Finite Group Databasebeta

← #27406530

Subgroups — #27406530

Order 13568.

1046 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810821C211yesmaximal, characteristic
2C2×#16810708C211yesmaximal, characteristic, complemented
3#20277777C211yesmaximal, characteristic
4#20277633C211yesmaximal, characteristic, complemented
5#20275537C211yesmaximal, characteristic
6#20275480C211yesmaximal, characteristic, complemented
7#20275412C211yesmaximal, characteristic, complemented
8#20275395C211yesmaximal, characteristic, complemented
9#20275072C211yesmaximal, characteristic, complemented
10#20275070C211yesmaximal, characteristic, complemented
11#20274976C211yesmaximal, characteristic, complemented
12#20274959C211yesmaximal, characteristic, complemented
13#20274591C211yesmaximal, characteristic, complemented
14#20274547C211yesmaximal, characteristic, complemented
15C2×C53×#440C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C2×#13133213C2211yescharacteristic
18C2×Q8×Dic53C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic
20C2×#13133179C2211yescharacteristic
21C2×C4×C22⋊D53—21no—
22#16810821C418yescomplemented
23#16810708—24no—
24C2×#13133148C2211yescharacteristic
25C2×#13133146C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133139C2211yescharacteristic
28C2×#13133139C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33C2×C8×Dic53C2211yescharacteristic
34#16810526C2211yescharacteristic
35#16810525C2211yescharacteristic
36#16810523—21no—
37#16810521—21no—
38#16810521C2211yescharacteristic
39#16810519—21no—
40#16810519C2211yescharacteristic
41#16810502—21no—
42#16810499—21no—
43#16810488—21no—
44#16810488C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C4×#11719919—21no—
47C4×#11719919C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810378C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×SD16×C53C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C53×#440—24no—
58C2×#107×C53C2211yescharacteristic
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C22⋊D53—21no—
65C22×C4×D53—21no—
66C2×#11719924—22no—
67C2×#11719924—22no—
68C2×#11719924C2×C414yescomplemented
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133213—22no—
72#13133213C2×C414yes—
73Q8×Dic53—22no—
74Q8×Dic53—22no—
75Q8×Dic53—41no—
76Q8×Dic53C2×C414yescomplemented
77#13133179—22no—
78#13133179—41no—
79C4×C22⋊D53—44no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53—21no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919D411yescharacteristic
88C2×#11719919D411yescharacteristic
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×C4×Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97C2×C4×Dic53C2311yescharacteristic
98C2×C4×Dic53C2311yescharacteristic
99#13133148—22no—
100#13133146C2×C414yescomplemented
101#13133141—22no—
102#13133139—22no—
103#13133139C2×C414yescomplemented
104#13133138—41no—
105#13133138C2×C414yescomplemented
106#13133137—41no—
107#13133127—22no—
108C8×Dic53—22no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124D411yescharacteristic
115#13133124D411yescharacteristic
116C22×Q8×C53C2311yescharacteristic
117C22×D4×C53C2311yescharacteristic
118C23×C4×C53—21no—
119C2×SD16×C53—22no—
120C2×SD16×C53—22no—
121C2×SD16×C53C2×C414yescomplemented
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124C4×Q8×C53—22no—
125C4×Q8×C53—41no—
126C4×D4×C53—22no—
127C4×D4×C53—41no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C22⋊C4×C53—21no—
132C2×C42×C53—21no—
133C2×C42×C53C2311yescharacteristic
134#107×C53—22no—
135#103×C53D414yescomplemented
136#102×C53—22no—
137#97×C53—22no—
138C24×C53—21no—
139C23×D53—21no—
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53C22×C412yes—
144C2×Q8×C53C2×D412yes—
145C2×Q8×C53#4112yes—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53C22×C412yes—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53—81no—
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2411yescharacteristic
161C2×C22⋊D53—24no—
162C2×C22⋊D53—24no—
163C2×C22⋊D53—42no—
164C2×C22⋊D53—42no—
165C2×C22⋊D53—81no—
166C2×C22⋊D53—81no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53C2×D411yescharacteristic
171C22×Dic53C2×D411yescharacteristic
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212C22×C412yes—
180C2×C4×D53—42no—
181C2×C4×D53—42no—
182C2×C4×D53—81no—
183SD16×C53—28no—
184C2×C8×C53—21no—
185C2×C8×C53—21no—
186C2×C8×C53—21no—
187C2×C8×C53—21no—
188C2×C8×C53C22×C412yes—
189C2×C8×C53C2×D412yes—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—42no—
194C4⋊C4×C53C2×D412yes—
195C22⋊C4×C53—42no—
196C42×C53—21no—
197C42×C53—21no—
198C42×C53—42no—
199C22⋊Dic53—42no—
200C22⋊Dic53—81no—
201#11719924—28no—
202#11719921—42no—
203#11719921—42no—
204#11719921—81no—
205C4⋊Dic53—21no—
206C4⋊Dic53—24no—
207C4⋊Dic53—21no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—42no—
212C4⋊Dic53C22×C412yes—
213#11719919—22no—
214#11719919—41no—
215#11719919—42no—
216#11719919—42no—
217C4×Dic53—21no—
218C4×Dic53—21no—
219C4×Dic53—24no—
220C4×Dic53—42no—
221C4×Dic53—42no—
222C4×Dic53C22×C412yes—
223C4×Dic53#4112yes—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322C22×C412yes—
230C23×C53—22no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53C22×D411yescharacteristic
238C22×D53—22no—
239C22×D53—41no—
240C22×D53—41no—
241C22×D53—41no—
242C22×D53—41no—
243C22×D53—41no—
244C22×D53—41no—
245Q8×C53—22no—
246Q8×C53—22no—
247Q8×C53—22no—
248Q8×C53C4×D414yescomplemented
249D4×C53—22no—
250D4×C53—22no—
251D4×C53—41no—
252D4×C53—41no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—84no—
269C2×C4×C53C23×C411yescharacteristic
270C2×C4×C53C22×D411yescharacteristic
271C2×C4×C53C2×#4111yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53H(5,𝔽2)11yescharacteristic
274C2×C4×C532−1+411yescharacteristic
275C22⋊D53—48no—
276C22⋊D53—84no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—22no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53C4×D412yes—
296C2×Dic53C4×D412yes—
297C2×Dic53AGL(1,ℤ/8)12yes—
298D212—22no—
299D212—22no—
300D212—41no—
301D212—41no—
302C4×D53—84no—
303C8×C53—22no—
304C8×C53—22no—
305#88322—22no—
306#88322—41no—
307#23010—531nomaximal, Sylow
308C22×C53—42no—
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—81no—
312C22×C53—81no—
313C22×C53—81no—
314C22×C53—81no—
315C22×C53C2×C4×D411yescharacteristic
316C22×C53D4211yescharacteristic
317C22×C53#54811yescharacteristic
318C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C53#57511yescharacteristic
320C22×C53#57711yescharacteristic
321C22×C53#57711yescharacteristic
322C2×D53—42no—
323C2×D53—42no—
324C2×D53—42no—
325C2×D53—81no—
326C2×D53—81no—
327C2×D53—81no—
328C2×D53—81no—
329C4×C53—24no—
330C4×C53—42no—
331C4×C53—41no—
332C4×C53—41no—
333C4×C53—81no—
334C4×C53C2×C4×D411yescharacteristic
335C4×C53#52011yescharacteristic
336C4×C53#54711yescharacteristic
337C4×C53#55311yescharacteristic
338Dic53—22no—
339Dic53—22no—
340Dic53—22no—
341Dic53—42no—
342Dic53—41no—
343Dic53—81no—
344Dic53—81no—
345C2×#460—531no—
346C2×#440D5311yescharacteristic, complemented
347C2×C4×SD16—531no—
348#2366—531no—
349#2351—531no—
350#1961—531no—
351#1949—531no—
352#1936—531no—
353#1934—531no—
354#1880—531no—
355#1880—531no—
356#1864—531no—
357#1862—531no—
358#1771—531no—
359#1763—531no—
360C2×C53—82no—
361C2×C53#236111yescharacteristic
362C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
363C2×C53#294911yescharacteristic
364C2×C53#326511yescharacteristic
365C2×C53#327111yescharacteristic
366C2×C53#336811yescharacteristic
367C2×C53#337111yescharacteristic
368D53—82no—
369C22×SD16—531no—
370C22×SD16C2×D5311yescharacteristic
371C2×#127—531no—
372C2×C4×Q8—531no—
373C2×C4×Q8—531no—
374C2×C4×Q8C2×D5311yescharacteristic
375C2×C4×D4—531no—
376C2×C4×D4—1061no—
377C2×C4×D4C2×D5311yescharacteristic
378#460—538no—
379#440—24no—
380C4×SD16—1064no—
381C2×#107C2×D5311yescharacteristic
382C2×#106—531no—
383C2×C4⋊C8—531no—
384C2×#103—531no—
385C2×#103C2×D5311yescharacteristic
386C2×#102—531no—
387C2×#102—531no—
388C2×#102—531no—
389C2×#102—531no—
390C2×#102—531no—
391C2×#102C2×D5311yescharacteristic
392C2×#97—531no—
393C2×#97C2×D5311yescharacteristic
394C2×C4×C8—531no—
395#390—531no—
396#390—531no—
397#390—1061no—
398#389—531no—
399#389—531no—
400#389—1061no—
401#389—1061no—
402#386—1061no—
403#386—1061no—
404#382—531no—
405#382—1061no—
406C4×C4⋊C4—531no—
407C4×C4⋊C4—531no—
408C4×C4⋊C4—1061no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#336—531no—
414#336—531no—
415C53#2301011yescharacteristic, complemented, Sylow
416C22×Q8C22×D5311yescharacteristic
417C22×D4—531no—
418C22×D4—1061no—
419C22×D4—1061no—
420C22×D4C22×D5311yescharacteristic
421C23×C4—21no—
422C23×C4—1061no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—534no—
426C2×SD16—1062no—
427C2×SD16—1062no—
428C2×SD16C4×D5314yescomplemented
429C22×C8—531no—
430C22×C8—531no—
431C22×C8C22×D5311yescharacteristic
432C22×C8C22×D5311yescharacteristic
433#127—534no—
434#127—1062no—
435C4×Q8—22no—
436C4×Q8—41no—
437C4×Q8—534no—
438C4×Q8—1062no—
439C4×Q8—1062no—
440C4×Q8—2121no—
441C4×D4—22no—
442C4×D4—41no—
443C4×D4—1062no—
444C4×D4—2121no—
445C4×D4—2124no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—531no—
448C2×C4⋊C4—531no—
449C2×C4⋊C4—531no—
450C2×C4⋊C4—531no—
451C2×C4⋊C4—531no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—1061no—
454C2×C4⋊C4—1061no—
455C2×C4⋊C4—1061no—
456C2×C4⋊C4C22×D5311yescharacteristic
457C2×C4⋊C4C22×D5311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—1061no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4—1061no—
463C2×C22⋊C4—1061no—
464C2×C42—21no—
465C2×C42—531no—
466C2×C42—531no—
467C2×C42—1061no—
468C2×C42—1061no—
469C2×C42—1061no—
470C2×C42C22×D5311yescharacteristic
471#107—22no—
472#106—1062no—
473C4⋊C8—534no—
474#103—1062no—
475#103C22⋊D5314yescomplemented
476#102—22no—
477#102—534no—
478#102—534no—
479#102—1062no—
480#102—2121no—
481#102—2121no—
482#97—22no—
483#97—1062no—
484C4×C8—1062no—
485#95—531no—
486#95—531no—
487#95—1061no—
488#95—1061no—
489#95—1061no—
490#95—1061no—
491#95—1061no—
492C24—21no—
493C24—1061no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×C4×D5312yes—
498C2×Q8#1171994512yes—
499C2×Q8C2×C22⋊D5312yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—532no—
506C2×D4—1064no—
507C2×D4—1064no—
508C2×D4—1061no—
509C2×D4—1061no—
510C2×D4—1061no—
511C2×D4—1061no—
512C2×D4—1061no—
513C2×D4—4241no—
514C2×D4—4241no—
515C2×D4—2122no—
516C2×D4—2122no—
517C2×D4C2×C4×D5312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—531no—
525C22×C4—531no—
526C22×C4—531no—
527C22×C4—531no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—4241no—
532C22×C4—2122no—
533C22×C4—2122no—
534C22×C4D4×D5311yescharacteristic
535C22×C4D4×D5311yescharacteristic
536C22×C4C23×D5311yescharacteristic
537SD16—28no—
538SD16—1068no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—532no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8C2×C4×D5312yes—
550C2×C8C2×C22⋊D5312yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—532no—
556C4⋊C4—1062no—
557C4⋊C4—1064no—
558C4⋊C4—1061no—
559C4⋊C4—1061no—
560C4⋊C4—1061no—
561C4⋊C4—1061no—
562C4⋊C4—1061no—
563C4⋊C4—2121no—
564C4⋊C4—2122no—
565C4⋊C4—2122no—
566C4⋊C4—2122no—
567C4⋊C4C2×C22⋊D5312yes—
568C22⋊C4—42no—
569C22⋊C4—4241no—
570C22⋊C4—4241no—
571C22⋊C4—2122no—
572C22⋊C4—2122no—
573C22⋊C4—2122no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—532no—
578C42—532no—
579C42—1064no—
580C42—1061no—
581C42—1061no—
582C42—2122no—
583C42—2122no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—1062no—
592C23—2121no—
593C23—2121no—
594C23—2121no—
595C23—2121no—
596C23—2121no—
597C23—2121no—
598C23C2×D4×D5311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8C4×C22⋊D5314yescomplemented
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—1062no—
608D4—1062no—
609D4—4244no—
610D4—2128no—
611D4—2121no—
612D4—2121no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—84no—
629C2×C4—532no—
630C2×C4—532no—
631C2×C4—532no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1062no—
639C2×C4—1061no—
640C2×C4—1061no—
641C2×C4—1061no—
642C2×C4—4244no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4C22×C4×D5311yescharacteristic
652C2×C4C22×C22⋊D5311yescharacteristic
653C2×C4#41×D5311yescharacteristic
654C2×C4C2×#1171994511yescharacteristic
655C2×C4#1313326211yescharacteristic
656C2×C4#1313326411yescharacteristic
657C8—22no—
658C8—22no—
659C8—1062no—
660C8—2121no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—4241no—
669C22—4241no—
670C22—4241no—
671C22—4241no—
672C22—2122no—
673C22—2122no—
674C22—2122no—
675C22C4×D4×D5311yescharacteristic
676C22D4×C22⋊D5311yescharacteristic
677C22#1681128211yescharacteristic
678C22AGL(1,ℤ/8)×D5311yescharacteristic
679C22#1681142211yescharacteristic
680C22#1681143211yescharacteristic
681C22#1681143311yescharacteristic
682C4—24no—
683C4—41no—
684C4—41no—
685C4—42no—
686C4—81no—
687C4—1062no—
688C4—1062no—
689C4—1062no—
690C4—4241no—
691C4—4241no—
692C4—2121no—
693C4—2122no—
694C4C2×C4×C22⋊D5311yescharacteristic
695C4#1681110211yescharacteristic
696C4#1681127211yescharacteristic
697C4#1681132211yescharacteristic
698C2—82no—
699C2—4242no—
700C2#2027773211yescharacteristic
701C2#2028352011yescharacteristic
702C2#2028357111yescharacteristic
703C2#2028620411yescharacteristic
704C2#2028629411yescharacteristic
705C2#2028744511yescharacteristic
706C2#2028748811yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#13133213C22
cosocleC22×C4×C53C24
hypercenterC2×#440D53
hypocenterC53#23010
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16810708C2semidirect
4. #20277633C2semidirect
6. #20275480C2semidirect
7. #20275412C2semidirect
8. #20275395C2semidirect
9. #20275072C2semidirect
10. #20275070C2semidirect
11. #20274976C2semidirect
12. #20274959C2semidirect
13. #20274591C2semidirect
14. #20274547C2semidirect
15. C2×C53×#440C2semidirect
22. #16810821C4semidirect
68. C2×#11719924C2×C4semidirect
76. Q8×Dic53C2×C4semidirect
100. #13133146C2×C4semidirect
103. #13133139C2×C4semidirect
105. #13133138C2×C4semidirect
121. C2×SD16×C53C2×C4semidirect
135. #103×C53D4semidirect
248. Q8×C53C4×D4semidirect
346. C2×#440D53semidirect
415. C53#23010semidirect
428. C2×SD16C4×D53semidirect
475. #103C22⋊D53semidirect
602. Q8C4×C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168108212
C2×#168107082
#202777772
#202776332
#202755372
#202754802
#202754122
#202753952
#202750722
#202750702
#202749762
#202749592
#202745912
#202745472
C2×C53×#4402
#2301053