Finite Group Databasebeta

← #28328897

Subgroups — #28328897

Order 13568.

2198 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291235C213yesmaximal, complemented
2#20291234C213yesmaximal, complemented
3#20291230C211yesmaximal, characteristic, complemented
4Q8×C4⋊#6157C211yesmaximal, characteristic, complemented
5#20291226C213yesmaximal
6#20291225C213yesmaximal
7Q8×C22⋊#6157C211yesmaximal, characteristic
8Q8×C22⋊#6157C211yesmaximal, characteristic
9#20291199C213yesmaximal, complemented
10#20291193C213yesmaximal
11#20291177C213yesmaximal
12#20291174C213yesmaximal, complemented
13#20291155C211yesmaximal, characteristic, complemented
14C4×Q8×#6157C211yesmaximal, characteristic, complemented
15#519×D53C211yesmaximal, characteristic
16C2×Q8×#6157C2211yescharacteristic
17C2×Q8×#6157C2211yescharacteristic
18C2×Q8×#6157C2211yescharacteristic
19C2×Q8×#6157C2211yescharacteristic
20(C2×#6157)⋊Q8C2213yes—
21(C2×#6157)⋊Q8C2213yes—
22(C2×#6157)⋊Q8C2213yes—
23(C2×#6157)⋊Q8C2213yes—
24#16811574C2213yes—
25#16811574C2213yes—
26#16811574C2213yes—
27#16811574C2213yes—
28#16811573C2211yescharacteristic
29#16811573C2213yes—
30#16811573C2213yes—
31#16811573C2213yes—
32#16811573C2216yes—
33#16811572C2213yes—
34#16811572C2216yes—
35#16811572C2213yes—
36#16811572C2213yes—
37#16811572C2213yes—
38#16811572C2216yes—
39#16811569C2213yes—
40#16811568C2216yes—
41#16811567C2213yes—
42#16811567C2216yes—
43#16811565C2213yes—
44#16811565C2213yes—
45C4⋊C4×#6157C2213yes—
46C4⋊C4×#6157C2213yes—
47C4⋊C4×#6157C2213yes—
48C4⋊C4×#6157C2213yes—
49C4×C4⋊#6157C2213yes—
50C4×C4⋊#6157C2213yes—
51C4×C4⋊#6157C2216yes—
52C4×C4⋊#6157C2213yes—
53C4×C4⋊#6157C2213yes—
54C4×C22⋊#6157C2213yes—
55C4×C22⋊#6157C2213yes—
56#16811559C2213yes—
57#16811559C2216yes—
58C42×#6157C2213yes—
59C22×Q8×D53C2211yescharacteristic
60#16811101C411yescharacteristic, complemented
61#16811100C413yescomplemented
62#16811100C413yescomplemented
63#16811099C413yescomplemented
64#16811099C413yescomplemented
65#16811099C411yescharacteristic, complemented
66#16811099C411yescharacteristic, complemented
67C4×Q8×D53C2211yescharacteristic
68C4×Q8×D53C2213yes—
69C4×Q8×D53C2211yescharacteristic
70C4×Q8×D53C2213yes—
71#117×D53C2213yes—
72#117×D53C2213yes—
73C53×#519C411yescharacteristic, complemented
74Q8×#6157—24no—
75Q8×#6157—24no—
76Q8×#6157—24no—
77Q8×#6157—24no—
78C2×C4⋊#6157C2311yescharacteristic
79C2×C4⋊#6157C2313yes—
80C2×C4⋊#6157C2313yes—
81C2×C4⋊#6157C2313yes—
82C2×C4⋊#6157C2313yes—
83C2×C4⋊#6157C2313yes—
84C2×C4⋊#6157C2313yes—
85C2×C4⋊#6157C2316yes—
86C2×C4⋊#6157C2313yes—
87C2×C22⋊#6157C2311yescharacteristic
88C2×C22⋊#6157C2311yescharacteristic
89C2×C22⋊#6157C2313yes—
90C2×C22⋊#6157C2313yes—
91C2×C4×#6157C2311yescharacteristic
92C2×C4×#6157C2313yes—
93C2×C4×#6157C2313yes—
94C2×C4×#6157C2313yes—
95C2×C4×#6157C2313yes—
96C2×C4×#6157C2313yes—
97C2×C4×#6157C2313yes—
98C2×C4×#6157C2313yes—
99C2×C4×#6157C2316yes—
100(C2×#6157)⋊C4C2311yescharacteristic
101(C2×#6157)⋊C4C2313yes—
102(C2×#6157)⋊C4C2313yes—
103(C2×#6157)⋊C4C2313yes—
104(C2×#6157)⋊C4C2313yes—
105(C2×#6157)⋊C4C2313yes—
106(C2×#6157)⋊C4C2316yes—
107(C2×#6157)⋊C4C2316yes—
108(C2×#6157)⋊C4C2313yes—
109(C2×#6157)⋊C4C2313yes—
110(C2×#6157)⋊C4C2313yes—
111(C2×#6157)⋊C4C2311yescharacteristic
112(C2×#6157)⋊C4C2316yes—
113(C2×#6157)⋊C4C2316yes—
114(C2×#6157)⋊C4C2313yes—
115(C2×#6157)⋊C4C2313yes—
116C22×Dic106C2×C413yes—
117C2×Q8×D53—24no—
118C2×Q8×D53—24no—
119C2×Q8×D53C2×C411yescharacteristic
120C2×Q8×D53C2×C413yes—
121C2×Q8×D53C2313yes—
122C2×Q8×D53C2311yescharacteristic
123C22×C4×D53C2313yes—
124Q8×Dic53C2×C413yes—
125Q8×Dic53C2×C413yes—
126Q8×Dic53C2×C411yescharacteristic
127Q8×Dic53C2×C411yescharacteristic
128C4×Dic106C2×C413yes—
129C4×Dic106C2×C416yes—
130C4×Dic106C2×C413yes—
131C4×Dic106C2×C416yes—
132C4×Dic106C2×C413yes—
133C4×Dic106C2×C413yes—
134#13133182C2×C413yes—
135#13133182C2×C416yes—
136#13133182C2×C413yes—
137#13133182C2×C416yes—
138#13133182C2×C413yes—
139#13133182C2×C413yes—
140#13133176C2×C413yes—
141#13133176C2×C413yes—
142#13133175C2×C413yes—
143#13133175C2×C413yes—
144#13133175C2×C413yes—
145#13133175C2×C413yes—
146#13133174C2×C413yes—
147#13133174C2×C413yes—
148#13133174C2×C416yes—
149#13133173C2×C413yes—
150#13133173C2×C413yes—
151#13133173C2×C416yes—
152C4⋊C4×D53C2313yes—
153C4⋊C4×D53C2313yes—
154C4⋊C4×D53C2313yes—
155C4⋊C4×D53C2313yes—
156C22⋊C4×D53C2311yescharacteristic
157C22⋊C4×D53C2313yes—
158C42×D53C2313yes—
159C42×D53C2316yes—
160C42×D53C2313yes—
161C22×Q8×C53C2×C411yescharacteristic
162C4×Q8×C53C2×C413yes—
163C4×Q8×C53C2×C413yes—
164C4×Q8×C53C2×C411yescharacteristic
165C4×Q8×C53C2×C411yescharacteristic
166#117×C53C2×C413yes—
167#117×C53C2×C413yes—
168C23×D53C2411yescharacteristic
169C22×#6157C2411yescharacteristic
170C22×#6157C2411yescharacteristic
171C22×#6157C2413yes—
172C22×#6157C2413yes—
173C22×#6157C2413yes—
174C22×#6157C2413yes—
175C22×#6157C2411yescharacteristic
176C22×#6157C2411yescharacteristic
177C2×Q8×C53—24no—
178C2×Q8×C53C22×C413yes—
179C2×Q8×C53C22×C411yescharacteristic
180C22×C4×C53C22×C413yes—
181C22×Dic53C22×C413yes—
182Q8×D53—24no—
183Q8×D53—26no—
184Q8×D53—26no—
185Q8×D53—212no—
186Q8×D53#4114yes—
187Q8×D53#4114yes—
188C2×C4×D53—26no—
189C2×C4×D53—26no—
190C2×C4×D53C22×C413yes—
191C2×C4×D53C22×C413yes—
192C2×C4×D53C2411yescharacteristic
193C2×C4×D53C2413yes—
194C2×C4×D53C2413yes—
195C2×C4×D53C2411yescharacteristic
196C2×C4×D53C2413yes—
197C2×C4×D53C2413yes—
198C2×Dic106—212no—
199C2×Dic106C22×C413yes—
200C2×Dic106C22×C416yes—
201C2×Dic106C22×C413yes—
202C22⋊#6157—22no—
203C22⋊#6157—22no—
204C22⋊#6157—43no—
205C22⋊#6157—43no—
206C4⋊#6157—22no—
207C4⋊#6157—26no—
208C4⋊#6157—26no—
209C4⋊#6157—26no—
210C4⋊#6157—26no—
211C4⋊#6157—26no—
212C4⋊#6157—43no—
213C4⋊#6157—46no—
214C4⋊#6157—43no—
215C4×#6157—22no—
216C4×#6157—26no—
217C4×#6157—26no—
218C4×#6157—26no—
219C4×#6157—26no—
220C4×#6157—26no—
221C4×#6157—43no—
222C4×#6157—46no—
223C4×#6157—43no—
224C4⋊C4×C53C22×C413yes—
225C4⋊C4×C53C22×C413yes—
226C4⋊C4×C53C22×C413yes—
227C4⋊C4×C53C22×C413yes—
228C22⋊C4×C53C22×C411yescharacteristic
229C22⋊C4×C53C22×C413yes—
230C42×C53C22×C416yes—
231C42×C53C22×C413yes—
232C42×C53C22×C413yes—
233C22⋊Dic53C22×C411yescharacteristic
234C22⋊Dic53C22×C413yes—
235#11719921C22×C411yescharacteristic
236#11719921C22×C413yes—
237#11719921C22×C411yescharacteristic
238#11719921C22×C413yes—
239C4⋊Dic53C22×C413yes—
240C4⋊Dic53C22×C413yes—
241C4⋊Dic53C22×C413yes—
242C4⋊Dic53C22×C413yes—
243#11719919C22×C413yes—
244#11719919C22×C413yes—
245#11719919C22×C413yes—
246#11719919C22×C413yes—
247#11719919C22×C416yes—
248#11719919C22×C416yes—
249C4×Dic53C22×C416yes—
250C4×Dic53C22×C416yes—
251C4×Dic53C22×C413yes—
252C4×Dic53C22×C413yes—
253C4×Dic53C22×C413yes—
254C4×Dic53C22×C413yes—
255C4×Dic53C22×C416yes—
256C4×Dic53C22×C413yes—
257C4×Dic53C22×C413yes—
258C23×C53C23×C411yescharacteristic
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53C23×C411yescharacteristic
266C22×D53C2511yescharacteristic
267C2×#6157—21no—
268C2×#6157—21no—
269C2×#6157—21no—
270C2×#6157—21no—
271C2×#6157—21no—
272C2×#6157—21no—
273C2×#6157—23no—
274C2×#6157—23no—
275C2×#6157—23no—
276C2×#6157—23no—
277C2×#6157—23no—
278C2×#6157—23no—
279C2×#6157—21no—
280C2×#6157—21no—
281C2×#6157—21no—
282C2×#6157—23no—
283C2×#6157—23no—
284C2×#6157—23no—
285C2×#6157—23no—
286C2×#6157—23no—
287C2×#6157—21no—
288C2×#6157—23no—
289C2×#61572−1+412yes—
290C2×#61572−1+412yes—
291Q8×C53—26no—
292Q8×C53#11714yes—
293C2×C4×C53—26no—
294C2×C4×C53C23×C413yes—
295C2×C4×C53C23×C411yescharacteristic
296C2×C4×C53C23×C413yes—
297C2×C4×C53C23×C413yes—
298C2×C4×C53C23×C411yescharacteristic
299C2×C4×C53C23×C413yes—
300C2×Dic53—26no—
301C2×Dic53C23×C413yes—
302C2×Dic53C23×C411yescharacteristic
303C2×Dic53C23×C413yes—
304C2×Dic53C23×C413yes—
305C2×Dic53C23×C411yescharacteristic
306C2×Dic53C23×C413yes—
307C4×D53—23no—
308C4×D53—23no—
309C4×D53—21no—
310C4×D53—23no—
311C4×D53—23no—
312C4×D53—21no—
313C4×D53—23no—
314C4×D53—21no—
315C4×D53—21no—
316C4×D53—23no—
317C4×D53—26no—
318C4×D53—26no—
319C4×D53C2×#4116yes—
320C4×D53C2×#4116yes—
321Dic106—26no—
322Dic106—212no—
323Dic106#117112yes—
324#34262—531nomaximal, Sylow
325C22×C53—21no—
326C22×C53—21no—
327C22×C53—21no—
328C22×C53C24×C411yescharacteristic
329C2×D53—21no—
330C2×D53—21no—
331C2×D53—21no—
332C2×D53—41no—
333C2×D53—41no—
334C2×D53—41no—
335C2×D53—41no—
336C2×D53C22×#4111yescharacteristic
337C2×D53C22×#4111yescharacteristic
338C2×D53C2×2−1+411yescharacteristic
339C2×D53C2×2−1+411yescharacteristic
340C2×D53#58511yescharacteristic
341C2×D53#58511yescharacteristic
342#6157—22no—
343#6157—22no—
344#6157—43no—
345#6157—41no—
346#6157—43no—
347#6157—41no—
348#6157—43no—
349#6157—43no—
350C4×C53—23no—
351C4×C53—21no—
352C4×C53—23no—
353C4×C53—23no—
354C4×C53—21no—
355C4×C53C2×#11716yes—
356Dic53—23no—
357Dic53—21no—
358Dic53—23no—
359Dic53—23no—
360Dic53—21no—
361Dic53C2×#11716yes—
362C2×#519—531no—
363#2356—533no—
364#2355—533no—
365#2351—531no—
366Q8×C4⋊C4—531no—
367#2347—533no—
368#2346—533no—
369Q8×C22⋊C4—531no—
370Q8×C22⋊C4—531no—
371#2320—533no—
372#2314—533no—
373#2298—533no—
374#2295—533no—
375#2276—531no—
376C42×Q8—531no—
377C2×C53—41no—
378C2×C53C22×#11711yescharacteristic
379C2×C53C4×2−1+411yescharacteristic
380C2×C53C4×2−1+411yescharacteristic
381D53—41no—
382D53#351611yescharacteristic
383D53#351811yescharacteristic
384D53#352311yescharacteristic
385D53#352411yescharacteristic
386C23×Q8—531no—
387#519—531no—
388#519—533no—
389#519—533no—
390#519—531no—
391#519—531no—
392#519—533no—
393#519—533no—
394#519#615711yescharacteristic, complemented
395C2×C4×Q8—533no—
396C2×C4×Q8—531no—
397C2×C4×Q8—533no—
398C2×C4×Q8—531no—
399C2×C4×Q8—531no—
400C2×C4×Q8—531no—
401C2×C4×Q8—531no—
402C2×C4×Q8—531no—
403C2×#117—533no—
404C2×#117—533no—
405#391—533no—
406#391—533no—
407#391—533no—
408#391—533no—
409#389—533no—
410#389—533no—
411#389—533no—
412#389—533no—
413#388—533no—
414#388—536no—
415#388—533no—
416#388—533no—
417#388—531no—
418#387—536no—
419#387—536no—
420#387—533no—
421#387—533no—
422#387—533no—
423#387—533no—
424#384—533no—
425#383—536no—
426#382—533no—
427#382—536no—
428#380—533no—
429#380—533no—
430C4×C4⋊C4—533no—
431C4×C4⋊C4—533no—
432C4×C4⋊C4—533no—
433C4×C4⋊C4—533no—
434C4×C4⋊C4—536no—
435C4×C4⋊C4—533no—
436C4×C4⋊C4—533no—
437C4×C4⋊C4—533no—
438C4×C4⋊C4—533no—
439C4×C22⋊C4—533no—
440C4×C22⋊C4—533no—
441#376—533no—
442#376—536no—
443C43—533no—
444C53#3426211yescharacteristic, complemented, Sylow
445C22×Q8—531no—
446C22×Q8—533no—
447C22×Q8—533no—
448C22×Q8—531no—
449C22×Q8—533no—
450C22×Q8—1064no—
451C22×Q8—1064no—
452C22×Q8C2×#615711yescharacteristic
453C23×C4—533no—
454C4×Q8—533no—
455C4×Q8—533no—
456C4×Q8—531no—
457C4×Q8—531no—
458C4×Q8—533no—
459C4×Q8—533no—
460C4×Q8—536no—
461C4×Q8—533no—
462C4×Q8—536no—
463C4×Q8—533no—
464C4×Q8—533no—
465C4×Q8—533no—
466C4×Q8—536no—
467C4×Q8—533no—
468C4×Q8—536no—
469C4×Q8—533no—
470C4×Q8—1064no—
471C4×Q8—1064no—
472C4×Q8—1064no—
473C4×Q8—1064no—
474C4×Q8C2×#615713yes—
475C4×Q8C2×#615713yes—
476C4×Q8C2×#615711yescharacteristic
477C4×Q8C2×#615711yescharacteristic
478#117—533no—
479#117—533no—
480#117—533no—
481#117—533no—
482#117—533no—
483#117—533no—
484#117—533no—
485#117—533no—
486#117—536no—
487#117—533no—
488#117—533no—
489#117—536no—
490#117C2×#615713yes—
491#117C2×#615713yes—
492C2×C4⋊C4—533no—
493C2×C4⋊C4—533no—
494C2×C4⋊C4—533no—
495C2×C4⋊C4—533no—
496C2×C4⋊C4—533no—
497C2×C4⋊C4—533no—
498C2×C4⋊C4—533no—
499C2×C4⋊C4—533no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—533no—
502C2×C4⋊C4—533no—
503C2×C4⋊C4—536no—
504C2×C4⋊C4—533no—
505C2×C22⋊C4—531no—
506C2×C22⋊C4—533no—
507C2×C22⋊C4—531no—
508C2×C22⋊C4—531no—
509C2×C22⋊C4—533no—
510C2×C22⋊C4—533no—
511C2×C42—533no—
512C2×C42—536no—
513C2×C42—533no—
514C2×C42—533no—
515C2×C42—533no—
516C2×C42—533no—
517C2×C42—533no—
518C2×C42—531no—
519C2×C42—533no—
520C2×C42—533no—
521C2×C42—533no—
522C2×C42—536no—
523#95—531no—
524#95—533no—
525#95—533no—
526#95—533no—
527#95—533no—
528#95—533no—
529#95—536no—
530#95—536no—
531#95—533no—
532#95—533no—
533#95—533no—
534#95—536no—
535#95—531no—
536#95—536no—
537#95—533no—
538#95—533no—
539C24—531no—
540C2×Q8—24no—
541C2×Q8—534no—
542C2×Q8—534no—
543C2×Q8—533no—
544C2×Q8—536no—
545C2×Q8—533no—
546C2×Q8—10612no—
547C2×Q8—1066no—
548C2×Q8—1066no—
549C2×Q8—10612no—
550C2×Q8—1064no—
551C2×Q8C22×#615713yes—
552C2×Q8C22×#615711yescharacteristic
553C22×C4—533no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—533no—
557C22×C4—533no—
558C22×C4—533no—
559C22×C4—533no—
560C22×C4—531no—
561C22×C4—533no—
562C22×C4—533no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—531no—
566C22×C4—533no—
567C22×C4—533no—
568C22×C4—533no—
569C22×C4—533no—
570C22×C4—1066no—
571C22×C4—1066no—
572C22×C4C22×#615713yes—
573C4⋊C4—536no—
574C4⋊C4—536no—
575C4⋊C4—533no—
576C4⋊C4—533no—
577C4⋊C4—533no—
578C4⋊C4—533no—
579C4⋊C4—533no—
580C4⋊C4—533no—
581C4⋊C4—533no—
582C4⋊C4—533no—
583C4⋊C4—1062no—
584C4⋊C4—1066no—
585C4⋊C4—1066no—
586C4⋊C4—1066no—
587C4⋊C4—1066no—
588C4⋊C4—1066no—
589C4⋊C4—2123no—
590C4⋊C4—2123no—
591C4⋊C4—2126no—
592C4⋊C4C22×#615713yes—
593C4⋊C4C22×#615713yes—
594C4⋊C4C22×#615713yes—
595C4⋊C4C22×#615713yes—
596C22⋊C4—531no—
597C22⋊C4—533no—
598C22⋊C4—531no—
599C22⋊C4—533no—
600C22⋊C4—531no—
601C22⋊C4—533no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—2123no—
605C22⋊C4—2123no—
606C22⋊C4C22×#615711yescharacteristic
607C22⋊C4C22×#615713yes—
608C42—533no—
609C42—533no—
610C42—533no—
611C42—533no—
612C42—536no—
613C42—533no—
614C42—533no—
615C42—536no—
616C42—536no—
617C42—1066no—
618C42—1062no—
619C42—1066no—
620C42—1066no—
621C42—1066no—
622C42—1066no—
623C42—2123no—
624C42—2126no—
625C42—2123no—
626C42C22×#615716yes—
627C42C22×#615713yes—
628C42C22×#615713yes—
629C23—531no—
630C23—531no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23C23×#615711yescharacteristic
638Q8—26no—
639Q8—5312no—
640Q8—10612no—
641Q8—1066no—
642Q8#1313329614yes—
643C2×C4—26no—
644C2×C4—533no—
645C2×C4—536no—
646C2×C4—536no—
647C2×C4—532no—
648C2×C4—532no—
649C2×C4—531no—
650C2×C4—533no—
651C2×C4—531no—
652C2×C4—533no—
653C2×C4—533no—
654C2×C4—1066no—
655C2×C4—1061no—
656C2×C4—1063no—
657C2×C4—1063no—
658C2×C4—1061no—
659C2×C4—1063no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1063no—
663C2×C4—1063no—
664C2×C4—1063no—
665C2×C4—1066no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1066no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1063no—
674C2×C4—1063no—
675C2×C4—1063no—
676C2×C4—1063no—
677C2×C4—1063no—
678C2×C4—1063no—
679C2×C4—1063no—
680C2×C4—1063no—
681C2×C4—1063no—
682C2×C4—1063no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1063no—
686C2×C4—1061no—
687C2×C4—1063no—
688C2×C4—1061no—
689C2×C4C23×#615711yescharacteristic
690C2×C4C23×#615713yes—
691C2×C4C23×#615711yescharacteristic
692C2×C4C23×#615713yes—
693C2×C4C23×#615713yes—
694C2×C4C23×#615713yes—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—531no—
699C22—531no—
700C22—531no—
701C22—531no—
702C22—531no—
703C22—531no—
704C22—1061no—
705C22—1061no—
706C22—1061no—
707C22—2121no—
708C22—2121no—
709C22—2121no—
710C22—2121no—
711C22C24×#615711yescharacteristic
712C4—23no—
713C4—23no—
714C4—21no—
715C4—21no—
716C4—23no—
717C4—536no—
718C4—1062no—
719C4—1062no—
720C4—1063no—
721C4—1063no—
722C4—1061no—
723C4—1061no—
724C4—1063no—
725C4—2123no—
726C4—2121no—
727C4—2123no—
728C4—2123no—
729C4—2121no—
730C4—2123no—
731C4C2×#1313329616yes—
732C2—41no—
733C2—531no—
734C2—531no—
735C2—531no—
736C2—531no—
737C2—2121no—
738C2C22×#1313329611yescharacteristic
739C22−1+4×#615711yescharacteristic
740C22−1+4×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#519C4
prime radicalC23×D53C24
cosocleC22×D53C25
hypercenter#519#6157
hypocenterC53#34262
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #20291235C2semidirect
2. #20291234C2semidirect
3. #20291230C2semidirect
4. Q8×C4⋊#6157C2semidirect
9. #20291199C2semidirect
12. #20291174C2semidirect
13. #20291155C2semidirect
14. C4×Q8×#6157C2semidirect
60. #16811101C4semidirect
61. #16811100C4semidirect
62. #16811100C4semidirect
63. #16811099C4semidirect
64. #16811099C4semidirect
65. #16811099C4semidirect
66. #16811099C4semidirect
73. C53×#519C4semidirect
394. #519#6157semidirect
444. C53#34262semidirect

Maximal subgroups

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

subgroupindex
#202912352
#202912342
#202912302
Q8×C4⋊#61572
#202912262
#202912252
Q8×C22⋊#61572
#202911992
#202911932
#202911772
#202911742
#202911552
C4×Q8×#61572
#519×D532
#3426253