Finite Group Databasebeta

← #27312015

Subgroups — #27312015

Order 13568.

2118 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810526C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810498C212yesmaximal, complemented
4C2×#16810483C212yesmaximal, complemented
5#20272980C212yesmaximal, complemented
6#20272960C212yesmaximal, complemented
7#20272960C212yesmaximal, complemented
8#20272949C212yesmaximal, complemented
9C2×C53×#386C211yesmaximal, characteristic
10C24×Dic53C2211yescharacteristic
11C22×C4⋊Dic53C2212yes—
12C22×C4⋊Dic53C2212yes—
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C22⋊Dic53C2212yes—
16C22×C22⋊Dic53C2212yes—
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20#16810526—24no—
21#16810503—24no—
22#16810498—28no—
23#16810483—28no—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C23×D4×C53C2211yescharacteristic
31C24×C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2212yes—
33C22×C22⋊C4×C53C2211yescharacteristic
34C53×#386C418yescomplemented
35C2×#95×C53C2212yes—
36C23×Dic53—22no—
37C23×Dic53—24no—
38C23×Dic53—42no—
39C23×Dic53—41no—
40C23×Dic53—41no—
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C2×C4⋊Dic53—24no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—24no—
48C2×C4⋊Dic53—24no—
49C2×C4⋊Dic53—24no—
50C2×C4⋊Dic53—24no—
51C2×C4⋊Dic53—42no—
52C2×C4⋊Dic53—42no—
53C2×C4⋊Dic53—42no—
54C2×C4⋊Dic53—42no—
55C2×C4⋊Dic53—41no—
56C2×C4⋊Dic53—41no—
57C2×C22⋊Dic53—24no—
58C2×C22⋊Dic53—22no—
59C2×C22⋊Dic53—24no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53—24no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—42no—
65C2×C22⋊Dic53—42no—
66C2×C22⋊Dic53—42no—
67C2×C22⋊Dic53—41no—
68C2×C22⋊Dic53—41no—
69C2×C4×Dic53—22no—
70C2×C4×Dic53—41no—
71C2×C4×Dic53—41no—
72#13133124—24no—
73#13133124—24no—
74#13133124—24no—
75#13133124—42no—
76#13133124—42no—
77#13133124D418yescomplemented
78C25×C53C2311yescharacteristic
79C25×C53C2311yescharacteristic
80C22×D4×C53—41no—
81C22×D4×C53—41no—
82C22×D4×C53—41no—
83C22×D4×C53—41no—
84C22×D4×C53C2×C414yes—
85C22×D4×C53D414yes—
86C22×D4×C53Q814yes—
87C23×C4×C53—24no—
88C23×C4×C53—24no—
89C23×C4×C53—41no—
90C23×C4×C53—41no—
91C23×C4×C53C2×C414yescomplemented
92C23×C4×C53C2312yes—
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C2×C22⋊C4×C53—24no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53—41no—
98C2×C22⋊C4×C53—41no—
99C2×C22⋊C4×C53C2×C418yes—
100C2×C22⋊C4×C53C2×C414yescomplemented
101#95×C53C2×C418yescomplemented
102C24×C53—22no—
103C24×C53—22no—
104C24×C53—22no—
105C24×C53—22no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53C22×C412yes—
119C24×C53C22×C412yes—
120C24×C53C2×D412yes—
121C24×C53C2×D412yes—
122C24×C53C2×Q812yes—
123C24×C53C2×Q812yes—
124C24×C53C2411yescharacteristic
125C2×D4×C53—44no—
126C2×D4×C53—44no—
127C2×D4×C53—44no—
128C2×D4×C53—44no—
129C2×D4×C53—44no—
130C2×D4×C53—44no—
131C2×D4×C53C4⋊C4116yescomplemented
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—216no—
147C22×C4×C53—44no—
148C22×C4×C53—44no—
149C22×C4×C53—48no—
150C22×C4×C53—44no—
151C22×C4×C53C22×C414yes—
152C22×C4×C53C22×C412yes—
153C22×C4×C53C22×C414yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×D414yes—
156C22×C4×C53C2×Q812yes—
157C22×C4×C53#4114yes—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—44no—
185C22×Dic53—48no—
186C22×Dic53—48no—
187C22×Dic53—44no—
188C22×Dic53—44no—
189C22×Dic53C2×D414yes—
190C22×Dic53C2×D414yes—
191C22⋊C4×C53—216no—
192C22⋊C4×C53—44no—
193C22⋊Dic53—48no—
194C22⋊Dic53—48no—
195C22⋊Dic53—48no—
196C22⋊Dic53—44no—
197C4⋊Dic53—48no—
198C4⋊Dic53—48no—
199C4⋊Dic53—48no—
200C4⋊Dic53—44no—
201C4×Dic53—44no—
202C23×C53—24no—
203C23×C53—24no—
204C23×C53—22no—
205C23×C53—22no—
206C23×C53—22no—
207C23×C53—22no—
208C23×C53—24no—
209C23×C53—24no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—42no—
227C23×C53—42no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—42no—
243C23×C53—42no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53C2×C4⋊C414yes—
247C23×C53C2×C4⋊C414yes—
248C23×C53C23×C411yescharacteristic
249C23×C53C22×D412yes—
250C23×C53C22×D411yescharacteristic
251C23×C53C22×Q811yescharacteristic
252C23×C53C2×#4112yes—
253C23×C53H(5,𝔽2)11yescharacteristic
254C23×C53H(5,𝔽2)11yescharacteristic
255C23×C53H(5,𝔽2)11yescharacteristic
256C23×C53H(5,𝔽2)11yescharacteristic
257C23×C53H(5,𝔽2)12yes—
258C23×C532−1+412yes—
259D4×C53—416no—
260C2×C4×C53—24no—
261C2×C4×C53—24no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—24no—
274C2×C4×C53—24no—
275C2×C4×C53—416no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53C2×C4⋊C414yes—
281C2×C4×C53C4×D418yes—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—24no—
285C2×Dic53—24no—
286C2×Dic53—24no—
287C2×Dic53—24no—
288C2×Dic53—416no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311#14401—531nomaximal, Sylow
312C22×C53—24no—
313C22×C53—24no—
314C22×C53—28no—
315C22×C53—28no—
316C22×C53—44no—
317C22×C53—44no—
318C22×C53—42no—
319C22×C53—42no—
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—44no—
325C22×C53—44no—
326C22×C53—42no—
327C22×C53—42no—
328C22×C53—44no—
329C22×C53—44no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53C22×C4⋊C411yescharacteristic
335C22×C53C2×C4×D412yes—
336C22×C53#51811yescharacteristic
337C22×C53#51811yescharacteristic
338C22×C53#52012yes—
339C22×C53#53411yescharacteristic
340C22×C53#53411yescharacteristic
341C22×C53#53512yes—
342C22×C53#53712yes—
343C22×C53#54012yes—
344C22×C53#54212yes—
345C22×C53#54311yescharacteristic
346C22×C53#54311yescharacteristic
347C22×C53D4211yescharacteristic
348C22×C53D4212yes—
349C22×C53#54612yes—
350C22×C53#54712yes—
351C22×C53D4×Q812yes—
352C22×C53#55111yescharacteristic
353C22×C53#55412yes—
354C22×C53#56011yescharacteristic
355C22×C53#56212yes—
356C22×C53#56311yescharacteristic
357C4×C53—24no—
358C4×C53—28no—
359C4×C53—44no—
360Dic53—44no—
361Dic53—44no—
362Dic53—82no—
363Dic53—82no—
364C2×#390—531no—
365C2×#386—531no—
366C2×#386D5311yescharacteristic
367C2×#385—532no—
368C2×#380—532no—
369#1444—532no—
370#1439—532no—
371#1439—532no—
372#1436—532no—
373C2×C53—44no—
374C2×C53—44no—
375C2×C53#231511yescharacteristic
376C2×C53#232412yes—
377C2×C53D4×C4⋊C412yes—
378C2×C53#235811yescharacteristic
379C2×C53#237611yescharacteristic
380C2×C53#266911yescharacteristic
381C2×C53#267112yes—
382C2×C53#268311yescharacteristic
383C2×C53#269212yes—
384C2×C53#271711yescharacteristic
385C2×C53#274811yescharacteristic
386C23×D4C2×D5311yescharacteristic
387C24×C4—531no—
388C24×C4C2×D5311yescharacteristic
389C22×C4⋊C4—532no—
390C22×C4⋊C4—532no—
391C22×C4⋊C4—532no—
392C22×C4⋊C4—531no—
393C22×C22⋊C4—532no—
394C22×C22⋊C4—532no—
395C22×C22⋊C4—532no—
396C22×C22⋊C4—531no—
397C22×C22⋊C4C2×D5312yes—
398C22×C22⋊C4C2×D5311yescharacteristic
399C22×C42—531no—
400#390—1064no—
401#386—1064no—
402#386Dic5318yescomplemented
403#385—1068no—
404#380—1068no—
405C2×#95—532no—
406C2×#95—532no—
407C2×#95—532no—
408C2×#95—532no—
409C2×#95—532no—
410C2×#95—532no—
411C2×#95C2×D5312yes—
412C53#1440111yescharacteristic, complemented, Sylow
413C25C22×D5311yescharacteristic
414C25C22×D5311yescharacteristic
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4Dic10614yes—
420C22×D4D21214yes—
421C22×D4C2×Dic5314yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—532no—
427C23×C4—532no—
428C23×C4—532no—
429C23×C4—532no—
430C23×C4—1064no—
431C23×C4—1062no—
432C23×C4—2121no—
433C23×C4—2121no—
434C23×C4—2122no—
435C23×C4C2×Dic5314yescomplemented
436C23×C4C22×D5312yes—
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5312yes—
439C2×C4⋊C4—1064no—
440C2×C4⋊C4—1064no—
441C2×C4⋊C4—1064no—
442C2×C4⋊C4—1062no—
443C2×C4⋊C4—1064no—
444C2×C4⋊C4—1064no—
445C2×C4⋊C4—2122no—
446C2×C4⋊C4—2122no—
447C2×C4⋊C4—2121no—
448C2×C4⋊C4—2121no—
449C2×C4⋊C4—2122no—
450C2×C4⋊C4—2122no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—41no—
455C2×C22⋊C4—1064no—
456C2×C22⋊C4—1064no—
457C2×C22⋊C4—1064no—
458C2×C22⋊C4—1064no—
459C2×C22⋊C4—1062no—
460C2×C22⋊C4—1064no—
461C2×C22⋊C4—1064no—
462C2×C22⋊C4—2122no—
463C2×C22⋊C4—2122no—
464C2×C22⋊C4—2122no—
465C2×C22⋊C4—2121no—
466C2×C22⋊C4—2121no—
467C2×C22⋊C4C2×Dic5318yes—
468C2×C22⋊C4C2×Dic5314yescomplemented
469C2×C42—1062no—
470C2×C42—2121no—
471C2×C42—2121no—
472#95—538no—
473#95—1064no—
474#95—1064no—
475#95—1064no—
476#95—2122no—
477#95—2122no—
478#95C2×Dic5318yescomplemented
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24C2×Dic10612yes—
496C24C2×Dic10612yes—
497C24C2×D21212yes—
498C24C2×D21212yes—
499C24C22×Dic5312yes—
500C24C22×Dic5312yes—
501C24C23×D5311yescharacteristic
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4C4⋊Dic53116yescomplemented
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—216no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—534no—
529C22×C4—534no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—2124no—
557C22×C4—2128no—
558C22×C4—2128no—
559C22×C4—2124no—
560C22×C4—2124no—
561C22×C4C2×Dic10612yes—
562C22×C4C2×D21212yes—
563C22×C4D4×D5314yes—
564C22×C4#1171994714yes—
565C22×C4C22×Dic5314yes—
566C22×C4C22×Dic5312yes—
567C22×C4C22×Dic5314yes—
568C4⋊C4—2128no—
569C4⋊C4—2128no—
570C4⋊C4—2124no—
571C4⋊C4—2128no—
572C22⋊C4—216no—
573C22⋊C4—44no—
574C22⋊C4—2128no—
575C22⋊C4—2128no—
576C22⋊C4—2128no—
577C22⋊C4—2124no—
578C42—2124no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23C2×C4⋊Dic5314yes—
624C23C2×C4⋊Dic5314yes—
625C23C23×Dic5311yescharacteristic
626C23C2×D4×D5312yes—
627C23C22×D21211yescharacteristic
628C23C22×Dic10611yescharacteristic
629C23C2×#1171994712yes—
630C23#1313326211yescharacteristic
631C23#1313326211yescharacteristic
632C23#1313326211yescharacteristic
633C23#1313326211yescharacteristic
634C23#1313326312yes—
635C23#1313326412yes—
636D4—416no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—416no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—1064no—
658C2×C4—1064no—
659C2×C4—1064no—
660C2×C4—1064no—
661C2×C4—1064no—
662C2×C4—1064no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4—2122no—
677C2×C4—21216no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4C2×C4⋊Dic5314yes—
687C2×C4D4×Dic5318yes—
688C22—24no—
689C22—24no—
690C22—28no—
691C22—28no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C22×C4⋊Dic5311yescharacteristic
711C22C2×D4×Dic5312yes—
712C22#1681109811yescharacteristic
713C22#1681109811yescharacteristic
714C22#1681110612yes—
715C22#1681118511yescharacteristic
716C22#1681118511yescharacteristic
717C22#1681118912yes—
718C22#1681120212yes—
719C22#1681122612yes—
720C22#1681124012yes—
721C22#1681124911yescharacteristic
722C22#1681124911yescharacteristic
723C22#1681125511yescharacteristic
724C22D4×D21212yes—
725C22#1681126012yes—
726C22#1681127712yes—
727C22D4×Dic10612yes—
728C22#1681130411yescharacteristic
729C22#1681133012yes—
730C22#1681136311yescharacteristic
731C22#1681137012yes—
732C22#1681137611yescharacteristic
733C4—24no—
734C4—28no—
735C4—44no—
736C4—4242no—
737C4—4242no—
738C4—2124no—
739C4—2124no—
740C2—44no—
741C2—44no—
742C2#2027732911yescharacteristic
743C2#2027741012yes—
744C2D4×C4⋊Dic5312yes—
745C2#2027769911yescharacteristic
746C2#2027786311yescharacteristic
747C2#2028093311yescharacteristic
748C2#2028094912yes—
749C2#2028108811yescharacteristic
750C2#2028121512yes—
751C2#2028155311yescharacteristic
752C2#2028193011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#386C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#386D53
hypocenterC53#14401
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#16810498C2semidirect
4. C2×#16810483C2semidirect
5. #20272980C2semidirect
6. #20272960C2semidirect
7. #20272960C2semidirect
8. #20272949C2semidirect
34. C53×#386C4semidirect
77. #13133124D4semidirect
91. C23×C4×C53C2×C4semidirect
100. C2×C22⋊C4×C53C2×C4semidirect
101. #95×C53C2×C4semidirect
131. C2×D4×C53C4⋊C4semidirect
402. #386Dic53semidirect
412. C53#14401semidirect
435. C23×C4C2×Dic53semidirect
468. C2×C22⋊C4C2×Dic53semidirect
478. #95C2×Dic53semidirect
508. C2×D4C4⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105262
C2×#168105032
C2×#168104982
C2×#168104832
#202729802
#202729602
#202729492
C2×C53×#3862
#1440153