Finite Group Databasebeta

← #27390532

Subgroups — #27390532

Order 13568.

922 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20284166C211yesmaximal, characteristic
2C2×#16810738C211yesmaximal, characteristic, complemented
3#20283425C211yesmaximal, characteristic, complemented
4#131×Dic53C211yesmaximal, characteristic, complemented
5#20275632C211yesmaximal, characteristic, complemented
6#20275487C211yesmaximal, characteristic, complemented
7#20275366C211yesmaximal, characteristic, complemented
8#20275362C211yesmaximal, characteristic, complemented
9#20275044C211yesmaximal, characteristic, complemented
10#20275040C211yesmaximal, characteristic, complemented
11#20274733C211yesmaximal, characteristic, complemented
12C8×#11719919C211yesmaximal, characteristic, complemented
13#20274552C211yesmaximal, characteristic, complemented
14#20274550C211yesmaximal, characteristic, complemented
15C2×C53×#443C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133224C2211yescharacteristic
18C2×#13133223C2211yescharacteristic
19#16811169C2211yescharacteristic
20#41×Dic53C2211yescharacteristic
21#16810847C411yescharacteristic, complemented
22#16810843C411yescharacteristic, complemented
23#16810840C411yescharacteristic, complemented
24#16810836C411yescharacteristic, complemented
25#16810831C411yescharacteristic, complemented
26#16810826C411yescharacteristic, complemented
27#16810821C411yescharacteristic, complemented
28#16810816C411yescharacteristic, complemented
29#16810738—24no—
30#16810699—21no—
31#16810699—21no—
32C8×C22⋊D53—21no—
33C8×C22⋊D53—21no—
34C2×#13133152C2211yescharacteristic
35#16810646C2211yescharacteristic
36C2×#13133146C2211yescharacteristic
37C2×#13133145C2211yescharacteristic
38C2×#13133144C2211yescharacteristic
39C2×#13133144C2211yescharacteristic
40C2×#13133143C2211yescharacteristic
41#16810620C2211yescharacteristic
42#16810619C2211yescharacteristic
43#16810591C2211yescharacteristic
44#16810590C2211yescharacteristic
45#16810581—21no—
46#16810581C2211yescharacteristic
47#16810578—21no—
48#16810578C2211yescharacteristic
49M16×Dic53—21no—
50M16×Dic53C2211yescharacteristic
51C2×C8×Dic53—21no—
52C2×C8×Dic53C2211yescharacteristic
53C2×C8×Dic53C2211yescharacteristic
54C4×#11719919C2211yescharacteristic
55#16810388C2211yescharacteristic
56#16810387C2211yescharacteristic
57#16810384C2211yescharacteristic
58#16810383C2211yescharacteristic
59#16810378C2211yescharacteristic
60#16810377C2211yescharacteristic
61C2×#135×C53C2211yescharacteristic
62C2×#131×C53C2211yescharacteristic
63C2×#131×C53C2211yescharacteristic
64C53×#443—24no—
65C2×#108×C53C2211yescharacteristic
66C2×#104×C53C2211yescharacteristic
67C2×#104×C53C2211yescharacteristic
68C2×C4×C8×C53C2211yescharacteristic
69C2×#11719945C2311yescharacteristic
70#13133237—22no—
71#13133237—22no—
72C2×#11719925C2×C411yescharacteristic
73C2×#11719923C2×C411yescharacteristic
74C2×#11719924C2×C411yescharacteristic
75C2×#11719922C2×C411yescharacteristic
76#13133224—22no—
77#13133224—22no—
78#13133223—22no—
79#13133223—22no—
80C2×#11719917—21no—
81C2×#11719917C2311yescharacteristic
82C2×#11719917C2311yescharacteristic
83C2×#11719912—21no—
84C22×#88322—21no—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C2×C8×D53—21no—
88#13133215C2×C411yescharacteristic
89#13133213C2×C411yescharacteristic
90#13133206C2×C411yescharacteristic
91#13133204C2×C411yescharacteristic
92#13133189—21no—
93#13133189—21no—
94Q8×Dic53C2×C411yescharacteristic
95Q8×Dic53C2×C411yescharacteristic
96D4×Dic53—21no—
97D4×Dic53—21no—
98D4×Dic53C2×C411yescharacteristic
99D4×Dic53C2×C411yescharacteristic
100C4×C22⋊D53—21no—
101C4×C22⋊D53—21no—
102#13133176—21no—
103#13133176C2311yescharacteristic
104C2×#11719919—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53C2311yescharacteristic
107C2×C4×Dic53C2311yescharacteristic
108#13133152—22no—
109#13133146—21no—
110#13133146—21no—
111#13133146C2×C411yescharacteristic
112#13133146C2×C411yescharacteristic
113#13133146C2×C411yescharacteristic
114#13133146C2×C411yescharacteristic
115#13133145—22no—
116#13133144—22no—
117#13133144—22no—
118#13133143—22no—
119#13133142C2×C411yescharacteristic
120#13133142C2×C411yescharacteristic
121#13133141C2×C411yescharacteristic
122#13133141C2×C411yescharacteristic
123#13133139C2×C411yescharacteristic
124#13133139C2×C411yescharacteristic
125#13133138C2×C411yescharacteristic
126#13133138C2×C411yescharacteristic
127C22⋊#88322—21no—
128C22⋊#88322—21no—
129#13133129—21no—
130#13133129—21no—
131#13133127—21no—
132#13133127—21no—
133#13133127—21no—
134C8×Dic53—21no—
135C8×Dic53—22no—
136C8×Dic53—21no—
137C8×Dic53—21no—
138C8×Dic53D411yescharacteristic
139C8×Dic53D411yescharacteristic
140C8×Dic53D411yescharacteristic
141C8×Dic53D411yescharacteristic
142#13133124—21no—
143C2×#41×C53C2311yescharacteristic
144C2×#41×C53C2311yescharacteristic
145#135×C53—22no—
146#135×C53—22no—
147C2×Q16×C53C2×C411yescharacteristic
148C2×SD16×C53C2×C411yescharacteristic
149C2×SD16×C53C2×C411yescharacteristic
150C2×D8×C53C2×C411yescharacteristic
151#131×C53—22no—
152#131×C53—22no—
153#131×C53—22no—
154#131×C53D414yescomplemented
155C2×M16×C53—21no—
156C2×M16×C53—21no—
157C2×M16×C53C2311yescharacteristic
158C2×M16×C53C2311yescharacteristic
159C22×C8×C53—21no—
160C22×C8×C53—21no—
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C2×C42×C53C2311yescharacteristic
164#108×C53—22no—
165#104×C53—22no—
166#104×C53—22no—
167C4×C8×C53—22no—
168#41×C53—21no—
169#41×C53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173#41×C53—21no—
174#41×C53C2×D412yes—
175#41×C53#4112yes—
176C2×Q8×C53C22×C411yescharacteristic
177C2×Q8×C53C22×C411yescharacteristic
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53C22×C411yescharacteristic
181C2×D4×C53C22×C411yescharacteristic
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53C2411yescharacteristic
186C2×C22⋊D53—21no—
187C2×C22⋊D53—21no—
188C2×C22⋊D53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53#4111yescharacteristic
193C22×Dic53#4111yescharacteristic
194#11719945—21no—
195#11719945—21no—
196#11719945—21no—
197#11719945—21no—
198C2×D212C22×C411yescharacteristic
199C2×C4×D53—21no—
200C2×Dic106C22×C411yescharacteristic
201Q16×C53—22no—
202SD16×C53—22no—
203SD16×C53—22no—
204D8×C53—22no—
205M16×C53—21no—
206M16×C53—24no—
207M16×C53—21no—
208M16×C53—21no—
209M16×C53—42no—
210M16×C53C2×D412yes—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—21no—
214C2×C8×C53—24no—
215C2×C8×C53—21no—
216C2×C8×C53—42no—
217C2×C8×C53C22×C411yescharacteristic
218C2×C8×C53C22×C411yescharacteristic
219C2×C8×C53C2×D411yescharacteristic
220C2×C8×C53C2×D411yescharacteristic
221C2×C8×C53C2×D412yes—
222C2×C8×C53#4112yes—
223C42×C53—21no—
224C42×C53—21no—
225C22⋊Dic53—21no—
226C22⋊Dic53—21no—
227C22⋊Dic53—21no—
228C22⋊Dic53—21no—
229C22⋊Dic53—21no—
230#11719925—22no—
231#11719924—22no—
232#11719923—22no—
233#11719922—22no—
234#11719921—21no—
235#11719921—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53C22×C411yescharacteristic
239C4⋊Dic53C22×C411yescharacteristic
240#11719919—24no—
241#11719919—21no—
242#11719919—21no—
243C4×Dic53—21no—
244C4×Dic53—21no—
245C4×Dic53—21no—
246C4×Dic53—21no—
247C4×Dic53—21no—
248C4×Dic53C22×C411yescharacteristic
249C4×Dic53C22×C411yescharacteristic
250C4×Dic53C2×D411yescharacteristic
251C4×Dic53C2×D411yescharacteristic
252#11719917—24no—
253#11719917—21no—
254#11719917—21no—
255#11719917—21no—
256#11719917#4112yes—
257C2×#88322—24no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322C22×C411yescharacteristic
265C2×#88322C22×C411yescharacteristic
266C2×#88322C2×D411yescharacteristic
267C2×#88322C2×D411yescharacteristic
268#11719912—42no—
269C8×D53—42no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53C2×#4111yescharacteristic
273C22×D53—21no—
274Q8×C53—21no—
275Q8×C53—21no—
276Q8×C53—21no—
277Q8×C53C4×D412yes—
278D4×C53—22no—
279D4×C53—22no—
280D4×C53—21no—
281D4×C53—21no—
282D4×C53—21no—
283D4×C53—41no—
284D4×C53—41no—
285D4×C53C4×D412yes—
286C2×C4×C53—21no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—21no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53C23×C411yescharacteristic
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C22⋊D53—42no—
302C22⋊D53—41no—
303C22⋊D53—41no—
304C22⋊D53—42no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—41no—
311C2×Dic53—42no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—42no—
315C2×Dic53C4×D411yescharacteristic
316C2×Dic53C4×D411yescharacteristic
317C2×Dic53C4×D411yescharacteristic
318C2×Dic53C4×D411yescharacteristic
319D212—21no—
320D212—21no—
321C4×D53—41no—
322C4×D53—41no—
323Dic106—21no—
324Dic106—21no—
325C8×C53—21no—
326C8×C53—21no—
327C8×C53—22no—
328C8×C53—41no—
329C8×C53#12112yes—
330C8×C53#12112yes—
331#88322—21no—
332#88322—21no—
333#88322—21no—
334#88322—22no—
335#88322—21no—
336#88322—41no—
337#21517—531nomaximal, Sylow
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—22no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53C2×C4×D411yescharacteristic
347C22×C53#52911yescharacteristic
348C22×C53#53211yescharacteristic
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C4×C53—22no—
353C4×C53—42no—
354C4×C53—41no—
355C4×C53C2×C4×D411yescharacteristic
356C4×C53C4×#4111yescharacteristic
357C4×C53C2×#12111yescharacteristic
358C4×C53#52511yescharacteristic
359Dic53—21no—
360Dic53—21no—
361Dic53—21no—
362Dic53—42no—
363Dic53—41no—
364Dic53—41no—
365Dic53—41no—
366Dic53#44312yescomplemented
367#3035—531no—
368C2×#443—531no—
369C2×#443D5311yescharacteristic, complemented
370#2931—531no—
371C4×#131—531no—
372#1980—531no—
373#1950—531no—
374#1929—531no—
375#1929—531no—
376#1876—531no—
377#1876—531no—
378#1806—531no—
379C8×C4⋊C4—531no—
380#1764—531no—
381#1764—531no—
382C2×C53—21no—
383C2×C53—21no—
384C2×C53—42no—
385C2×C53—81no—
386C2×C53C4×#12111yescharacteristic
387C2×C53C2×#44311yescharacteristic
388C2×C53#295511yescharacteristic
389D53—81no—
390C2×#135—531no—
391C2×#135C2×D5311yescharacteristic
392C2×#131—531no—
393C2×#131—531no—
394C2×#131C2×D5311yescharacteristic
395C2×#131C2×D5311yescharacteristic
396#532—531no—
397C4×#41—531no—
398#464—531no—
399#464—531no—
400#463—531no—
401#463—531no—
402#462—531no—
403#461—531no—
404#460—531no—
405#459—531no—
406#443—24no—
407#443—1064no—
408#436—1061no—
409#436—1061no—
410C8×D4—1061no—
411C8×D4—1061no—
412C2×#108—531no—
413C2×#108C2×D5311yescharacteristic
414#423—531no—
415C2×C4⋊C8—531no—
416C2×#104—531no—
417C2×#104—531no—
418C2×#104—531no—
419C2×#104—531no—
420C2×#104C2×D5311yescharacteristic
421C2×#104C2×D5311yescharacteristic
422#416—531no—
423#416—531no—
424#408—531no—
425#408—531no—
426#405—531no—
427#405—531no—
428#405—1061no—
429#405—1061no—
430C4×M16—531no—
431C4×M16—1061no—
432C2×C4×C8—531no—
433C2×C4×C8—531no—
434C2×C4×C8—1061no—
435C2×C4×C8C2×D5311yescharacteristic
436C4×C4⋊C4—531no—
437#341—531no—
438#341—531no—
439#339—531no—
440#339—531no—
441#336—531no—
442#336—531no—
443C53#2151711yescharacteristic, complemented, Sylow
444C2×#41—531no—
445C2×#41C22×D5311yescharacteristic
446C2×#41C22×D5311yescharacteristic
447#135—22no—
448#135—22no—
449#135—1062no—
450#135—1062no—
451C2×Q16—531no—
452C2×Q16C4×D5311yescharacteristic
453C2×SD16—531no—
454C2×SD16—531no—
455C2×SD16C4×D5311yescharacteristic
456C2×SD16C4×D5311yescharacteristic
457C2×D8—531no—
458C2×D8C4×D5311yescharacteristic
459#131—22no—
460#131—22no—
461#131—22no—
462#131—1062no—
463#131—1062no—
464#131—1062no—
465#131—1062no—
466#131C22⋊D5314yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—531no—
470C2×M16—531no—
471C2×M16—1061no—
472C2×M16—1061no—
473C2×M16C22×D5311yescharacteristic
474C2×M16C22×D5311yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—1061no—
480C22×C8—1061no—
481C22×C8C22×D5311yescharacteristic
482C22×C8C22×D5311yescharacteristic
483C4⋊Q8—531no—
484#127—531no—
485#124—531no—
486#124—531no—
487#121—1061no—
488#121—1061no—
489C4×Q8—531no—
490C4×Q8—531no—
491C4×D4—531no—
492C4×D4—531no—
493C4×D4—1061no—
494C4×D4—1061no—
495C4×D4—1061no—
496C4×D4—1061no—
497#117—531no—
498#117—1061no—
499C2×C4⋊C4—1061no—
500C2×C42—531no—
501C2×C42—531no—
502C2×C42—1061no—
503C2×C42C22×D5311yescharacteristic
504#108—22no—
505#108—1062no—
506C4⋊C8—531no—
507C4⋊C8—531no—
508C4⋊C8—531no—
509C4⋊C8—531no—
510C4⋊C8—1061no—
511C4⋊C8—1061no—
512#104—22no—
513#104—22no—
514#104—1062no—
515#104—1062no—
516#104—1062no—
517#104—1062no—
518#103—531no—
519#103—531no—
520#103—531no—
521#103—531no—
522#102—531no—
523#102—531no—
524#102—531no—
525#102—531no—
526C22⋊C8—1061no—
527C22⋊C8—1061no—
528C22⋊C8—1061no—
529C22⋊C8—1061no—
530#97—1061no—
531#97—1061no—
532#97—1061no—
533C4×C8—22no—
534C4×C8—531no—
535C4×C8—531no—
536C4×C8—531no—
537C4×C8—531no—
538C4×C8—1061no—
539C4×C8—1061no—
540C4×C8—1061no—
541C4×C8—1062no—
542#95—1061no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—1061no—
550#41—1061no—
551#41—1061no—
552#41—1061no—
553#41#1171994512yes—
554#41C2×C22⋊D5312yes—
555C2×Q8—531no—
556C2×Q8C2×C4×D5311yescharacteristic
557C2×Q8C2×C4×D5311yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—531no—
561C2×D4—1061no—
562C2×D4—1061no—
563C2×D4—1061no—
564C2×D4C2×C4×D5311yescharacteristic
565C2×D4C2×C4×D5311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4C23×D5311yescharacteristic
576Q16—22no—
577Q16—1062no—
578SD16—22no—
579SD16—22no—
580SD16—1062no—
581SD16—1062no—
582D8—22no—
583D8—1062no—
584M16—21no—
585M16—24no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—532no—
590M16—1064no—
591M16—1061no—
592M16—1061no—
593M16—1061no—
594M16—2122no—
595M16C2×C22⋊D5312yes—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—24no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—531no—
603C2×C8—531no—
604C2×C8—531no—
605C2×C8—531no—
606C2×C8—1064no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—1061no—
613C2×C8—2122no—
614C2×C8C2×C4×D5311yescharacteristic
615C2×C8C2×C4×D5311yescharacteristic
616C2×C8D4×D5311yescharacteristic
617C2×C8D4×D5311yescharacteristic
618C2×C8#1171994712yes—
619C2×C8C2×C22⋊D5312yes—
620C4⋊C4—531no—
621C4⋊C4—531no—
622C4⋊C4—1061no—
623C4⋊C4—1061no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—1064no—
627C22⋊C4—1061no—
628C22⋊C4—1061no—
629C22⋊C4—1061no—
630C22⋊C4—1061no—
631C22⋊C4—1061no—
632C22⋊C4—1061no—
633C22⋊C4—1061no—
634C42—21no—
635C42—21no—
636C42—531no—
637C42—531no—
638C42—531no—
639C42—531no—
640C42—1061no—
641C42—1061no—
642C42—1061no—
643C42—1061no—
644C42—1061no—
645C23—21no—
646C23—21no—
647C23—1061no—
648C23#41×D5311yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—1061no—
653Q8—1061no—
654Q8C4×C22⋊D5312yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—41no—
661D4—41no—
662D4—1061no—
663D4—1061no—
664D4—2122no—
665D4—2122no—
666D4—2121no—
667D4—2121no—
668D4C4×C22⋊D5312yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—531no—
679C2×C4—531no—
680C2×C4—531no—
681C2×C4—531no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—2122no—
688C2×C4—2121no—
689C2×C4—2122no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4C22×C4×D5311yescharacteristic
695C2×C4C2×D4×D5311yescharacteristic
696C2×C4C22×C22⋊D5311yescharacteristic
697C2×C4#41×D5311yescharacteristic
698C2×C4C2×#1171994711yescharacteristic
699C2×C4C2×#1171994511yescharacteristic
700C8—21no—
701C8—21no—
702C8—22no—
703C8—41no—
704C8—1061no—
705C8—1061no—
706C8—1061no—
707C8—1061no—
708C8—1062no—
709C8—2121no—
710C8#1313318912yes—
711C8#1313318912yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22C4×D4×D5311yescharacteristic
724C22#1681115311yescharacteristic
725C22#1681116911yescharacteristic
726C4—22no—
727C4—42no—
728C4—41no—
729C4—532no—
730C4—1061no—
731C4—1061no—
732C4—1061no—
733C4—2122no—
734C4—2121no—
735C4—2121no—
736C4—2121no—
737C4C2×C4×C22⋊D5311yescharacteristic
738C4C4×#1171994711yescharacteristic
739C4C2×#1313318911yescharacteristic
740C4#1681113211yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—4241no—
746C2C4×#1313318911yescharacteristic
747C2#443×D5311yescharacteristic
748C2#2028361311yescharacteristic
subgroupG/H
centerC2×C8D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#443C2
socleC22×C53C2×C4×D4
prime radical#20284166C2
cosocleC22×C4×C53C24
hypercenterC2×#443D53
hypocenterC53#21517
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#16810738C2semidirect
3. #20283425C2semidirect
4. #131×Dic53C2semidirect
5. #20275632C2semidirect
6. #20275487C2semidirect
7. #20275366C2semidirect
8. #20275362C2semidirect
9. #20275044C2semidirect
10. #20275040C2semidirect
11. #20274733C2semidirect
12. C8×#11719919C2semidirect
13. #20274552C2semidirect
14. #20274550C2semidirect
15. C2×C53×#443C2semidirect
21. #16810847C4semidirect
22. #16810843C4semidirect
23. #16810840C4semidirect
24. #16810836C4semidirect
25. #16810831C4semidirect
26. #16810826C4semidirect
27. #16810821C4semidirect
28. #16810816C4semidirect
154. #131×C53D4semidirect
366. Dic53#443semidirect
369. C2×#443D53semidirect
443. C53#21517semidirect
466. #131C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
#202841662
C2×#168107382
#202834252
#131×Dic532
#202756322
#202754872
#202753662
#202753622
#202750442
#202750402
#202747332
C8×#117199192
#202745522
#202745502
C2×C53×#4432
#2151753