Finite Group Databasebeta

← #27404458

Subgroups — #27404458

Order 13568.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810730C211yesmaximal, characteristic, complemented
2C2×#16810619C211yesmaximal, characteristic
3#20277746C211yesmaximal, characteristic, complemented
4#20277556C211yesmaximal, characteristic
5#20275598C211yesmaximal, characteristic, complemented
6#20275414C211yesmaximal, characteristic, complemented
7#20275344C211yesmaximal, characteristic, complemented
8#20275139C211yesmaximal, characteristic, complemented
9#20275072C211yesmaximal, characteristic, complemented
10#20275058C211yesmaximal, characteristic, complemented
11#20274971C211yesmaximal, characteristic, complemented
12#20274916C211yesmaximal, characteristic, complemented
13#20274547C211yesmaximal, characteristic, complemented
14#20274494C211yesmaximal, characteristic, complemented
15C2×C53×#452C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×Q8×Dic53C2211yescharacteristic
18C2×Q8×Dic53C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810730—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#16810526—21no—
35#16810526—21no—
36#16810526C2211yescharacteristic
37#16810526C2211yescharacteristic
38#16810522C2211yescharacteristic
39#16810516—21no—
40#16810516—21no—
41#16810509—21no—
42#16810483—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53—21no—
45C4⋊C4×Dic53C2211yescharacteristic
46C4×C22⋊Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
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
62C22×#88322—22no—
63C22×#88322—22no—
64C22×#88322—41no—
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67Q8×Dic53—22no—
68Q8×Dic53—22no—
69Q8×Dic53—22no—
70Q8×Dic53—41no—
71Q8×Dic53—41no—
72Q8×Dic53—41no—
73#13133176—22no—
74#13133176—41no—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53—21no—
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⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53D411yescharacteristic
90C2×C22⋊Dic53D411yescharacteristic
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53C2311yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98#13133151—41no—
99#13133149—22no—
100#13133141—22no—
101#13133141—22no—
102#13133141—41no—
103#13133141D414yes—
104#13133138—22no—
105#13133138—22no—
106#13133127—22no—
107#13133127—41no—
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—22no—
128C2×Q16×C53—22no—
129C2×Q16×C53C2×C414yes—
130C2×SD16×C53—41no—
131C2×SD16×C53—41no—
132C2×SD16×C53C2×C414yes—
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C22⋊Q8×C53—22no—
136C22⋊Q8×C53C2×C414yes—
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140#103×C53C2×C414yes—
141#102×C53C2×C414yes—
142C22⋊C8×C53C2×C414yes—
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×C53C22×C412yes—
158C2×Q8×C53C22×C412yes—
159C2×Q8×C53C2×D412yes—
160C2×Q8×C53#4112yes—
161C2×D4×C53—24no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—42no—
168C2×D4×C53—42no—
169C2×D4×C53C22×C412yes—
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×Dic53C2×D411yescharacteristic
189C22×Dic53C2×D411yescharacteristic
190C22×Dic53C2×D411yescharacteristic
191C22×Dic53C2×D411yescharacteristic
192Q16×C53—28no—
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—41no—
205C22⋊Dic53—41no—
206C22⋊Dic53—42no—
207C22⋊Dic53—42no—
208C22⋊Dic53—42no—
209C22⋊Dic53—81no—
210C22⋊Dic53—81no—
211C22⋊Dic53—81no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—42no—
220C4⋊Dic53—42no—
221C4⋊Dic53—42no—
222C4⋊Dic53—42no—
223C4⋊Dic53C2×D412yes—
224C4×Dic53—21no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—42no—
229C4×Dic53—42no—
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—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—22no—
247C23×C53—41no—
248C23×C53—41no—
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—22no—
260Q8×C53—41no—
261Q8×C53—41no—
262Q8×C53C4×D414yes—
263D4×C53—22no—
264D4×C53—22no—
265D4×C53—48no—
266D4×C53—41no—
267D4×C53—41no—
268C2×C4×C53—22no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—48no—
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—
315C8×C53—22no—
316C8×C53—22no—
317#88322—22no—
318#88322—41no—
319#22861—531nomaximal, Sylow
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—22no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—81no—
331C22×C53—81no—
332C22×C53—81no—
333C22×C53—81no—
334C22×C53C2×C4×D411yescharacteristic
335C22×C53D4211yescharacteristic
336C22×C53#54611yescharacteristic
337C22×C53#57511yescharacteristic
338C22×C53#57511yescharacteristic
339C22×C53#57711yescharacteristic
340C22×C53#57811yescharacteristic
341C4×C53—22no—
342C4×C53—24no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53C2×C4×D411yescharacteristic
346C4×C53#51811yescharacteristic
347C4×C53#54611yescharacteristic
348C4×C53#55111yescharacteristic
349Dic53—41no—
350Dic53—42no—
351Dic53—41no—
352Dic53—41no—
353Dic53—41no—
354Dic53—81no—
355Dic53—81no—
356Dic53—81no—
357C2×#452D5311yescharacteristic
358C2×#441—531no—
359C2×#416—531no—
360#2362—531no—
361#2341—531no—
362#1973—531no—
363#1936—531no—
364#1926—531no—
365#1892—531no—
366#1880—531no—
367#1878—531no—
368#1863—531no—
369#1854—531no—
370#1763—531no—
371#1752—531no—
372C2×C53—42no—
373C2×C53—82no—
374C2×C53#235811yescharacteristic
375C2×C53#294311yescharacteristic
376C2×C53#294711yescharacteristic
377C2×C53#326911yescharacteristic
378C2×C53#327111yescharacteristic
379C2×C53#331311yescharacteristic
380C2×C53#331711yescharacteristic
381C22×#41C2×D5311yescharacteristic
382C22×Q16C2×D5311yescharacteristic
383C22×SD16C2×D5311yescharacteristic
384C23×C8—531no—
385C2×C22⋊Q8C2×D5311yescharacteristic
386C2×C4×Q8—531no—
387C2×C4×Q8—531no—
388C2×C4×Q8—531no—
389C2×#117—531no—
390#452Dic5318yescomplemented
391#441—1064no—
392C2×#107—531no—
393C2×#106—531no—
394#416—1064no—
395C2×#103—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103C2×D5311yescharacteristic
400C2×#102—531no—
401C2×#102—531no—
402C2×#102C2×D5311yescharacteristic
403C2×C22⋊C8C2×D5311yescharacteristic
404C2×#97—531no—
405C2×#97—531no—
406#391—531no—
407#390—531no—
408#390—531no—
409#390—1061no—
410#390—1061no—
411#389—531no—
412#388—1061no—
413#388—1061no—
414#387—1061no—
415#380—531no—
416#380—1061no—
417C4×C4⋊C4—531no—
418C4×C4⋊C4—1061no—
419C4×C22⋊C4—531no—
420C4×C22⋊C4—1061no—
421#340—531no—
422#340—531no—
423#340—531no—
424#340—531no—
425#336—531no—
426#336—531no—
427C53#2286111yescharacteristic, complemented, Sylow
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41C2×Dic5314yes—
434C22×Q8C22×D5311yescharacteristic
435C22×Q8C22×D5311yescharacteristic
436C22×D4—21no—
437C22×D4C22×D5311yescharacteristic
438C23×C4—21no—
439C23×C4C22×D5311yescharacteristic
440C2×Q16—22no—
441C2×Q16—22no—
442C2×Q16C2×Dic5314yes—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×SD16C2×Dic5314yes—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8—1062no—
449C22×C8—1062no—
450C22×C8—2121no—
451C22×C8C22×D5311yescharacteristic
452C22×C8C22×D5311yescharacteristic
453C22⋊Q8—22no—
454C22⋊Q8C2×Dic5314yes—
455C4×Q8—1062no—
456C4×Q8—1062no—
457C4×Q8—1062no—
458C4×Q8—2121no—
459C4×Q8—2121no—
460C4×Q8—2121no—
461#117—1062no—
462#117—2121no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—531no—
468C2×C4⋊C4—1061no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4C22×D5311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—531no—
475C2×C22⋊C4—531no—
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×C42—531no—
483C2×C42—531no—
484C2×C42—1061no—
485C2×C42—1061no—
486C2×C42—1061no—
487C2×C42—1061no—
488C2×C42—1061no—
489#107—2121no—
490#106—1062no—
491#103—534no—
492#103—1062no—
493#103—1062no—
494#103—2121no—
495#103C2×Dic5314yes—
496#102—1062no—
497#102—1062no—
498#102C2×Dic5314yes—
499C22⋊C8C2×Dic5314yes—
500#97—1062no—
501#97—2121no—
502#95—531no—
503#95—531no—
504#95—1061no—
505#95—1061no—
506#95—1061no—
507#95—1061no—
508#95—1061no—
509C24—21no—
510C24D4×D5311yescharacteristic
511#41—28no—
512#41—44no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8D4×D5312yes—
524C2×Q8#1171994712yes—
525C2×Q8C22×Dic5312yes—
526C2×Q8C22×Dic5312yes—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C22×Dic5312yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—531no—
547C22×C4—531no—
548C22×C4—531no—
549C22×C4—531no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4D4×D5311yescharacteristic
555C22×C4#1171994712yes—
556C22×C4C22×Dic5312yes—
557C22×C4C23×D5311yescharacteristic
558Q16—28no—
559SD16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—532no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—2124no—
571C2×C8C22×Dic5312yes—
572C2×C8C22×Dic5312yes—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—532no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—2122no—
584C4⋊C4—2122no—
585C4⋊C4—2122no—
586C4⋊C4—2122no—
587C4⋊C4C22×Dic5312yes—
588C22⋊C4—24no—
589C22⋊C4—4241no—
590C22⋊C4—4241no—
591C22⋊C4—4241no—
592C22⋊C4—2121no—
593C22⋊C4—2121no—
594C22⋊C4—2122no—
595C22⋊C4—2122no—
596C22⋊C4—2122no—
597C42—1061no—
598C42—1061no—
599C42—1061no—
600C42—1061no—
601C42—2122no—
602C42—2122no—
603C42—2122no—
604C42—2122no—
605C42—2122no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23D4×Dic5312yes—
620C23C2×D4×D5311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—41no—
627Q8—41no—
628Q8D4×Dic5314yes—
629D4—22no—
630D4—22no—
631D4—48no—
632D4—41no—
633D4—41no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
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—1061no—
651C2×C4—1061no—
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—1062no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—2121no—
664C2×C4—2121no—
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×C4D4×Dic5312yes—
675C2×C4C23×Dic5311yescharacteristic
676C2×C4C2×D4×D5311yescharacteristic
677C2×C4C2×#1171994711yescharacteristic
678C2×C4C2×#1171994711yescharacteristic
679C2×C4#1313326211yescharacteristic
680C2×C4#1313326211yescharacteristic
681C8—22no—
682C8—22no—
683C8—1062no—
684C8—2121no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22C2×D4×Dic5311yescharacteristic
700C22#1681125511yescharacteristic
701C22#1681126011yescharacteristic
702C22#1681142011yescharacteristic
703C22#1681142011yescharacteristic
704C22#1681143211yescharacteristic
705C22#1681143911yescharacteristic
706C4—22no—
707C4—24no—
708C4—42no—
709C4—42no—
710C4—4241no—
711C4—4241no—
712C4—4241no—
713C4—2121no—
714C4—2122no—
715C4—2121no—
716C4—2121no—
717C4—2121no—
718C4C2×D4×Dic5311yescharacteristic
719C4#1681109811yescharacteristic
720C4#1681126011yescharacteristic
721C4#1681130411yescharacteristic
722C2—42no—
723C2—82no—
724C2#2027769911yescharacteristic
725C2#2028351611yescharacteristic
726C2#2028355911yescharacteristic
727C2#2028626311yescharacteristic
728C2#2028630411yescharacteristic
729C2#2028678511yescharacteristic
730C2#2028684511yescharacteristic
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#22861
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×#16810730C2semidirect
3. #20277746C2semidirect
5. #20275598C2semidirect
6. #20275414C2semidirect
7. #20275344C2semidirect
8. #20275139C2semidirect
9. #20275072C2semidirect
10. #20275058C2semidirect
11. #20274971C2semidirect
12. #20274916C2semidirect
13. #20274547C2semidirect
14. #20274494C2semidirect
58. C53×#452C4semidirect
390. #452Dic53semidirect
427. C53#22861semidirect

Maximal subgroups

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

subgroupindex
C2×#168107302
C2×#168106192
#202777462
#202775562
#202755982
#202754142
#202753442
#202751392
#202750722
#202750582
#202749712
#202749162
#202745472
#202744942
C2×C53×#4522
#2286153