Finite Group Databasebeta

← #27305491

Subgroups — #27305491

Order 13568.

4254 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719921C211yesmaximal, characteristic
2C22×C22⋊C4×D53C211yesmaximal, characteristic
3C2×#16810478C211yesmaximal, characteristic
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
6C2×#16810470C212yesmaximal, complemented
7#20272951C212yesmaximal, complemented
8#20272951C212yesmaximal, complemented
9#20272937C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2212yes—
15C22×C22⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53C2211yescharacteristic
17C22×#11719921—28no—
18C22×#11719921C418yescomplemented
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2212yes—
25C22×#11719921C2211yescharacteristic
26C2×C22⋊C4×D53—24no—
27C2×C22⋊C4×D53—24no—
28C2×C22⋊C4×D53C418yescomplemented
29C22×C4×Dic53C2212yescomplemented
30C22×C4×Dic53C2212yescomplemented
31#16810478C418yescomplemented
32C22⋊C4×Dic53—24no—
33C4×C22⋊Dic53—24no—
34#16810470—28no—
35C2×#13133124C2212yescomplemented
36C2×#13133124C2212yescomplemented
37C2×#13133124C2212yescomplemented
38C2×#13133124C2212yescomplemented
39C24×C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C2×#95×C53C2212yescomplemented
43C2×#95×C53C2212yescomplemented
44C24×D53—22no—
45C24×D53—22no—
46C24×D53—22no—
47C24×D53—22no—
48C24×D53—24no—
49C24×D53—24no—
50C24×D53—42no—
51C24×D53—42no—
52C24×D53C2×C414yes—
53C24×D53C2×C414yes—
54C24×D53C2×C414yes—
55C24×D53C2311yescharacteristic
56C24×D53C2311yescharacteristic
57C23×Dic53—22no—
58C23×Dic53—22no—
59C23×Dic53—24no—
60C23×Dic53—42no—
61C23×Dic53C2×C414yescomplemented
62C23×Dic53C2312yes—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2312yes—
66C22×C4×D53—24no—
67C22×C4×D53—24no—
68C22×C4×D53—24no—
69C22×C4×D53—24no—
70C22×C4×D53—42no—
71C22×C4×D53—42no—
72C22×C4×D53C2×C418yescomplemented
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53C2×C414yes—
76C2×C22⋊Dic53C2×C414yescomplemented
77C2×C22⋊Dic53D414yes—
78C2×C22⋊Dic53D414yes—
79C2×#11719921—232no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—24no—
84C2×#11719921—24no—
85C2×#11719921—24no—
86C2×#11719921—24no—
87C2×#11719921—42no—
88C2×#11719921—42no—
89C2×#11719921C2×C414yes—
90C2×#11719921C2×C414yes—
91C2×#11719921C2×C418yescomplemented
92C2×#11719921C2×C414yescomplemented
93C2×#11719921C2×C414yescomplemented
94C2×#11719921C2×C418yescomplemented
95C2×#11719921C2×C418yescomplemented
96C2×#11719921D418yes—
97C22⋊C4×D53—232no—
98C2×C4×Dic53—24no—
99C2×C4×Dic53—24no—
100C2×C4×Dic53—24no—
101C2×C4×Dic53—24no—
102C2×C4×Dic53—42no—
103C2×C4×Dic53—42no—
104#13133124—24no—
105#13133124—24no—
106#13133124—24no—
107#13133124—42no—
108C25×C53C2311yescharacteristic
109C23×C4×C53—22no—
110C23×C4×C53—22no—
111C23×C4×C53—24no—
112C23×C4×C53—42no—
113C23×C4×C53C2×C414yescomplemented
114C23×C4×C53C2312yes—
115C23×C4×C53C2312yes—
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53C2×C414yes—
123C2×C22⋊C4×C53C2×C414yescomplemented
124#95×C53—24no—
125#95×C53—42no—
126C24×C53—22no—
127C24×C53—22no—
128C24×C53—22no—
129C24×C53—22no—
130C24×C53C22×C412yes—
131C24×C53C22×C412yes—
132C24×C53C22×C412yes—
133C24×C53C2×D412yes—
134C24×C53C2×D412yes—
135C24×C53#4112yes—
136C24×C53#4112yes—
137C24×C53C2411yescharacteristic
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—22no—
143C23×D53—22no—
144C23×D53—28no—
145C23×D53—28no—
146C23×D53—28no—
147C23×D53—28no—
148C23×D53—28no—
149C23×D53—28no—
150C23×D53—22no—
151C23×D53—21no—
152C23×D53—21no—
153C23×D53—22no—
154C23×D53—21no—
155C23×D53—21no—
156C23×D53—22no—
157C23×D53—22no—
158C23×D53—28no—
159C23×D53—28no—
160C23×D53—216no—
161C23×D53—216no—
162C23×D53—48no—
163C23×D53—44no—
164C23×D53—44no—
165C23×D53—48no—
166C23×D53—48no—
167C23×D53—48no—
168C23×D53—48no—
169C23×D53—48no—
170C23×D53—48no—
171C23×D53—48no—
172C23×D53—48no—
173C23×D53—48no—
174C23×D53C42116yescomplemented
175C23×D53C22×C412yes—
176C23×D53C22×C412yes—
177C23×D53C22×C412yes—
178C23×D53C22×C412yes—
179C23×D53C22×C412yes—
180C23×D53C22×C412yes—
181C23×D53C2×D414yes—
182C23×D53#4114yes—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—22no—
186C22×C4×C53—28no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—21no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—28no—
204C22×C4×C53—44no—
205C22×C4×C53—48no—
206C22×C4×C53—48no—
207C22×C4×C53C22×C414yes—
208C22×C4×C53C22×C414yes—
209C22×C4×C53C22×C412yes—
210C22×C4×C53C22×C412yes—
211C22×C4×C53C2×D414yes—
212C22×Dic53—22no—
213C22×Dic53—21no—
214C22×Dic53—22no—
215C22×Dic53—21no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—28no—
220C22×Dic53—21no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53—22no—
224C22×Dic53—22no—
225C22×Dic53—22no—
226C22×Dic53—21no—
227C22×Dic53—22no—
228C22×Dic53—22no—
229C22×Dic53—22no—
230C22×Dic53—28no—
231C22×Dic53—44no—
232C22×Dic53—48no—
233C22×Dic53—48no—
234C22×Dic53C22×C412yes—
235C22×Dic53C22×C414yes—
236C22×Dic53C22×C412yes—
237C22×Dic53C22×C414yes—
238C22×Dic53C2×D414yes—
239C22×Dic53C2×D414yes—
240C22×Dic53C2×D414yes—
241C2×C4×D53—216no—
242C2×C4×D53—216no—
243C2×C4×D53—48no—
244C2×C4×D53—48no—
245C2×C4×D53—48no—
246C2×C4×D53—48no—
247C2×C4×D53—48no—
248C22⋊C4×C53—28no—
249C22⋊C4×C53—28no—
250C22⋊Dic53—28no—
251C22⋊Dic53C22⋊C4116yescomplemented
252#11719921—28no—
253#11719921—216no—
254#11719921—28no—
255#11719921—216no—
256#11719921—28no—
257#11719921—48no—
258#11719921C22⋊C4116yescomplemented
259C4×Dic53—48no—
260C4×Dic53—48no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—24no—
264C23×C53—24no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—24no—
268C23×C53—24no—
269C23×C53—24no—
270C23×C53—24no—
271C23×C53—24no—
272C23×C53—24no—
273C23×C53—24no—
274C23×C53—24no—
275C23×C53—24no—
276C23×C53—24no—
277C23×C53C2×C4214yes—
278C23×C53C2×C22⋊C414yes—
279C23×C53#11714yes—
280C23×C53C4×D414yes—
281C23×C53C4×D414yes—
282C23×C53C4×D414yes—
283C23×C53C4×D414yes—
284C23×C53C23×C411yescharacteristic
285C23×C53C23×C411yescharacteristic
286C23×C53C23×C411yescharacteristic
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C23×C53C22×D411yescharacteristic
290C23×C53C2×#4112yes—
291C23×C53C2×#4111yescharacteristic
292C23×C53C2×#4111yescharacteristic
293C23×C53H(5,𝔽2)12yes—
294C23×C53H(5,𝔽2)12yes—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—24no—
302C22×D53—24no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—24no—
306C22×D53—24no—
307C22×D53—24no—
308C22×D53—24no—
309C22×D53—24no—
310C22×D53—24no—
311C22×D53—24no—
312C22×D53—24no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—24no—
318C22×D53—24no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—24no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—24no—
327C22×D53—232no—
328C22×D53—232no—
329C22×D53—416no—
330C22×D53—432no—
331C22×D53—416no—
332C22×D53—416no—
333C22×D53—416no—
334C22×D53—416no—
335C22×D53—432no—
336C22×D53—432no—
337C22×D53—432no—
338C22×D53—42no—
339C22×D53—42no—
340C22×D53—42no—
341C22×D53—42no—
342C22×D53—42no—
343C22×D53—42no—
344C22×D53—42no—
345C22×D53—42no—
346C22×D53C2×C4214yes—
347C22×D53C2×C4214yes—
348C22×D53C2×C22⋊C414yes—
349C22×D53#11714yes—
350C22×D53C4×D418yes—
351C22×D53C4×D418yes—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—24no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—24no—
359C2×C4×C53—22no—
360C2×C4×C53—24no—
361C2×C4×C53—24no—
362C2×C4×C53—24no—
363C2×C4×C53—22no—
364C2×C4×C53—24no—
365C2×C4×C53—416no—
366C2×C4×C53—42no—
367C2×C4×C53—42no—
368C2×C4×C53—42no—
369C2×C4×C53—42no—
370C2×C4×C53—42no—
371C2×C4×C53—42no—
372C2×C4×C53—42no—
373C2×C4×C53—42no—
374C2×C4×C53—42no—
375C2×C4×C53—42no—
376C2×C4×C53C2×C22⋊C414yescomplemented
377C2×Dic53—24no—
378C2×Dic53—22no—
379C2×Dic53—24no—
380C2×Dic53—22no—
381C2×Dic53—24no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53—24no—
385C2×Dic53—24no—
386C2×Dic53—24no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—24no—
390C2×Dic53—24no—
391C2×Dic53—22no—
392C2×Dic53—24no—
393C2×Dic53—416no—
394C2×Dic53—42no—
395C2×Dic53—42no—
396C2×Dic53—42no—
397C2×Dic53—42no—
398C2×Dic53—42no—
399C2×Dic53—42no—
400C2×Dic53C2×C22⋊C418yescomplemented
401C2×Dic53C2×C22⋊C414yescomplemented
402C4×D53—432no—
403C22⋊C42—531nomaximal, Sylow
404C22×C53—24no—
405C22×C53—24no—
406C22×C53—28no—
407C22×C53—28no—
408C22×C53—24no—
409C22×C53—24no—
410C22×C53—28no—
411C22×C53—28no—
412C22×C53—24no—
413C22×C53—24no—
414C22×C53C4×C22⋊C418yescomplemented
415C22×C53C22×C4211yescharacteristic
416C22×C53C22×C22⋊C411yescharacteristic
417C22×C53C22×C22⋊C411yescharacteristic
418C22×C53C2×#11711yescharacteristic
419C22×C53C2×#11711yescharacteristic
420C22×C53C2×C4×D412yes—
421C22×C53C2×C4×D412yes—
422C22×C53C2×C4×D411yescharacteristic
423C22×C53C2×C4×D411yescharacteristic
424C22×C53C2×C4×D411yescharacteristic
425C22×C53C2×C4×D411yescharacteristic
426C22×C53#51812yes—
427C22×C53#51812yes—
428C22×C53#51811yescharacteristic
429C22×C53#51811yescharacteristic
430C22×C53D4212yes—
431C22×C53D4212yes—
432C22×C53#54612yes—
433C22×C53#54612yes—
434C22×C53#54612yes—
435C22×C53#54612yes—
436C22×C53#55112yes—
437C22×C53#55112yes—
438C2×D53—28no—
439C2×D53—24no—
440C2×D53—24no—
441C2×D53—24no—
442C2×D53—24no—
443C2×D53—28no—
444C2×D53—28no—
445C2×D53—28no—
446C2×D53—24no—
447C2×D53—24no—
448C2×D53—24no—
449C2×D53—24no—
450C2×D53—24no—
451C2×D53—464no—
452C2×D53—42no—
453C2×D53—44no—
454C2×D53—42no—
455C2×D53—42no—
456C2×D53—42no—
457C2×D53—44no—
458C2×D53—44no—
459C2×D53—44no—
460C2×D53C4×C22⋊C418yescomplemented
461C4×C53—24no—
462C4×C53—44no—
463C4×C53—42no—
464C4×C53—44no—
465Dic53—28no—
466Dic53—24no—
467Dic53—42no—
468Dic53—44no—
469C23×C22⋊C4—531no—
470C23×C22⋊C4—531no—
471C2×#379—531no—
472C2×C4×C22⋊C4—532no—
473C2×C4×C22⋊C4—531no—
474C2×C4×C22⋊C4—531no—
475#1437—532no—
476#1437—532no—
477C22⋊#95—532no—
478C22⋊#95—531no—
479C22⋊#95D5311yescharacteristic, complemented
480C2×C53—28no—
481C2×C53C2×C4×C22⋊C411yescharacteristic
482C2×C53C2×C4×C22⋊C411yescharacteristic
483C2×C53#227311yescharacteristic
484C2×C53D4×C22⋊C411yescharacteristic
485C2×C53D4×C22⋊C412yes—
486C2×C53D4×C22⋊C411yescharacteristic
487C2×C53#234211yescharacteristic
488C2×C53#234211yescharacteristic
489C2×C53#234212yes—
490C2×C53#235812yes—
491C2×C53#235812yes—
492D53—28no—
493D53—44no—
494C26—531no—
495C24×C4—531no—
496C24×C4—532no—
497C24×C4C2×D5311yescharacteristic
498C22×C22⋊C4—531no—
499C22×C22⋊C4—531no—
500C22×C22⋊C4—531no—
501C22×C22⋊C4—538no—
502C22×C22⋊C4—531no—
503C22×C22⋊C4—531no—
504C22×C22⋊C4—532no—
505C22×C22⋊C4—531no—
506C22×C22⋊C4—532no—
507C22×C22⋊C4—532no—
508C22×C22⋊C4—538no—
509C22×C22⋊C4—1064no—
510C22×C22⋊C4—1064no—
511C22×C22⋊C4—1068no—
512C22×C22⋊C4C2×D5311yescharacteristic
513C22×C22⋊C4C2×D5311yescharacteristic
514C22×C42—532no—
515C22×C42—532no—
516#379—538no—
517C4×C22⋊C4—1068no—
518C4×C22⋊C4—1064no—
519C4×C22⋊C4—1064no—
520C2×#95—532no—
521C2×#95—532no—
522C2×#95—532no—
523C2×#95—532no—
524C2×#95C2×D5312yescomplemented
525C2×#95C2×D5312yescomplemented
526C53C22⋊C4211yescharacteristic, complemented, Sylow
527C25—531no—
528C25—531no—
529C25—534no—
530C25—534no—
531C25—534no—
532C25—1064no—
533C25—1064no—
534C25—1062no—
535C25—1062no—
536C25—1062no—
537C25—1062no—
538C25—2122no—
539C25—2122no—
540C25C22×D5311yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—532no—
546C23×C4—531no—
547C23×C4—532no—
548C23×C4—531no—
549C23×C4—534no—
550C23×C4—538no—
551C23×C4—1064no—
552C23×C4—1064no—
553C23×C4—1064no—
554C23×C4—1064no—
555C23×C4—1064no—
556C23×C4—1062no—
557C23×C4—1062no—
558C23×C4—2122no—
559C23×C4—2122no—
560C23×C4—2122no—
561C23×C4C4×D5314yescomplemented
562C23×C4C22×D5312yes—
563C23×C4C22×D5311yescharacteristic
564C23×C4C22×D5312yes—
565C23×C4C22×D5311yescharacteristic
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—534no—
571C2×C22⋊C4—534no—
572C2×C22⋊C4—534no—
573C2×C22⋊C4—534no—
574C2×C22⋊C4—538no—
575C2×C22⋊C4—534no—
576C2×C22⋊C4—534no—
577C2×C22⋊C4—534no—
578C2×C22⋊C4—538no—
579C2×C22⋊C4—534no—
580C2×C22⋊C4—538no—
581C2×C22⋊C4—538no—
582C2×C22⋊C4—10632no—
583C2×C22⋊C4—10632no—
584C2×C22⋊C4—1064no—
585C2×C22⋊C4—1064no—
586C2×C22⋊C4—1064no—
587C2×C22⋊C4—1064no—
588C2×C22⋊C4—1064no—
589C2×C22⋊C4—1064no—
590C2×C22⋊C4—1062no—
591C2×C22⋊C4—1062no—
592C2×C22⋊C4—1064no—
593C2×C22⋊C4—2122no—
594C2×C22⋊C4—2122no—
595C2×C22⋊C4C4×D5314yes—
596C2×C22⋊C4C4×D5314yescomplemented
597C2×C42—1064no—
598C2×C42—1064no—
599C2×C42—1064no—
600C2×C42—1064no—
601C2×C42—2122no—
602C2×C42—2122no—
603#95—24no—
604#95—42no—
605#95—1064no—
606#95—1064no—
607#95—1064no—
608#95—2122no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—532no—
614C24—532no—
615C24—532no—
616C24—534no—
617C24—534no—
618C24—532no—
619C24—532no—
620C24—532no—
621C24—5316no—
622C24—1068no—
623C24—1068no—
624C24—10616no—
625C24—10616no—
626C24—1061no—
627C24—1061no—
628C24—1061no—
629C24—1061no—
630C24—1062no—
631C24—1062no—
632C24—1068no—
633C24—1068no—
634C24—1068no—
635C24—1068no—
636C24—1068no—
637C24—1068no—
638C24—1062no—
639C24—1061no—
640C24—1061no—
641C24—1062no—
642C24—1061no—
643C24—1061no—
644C24—1062no—
645C24—1062no—
646C24—2128no—
647C24—2128no—
648C24—2124no—
649C24—2124no—
650C24—2128no—
651C24—2128no—
652C24—2128no—
653C24—2128no—
654C24—2128no—
655C24—2128no—
656C24—2128no—
657C24—2128no—
658C24C2×C4×D5312yes—
659C24C2×C4×D5312yes—
660C24C2×C4×D5312yes—
661C24D4×D5312yes—
662C24D4×D5312yes—
663C24#1171994712yes—
664C24#1171994912yes—
665C24C23×D5311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—28no—
687C22×C4—44no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—534no—
691C22×C4—532no—
692C22×C4—534no—
693C22×C4—534no—
694C22×C4—534no—
695C22×C4—534no—
696C22×C4—532no—
697C22×C4—10616no—
698C22×C4—10616no—
699C22×C4—1068no—
700C22×C4—1062no—
701C22×C4—1061no—
702C22×C4—1062no—
703C22×C4—1061no—
704C22×C4—1062no—
705C22×C4—1062no—
706C22×C4—1062no—
707C22×C4—1068no—
708C22×C4—1061no—
709C22×C4—1062no—
710C22×C4—1062no—
711C22×C4—1062no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1061no—
715C22×C4—1062no—
716C22×C4—1062no—
717C22×C4—1062no—
718C22×C4—2128no—
719C22×C4—2128no—
720C22×C4—2128no—
721C22×C4—2128no—
722C22×C4—2128no—
723C22×C4—2124no—
724C22×C4—2128no—
725C22×C4—2128no—
726C22×C4C2×C4×D5314yes—
727C22×C4C2×C4×D5312yes—
728C22×C4C2×C4×D5314yes—
729C22×C4C2×C4×D5312yes—
730C22×C4D4×D5314yes—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—5316no—
734C22⋊C4—5316no—
735C22⋊C4—10616no—
736C22⋊C4—1068no—
737C22⋊C4—1068no—
738C22⋊C4—10616no—
739C22⋊C4—1068no—
740C22⋊C4—1068no—
741C22⋊C4—2128no—
742C42—2128no—
743C42—2128no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—22no—
749C23—22no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—22no—
755C23—22no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—534no—
761C23—534no—
762C23—534no—
763C23—538no—
764C23—538no—
765C23—534no—
766C23—10632no—
767C23—1064no—
768C23—1064no—
769C23—1064no—
770C23—1064no—
771C23—1062no—
772C23—1062no—
773C23—1062no—
774C23—1062no—
775C23—1062no—
776C23—1062no—
777C23—1064no—
778C23—1064no—
779C23—1062no—
780C23—1062no—
781C23—1064no—
782C23—1064no—
783C23—1064no—
784C23—1064no—
785C23—1062no—
786C23—1062no—
787C23—1062no—
788C23—1062no—
789C23—1064no—
790C23—1064no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—1062no—
795C23—1064no—
796C23—1064no—
797C23—1062no—
798C23—1062no—
799C23—10632no—
800C23—21216no—
801C23—21216no—
802C23—21232no—
803C23—21216no—
804C23—21216no—
805C23—21216no—
806C23—21232no—
807C23—21232no—
808C23—21232no—
809C23—2122no—
810C23—2122no—
811C23—2122no—
812C23—2122no—
813C23—2122no—
814C23—2122no—
815C23—2122no—
816C23—2122no—
817C23C42×D5314yes—
818C23C22⋊C4×D5314yes—
819C23#1313317514yes—
820C23#1313317714yes—
821C23#1313317714yes—
822C23#1313317914yes—
823C23#1313317914yes—
824C23C22×C4×D5311yescharacteristic
825C23C22×C4×D5311yescharacteristic
826C23C22×C4×D5311yescharacteristic
827C23C2×D4×D5312yes—
828C23C2×D4×D5311yescharacteristic
829C23C2×D4×D5311yescharacteristic
830C23#41×D5312yes—
831C23C2×#1171994711yescharacteristic
832C23C2×#1171994911yescharacteristic
833C23#1313326212yes—
834C23#1313326312yes—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—538no—
860C2×C4—534no—
861C2×C4—1064no—
862C2×C4—1064no—
863C2×C4—1064no—
864C2×C4—1062no—
865C2×C4—1064no—
866C2×C4—1062no—
867C2×C4—1064no—
868C2×C4—1064no—
869C2×C4—1064no—
870C2×C4—1064no—
871C2×C4—1062no—
872C2×C4—1064no—
873C2×C4—1064no—
874C2×C4—1062no—
875C2×C4—1064no—
876C2×C4—1062no—
877C2×C4—21232no—
878C2×C4—21216no—
879C2×C4—2122no—
880C2×C4—2122no—
881C2×C4—2122no—
882C2×C4—2122no—
883C2×C4—2122no—
884C2×C4—2122no—
885C2×C4C22⋊C4×D5314yescomplemented
886C22—24no—
887C22—28no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28no—
893C22—24no—
894C22—28no—
895C22—28no—
896C22—538no—
897C22—1064no—
898C22—1068no—
899C22—1064no—
900C22—1064no—
901C22—1064no—
902C22—1064no—
903C22—1068no—
904C22—1064no—
905C22—1068no—
906C22—1068no—
907C22—1064no—
908C22—1064no—
909C22—1064no—
910C22—21264no—
911C22—2122no—
912C22—2124no—
913C22—2122no—
914C22—2122no—
915C22—2122no—
916C22—2124no—
917C22—2124no—
918C22—2124no—
919C22#1681047018yescomplemented
920C22C2×C42×D5311yescharacteristic
921C22C2×C22⋊C4×D5311yescharacteristic
922C22C2×C22⋊C4×D5311yescharacteristic
923C22#117×D5311yescharacteristic
924C22C2×#1313317511yescharacteristic
925C22C4×D4×D5312yes—
926C22C4×D4×D5312yes—
927C22C2×#1313317711yescharacteristic
928C22C2×#1313317711yescharacteristic
929C22C2×#1313317911yescharacteristic
930C22C2×#1313317911yescharacteristic
931C22#1681109512yes—
932C22#1681109512yes—
933C22#1681109611yescharacteristic
934C22#1681109711yescharacteristic
935C22#1681125512yes—
936C22#1681125712yes—
937C22#1681126012yes—
938C22#1681126212yes—
939C22#1681126412yes—
940C22#1681126512yes—
941C22#1681129612yes—
942C22#1681130012yes—
943C4—24no—
944C4—42no—
945C4—44no—
946C4—44no—
947C4—1068no—
948C4—1064no—
949C4—2122no—
950C4—2124no—
951C2—28no—
952C2—1068no—
953C2—2124no—
954C2C4×C22⋊C4×D5311yescharacteristic
955C2C2×#1681047011yescharacteristic
956C2#2027706711yescharacteristic
957C2#2027753111yescharacteristic
958C2#2027753312yes—
959C2#2027753511yescharacteristic
960C2#2027755711yescharacteristic
961C2#2027756111yescharacteristic
962C2#2027756212yes—
963C2#2027769112yes—
964C2#2027769512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC25×D53C22
hypercenterC22⋊#95D53
hypocenterC53C22⋊C42
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic53C2semidirect
5. C2×C4×C22⋊Dic53C2semidirect
6. C2×#16810470C2semidirect
7. #20272951C2semidirect
8. #20272951C2semidirect
9. #20272937C2semidirect
10. #20272936C2semidirect
11. C53×C22⋊#95C2semidirect
18. C22×#11719921C4semidirect
28. C2×C22⋊C4×D53C4semidirect
29. C22×C4×Dic53C22semidirect
30. C22×C4×Dic53C22semidirect
31. #16810478C4semidirect
35. C2×#13133124C22semidirect
36. C2×#13133124C22semidirect
37. C2×#13133124C22semidirect
38. C2×#13133124C22semidirect
42. C2×#95×C53C22semidirect
43. C2×#95×C53C22semidirect
61. C23×Dic53C2×C4semidirect
72. C22×C4×D53C2×C4semidirect
76. C2×C22⋊Dic53C2×C4semidirect
91. C2×#11719921C2×C4semidirect
92. C2×#11719921C2×C4semidirect
93. C2×#11719921C2×C4semidirect
94. C2×#11719921C2×C4semidirect
95. C2×#11719921C2×C4semidirect
113. C23×C4×C53C2×C4semidirect
123. C2×C22⋊C4×C53C2×C4semidirect
174. C23×D53C42semidirect
251. C22⋊Dic53C22⋊C4semidirect
258. #11719921C22⋊C4semidirect
376. C2×C4×C53C2×C22⋊C4semidirect
400. C2×Dic53C2×C22⋊C4semidirect
401. C2×Dic53C2×C22⋊C4semidirect
414. C22×C53C4×C22⋊C4semidirect
460. C2×D53C4×C22⋊C4semidirect
479. C22⋊#95D53semidirect
524. C2×#95C2×D53semidirect
525. C2×#95C2×D53semidirect
526. C53C22⋊C42semidirect
561. C23×C4C4×D53semidirect
596. C2×C22⋊C4C4×D53semidirect
885. C2×C4C22⋊C4×D53semidirect
919. C22#16810470semidirect

Maximal subgroups

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

subgroupindex
C23×#117199212
C22×C22⋊C4×D532
C2×#168104782
C2×C22⋊C4×Dic532
C2×C4×C22⋊Dic532
C2×#168104702
#202729512
#202729372
#202729362
C53×C22⋊#952
C22⋊C4253