Finite Group Databasebeta

← #27306113

Subgroups — #27306113

Order 13568.

1486 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810508C212yesmaximal
2C2×#16810492C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic
4C2×C4×C4⋊Dic53C211yesmaximal, characteristic
5#20272970C212yesmaximal
6#20272967C212yesmaximal
7#20272950C212yesmaximal
8#20272945C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10#20272944C211yesmaximal, characteristic
11C53×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4⋊Dic53C2211yescharacteristic
16C22×#11719919C2212yes—
17C22×#11719919C2212yes—
18C22×C4×Dic53C2212yes—
19C22×C4×Dic53C2211yescharacteristic
20C22×C4×Dic53C2211yescharacteristic
21#16810508—28no—
22#16810492—24no—
23C4⋊C4×Dic53—24no—
24C4×C4⋊Dic53C418yescomplemented
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C22×C4⋊C4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C2×#95×C53C2212yes—
38C2×#95×C53C2212yes—
39C23×Dic53C2312yes—
40C23×Dic53C2311yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53C2×C414yes—
53C2×C4⋊Dic53C2×C414yes—
54C2×C4⋊Dic53D414yes—
55C2×C4⋊Dic53Q814yes—
56C2×C4⋊Dic53Q814yes—
57C2×#11719919—24no—
58C2×#11719919—24no—
59C2×#11719919—24no—
60C2×#11719919—24no—
61C2×#11719919—42no—
62C2×#11719919—42no—
63C2×C4×Dic53—22no—
64C2×C4×Dic53—22no—
65C2×C4×Dic53—24no—
66C2×C4×Dic53—22no—
67C2×C4×Dic53—22no—
68C2×C4×Dic53—24no—
69C2×C4×Dic53—42no—
70C2×C4×Dic53C2×C414yes—
71C2×C4×Dic53C2×C414yes—
72#13133124—24no—
73#13133124—24no—
74#13133124—24no—
75#13133124—24no—
76#13133124—24no—
77#13133124—42no—
78#13133124—42no—
79#13133124C2×C414yes—
80#13133124C2×C414yes—
81C23×C4×C53C2312yes—
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2312yes—
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C2×C4⋊C4×C53—22no—
87C2×C4⋊C4×C53—22no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53—22no—
90C2×C4⋊C4×C53—22no—
91C2×C4⋊C4×C53D414yes—
92C2×C42×C53—22no—
93C2×C42×C53—22no—
94C2×C42×C53C2×C414yes—
95#95×C53—24no—
96#95×C53—42no—
97C24×C53C2411yescharacteristic
98C22×C4×C53—21no—
99C22×C4×C53—21no—
100C22×C4×C53—21no—
101C22×C4×C53—21no—
102C22×C4×C53—22no—
103C22×C4×C53—21no—
104C22×C4×C53—21no—
105C22×C4×C53—22no—
106C22×C4×C53—22no—
107C22×C4×C53—22no—
108C22×C4×C53—21no—
109C22×C4×C53—22no—
110C22×C4×C53—21no—
111C22×C4×C53—22no—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—22no—
115C22×C4×C53—22no—
116C22×C4×C53—22no—
117C22×C4×C53—22no—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—22no—
121C22×C4×C53C22×C412yes—
122C22×C4×C53C22×C412yes—
123C22×C4×C53C22×C412yes—
124C22×C4×C53C2×D414yes—
125C22×C4×C53C2×D412yes—
126C22×C4×C53C2×D412yes—
127C22×C4×C53C2×Q812yes—
128C22×C4×C53C2×Q812yes—
129C22×C4×C53#4112yes—
130C22×C4×C53#4112yes—
131C22×C4×C53#4112yes—
132C22×C4×C53#4112yes—
133C22×Dic53—21no—
134C22×Dic53—21no—
135C22×Dic53—21no—
136C22×Dic53—21no—
137C22×Dic53—21no—
138C22×Dic53—21no—
139C22×Dic53—21no—
140C22×Dic53—21no—
141C22×Dic53—21no—
142C22×Dic53—21no—
143C22×Dic53—21no—
144C22×Dic53—21no—
145C22×Dic53—21no—
146C22×Dic53—22no—
147C22×Dic53—22no—
148C22×Dic53—22no—
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—22no—
153C22×Dic53—21no—
154C22×Dic53—22no—
155C22×Dic53—21no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53C22×C412yes—
165C22×Dic53C22×C412yes—
166C22×Dic53C22×C412yes—
167C22×Dic53C22×C412yes—
168C22×Dic53C2×D412yes—
169C22×Dic53C2×D412yes—
170C22×Dic53C2×Q814yes—
171C22×Dic53C2×Q812yes—
172C22×Dic53C2×Q812yes—
173C22×Dic53#4112yes—
174C22×Dic53#4112yes—
175C4⋊C4×C53—28no—
176C4⋊C4×C53—44no—
177C42×C53—28no—
178C4⋊Dic53—28no—
179C4⋊Dic53—28no—
180C4⋊Dic53—44no—
181C4⋊Dic53C4⋊C4116yescomplemented
182#11719919—48no—
183#11719919—48no—
184C4×Dic53—28no—
185C4×Dic53—28no—
186C4×Dic53—48no—
187C23×C53C23×C411yescharacteristic
188C23×C53C22×D411yescharacteristic
189C23×C53C22×D411yescharacteristic
190C23×C53C22×Q811yescharacteristic
191C23×C53C22×Q811yescharacteristic
192C23×C53C2×#4111yescharacteristic
193C23×C53C2×#4111yescharacteristic
194C23×C53C2×#4111yescharacteristic
195C23×C53C2×#4111yescharacteristic
196C23×C53C2×#4111yescharacteristic
197C23×C53C2×#4111yescharacteristic
198C23×C53H(5,𝔽2)11yescharacteristic
199C23×C53H(5,𝔽2)11yescharacteristic
200C23×C532−1+411yescharacteristic
201C23×C532−1+411yescharacteristic
202C2×C4×C53—22no—
203C2×C4×C53—22no—
204C2×C4×C53—22no—
205C2×C4×C53—22no—
206C2×C4×C53—22no—
207C2×C4×C53—22no—
208C2×C4×C53—22no—
209C2×C4×C53—22no—
210C2×C4×C53—22no—
211C2×C4×C53—24no—
212C2×C4×C53—24no—
213C2×C4×C53—24no—
214C2×C4×C53—42no—
215C2×C4×C53—41no—
216C2×C4×C53—42no—
217C2×C4×C53—41no—
218C2×C4×C53—41no—
219C2×C4×C53—41no—
220C2×C4×C53—42no—
221C2×C4×C53—42no—
222C2×C4×C53—42no—
223C2×C4×C53—42no—
224C2×C4×C53—42no—
225C2×C4×C53—42no—
226C2×C4×C53—42no—
227C2×C4×C53—42no—
228C2×C4×C53—42no—
229C2×C4×C53C2×C4⋊C414yes—
230C2×C4×C53#11714yes—
231C2×C4×C53C4×D414yes—
232C2×C4×C53C4×Q814yes—
233C2×C4×C53C22⋊Q814yes—
234C2×C4×C53#12314yes—
235C2×C4×C53#12514yes—
236C2×C4×C53#12614yes—
237C2×Dic53—22no—
238C2×Dic53—22no—
239C2×Dic53—22no—
240C2×Dic53—22no—
241C2×Dic53—22no—
242C2×Dic53—22no—
243C2×Dic53—22no—
244C2×Dic53—22no—
245C2×Dic53—22no—
246C2×Dic53—22no—
247C2×Dic53—22no—
248C2×Dic53—22no—
249C2×Dic53—22no—
250C2×Dic53—22no—
251C2×Dic53—22no—
252C2×Dic53—22no—
253C2×Dic53—22no—
254C2×Dic53—22no—
255C2×Dic53—22no—
256C2×Dic53—22no—
257C2×Dic53—22no—
258C2×Dic53—24no—
259C2×Dic53—24no—
260C2×Dic53—24no—
261C2×Dic53—42no—
262C2×Dic53—42no—
263C2×Dic53—42no—
264C2×Dic53—41no—
265C2×Dic53—41no—
266C2×Dic53—42no—
267C2×Dic53—41no—
268C2×Dic53—41no—
269C2×Dic53—42no—
270C2×Dic53—42no—
271C2×Dic53—42no—
272C2×Dic53—42no—
273C2×Dic53—42no—
274C2×Dic53—42no—
275C2×Dic53—42no—
276C2×Dic53C2×C4⋊C414yes—
277C2×Dic53C2×C4⋊C414yes—
278C2×Dic53#11714yes—
279#13884—531nomaximal, Sylow
280C22×C53C22×C4⋊C411yescharacteristic
281C22×C53C2×#11711yescharacteristic
282C22×C53C2×#11711yescharacteristic
283C22×C53C2×C4×D411yescharacteristic
284C22×C53C2×C4×Q811yescharacteristic
285C22×C53#52011yescharacteristic
286C22×C53#52011yescharacteristic
287C22×C53C2×C22⋊Q811yescharacteristic
288C22×C53C2×#12311yescharacteristic
289C22×C53C2×#12511yescharacteristic
290C22×C53C2×#12611yescharacteristic
291C22×C53#53211yescharacteristic
292C22×C53#53211yescharacteristic
293C22×C53#53311yescharacteristic
294C22×C53#53311yescharacteristic
295C22×C53#54011yescharacteristic
296C22×C53#54111yescharacteristic
297C22×C53#54211yescharacteristic
298C22×C53#54211yescharacteristic
299C22×C53D4211yescharacteristic
300C22×C53#54611yescharacteristic
301C22×C53#54711yescharacteristic
302C22×C53#54811yescharacteristic
303C22×C53D4×Q811yescharacteristic
304C22×C53D4×Q811yescharacteristic
305C22×C53#55011yescharacteristic
306C22×C53#55211yescharacteristic
307C22×C53#55311yescharacteristic
308C22×C53#55411yescharacteristic
309C22×C53#55411yescharacteristic
310C22×C53#55611yescharacteristic
311C22×C53#55711yescharacteristic
312C22×C53#55711yescharacteristic
313C22×C53Q8211yescharacteristic
314C22×C53#55911yescharacteristic
315C4×C53—24no—
316C4×C53—42no—
317C4×C53—44no—
318C4×C53—82no—
319C4×C53#38718yescomplemented
320Dic53—24no—
321Dic53—24no—
322Dic53—24no—
323Dic53—42no—
324Dic53—44no—
325Dic53—82no—
326C2×#387—532no—
327C2×#384—531no—
328C2×C4×C4⋊C4—531no—
329C2×C4×C4⋊C4—531no—
330#1442—532no—
331#1441—532no—
332#1436—532no—
333C4⋊#95—531no—
334C4⋊#95—531no—
335C4⋊#95—531no—
336C4⋊#95D5311yescharacteristic
337C2×C53#228511yescharacteristic
338C2×C53C2×#38711yescharacteristic
339C2×C53#231411yescharacteristic
340C2×C53D4×C4⋊C411yescharacteristic
341C2×C53Q8×C4⋊C411yescharacteristic
342C2×C53#235211yescharacteristic
343C2×C53#235511yescharacteristic
344C2×C53#244511yescharacteristic
345C2×C53#244611yescharacteristic
346C2×C53#245111yescharacteristic
347C2×C53#245211yescharacteristic
348C2×C53#250611yescharacteristic
349C2×C53#250711yescharacteristic
350C2×C53#251111yescharacteristic
351C2×C53#251211yescharacteristic
352C22×C4⋊C4—531no—
353C22×C4⋊C4—531no—
354C22×C4⋊C4—531no—
355C22×C4⋊C4—531no—
356C22×C4⋊C4—532no—
357C22×C4⋊C4—532no—
358C22×C4⋊C4C2×D5311yescharacteristic
359C22×C4⋊C4C2×D5311yescharacteristic
360C22×C42—531no—
361C22×C42—531no—
362C22×C42—532no—
363C22×C42C2×D5311yescharacteristic
364#387—1068no—
365#384—1064no—
366C4×C4⋊C4—538no—
367C4×C4⋊C4—1064no—
368C2×#95—531no—
369C2×#95—531no—
370C2×#95—532no—
371C2×#95—532no—
372C2×#95—532no—
373C2×#95—532no—
374C2×#95—532no—
375C2×#95—532no—
376C2×#95—532no—
377C2×#95C2×D5312yes—
378C2×#95C2×D5312yes—
379C53#1388411yescharacteristic, complemented, Sylow
380C23×C4—531no—
381C23×C4—531no—
382C23×C4—531no—
383C23×C4—531no—
384C23×C4—532no—
385C23×C4—532no—
386C23×C4C22×D5312yes—
387C23×C4C22×D5311yescharacteristic
388C23×C4C22×D5312yes—
389C23×C4C22×D5311yescharacteristic
390C23×C4C22×D5311yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—534no—
397C2×C4⋊C4—534no—
398C2×C4⋊C4—534no—
399C2×C4⋊C4—534no—
400C2×C4⋊C4—534no—
401C2×C4⋊C4—1062no—
402C2×C4⋊C4—1062no—
403C2×C4⋊C4—1062no—
404C2×C4⋊C4—1062no—
405C2×C4⋊C4—1064no—
406C2×C4⋊C4—1064no—
407C2×C4⋊C4—1064no—
408C2×C4⋊C4—1064no—
409C2×C4⋊C4—1062no—
410C2×C4⋊C4—1062no—
411C2×C4⋊C4—1062no—
412C2×C4⋊C4—2122no—
413C2×C4⋊C4—2122no—
414C2×C4⋊C4D21214yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—534no—
418C2×C42—534no—
419C2×C42—1062no—
420C2×C42—1062no—
421C2×C42—1062no—
422C2×C42—1062no—
423C2×C42—1064no—
424C2×C42—1064no—
425C2×C42—2122no—
426C2×C42C4×D5314yes—
427#95—24no—
428#95—42no—
429#95—534no—
430#95—534no—
431#95—1064no—
432#95—1064no—
433#95—1064no—
434#95—1064no—
435#95—1064no—
436#95—2122no—
437#95—2122no—
438C24C23×D5311yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—532no—
463C22×C4—532no—
464C22×C4—532no—
465C22×C4—532no—
466C22×C4—532no—
467C22×C4—532no—
468C22×C4—532no—
469C22×C4—532no—
470C22×C4—532no—
471C22×C4—532no—
472C22×C4—534no—
473C22×C4—1061no—
474C22×C4—1061no—
475C22×C4—1061no—
476C22×C4—1061no—
477C22×C4—1061no—
478C22×C4—1061no—
479C22×C4—1061no—
480C22×C4—1061no—
481C22×C4—1061no—
482C22×C4—1061no—
483C22×C4—1061no—
484C22×C4—1061no—
485C22×C4—1062no—
486C22×C4—1061no—
487C22×C4—1062no—
488C22×C4—1062no—
489C22×C4—1061no—
490C22×C4—1061no—
491C22×C4—1062no—
492C22×C4—1061no—
493C22×C4—1061no—
494C22×C4—1062no—
495C22×C4—1062no—
496C22×C4—1061no—
497C22×C4—1062no—
498C22×C4—1062no—
499C22×C4—1062no—
500C22×C4—1062no—
501C22×C4—1062no—
502C22×C4—1062no—
503C22×C4—1062no—
504C22×C4C2×C4×D5312yes—
505C22×C4C2×C4×D5312yes—
506C22×C4C2×C4×D5312yes—
507C22×C4C2×D21214yes—
508C22×C4C2×D21212yes—
509C22×C4#1171994512yes—
510C22×C4D4×D5312yes—
511C22×C4#1171994712yes—
512C22×C4#1171994712yes—
513C22×C4#1171994712yes—
514C22×C4Q8×D5312yes—
515C22×C4Q8×D5312yes—
516C4⋊C4—28no—
517C4⋊C4—44no—
518C4⋊C4—5316no—
519C4⋊C4—1068no—
520C4⋊C4—1068no—
521C4⋊C4—2128no—
522C4⋊C4—2128no—
523C4⋊C4—2124no—
524C42—28no—
525C42—1068no—
526C42—1068no—
527C42—2128no—
528C23C22×C4×D5311yescharacteristic
529C23C2×D4×D5311yescharacteristic
530C23C22×D21211yescharacteristic
531C23C2×Q8×D5311yescharacteristic
532C23C2×Q8×D5311yescharacteristic
533C23#41×D5311yescharacteristic
534C23#41×D5311yescharacteristic
535C23C2×#1171994711yescharacteristic
536C23C2×#1171994711yescharacteristic
537C23C2×#1171994711yescharacteristic
538C23C2×#1171994511yescharacteristic
539C23#1313326211yescharacteristic
540C23#1313326311yescharacteristic
541C23#1313326411yescharacteristic
542C23#1313326511yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—534no—
571C2×C4—534no—
572C2×C4—534no—
573C2×C4—1062no—
574C2×C4—1062no—
575C2×C4—1062no—
576C2×C4—1062no—
577C2×C4—1062no—
578C2×C4—1062no—
579C2×C4—1062no—
580C2×C4—1062no—
581C2×C4—1062no—
582C2×C4—1062no—
583C2×C4—1062no—
584C2×C4—1062no—
585C2×C4—1062no—
586C2×C4—1062no—
587C2×C4—1062no—
588C2×C4—1062no—
589C2×C4—1062no—
590C2×C4—1062no—
591C2×C4—1064no—
592C2×C4—1064no—
593C2×C4—1062no—
594C2×C4—1062no—
595C2×C4—1062no—
596C2×C4—1064no—
597C2×C4—2122no—
598C2×C4—2122no—
599C2×C4—2122no—
600C2×C4—2122no—
601C2×C4—2122no—
602C2×C4—2122no—
603C2×C4—2122no—
604C2×C4—2121no—
605C2×C4—2122no—
606C2×C4—2121no—
607C2×C4—2121no—
608C2×C4—2121no—
609C2×C4—2122no—
610C2×C4—2122no—
611C2×C4—2122no—
612C2×C4C4⋊C4×D5314yes—
613C2×C4#1313317314yes—
614C2×C4C4×D21214yes—
615C2×C4#1313318214yes—
616C2×C4#1313319714yes—
617C2×C4#1313320114yes—
618C2×C4#1313320714yes—
619C2×C4#1313321014yes—
620C22C2×C4⋊C4×D5311yescharacteristic
621C22#117×D5311yescharacteristic
622C22C2×#1313317311yescharacteristic
623C22C2×C4×D21211yescharacteristic
624C22C2×#1313318211yescharacteristic
625C22#1681110311yescharacteristic
626C22#1681110411yescharacteristic
627C22C2×#1313319711yescharacteristic
628C22C2×#1313320111yescharacteristic
629C22C2×#1313320711yescharacteristic
630C22C2×#1313321011yescharacteristic
631C22#1681116811yescharacteristic
632C22#1681116811yescharacteristic
633C22#1681117511yescharacteristic
634C22#1681117511yescharacteristic
635C22#1681122611yescharacteristic
636C22#1681123311yescharacteristic
637C22#1681124011yescharacteristic
638C22#1681124611yescharacteristic
639C22D4×D21211yescharacteristic
640C22#1681126811yescharacteristic
641C22#1681127811yescharacteristic
642C22#1681128511yescharacteristic
643C22#1681128811yescharacteristic
644C22Q8×D21211yescharacteristic
645C22#1681129311yescharacteristic
646C22#1681131411yescharacteristic
647C22#1681132311yescharacteristic
648C22#1681132911yescharacteristic
649C22#1681133311yescharacteristic
650C22#1681134211yescharacteristic
651C22#1681134811yescharacteristic
652C22#1681135011yescharacteristic
653C22#1681135311yescharacteristic
654C22#1681135511yescharacteristic
655C4—24no—
656C4—42no—
657C4—44no—
658C4—82no—
659C4—1064no—
660C4—1064no—
661C4—1064no—
662C4—4242no—
663C4—2124no—
664C4—2122no—
665C4#1681050818yescomplemented
666C2#2027711711yescharacteristic
667C2C2×#1681050811yescharacteristic
668C2#2027732211yescharacteristic
669C2C4⋊C4×D21211yescharacteristic
670C2#2027762711yescharacteristic
671C2#2027764711yescharacteristic
672C2#2027766711yescharacteristic
673C2#2027847811yescharacteristic
674C2#2027848911yescharacteristic
675C2#2027855211yescharacteristic
676C2#2027856311yescharacteristic
677C2#2027922911yescharacteristic
678C2#2027924011yescharacteristic
679C2#2027928811yescharacteristic
680C2#2027929911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, prime radical, cosocleC24×C53C24
hypercenterC4⋊#95D53
hypocenterC53#13884
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
24. C4×C4⋊Dic53C4semidirect
181. C4⋊Dic53C4⋊C4semidirect
319. C4×C53#387semidirect
379. C53#13884semidirect
665. C4#16810508semidirect

Maximal subgroups

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

subgroupindex
C2×#168105082
C2×#168104922
C2×C4⋊C4×Dic532
C2×C4×C4⋊Dic532
#202729702
#202729672
#202729502
#202729452
#202729442
C53×C4⋊#952
#1388453