Finite Group Databasebeta

← #27417910

Subgroups — #27417910

Order 13568.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810961C211yesmaximal, characteristic, complemented
2C2×#16810663C211yesmaximal, characteristic, complemented
3#20279012C211yesmaximal, characteristic
4#20276045C211yesmaximal, characteristic, complemented
5#20276040C211yesmaximal, characteristic, complemented
6#20275915C211yesmaximal, characteristic, complemented
7#20275908C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275013C211yesmaximal, characteristic
10#20274983C211yesmaximal, characteristic, complemented
11#20274969C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14#20274801C211yesmaximal, characteristic, complemented
15C2×C53×#554C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18#16810961—24no—
19#16810663—24no—
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33#16810551—21no—
34#16810537—21no—
35#16810521C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810511—21no—
38#16810504—21no—
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#554—24no—
51C53×#554—24no—
52C2×C4⋊Q8×C53C2211yescharacteristic
53C2×#125×C53—21no—
54C2×C22⋊Q8×C53—21no—
55C2×C22⋊Q8×C53—21no—
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×C22⋊Q8×C53C2211yescharacteristic
58C2×C4×Q8×C53C2211yescharacteristic
59C2×C4×D4×C53—21no—
60C2×C4×D4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C2×#11719917—22no—
64C2×#11719917—22no—
65C2×#11719917—22no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133176—22no—
71#13133176—22no—
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133150—22no—
85#13133150—22no—
86#13133148—22no—
87#13133148—22no—
88#13133148—22no—
89#13133141—22no—
90#13133141—22no—
91#13133141—22no—
92#13133141—22no—
93C22⋊#88322—22no—
94C22⋊#88322—22no—
95C22⋊#88322—22no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101C22×Q8×C53—21no—
102C22×Q8×C53C2311yescharacteristic
103C22×D4×C53D411yescharacteristic
104C23×C4×C53—21no—
105C23×C4×C53—21no—
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108C4⋊Q8×C53—22no—
109C4⋊Q8×C53—22no—
110#125×C53—28no—
111C22⋊Q8×C53—28no—
112C22⋊Q8×C53—28no—
113C22⋊Q8×C53—22no—
114C22⋊Q8×C53—22no—
115C22⋊Q8×C53—22no—
116C22⋊Q8×C53D414yes—
117C4×Q8×C53—22no—
118C4×Q8×C53—22no—
119C4×D4×C53—28no—
120C4×D4×C53—22no—
121C4×D4×C53—22no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53D414yes—
132C2×C4⋊C4×C53D411yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53D411yescharacteristic
139C2×C22⋊C4×C53D411yescharacteristic
140C2×C42×C53—21no—
141C2×C42×C53C2311yescharacteristic
142C24×C53C2×D411yescharacteristic
143C24×C53C2×D411yescharacteristic
144C2×Q8×C53—24no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—81no—
151C2×Q8×C53—81no—
152C2×Q8×C53C2×D412yes—
153C2×D4×C53—22no—
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—24no—
165C22×C4×C53—24no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—81no—
173C22×C4×C53—81no—
174C22×C4×C53—81no—
175C22×C4×C53—81no—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2411yescharacteristic
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C4⋊C4×C53—24no—
188C4⋊C4×C53—24no—
189C4⋊C4×C53—24no—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—24no—
193C4⋊C4×C53—22no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53C2×D412yes—
198C4⋊C4×C53C2×D412yes—
199C4⋊C4×C53C2×D412yes—
200C22⋊C4×C53—24no—
201C22⋊C4×C53—24no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—22no—
204C42×C53—24no—
205C42×C53—21no—
206C42×C53—21no—
207C22⋊Dic53—42no—
208C22⋊Dic53—42no—
209C22⋊Dic53—81no—
210C22⋊Dic53—81no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219#11719919—42no—
220#11719919—81no—
221C4×Dic53—42no—
222#11719917—28no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322#4112yes—
234C2×#88322#4112yes—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53#12012yes—
248C23×C53#13712yes—
249C23×C53C22×D411yescharacteristic
250Q8×C53—22no—
251Q8×C53—22no—
252Q8×C53—41no—
253Q8×C53—41no—
254Q8×C53—84no—
255D4×C53—28no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
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×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—84no—
287C2×C4×C53—84no—
288C2×C4×C53#12012yes—
289C2×C4×C53#13712yes—
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C53C22×D411yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C53C2×#4111yescharacteristic
294C2×C4×C532−1+411yescharacteristic
295C2×C4×C532−1+411yescharacteristic
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
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—
308#88322—22no—
309#88322—22no—
310#88322—41no—
311#88322—41no—
312#24109—531nomaximal, Sylow
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53C2×#12011yescharacteristic
328C22×C53#54711yescharacteristic
329C22×C53#54711yescharacteristic
330C22×C53C2×#13711yescharacteristic
331C22×C53C2×#13711yescharacteristic
332C22×C53#57611yescharacteristic
333C22×C53#57711yescharacteristic
334C4×C53—22no—
335C4×C53—22no—
336C4×C53—41no—
337C4×C53—42no—
338C4×C53—41no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53#52511yescharacteristic
343C4×C53#53611yescharacteristic
344C4×C53#54711yescharacteristic
345C4×C53#54711yescharacteristic
346Dic53—81no—
347Dic53—81no—
348Dic53—81no—
349Dic53—81no—
350C2×#554D5311yescharacteristic
351C2×#485—531no—
352C2×#428—531no—
353#2485—531no—
354#2058—531no—
355#2057—531no—
356#2036—531no—
357#2035—531no—
358#1894—531no—
359#1870—531no—
360#1865—531no—
361#1863—531no—
362#1853—531no—
363#1852—531no—
364#1823—531no—
365C2×C53—42no—
366C2×C53—42no—
367C2×C53#240611yescharacteristic
368C2×C53#300411yescharacteristic
369C2×C53#301211yescharacteristic
370C2×C53#334411yescharacteristic
371C2×C53#334611yescharacteristic
372C2×C53#335611yescharacteristic
373C2×C53#335711yescharacteristic
374C22×M16—531no—
375#554—24no—
376#554—24no—
377C2×C4⋊Q8C2×D5311yescharacteristic
378C2×#125—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D5311yescharacteristic
382C2×C22⋊Q8C2×D5311yescharacteristic
383C2×C4×Q8C2×D5311yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4C2×D5311yescharacteristic
386C2×#117—531no—
387C22×C4⋊C4C2×D5311yescharacteristic
388C22×C4⋊C4C2×D5311yescharacteristic
389#485—1064no—
390#428—1064no—
391C2×#107—531no—
392C2×#107—531no—
393C2×#107—531no—
394C2×#106—531no—
395C2×#106—531no—
396C2×#106—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103—531no—
400C2×#103—531no—
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404#397—1061no—
405#394—1061no—
406#389—531no—
407#389—531no—
408#388—1061no—
409#387—1061no—
410#380—531no—
411#380—531no—
412#380—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419#336—531no—
420#336—531no—
421C53#2410911yescharacteristic, complemented, Sylow
422C22×Q8—21no—
423C22×Q8C22×D5311yescharacteristic
424C22×D4C22⋊D5311yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C22×D5311yescharacteristic
428C23×C4C22×D5311yescharacteristic
429C2×M16—1062no—
430C2×M16—1062no—
431C2×M16—1062no—
432C22×C8—531no—
433C22×C8—531no—
434C22×C8—531no—
435C22×C8—531no—
436C4⋊Q8—22no—
437C4⋊Q8—22no—
438#125—28no—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8C22⋊D5314yes—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×D4—28no—
448C4×D4—22no—
449C4×D4—22no—
450#117—1062no—
451#117—1062no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—1061no—
466C2×C4⋊C4—1061no—
467C2×C4⋊C4C22⋊D5311yescharacteristic
468C2×C4⋊C4C22⋊D5314yes—
469C2×C4⋊C4C22×D5311yescharacteristic
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C4⋊C4C22×D5311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C22⋊C4C22⋊D5311yescharacteristic
479C2×C22⋊C4C22⋊D5311yescharacteristic
480C2×C42—21no—
481C2×C42—1061no—
482C2×C42C22×D5311yescharacteristic
483#107—1062no—
484#107—1062no—
485#107—1062no—
486#106—1062no—
487#106—1062no—
488#106—1062no—
489#103—1062no—
490#103—1062no—
491#103—1062no—
492#103—1062no—
493C22⋊C8—1062no—
494C22⋊C8—1062no—
495C22⋊C8—1062no—
496#95—1061no—
497#95—1061no—
498#95—1061no—
499#95—1061no—
500#95—1061no—
501C24C2×C22⋊D5311yescharacteristic
502C24C2×C22⋊D5311yescharacteristic
503C2×Q8—24no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—81no—
510C2×Q8—81no—
511C2×Q8C2×C22⋊D5312yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4C2×C22⋊D5311yescharacteristic
540C22×C4C2×C22⋊D5311yescharacteristic
541C22×C4C2×C22⋊D5311yescharacteristic
542C22×C4C2×C22⋊D5312yes—
543C22×C4C2×C22⋊D5312yes—
544C22×C4C2×C22⋊D5311yescharacteristic
545C22×C4C23×D5311yescharacteristic
546M16—1068no—
547C2×C8—532no—
548C2×C8—532no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—1061no—
552C2×C8—1061no—
553C2×C8—1061no—
554C2×C8—1061no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—1061no—
570C4⋊C4—1061no—
571C4⋊C4—1061no—
572C4⋊C4—1061no—
573C4⋊C4—1061no—
574C4⋊C4—1061no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—4241no—
578C4⋊C4—2122no—
579C4⋊C4C2×C22⋊D5312yes—
580C4⋊C4C2×C22⋊D5312yes—
581C4⋊C4C2×C22⋊D5312yes—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—4241no—
587C22⋊C4—4241no—
588C22⋊C4—2122no—
589C22⋊C4—2122no—
590C42—24no—
591C42—21no—
592C42—21no—
593C42—2122no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23#1313318612yes—
607C23#1313324812yes—
608C23C22×C22⋊D5311yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—84no—
614D4—28no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
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—84no—
646C2×C4—84no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4#1313318612yes—
660C2×C4#1313324812yes—
661C2×C4C22×C22⋊D5311yescharacteristic
662C2×C4C22×C22⋊D5311yescharacteristic
663C2×C4#41×D5311yescharacteristic
664C2×C4#41×D5311yescharacteristic
665C2×C4#1313326411yescharacteristic
666C2×C4#1313326411yescharacteristic
667C8—1062no—
668C8—1062no—
669C8—2121no—
670C8—2121no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×#1313318611yescharacteristic
686C22#1681127211yescharacteristic
687C22#1681127211yescharacteristic
688C22C2×#1313324811yescharacteristic
689C22C2×#1313324811yescharacteristic
690C22#1681142611yescharacteristic
691C22#1681143411yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—4241no—
701C4—4241no—
702C4—4241no—
703C4—4241no—
704C4#1681113011yescharacteristic
705C4#1681119411yescharacteristic
706C4#1681127211yescharacteristic
707C4#1681127211yescharacteristic
708C2—42no—
709C2—42no—
710C2#2027804611yescharacteristic
711C2#2028394911yescharacteristic
712C2#2028401911yescharacteristic
713C2#2028716411yescharacteristic
714C2#2028719411yescharacteristic
715C2#2028733011yescharacteristic
716C2#2028734111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#554D53
hypocenterC53#24109
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16810961C2semidirect
2. C2×#16810663C2semidirect
4. #20276045C2semidirect
5. #20276040C2semidirect
6. #20275915C2semidirect
7. #20275908C2semidirect
8. #20275149C2semidirect
10. #20274983C2semidirect
11. #20274969C2semidirect
12. #20274908C2semidirect
13. #20274903C2semidirect
14. #20274801C2semidirect
421. C53#24109semidirect

Maximal subgroups

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

subgroupindex
C2×#168109612
C2×#168106632
#202790122
#202760452
#202760402
#202759152
#202759082
#202751492
#202750132
#202749832
#202749692
#202749082
#202749032
#202748012
C2×C53×#5542
#2410953