C2×D5311yescharacteristic
635C22×C22⋊C4C2×D5311yescharacteristic
636C22×C42—531no—
637C22×C42—531no—
638C22×C42—531no—
639C22×C42—531no—
640C22×C42C2×D5311yescharacteristic
641#391—1064no—
642#390—1064no—
643#390—1064no—
644C2×#95—531no—
645C2×#95—531no—
646C2×#95—531no—
647C2×#95—531no—
648C2×#95—531no—
649C2×#95—531no—
650C2×#95—531no—
651C2×#95—531no—
652C2×#95—531no—
653C2×#95C2×D5311yescharacteristic
654C2×#95C2×D5311yescharacteristic
655C2×#95C2×D5311yescharacteristic
656C53#1402611yescharacteristic, complemented, Sylow
657C25—531no—
658C25C22×D5311yescharacteristic
659C22×Q8—534no—
660C22×Q8—534no—
661C22×Q8—534no—
662C22×Q8—1062no—
663C22×Q8—1062no—
664C22×Q8—1062no—
665C22×Q8—1062no—
666C22×D4—534no—
667C22×D4—1062no—
668C22×D4—1062no—
669C22×D4—1062no—
670C22×D4—1062no—
671C22×D4—1062no—
672C22×D4—1062no—
673C23×C4—531no—
674C23×C4—531no—
675C23×C4—531no—
676C23×C4—531no—
677C23×C4—531no—
678C23×C4—531no—
679C23×C4—531no—
680C23×C4C22×D5311yescharacteristic
681C23×C4C22×D5311yescharacteristic
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686#124—10632no—
687C4×Q8—10632no—
688C2×C4⋊C4—534no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—1062no—
691C2×C4⋊C4—1062no—
692C2×C4⋊C4—1062no—
693C2×C4⋊C4—1062no—
694C2×C4⋊C4—1062no—
695C2×C4⋊C4—1062no—
696C2×C4⋊C4—1062no—
697C2×C4⋊C4—1062no—
698C2×C4⋊C4—1062no—
699C2×C4⋊C4—1062no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—534no—
709C2×C22⋊C4—534no—
710C2×C22⋊C4—534no—
711C2×C22⋊C4—1062no—
712C2×C22⋊C4—1062no—
713C2×C22⋊C4—1062no—
714C2×C22⋊C4—1062no—
715C2×C22⋊C4—1062no—
716C2×C22⋊C4—1062no—
717C2×C22⋊C4—1062no—
718C2×C22⋊C4—1062no—
719C2×C22⋊C4—1062no—
720C2×C22⋊C4—1062no—
721C2×C22⋊C4—1062no—
722C2×C22⋊C4—1062no—
723C2×C22⋊C4—1062no—
724C2×C22⋊C4—1062no—
725C2×C22⋊C4—1062no—
726C2×C22⋊C4—1062no—
727C2×C22⋊C4—1062no—
728C2×C22⋊C4—2121no—
729C2×C22⋊C4—2121no—
730C2×C22⋊C4—2121no—
731C2×C22⋊C4—2121no—
732C2×C22⋊C4—2121no—
733C2×C22⋊C4—2121no—
734C2×C22⋊C4—2121no—
735C2×C22⋊C4C4×D5314yes—
736C2×C42—22no—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—534no—
740C2×C42—534no—
741C2×C42—1062no—
742C2×C42—1062no—
743C2×C42—1062no—
744C2×C42—1062no—
745C2×C42—1062no—
746C2×C42—1062no—
747C2×C42—1062no—
748C2×C42—1062no—
749C2×C42—1062no—
750C2×C42—1062no—
751#95—22no—
752#95—22no—
753#95—41no—
754#95—1062no—
755#95—1062no—
756#95—1062no—
757#95—1062no—
758#95—1062no—
759#95—1062no—
760#95—2121no—
761#95—2121no—
762#95—2121no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—532no—
778C24—1061no—
779C24—1061no—
780C24—1061no—
781C24—1061no—
782C24—1061no—
783C24—1061no—
784C24—1061no—
785C24—1061no—
786C24—1061no—
787C24—1061no—
788C24—1061no—
789C24—1061no—
790C24—1061no—
791C24—1061no—
792C24C2×C4×D5312yes—
793C24C23×D5311yescharacteristic
794C2×Q8—5316no—
795C2×Q8—1068no—
796C2×Q8—1068no—
797C2×Q8—1068no—
798C2×Q8—1068no—
799C2×Q8—1068no—
800C2×Q8—1068no—
801C2×D4—1068no—
802C2×D4—1068no—
803C2×D4—1068no—
804C2×D4—2124no—
805C2×D4—2124no—
806C2×D4—2124no—
807C2×D4—2124no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
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—21no—
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—532no—
842C22×C4—532no—
843C22×C4—532no—
844C22×C4—532no—
845C22×C4—532no—
846C22×C4—532no—
847C22×C4—532no—
848C22×C4—532no—
849C22×C4—532no—
850C22×C4—532no—
851C22×C4—532no—
852C22×C4—532no—
853C22×C4—532no—
854C22×C4—532no—
855C22×C4—1061no—
856C22×C4—1061no—
857C22×C4—1061no—
858C22×C4—1061no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
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×C4C2×C4×D5312yes—
891C22×C4C2×C4×D5312yes—
892C22×C4#1171994512yes—
893C22×C4#1171994512yes—
894C22×C4D4×D5312yes—
895C22×C4D4×D5312yes—
896C22×C4D4×D5312yes—
897C22×C4D4×D5312yes—
898C22×C4#1171994712yes—
899C4⋊C4—1068no—
900C4⋊C4—1068no—
901C4⋊C4—1068no—
902C4⋊C4—2124no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—1068no—
907C22⋊C4—1068no—
908C22⋊C4—1068no—
909C22⋊C4—2124no—
910C22⋊C4—2124no—
911C22⋊C4—2124no—
912C22⋊C4—2124no—
913C22⋊C4—2124no—
914C22⋊C4—2124no—
915C42—28no—
916C42—1068no—
917C42—1068no—
918C42—1068no—
919C42—2124no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—1062no—
956C23—1062no—
957C23—1062no—
958C23—1062no—
959C23—1062no—
960C23—1062no—
961C23—1062no—
962C23—2121no—
963C23—2121no—
964C23—2121no—
965C23—2121no—
966C23—2121no—
967C23—2121no—
968C23—2121no—
969C23—2121no—
970C23—2121no—
971C23—2121no—
972C23—2121no—
973C23—2121no—
974C23—2121no—
975C23—2121no—
976C23—2121no—
977C23—2121no—
978C23—2121no—
979C23—2121no—
980C23—2121no—
981C23—2121no—
982C23—2121no—
983C23—2121no—
984C23—2121no—
985C23—2121no—
986C23—2121no—
987C23—2121no—
988C23—2121no—
989C23—2121no—
990C23C22×C4×D5311yescharacteristic
991C23C2×D4×D5311yescharacteristic
992C23C2×D4×D5311yescharacteristic
993C23C2×D4×D5311yescharacteristic
994C23C2×D4×D5311yescharacteristic
995C23#41×D5311yescharacteristic
996C23#41×D5311yescharacteristic
997C23#41×D5311yescharacteristic
998C23C2×#1171994711yescharacteristic
999C23C2×#1171994511yescharacteristic
1000C23C2×#1171994511yescharacteristic
1001C23#1313326211yescharacteristic
1002C23#1313326311yescharacteristic
1003C23#1313326411yescharacteristic
1004C23#1313326411yescharacteristic
1005Q8—10632no—
1006D4—21216no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—534no—
1048C2×C4—534no—
1049C2×C4—534no—
1050C2×C4—534no—
1051C2×C4—534no—
1052C2×C4—534no—
1053C2×C4—534no—
1054C2×C4—534no—
1055C2×C4—1062no—
1056C2×C4—1062no—
1057C2×C4—1062no—
1058C2×C4—1062no—
1059C2×C4—1062no—
1060C2×C4—1062no—
1061C2×C4—1062no—
1062C2×C4—1062no—
1063C2×C4—1062no—
1064C2×C4—1062no—
1065C2×C4—1062no—
1066C2×C4—1062no—
1067C2×C4—1062no—
1068C2×C4—1062no—
1069C2×C4—1062no—
1070C2×C4—1062no—
1071C2×C4—1062no—
1072C2×C4—1062no—
1073C2×C4—2121no—
1074C2×C4—2121no—
1075C2×C4—2121no—
1076C2×C4—2121no—
1077C2×C4—2121no—
1078C2×C4—2121no—
1079C2×C4—2121no—
1080C2×C4—2121no—
1081C2×C4—2121no—
1082C2×C4—2121no—
1083C2×C4—2121no—
1084C2×C4—2121no—
1085C2×C4—2121no—
1086C2×C4—2121no—
1087C2×C4—2121no—
1088C2×C4—2121no—
1089C2×C4—2121no—
1090C2×C4—2121no—
1091C2×C4—2121no—
1092C2×C4—2121no—
1093C2×C4—2121no—
1094C2×C4—2121no—
1095C2×C4—2121no—
1096C2×C4C22⋊C4×D5314yes—
1097C2×C4#1313320314yescomplemented
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—4241no—
1114C22—4241no—
1115C22—4241no—
1116C22—4241no—
1117C22—4241no—
1118C22—4241no—
1119C22—4241no—
1120C22—4241no—
1121C22—2122no—
1122C22—2122no—
1123C22—2122no—
1124C22—2122no—
1125C22—2122no—
1126C22—2122no—
1127C22—2122no—
1128C22C2×C22⋊C4×D5311yescharacteristic
1129C22C4×D4×D5311yescharacteristic
1130C22C4×D4×D5311yescharacteristic
1131C22C4×#1171994711yescharacteristic
1132C22C4×#1171994511yescharacteristic
1133C22#1681110211yescharacteristic
1134C22#1681110311yescharacteristic
1135C22#120×D5311yescharacteristic
1136C22#121×D5311yescharacteristic
1137C22#121×D5311yescharacteristic
1138C22#123×D5311yescharacteristic
1139C22C2×#1313320311yescharacteristic
1140C22#1681115111yescharacteristic
1141C22#1681115311yescharacteristic
1142C22#1681117011yescharacteristic
1143C22#1681118911yescharacteristic
1144C22#1681119511yescharacteristic
1145C22#1681123711yescharacteristic
1146C22#1681123911yescharacteristic
1147C22#1681126311yescharacteristic
1148C22#1681126511yescharacteristic
1149C22#1681127911yescharacteristic
1150C22#1681127911yescharacteristic
1151C22#1681128111yescharacteristic
1152C22#1681128211yescharacteristic
1153C22#1681128211yescharacteristic
1154C22#1681128211yescharacteristic
1155C22#1681129111yescharacteristic
1156C22#1681129311yescharacteristic
1157C22#1681129411yescharacteristic
1158C22#1681129411yescharacteristic
1159C22#1681134011yescharacteristic
1160C22#1681134111yescharacteristic
1161C22#1681135511yescharacteristic
1162C22#1681135611yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—538no—
1170C4—1064no—
1171C4—4241no—
1172C4—2122no—
1173C4—2122no—
1174C4—2122no—
1175C4—2122no—
1176C2—82no—
1177C2—4242no—
1178C2#386×D5311yescharacteristic
1179C2C4×#1313320311yescharacteristic
1180C2#2027742411yescharacteristic
1181C2#2027755411yescharacteristic
1182C2#2027755511yescharacteristic
1183C2#2027778711yescharacteristic
1184C2#2027778911yescharacteristic
1185C2#2027827811yescharacteristic
1186C2#2027828011yescharacteristic
1187C2#2027833211yescharacteristic
1188C2#2027837111yescharacteristic
1189C2#2027851011yescharacteristic
1190C2#2027851211yescharacteristic
1191C2#2027969311yescharacteristic
1192C2#2027971611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53#14026
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic106C2semidirect
3. C2×#16810527C2semidirect
6. #20272961C2semidirect
7. #20272960C2semidirect
8. #20272959C2semidirect
9. #20272958C2semidirect
10. #20272953C2semidirect
11. #20272952C2semidirect
12. #20272951C2semidirect
13. #20272943C2semidirect
14. #95×Dic53C2semidirect
15. C53×#1437C2semidirect
20. C2×#13133203C4semidirect
301. C2×Dic106C22⋊C4semidirect
449. C2×C4×C53#124semidirect
592. #1437D53semidirect
656. C53#14026semidirect
1097. C2×C4#13133203semidirect

Maximal subgroups

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

subgroupindex
C22×#131332032
C22×C4×Dic1062
C2×#168105272
C2×#168105232
#202729612
#202729602
#202729592
#202729582
#202729532
#202729522
#202729512
#202729432
#95×Dic532
C53×#14372
#1402653