Finite Group Databasebeta

← #27400377

Subgroups — #27400377

Order 13568.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811314C211yesmaximal, characteristic
2C2×#16810693C211yesmaximal, characteristic
3#20277615C211yesmaximal, characteristic
4#20275683C211yesmaximal, characteristic, complemented
5#20275670C211yesmaximal, characteristic, complemented
6#20275145C211yesmaximal, characteristic, complemented
7#20275135C211yesmaximal, characteristic, complemented
8#20275019C211yesmaximal, characteristic, complemented
9#20275019C211yesmaximal, characteristic, complemented
10#20274809C211yesmaximal, characteristic, complemented
11#20274800C211yesmaximal, characteristic, complemented
12#20274545C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1803C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811314—24no—
19#16811314C418yescomplemented
20C2×#13133211—21no—
21C2×#13133209C2211yescharacteristic
22C2×#13133207—21no—
23C2×#13133202—21no—
24C2×#13133193C2211yescharacteristic
25C2×#13133193C2211yescharacteristic
26C2×C4×D212C2211yescharacteristic
27C2×#13133179—21no—
28C2×#13133175C2211yescharacteristic
29C2×#13133174—21no—
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32C2×C4⋊C4×D53C2211yescharacteristic
33#16810693—24no—
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133128C2211yescharacteristic
39#16810519—21no—
40#16810494—21no—
41#16810494—21no—
42#16810480C2211yescharacteristic
43#16810480C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C53×#384C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×D212D411yescharacteristic
63C22×C4×D53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C22×C4×D53C2311yescharacteristic
67C22×C4×D53C2311yescharacteristic
68C2×#11719912—22no—
69C2×#11719912—22no—
70C2×#11719912—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C2×C8×D53—22no—
74C2×C8×D53—22no—
75C2×C8×D53—41no—
76#13133211—28no—
77#13133209—22no—
78#13133209C2×C414yescomplemented
79#13133207—28no—
80#13133202—28no—
81#13133193—22no—
82#13133193—22no—
83#13133193C2×C414yescomplemented
84#13133193C2×C414yescomplemented
85C4×D212C2×C414yes—
86C4×D212D414yes—
87#13133179—44no—
88#13133175—22no—
89#13133175C2×C414yescomplemented
90#13133174—28no—
91C2×C4⋊Dic53D411yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919—21no—
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C4⋊C4×D53—22no—
104C4⋊C4×D53—22no—
105C4⋊C4×D53—22no—
106C4⋊C4×D53—41no—
107C4⋊C4×D53—41no—
108C4⋊C4×D53C2×C414yescomplemented
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921D411yescharacteristic
115C2×#11719921D411yescharacteristic
116C2×C4×Dic53—21no—
117C2×C4×Dic53—21no—
118#13133141—22no—
119#13133141—22no—
120#13133129—22no—
121#13133129—22no—
122#13133128—22no—
123#13133124—21no—
124#13133124—21no—
125#13133124—21no—
126C22×Q8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C4×Q8×C53—22no—
130C4×Q8×C53C2×C414yescomplemented
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C42×C53—21no—
138C2×C42×C53C2311yescharacteristic
139C4⋊C8×C53—22no—
140#103×C53—41no—
141#103×C53—41no—
142C23×D53C2×D411yescharacteristic
143C23×D53C2×D411yescharacteristic
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53C22×C412yes—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2411yescharacteristic
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53C2×D411yescharacteristic
162C22×Dic53C2×D411yescharacteristic
163C2×D212—22no—
164C2×D212—22no—
165C2×D212C22⋊C414yes—
166C2×C4×D53—21no—
167C2×C4×D53—21no—
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—24no—
175C2×C4×D53—42no—
176C2×C4×D53—42no—
177C2×C4×D53—42no—
178C2×C4×D53—42no—
179C2×C4×D53—42no—
180C2×C4×D53—42no—
181C2×C4×D53—81no—
182C2×C4×D53—81no—
183C2×C4×D53C22×C412yes—
184C2×C4×D53C22×C412yes—
185C2×C4×D53C2×D412yes—
186C2×C4×D53C2×D412yes—
187C2×C8×C53—21no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C4⋊C4×C53—24no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—42no—
200C4⋊C4×C53—81no—
201C4⋊C4×C53C22×C412yes—
202C42×C53—24no—
203C42×C53C22×C412yes—
204C42×C53C2×D412yes—
205#11719921—24no—
206#11719921—24no—
207#11719921—24no—
208#11719921—42no—
209#11719921—42no—
210#11719921C22⋊C414yes—
211#11719921C22⋊C414yes—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53C22⋊C414yes—
218C4⋊Dic53C22×C412yes—
219C4⋊Dic53C22×C412yes—
220C4⋊Dic53#4112yes—
221#11719919—24no—
222#11719919—24no—
223#11719919—24no—
224#11719919—24no—
225#11719919—24no—
226#11719919—42no—
227#11719919—42no—
228C4×Dic53—24no—
229C4×Dic53—42no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322#4112yes—
236#11719912—44no—
237C8×D53—44no—
238C23×C53C22×D411yescharacteristic
239C22×D53—21no—
240C22×D53—21no—
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53C2×C22⋊C412yes—
250C22×D53C2×C22⋊C412yes—
251C22×D53AGL(1,ℤ/8)12yes—
252C22×D53#13712yes—
253Q8×C53—22no—
254Q8×C53—22no—
255Q8×C53—41no—
256Q8×C53—41no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53C2×C22⋊C412yes—
274C2×C4×C53C2×C22⋊C412yes—
275C2×C4×C53C23×C411yescharacteristic
276C2×C4×C53C22×D411yescharacteristic
277C2×C4×C53C2×#4111yescharacteristic
278C2×C4×C53C2×#4111yescharacteristic
279C2×C4×C53H(5,𝔽2)11yescharacteristic
280C2×C4×C532−1+411yescharacteristic
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53C2×C22⋊C412yes—
298C2×Dic53C2×C22⋊C412yes—
299D212—28no—
300C4×D53—22no—
301C4×D53—22no—
302C4×D53—22no—
303C4×D53—22no—
304C4×D53—22no—
305C4×D53—22no—
306C4×D53—22no—
307C4×D53—22no—
308C4×D53—48no—
309C4×D53—84no—
310C4×D53—84no—
311C8×C53—41no—
312C8×C53—41no—
313#88322—22no—
314#88322—41no—
315#22491—531nomaximal, Sylow
316C22×C53C22×C22⋊C411yescharacteristic
317C22×C53#54611yescharacteristic
318C22×C53#54711yescharacteristic
319C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C53C2×#13711yescharacteristic
321C22×C53#57711yescharacteristic
322C22×C53#57811yescharacteristic
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—22no—
328C2×D53—22no—
329C2×D53—22no—
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—41no—
333C2×D53—41no—
334C2×D53—41no—
335C2×D53—41no—
336C2×D53#41714yes—
337C4×C53—22no—
338C4×C53—22no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—81no—
342C4×C53—81no—
343C4×C53C4×#4111yescharacteristic
344C4×C53#52011yescharacteristic
345C4×C53#54611yescharacteristic
346C4×C53#54711yescharacteristic
347Dic53—22no—
348Dic53—22no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—81no—
353C2×#552—531no—
354C2×#435—531no—
355D4×C4⋊C4—531no—
356#1992—531no—
357#1989—531no—
358#1894—531no—
359#1892—531no—
360#1872—531no—
361#1872—531no—
362#1825—531no—
363#1823—531no—
364#1803D5311yescharacteristic, complemented
365#1763—531no—
366#1736—531no—
367C2×#340—531no—
368C2×C53#233911yescharacteristic
369C2×C53C2×#41711yescharacteristic
370C2×C53#289811yescharacteristic
371C2×C53#331011yescharacteristic
372C2×C53#331211yescharacteristic
373C2×C53#334311yescharacteristic
374C2×C53#334411yescharacteristic
375D53—24no—
376D53—42no—
377C22×M16—531no—
378C23×C8—531no—
379#552—538no—
380#552—1064no—
381C2×#126—1061no—
382C2×#125—531no—
383C2×#125—1061no—
384C2×#123—1061no—
385C2×C22⋊Q8—531no—
386C2×C22⋊Q8—531no—
387C2×C4×Q8C2×D5311yescharacteristic
388C2×C4×D4—531no—
389C2×C4×D4—1061no—
390C2×#117—531no—
391C2×#117—1061no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394C22×C4⋊C4—531no—
395#435—1064no—
396C2×C4⋊C8C2×D5311yescharacteristic
397C2×#103—531no—
398C2×#103—531no—
399C2×#103C2×D5311yescharacteristic
400C2×#103C2×D5311yescharacteristic
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×#97—531no—
404#389—1061no—
405#385—1061no—
406#385—1061no—
407#384C2×D5311yescharacteristic
408#380—531no—
409#380—531no—
410C4×C4⋊C4—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340C2×D5311yescharacteristic
422#340C2×D5311yescharacteristic
423C53#2249111yescharacteristic, complemented, Sylow
424C22×Q8C22×D5311yescharacteristic
425C22×D4—531no—
426C23×C4—531no—
427C23×C4—531no—
428C23×C4—1061no—
429C23×C4—1061no—
430C23×C4—1061no—
431C2×M16—1062no—
432C2×M16—1062no—
433C2×M16—2121no—
434C22×C8—531no—
435C22×C8—531no—
436C22×C8—1062no—
437C22×C8—1062no—
438C22×C8—2121no—
439C22×C8C22×D5311yescharacteristic
440C22×C8C22×D5311yescharacteristic
441#126—1068no—
442#125—534no—
443#125—1068no—
444#125—1062no—
445#123—1068no—
446C22⋊Q8—534no—
447C22⋊Q8—534no—
448C22⋊Q8—1062no—
449C22⋊Q8—1062no—
450C4×Q8—22no—
451C4×Q8C4×D5314yescomplemented
452C4×D4—534no—
453C4×D4—534no—
454C4×D4—2124no—
455#117—534no—
456#117—1068no—
457#117—1062no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—534no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4—1062no—
469C2×C4⋊C4—1062no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—2121no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C42—21no—
490C2×C42—1061no—
491C2×C42—1061no—
492C2×C42C22×D5311yescharacteristic
493C4⋊C8—22no—
494#103—41no—
495#103—41no—
496#103—1062no—
497#103—1062no—
498C22⋊C8—1062no—
499C22⋊C8—1062no—
500#97—1062no—
501#95—1061no—
502#95—1061no—
503#95—1061no—
504C24—531no—
505C24—531no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×C4×D5312yes—
512C2×D4—534no—
513C2×D4—1062no—
514C2×D4—1062no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—531no—
520C22×C4—531no—
521C22×C4—532no—
522C22×C4—532no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—1064no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—4241no—
539C22×C4—4241no—
540C22×C4—2122no—
541C22×C4—2122no—
542C22×C4—2122no—
543C22×C4—2122no—
544C22×C4—2122no—
545C22×C4—2122no—
546C22×C4D4×D5311yescharacteristic
547C22×C4D4×D5311yescharacteristic
548C22×C4C23×D5311yescharacteristic
549M16—2124no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—532no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—2124no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4—534no—
572C4⋊C4—532no—
573C4⋊C4—532no—
574C4⋊C4—532no—
575C4⋊C4—1064no—
576C4⋊C4—1064no—
577C4⋊C4—1064no—
578C4⋊C4—1064no—
579C4⋊C4—1064no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—2122no—
586C4⋊C4—2122no—
587C4⋊C4C2×C4×D5312yes—
588C22⋊C4—534no—
589C22⋊C4—534no—
590C22⋊C4—1064no—
591C22⋊C4—1064no—
592C22⋊C4—1064no—
593C22⋊C4—2122no—
594C22⋊C4—2122no—
595C42—24no—
596C42—1064no—
597C42—2122no—
598C42C2×C4×D5312yes—
599C42D4×D5312yes—
600C23—532no—
601C23—532no—
602C23—532no—
603C23—532no—
604C23—1061no—
605C23—1061no—
606C23—1061no—
607C23—1061no—
608C23—1061no—
609C23—1061no—
610C23—1061no—
611C23—1061no—
612C23—1061no—
613C23—1061no—
614C23C2×D4×D5311yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—1068no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—532no—
637C2×C4—532no—
638C2×C4—1061no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—1061no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—1062no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—4244no—
654C2×C4—4244no—
655C2×C4—2128no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4C22⋊C4×D5312yes—
666C2×C4C22⋊C4×D5312yes—
667C2×C4C22×C4×D5311yescharacteristic
668C2×C4C2×D4×D5311yescharacteristic
669C2×C4#41×D5311yescharacteristic
670C2×C4#41×D5311yescharacteristic
671C2×C4#1313326211yescharacteristic
672C2×C4#1313326511yescharacteristic
673C8—41no—
674C8—41no—
675C8—1062no—
676C8—2121no—
677C22—534no—
678C22—1062no—
679C22—1062no—
680C22—1062no—
681C22—1062no—
682C22—1062no—
683C22—1062no—
684C22—1062no—
685C22—1062no—
686C22—1062no—
687C22—2121no—
688C22—2121no—
689C22—2121no—
690C22—2121no—
691C22C2×C22⋊C4×D5311yescharacteristic
692C22#1681127011yescharacteristic
693C22#1681127511yescharacteristic
694C22AGL(1,ℤ/8)×D5311yescharacteristic
695C22#137×D5311yescharacteristic
696C22#1681142911yescharacteristic
697C22#1681143611yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—1062no—
705C4—1062no—
706C4—4241no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4#1681109111yescharacteristic
711C4#1681110411yescharacteristic
712C4#1681127011yescharacteristic
713C4#1681127511yescharacteristic
714C2—1064no—
715C2—2122no—
716C2#2027754311yescharacteristic
717C2#417×D5311yescharacteristic
718C2#2028324311yescharacteristic
719C2#2028674311yescharacteristic
720C2#2028677311yescharacteristic
721C2#2028715211yescharacteristic
722C2#2028716711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1803C2
socleC23×C53C22×D4
prime radicalC22×D212D4
cosocleC22×C4×C53C24
hypercenter#1803D53
hypocenterC53#22491
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #20275683C2semidirect
5. #20275670C2semidirect
6. #20275145C2semidirect
7. #20275135C2semidirect
8. #20275019C2semidirect
9. #20275019C2semidirect
10. #20274809C2semidirect
11. #20274800C2semidirect
12. #20274545C2semidirect
13. #20274433C2semidirect
14. #340×D53C2semidirect
15. C53×#1803C2semidirect
19. #16811314C4semidirect
78. #13133209C2×C4semidirect
83. #13133193C2×C4semidirect
84. #13133193C2×C4semidirect
89. #13133175C2×C4semidirect
108. C4⋊C4×D53C2×C4semidirect
130. C4×Q8×C53C2×C4semidirect
364. #1803D53semidirect
423. C53#22491semidirect
451. C4×Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113142
C2×#168106932
#202776152
#202756832
#202756702
#202751452
#202751352
#202750192
#202748092
#202748002
#202745452
#202744332
#340×D532
C53×#18032
#2249153