Finite Group Databasebeta

← #27307798

Subgroups — #27307798

Order 13568.

2366 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×#16810522C212yesmaximal, complemented
3C2×#16810498C211yesmaximal, characteristic
4C2×#16810498C211yesmaximal, characteristic
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic
6#20272980C212yesmaximal, complemented
7#20272968C212yesmaximal, complemented
8#20272949C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic
10#20272937C211yesmaximal, characteristic
11C2×C53×#385C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×C4⋊Dic53—24no—
15C22×C4⋊Dic53—28no—
16C22×C4⋊Dic53C2212yes—
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2212yes—
19C22×C4⋊Dic53C2212yes—
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C4×Dic53C2212yes—
24#16810522—28no—
25#16810498—24no—
26#16810498—24no—
27C22⋊C4×Dic53—24no—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C53×#385C418yescomplemented
41C2×#95×C53C2212yes—
42C23×Dic53—22no—
43C23×Dic53—22no—
44C23×Dic53—22no—
45C23×Dic53—24no—
46C23×Dic53—24no—
47C23×Dic53—22no—
48C23×Dic53—22no—
49C23×Dic53—42no—
50C23×Dic53—42no—
51C23×Dic53D414yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2312yes—
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C2×C4⋊Dic53—232no—
59C2×C4⋊Dic53—24no—
60C2×C4⋊Dic53—24no—
61C2×C4⋊Dic53—24no—
62C2×C4⋊Dic53—24no—
63C2×C4⋊Dic53—24no—
64C2×C4⋊Dic53—24no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—24no—
68C2×C4⋊Dic53—24no—
69C2×C4⋊Dic53—42no—
70C2×C4⋊Dic53—42no—
71C2×C4⋊Dic53D418yes—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53Q814yes—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—42no—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—24no—
85#13133124—22no—
86#13133124—22no—
87#13133124—24no—
88#13133124—42no—
89C25×C53C2311yescharacteristic
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—24no—
93C23×C4×C53—24no—
94C23×C4×C53C2×C414yes—
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2312yes—
98C23×C4×C53C2312yes—
99C2×C4⋊C4×C53—24no—
100C2×C4⋊C4×C53—24no—
101C2×C4⋊C4×C53C2×C418yescomplemented
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53C2×C414yes—
105C2×C22⋊C4×C53C2×C414yes—
106C2×C22⋊C4×C53D414yes—
107C2×C22⋊C4×C53Q814yes—
108#95×C53C2×C418yescomplemented
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—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—216no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53C22×C412yes—
143C22×C4×C53C22×C412yes—
144C22×C4×C53C22×C414yes—
145C22×C4×C53C22×C414yes—
146C22×C4×C53C2×D414yes—
147C22×C4×C53C2×D414yes—
148C22×C4×C53C2×Q814yes—
149C22×C4×C53#4114yes—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—22no—
153C22×Dic53—28no—
154C22×Dic53—28no—
155C22×Dic53—22no—
156C22×Dic53—21no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—28no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—44no—
183C22×Dic53—48no—
184C22×Dic53—48no—
185C22×Dic53—48no—
186C22×Dic53—48no—
187C22×Dic53—44no—
188C22×Dic53—44no—
189C22×Dic53C2×D412yes—
190C22×Dic53C2×D414yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×D414yes—
193C22×Dic53C2×Q814yes—
194C4⋊C4×C53—216no—
195C22⋊C4×C53—28no—
196C22⋊C4×C53C4⋊C4116yescomplemented
197C22⋊Dic53—28no—
198C22⋊Dic53—44no—
199C4⋊Dic53—216no—
200C4⋊Dic53—216no—
201C4⋊Dic53—48no—
202C4⋊Dic53—44no—
203C4⋊Dic53—44no—
204C4×Dic53—48no—
205C23×C53—24no—
206C23×C53—24no—
207C23×C53—22no—
208C23×C53—22no—
209C23×C53—24no—
210C23×C53—22no—
211C23×C53—22no—
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×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×#4111yescharacteristic
235C23×C53C2×#4112yes—
236C23×C53C2×#4111yescharacteristic
237C23×C53H(5,𝔽2)12yes—
238C23×C532−1+412yes—
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—24no—
250C2×C4×C53—24no—
251C2×C4×C53—24no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—24no—
255C2×C4×C53—24no—
256C2×C4×C53—41no—
257C2×C4×C53—41no—
258C2×C4×C53—42no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—42no—
262C2×C4×C53C2×C4⋊C418yescomplemented
263C2×C4×C53C4×D418yes—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—24no—
267C2×Dic53—24no—
268C2×Dic53—24no—
269C2×Dic53—22no—
270C2×Dic53—22no—
271C2×Dic53—24no—
272C2×Dic53—22no—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—416no—
278C2×Dic53—416no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53#12014yes—
300#14043—531nomaximal, Sylow
301C22×C53—24no—
302C22×C53—24no—
303C22×C53—28no—
304C22×C53—28no—
305C22×C53—24no—
306C22×C53—24no—
307C22×C53—24no—
308C22×C53—28no—
309C22×C53—28no—
310C22×C53—24no—
311C22×C53#38918yescomplemented
312C22×C53C22×C4⋊C411yescharacteristic
313C22×C53C2×C4×D411yescharacteristic
314C22×C53C2×C4×D412yes—
315C22×C53C2×C4×Q811yescharacteristic
316C22×C53#52012yes—
317C22×C53C2×#12011yescharacteristic
318C22×C53C2×#12111yescharacteristic
319C22×C53C2×C22⋊Q811yescharacteristic
320C22×C53#52511yescharacteristic
321C22×C53#52512yes—
322C22×C53C2×#12511yescharacteristic
323C22×C53C2×C4⋊Q811yescharacteristic
324C22×C53#53411yescharacteristic
325C22×C53#53611yescharacteristic
326C22×C53#53912yes—
327C22×C53D4212yes—
328C22×C53#54612yes—
329C22×C53#54712yes—
330C22×C53D4×Q812yes—
331C22×C53D4×Q812yes—
332C22×C53#55212yes—
333C22×C53#55412yes—
334C22×C53#55412yes—
335C4×C53—28no—
336C4×C53—28no—
337C4×C53—42no—
338C4×C53—42no—
339Dic53—24no—
340Dic53—42no—
341Dic53—44no—
342Dic53—44no—
343Dic53—81no—
344Dic53—81no—
345C23×C4⋊C4—531no—
346C2×#389—532no—
347C2×#385—531no—
348C2×#385—531no—
349C2×#385D5311yescharacteristic
350C2×C4×C22⋊C4—531no—
351#1444—532no—
352#1441—532no—
353#1436—532no—
354C22⋊#95—531no—
355C22⋊#95—531no—
356C2×C53—28no—
357C2×C53C2×#38911yescharacteristic
358C2×C53C4×#12011yescharacteristic
359C2×C53#232211yescharacteristic
360C2×C53D4×C4⋊C412yes—
361C2×C53#236012yes—
362C2×C53#241011yescharacteristic
363C2×C53#241311yescharacteristic
364C2×C53#243411yescharacteristic
365C2×C53#244912yes—
366C2×C53#247312yes—
367C2×C53#258311yescharacteristic
368C24×C4—531no—
369C24×C4—531no—
370C24×C4C2×D5311yescharacteristic
371C22×C4⋊C4—532no—
372C22×C4⋊C4—532no—
373C22×C4⋊C4—531no—
374C22×C4⋊C4—532no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—1068no—
377C22×C4⋊C4—1064no—
378C22×C4⋊C4C2×D5312yes—
379C22×C22⋊C4—531no—
380C22×C22⋊C4—531no—
381C22×C22⋊C4C2×D5311yescharacteristic
382C22×C22⋊C4C2×D5311yescharacteristic
383C22×C42—532no—
384#389—1068no—
385#385—1064no—
386#385—1064no—
387#385Dic5318yescomplemented
388C4×C22⋊C4—1064no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95—532no—
392C2×#95—531no—
393C2×#95—532no—
394C2×#95—531no—
395C2×#95—532no—
396C2×#95—532no—
397C2×#95C2×D5312yes—
398C53#1404311yescharacteristic, complemented, Sylow
399C25C22×D5311yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4—532no—
407C23×C4—531no—
408C23×C4—534no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—1064no—
412C23×C4—1064no—
413C23×C4—1062no—
414C23×C4—1062no—
415C23×C4—1062no—
416C23×C4—1062no—
417C23×C4—1062no—
418C23×C4—2122no—
419C23×C4—2122no—
420C23×C4C2×Dic5314yes—
421C23×C4C22×D5311yescharacteristic
422C23×C4C22×D5311yescharacteristic
423C23×C4C22×D5312yes—
424C23×C4C22×D5312yes—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—538no—
428C2×C4⋊C4—1064no—
429C2×C4⋊C4—1064no—
430C2×C4⋊C4—1064no—
431C2×C4⋊C4—1064no—
432C2×C4⋊C4—10632no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1062no—
435C2×C4⋊C4—1062no—
436C2×C4⋊C4—1064no—
437C2×C4⋊C4—1064no—
438C2×C4⋊C4—1064no—
439C2×C4⋊C4—2122no—
440C2×C4⋊C4—2122no—
441C2×C4⋊C4C2×Dic5318yescomplemented
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—534no—
445C2×C22⋊C4—1062no—
446C2×C22⋊C4—1062no—
447C2×C22⋊C4—1062no—
448C2×C22⋊C4—1062no—
449C2×C22⋊C4—1062no—
450C2×C22⋊C4Dic10614yes—
451C2×C22⋊C4D21214yes—
452C2×C22⋊C4C2×Dic5314yes—
453C2×C22⋊C4C2×Dic5314yes—
454C2×C42—1064no—
455C2×C42—1064no—
456C2×C42—2122no—
457#95—1062no—
458#95—1062no—
459#95—1064no—
460#95—1064no—
461#95—1064no—
462#95—1064no—
463#95—1064no—
464#95—2122no—
465#95C2×Dic5318yescomplemented
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×Dic10612yes—
471C24C2×D21212yes—
472C24D4×D5312yes—
473C24#1171994712yes—
474C24Q8×D5312yes—
475C24#1171994912yes—
476C24C22×Dic5312yes—
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—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—216no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—532no—
500C22×C4—534no—
501C22×C4—534no—
502C22×C4—532no—
503C22×C4—534no—
504C22×C4—1068no—
505C22×C4—1061no—
506C22×C4—1061no—
507C22×C4—1062no—
508C22×C4—1068no—
509C22×C4—1068no—
510C22×C4—1062no—
511C22×C4—1062no—
512C22×C4—1062no—
513C22×C4—1062no—
514C22×C4—1061no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4—1061no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1061no—
527C22×C4—1062no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1062no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—2124no—
537C22×C4—2128no—
538C22×C4—2128no—
539C22×C4—2128no—
540C22×C4—2128no—
541C22×C4—2124no—
542C22×C4—2124no—
543C22×C4C2×Dic10614yes—
544C22×C4C2×D21214yes—
545C22×C4D4×D5314yes—
546C22×C4#1171994714yes—
547C22×C4C22×Dic5312yes—
548C22×C4C22×Dic5312yes—
549C22×C4C22×Dic5314yes—
550C22×C4C22×Dic5314yes—
551C4⋊C4—216no—
552C4⋊C4—10616no—
553C4⋊C4—10616no—
554C4⋊C4—2128no—
555C4⋊C4—2124no—
556C4⋊C4—2124no—
557C22⋊C4—28no—
558C22⋊C4—1068no—
559C22⋊C4—2124no—
560C22⋊C4C4⋊Dic53116yescomplemented
561C42—2128no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23C2×C4⋊Dic5314yes—
579C23D4×Dic5314yes—
580C23Q8×Dic5314yes—
581C23#1313319214yes—
582C23#1313319714yes—
583C23#1313320814yes—
584C23#1313321614yes—
585C23C23×Dic5311yescharacteristic
586C23C2×D4×D5312yes—
587C23C2×D4×D5311yescharacteristic
588C23C22×D21211yescharacteristic
589C23C2×Q8×D5311yescharacteristic
590C23C22×Dic10611yescharacteristic
591C23C2×#1171994712yes—
592C23C2×#1171994711yescharacteristic
593C23C2×#1171994911yescharacteristic
594C23#1313326312yes—
595C23#1313326412yes—
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—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—534no—
620C2×C4—1064no—
621C2×C4—1062no—
622C2×C4—1062no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—1064no—
627C2×C4—1064no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1064no—
631C2×C4—1062no—
632C2×C4—1064no—
633C2×C4—21216no—
634C2×C4—2122no—
635C2×C4—2122no—
636C2×C4—2122no—
637C2×C4—2121no—
638C2×C4—2121no—
639C2×C4—2121no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2122no—
644C2×C4—21216no—
645C2×C4—2122no—
646C2×C4—2122no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4—2122no—
650C2×C4—2122no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4C2×C4⋊Dic5318yescomplemented
656C2×C4D4×Dic5318yes—
657C22—24no—
658C22—24no—
659C22—28no—
660C22—24no—
661C22—24no—
662C22—28no—
663C22—24no—
664C22—28no—
665C22—24no—
666C22—28no—
667C22#1681052218yescomplemented
668C22C22×C4⋊Dic5311yescharacteristic
669C22C2×D4×Dic5312yes—
670C22C2×D4×Dic5311yescharacteristic
671C22C2×Q8×Dic5311yescharacteristic
672C22#1681110612yes—
673C22#120×D5311yescharacteristic
674C22C2×#1313319211yescharacteristic
675C22C2×#1313319711yescharacteristic
676C22#1681112911yescharacteristic
677C22#1681112912yes—
678C22C2×#1313320811yescharacteristic
679C22C2×#1313321611yescharacteristic
680C22#1681118411yescharacteristic
681C22#1681119511yescharacteristic
682C22#1681121712yes—
683C22D4×D21212yes—
684C22#1681126412yes—
685C22#1681127712yes—
686C22#1681128612yes—
687C22D4×Dic10612yes—
688C22#1681131512yes—
689C22#1681133012yes—
690C22#1681133112yes—
691C4—28no—
692C4—28no—
693C4—42no—
694C4—42no—
695C4—1064no—
696C4—4241no—
697C4—4241no—
698C4—2124no—
699C4—2122no—
700C4—2124no—
701C2—28no—
702C2C2×#1681052211yescharacteristic
703C2#120×Dic5311yescharacteristic
704C2#2027738711yescharacteristic
705C2D4×C4⋊Dic5312yes—
706C2#2027772412yes—
707C2#2027808711yescharacteristic
708C2#2027812011yescharacteristic
709C2#2027835711yescharacteristic
710C2#2027852212yes—
711C2#2027885512yes—
712C2#2028009211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53#14043
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
6. #20272980C2semidirect
7. #20272968C2semidirect
8. #20272949C2semidirect
40. C53×#385C4semidirect
101. C2×C4⋊C4×C53C2×C4semidirect
108. #95×C53C2×C4semidirect
196. C22⋊C4×C53C4⋊C4semidirect
262. C2×C4×C53C2×C4⋊C4semidirect
311. C22×C53#389semidirect
387. #385Dic53semidirect
398. C53#14043semidirect
441. C2×C4⋊C4C2×Dic53semidirect
465. #95C2×Dic53semidirect
560. C22⋊C4C4⋊Dic53semidirect
655. C2×C4C2×C4⋊Dic53semidirect
667. C22#16810522semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic532
C2×#168105222
C2×#168104982
C2×C22⋊C4×Dic532
#202729802
#202729682
#202729492
#202729382
#202729372
C2×C53×#3852
#1404353