Finite Group Databasebeta

← #27306848

Subgroups — #27306848

Order 13568.

2150 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810498C211yesmaximal, characteristic
2C2×#16810496C211yesmaximal, characteristic
3C2×#16810495C211yesmaximal, characteristic
4C2×#16810481C211yesmaximal, characteristic
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic
6C22×#13133124C211yesmaximal, characteristic
7#20272979C212yesmaximal, complemented
8#20272978C212yesmaximal, complemented
9#20272944C212yesmaximal, complemented
10#20272943C212yesmaximal, complemented
11C2×C53×#385C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×#11719919C2212yes—
16C22×#11719919C2212yes—
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C4×Dic53C2212yes—
22#16810498—24no—
23#16810496—24no—
24#16810495—24no—
25#16810481—24no—
26C22⋊C4×Dic53C418yescomplemented
27C2×#13133124—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C53×#385—24no—
41C2×#95×C53C2212yes—
42C23×Dic53—22no—
43C23×Dic53—24no—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—42no—
47C23×Dic53—42no—
48C23×Dic53—42no—
49C23×Dic53C2×C414yes—
50C23×Dic53D414yes—
51C23×Dic53Q814yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C2×C4⋊Dic53—24no—
59C2×C4⋊Dic53—24no—
60C2×C4⋊Dic53—42no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—22no—
64C2×#11719919—22no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—42no—
68C2×#11719919—42no—
69C2×#11719919—42no—
70C2×#11719919—42no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53C2×C414yes—
75C2×C22⋊Dic53D414yes—
76C2×C22⋊Dic53Q814yes—
77C2×C4×Dic53—42no—
78C2×C4×Dic53—42no—
79C2×C4×Dic53C2×C418yescomplemented
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—22no—
85#13133124—22no—
86#13133124—24no—
87#13133124C2×C418yescomplemented
88C25×C53C2311yescharacteristic
89C23×C4×C53—22no—
90C23×C4×C53—24no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—42no—
94C23×C4×C53C2311yescharacteristic
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2312yes—
97C23×C4×C53C2312yes—
98C2×C4⋊C4×C53—24no—
99C2×C4⋊C4×C53—24no—
100C2×C4⋊C4×C53—42no—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53C2×C414yes—
105C2×C22⋊C4×C53D414yes—
106C2×C22⋊C4×C53Q814yes—
107#95×C53—24no—
108C24×C53—22no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53C22×C412yes—
113C24×C53C2×D412yes—
114C24×C53C2×D412yes—
115C24×C53C2×D412yes—
116C24×C53C2×Q812yes—
117C24×C53C2×Q812yes—
118C24×C53C2×Q812yes—
119C24×C53C2411yescharacteristic
120C22×C4×C53—22no—
121C22×C4×C53—22no—
122C22×C4×C53—22no—
123C22×C4×C53—22no—
124C22×C4×C53—28no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—48no—
142C22×C4×C53—48no—
143C22×C4×C53—44no—
144C22×C4×C53—44no—
145C22×C4×C53C22×C414yes—
146C22×C4×C53C2×D414yes—
147C22×C4×C53C2×Q814yes—
148C22×C4×C53#4114yes—
149C22×Dic53—22no—
150C22×Dic53—22no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—28no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—48no—
175C22×Dic53—44no—
176C22×Dic53—44no—
177C22×Dic53—48no—
178C22×Dic53—48no—
179C22×Dic53—48no—
180C22×Dic53—44no—
181C22×Dic53—44no—
182C22×Dic53C4⋊C4116yescomplemented
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C414yes—
185C22×Dic53C22×C412yes—
186C22×Dic53C2×D412yes—
187C22×Dic53C2×D414yes—
188C22×Dic53C2×D412yes—
189C22×Dic53C2×Q814yes—
190C22×Dic53C2×Q812yes—
191C22×Dic53C2×Q812yes—
192C22×Dic53#4114yes—
193C4⋊C4×C53—48no—
194C22⋊C4×C53—44no—
195C22⋊C4×C53C4⋊C4116yescomplemented
196C22⋊Dic53—44no—
197C22⋊Dic53C4⋊C4116yescomplemented
198C4⋊Dic53—48no—
199#11719919—48no—
200#11719919—48no—
201#11719919—44no—
202#11719919—44no—
203C4×Dic53—48no—
204C23×C53—24no—
205C23×C53—24no—
206C23×C53—22no—
207C23×C53—22no—
208C23×C53—24no—
209C23×C53—22no—
210C23×C53—22no—
211C23×C53—24no—
212C23×C53—24no—
213C23×C53—24no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53C2×C4⋊C414yes—
221C23×C53C2×C4⋊C414yes—
222C23×C53C2×C4⋊C414yes—
223C23×C53#12714yes—
224C23×C53C4⋊Q814yes—
225C23×C53C4⋊Q814yes—
226C23×C53C4⋊Q814yes—
227C23×C53C23×C411yescharacteristic
228C23×C53C22×D411yescharacteristic
229C23×C53C22×D411yescharacteristic
230C23×C53C22×D411yescharacteristic
231C23×C53C22×Q811yescharacteristic
232C23×C53C22×Q811yescharacteristic
233C23×C53C22×Q811yescharacteristic
234C23×C53C2×#4112yes—
235C23×C53C2×#4112yes—
236C23×C53H(5,𝔽2)12yes—
237C23×C53H(5,𝔽2)12yes—
238C2×C4×C53—24no—
239C2×C4×C53—24no—
240C2×C4×C53—24no—
241C2×C4×C53—24no—
242C2×C4×C53—24no—
243C2×C4×C53—24no—
244C2×C4×C53—24no—
245C2×C4×C53—24no—
246C2×C4×C53—24no—
247C2×C4×C53—416no—
248C2×C4×C53—42no—
249C2×C4×C53—42no—
250C2×C4×C53—42no—
251C2×C4×C53—42no—
252C2×C4×C53—41no—
253C2×C4×C53—41no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—42no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53C2×C4⋊C418yes—
263C2×Dic53—24no—
264C2×Dic53—24no—
265C2×Dic53—24no—
266C2×Dic53—24no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—22no—
271C2×Dic53—24no—
272C2×Dic53—24no—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—416no—
281C2×Dic53—416no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53C2×C4⋊C414yes—
297C2×Dic53C2×C4⋊C414yes—
298C2×Dic53C2×C4⋊C418yes—
299#13965—531nomaximal, Sylow
300C22×C53—24no—
301C22×C53—24no—
302C22×C53—24no—
303C22×C53—28no—
304C22×C53—28no—
305C22×C53—24no—
306C22×C53—24no—
307C22×C53—28no—
308C22×C53—28no—
309C22×C53—24no—
310C22×C53#38418yes—
311C22×C53C22×C4⋊C411yescharacteristic
312C22×C53C22×C4⋊C411yescharacteristic
313C22×C53C22×C4⋊C411yescharacteristic
314C22×C53C4×#4112yes—
315C22×C53#51812yes—
316C22×C53#52511yescharacteristic
317C22×C53#52511yescharacteristic
318C22×C53C2×#12711yescharacteristic
319C22×C53C2×C4⋊Q811yescharacteristic
320C22×C53C2×C4⋊Q811yescharacteristic
321C22×C53C2×C4⋊Q811yescharacteristic
322C22×C53#53312yes—
323C22×C53#53411yescharacteristic
324C22×C53#53411yescharacteristic
325C22×C53#54312yes—
326C22×C53#54612yes—
327C22×C53#54612yes—
328C22×C53#54612yes—
329C22×C53#54612yes—
330C22×C53#55412yes—
331C22×C53#55412yes—
332C22×C53#55412yes—
333C22×C53#55412yes—
334C4×C53—28no—
335C4×C53—44no—
336C4×C53—81no—
337C4×C53—81no—
338Dic53—24no—
339Dic53—24no—
340Dic53—28no—
341Dic53—44no—
342Dic53—81no—
343Dic53—81no—
344C2×#385—531no—
345C2×#385—531no—
346C2×#385—531no—
347C2×#385D5311yescharacteristic
348C2×#380—531no—
349C2×C4×C22⋊C4—531no—
350C22×#95—531no—
351#1444—532no—
352#1444—532no—
353C4⋊#95—532no—
354C4⋊#95—532no—
355C2×C53—28no—
356C2×C53C2×#38411yescharacteristic
357C2×C53#229611yescharacteristic
358C2×C53#231511yescharacteristic
359C2×C53#234912yes—
360C2×C53#234912yes—
361C2×C53#253911yescharacteristic
362C2×C53#253911yescharacteristic
363C2×C53#254912yes—
364C2×C53#254912yes—
365C2×C53#258311yescharacteristic
366C2×C53#258311yescharacteristic
367C24×C4—531no—
368C24×C4—531no—
369C24×C4C2×D5311yescharacteristic
370C22×C4⋊C4—532no—
371C22×C4⋊C4—532no—
372C22×C4⋊C4—532no—
373C22×C4⋊C4—531no—
374C22×C4⋊C4—531no—
375C22×C4⋊C4C2×D5312yes—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4C2×D5311yescharacteristic
379C22×C22⋊C4C2×D5311yescharacteristic
380C22×C42—532no—
381#385—24no—
382#385—1064no—
383#385—1064no—
384#385—1064no—
385#380—1064no—
386C4×C22⋊C4—538no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—531no—
390C2×#95—531no—
391C2×#95—532no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—532no—
395C2×#95—1064no—
396C2×#95C2×D5312yes—
397C53#1396511yescharacteristic, complemented, Sylow
398C25C22×D5311yescharacteristic
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—532no—
405C23×C4—531no—
406C23×C4—531no—
407C23×C4—534no—
408C23×C4—534no—
409C23×C4—534no—
410C23×C4—532no—
411C23×C4—531no—
412C23×C4—531no—
413C23×C4—1064no—
414C23×C4—1062no—
415C23×C4—1062no—
416C23×C4—1062no—
417C23×C4—2122no—
418C23×C4—2122no—
419C23×C4—2122no—
420C23×C4C22×D5311yescharacteristic
421C23×C4C22×D5311yescharacteristic
422C23×C4C22×D5312yes—
423C23×C4C22×D5312yes—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—1064no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4—1062no—
430C2×C4⋊C4—1064no—
431C2×C4⋊C4—1064no—
432C2×C4⋊C4—1064no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1064no—
435C2×C4⋊C4—2122no—
436C2×C4⋊C4—2122no—
437C2×C4⋊C4—2122no—
438C2×C4⋊C4—2122no—
439C2×C4⋊C4—2122no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—534no—
444C2×C22⋊C4—534no—
445C2×C22⋊C4—534no—
446C2×C22⋊C4—1062no—
447C2×C22⋊C4—1062no—
448C2×C22⋊C4—1062no—
449C2×C22⋊C4Dic10614yes—
450C2×C22⋊C4C4×D5314yes—
451C2×C22⋊C4C22⋊D5314yes—
452C2×C42—538no—
453C2×C42—2122no—
454C2×C42—2122no—
455#95—24no—
456#95—538no—
457#95—1064no—
458#95—1064no—
459#95—1062no—
460#95—1062no—
461#95—1064no—
462#95—1064no—
463#95—1064no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24C2×Dic10612yes—
469C24C2×C4×D5312yes—
470C24D4×D5312yes—
471C24D4×D5312yes—
472C24Q8×D5312yes—
473C24Q8×D5312yes—
474C24C2×C22⋊D5312yes—
475C24C23×D5311yescharacteristic
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—532no—
502C22×C4—534no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—534no—
506C22×C4—532no—
507C22×C4—534no—
508C22×C4—532no—
509C22×C4—532no—
510C22×C4—5316no—
511C22×C4—534no—
512C22×C4—1062no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4—1068no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—2128no—
538C22×C4—2124no—
539C22×C4—2124no—
540C22×C4—2128no—
541C22×C4—2128no—
542C22×C4—2128no—
543C22×C4—2124no—
544C22×C4—2124no—
545C22×C4C2×Dic10614yes—
546C22×C4C2×C4×D5314yes—
547C22×C4#1171994714yes—
548C22×C4C2×C22⋊D5314yes—
549C4⋊C4—48no—
550C4⋊C4—2128no—
551C4⋊C4—2128no—
552C4⋊C4—2128no—
553C4⋊C4—2124no—
554C4⋊C4—2124no—
555C22⋊C4—44no—
556C22⋊C4—5316no—
557C22⋊C4—2124no—
558C22⋊C4#11719919116yescomplemented
559C42—2128no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23C4⋊C4×D5314yes—
577C23C4⋊C4×D5314yes—
578C23C2×#1171991914yes—
579C23#1313321314yes—
580C23#1313321514yes—
581C23#1313321614yes—
582C23#1313321614yes—
583C23C22×C4×D5311yescharacteristic
584C23C2×D4×D5311yescharacteristic
585C23C2×D4×D5311yescharacteristic
586C23C22×C22⋊D5311yescharacteristic
587C23C2×Q8×D5311yescharacteristic
588C23C2×Q8×D5311yescharacteristic
589C23C22×Dic10611yescharacteristic
590C23#41×D5312yes—
591C23C2×#1171994712yes—
592C23#1313326212yes—
593C23#1313326312yes—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—416no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—538no—
619C2×C4—534no—
620C2×C4—534no—
621C2×C4—1064no—
622C2×C4—1064no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—1064no—
627C2×C4—1064no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1062no—
632C2×C4—1064no—
633C2×C4—1064no—
634C2×C4—1064no—
635C2×C4—1064no—
636C2×C4—1064no—
637C2×C4—1064no—
638C2×C4—21216no—
639C2×C4—2122no—
640C2×C4—2122no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4—21216no—
650C2×C4—2122no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4C2×#1171991918yes—
655C22—24no—
656C22—24no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—28no—
662C22—28no—
663C22—28no—
664C22—24no—
665C22#1681049218yes—
666C22C2×C4⋊C4×D5311yescharacteristic
667C22C2×C4⋊C4×D5311yescharacteristic
668C22C22×#1171991911yescharacteristic
669C22C4×#1171994712yes—
670C22#1681109512yes—
671C22#1681112911yescharacteristic
672C22#1681113111yescharacteristic
673C22C2×#1313321311yescharacteristic
674C22C2×#1313321511yescharacteristic
675C22C2×#1313321611yescharacteristic
676C22C2×#1313321611yescharacteristic
677C22#1681117512yes—
678C22#1681118311yescharacteristic
679C22#1681118411yescharacteristic
680C22#1681124812yes—
681C22#1681126012yes—
682C22#1681126112yes—
683C22#1681126512yes—
684C22#1681126712yes—
685C22#1681132712yes—
686C22#1681133012yes—
687C22#1681133112yes—
688C22#1681133212yes—
689C4—28no—
690C4—44no—
691C4—81no—
692C4—81no—
693C4—1064no—
694C4—1064no—
695C4—1068no—
696C4—4241no—
697C4—4241no—
698C4—2124no—
699C2—28no—
700C2C2×#1681049211yescharacteristic
701C2#2027719411yescharacteristic
702C2#2027732611yescharacteristic
703C2#2027762012yes—
704C2#2027762112yes—
705C2#2027964311yescharacteristic
706C2#2027964511yescharacteristic
707C2#2027972312yes—
708C2#2027972812yes—
709C2#2028009211yescharacteristic
710C2#2028009411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53#13965
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
7. #20272979C2semidirect
8. #20272978C2semidirect
9. #20272944C2semidirect
10. #20272943C2semidirect
26. C22⋊C4×Dic53C4semidirect
79. C2×C4×Dic53C2×C4semidirect
87. #13133124C2×C4semidirect
182. C22×Dic53C4⋊C4semidirect
195. C22⋊C4×C53C4⋊C4semidirect
197. C22⋊Dic53C4⋊C4semidirect
397. C53#13965semidirect
558. C22⋊C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168104982
C2×#168104962
C2×#168104952
C2×#168104812
C2×C22⋊C4×Dic532
C22×#131331242
#202729792
#202729782
#202729442
#202729432
C2×C53×#3852
#1396553