Finite Group Databasebeta

← #27306010

Subgroups — #27306010

Order 13568.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810516C212yesmaximal, complemented
2C2×#16810483C211yesmaximal, characteristic, complemented
3C2×#16810479C211yesmaximal, characteristic
4C2×#16810479C211yesmaximal, characteristic
5C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
6#20272964C212yesmaximal, complemented
7#20272960C212yesmaximal, complemented
8#20272952C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic, complemented
10#20272938C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2212yescomplemented
13C22×C22⋊Dic53C2211yescharacteristic
14C22×C22⋊Dic53C2211yescharacteristic
15C22×C22⋊Dic53C2212yes—
16C22×C22⋊Dic53C2212yes—
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C4×Dic53C2212yescomplemented
22#16810516—28no—
23#16810483—24no—
24#16810479—24no—
25#16810479—24no—
26C4×C22⋊Dic53—24no—
27C2×#13133124C2212yescomplemented
28C2×#13133124C2212yescomplemented
29C2×#13133124C2212yescomplemented
30C2×#13133124C2212yescomplemented
31C2×#13133124C2212yescomplemented
32C2×#13133124C2212yescomplemented
33C26×C53C2211yescharacteristic
34C24×C4×C53C2211yescharacteristic
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53—28no—
37C22×C22⋊C4×C53C418yescomplemented
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C23×Dic53C2312yes—
46C2×C4⋊Dic53—24no—
47C2×C4⋊Dic53—24no—
48C2×C4⋊Dic53—42no—
49C2×C22⋊Dic53—22no—
50C2×C22⋊Dic53—24no—
51C2×C22⋊Dic53—24no—
52C2×C22⋊Dic53—22no—
53C2×C22⋊Dic53—22no—
54C2×C22⋊Dic53—22no—
55C2×C22⋊Dic53—22no—
56C2×C22⋊Dic53—22no—
57C2×C22⋊Dic53—22no—
58C2×C22⋊Dic53—24no—
59C2×C22⋊Dic53—24no—
60C2×C22⋊Dic53—22no—
61C2×C22⋊Dic53—22no—
62C2×C22⋊Dic53—22no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—24no—
65C2×C22⋊Dic53—24no—
66C2×C22⋊Dic53—24no—
67C2×C22⋊Dic53—42no—
68C2×C22⋊Dic53—42no—
69C2×C22⋊Dic53—42no—
70C2×C22⋊Dic53—42no—
71C2×C22⋊Dic53D414yes—
72C2×C22⋊Dic53D414yes—
73C2×C4×Dic53—24no—
74C2×C4×Dic53—24no—
75C2×C4×Dic53—42no—
76#13133124—24no—
77#13133124—24no—
78#13133124—24no—
79#13133124—24no—
80#13133124—42no—
81#13133124—42no—
82C25×C53—24no—
83C25×C53—24no—
84C25×C53—22no—
85C25×C53—22no—
86C25×C53—22no—
87C25×C53—22no—
88C25×C53—22no—
89C25×C53—22no—
90C25×C53—42no—
91C25×C53—42no—
92C25×C53C2×C414yes—
93C25×C53C2311yescharacteristic
94C25×C53C2311yescharacteristic
95C25×C53C2311yescharacteristic
96C23×C4×C53—22no—
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53—24no—
101C23×C4×C53—24no—
102C23×C4×C53—42no—
103C23×C4×C53—42no—
104C23×C4×C53C2×C414yes—
105C23×C4×C53C2×C414yes—
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110C2×C22⋊C4×C53—232no—
111C2×C22⋊C4×C53—24no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53C2×C414yes—
115C2×C22⋊C4×C53C2×C414yes—
116C2×C22⋊C4×C53C2×C414yes—
117C2×C22⋊C4×C53C2×C414yes—
118C2×C22⋊C4×C53D418yes—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—22no—
122C24×C53—22no—
123C24×C53—216no—
124C24×C53—216no—
125C24×C53—28no—
126C24×C53—28no—
127C24×C53—28no—
128C24×C53—22no—
129C24×C53—21no—
130C24×C53—21no—
131C24×C53—21no—
132C24×C53—21no—
133C24×C53—21no—
134C24×C53—21no—
135C24×C53—22no—
136C24×C53—21no—
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—28no—
147C24×C53—28no—
148C24×C53—44no—
149C24×C53—44no—
150C24×C53—48no—
151C24×C53—48no—
152C24×C53—48no—
153C24×C53—48no—
154C24×C53—48no—
155C24×C53—48no—
156C24×C53—48no—
157C24×C53—48no—
158C24×C53—48no—
159C24×C53—48no—
160C24×C53—44no—
161C24×C53—44no—
162C24×C53—44no—
163C24×C53—44no—
164C24×C53C22×C412yes—
165C24×C53C22×C412yes—
166C24×C53C22×C412yes—
167C24×C53C2×D414yes—
168C24×C53C2×D412yes—
169C24×C53C2×D412yes—
170C24×C53#4114yes—
171C24×C53#4112yes—
172C24×C53#4112yes—
173C24×C53#4112yes—
174C24×C53#4112yes—
175C24×C53C2411yescharacteristic
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—28no—
183C22×C4×C53—28no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—28no—
193C22×C4×C53—28no—
194C22×C4×C53—44no—
195C22×C4×C53—44no—
196C22×C4×C53—48no—
197C22×C4×C53—48no—
198C22×C4×C53—48no—
199C22×C4×C53—48no—
200C22×C4×C53C22×C412yes—
201C22×C4×C53C22×C412yes—
202C22×C4×C53C22×C412yes—
203C22×C4×C53C22×C412yes—
204C22×C4×C53C2×D414yes—
205C22×C4×C53C2×D414yes—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53—22no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53—22no—
224C22×Dic53—22no—
225C22×Dic53—22no—
226C22×Dic53—22no—
227C22×Dic53—22no—
228C22×Dic53—22no—
229C22×Dic53—22no—
230C22×Dic53—22no—
231C22×Dic53—22no—
232C22×Dic53C2×D414yes—
233C22×Dic53C2×D414yes—
234C22⋊C4×C53—28no—
235C22⋊C4×C53—28no—
236C22⋊C4×C53—28no—
237C22⋊C4×C53C22⋊C4116yescomplemented
238C22⋊Dic53—28no—
239C22⋊Dic53—28no—
240C22⋊Dic53—48no—
241C22⋊Dic53—48no—
242C22⋊Dic53—48no—
243C22⋊Dic53—48no—
244C22⋊Dic53—44no—
245C22⋊Dic53—44no—
246C4⋊Dic53—48no—
247C4×Dic53—48no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—24no—
253C23×C53—24no—
254C23×C53—24no—
255C23×C53—24no—
256C23×C53—24no—
257C23×C53—24no—
258C23×C53—24no—
259C23×C53—24no—
260C23×C53—24no—
261C23×C53—24no—
262C23×C53—24no—
263C23×C53—24no—
264C23×C53—232no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—24no—
278C23×C53—24no—
279C23×C53—24no—
280C23×C53—24no—
281C23×C53—24no—
282C23×C53—24no—
283C23×C53—24no—
284C23×C53—24no—
285C23×C53—24no—
286C23×C53—24no—
287C23×C53—24no—
288C23×C53—24no—
289C23×C53—416no—
290C23×C53—416no—
291C23×C53—416no—
292C23×C53—416no—
293C23×C53—416no—
294C23×C53—432no—
295C23×C53—432no—
296C23×C53—432no—
297C23×C53—432no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53—416no—
319C23×C53C2×C22⋊C414yes—
320C23×C53#11714yes—
321C23×C53#11714yes—
322C23×C53C4×D414yes—
323C23×C53C4×D414yes—
324C23×C53#12114yes—
325C23×C53#12314yes—
326C23×C53#12414yes—
327C23×C53#12614yes—
328C23×C53C23×C411yescharacteristic
329C23×C53C22×D411yescharacteristic
330C23×C53C22×D411yescharacteristic
331C23×C53C22×D412yes—
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4111yescharacteristic
335C23×C53C2×#4111yescharacteristic
336C23×C53C2×#4112yes—
337C23×C53H(5,𝔽2)12yes—
338C23×C53H(5,𝔽2)12yes—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—24no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—24no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—416no—
354C2×C4×C53—416no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53—42no—
359C2×C4×C53C2×C22⋊C414yes—
360C2×C4×C53C2×C22⋊C414yes—
361C2×Dic53—24no—
362C2×Dic53—24no—
363C2×Dic53—24no—
364C2×Dic53—24no—
365C2×Dic53—24no—
366C2×Dic53—24no—
367C2×Dic53—42no—
368C2×Dic53—42no—
369C2×Dic53—42no—
370C2×Dic53—42no—
371C2×Dic53—42no—
372C2×Dic53—42no—
373C2×Dic53—42no—
374C2×Dic53—42no—
375C2×Dic53—42no—
376C2×Dic53—42no—
377C2×Dic53—42no—
378C2×Dic53—42no—
379C2×Dic53—42no—
380C2×Dic53—42no—
381C2×Dic53—42no—
382C2×Dic53—42no—
383C2×Dic53—42no—
384C2×Dic53—42no—
385C2×Dic53—42no—
386C2×Dic53—42no—
387C2×Dic53—42no—
388C2×Dic53—42no—
389#13873—531nomaximal, Sylow
390C22×C53—24no—
391C22×C53—24no—
392C22×C53—24no—
393C22×C53—24no—
394C22×C53—24no—
395C22×C53—28no—
396C22×C53—28no—
397C22×C53—28no—
398C22×C53—28no—
399C22×C53—24no—
400C22×C53—24no—
401C22×C53—24no—
402C22×C53—24no—
403C22×C53—24no—
404C22×C53—24no—
405C22×C53—24no—
406C22×C53—464no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—42no—
413C22×C53—44no—
414C22×C53—44no—
415C22×C53—44no—
416C22×C53—44no—
417C22×C53—44no—
418C22×C53—44no—
419C22×C53—44no—
420C22×C53—44no—
421C22×C53—42no—
422C22×C53—42no—
423C22×C53#38818yescomplemented
424C22×C53C22×C22⋊C411yescharacteristic
425C22×C53C2×#11711yescharacteristic
426C22×C53C2×#11711yescharacteristic
427C22×C53C2×C4×D411yescharacteristic
428C22×C53C2×C4×D411yescharacteristic
429C22×C53#51811yescharacteristic
430C22×C53#51811yescharacteristic
431C22×C53C2×#12111yescharacteristic
432C22×C53C2×#12311yescharacteristic
433C22×C53#52512yes—
434C22×C53#52512yes—
435C22×C53C2×#12411yescharacteristic
436C22×C53C2×#12611yescharacteristic
437C22×C53#53812yes—
438C22×C53#53812yes—
439C22×C53D4212yes—
440C22×C53D4212yes—
441C22×C53#54612yes—
442C22×C53#54612yes—
443C22×C53#54612yes—
444C22×C53#54612yes—
445C22×C53#55112yes—
446C22×C53#55112yes—
447C4×C53—24no—
448C4×C53—24no—
449C4×C53—42no—
450C4×C53—42no—
451Dic53—44no—
452Dic53—44no—
453Dic53—82no—
454Dic53—82no—
455C23×C22⋊C4D5311yescharacteristic
456C2×#388—532no—
457C2×#380—531no—
458C2×#379—531no—
459C2×#379—531no—
460C2×C4×C22⋊C4—531no—
461#1440—532no—
462#1439—532no—
463#1437—532no—
464C22⋊#95—531no—
465C22⋊#95—531no—
466C2×C53—28no—
467C2×C53—44no—
468C2×C53—44no—
469C2×C53#228011yescharacteristic
470C2×C53C2×#38811yescharacteristic
471C2×C53#231211yescharacteristic
472C2×C53D4×C22⋊C411yescharacteristic
473C2×C53D4×C22⋊C411yescharacteristic
474C2×C53#234211yescharacteristic
475C2×C53#234211yescharacteristic
476C2×C53#241812yes—
477C2×C53#242412yes—
478C2×C53#247212yes—
479C2×C53#248012yes—
480C26C2×D5311yescharacteristic
481C24×C4C2×D5311yescharacteristic
482C24×C4C2×D5311yescharacteristic
483C22×C4⋊C4—532no—
484C22×C22⋊C4—28no—
485C22×C22⋊C4—531no—
486C22×C22⋊C4—531no—
487C22×C22⋊C4—531no—
488C22×C22⋊C4—531no—
489C22×C22⋊C4—532no—
490C22×C22⋊C4—532no—
491C22×C22⋊C4—532no—
492C22×C22⋊C4—532no—
493C22×C22⋊C4Dic5318yescomplemented
494C22×C22⋊C4C2×D5311yescharacteristic
495C22×C22⋊C4C2×D5311yescharacteristic
496C22×C22⋊C4C2×D5311yescharacteristic
497C22×C22⋊C4C2×D5311yescharacteristic
498C22×C42—532no—
499#388—1068no—
500#380—1064no—
501#379—1064no—
502#379—1064no—
503C4×C22⋊C4—1064no—
504C2×#95—532no—
505C2×#95—532no—
506C2×#95—532no—
507C2×#95—532no—
508C2×#95—532no—
509C2×#95—532no—
510C53#1387311yescharacteristic, complemented, Sylow
511C25—24no—
512C25—22no—
513C25—22no—
514C25—24no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×Dic5314yes—
522C25C22×D5311yescharacteristic
523C25C22×D5311yescharacteristic
524C25C22×D5311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—532no—
534C23×C4—532no—
535C23×C4—532no—
536C23×C4—532no—
537C23×C4C2×Dic5314yes—
538C23×C4C2×Dic5314yes—
539C23×C4C22×D5311yescharacteristic
540C23×C4C22×D5311yescharacteristic
541C23×C4C22×D5311yescharacteristic
542C23×C4C22×D5311yescharacteristic
543C2×C4⋊C4—1064no—
544C2×C4⋊C4—1064no—
545C2×C4⋊C4—2122no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—232no—
550C2×C22⋊C4—534no—
551C2×C22⋊C4—534no—
552C2×C22⋊C4—1062no—
553C2×C22⋊C4—1062no—
554C2×C22⋊C4—1062no—
555C2×C22⋊C4—1062no—
556C2×C22⋊C4—1064no—
557C2×C22⋊C4—1064no—
558C2×C22⋊C4—1064no—
559C2×C22⋊C4—1064no—
560C2×C22⋊C4—1064no—
561C2×C22⋊C4—1064no—
562C2×C22⋊C4—1062no—
563C2×C22⋊C4—1062no—
564C2×C22⋊C4—1062no—
565C2×C22⋊C4—1062no—
566C2×C22⋊C4—1062no—
567C2×C22⋊C4—1062no—
568C2×C22⋊C4—1064no—
569C2×C22⋊C4—1064no—
570C2×C22⋊C4—2122no—
571C2×C22⋊C4—2122no—
572C2×C22⋊C4—2122no—
573C2×C22⋊C4—2122no—
574C2×C22⋊C4C2×Dic5314yes—
575C2×C22⋊C4C2×Dic5314yes—
576C2×C22⋊C4C2×Dic5314yes—
577C2×C22⋊C4C2×Dic5314yes—
578C2×C22⋊C4C22⋊D5318yes—
579C2×C42—1064no—
580C2×C42—1064no—
581C2×C42—2122no—
582#95—1064no—
583#95—1064no—
584#95—1064no—
585#95—1064no—
586#95—2122no—
587#95—2122no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24#1171994514yes—
634C24#1171994512yes—
635C24#1171994512yes—
636C24D4×D5312yes—
637C24D4×D5312yes—
638C24#1171994712yes—
639C24#1171994712yes—
640C24C22×Dic5312yes—
641C24C22×Dic5312yes—
642C24C22×Dic5312yes—
643C24C2×C22⋊D5314yes—
644C24C23×D5311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—534no—
670C22×C4—534no—
671C22×C4—1062no—
672C22×C4—1062no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4—1062no—
678C22×C4—1062no—
679C22×C4—1062no—
680C22×C4—1062no—
681C22×C4—1062no—
682C22×C4—1062no—
683C22×C4—1062no—
684C22×C4—1062no—
685C22×C4—1062no—
686C22×C4—1062no—
687C22×C4—1062no—
688C22×C4—1062no—
689C22×C4—1062no—
690C22×C4—1062no—
691C22×C4—1062no—
692C22×C4—1062no—
693C22×C4—1062no—
694C22×C4—1062no—
695C22×C4—1062no—
696C22×C4—1062no—
697C22×C4C22×Dic5312yes—
698C22×C4C22×Dic5312yes—
699C22×C4C22×Dic5312yes—
700C22×C4C22×Dic5312yes—
701C22×C4C2×C22⋊D5314yes—
702C22×C4C2×C22⋊D5314yes—
703C4⋊C4—2128no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—1068no—
708C22⋊C4—1068no—
709C22⋊C4—2128no—
710C22⋊C4—2128no—
711C22⋊C4—2128no—
712C22⋊C4—2128no—
713C22⋊C4—2124no—
714C22⋊C4—2124no—
715C22⋊C4C22⋊Dic53116yescomplemented
716C42—2128no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—416no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—42no—
768C23—42no—
769C23—416no—
770C23—42no—
771C23—42no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23C2×C22⋊Dic5314yes—
789C23#1313317614yes—
790C23#1313317614yes—
791C23D4×Dic5314yes—
792C23D4×Dic5314yes—
793C23#1313319014yes—
794C23#1313319914yes—
795C23#1313320314yes—
796C23#1313321014yes—
797C23C23×Dic5311yescharacteristic
798C23C2×D4×D5311yescharacteristic
799C23C2×D4×D5311yescharacteristic
800C23C22×C22⋊D5312yes—
801C23C2×#1171994711yescharacteristic
802C23C2×#1171994711yescharacteristic
803C23C2×#1171994512yes—
804C23C2×#1171994511yescharacteristic
805C23C2×#1171994511yescharacteristic
806C23#1313326212yes—
807C23#1313326212yes—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—1064no—
829C2×C4—1064no—
830C2×C4—1064no—
831C2×C4—1064no—
832C2×C4—1064no—
833C2×C4—1064no—
834C2×C4—2122no—
835C2×C4—2122no—
836C2×C4—2122no—
837C2×C4—2122no—
838C2×C4—2122no—
839C2×C4—2122no—
840C2×C4—2122no—
841C2×C4—2122no—
842C2×C4—2122no—
843C2×C4—2122no—
844C2×C4—2122no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4—2122no—
848C2×C4—2122no—
849C2×C4—2122no—
850C2×C4—2122no—
851C2×C4—2122no—
852C2×C4—2122no—
853C2×C4—2122no—
854C2×C4—2122no—
855C2×C4—2122no—
856C2×C4C2×C22⋊Dic5314yes—
857C2×C4C2×C22⋊Dic5314yes—
858C22—24no—
859C22—24no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#1681051618yescomplemented
892C22C22×C22⋊Dic5311yescharacteristic
893C22C2×#1313317611yescharacteristic
894C22C2×#1313317611yescharacteristic
895C22C2×D4×Dic5311yescharacteristic
896C22C2×D4×Dic5311yescharacteristic
897C22#1681109811yescharacteristic
898C22#1681109811yescharacteristic
899C22C2×#1313319011yescharacteristic
900C22C2×#1313319911yescharacteristic
901C22#1681113412yes—
902C22#1681113412yes—
903C22C2×#1313320311yescharacteristic
904C22C2×#1313321011yescharacteristic
905C22#1681121112yes—
906C22#1681121112yes—
907C22D4×C22⋊D5312yes—
908C22D4×C22⋊D5312yes—
909C22#1681126312yes—
910C22#1681126312yes—
911C22#1681126712yes—
912C22#1681126712yes—
913C22#1681129912yes—
914C22#1681129912yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—4242no—
920C4—4242no—
921C4—2124no—
922C4—2124no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#2027709811yescharacteristic
927C2C2×#1681051611yescharacteristic
928C2#2027731311yescharacteristic
929C2D4×C22⋊Dic5311yescharacteristic
930C2D4×C22⋊Dic5311yescharacteristic
931C2#2027756411yescharacteristic
932C2#2027756411yescharacteristic
933C2#2027817712yes—
934C2#2027825112yes—
935C2#2027883512yes—
936C2#2027895512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC23×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC26×C53C22
hypercenterC23×C22⋊C4D53
hypocenterC53#13873
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810516C2semidirect
2. C2×#16810483C2semidirect
5. C2×C4×C22⋊Dic53C2semidirect
6. #20272964C2semidirect
7. #20272960C2semidirect
8. #20272952C2semidirect
9. #20272938C2semidirect
10. #20272938C2semidirect
12. C22×C4⋊Dic53C22semidirect
21. C22×C4×Dic53C22semidirect
27. C2×#13133124C22semidirect
28. C2×#13133124C22semidirect
29. C2×#13133124C22semidirect
30. C2×#13133124C22semidirect
31. C2×#13133124C22semidirect
32. C2×#13133124C22semidirect
37. C22×C22⋊C4×C53C4semidirect
237. C22⋊C4×C53C22⋊C4semidirect
423. C22×C53#388semidirect
493. C22×C22⋊C4Dic53semidirect
510. C53#13873semidirect
715. C22⋊C4C22⋊Dic53semidirect
891. C22#16810516semidirect

Maximal subgroups

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

subgroupindex
C2×#168105162
C2×#168104832
C2×#168104792
C2×C4×C22⋊Dic532
#202729642
#202729602
#202729522
#202729382
C23×C22⋊C4×C532
#1387353