Finite Group Databasebeta

← #27395325

Subgroups — #27395325

Order 13568.

1000 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic53C211yesmaximal, characteristic, complemented
2#20277206C211yesmaximal, characteristic
3#20275598C211yesmaximal, characteristic, complemented
4#20275587C211yesmaximal, characteristic, complemented
5#20275414C211yesmaximal, characteristic, complemented
6#20275407C211yesmaximal, characteristic, complemented
7#20275358C211yesmaximal, characteristic, complemented
8#20275344C211yesmaximal, characteristic, complemented
9#20275072C211yesmaximal, characteristic, complemented
10#20275058C211yesmaximal, characteristic, complemented
11#20275028C211yesmaximal, characteristic, complemented
12#20274916C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic
14#20274479C211yesmaximal, characteristic, complemented
15C2×C53×#452C211yesmaximal, characteristic
16C2×Q8×Dic53C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18C22×C4×Dic53C2211yescharacteristic
19C2×#13133151C2211yescharacteristic
20C2×#13133149C2211yescharacteristic
21C2×#13133141C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133127C2211yescharacteristic
29C2×#13133127C2211yescharacteristic
30#16810530C2211yescharacteristic
31#16810530C2211yescharacteristic
32#16810530C2211yescharacteristic
33#16810526C2211yescharacteristic
34#16810526C2211yescharacteristic
35#16810522C2211yescharacteristic
36#16810509—21no—
37#16810503—21no—
38#16810503—21no—
39#16810498—21no—
40#16810483C2211yescharacteristic
41C4⋊C4×Dic53—21no—
42C4⋊C4×Dic53C2211yescharacteristic
43C22⋊C4×Dic53—21no—
44C4×C22⋊Dic53—21no—
45C4×C22⋊Dic53—21no—
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52C22×#41×C53C2211yescharacteristic
53C22×Q16×C53C2211yescharacteristic
54C22×SD16×C53C2211yescharacteristic
55C2×C22⋊Q8×C53C2211yescharacteristic
56C53×#452C418yescomplemented
57C2×#103×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C23×Dic53D411yescharacteristic
61C23×Dic53D411yescharacteristic
62C22×#88322C2311yescharacteristic
63C22×#88322C2311yescharacteristic
64Q8×Dic53—41no—
65Q8×Dic53—41no—
66#13133176—41no—
67#13133176—41no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53C2311yescharacteristic
71C2×C4⋊Dic53C2311yescharacteristic
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C22⋊Dic53—21no—
75C2×C22⋊Dic53—21no—
76C2×C22⋊Dic53—21no—
77C2×C22⋊Dic53—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C4×Dic53—21no—
81C2×C4×Dic53—21no—
82C2×C4×Dic53—21no—
83C2×C4×Dic53—41no—
84C2×C4×Dic53—41no—
85C2×C4×Dic53D411yescharacteristic
86C2×C4×Dic53D411yescharacteristic
87C2×C4×Dic53C2311yescharacteristic
88C2×C4×Dic53C2311yescharacteristic
89#13133151—41no—
90#13133149—41no—
91#13133141—41no—
92#13133141—41no—
93#13133141—41no—
94#13133141—41no—
95#13133138—41no—
96#13133138—41no—
97C22⋊#88322—22no—
98#13133127—41no—
99#13133127—41no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109C2×#41×C53—22no—
110C2×#41×C53—41no—
111C2×#41×C53—41no—
112C2×#41×C53—41no—
113C2×#41×C53—41no—
114C2×#41×C53C2×C414yes—
115C22×Q8×C53C2311yescharacteristic
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53—21no—
118C22×D4×C53C2311yescharacteristic
119C23×C4×C53—21no—
120C23×C4×C53C2311yescharacteristic
121C2×Q16×C53—41no—
122C2×Q16×C53—41no—
123C2×Q16×C53C2×C414yescomplemented
124C2×SD16×C53—41no—
125C2×SD16×C53—41no—
126C2×SD16×C53C2×C414yescomplemented
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C22⋊Q8×C53—22no—
130C22⋊Q8×C53C2×C414yes—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134#103×C53C2×C414yescomplemented
135#102×C53C2×C414yescomplemented
136C22⋊C8×C53C2×C414yes—
137C24×C53—21no—
138C24×C53C2×D411yescharacteristic
139#41×C53—44no—
140#41×C53—44no—
141#41×C53—44no—
142#41×C53—44no—
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53C22×C412yes—
154C2×Q8×C53C22×C412yes—
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53C22×C412yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—24no—
172C22×C4×C53—42no—
173C22×C4×C53—42no—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53#4112yes—
177C22×C4×C53C2411yescharacteristic
178C22×Dic53—22no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—41no—
184C22×Dic53—41no—
185C22×Dic53—41no—
186C22×Dic53—41no—
187C22×Dic53—41no—
188C22×Dic53C2×D411yescharacteristic
189C22×Dic53C2×D411yescharacteristic
190C22×Dic53C2×D411yescharacteristic
191C22×Dic53C2×D411yescharacteristic
192Q16×C53—44no—
193SD16×C53—44no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53C22×C412yes—
199C2×C8×C53C22×C412yes—
200C4⋊C4×C53—24no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53C22×C412yes—
203C22⋊C4×C53—24no—
204C22⋊Dic53—42no—
205C22⋊Dic53—42no—
206C22⋊Dic53—42no—
207C22⋊Dic53—42no—
208C22⋊Dic53—42no—
209C22⋊Dic53—42no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—42no—
219C4⋊Dic53—42no—
220C4×Dic53—21no—
221C4×Dic53—21no—
222C4×Dic53—21no—
223C4×Dic53—21no—
224C4×Dic53—41no—
225C4×Dic53—41no—
226C4×Dic53—42no—
227C4×Dic53—42no—
228C4×Dic53—42no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—22no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53C4×D412yes—
249C23×C53C22×D411yescharacteristic
250Q8×C53—22no—
251Q8×C53—22no—
252Q8×C53—22no—
253Q8×C53—22no—
254Q8×C53—41no—
255Q8×C53—41no—
256Q8×C53—41no—
257Q8×C53—41no—
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—48no—
261D4×C53—41no—
262D4×C53—41no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—48no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53C4×D412yes—
280C2×C4×C53C23×C411yescharacteristic
281C2×C4×C53C2×#4111yescharacteristic
282C2×C4×C53H(5,𝔽2)11yescharacteristic
283C2×C4×C53H(5,𝔽2)11yescharacteristic
284C2×C4×C53H(5,𝔽2)11yescharacteristic
285C2×C4×C53H(5,𝔽2)11yescharacteristic
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—44no—
298C2×Dic53—44no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53#13712yes—
312C8×C53—22no—
313C8×C53—22no—
314#88322—41no—
315#88322—41no—
316#22048—531nomaximal, Sylow
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—42no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53—81no—
328C22×C53—81no—
329C22×C53—81no—
330C22×C53—81no—
331C22×C53C2×C4×D411yescharacteristic
332C22×C53#53411yescharacteristic
333C22×C53#53511yescharacteristic
334C22×C53C2×#13711yescharacteristic
335C22×C53#57511yescharacteristic
336C22×C53#57511yescharacteristic
337C22×C53#57511yescharacteristic
338C4×C53—22no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53#51811yescharacteristic
343C4×C53#51811yescharacteristic
344C4×C53#53811yescharacteristic
345C4×C53#53811yescharacteristic
346Dic53—22no—
347Dic53—41no—
348Dic53—41no—
349Dic53—41no—
350Dic53—81no—
351Dic53—81no—
352Dic53—81no—
353Dic53—81no—
354C2×#452D5311yescharacteristic
355C4×C22⋊Q8—531no—
356#2297—531no—
357#1973—531no—
358#1971—531no—
359#1936—531no—
360#1935—531no—
361#1928—531no—
362#1926—531no—
363#1880—531no—
364#1878—531no—
365#1873—531no—
366#1854—531no—
367#1788—531no—
368#1749—531no—
369C2×C53—42no—
370C2×C53—82no—
371C2×C53#232111yescharacteristic
372C2×C53#294311yescharacteristic
373C2×C53C4×#13711yescharacteristic
374C2×C53#319611yescharacteristic
375C2×C53#319711yescharacteristic
376C2×C53#321611yescharacteristic
377C2×C53#321911yescharacteristic
378C22×#41C2×D5311yescharacteristic
379C22×Q16C2×D5311yescharacteristic
380C22×SD16C2×D5311yescharacteristic
381C2×C22⋊Q8C2×D5311yescharacteristic
382C2×C4×Q8—531no—
383C2×#117—531no—
384C22×C42—531no—
385#452Dic5318yescomplemented
386C2×#107—531no—
387C2×#106—531no—
388C2×#103—531no—
389C2×#103—531no—
390C2×#103—531no—
391C2×#103—531no—
392C2×#103C2×D5311yescharacteristic
393C2×#102—531no—
394C2×#102—531no—
395C2×#102C2×D5311yescharacteristic
396C2×C22⋊C8—531no—
397C2×C22⋊C8C2×D5311yescharacteristic
398C2×#97—531no—
399C2×#97—531no—
400#391—531no—
401#391—531no—
402#391—531no—
403#390—531no—
404#390—531no—
405#389—531no—
406#387—1061no—
407#386—1061no—
408#386—1061no—
409#385—1061no—
410#380—531no—
411C4×C4⋊C4—531no—
412C4×C4⋊C4—1061no—
413C4×C22⋊C4—1061no—
414C4×C22⋊C4—1061no—
415C4×C22⋊C4—1061no—
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#336—531no—
421#336—531no—
422C53#2204811yescharacteristic, complemented, Sylow
423C2×#41—22no—
424C2×#41—41no—
425C2×#41—41no—
426C2×#41—41no—
427C2×#41—41no—
428C2×#41C2×Dic5314yes—
429C22×Q8C22×D5311yescharacteristic
430C22×Q8C22×D5311yescharacteristic
431C22×D4—21no—
432C22×D4C22×D5311yescharacteristic
433C23×C4—21no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4C22×D5311yescharacteristic
437C2×Q16—41no—
438C2×Q16—41no—
439C2×Q16C2×Dic5314yescomplemented
440C2×SD16—41no—
441C2×SD16—41no—
442C2×SD16C2×Dic5314yescomplemented
443C22×C8—531no—
444C22×C8—531no—
445C22×C8C22×D5311yescharacteristic
446C22×C8C22×D5311yescharacteristic
447C22⋊Q8—22no—
448C22⋊Q8C2×Dic5314yes—
449C4×Q8—2121no—
450C4×Q8—2121no—
451#117—2121no—
452#117—2121no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—1061no—
459C2×C4⋊C4—1061no—
460C2×C4⋊C4C22×D5311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C22⋊C4—1061no—
465C2×C22⋊C4—1061no—
466C2×C22⋊C4—1061no—
467C2×C22⋊C4—1061no—
468C2×C42—531no—
469C2×C42—531no—
470C2×C42—531no—
471C2×C42—531no—
472C2×C42—1061no—
473C2×C42—1061no—
474C2×C42—1061no—
475C2×C42—2121no—
476C2×C42—2121no—
477#107—2121no—
478#106—2121no—
479#103—2121no—
480#103—2121no—
481#103—2121no—
482#103—2121no—
483#103C2×Dic5314yescomplemented
484#102—2121no—
485#102—2121no—
486#102C2×Dic5314yescomplemented
487C22⋊C8—1062no—
488C22⋊C8C2×Dic5314yes—
489#97—2121no—
490#97—2121no—
491#95—1061no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497#95—1061no—
498#95—1061no—
499#95—1061no—
500C24—21no—
501C24D4×D5311yescharacteristic
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C22×Dic5312yes—
517C2×Q8C22×Dic5312yes—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4C22×Dic5312yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—531no—
538C22×C4—531no—
539C22×C4—531no—
540C22×C4—531no—
541C22×C4—1062no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—2121no—
547C22×C4—2121no—
548C22×C4—2121no—
549C22×C4—2121no—
550C22×C4—2121no—
551C22×C4D4×D5311yescharacteristic
552C22×C4#1171994712yes—
553C22×C4C22×Dic5312yes—
554C22×C4C23×D5311yescharacteristic
555Q16—44no—
556SD16—44no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8C22×Dic5312yes—
568C2×C8C22×Dic5312yes—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—1061no—
572C4⋊C4—1061no—
573C4⋊C4—1061no—
574C4⋊C4—1061no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—1061no—
579C4⋊C4—2122no—
580C4⋊C4—2122no—
581C4⋊C4C22×Dic5312yes—
582C22⋊C4—24no—
583C22⋊C4—2122no—
584C22⋊C4—2122no—
585C22⋊C4—2122no—
586C22⋊C4—2122no—
587C22⋊C4—2122no—
588C22⋊C4—2122no—
589C42—1061no—
590C42—1061no—
591C42—1061no—
592C42—1061no—
593C42—2121no—
594C42—2121no—
595C42—2122no—
596C42—2122no—
597C42—2122no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23D4×Dic5312yes—
612C23C2×D4×D5311yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—48no—
624D4—41no—
625D4—41no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—532no—
643C2×C4—1061no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1061no—
648C2×C4—1061no—
649C2×C4—1061no—
650C2×C4—1061no—
651C2×C4—1061no—
652C2×C4—1061no—
653C2×C4—1061no—
654C2×C4—2124no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4—2124no—
668C2×C4D4×Dic5312yes—
669C2×C4C23×Dic5311yescharacteristic
670C2×C4C2×#1171994711yescharacteristic
671C2×C4#1313326211yescharacteristic
672C2×C4#1313326211yescharacteristic
673C2×C4#1313326211yescharacteristic
674C2×C4#1313326211yescharacteristic
675C8—22no—
676C8—22no—
677C8—2121no—
678C8—2121no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×D4×Dic5311yescharacteristic
694C22#1681118311yescharacteristic
695C22#1681118811yescharacteristic
696C22#137×D5311yescharacteristic
697C22#1681142011yescharacteristic
698C22#1681142011yescharacteristic
699C22#1681142211yescharacteristic
700C4—22no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—1062no—
705C4—4241no—
706C4—4241no—
707C4—4241no—
708C4—4241no—
709C4—2121no—
710C4—2121no—
711C4—2121no—
712C4#1681109811yescharacteristic
713C4#1681109811yescharacteristic
714C4#1681120811yescharacteristic
715C4#1681120811yescharacteristic
716C2—42no—
717C2—82no—
718C2#2027737611yescharacteristic
719C2#2028351611yescharacteristic
720C2#137×Dic5311yescharacteristic
721C2#2028554311yescharacteristic
722C2#2028555611yescharacteristic
723C2#2028572311yescharacteristic
724C2#2028575611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#452D53
hypocenterC53#22048
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×Dic53C2semidirect
3. #20275598C2semidirect
4. #20275587C2semidirect
5. #20275414C2semidirect
6. #20275407C2semidirect
7. #20275358C2semidirect
8. #20275344C2semidirect
9. #20275072C2semidirect
10. #20275058C2semidirect
11. #20275028C2semidirect
12. #20274916C2semidirect
14. #20274479C2semidirect
56. C53×#452C4semidirect
123. C2×Q16×C53C2×C4semidirect
126. C2×SD16×C53C2×C4semidirect
134. #103×C53C2×C4semidirect
135. #102×C53C2×C4semidirect
385. #452Dic53semidirect
422. C53#22048semidirect
439. C2×Q16C2×Dic53semidirect
442. C2×SD16C2×Dic53semidirect
483. #103C2×Dic53semidirect
486. #102C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic532
#202772062
#202755982
#202755872
#202754142
#202754072
#202753582
#202753442
#202750722
#202750582
#202750282
#202749162
#202746552
#202744792
C2×C53×#4522
#2204853