Finite Group Databasebeta

← #27315509

Subgroups — #27315509

Order 13568.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133194C211yesmaximal, characteristic
2C23×#11719919C211yesmaximal, characteristic
3C2×#16810543C212yesmaximal, complemented
4C2×#16810496C211yesmaximal, characteristic
5#20272979C212yesmaximal, complemented
6#20272978C212yesmaximal, complemented
7#20272966C212yesmaximal, complemented
8#20272937C211yesmaximal, characteristic
9#20272937C211yesmaximal, characteristic
10#20272937C211yesmaximal, characteristic
11C2×C53×#385C211yesmaximal, characteristic
12C23×Dic106C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×#13133194—24no—
16C2×#13133194—24no—
17C2×#13133194—24no—
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919—24no—
20C22×#11719919—28no—
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2212yes—
24C22×#11719919C2212yes—
25C22×#11719919C2212yes—
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28#16810543—28no—
29#16810496—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C24×C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C53×#385—24no—
42C2×#95×C53C2212yes—
43C22×Dic106—22no—
44C22×Dic106—22no—
45C22×Dic106—22no—
46C22×Dic106—24no—
47C22×Dic106—42no—
48C23×Dic53—22no—
49C23×Dic53—22no—
50C23×Dic53—24no—
51C23×Dic53—24no—
52C23×Dic53—22no—
53C23×Dic53—22no—
54C23×Dic53—24no—
55C23×Dic53—42no—
56C23×Dic53D414yes—
57C23×Dic53Q814yescomplemented
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2312yes—
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2312yes—
64#13133194—232no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×#11719919—232no—
69C2×#11719919—24no—
70C2×#11719919—22no—
71C2×#11719919—22no—
72C2×#11719919—24no—
73C2×#11719919—24no—
74C2×#11719919—24no—
75C2×#11719919—24no—
76C2×#11719919—24no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—24no—
82C2×#11719919—42no—
83C2×#11719919D418yes—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53D414yes—
89C2×C22⋊Dic53Q814yescomplemented
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—42no—
97C25×C53C2311yescharacteristic
98C23×C4×C53—22no—
99C23×C4×C53—24no—
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—42no—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C23×C4×C53C2312yes—
107C2×C4⋊C4×C53—24no—
108C2×C4⋊C4×C53—24no—
109C2×C4⋊C4×C53—42no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53D414yes—
115C2×C22⋊C4×C53Q814yescomplemented
116#95×C53—24no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53C2×D412yes—
122C24×C53C2×D412yes—
123C24×C53C2×D412yes—
124C24×C53C2×Q812yes—
125C24×C53C2×Q812yes—
126C24×C53C2×Q812yes—
127C24×C53#4112yes—
128C24×C53C2411yescharacteristic
129C22×C4×C53—28no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
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—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—48no—
151C22×C4×C53—48no—
152C22×C4×C53—44no—
153C22×C4×C53—44no—
154C22×C4×C53C2×D414yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×Q814yes—
158C22×Dic53—28no—
159C22×Dic53—216no—
160C22×Dic53—28no—
161C22×Dic53—28no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—216no—
170C22×Dic53—28no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—22no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—28no—
190C22×Dic53—44no—
191C22×Dic53—48no—
192C22×Dic53—48no—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×D414yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×D414yes—
199C22×Dic53C2×Q814yes—
200C22×Dic53C2×Q814yes—
201C22×Dic53#4114yes—
202C2×Dic106—28no—
203C2×Dic106—48no—
204C2×Dic106—48no—
205C2×Dic106—44no—
206C2×Dic106—44no—
207C4⋊C4×C53—48no—
208C22⋊C4×C53—28no—
209C22⋊C4×C53—28no—
210C22⋊Dic53—28no—
211C22⋊Dic53—28no—
212C4⋊Dic53—28no—
213#11719919—216no—
214#11719919—28no—
215#11719919—28no—
216#11719919—216no—
217#11719919—48no—
218C23×C53—22no—
219C23×C53—24no—
220C23×C53—22no—
221C23×C53—24no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53—24no—
231C23×C53—24no—
232C23×C53—24no—
233C23×C53—24no—
234C23×C53#12014yes—
235C23×C53C22⋊Q814yes—
236C23×C53C22⋊Q814yes—
237C23×C53C22⋊Q814yes—
238C23×C53C4⋊Q814yes—
239C23×C53C4⋊Q814yes—
240C23×C53C4⋊Q814yes—
241C23×C53C22×D411yescharacteristic
242C23×C53C22×D412yes—
243C23×C53C22×D411yescharacteristic
244C23×C53C22×D411yescharacteristic
245C23×C53C22×Q811yescharacteristic
246C23×C53C22×Q811yescharacteristic
247C23×C53C22×Q811yescharacteristic
248C23×C53C2×#4112yes—
249C23×C53C2×#4111yescharacteristic
250C23×C53H(5,𝔽2)12yes—
251C23×C532−1+412yes—
252C2×C4×C53—22no—
253C2×C4×C53—24no—
254C2×C4×C53—22no—
255C2×C4×C53—24no—
256C2×C4×C53—24no—
257C2×C4×C53—24no—
258C2×C4×C53—24no—
259C2×C4×C53—24no—
260C2×C4×C53—24no—
261C2×C4×C53—24no—
262C2×C4×C53—416no—
263C2×C4×C53—41no—
264C2×C4×C53—42no—
265C2×C4×C53—41no—
266C2×C4×C53—42no—
267C2×C4×C53—41no—
268C2×C4×C53—42no—
269C2×C4×C53—41no—
270C2×C4×C53—42no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—42no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×Dic53—232no—
278C2×Dic53—22no—
279C2×Dic53—24no—
280C2×Dic53—24no—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—24no—
285C2×Dic53—22no—
286C2×Dic53—24no—
287C2×Dic53—24no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—24no—
293C2×Dic53—22no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—416no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—42no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53#12014yes—
312C2×Dic53C22⋊Q818yescomplemented
313Dic106—416no—
314#14720—531nomaximal, Sylow
315C22×C53—24no—
316C22×C53—24no—
317C22×C53—24no—
318C22×C53—24no—
319C22×C53—24no—
320C22×C53—24no—
321C22×C53—28no—
322C22×C53—28no—
323C22×C53—28no—
324C22×C53—28no—
325C22×C53#39518yescomplemented
326C22×C53C2×#12011yescharacteristic
327C22×C53C2×#12011yescharacteristic
328C22×C53C2×C22⋊Q812yes—
329C22×C53C2×C22⋊Q811yescharacteristic
330C22×C53C2×C22⋊Q811yescharacteristic
331C22×C53C2×C22⋊Q811yescharacteristic
332C22×C53#52511yescharacteristic
333C22×C53#52512yes—
334C22×C53C2×C4⋊Q811yescharacteristic
335C22×C53C2×C4⋊Q811yescharacteristic
336C22×C53C2×C4⋊Q811yescharacteristic
337C22×C53#53411yescharacteristic
338C22×C53#53611yescharacteristic
339C22×C53#53912yes—
340C22×C53#54412yes—
341C22×C53D4212yes—
342C22×C53D4212yes—
343C22×C53#54712yes—
344C22×C53#54712yes—
345C22×C53D4×Q812yes—
346C22×C53D4×Q812yes—
347C22×C53#55412yes—
348C22×C53#55412yes—
349C4×C53—42no—
350C4×C53—44no—
351C4×C53—42no—
352C4×C53—44no—
353Dic53—28no—
354Dic53—24no—
355Dic53—42no—
356Dic53—42no—
357Dic53—42no—
358Dic53—44no—
359C22×C22⋊Q8—531no—
360C23×C4⋊C4—531no—
361C2×#395—532no—
362C2×#385—531no—
363C2×#385D5311yescharacteristic
364#1444—532no—
365#1444—532no—
366#1441—532no—
367C22⋊#95—531no—
368C22⋊#95—531no—
369C22⋊#95—531no—
370C2×C53—28no—
371C2×C53C2×#39511yescharacteristic
372C2×C53#240311yescharacteristic
373C2×C53#240611yescharacteristic
374C2×C53#243411yescharacteristic
375C2×C53#244012yes—
376C2×C53#244012yes—
377C2×C53#244912yes—
378C2×C53#244912yes—
379C2×C53#258311yescharacteristic
380C2×C53#262711yescharacteristic
381C2×C53#284811yescharacteristic
382C23×Q8—531no—
383C24×C4—531no—
384C24×C4—531no—
385C24×C4C2×D5311yescharacteristic
386C2×C22⋊Q8—1064no—
387C2×C22⋊Q8—1064no—
388C2×C22⋊Q8—1064no—
389C22×C4⋊C4—532no—
390C22×C4⋊C4—532no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394C22×C4⋊C4—532no—
395C22×C4⋊C4—1068no—
396C22×C4⋊C4—1064no—
397C22×C4⋊C4C2×D5312yes—
398C22×C22⋊C4—531no—
399C22×C22⋊C4—531no—
400C22×C22⋊C4C2×D5311yescharacteristic
401C22×C22⋊C4C2×D5311yescharacteristic
402#395—1068no—
403#385—24no—
404#385—1064no—
405C2×#95—532no—
406C2×#95—532no—
407C2×#95—532no—
408C2×#95—532no—
409C2×#95—532no—
410C2×#95—532no—
411C2×#95—532no—
412C2×#95C2×D5312yes—
413C53#1472011yescharacteristic, complemented, Sylow
414C25C22×D5311yescharacteristic
415C22×Q8—1062no—
416C22×Q8—1062no—
417C22×Q8—1064no—
418C22×Q8—1062no—
419C22×Q8—2122no—
420C23×C4—22no—
421C23×C4—24no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4—531no—
426C23×C4—532no—
427C23×C4—534no—
428C23×C4—531no—
429C23×C4—531no—
430C23×C4—532no—
431C23×C4—531no—
432C23×C4—534no—
433C23×C4—1064no—
434C23×C4—1064no—
435C23×C4—1064no—
436C23×C4—1062no—
437C23×C4—1062no—
438C23×C4—1062no—
439C23×C4—1062no—
440C23×C4—2122no—
441C23×C4C22×D5312yes—
442C23×C4C22×D5312yes—
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C22⋊Q8—10632no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—538no—
450C2×C4⋊C4—1064no—
451C2×C4⋊C4—1064no—
452C2×C4⋊C4—1064no—
453C2×C4⋊C4—1064no—
454C2×C4⋊C4—1062no—
455C2×C4⋊C4—1062no—
456C2×C4⋊C4—1062no—
457C2×C4⋊C4—1062no—
458C2×C4⋊C4—1062no—
459C2×C4⋊C4—1062no—
460C2×C4⋊C4—10632no—
461C2×C4⋊C4—1064no—
462C2×C4⋊C4—1062no—
463C2×C4⋊C4—1062no—
464C2×C4⋊C4—1062no—
465C2×C4⋊C4—1064no—
466C2×C4⋊C4—1064no—
467C2×C4⋊C4—2122no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—534no—
474C2×C22⋊C4—1062no—
475C2×C22⋊C4—1062no—
476C2×C22⋊C4—1062no—
477C2×C22⋊C4—1062no—
478C2×C22⋊C4Dic10614yescomplemented
479C2×C22⋊C4C22⋊D5314yes—
480#95—24no—
481#95—1064no—
482#95—1064no—
483#95—1064no—
484#95—1064no—
485#95—1064no—
486#95—1064no—
487#95—2122no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C2×Dic10612yes—
493C24#1171994512yes—
494C24D4×D5312yes—
495C24D4×D5312yes—
496C24Q8×D5312yes—
497C24Q8×D5312yes—
498C24C2×C22⋊D5312yes—
499C24C23×D5311yescharacteristic
500C2×Q8—1068no—
501C2×Q8—2128no—
502C2×Q8—2124no—
503C2×Q8—2128no—
504C2×Q8—2124no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—534no—
531C22×C4—534no—
532C22×C4—532no—
533C22×C4—534no—
534C22×C4—534no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—534no—
539C22×C4—10616no—
540C22×C4—1068no—
541C22×C4—1068no—
542C22×C4—1068no—
543C22×C4—10616no—
544C22×C4—1068no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1068no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1062no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—2124no—
572C22×C4—2128no—
573C22×C4—2128no—
574C22×C4C2×Dic10614yes—
575C22×C4D4×D5314yes—
576C22×C4C2×C22⋊D5312yes—
577C22×C4C2×C22⋊D5312yes—
578C4⋊C4—48no—
579C4⋊C4—10616no—
580C4⋊C4—10616no—
581C4⋊C4—1068no—
582C4⋊C4—1068no—
583C4⋊C4—1068no—
584C4⋊C4—2128no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1068no—
588C22⋊C4—1068no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—24no—
597C23—22no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23#1313318514yes—
606C23#1313319514yes—
607C23#1313319514yes—
608C23#1313319614yes—
609C23#1313321514yes—
610C23#1313321614yes—
611C23#1313321614yes—
612C23C2×D4×D5311yescharacteristic
613C23C2×D4×D5312yes—
614C23C2×D4×D5311yescharacteristic
615C23C22×C22⋊D5311yescharacteristic
616C23C2×Q8×D5311yescharacteristic
617C23C2×Q8×D5311yescharacteristic
618C23C22×Dic10611yescharacteristic
619C23#41×D5312yes—
620C23C2×#1171994511yescharacteristic
621C23#1313326212yes—
622C23#1313326412yes—
623Q8—21216no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—416no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—534no—
650C2×C4—538no—
651C2×C4—10632no—
652C2×C4—1064no—
653C2×C4—1062no—
654C2×C4—1064no—
655C2×C4—1064no—
656C2×C4—1064no—
657C2×C4—1064no—
658C2×C4—1064no—
659C2×C4—1062no—
660C2×C4—1064no—
661C2×C4—1064no—
662C2×C4—1064no—
663C2×C4—1064no—
664C2×C4—1064no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1064no—
670C2×C4—1062no—
671C2×C4—1064no—
672C2×C4—21216no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2122no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—24no—
690C22—28no—
691C22—28no—
692C22—24no—
693C22—28no—
694C22—28no—
695C22#1681054318yescomplemented
696C22#120×D5311yescharacteristic
697C22C2×#1313318511yescharacteristic
698C22C22⋊Q8×D5312yes—
699C22C2×#1313319511yescharacteristic
700C22C2×#1313319511yescharacteristic
701C22C2×#1313319611yescharacteristic
702C22#1681113111yescharacteristic
703C22#1681113212yes—
704C22C2×#1313321511yescharacteristic
705C22C2×#1313321611yescharacteristic
706C22C2×#1313321611yescharacteristic
707C22#1681118311yescharacteristic
708C22#1681119511yescharacteristic
709C22#1681121512yes—
710C22#1681125212yes—
711C22#1681125512yes—
712C22D4×C22⋊D5312yes—
713C22#1681127112yes—
714C22#1681127212yes—
715C22#1681128612yes—
716C22D4×Dic10612yes—
717C22#1681132712yes—
718C22#1681133212yes—
719C4—44no—
720C4—42no—
721C4—42no—
722C4—44no—
723C4—1064no—
724C4—1068no—
725C4—2122no—
726C4—2122no—
727C4—2122no—
728C4—2124no—
729C2—28no—
730C2C2×#1681054311yescharacteristic
731C2#2027802611yescharacteristic
732C2#2027804711yescharacteristic
733C2#2027835711yescharacteristic
734C2#2027841412yes—
735C2#2027841612yes—
736C2#2027851812yes—
737C2#2027852612yes—
738C2#2028009411yescharacteristic
739C2#2028053411yescharacteristic
740C2#2028300111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC2×C53×#385C2
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53#14720
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×#16810543C2semidirect
5. #20272979C2semidirect
6. #20272978C2semidirect
7. #20272966C2semidirect
57. C23×Dic53Q8semidirect
89. C2×C22⋊Dic53Q8semidirect
115. C2×C22⋊C4×C53Q8semidirect
312. C2×Dic53C22⋊Q8semidirect
325. C22×C53#395semidirect
413. C53#14720semidirect
478. C2×C22⋊C4Dic106semidirect
695. C22#16810543semidirect

Maximal subgroups

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

subgroupindex
C22×#131331942
C23×#117199192
C2×#168105432
C2×#168104962
#202729792
#202729782
#202729662
#202729372
C2×C53×#3852
#1472053