Finite Group Databasebeta

← #27401355

Subgroups — #27401355

Order 13568.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810628C211yesmaximal, characteristic
2#20277610C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic53C211yesmaximal, characteristic
4#20275409C211yesmaximal, characteristic, complemented
5#20275395C211yesmaximal, characteristic, complemented
6#20275345C211yesmaximal, characteristic, complemented
7#20275338C211yesmaximal, characteristic, complemented
8#20274974C211yesmaximal, characteristic, complemented
9#20274960C211yesmaximal, characteristic, complemented
10#20274811C211yesmaximal, characteristic, complemented
11#20274746C211yesmaximal, characteristic, complemented
12#20274542C211yesmaximal, characteristic, complemented
13#102×Dic53C211yesmaximal, characteristic, complemented
14#20274501C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×D4×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20C22×C22⋊Dic53—21no—
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23#16810628C418yescomplemented
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133127C2211yescharacteristic, complemented
29C2×C8×Dic53C2211yescharacteristic, complemented
30#16810526C2211yescharacteristic
31#16810526C2211yescharacteristic
32#16810519C2211yescharacteristic, complemented
33#16810519C2211yescharacteristic, complemented
34#16810511—21no—
35#16810511—21no—
36#16810503—21no—
37#16810503—21no—
38#16810490—21no—
39#16810483C2211yescharacteristic
40#16810479—21no—
41C4⋊C4×Dic53C2211yescharacteristic, complemented
42C4⋊C4×Dic53C2211yescharacteristic, complemented
43#16810474—21no—
44C4×C22⋊Dic53C2211yescharacteristic
45#16810386C2211yescharacteristic, complemented
46#16810386C2211yescharacteristic, complemented
47#16810386C2211yescharacteristic, complemented
48#16810386C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810377C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53C23×D4×C53C2211yescharacteristic
54C2×#102×C53C2211yescharacteristic
55C2×#102×C53C2211yescharacteristic
56C2×#102×C53C2211yescharacteristic
57C2×#102×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C23×Dic53—21no—
61C23×Dic53—21no—
62C2×#11719917—41no—
63C2×#11719917—41no—
64C2×#11719917C2×C414yescomplemented
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67D4×Dic53—22no—
68D4×Dic53—22no—
69D4×Dic53—41no—
70D4×Dic53—41no—
71#13133176—22no—
72#13133176C2×C414yescomplemented
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×C4⋊Dic53C2311yescharacteristic
77C2×#11719919—21no—
78C2×#11719919—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—44no—
88C2×C22⋊Dic53D411yescharacteristic
89C2×C22⋊Dic53D411yescharacteristic
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53C2311yescharacteristic
94C2×C4×Dic53C2311yescharacteristic
95#13133150—41no—
96#13133148—41no—
97#13133138C2×C414yes—
98#13133138C2×C414yes—
99#13133138C2×C414yescomplemented
100#13133138C2×C414yescomplemented
101#13133127—41no—
102C8×Dic53—41no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124D411yescharacteristic
109#13133124D411yescharacteristic
110C25×C53—21no—
111C22×D4×C53—22no—
112C22×D4×C53—22no—
113C22×D4×C53—21no—
114C22×D4×C53—22no—
115C22×D4×C53—41no—
116C22×D4×C53—41no—
117C22×D4×C53C2×C414yes—
118C22×D4×C53C2311yescharacteristic
119C22×D4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126#102×C53—22no—
127#102×C53—22no—
128#102×C53—41no—
129#102×C53—41no—
130C22⋊C8×C53—22no—
131#95×C53—21no—
132C24×C53—21no—
133C24×C53—21no—
134C24×C53—24no—
135C24×C53—42no—
136C24×C53—42no—
137C24×C53—42no—
138C24×C53—42no—
139C24×C53—81no—
140C24×C53—81no—
141C24×C53C2×D411yescharacteristic
142C2×D4×C53—28no—
143C2×D4×C53—24no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—44no—
153C2×D4×C53—44no—
154C2×D4×C53—44no—
155C2×D4×C53—42no—
156C2×D4×C53—42no—
157C2×D4×C53C22×C412yes—
158C2×D4×C53C22×C412yes—
159C2×D4×C53#4112yes—
160C2×D4×C53#4112yes—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53C22×C412yes—
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53#4112yes—
170C22×C4×C53C2411yescharacteristic
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—42no—
176C22×Dic53—42no—
177C22×Dic53—42no—
178C22×Dic53—42no—
179C22×Dic53—81no—
180C22×Dic53—81no—
181C22×Dic53C2×D411yescharacteristic
182C22×Dic53C2×D411yescharacteristic
183C22×Dic53C2×D411yescharacteristic
184C22×Dic53C2×D411yescharacteristic
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C22⋊C4×C53—81no—
196C22⋊Dic53—24no—
197C22⋊Dic53—22no—
198C22⋊Dic53—41no—
199C22⋊Dic53—42no—
200C22⋊Dic53—42no—
201C22⋊Dic53—42no—
202C22⋊Dic53—42no—
203C22⋊Dic53—42no—
204C22⋊Dic53—81no—
205C22⋊Dic53—81no—
206C4⋊Dic53—21no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53C22×C412yes—
213C4⋊Dic53C22×C412yes—
214#11719919—42no—
215#11719919—42no—
216C4×Dic53—24no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—21no—
220C4×Dic53—21no—
221C4×Dic53—81no—
222C4×Dic53—81no—
223#11719917—44no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322C22×C412yes—
229C2×#88322C22×C412yes—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—22no—
240C23×C53—48no—
241C23×C53—48no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—84no—
253C23×C53—84no—
254C23×C53—84no—
255C23×C53—84no—
256C23×C53—84no—
257C23×C53C4×D412yes—
258C23×C53C22×D411yescharacteristic
259D4×C53—22no—
260D4×C53—22no—
261D4×C53—22no—
262D4×C53—22no—
263D4×C53—22no—
264D4×C53—48no—
265D4×C53—41no—
266D4×C53—41no—
267D4×C53#11714yes—
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—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53C4×D412yes—
281C2×C4×C53C23×C411yescharacteristic
282C2×C4×C53C2×#4111yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53H(5,𝔽2)11yescharacteristic
286C2×C4×C53H(5,𝔽2)11yescharacteristic
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—21no—
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—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—84no—
311C2×Dic53—84no—
312C2×Dic53AGL(1,ℤ/8)12yes—
313C8×C53—41no—
314C8×C53—41no—
315#88322—22no—
316#88322—22no—
317#22580—531nomaximal, Sylow
318C22×C53—22no—
319C22×C53—24no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—41no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—41no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—816no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53C2×C4×D411yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53#54611yescharacteristic
343C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C53#57511yescharacteristic
345C22×C53#57611yescharacteristic
346C22×C53#57711yescharacteristic
347C4×C53—22no—
348C4×C53—81no—
349C4×C53—81no—
350C4×C53C2×#11711yescharacteristic
351C4×C53#51811yescharacteristic
352C4×C53#55111yescharacteristic
353C4×C53#55111yescharacteristic
354Dic53—22no—
355Dic53—42no—
356Dic53—42no—
357Dic53—41no—
358Dic53—41no—
359Dic53—41no—
360Dic53—81no—
361Dic53—81no—
362C2×#418—531no—
363#2347—531no—
364D4×C22⋊C4—531no—
365#1936—531no—
366#1934—531no—
367#1926—531no—
368#1925—531no—
369#1864—531no—
370#1862—531no—
371#1825—531no—
372#1809—531no—
373#1786D5311yescharacteristic
374#1762—531no—
375C4×#102—531no—
376#1753—531no—
377C2×C53—42no—
378C2×C53—44no—
379C2×C53—82no—
380C2×C53#234211yescharacteristic
381C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C53#294611yescharacteristic
383C2×C53#331111yescharacteristic
384C2×C53#331811yescharacteristic
385C2×C53#332211yescharacteristic
386C2×C53#332411yescharacteristic
387C23×D4C2×D5311yescharacteristic
388C22×M16—531no—
389C2×C4×D4—531no—
390C2×C4×D4—531no—
391C2×#117—531no—
392C22×C22⋊C4—1061no—
393C2×#107—531no—
394C2×#106—531no—
395#418—538no—
396C2×#102—531no—
397C2×#102—531no—
398C2×#102—531no—
399C2×#102—531no—
400C2×#102C2×D5311yescharacteristic
401C2×#102C2×D5311yescharacteristic
402C2×#102C2×D5311yescharacteristic
403C2×#102C2×D5311yescharacteristic
404C2×C22⋊C8C2×D5311yescharacteristic
405C2×#97—531no—
406C2×C4×C8—531no—
407#390—531no—
408#390—531no—
409#389—531no—
410#389—531no—
411#388—1061no—
412#388—1061no—
413#386—1061no—
414#386—1061no—
415#383—1061no—
416#380—531no—
417#380C2×D5311yescharacteristic
418#379—1061no—
419C4×C4⋊C4—531no—
420C4×C4⋊C4—531no—
421C4×C4⋊C4—1061no—
422C4×C22⋊C4—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#336—531no—
430#336—531no—
431C53#2258011yescharacteristic, complemented, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C4×D5314yes—
440C22×D4C22×D5311yescharacteristic
441C22×D4C22×D5311yescharacteristic
442C23×C4—1061no—
443C23×C4—1061no—
444C23×C4C22×D5311yescharacteristic
445C2×M16—534no—
446C2×M16—2121no—
447C2×M16—2121no—
448C22×C8—531no—
449C22×C8—531no—
450C22×C8C22×D5311yescharacteristic
451C22×C8C22×D5311yescharacteristic
452C4×D4—1062no—
453C4×D4—1062no—
454C4×D4—2121no—
455C4×D4—2121no—
456#117—534no—
457#117—1062no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—1061no—
463C2×C4⋊C4—1061no—
464C2×C4⋊C4C22×D5311yescharacteristic
465C2×C4⋊C4C22×D5311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—1061no—
470C2×C22⋊C4—1061no—
471C2×C22⋊C4—1061no—
472C2×C22⋊C4—1061no—
473C2×C22⋊C4—1061no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—2124no—
478C2×C42—531no—
479C2×C42—531no—
480C2×C42—1061no—
481C2×C42—1061no—
482C2×C42—1061no—
483#107—2121no—
484#106—2121no—
485#102—22no—
486#102—22no—
487#102—41no—
488#102—41no—
489#102—534no—
490#102—534no—
491#102—534no—
492#102—534no—
493C22⋊C8—22no—
494#97—2121no—
495C4×C8—2121no—
496#95—21no—
497#95—531no—
498#95—531no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503#95—1061no—
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24D4×D5311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C2×C4×D5312yes—
530C2×D4C2×C4×D5312yes—
531C2×D4#1171994712yes—
532C2×D4#1171994712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—531no—
540C22×C4—531no—
541C22×C4—531no—
542C22×C4—531no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—4241no—
548C22×C4—4241no—
549C22×C4—2122no—
550C22×C4—2122no—
551C22×C4—2122no—
552C22×C4—2122no—
553C22×C4C2×C4×D5312yes—
554C22×C4D4×D5311yescharacteristic
555C22×C4#1171994712yes—
556C22×C4C23×D5311yescharacteristic
557M16—2124no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—532no—
565C2×C8—532no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—532no—
575C4⋊C4—532no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—2122no—
583C4⋊C4—2122no—
584C22⋊C4—81no—
585C22⋊C4—1062no—
586C22⋊C4—1064no—
587C22⋊C4—4241no—
588C22⋊C4—4241no—
589C22⋊C4—2122no—
590C22⋊C4—2121no—
591C22⋊C4—2122no—
592C22⋊C4—2122no—
593C22⋊C4—2122no—
594C22⋊C4—2122no—
595C42—1064no—
596C42—1061no—
597C42—1061no—
598C42—1061no—
599C42—1061no—
600C42—4241no—
601C42—4241no—
602C23—22no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—22no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23#1313317712yes—
630C23C2×D4×D5311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1313317314yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—532no—
653C2×C4—1061no—
654C2×C4—1061no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1061no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—4244no—
667C2×C4—4244no—
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×C4#1313317712yes—
679C2×C4C22×C4×D5311yescharacteristic
680C2×C4C2×#1171994711yescharacteristic
681C2×C4C2×#1171994711yescharacteristic
682C2×C4C2×#1171994711yescharacteristic
683C2×C4#1313326211yescharacteristic
684C2×C4#1313326211yescharacteristic
685C8—41no—
686C8—41no—
687C8—1062no—
688C8—1062no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×#1313317711yescharacteristic
712C22#1681126011yescharacteristic
713C22#1681126011yescharacteristic
714C22AGL(1,ℤ/8)×D5311yescharacteristic
715C22#1681141911yescharacteristic
716C22#1681142411yescharacteristic
717C22#1681142911yescharacteristic
718C4—22no—
719C4—81no—
720C4—81no—
721C4—1062no—
722C4—4241no—
723C4—4241no—
724C4—2121no—
725C4—2122no—
726C4—2122no—
727C4—2121no—
728C4—2121no—
729C4C2×#1313317311yescharacteristic
730C4#1681109611yescharacteristic
731C4#1681130411yescharacteristic
732C4#1681130411yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2027756611yescharacteristic
737C2#2028351911yescharacteristic
738C2#2028354111yescharacteristic
739C2#2028674411yescharacteristic
740C2#2028684911yescharacteristic
741C2#2028692011yescharacteristic
742C2#2028693911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1786C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
cosocleC22×C4×C53C24
hypercenter#1786D53
hypocenterC53#22580
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #20277610C2semidirect
4. #20275409C2semidirect
5. #20275395C2semidirect
6. #20275345C2semidirect
7. #20275338C2semidirect
8. #20274974C2semidirect
9. #20274960C2semidirect
10. #20274811C2semidirect
11. #20274746C2semidirect
12. #20274542C2semidirect
13. #102×Dic53C2semidirect
14. #20274501C2semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. #16810628C4semidirect
28. C2×#13133127C22semidirect
29. C2×C8×Dic53C22semidirect
32. #16810519C22semidirect
33. #16810519C22semidirect
41. C4⋊C4×Dic53C22semidirect
42. C4⋊C4×Dic53C22semidirect
45. #16810386C22semidirect
46. #16810386C22semidirect
47. #16810386C22semidirect
48. #16810386C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810377C22semidirect
52. #16810377C22semidirect
64. C2×#11719917C2×C4semidirect
72. #13133176C2×C4semidirect
99. #13133138C2×C4semidirect
100. #13133138C2×C4semidirect
431. C53#22580semidirect

Maximal subgroups

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

subgroupindex
C2×#168106282
#202776102
D4×C22⋊Dic532
#202754092
#202753952
#202753452
#202753382
#202749742
#202749602
#202748112
#202747462
#202745422
#102×Dic532
#202745012
C53×#17862
#2258053