Finite Group Databasebeta

← #27404383

Subgroups — #27404383

Order 13568.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810724C211yesmaximal, characteristic, complemented
2C2×#16810619C211yesmaximal, characteristic
3#20277746C211yesmaximal, characteristic, complemented
4#20277545C211yesmaximal, characteristic
5#20275587C211yesmaximal, characteristic, complemented
6#20275407C211yesmaximal, characteristic, complemented
7#20275358C211yesmaximal, characteristic, complemented
8#20275139C211yesmaximal, characteristic, complemented
9#20275058C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20274978C211yesmaximal, characteristic, complemented
12#20274916C211yesmaximal, characteristic, complemented
13#20274542C211yesmaximal, characteristic, complemented
14#20274494C211yesmaximal, characteristic, complemented
15C2×C53×#452C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×Q8×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810724—24no—
22C2×#13133151C2211yescharacteristic
23C2×#13133149C2211yescharacteristic
24#16810619—24no—
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33#16810530C2211yescharacteristic
34#16810530C2211yescharacteristic
35#16810530C2211yescharacteristic
36#16810522C2211yescharacteristic
37#16810516—21no—
38#16810516—21no—
39#16810509—21no—
40#16810503—21no—
41#16810503—21no—
42#16810486—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53—21no—
45C4⋊C4×Dic53C2211yescharacteristic
46C4×C22⋊Dic53C2211yescharacteristic
47C2×#13133124—21no—
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×#41×C53C2211yescharacteristic
55C22×Q16×C53C2211yescharacteristic
56C22×SD16×C53C2211yescharacteristic
57C2×C22⋊Q8×C53C2211yescharacteristic
58C53×#452C418yescomplemented
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C23×Dic53—21no—
63C23×Dic53—21no—
64C22×#88322—22no—
65C22×#88322—22no—
66C22×#88322—41no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69Q8×Dic53—22no—
70Q8×Dic53—41no—
71D4×Dic53—22no—
72D4×Dic53—22no—
73D4×Dic53—41no—
74D4×Dic53—41no—
75#13133176—22no—
76#13133176—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53D411yescharacteristic
88C2×C22⋊Dic53D411yescharacteristic
89C2×C4×Dic53—21no—
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53C2311yescharacteristic
93C2×C4×Dic53C2311yescharacteristic
94#13133151—22no—
95#13133149—41no—
96#13133141—22no—
97#13133141—22no—
98#13133141—22no—
99#13133141—41no—
100#13133138—22no—
101#13133138D414yes—
102#13133127—22no—
103#13133127—41no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124D411yescharacteristic
114#13133124D411yescharacteristic
115C2×#41×C53—22no—
116C2×#41×C53—22no—
117C2×#41×C53—22no—
118C2×#41×C53—41no—
119C2×#41×C53—41no—
120C2×#41×C53C2×C414yes—
121C22×Q8×C53C2311yescharacteristic
122C22×Q8×C53C2311yescharacteristic
123C22×D4×C53—21no—
124C22×D4×C53C2311yescharacteristic
125C23×C4×C53—21no—
126C23×C4×C53C2311yescharacteristic
127C2×Q16×C53—41no—
128C2×Q16×C53—41no—
129C2×Q16×C53C2×C414yescomplemented
130C2×SD16×C53—22no—
131C2×SD16×C53—22no—
132C2×SD16×C53C2×C414yes—
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C22⋊Q8×C53—22no—
136C22⋊Q8×C53C2×C414yescomplemented
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140#103×C53C2×C414yescomplemented
141#102×C53C2×C414yes—
142C22⋊C8×C53C2×C414yescomplemented
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145#41×C53—28no—
146#41×C53—44no—
147#41×C53—44no—
148#41×C53—44no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53C22×C412yes—
160C2×Q8×C53C22×C412yes—
161C2×D4×C53—24no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—42no—
166C2×D4×C53—42no—
167C2×D4×C53C22×C412yes—
168C2×D4×C53C2×D412yes—
169C2×D4×C53#4112yes—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—24no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53#4112yes—
183C22×C4×C53C2411yescharacteristic
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—42no—
189C22×Dic53—42no—
190C22×Dic53—42no—
191C22×Dic53—42no—
192C22×Dic53—81no—
193C22×Dic53—81no—
194C22×Dic53C2×D411yescharacteristic
195C22×Dic53C2×D411yescharacteristic
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198Q16×C53—44no—
199SD16×C53—28no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53C22×C412yes—
205C2×C8×C53C22×C412yes—
206C4⋊C4×C53—24no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53C22×C412yes—
209C22⋊C4×C53—24no—
210C22⋊Dic53—41no—
211C22⋊Dic53—41no—
212C22⋊Dic53—42no—
213C22⋊Dic53—42no—
214C22⋊Dic53—42no—
215C22⋊Dic53—81no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—42no—
224C4⋊Dic53—42no—
225C4⋊Dic53C2×D412yes—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—42no—
231C4×Dic53—42no—
232C4×Dic53—42no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—44no—
239C2×#88322C2×D412yes—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—21no—
243C23×C53—22no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53C4×D412yes—
254C23×C53C22×D411yescharacteristic
255Q8×C53—22no—
256Q8×C53—22no—
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—41no—
260Q8×C53—41no—
261Q8×C53—41no—
262Q8×C53—41no—
263D4×C53—22no—
264D4×C53—22no—
265D4×C53—22no—
266D4×C53—48no—
267D4×C53C4×D414yes—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—48no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53C4×D412yes—
285C2×C4×C53C23×C411yescharacteristic
286C2×C4×C53C22×D411yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C2×C4×C53C2×#4111yescharacteristic
289C2×C4×C53H(5,𝔽2)11yescharacteristic
290C2×C4×C53H(5,𝔽2)11yescharacteristic
291C2×Dic53—22no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—84no—
316C2×Dic53—84no—
317C8×C53—22no—
318C8×C53—22no—
319#88322—22no—
320#88322—41no—
321#22856—531nomaximal, Sylow
322C22×C53—22no—
323C22×C53—24no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—42no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—42no—
336C22×C53C2×C4×D411yescharacteristic
337C22×C53D4211yescharacteristic
338C22×C53#54611yescharacteristic
339C22×C53#57511yescharacteristic
340C22×C53#57511yescharacteristic
341C22×C53#57711yescharacteristic
342C22×C53#57811yescharacteristic
343C4×C53—22no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53C2×C4×D411yescharacteristic
348C4×C53#51811yescharacteristic
349C4×C53#54611yescharacteristic
350C4×C53#55111yescharacteristic
351Dic53—41no—
352Dic53—42no—
353Dic53—41no—
354Dic53—41no—
355Dic53—41no—
356Dic53—81no—
357Dic53—81no—
358Dic53—81no—
359C2×#452D5311yescharacteristic
360C2×#440—531no—
361C2×#416—531no—
362#2362—531no—
363#2339—531no—
364#1971—531no—
365#1935—531no—
366#1928—531no—
367#1892—531no—
368#1878—531no—
369#1877—531no—
370#1864—531no—
371#1854—531no—
372#1762—531no—
373#1752—531no—
374C2×C53—42no—
375C2×C53—44no—
376C2×C53#235811yescharacteristic
377C2×C53#294311yescharacteristic
378C2×C53#294711yescharacteristic
379C2×C53#326711yescharacteristic
380C2×C53#326911yescharacteristic
381C2×C53#331111yescharacteristic
382C2×C53#331511yescharacteristic
383C22×#41C2×D5311yescharacteristic
384C22×Q16C2×D5311yescharacteristic
385C22×SD16C2×D5311yescharacteristic
386C23×C8—531no—
387C2×C22⋊Q8C2×D5311yescharacteristic
388C2×C4×Q8—531no—
389C2×C4×D4—531no—
390C2×C4×D4—531no—
391C2×#117—531no—
392#452Dic5318yescomplemented
393#440—1064no—
394C2×#107—531no—
395C2×#106—531no—
396#416—1064no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103—531no—
400C2×#103—531no—
401C2×#103C2×D5311yescharacteristic
402C2×#102—531no—
403C2×#102—531no—
404C2×#102C2×D5311yescharacteristic
405C2×C22⋊C8C2×D5311yescharacteristic
406C2×#97—531no—
407C2×#97—531no—
408#391—531no—
409#391—531no—
410#391—531no—
411#389—531no—
412#388—1061no—
413#388—1061no—
414#387—1061no—
415#386—1061no—
416#386—1061no—
417#381—1061no—
418#380—531no—
419C4×C4⋊C4—531no—
420C4×C4⋊C4—1061no—
421C4×C22⋊C4—531no—
422C2×#95—1061no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#336—531no—
428#336—531no—
429C53#2285611yescharacteristic, complemented, Sylow
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C2×Dic5314yes—
436C22×Q8C22×D5311yescharacteristic
437C22×Q8C22×D5311yescharacteristic
438C22×D4—21no—
439C22×D4C22×D5311yescharacteristic
440C23×C4—21no—
441C23×C4—1061no—
442C23×C4—1061no—
443C23×C4C22×D5311yescharacteristic
444C2×Q16—41no—
445C2×Q16—41no—
446C2×Q16C2×Dic5314yescomplemented
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16C2×Dic5314yes—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—1062no—
453C22×C8—1062no—
454C22×C8—2121no—
455C22×C8C22×D5311yescharacteristic
456C22×C8C22×D5311yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8C2×Dic5314yescomplemented
459C4×Q8—1062no—
460C4×Q8—2121no—
461C4×D4—1062no—
462C4×D4—1062no—
463C4×D4—2121no—
464C4×D4—2121no—
465#117—1062no—
466#117—2121no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4C22×D5311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—531no—
477C2×C22⋊C4—531no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C42—531no—
483C2×C42—531no—
484C2×C42—1061no—
485C2×C42—1061no—
486C2×C42—1061no—
487#107—1062no—
488#106—2121no—
489#103—1062no—
490#103—1062no—
491#103—1062no—
492#103—2121no—
493#103C2×Dic5314yescomplemented
494#102—534no—
495#102—1062no—
496#102C2×Dic5314yes—
497C22⋊C8C2×Dic5314yescomplemented
498#97—1062no—
499#97—2121no—
500#95—531no—
501#95—531no—
502#95—1061no—
503#95—1061no—
504#95—1061no—
505#95—1061no—
506#95—1061no—
507#95—1061no—
508#95—1061no—
509#95—1061no—
510#95—1061no—
511C24—21no—
512C24D4×D5311yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C22×Dic5312yes—
528C2×Q8C22×Dic5312yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4D4×D5312yes—
536C2×D4#1171994712yes—
537C2×D4C22×Dic5312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—531no—
549C22×C4—531no—
550C22×C4—531no—
551C22×C4—531no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—4241no—
557C22×C4—4241no—
558C22×C4—2122no—
559C22×C4—2122no—
560C22×C4—2122no—
561C22×C4—2122no—
562C22×C4D4×D5311yescharacteristic
563C22×C4#1171994712yes—
564C22×C4C22×Dic5312yes—
565C22×C4C23×D5311yescharacteristic
566Q16—44no—
567SD16—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—532no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—2124no—
579C2×C8C22×Dic5312yes—
580C2×C8C22×Dic5312yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—532no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—2122no—
592C4⋊C4—2122no—
593C4⋊C4C22×Dic5312yes—
594C22⋊C4—24no—
595C22⋊C4—4241no—
596C22⋊C4—2121no—
597C22⋊C4—2121no—
598C22⋊C4—2122no—
599C22⋊C4—2122no—
600C22⋊C4—2122no—
601C42—1061no—
602C42—1061no—
603C42—1061no—
604C42—1061no—
605C42—2122no—
606C42—2122no—
607C42—2122no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—22no—
615C23—22no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23D4×Dic5312yes—
622C23C2×D4×D5311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4D4×Dic5314yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—1061no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1062no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—4244no—
666C2×C4—4244no—
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×C4—2121no—
678C2×C4D4×Dic5312yes—
679C2×C4C23×Dic5311yescharacteristic
680C2×C4C2×D4×D5311yescharacteristic
681C2×C4C2×#1171994711yescharacteristic
682C2×C4C2×#1171994711yescharacteristic
683C2×C4#1313326211yescharacteristic
684C2×C4#1313326211yescharacteristic
685C8—22no—
686C8—22no—
687C8—1062no—
688C8—2121no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×D4×Dic5311yescharacteristic
704C22#1681125511yescharacteristic
705C22#1681126011yescharacteristic
706C22#1681142011yescharacteristic
707C22#1681142011yescharacteristic
708C22#1681143211yescharacteristic
709C22#1681143911yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—4241no—
715C4—4241no—
716C4—4241no—
717C4—2121no—
718C4—2121no—
719C4—2122no—
720C4—2121no—
721C4—2121no—
722C4C2×D4×Dic5311yescharacteristic
723C4#1681109811yescharacteristic
724C4#1681126011yescharacteristic
725C4#1681130411yescharacteristic
726C2—42no—
727C2—44no—
728C2#2027769911yescharacteristic
729C2#2028351611yescharacteristic
730C2#2028355911yescharacteristic
731C2#2028624411yescharacteristic
732C2#2028627411yescharacteristic
733C2#2028675511yescharacteristic
734C2#2028681511yescharacteristic
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#22856
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. C2×#16810724C2semidirect
3. #20277746C2semidirect
5. #20275587C2semidirect
6. #20275407C2semidirect
7. #20275358C2semidirect
8. #20275139C2semidirect
9. #20275058C2semidirect
10. #20275051C2semidirect
11. #20274978C2semidirect
12. #20274916C2semidirect
13. #20274542C2semidirect
14. #20274494C2semidirect
58. C53×#452C4semidirect
129. C2×Q16×C53C2×C4semidirect
136. C22⋊Q8×C53C2×C4semidirect
140. #103×C53C2×C4semidirect
142. C22⋊C8×C53C2×C4semidirect
392. #452Dic53semidirect
429. C53#22856semidirect
446. C2×Q16C2×Dic53semidirect
458. C22⋊Q8C2×Dic53semidirect
493. #103C2×Dic53semidirect
497. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107242
C2×#168106192
#202777462
#202775452
#202755872
#202754072
#202753582
#202751392
#202750582
#202750512
#202749782
#202749162
#202745422
#202744942
C2×C53×#4522
#2285653