Finite Group Databasebeta

← #27394396

Subgroups — #27394396

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810588C211yesmaximal, characteristic
2#20277308C211yesmaximal, characteristic
3#20277304C211yesmaximal, characteristic
4#20274917C211yesmaximal, characteristic, complemented
5#20274916C211yesmaximal, characteristic, complemented
6#20274915C211yesmaximal, characteristic, complemented
7#20274912C211yesmaximal, characteristic, complemented
8#20274908C211yesmaximal, characteristic, complemented
9#20274906C211yesmaximal, characteristic, complemented
10#20274906C211yesmaximal, characteristic, complemented
11#20274747C211yesmaximal, characteristic, complemented
12#20274745C211yesmaximal, characteristic, complemented
13#20274739C211yesmaximal, characteristic, complemented
14#20274737C211yesmaximal, characteristic, complemented
15C53×#1853C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20C2×#13133175C2211yescharacteristic
21C2×C4⋊C4×D53C2211yescharacteristic
22C2×#13133151C2211yescharacteristic
23C2×#13133150C2211yescharacteristic
24C2×#13133149C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133148C2211yescharacteristic
27C2×#13133148C2211yescharacteristic
28#16810588C418yescomplemented
29C2×C22⋊#88322C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32#16810528—21no—
33#16810527—21no—
34#16810524—21no—
35#16810523—21no—
36#16810502—21no—
37#16810502—21no—
38#16810501—21no—
39#16810499—21no—
40#16810483C2211yescharacteristic
41#16810480C2211yescharacteristic
42#16810480C2211yescharacteristic
43#16810480C2211yescharacteristic
44#16810480C2211yescharacteristic
45#16810480C2211yescharacteristic
46#16810480C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C2×#106×C53C2211yescharacteristic
55C2×#106×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#340C2211yescharacteristic
60C2×#11719945—41no—
61C2×#11719945—41no—
62C2×#11719945—41no—
63C2×#11719945—41no—
64C2×#11719945C2×C414yes—
65C2×#11719945Q814yes—
66C22×Dic106D411yescharacteristic
67C22×D212D411yescharacteristic
68C22×C22⋊D53D411yescharacteristic
69C22×C22⋊D53D411yescharacteristic
70C22×C4×D53—21no—
71C22×C4×D53C2311yescharacteristic
72C22×C4×D53C2311yescharacteristic
73C2×#11719912—41no—
74C2×#11719912—41no—
75C2×#11719912C2×C414yescomplemented
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C2×C8×D53—41no—
79C2×C8×D53—41no—
80C2×C8×D53C2×C414yescomplemented
81#13133176—41no—
82#13133176—41no—
83#13133175—41no—
84#13133175—41no—
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2311yescharacteristic
89C2×#11719919—21no—
90C4⋊C4×D53—41no—
91C4⋊C4×D53—41no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53—21no—
103#13133151—41no—
104#13133150—41no—
105#13133149—41no—
106#13133148—41no—
107#13133148—41no—
108#13133148—41no—
109C22⋊#88322C2×C414yescomplemented
110#13133129C2×C414yescomplemented
111#13133129C2×C414yescomplemented
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118#13133124—21no—
119C23×C4×C53—21no—
120C23×C4×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—41no—
125C2×C4⋊C4×C53—41no—
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131#106×C53—41no—
132#106×C53—41no—
133C22⋊C8×C53C2×C414yescomplemented
134#95×C53—21no—
135C24×C53C2×D411yescharacteristic
136C23×D53C2×D411yescharacteristic
137C23×D53C2×D411yescharacteristic
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—42no—
147C22×C4×C53—81no—
148C22×C4×C53—81no—
149C22×C4×C53C22×C412yes—
150C22×C4×C53C2×D411yescharacteristic
151C22×C4×C53C2×Q812yes—
152C22×C4×C53C2411yescharacteristic
153C2×C22⋊D53—41no—
154C2×C22⋊D53—41no—
155C2×C22⋊D53—41no—
156C2×C22⋊D53—41no—
157C2×C22⋊D53C4⋊C414yes—
158C2×C22⋊D53C4⋊C414yes—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53C2×D411yescharacteristic
164C22×Dic53C2×D411yescharacteristic
165#11719945—44no—
166#11719945—44no—
167#11719945—44no—
168#11719945—44no—
169C2×D212—41no—
170C2×D212—41no—
171C2×D212C4⋊C414yes—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—42no—
181C2×C4×D53—81no—
182C2×C4×D53—81no—
183C2×C4×D53C22×C412yes—
184C2×C4×D53C22×C412yes—
185C2×C4×D53C2×Q812yes—
186C2×C4×D53C2×Q812yes—
187C2×Dic106—41no—
188C2×Dic106—41no—
189C2×Dic106C4⋊C414yes—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53C22×C412yes—
195C2×C8×C53C22×C412yes—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—42no—
205C22⋊C4×C53—81no—
206C22⋊Dic53—42no—
207C22⋊Dic53—81no—
208#11719921—42no—
209#11719921—81no—
210#11719921—81no—
211#11719921—81no—
212#11719921—81no—
213#11719921—81no—
214#11719921—81no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223#11719919—42no—
224C4×Dic53—42no—
225C4×Dic53—42no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322C22×C412yes—
231C2×#88322C22×C412yes—
232#11719912—44no—
233C8×D53—44no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53C2×C4⋊C412yes—
241C23×C53C22×D411yescharacteristic
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53C2×C4⋊C412yes—
255C22×D53C2×C4⋊C412yes—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—84no—
275C2×C4×C53C2×C4⋊C412yes—
276C2×C4×C53C23×C411yescharacteristic
277C2×C4×C53C22×Q811yescharacteristic
278C2×C4×C53H(5,𝔽2)11yescharacteristic
279C2×C4×C53H(5,𝔽2)11yescharacteristic
280C2×C4×C53H(5,𝔽2)11yescharacteristic
281C2×C4×C53H(5,𝔽2)11yescharacteristic
282C22⋊D53—44no—
283C22⋊D53—44no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53C2×C4⋊C412yes—
301C2×Dic53C2×C4⋊C412yes—
302D212—44no—
303C4×D53—22no—
304C4×D53—22no—
305C4×D53—22no—
306C4×D53—22no—
307C4×D53—22no—
308C4×D53—22no—
309C4×D53—22no—
310C4×D53—22no—
311C4×D53—84no—
312Dic106—44no—
313C8×C53—22no—
314C8×C53—22no—
315#88322—22no—
316#88322—22no—
317#21946—531nomaximal, Sylow
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53C22×C4⋊C411yescharacteristic
326C22×C53#53411yescharacteristic
327C22×C53#53411yescharacteristic
328C22×C53#57711yescharacteristic
329C22×C53#57711yescharacteristic
330C22×C53#57711yescharacteristic
331C22×C53#57711yescharacteristic
332C2×D53—22no—
333C2×D53—22no—
334C2×D53—22no—
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—41no—
339C2×D53—41no—
340C2×D53—41no—
341C2×D53—41no—
342C2×D53—41no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C4×C53—22no—
347C4×C53—81no—
348C4×C53—81no—
349C4×C53—81no—
350C4×C53—81no—
351C4×C53#51811yescharacteristic
352C4×C53#51811yescharacteristic
353C4×C53#54311yescharacteristic
354C4×C53#54311yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—81no—
358Dic53—81no—
359Dic53—81no—
360Dic53—81no—
361C2×#408—531no—
362#2311—531no—
363#2311—531no—
364#1854—531no—
365#1854—531no—
366#1854—531no—
367#1854—531no—
368#1853—531no—
369#1853—531no—
370#1853—531no—
371#1853D5311yescharacteristic, complemented
372#1809—531no—
373#1809—531no—
374#1807—531no—
375#1807—531no—
376C2×C53—42no—
377C2×C53#231511yescharacteristic
378C2×C53#291211yescharacteristic
379C2×C53#291211yescharacteristic
380C2×C53#320011yescharacteristic
381C2×C53#320011yescharacteristic
382C2×C53#320411yescharacteristic
383C2×C53#320411yescharacteristic
384D53—42no—
385D53—42no—
386C22×#41—531no—
387C22×M16—531no—
388C23×C8—531no—
389C2×#117—531no—
390C2×#117—531no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4C2×D5311yescharacteristic
393C2×#107—531no—
394C2×#107—531no—
395C2×#106—531no—
396C2×#106—531no—
397C2×#106—531no—
398C2×#106—531no—
399C2×#106C2×D5311yescharacteristic
400C2×#106C2×D5311yescharacteristic
401#408—538no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8C2×D5311yescharacteristic
406#391—1061no—
407#391—1061no—
408#390—1061no—
409#390—1061no—
410#386—1061no—
411#386—1061no—
412#386—1061no—
413#386—1061no—
414#380—531no—
415#380—531no—
416#380—531no—
417#380—531no—
418#380—531no—
419#380—531no—
420#380—531no—
421#380C2×D5311yescharacteristic
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340C2×D5311yescharacteristic
429#340C2×D5311yescharacteristic
430C53#2194611yescharacteristic, complemented, Sylow
431C2×#41—534no—
432C2×#41—534no—
433C2×#41—2121no—
434C2×#41—2121no—
435C2×#41—2121no—
436C2×#41—2121no—
437C22×Q8—531no—
438C22×D4—531no—
439C22×D4—531no—
440C22×D4—531no—
441C23×C4—21no—
442C23×C4—531no—
443C23×C4—531no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×M16—534no—
447C2×M16—2121no—
448C2×M16—2121no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—534no—
452C22×C8—2121no—
453C22×C8—2121no—
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456#117—2121no—
457#117—2121no—
458#117—2121no—
459#117—2121no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—1061no—
468C2×C4⋊C4—2121no—
469C2×C4⋊C4—2121no—
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C4⋊C4C22×D5311yescharacteristic
472C2×C4⋊C4C22×D5311yescharacteristic
473C2×C4⋊C4C22×D5311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C42—1061no—
485C2×C42—1061no—
486#107—2121no—
487#107—2121no—
488#106—41no—
489#106—41no—
490#106—2121no—
491#106—2121no—
492#106—2121no—
493#106—2121no—
494C22⋊C8—534no—
495C22⋊C8—534no—
496C22⋊C8—534no—
497C22⋊C8C4×D5314yescomplemented
498#95—21no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503#95—1061no—
504#95—1061no—
505#95—1061no—
506C24—531no—
507C24—531no—
508C24D4×D5311yescharacteristic
509#41—2124no—
510#41—2124no—
511#41—2124no—
512#41—2124no—
513C2×Q8—534no—
514C2×Q8—2121no—
515C2×Q8—2121no—
516C2×D4—534no—
517C2×D4—534no—
518C2×D4—534no—
519C2×D4—2121no—
520C2×D4—2121no—
521C2×D4—2121no—
522C2×D4—2121no—
523C2×D4—2121no—
524C2×D4—2121no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—531no—
537C22×C4—531no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—4241no—
555C22×C4—4241no—
556C22×C4—2122no—
557C22×C4C2×C4×D5312yes—
558C22×C4D4×D5311yescharacteristic
559C22×C4Q8×D5312yes—
560C22×C4C23×D5311yescharacteristic
561M16—2124no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—532no—
567C2×C8—532no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—2124no—
573C2×C8C2×C4×D5312yes—
574C2×C8C2×C4×D5312yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—2122no—
593C22⋊C4—81no—
594C22⋊C4—4241no—
595C22⋊C4—4241no—
596C22⋊C4—4241no—
597C22⋊C4—4241no—
598C22⋊C4—4241no—
599C22⋊C4—4241no—
600C22⋊C4—4241no—
601C22⋊C4—2122no—
602C22⋊C4—2122no—
603C42—2122no—
604C42—2122no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—532no—
612C23—532no—
613C23—1061no—
614C23—1061no—
615C23—1061no—
616C23—1061no—
617C23—1061no—
618C23—1061no—
619C23—1061no—
620C23—1061no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23—1061no—
625C23C4⋊C4×D5312yes—
626C23C2×D4×D5311yescharacteristic
627Q8—2124no—
628D4—2124no—
629D4—2124no—
630D4—2124no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—532no—
651C2×C4—532no—
652C2×C4—1061no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—4244no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4C4⋊C4×D5312yes—
678C2×C4C22×C4×D5311yescharacteristic
679C2×C4C2×Q8×D5311yescharacteristic
680C2×C4#1313326211yescharacteristic
681C2×C4#1313326211yescharacteristic
682C2×C4#1313326311yescharacteristic
683C2×C4#1313326311yescharacteristic
684C8—22no—
685C8—22no—
686C8—1062no—
687C8—1062no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—1062no—
696C22—1062no—
697C22—1062no—
698C22—1062no—
699C22—1062no—
700C22—1062no—
701C22—2121no—
702C22—2121no—
703C22—2121no—
704C22—2121no—
705C22—2121no—
706C22—2121no—
707C22—2121no—
708C22—2121no—
709C22C2×C4⋊C4×D5311yescharacteristic
710C22#1681118311yescharacteristic
711C22#1681118411yescharacteristic
712C22#1681142911yescharacteristic
713C22#1681142911yescharacteristic
714C22#1681143211yescharacteristic
715C22#1681143311yescharacteristic
716C4—22no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—1062no—
722C4—1062no—
723C4—4241no—
724C4—4241no—
725C4—4241no—
726C4—4241no—
727C4#1681109511yescharacteristic
728C4#1681109511yescharacteristic
729C4#1681124811yescharacteristic
730C4#1681124811yescharacteristic
731C2—42no—
732C2—2122no—
733C2—2122no—
734C2#2027732611yescharacteristic
735C2#2028330611yescharacteristic
736C2#2028330911yescharacteristic
737C2#2028558411yescharacteristic
738C2#2028558511yescharacteristic
739C2#2028562511yescharacteristic
740C2#2028562811yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1853C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1853D53
hypocenterC53#21946
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #20274917C2semidirect
5. #20274916C2semidirect
6. #20274915C2semidirect
7. #20274912C2semidirect
8. #20274908C2semidirect
9. #20274906C2semidirect
10. #20274906C2semidirect
11. #20274747C2semidirect
12. #20274745C2semidirect
13. #20274739C2semidirect
14. #20274737C2semidirect
15. C53×#1853C2semidirect
28. #16810588C4semidirect
75. C2×#11719912C2×C4semidirect
80. C2×C8×D53C2×C4semidirect
109. C22⋊#88322C2×C4semidirect
110. #13133129C2×C4semidirect
111. #13133129C2×C4semidirect
133. C22⋊C8×C53C2×C4semidirect
371. #1853D53semidirect
430. C53#21946semidirect
497. C22⋊C8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105882
#202773082
#202773042
#202749172
#202749162
#202749152
#202749122
#202749082
#202749062
#202747472
#202747452
#202747392
#202747372
C53×#18532
#2194653