Finite Group Databasebeta

← #27402429

Subgroups — #27402429

Order 13568.

1086 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810735C211yesmaximal, characteristic
2C2×#16810735C211yesmaximal, characteristic
3#20277620C211yesmaximal, characteristic, complemented
4D4×#11719919C211yesmaximal, characteristic, complemented
5#20275456C211yesmaximal, characteristic, complemented
6#20275443C211yesmaximal, characteristic, complemented
7#20274976C211yesmaximal, characteristic, complemented
8#20274974C211yesmaximal, characteristic, complemented
9#20274962C211yesmaximal, characteristic, complemented
10#20274960C211yesmaximal, characteristic, complemented
11#20274882C211yesmaximal, characteristic, complemented
12#20274723C211yesmaximal, characteristic, complemented
13#20274713C211yesmaximal, characteristic, complemented
14#20274589C211yesmaximal, characteristic, complemented
15C2×C4×D8×C53C211yesmaximal, characteristic
16C2×D4×Dic53C2211yescharacteristic
17C2×D4×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C22×#11719919—21no—
21#16810735—24no—
22#16810735C418yescomplemented
23C2×#13133150C2211yescharacteristic
24C2×#13133149C2211yescharacteristic
25C2×#13133149C2211yescharacteristic
26C2×#13133148C2211yescharacteristic
27C2×#13133146C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33C2×#13133127C2211yescharacteristic
34#16810521C2211yescharacteristic
35#16810521C2211yescharacteristic
36#16810519C2211yescharacteristic
37#16810519C2211yescharacteristic
38#16810496—21no—
39#16810496—21no—
40#16810495—21no—
41#16810495—21no—
42#16810492C2211yescharacteristic
43#16810488C2211yescharacteristic
44#16810481—21no—
45#16810481—21no—
46C4×#11719919C2211yescharacteristic
47C2×#13133124—21no—
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810378C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×D8×C53C2211yescharacteristic
55C2×C4×D4×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C4×D8×C53—24no—
58C2×#107×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×C4×C8×C53C2211yescharacteristic
62C23×Dic53—21no—
63C23×Dic53—21no—
64C23×Dic53—21no—
65C23×Dic53—21no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68D4×Dic53—22no—
69D4×Dic53—22no—
70D4×Dic53—22no—
71D4×Dic53—22no—
72D4×Dic53—41no—
73D4×Dic53—41no—
74D4×Dic53C2×C414yescomplemented
75D4×Dic53C2×C414yescomplemented
76C2×C4⋊Dic53C2311yescharacteristic
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×#11719919—21no—
81C2×#11719919—21no—
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×#11719919—44no—
87C2×#11719919D411yescharacteristic
88C2×#11719919D411yescharacteristic
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C4×Dic53C2311yescharacteristic
94C2×C4×Dic53C2311yescharacteristic
95#13133150—41no—
96#13133149—22no—
97#13133149C2×C414yescomplemented
98#13133148—41no—
99#13133146—22no—
100#13133138—22no—
101#13133138—22no—
102#13133138C2×C414yescomplemented
103#13133138C2×C414yescomplemented
104#13133127—22no—
105#13133127C2×C414yescomplemented
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124D411yescharacteristic
113#13133124D411yescharacteristic
114C22×D4×C53C2311yescharacteristic
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C2×D8×C53C2×C414yes—
119C2×D8×C53D414yes—
120C2×D8×C53Q814yes—
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C4×D4×C53—22no—
124C4×D4×C53—22no—
125C4×D4×C53—41no—
126C4×D4×C53—41no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C42×C53C2311yescharacteristic
132#107×C53—22no—
133#102×C53—22no—
134#102×C53—22no—
135C4×C8×C53—22no—
136C24×C53—21no—
137C24×C53—21no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—21no—
142C2×D4×C53—21no—
143C2×D4×C53—21no—
144C2×D4×C53C22×C412yes—
145C2×D4×C53C22×C412yes—
146C2×D4×C53C2×D412yes—
147C2×D4×C53C2×D412yes—
148C2×D4×C53C2×Q812yes—
149C2×D4×C53C2×Q812yes—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—81no—
157C22×C4×C53—81no—
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2411yescharacteristic
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—24no—
164C22×Dic53—24no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—42no—
168C22×Dic53—42no—
169C22×Dic53—42no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53—42no—
173C22×Dic53—81no—
174C22×Dic53—81no—
175C22×Dic53—81no—
176C22×Dic53—81no—
177C22×Dic53C2×D411yescharacteristic
178C22×Dic53C2×D411yescharacteristic
179C22×Dic53C2×D411yescharacteristic
180C22×Dic53C2×D411yescharacteristic
181D8×C53C4⋊C4116yescomplemented
182C2×C8×C53—21no—
183C2×C8×C53—21no—
184C2×C8×C53—21no—
185C2×C8×C53C22×C412yes—
186C2×C8×C53C2×D412yes—
187C2×C8×C53C2×Q812yes—
188C4⋊C4×C53—21no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C22⋊C4×C53—42no—
193C22⋊C4×C53—42no—
194C42×C53—21no—
195C42×C53—21no—
196C22⋊Dic53—24no—
197C22⋊Dic53—24no—
198C22⋊Dic53—42no—
199C22⋊Dic53—42no—
200C4⋊Dic53—21no—
201C4⋊Dic53—21no—
202C4⋊Dic53—21no—
203C4⋊Dic53—21no—
204C4⋊Dic53—21no—
205C4⋊Dic53—21no—
206C4⋊Dic53C22×C412yes—
207C4⋊Dic53C22×C412yes—
208#11719919—22no—
209#11719919—41no—
210#11719919—42no—
211#11719919—42no—
212#11719919—42no—
213#11719919—81no—
214#11719919—81no—
215#11719919—81no—
216C4×Dic53—21no—
217C4×Dic53—21no—
218C4×Dic53C22×C412yes—
219C4×Dic53#4112yes—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322C22×C412yes—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53C22×D411yescharacteristic
241D4×C53—22no—
242D4×C53—22no—
243D4×C53—22no—
244D4×C53—22no—
245D4×C53—22no—
246D4×C53—22no—
247D4×C53C2×C4⋊C414yes—
248D4×C53C2×C4⋊C414yescomplemented
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—21no—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—84no—
261C2×C4×C53—84no—
262C2×C4×C53AGL(1,ℤ/8)12yes—
263C2×C4×C53C23×C411yescharacteristic
264C2×C4×C53C22×D411yescharacteristic
265C2×C4×C53C22×Q811yescharacteristic
266C2×C4×C53C2×#4111yescharacteristic
267C2×C4×C53H(5,𝔽2)11yescharacteristic
268C2×C4×C532−1+411yescharacteristic
269C2×Dic53—21no—
270C2×Dic53—21no—
271C2×Dic53—21no—
272C2×Dic53—21no—
273C2×Dic53—22no—
274C2×Dic53—22no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—48no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—84no—
293C2×Dic53—84no—
294C2×Dic53—84no—
295C2×Dic53C4×D412yes—
296C2×Dic53C4×D412yes—
297C8×C53—41no—
298C8×C53C2×C4⋊C414yescomplemented
299#88322—22no—
300#88322—41no—
301#22676—531nomaximal, Sylow
302C22×C53—24no—
303C22×C53—24no—
304C22×C53—42no—
305C22×C53—42no—
306C22×C53—42no—
307C22×C53—42no—
308C22×C53—42no—
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—42no—
312C22×C53—42no—
313C22×C53—42no—
314C22×C53—42no—
315C22×C53—42no—
316C22×C53C2×C4×D411yescharacteristic
317C22×C53D4211yescharacteristic
318C22×C53D4×Q811yescharacteristic
319C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C53#57511yescharacteristic
321C22×C53#57611yescharacteristic
322C22×C53#57711yescharacteristic
323C4×C53—22no—
324C4×C53—41no—
325C4×C53—81no—
326C4×C53—81no—
327C4×C53C22×C4⋊C411yescharacteristic
328C4×C53#52011yescharacteristic
329C4×C53#54711yescharacteristic
330C4×C53#55411yescharacteristic
331Dic53—22no—
332Dic53—22no—
333Dic53—42no—
334Dic53—42no—
335Dic53—41no—
336Dic53—41no—
337Dic53—81no—
338Dic53—81no—
339C2×#442—531no—
340C2×#442—531no—
341C2×C4×D8D5311yescharacteristic
342#2349—531no—
343D4×C4⋊C4—531no—
344#1944—531no—
345#1941—531no—
346#1864—531no—
347#1864—531no—
348#1862—531no—
349#1862—531no—
350#1847—531no—
351#1804—531no—
352#1802—531no—
353#1771—531no—
354C2×C53—44no—
355C2×C53—44no—
356C2×C53D4×C4⋊C411yescharacteristic
357C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
358C2×C53#294611yescharacteristic
359C2×C53#326411yescharacteristic
360C2×C53#326711yescharacteristic
361C2×C53#338411yescharacteristic
362C2×C53#338911yescharacteristic
363C22×D8C2×D5311yescharacteristic
364C2×C4×D4—531no—
365C2×C4×D4—531no—
366C2×C4×D4—531no—
367C2×C4×D4—531no—
368C2×C4×D4C2×D5311yescharacteristic
369C2×C4×D4C2×D5311yescharacteristic
370C22×C4⋊C4—1061no—
371#442—538no—
372#442—1064no—
373C4×D8—24no—
374C2×#107—531no—
375C2×#107C2×D5311yescharacteristic
376C2×#106—531no—
377C2×#106—531no—
378C2×#106—531no—
379C2×C4⋊C8—531no—
380C2×#102—531no—
381C2×#102—531no—
382C2×#102—531no—
383C2×#102—531no—
384C2×#102C2×D5311yescharacteristic
385C2×#102C2×D5311yescharacteristic
386C2×#97—531no—
387C2×#97—531no—
388C2×C4×C8C2×D5311yescharacteristic
389#389—531no—
390#389—531no—
391#389—531no—
392#389—531no—
393#385—1061no—
394#385—1061no—
395#385—1061no—
396#385—1061no—
397#384—531no—
398#382—531no—
399#380—1061no—
400#380—1061no—
401C4×C4⋊C4—531no—
402C2×#95—1061no—
403#340—531no—
404#340—531no—
405#340—531no—
406#340—531no—
407#336—531no—
408#336—531no—
409C53#2267611yescharacteristic, complemented, Sylow
410C22×D4C22×D5311yescharacteristic
411C22×D4C22×D5311yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—1061no—
415C23×C4—1061no—
416C23×C4—1061no—
417C23×C4—1061no—
418C2×D8Dic10614yes—
419C2×D8C4×D5314yes—
420C2×D8C22⋊D5314yes—
421C22×C8—531no—
422C22×C8—531no—
423C22×C8C22×D5311yescharacteristic
424C22×C8C22×D5311yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—41no—
429C4×D4—534no—
430C4×D4—534no—
431C4×D4—1062no—
432C4×D4—1062no—
433C4×D4—1062no—
434C4×D4—1062no—
435C4×D4—2121no—
436C4×D4—2121no—
437C2×C4⋊C4—531no—
438C2×C4⋊C4—531no—
439C2×C4⋊C4—531no—
440C2×C4⋊C4—531no—
441C2×C4⋊C4—531no—
442C2×C4⋊C4—531no—
443C2×C4⋊C4—1061no—
444C2×C4⋊C4—1061no—
445C2×C4⋊C4—1061no—
446C2×C4⋊C4—1061no—
447C2×C4⋊C4—1061no—
448C2×C4⋊C4—1061no—
449C2×C4⋊C4—2124no—
450C2×C4⋊C4C22×D5311yescharacteristic
451C2×C4⋊C4C22×D5311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1061no—
455C2×C22⋊C4—1061no—
456C2×C22⋊C4—1061no—
457C2×C22⋊C4—1061no—
458C2×C42—531no—
459C2×C42—531no—
460C2×C42C22×D5311yescharacteristic
461#107—22no—
462#107—2121no—
463#106—534no—
464#106—1062no—
465#106—2121no—
466C4⋊C8—1062no—
467#102—22no—
468#102—22no—
469#102—534no—
470#102—534no—
471#102—1062no—
472#102—1062no—
473#97—534no—
474#97—1062no—
475C4×C8—22no—
476#95—531no—
477#95—531no—
478#95—1061no—
479#95—1061no—
480#95—1061no—
481#95—1061no—
482#95—1061no—
483#95—1061no—
484C24—21no—
485C24—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4C2×Dic10612yes—
493C2×D4C2×Dic10612yes—
494C2×D4C2×C4×D5312yes—
495C2×D4C2×C4×D5312yes—
496C2×D4C2×C22⋊D5312yes—
497C2×D4C2×C22⋊D5312yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—531no—
507C22×C4—531no—
508C22×C4—531no—
509C22×C4—531no—
510C22×C4—1064no—
511C22×C4—1064no—
512C22×C4—1061no—
513C22×C4—1061no—
514C22×C4—1061no—
515C22×C4—1061no—
516C22×C4—4241no—
517C22×C4—4241no—
518C22×C4—4241no—
519C22×C4—4241no—
520C22×C4—2122no—
521C22×C4—2122no—
522C22×C4—2122no—
523C22×C4—2122no—
524C22×C4—2122no—
525C22×C4—2122no—
526C22×C4D4×D5311yescharacteristic
527C22×C4D4×D5311yescharacteristic
528C22×C4C23×D5311yescharacteristic
529D8#11719919116yescomplemented
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—532no—
534C2×C8—1061no—
535C2×C8—1061no—
536C2×C8—1061no—
537C2×C8—1061no—
538C2×C8—1061no—
539C2×C8C2×Dic10612yes—
540C2×C8C2×C4×D5312yes—
541C2×C8C2×C22⋊D5312yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—532no—
547C4⋊C4—532no—
548C4⋊C4—1062no—
549C4⋊C4—1061no—
550C4⋊C4—1061no—
551C4⋊C4—1061no—
552C4⋊C4—1061no—
553C4⋊C4—1061no—
554C4⋊C4—1061no—
555C4⋊C4—4241no—
556C4⋊C4—4241no—
557C4⋊C4—4241no—
558C4⋊C4—2121no—
559C4⋊C4—2122no—
560C4⋊C4—2122no—
561C4⋊C4—2122no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—1064no—
565C22⋊C4—1064no—
566C22⋊C4—2122no—
567C22⋊C4—2122no—
568C42—21no—
569C42—21no—
570C42—532no—
571C42—532no—
572C42—1061no—
573C42—1061no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C2×D4×D5311yescharacteristic
589D4—22no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4C2×#1171991914yes—
596D4C2×#1171991914yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—532no—
611C2×C4—532no—
612C2×C4—1061no—
613C2×C4—1061no—
614C2×C4—1061no—
615C2×C4—1061no—
616C2×C4—1062no—
617C2×C4—1062no—
618C2×C4—1061no—
619C2×C4—1061no—
620C2×C4—1061no—
621C2×C4—1061no—
622C2×C4—1061no—
623C2×C4—1061no—
624C2×C4—4244no—
625C2×C4—4244no—
626C2×C4—4244no—
627C2×C4—2128no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4—2121no—
632C2×C4—2121no—
633C2×C4—2121no—
634C2×C4—2121no—
635C2×C4—2121no—
636C2×C4—2121no—
637C2×C4—2121no—
638C2×C4#1313324112yes—
639C2×C4C22×C4×D5311yescharacteristic
640C2×C4C22×C22⋊D5311yescharacteristic
641C2×C4C22×Dic10611yescharacteristic
642C2×C4#41×D5311yescharacteristic
643C2×C4#1313326211yescharacteristic
644C2×C4#1313326411yescharacteristic
645C8—41no—
646C8—1062no—
647C8—2121no—
648C8C2×#1171991914yescomplemented
649C22—24no—
650C22—24no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C4×D4×D5311yescharacteristic
664C22D4×C22⋊D5311yescharacteristic
665C22D4×Dic10611yescharacteristic
666C22C2×#1313324111yescharacteristic
667C22#1681142011yescharacteristic
668C22#1681142411yescharacteristic
669C22#1681143011yescharacteristic
670C4—22no—
671C4—41no—
672C4—81no—
673C4—81no—
674C4—1062no—
675C4—1062no—
676C4—4241no—
677C4—4241no—
678C4—2121no—
679C4—2122no—
680C4—2122no—
681C4—2121no—
682C4C22×#1171991911yescharacteristic
683C4#1681110211yescharacteristic
684C4#1681127211yescharacteristic
685C4#1681133211yescharacteristic
686C2—44no—
687C2—44no—
688C2D4×#1171991911yescharacteristic
689C2C4×#1313324111yescharacteristic
690C2#2028354011yescharacteristic
691C2#2028619511yescharacteristic
692C2#2028624011yescharacteristic
693C2#2028761211yescharacteristic
694C2#2028767111yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C4×D8×C53C2
socleC23×C53C22×D4
prime radicalC22×D8×C53C22
cosocleC22×C4×C53C24
hypercenterC2×C4×D8D53
hypocenterC53#22676
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
3. #20277620C2semidirect
4. D4×#11719919C2semidirect
5. #20275456C2semidirect
6. #20275443C2semidirect
7. #20274976C2semidirect
8. #20274974C2semidirect
9. #20274962C2semidirect
10. #20274960C2semidirect
11. #20274882C2semidirect
12. #20274723C2semidirect
13. #20274713C2semidirect
14. #20274589C2semidirect
22. #16810735C4semidirect
74. D4×Dic53C2×C4semidirect
75. D4×Dic53C2×C4semidirect
97. #13133149C2×C4semidirect
102. #13133138C2×C4semidirect
103. #13133138C2×C4semidirect
105. #13133127C2×C4semidirect
181. D8×C53C4⋊C4semidirect
248. D4×C53C2×C4⋊C4semidirect
298. C8×C53C2×C4⋊C4semidirect
409. C53#22676semidirect
529. D8#11719919semidirect
596. D4C2×#11719919semidirect
648. C8C2×#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168107352
#202776202
D4×#117199192
#202754562
#202754432
#202749762
#202749742
#202749622
#202749602
#202748822
#202747232
#202747132
#202745892
C2×C4×D8×C532
#2267653