Finite Group Databasebeta

← #27404510

Subgroups — #27404510

Order 13568.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810762C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C2×#16810632C211yesmaximal, characteristic, complemented
4#20277751C211yesmaximal, characteristic
5#20275572C211yesmaximal, characteristic, complemented
6#20275408C211yesmaximal, characteristic, complemented
7#20275353C211yesmaximal, characteristic, complemented
8#20275151C211yesmaximal, characteristic
9#20275070C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274983C211yesmaximal, characteristic, complemented
12#20274912C211yesmaximal, characteristic, complemented
13C4×#13133141C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×#13133176C2211yescharacteristic
22#16810762C418yescomplemented
23#16810721—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26#16810632—24no—
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810523—21no—
40#16810521C2211yescharacteristic
41#16810512—21no—
42#16810499—21no—
43C4×C4⋊Dic53C2211yescharacteristic
44#16810470—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C23×Q8×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C2×C4×Q8×C53C2211yescharacteristic
54C53×#391—21no—
55C53×#391—21no—
56C53×#391C2211yescharacteristic
57C53×#391C2211yescharacteristic
58C53×#380—21no—
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C4×C22⋊C4×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C4×D53—21no—
65C2×#11719924—22no—
66C2×#11719924—22no—
67C2×#11719924—41no—
68C2×#11719924—41no—
69C2×#11719924C2×C414yes—
70C2×#11719924C2×C414yes—
71C2×#11719917—22no—
72C2×#11719917—22no—
73C2×#11719917—41no—
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78#13133191—22no—
79#13133191C2×C414yes—
80C4×D212—22no—
81C4×D212—41no—
82#13133176—22no—
83#13133176—41no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×C4×Dic53—21no—
94C2×C4×Dic53—21no—
95#13133150—22no—
96#13133148—41no—
97#13133141—22no—
98#13133141—22no—
99#13133141—22no—
100#13133141C2×C414yescomplemented
101#13133141C2×C414yescomplemented
102#13133141D414yescomplemented
103#13133137—22no—
104#13133137—41no—
105C22⋊#88322C2×C414yescomplemented
106#13133128—22no—
107C4×#88322—41no—
108#13133124—21no—
109#13133124—21no—
110C22×Q8×C53—21no—
111C22×Q8×C53—22no—
112C22×Q8×C53—22no—
113C22×Q8×C53—22no—
114C22×Q8×C53—41no—
115C22×Q8×C53—41no—
116C22×Q8×C53C2×C414yescomplemented
117C22×Q8×C53C2311yescharacteristic
118C22×Q8×C53C2311yescharacteristic
119C23×C4×C53—21no—
120C23×C4×C53C2311yescharacteristic
121C4×Q8×C53—22no—
122C4×Q8×C53—22no—
123C4×Q8×C53—41no—
124C4×Q8×C53—41no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C42×C53—21no—
133C2×C42×C53—21no—
134C2×C42×C53C2311yescharacteristic
135C2×C42×C53C2311yescharacteristic
136#95×C53—21no—
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53D411yescharacteristic
142#95×C53D411yescharacteristic
143C24×C53C2×D411yescharacteristic
144C23×D53—21no—
145C2×Q8×C53—24no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—28no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—42no—
156C2×Q8×C53—42no—
157C2×Q8×C53—44no—
158C2×Q8×C53—44no—
159C2×Q8×C53—44no—
160C2×Q8×C53C22×C412yes—
161C2×Q8×C53C22×C412yes—
162C2×Q8×C53C2×D412yes—
163C2×Q8×C53#4112yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—24no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—42no—
174C22×C4×C53—42no—
175C22×C4×C53C22×C412yes—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53#4112yes—
182C22×C4×C53C2411yescharacteristic
183C2×C22⋊D53—24no—
184C2×C22⋊D53—81no—
185C2×C22⋊D53—81no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212C22×C412yes—
195C2×C4×D53—42no—
196C2×C4×D53—42no—
197C2×C4×D53—81no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—42no—
203C4⋊C4×C53—42no—
204C22⋊C4×C53—22no—
205C22⋊C4×C53—41no—
206C22⋊C4×C53—42no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53—42no—
212C42×C53—42no—
213C22⋊Dic53—42no—
214#11719924—28no—
215#11719924—44no—
216#11719921—24no—
217#11719921—42no—
218#11719921—42no—
219#11719921—81no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53C22×C412yes—
225C4⋊Dic53C2×D412yes—
226#11719919—81no—
227C4×Dic53—42no—
228C4×Dic53—81no—
229#11719917—44no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322C22×C412yes—
240C2×#88322C22×C412yes—
241C2×#88322C2×D412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53C4×D412yes—
249C23×C53C22×D411yescharacteristic
250C22×D53—22no—
251C22×D53—41no—
252C22×D53—41no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—48no—
263Q8×C53—41no—
264Q8×C53—41no—
265Q8×C53C4×D414yes—
266C2×C4×C53—22no—
267C2×C4×C53—21no—
268C2×C4×C53—22no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—48no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53C4×D412yes—
297C2×C4×C53#13712yes—
298C2×C4×C53C23×C411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×C4×C53H(5,𝔽2)11yescharacteristic
304C22⋊D53—84no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314D212—22no—
315D212—22no—
316D212—41no—
317D212—41no—
318C4×D53—84no—
319#88322—22no—
320#88322—22no—
321#88322—22no—
322#88322—41no—
323#22865—531nomaximal, Sylow
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53C2×C4×D411yescharacteristic
332C22×C53D4211yescharacteristic
333C22×C53#54611yescharacteristic
334C22×C53C2×#13711yescharacteristic
335C22×C53#57511yescharacteristic
336C22×C53#57711yescharacteristic
337C22×C53#57711yescharacteristic
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—42no—
341C2×D53—81no—
342C2×D53—81no—
343C2×D53—81no—
344C2×D53—81no—
345C4×C53—22no—
346C4×C53—24no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—41no—
352C4×C53—81no—
353C4×C53—81no—
354C4×C53C2×C4×D411yescharacteristic
355C4×C53#51811yescharacteristic
356C4×C53#54611yescharacteristic
357C4×C53#55111yescharacteristic
358Dic53—42no—
359Dic53—42no—
360Dic53—81no—
361C2×#448—531no—
362C2×#440—531no—
363C2×#419—531no—
364#2363—531no—
365Q8×C22⋊C4D5311yescharacteristic, complemented
366#1968—531no—
367#1935—531no—
368#1928—531no—
369#1895—531no—
370#1880—531no—
371#1877—531no—
372#1865—531no—
373#1854—531no—
374C4×#103—531no—
375#1753—531no—
376C2×C53—42no—
377C2×C53#235811yescharacteristic
378C2×C53C4×#13711yescharacteristic
379C2×C53#294911yescharacteristic
380C2×C53#327511yescharacteristic
381C2×C53#327811yescharacteristic
382C2×C53#332011yescharacteristic
383C2×C53#332111yescharacteristic
384D53—82no—
385C23×Q8C2×D5311yescharacteristic
386C22×SD16—531no—
387C22×SD16—531no—
388C22×M16—531no—
389C2×#121—531no—
390C2×C4×Q8C2×D5311yescharacteristic
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×D4—531no—
393C2×#117—531no—
394#448—538no—
395#440—1064no—
396C2×#107—531no—
397C2×#106—531no—
398#419—1064no—
399C2×#103—531no—
400C2×#103—531no—
401C2×#103—531no—
402C2×#103—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#102—531no—
406C2×#102—531no—
407C2×C22⋊C8—531no—
408C2×#97—531no—
409C2×C4×C8—531no—
410#391—21no—
411#391—21no—
412#391C2×D5311yescharacteristic
413#391C2×D5311yescharacteristic
414#390—531no—
415#390—1061no—
416#389—531no—
417#388—1061no—
418#386—1061no—
419#380—21no—
420#380C2×D5311yescharacteristic
421C4×C4⋊C4—531no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—1061no—
424C4×C22⋊C4C2×D5311yescharacteristic
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#336—531no—
430#336—531no—
431C53#2286511yescharacteristic, complemented, Sylow
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C4×D5314yescomplemented
439C22×Q8C22×D5311yescharacteristic
440C22×Q8C22×D5311yescharacteristic
441C22×D4—531no—
442C22×D4—1061no—
443C23×C4—21no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C2×SD16—534no—
447C2×SD16—534no—
448C2×SD16—1062no—
449C2×SD16—1062no—
450C2×SD16—2121no—
451C2×SD16—2121no—
452C2×M16—1062no—
453C2×M16—1062no—
454C2×M16—2121no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—531no—
459#121—534no—
460#121—1062no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×Q8—41no—
465C4×D4—1062no—
466C4×D4—2121no—
467#117—1062no—
468#117—2121no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4C22×D5311yescharacteristic
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4C22⋊D5311yescharacteristic
484C2×C22⋊C4C22⋊D5311yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—1061no—
488C2×C42—1061no—
489C2×C42C22×D5311yescharacteristic
490C2×C42C22×D5311yescharacteristic
491#107—1062no—
492#106—2121no—
493#103—534no—
494#103—534no—
495#103—534no—
496#103—1062no—
497#103—1062no—
498#103—1062no—
499#102—1062no—
500#102—2121no—
501C22⋊C8—534no—
502#97—1062no—
503C4×C8—2121no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—1061no—
510#95—1061no—
511#95C22⋊D5311yescharacteristic
512#95C22⋊D5311yescharacteristic
513C24—1061no—
514C24C2×C22⋊D5311yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C2×C4×D5312yes—
531C2×Q8C2×C4×D5312yes—
532C2×Q8D4×D5312yes—
533C2×Q8#1171994712yes—
534C2×D4—532no—
535C2×D4—1064no—
536C2×D4—1061no—
537C2×D4—1061no—
538C2×D4—1061no—
539C2×D4—1061no—
540C2×D4—1061no—
541C2×D4—4241no—
542C2×D4—4241no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—4241no—
558C22×C4—2122no—
559C22×C4—2122no—
560C22×C4C2×C4×D5312yes—
561C22×C4#1171994512yes—
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C2×C22⋊D5311yescharacteristic
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C23×D5311yescharacteristic
568SD16—1068no—
569SD16—2124no—
570M16—2124no—
571C2×C8—532no—
572C2×C8—532no—
573C2×C8—532no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—532no—
590C4⋊C4—532no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—4241no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—1064no—
600C22⋊C4—4241no—
601C22⋊C4—2122no—
602C22⋊C4—2122no—
603C22⋊C4—2122no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—42no—
610C42—4241no—
611C42—2122no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—1062no—
619C23—2121no—
620C23—2121no—
621C23—2121no—
622C23—2121no—
623C23—2121no—
624C23—2121no—
625C23C4×C22⋊D5312yes—
626C23C22×C22⋊D5311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8#1313317714yes—
636D4—1062no—
637D4—1062no—
638D4—4244no—
639D4—2121no—
640D4—2121no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—4244no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4C4×C22⋊D5312yes—
682C2×C4#1313324812yes—
683C2×C4C22×C4×D5311yescharacteristic
684C2×C4C2×D4×D5311yescharacteristic
685C2×C4C2×#1171994711yescharacteristic
686C2×C4C2×#1171994511yescharacteristic
687C2×C4#1313326211yescharacteristic
688C2×C4#1313326211yescharacteristic
689C8—1062no—
690C8—1062no—
691C8—1062no—
692C8—2121no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—4241no—
701C22—4241no—
702C22—4241no—
703C22—4241no—
704C22—2122no—
705C22—2122no—
706C22—2122no—
707C22C2×C4×C22⋊D5311yescharacteristic
708C22D4×C22⋊D5311yescharacteristic
709C22#1681126711yescharacteristic
710C22C2×#1313324811yescharacteristic
711C22#1681142111yescharacteristic
712C22#1681143111yescharacteristic
713C22#1681143111yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—4241no—
724C4—2122no—
725C4—2122no—
726C4C2×#1313317711yescharacteristic
727C4#1681109611yescharacteristic
728C4#1681126311yescharacteristic
729C4#1681129911yescharacteristic
730C2—42no—
731C2—4242no—
732C2#2027769411yescharacteristic
733C2C4×#1313324811yescharacteristic
734C2#2028357411yescharacteristic
735C2#2028634711yescharacteristic
736C2#2028637711yescharacteristic
737C2#2028688611yescharacteristic
738C2#2028690111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingQ8×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenterQ8×C22⋊C4D53
hypocenterC53#22865
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810721C2semidirect
3. C2×#16810632C2semidirect
5. #20275572C2semidirect
6. #20275408C2semidirect
7. #20275353C2semidirect
9. #20275070C2semidirect
10. #20275052C2semidirect
11. #20274983C2semidirect
12. #20274912C2semidirect
13. C4×#13133141C2semidirect
14. #20274499C2semidirect
15. Q8×C22⋊C4×C53C2semidirect
22. #16810762C4semidirect
100. #13133141C2×C4semidirect
101. #13133141C2×C4semidirect
102. #13133141D4semidirect
105. C22⋊#88322C2×C4semidirect
116. C22×Q8×C53C2×C4semidirect
365. Q8×C22⋊C4D53semidirect
431. C53#22865semidirect
438. C22×Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107622
C2×#168107212
C2×#168106322
#202777512
#202755722
#202754082
#202753532
#202751512
#202750702
#202750522
#202749832
#202749122
C4×#131331412
#202744992
Q8×C22⋊C4×C532
#2286553