Finite Group Databasebeta

← #27315335

Subgroups — #27315335

Order 13568.

2574 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic53C211yesmaximal, characteristic
2C2×#16810520C212yesmaximal, complemented
3C2×#16810498C211yesmaximal, characteristic
4C2×#16810495C211yesmaximal, characteristic
5C2×#16810481C211yesmaximal, characteristic
6C2×#16810481C211yesmaximal, characteristic
7#20272949C212yesmaximal, complemented
8#20272946C212yesmaximal, complemented
9#20272943C212yesmaximal, complemented
10#20272938C211yesmaximal, characteristic
11C53×C22⋊#95C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×#11719919C2211yescharacteristic
16C22×#11719919C2212yes—
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C4×Dic53—24no—
22C22×C4×Dic53—28no—
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2212yes—
25#16810520—28no—
26#16810498—24no—
27#16810495—24no—
28#16810481—24no—
29#16810481C418yescomplemented
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2212yes—
37C24×C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C23×Dic53—22no—
43C23×Dic53—22no—
44C23×Dic53—24no—
45C23×Dic53—24no—
46C23×Dic53—24no—
47C23×Dic53—24no—
48C23×Dic53C2×C414yes—
49C23×Dic53D414yes—
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—24no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—24no—
67C2×#11719919—24no—
68C2×#11719919—24no—
69C2×#11719919—24no—
70C2×#11719919C2×C418yescomplemented
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53C2×C414yes—
77C2×C4×Dic53—232no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53—24no—
82C2×C4×Dic53—24no—
83C2×C4×Dic53D418yes—
84#13133124—24no—
85#13133124—24no—
86#13133124—24no—
87#13133124—22no—
88#13133124—22no—
89#13133124—24no—
90#13133124C2×C418yescomplemented
91C25×C53C2311yescharacteristic
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—24no—
95C23×C4×C53—24no—
96C23×C4×C53Q814yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2312yes—
100C23×C4×C53C2312yes—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53C2×C414yes—
107#95×C53—24no—
108#95×C53—24no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53—22no—
113C24×C53C22×C412yes—
114C24×C53C2×D412yes—
115C24×C53C2×D412yes—
116C24×C53C2×Q812yes—
117C24×C53C2×Q812yes—
118C24×C53#4112yes—
119C24×C53#4112yes—
120C24×C53C2411yescharacteristic
121C22×C4×C53—216no—
122C22×C4×C53—28no—
123C22×C4×C53—28no—
124C22×C4×C53—28no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—216no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—22no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53C22×C414yes—
147C22×C4×C53C2×D414yes—
148C22×C4×C53C2×Q814yes—
149C22×C4×C53#4114yes—
150C22×Dic53—28no—
151C22×Dic53—216no—
152C22×Dic53—28no—
153C22×Dic53—28no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—216no—
161C22×Dic53—28no—
162C22×Dic53—216no—
163C22×Dic53—216no—
164C22×Dic53—28no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53C4⋊C4116yescomplemented
182C22×Dic53C22×C414yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C2×D412yes—
186C22×Dic53C2×D414yes—
187C22×Dic53C2×D414yes—
188C22×Dic53C2×D412yes—
189C22×Dic53C2×D414yes—
190C22×Dic53C2×Q812yes—
191C22×Dic53C2×Q812yes—
192C22×Dic53#4114yes—
193C22×Dic53#4114yes—
194C22⋊C4×C53—28no—
195C22⋊C4×C53—44no—
196C22⋊Dic53—28no—
197C22⋊Dic53—44no—
198C4⋊Dic53—48no—
199#11719919—216no—
200#11719919—44no—
201#11719919—48no—
202#11719919—44no—
203C4×Dic53—216no—
204C4×Dic53—216no—
205C23×C53—24no—
206C23×C53—24no—
207C23×C53—22no—
208C23×C53—24no—
209C23×C53—24no—
210C23×C53—24no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—24no—
214C23×C53—22no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53C2×C4⋊C414yes—
222C23×C53C4×D414yes—
223C23×C53C4×Q814yes—
224C23×C53#12114yes—
225C23×C53C22⋊Q814yes—
226C23×C53#12514yes—
227C23×C53C4⋊Q814yes—
228C23×C53C23×C411yescharacteristic
229C23×C53C22×D411yescharacteristic
230C23×C53C22×D412yes—
231C23×C53C22×D411yescharacteristic
232C23×C53C22×Q811yescharacteristic
233C23×C53C22×Q811yescharacteristic
234C23×C53C2×#4112yes—
235C23×C53C2×#4112yes—
236C23×C53C2×#4111yescharacteristic
237C23×C53C2×#4112yes—
238C23×C53C2×#4111yescharacteristic
239C2×C4×C53—232no—
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—24no—
248C2×C4×C53—24no—
249C2×C4×C53—42no—
250C2×C4×C53—42no—
251C2×C4×C53—42no—
252C2×C4×C53—42no—
253C2×C4×C53—41no—
254C2×C4×C53—42no—
255C2×C4×C53—41no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—41no—
259C2×C4×C53—41no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53C22⋊Q818yes—
264C2×Dic53—232no—
265C2×Dic53—24no—
266C2×Dic53—24no—
267C2×Dic53—22no—
268C2×Dic53—24no—
269C2×Dic53—24no—
270C2×Dic53—24no—
271C2×Dic53—22no—
272C2×Dic53—24no—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—232no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—41no—
284C2×Dic53—42no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53C2×C4⋊C414yes—
294C2×Dic53C2×C4⋊C414yes—
295C2×Dic53C4×D418yes—
296C2×Dic53#12014yes—
297C2×Dic53#12118yes—
298C2×Dic53C22⋊Q818yes—
299C2×Dic53#12314yes—
300#14697—531nomaximal, Sylow
301C22×C53—24no—
302C22×C53—24no—
303C22×C53—28no—
304C22×C53—24no—
305C22×C53—24no—
306C22×C53—28no—
307C22×C53—24no—
308C22×C53—24no—
309C22×C53—28no—
310C22×C53—28no—
311C22×C53#38918yescomplemented
312C22×C53C22×C4⋊C411yescharacteristic
313C22×C53C2×C4×D412yes—
314C22×C53C2×C4×D411yescharacteristic
315C22×C53C2×C4×Q811yescharacteristic
316C22×C53C4×#4112yes—
317C22×C53C2×#12011yescharacteristic
318C22×C53C2×#12112yes—
319C22×C53C2×#12111yescharacteristic
320C22×C53C2×C22⋊Q812yes—
321C22×C53C2×C22⋊Q811yescharacteristic
322C22×C53C2×C22⋊Q812yes—
323C22×C53C2×#12311yescharacteristic
324C22×C53#52512yes—
325C22×C53#52511yescharacteristic
326C22×C53#52511yescharacteristic
327C22×C53#52512yes—
328C22×C53C2×#12511yescharacteristic
329C22×C53#52912yes—
330C22×C53#52912yes—
331C22×C53C2×C4⋊Q811yescharacteristic
332C22×C53#53212yes—
333C22×C53#53312yes—
334C22×C53#53312yes—
335C4×C53—28no—
336C4×C53—44no—
337C4×C53—81no—
338C4×C53—81no—
339Dic53—28no—
340Dic53—24no—
341Dic53—44no—
342Dic53—81no—
343Dic53—81no—
344Dic53#38518yescomplemented
345C23×C42—531no—
346C2×#389—532no—
347C2×#385—531no—
348C2×#385—531no—
349C2×#380—531no—
350C2×#380—531no—
351#1436—532no—
352#1436—532no—
353C4⋊#95—532no—
354C22⋊#95—531no—
355C22⋊#95D5311yescharacteristic
356C2×C53—28no—
357C2×C53C2×#38511yescharacteristic
358C2×C53C2×#38911yescharacteristic
359C2×C53#229611yescharacteristic
360C2×C53C4×#12112yes—
361C2×C53C4×C22⋊Q812yes—
362C2×C53#284711yescharacteristic
363C2×C53#284811yescharacteristic
364C2×C53#285112yes—
365C2×C53#285411yescharacteristic
366C2×C53#285511yescharacteristic
367C2×C53#285712yes—
368C24×C4—531no—
369C24×C4—531no—
370C24×C4C2×D5311yescharacteristic
371C22×C4⋊C4—532no—
372C22×C4⋊C4—531no—
373C22×C4⋊C4—532no—
374C22×C4⋊C4—531no—
375C22×C4⋊C4—532no—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4C2×D5311yescharacteristic
379C22×C22⋊C4C2×D5311yescharacteristic
380C22×C42—532no—
381C22×C42—532no—
382C22×C42—1068no—
383C22×C42—1064no—
384#389—1068no—
385#385—1064no—
386#385—1064no—
387#380—538no—
388#380—1064no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95—532no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—531no—
395C2×#95—531no—
396C2×#95C2×D5312yes—
397C2×#95C2×D5312yes—
398C53#1469711yescharacteristic, complemented, Sylow
399C25C22×D5311yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—531no—
405C23×C4—534no—
406C23×C4—534no—
407C23×C4—534no—
408C23×C4—532no—
409C23×C4—531no—
410C23×C4—534no—
411C23×C4—532no—
412C23×C4—531no—
413C23×C4—531no—
414C23×C4—1064no—
415C23×C4—1064no—
416C23×C4—1064no—
417C23×C4—1064no—
418C23×C4—1062no—
419C23×C4—1062no—
420C23×C4Dic10614yes—
421C23×C4C22×D5311yescharacteristic
422C23×C4C22×D5311yescharacteristic
423C23×C4C22×D5312yes—
424C23×C4C22×D5312yes—
425C2×C4⋊C4—538no—
426C2×C4⋊C4—1064no—
427C2×C4⋊C4—1064no—
428C2×C4⋊C4—1064no—
429C2×C4⋊C4—1064no—
430C2×C4⋊C4—1062no—
431C2×C4⋊C4—1062no—
432C2×C4⋊C4—1064no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1064no—
435C2×C4⋊C4—1064no—
436C2×C4⋊C4—1064no—
437C2×C4⋊C4—1064no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—534no—
444C2×C22⋊C4—1062no—
445C2×C22⋊C4—1062no—
446C2×C22⋊C4—1062no—
447C2×C22⋊C4—1062no—
448C2×C22⋊C4—1062no—
449C2×C22⋊C4C4×D5314yes—
450C2×C42—538no—
451C2×C42—1064no—
452C2×C42—1064no—
453C2×C42—1064no—
454C2×C42—1064no—
455C2×C42—10632no—
456C2×C42—1064no—
457#95—24no—
458#95—24no—
459#95—538no—
460#95—1062no—
461#95—1062no—
462#95—1064no—
463#95—1064no—
464#95—1064no—
465#95—1064no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×Dic10612yes—
471C24C2×C4×D5312yes—
472C24#1171994512yes—
473C24D4×D5312yes—
474C24D4×D5312yes—
475C24#1171994712yes—
476C24Q8×D5312yes—
477C24C23×D5311yescharacteristic
478C22×C4—28no—
479C22×C4—216no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—216no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—532no—
504C22×C4—534no—
505C22×C4—532no—
506C22×C4—532no—
507C22×C4—534no—
508C22×C4—5316no—
509C22×C4—532no—
510C22×C4—532no—
511C22×C4—534no—
512C22×C4—534no—
513C22×C4—532no—
514C22×C4—534no—
515C22×C4—534no—
516C22×C4—1068no—
517C22×C4—10616no—
518C22×C4—10616no—
519C22×C4—1068no—
520C22×C4—10616no—
521C22×C4—1068no—
522C22×C4—1068no—
523C22×C4—10616no—
524C22×C4—1068no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1062no—
541C22×C4—1061no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4C2×Dic10614yes—
548C22×C4C2×C4×D5314yes—
549C22×C4D4×D5314yes—
550C22×C4#1171994714yes—
551C4⋊C4—10616no—
552C4⋊C4—2124no—
553C4⋊C4—2128no—
554C4⋊C4—2124no—
555C4⋊C4—2128no—
556C22⋊C4—28no—
557C22⋊C4—44no—
558C22⋊C4—1068no—
559C22⋊C4—2124no—
560C42—10616no—
561C42—10616no—
562C23—24no—
563C23—24no—
564C23—22no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—24no—
571C23—22no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23C4⋊C4×D5314yes—
579C23#1313317714yes—
580C23C4×Dic10614yes—
581C23#1313319014yes—
582C23#1313319414yes—
583C23#1313320714yes—
584C23#1313321614yes—
585C23C22×C4×D5311yescharacteristic
586C23C2×D4×D5311yescharacteristic
587C23C2×D4×D5312yes—
588C23C2×D4×D5311yescharacteristic
589C23C2×Q8×D5311yescharacteristic
590C23C22×Dic10611yescharacteristic
591C23#41×D5312yes—
592C23#41×D5312yes—
593C23C2×#1171994711yescharacteristic
594C23C2×#1171994712yes—
595C23C2×#1171994511yescharacteristic
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—534no—
621C2×C4—538no—
622C2×C4—534no—
623C2×C4—538no—
624C2×C4—534no—
625C2×C4—534no—
626C2×C4—538no—
627C2×C4—10632no—
628C2×C4—10632no—
629C2×C4—1064no—
630C2×C4—1064no—
631C2×C4—1062no—
632C2×C4—1064no—
633C2×C4—1064no—
634C2×C4—1064no—
635C2×C4—1062no—
636C2×C4—1064no—
637C2×C4—1064no—
638C2×C4—1064no—
639C2×C4—1064no—
640C2×C4—1064no—
641C2×C4—1064no—
642C2×C4—2121no—
643C2×C4—2122no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2122no—
650C2×C4—2122no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4—2122no—
656C2×C4#1313319418yes—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—24no—
662C22—24no—
663C22—28no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22#1681052018yescomplemented
668C22C2×C4⋊C4×D5311yescharacteristic
669C22C4×D4×D5312yes—
670C22C2×#1313317711yescharacteristic
671C22C2×C4×Dic10611yescharacteristic
672C22C4×#1171994712yes—
673C22#120×D5311yescharacteristic
674C22#121×D5312yes—
675C22C2×#1313319011yescharacteristic
676C22C22⋊Q8×D5312yes—
677C22C2×#1313319411yescharacteristic
678C22C2×#1313319412yes—
679C22#123×D5311yescharacteristic
680C22#1681112912yes—
681C22#1681112911yescharacteristic
682C22#1681113111yescharacteristic
683C22#1681113212yes—
684C22C2×#1313320711yescharacteristic
685C22#1681115012yes—
686C22#1681115312yes—
687C22C2×#1313321611yescharacteristic
688C22#1681116812yes—
689C22#1681117512yes—
690C22#1681117612yes—
691C4—28no—
692C4—44no—
693C4—81no—
694C4—81no—
695C4—538no—
696C4—1068no—
697C4—1064no—
698C4—4241no—
699C4—4241no—
700C4—2124no—
701C2—28no—
702C2#385×D5311yescharacteristic
703C2C2×#1681052011yescharacteristic
704C2#2027719411yescharacteristic
705C2#2027722512yes—
706C2C4×#1313319412yes—
707C2#2028299611yescharacteristic
708C2#2028300011yescharacteristic
709C2#2028302112yes—
710C2#2028304311yescharacteristic
711C2#2028305211yescharacteristic
712C2#2028306512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22⋊#95D53
hypocenterC53#14697
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16810520C2semidirect
7. #20272949C2semidirect
8. #20272946C2semidirect
9. #20272943C2semidirect
29. #16810481C4semidirect
70. C2×#11719919C2×C4semidirect
90. #13133124C2×C4semidirect
181. C22×Dic53C4⋊C4semidirect
311. C22×C53#389semidirect
344. Dic53#385semidirect
398. C53#14697semidirect
667. C22#16810520semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic532
C2×#168105202
C2×#168104982
C2×#168104952
C2×#168104812
#202729492
#202729462
#202729432
#202729382
C53×C22⋊#952
#1469753