Finite Group Databasebeta

← #27315382

Subgroups — #27315382

Order 13568.

2734 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133194C211yesmaximal, characteristic
2C23×C4×Dic53C211yesmaximal, characteristic
3C2×#16810527C212yesmaximal, complemented
4C2×#16810481C211yesmaximal, characteristic
5#20272949C212yesmaximal, complemented
6#20272946C212yesmaximal, complemented
7#20272943C212yesmaximal, complemented
8#20272938C211yesmaximal, characteristic
9#20272937C211yesmaximal, characteristic
10#20272937C211yesmaximal, characteristic
11C53×C22⋊#95C211yesmaximal, characteristic
12C23×Dic106C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C24×Dic53C2211yescharacteristic
15C2×#13133194—24no—
16C2×#13133194—24no—
17C2×#13133194C418yescomplemented
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C4×Dic53—24no—
25C22×C4×Dic53—28no—
26C22×C4×Dic53C2212yes—
27C22×C4×Dic53C2212yes—
28#16810527—28no—
29#16810481—24no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C24×C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C22×Dic106—24no—
43C22×Dic106—22no—
44C22×Dic106—22no—
45C22×Dic106—24no—
46C22×Dic106C2×C414yescomplemented
47C23×Dic53—22no—
48C23×Dic53—22no—
49C23×Dic53—24no—
50C23×Dic53—24no—
51C23×Dic53—24no—
52C23×Dic53—24no—
53C23×Dic53C2×C414yes—
54C23×Dic53D414yes—
55C23×Dic53D414yes—
56C23×Dic53Q814yescomplemented
57C23×Dic53C2312yes—
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2312yes—
62C23×Dic53C2311yescharacteristic
63#13133194—232no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53C2×C414yescomplemented
67C2×#11719919—22no—
68C2×#11719919—22no—
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919—24no—
72C2×#11719919—24no—
73C2×#11719919—24no—
74C2×#11719919C2×C414yescomplemented
75C2×#11719919C2×C414yescomplemented
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—22no—
78C2×C22⋊Dic53—22no—
79C2×C22⋊Dic53—22no—
80C2×C22⋊Dic53—22no—
81C2×C22⋊Dic53C2×C414yes—
82C2×C4×Dic53—232no—
83C2×C4×Dic53—24no—
84C2×C4×Dic53—24no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53—24no—
88C2×C4×Dic53D418yes—
89#13133124—24no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96C25×C53C2311yescharacteristic
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—24no—
100C23×C4×C53—24no—
101C23×C4×C53Q814yescomplemented
102C23×C4×C53C2312yes—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53C2×C414yes—
112#95×C53—24no—
113#95×C53—24no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53C22×C412yes—
119C24×C53C2×D412yes—
120C24×C53C2×D412yes—
121C24×C53C2×Q812yes—
122C24×C53C2×Q812yes—
123C24×C53#4112yes—
124C24×C53#4112yes—
125C24×C53C2411yescharacteristic
126C22×C4×C53—216no—
127C22×C4×C53—28no—
128C22×C4×C53—28no—
129C22×C4×C53—28no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—216no—
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—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53C22×C412yes—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C2×D414yes—
153C22×C4×C53C2×Q814yes—
154C22×C4×C53#4114yes—
155C22×Dic53—28no—
156C22×Dic53—216no—
157C22×Dic53—28no—
158C22×Dic53—28no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—216no—
166C22×Dic53—28no—
167C22×Dic53—216no—
168C22×Dic53—216no—
169C22×Dic53—28no—
170C22×Dic53—22no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
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—22no—
185C22×Dic53C22⋊C4116yes—
186C22×Dic53C22×C412yes—
187C22×Dic53C22×C412yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C22×C412yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×D414yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D414yes—
196C22×Dic53C2×Q814yes—
197C22×Dic53#4114yes—
198C22×Dic53#4114yes—
199C2×Dic106—28no—
200C2×Dic106—216no—
201C2×Dic106—44no—
202C2×Dic106—48no—
203C2×Dic106—44no—
204C22⋊C4×C53—28no—
205C22⋊C4×C53—44no—
206C22⋊Dic53—28no—
207C22⋊Dic53—44no—
208C4⋊Dic53—28no—
209#11719919—28no—
210#11719919—28no—
211#11719919—48no—
212C4×Dic53—216no—
213C4×Dic53—216no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—22no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—24no—
223C23×C53—22no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—24no—
229C23×C53—24no—
230C23×C53C2×C22⋊C414yes—
231C23×C53C4×Q814yes—
232C23×C53C4×Q814yes—
233C23×C53C22⋊Q814yes—
234C23×C53C22⋊Q814yes—
235C23×C53#12414yes—
236C23×C53C4⋊Q814yes—
237C23×C53C23×C411yescharacteristic
238C23×C53C22×D411yescharacteristic
239C23×C53C22×D411yescharacteristic
240C23×C53C22×D412yes—
241C23×C53C22×Q811yescharacteristic
242C23×C53C22×Q811yescharacteristic
243C23×C53C2×#4112yes—
244C23×C53C2×#4112yes—
245C23×C53C2×#4111yescharacteristic
246C23×C53C2×#4112yes—
247C23×C53C2×#4111yescharacteristic
248C2×C4×C53—232no—
249C2×C4×C53—24no—
250C2×C4×C53—24no—
251C2×C4×C53—24no—
252C2×C4×C53—24no—
253C2×C4×C53—24no—
254C2×C4×C53—24no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—24no—
258C2×C4×C53—24no—
259C2×C4×C53—41no—
260C2×C4×C53—42no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—42no—
265C2×C4×C53—42no—
266C2×C4×C53—42no—
267C2×C4×C53—42no—
268C2×C4×C53—42no—
269C2×C4×C53—42no—
270C2×C4×C53—42no—
271C2×C4×C53—42no—
272C2×C4×C53C22⋊Q818yescomplemented
273C2×Dic53—232no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—22no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—22no—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—24no—
284C2×Dic53—232no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—24no—
288C2×Dic53—24no—
289C2×Dic53—41no—
290C2×Dic53—42no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
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×Dic53C2×C22⋊C414yes—
303C2×Dic53C2×C22⋊C414yes—
304C2×Dic53C4×D418yes—
305C2×Dic53#12014yes—
306C2×Dic53#12118yes—
307C2×Dic53C22⋊Q818yescomplemented
308C2×Dic53#12314yes—
309Dic106—416no—
310#14702—531nomaximal, Sylow
311C22×C53—24no—
312C22×C53—24no—
313C22×C53—28no—
314C22×C53—24no—
315C22×C53—24no—
316C22×C53—28no—
317C22×C53—24no—
318C22×C53—24no—
319C22×C53—28no—
320C22×C53—28no—
321C22×C53#39118yescomplemented
322C22×C53C22×C22⋊C411yescharacteristic
323C22×C53C2×C4×D412yes—
324C22×C53C2×C4×Q811yescharacteristic
325C22×C53C2×C4×Q811yescharacteristic
326C22×C53C4×#4112yes—
327C22×C53C2×#12011yescharacteristic
328C22×C53C2×#12112yes—
329C22×C53C2×C22⋊Q812yes—
330C22×C53C2×C22⋊Q811yescharacteristic
331C22×C53C2×C22⋊Q812yes—
332C22×C53C2×C22⋊Q811yescharacteristic
333C22×C53C2×#12311yescharacteristic
334C22×C53#52512yes—
335C22×C53#52511yescharacteristic
336C22×C53#52511yescharacteristic
337C22×C53#52512yes—
338C22×C53C2×#12411yescharacteristic
339C22×C53#52912yes—
340C22×C53#52912yes—
341C22×C53C2×C4⋊Q811yescharacteristic
342C22×C53#53212yes—
343C22×C53#53312yes—
344C22×C53#53312yes—
345C4×C53—28no—
346C4×C53—42no—
347C4×C53—42no—
348C4×C53—82no—
349Dic53—28no—
350Dic53—24no—
351Dic53—42no—
352Dic53—42no—
353Dic53—82no—
354Dic53#38618yes—
355C22×C22⋊Q8—531no—
356C23×C42—531no—
357C2×#391—532no—
358C2×#380—531no—
359#1436—532no—
360#1436—532no—
361C4⋊#95—532no—
362C22⋊#95—531no—
363C22⋊#95—531no—
364C22⋊#95—531no—
365C22⋊#95D5311yescharacteristic
366C2×C53—28no—
367C2×C53C2×#38611yescharacteristic
368C2×C53C2×#39111yescharacteristic
369C2×C53#229711yescharacteristic
370C2×C53C4×C22⋊Q812yes—
371C2×C53C4×C22⋊Q812yes—
372C2×C53#284811yescharacteristic
373C2×C53#284811yescharacteristic
374C2×C53#285012yes—
375C2×C53#285511yescharacteristic
376C2×C53#285511yescharacteristic
377C2×C53#285712yes—
378C23×Q8—531no—
379C24×C4—531no—
380C24×C4—531no—
381C24×C4C2×D5311yescharacteristic
382C2×C22⋊Q8—538no—
383C2×C22⋊Q8—1064no—
384C2×C22⋊Q8—1064no—
385C22×C4⋊C4—531no—
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—532no—
389C22×C22⋊C4—531no—
390C22×C22⋊C4—531no—
391C22×C22⋊C4C2×D5311yescharacteristic
392C22×C22⋊C4C2×D5311yescharacteristic
393C22×C42—532no—
394C22×C42—532no—
395C22×C42—1068no—
396C22×C42—1064no—
397#391—1068no—
398#380—1064no—
399C2×#95—532no—
400C2×#95—532no—
401C2×#95—532no—
402C2×#95—532no—
403C2×#95—532no—
404C2×#95—532no—
405C2×#95—532no—
406C2×#95C2×D5312yes—
407C2×#95C2×D5312yes—
408C53#1470211yescharacteristic, complemented, Sylow
409C25C22×D5311yescharacteristic
410C22×Q8—534no—
411C22×Q8—1062no—
412C22×Q8—1062no—
413C22×Q8—1064no—
414C22×Q8—1064no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—531no—
420C23×C4—534no—
421C23×C4—534no—
422C23×C4—534no—
423C23×C4—531no—
424C23×C4—532no—
425C23×C4—534no—
426C23×C4—531no—
427C23×C4—531no—
428C23×C4—532no—
429C23×C4—1064no—
430C23×C4—1064no—
431C23×C4—1064no—
432C23×C4—1064no—
433C23×C4—1062no—
434C23×C4—1062no—
435C23×C4Dic10614yescomplemented
436C23×C4C22×D5312yes—
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5311yescharacteristic
439C23×C4C22×D5312yes—
440C22⋊Q8—10632no—
441C2×C4⋊C4—534no—
442C2×C4⋊C4—534no—
443C2×C4⋊C4—534no—
444C2×C4⋊C4—1062no—
445C2×C4⋊C4—1062no—
446C2×C4⋊C4—1062no—
447C2×C4⋊C4—1062no—
448C2×C4⋊C4—1062no—
449C2×C4⋊C4—1062no—
450C2×C4⋊C4—1064no—
451C2×C4⋊C4—1064no—
452C2×C4⋊C4—1064no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—534no—
459C2×C22⋊C4—1062no—
460C2×C22⋊C4—1062no—
461C2×C22⋊C4—1062no—
462C2×C22⋊C4—1062no—
463C2×C22⋊C4—1062no—
464C2×C22⋊C4C4×D5314yes—
465C2×C42—538no—
466C2×C42—1064no—
467C2×C42—1064no—
468C2×C42—1064no—
469C2×C42—1064no—
470C2×C42—10632no—
471C2×C42—1064no—
472#95—24no—
473#95—24no—
474#95—1064no—
475#95—1064no—
476#95—1064no—
477#95—1064no—
478#95—1064no—
479#95—1064no—
480#95—1064no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24C2×Dic10612yes—
486C24C2×C4×D5312yes—
487C24#1171994512yes—
488C24D4×D5312yes—
489C24D4×D5312yes—
490C24#1171994712yes—
491C24Q8×D5312yes—
492C24C23×D5311yescharacteristic
493C2×Q8—1068no—
494C2×Q8—10616no—
495C2×Q8—2124no—
496C2×Q8—2128no—
497C2×Q8—2124no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—216no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
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—532no—
523C22×C4—534no—
524C22×C4—532no—
525C22×C4—532no—
526C22×C4—534no—
527C22×C4—5316no—
528C22×C4—532no—
529C22×C4—534no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—534no—
533C22×C4—534no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—1068no—
537C22×C4—10616no—
538C22×C4—10616no—
539C22×C4—1068no—
540C22×C4—10616no—
541C22×C4—1068no—
542C22×C4—1068no—
543C22×C4—10616no—
544C22×C4—1068no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4C2×Dic10614yes—
567C22×C4C2×C4×D5312yes—
568C22×C4C2×C4×D5312yes—
569C22×C4D4×D5314yes—
570C22×C4#1171994714yes—
571C4⋊C4—1068no—
572C4⋊C4—1068no—
573C4⋊C4—1068no—
574C4⋊C4—2128no—
575C22⋊C4—28no—
576C22⋊C4—44no—
577C22⋊C4—1068no—
578C22⋊C4—2124no—
579C42—10616no—
580C42—10616no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23C22⋊C4×D5314yes—
598C23#1313318214yes—
599C23C4×Dic10614yes—
600C23#1313319414yes—
601C23#1313319514yes—
602C23#1313320314yes—
603C23#1313321614yes—
604C23C22×C4×D5311yescharacteristic
605C23C2×D4×D5311yescharacteristic
606C23C2×D4×D5311yescharacteristic
607C23C2×D4×D5312yes—
608C23C2×Q8×D5311yescharacteristic
609C23C22×Dic10611yescharacteristic
610C23#41×D5312yes—
611C23#41×D5312yes—
612C23C2×#1171994711yescharacteristic
613C23C2×#1171994712yes—
614C23C2×#1171994511yescharacteristic
615Q8—21216no—
616C2×C4—232no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—534no—
641C2×C4—538no—
642C2×C4—534no—
643C2×C4—538no—
644C2×C4—534no—
645C2×C4—534no—
646C2×C4—538no—
647C2×C4—10632no—
648C2×C4—10632no—
649C2×C4—1064no—
650C2×C4—1064no—
651C2×C4—1062no—
652C2×C4—1064no—
653C2×C4—1064no—
654C2×C4—1064no—
655C2×C4—1062no—
656C2×C4—1064no—
657C2×C4—1064no—
658C2×C4—1064no—
659C2×C4—1062no—
660C2×C4—1062no—
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—2121no—
671C2×C4—2122no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2122no—
676C2×C4#1313319418yescomplemented
677C22—24no—
678C22—24no—
679C22—28no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—28no—
684C22—24no—
685C22—28no—
686C22—28no—
687C22#1681052718yescomplemented
688C22C2×C22⋊C4×D5311yescharacteristic
689C22C4×D4×D5312yes—
690C22C2×#1313318211yescharacteristic
691C22C2×C4×Dic10611yescharacteristic
692C22C4×#1171994712yes—
693C22#120×D5311yescharacteristic
694C22#121×D5312yes—
695C22C22⋊Q8×D5312yes—
696C22C2×#1313319411yescharacteristic
697C22C2×#1313319412yes—
698C22C2×#1313319511yescharacteristic
699C22#123×D5311yescharacteristic
700C22#1681112912yes—
701C22#1681112911yescharacteristic
702C22#1681113111yescharacteristic
703C22#1681113212yes—
704C22C2×#1313320311yescharacteristic
705C22#1681115012yes—
706C22#1681115312yes—
707C22C2×#1313321611yescharacteristic
708C22#1681116812yes—
709C22#1681117512yes—
710C22#1681117612yes—
711C4—28no—
712C4—42no—
713C4—42no—
714C4—82no—
715C4—538no—
716C4—1068no—
717C4—1064no—
718C4—4242no—
719C4—2122no—
720C4—2122no—
721C2—28no—
722C2#386×D5311yescharacteristic
723C2C2×#1681052711yescharacteristic
724C2#2027720011yescharacteristic
725C2C4×#1313319412yes—
726C2#2027724712yes—
727C2#2028300011yescharacteristic
728C2#2028300111yescharacteristic
729C2#2028301212yes—
730C2#2028305111yescharacteristic
731C2#2028305211yescharacteristic
732C2#2028306512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22⋊#95D53
hypocenterC53#14702
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16810527C2semidirect
5. #20272949C2semidirect
6. #20272946C2semidirect
7. #20272943C2semidirect
17. C2×#13133194C4semidirect
46. C22×Dic106C2×C4semidirect
56. C23×Dic53Q8semidirect
66. C2×C4⋊Dic53C2×C4semidirect
74. C2×#11719919C2×C4semidirect
75. C2×#11719919C2×C4semidirect
101. C23×C4×C53Q8semidirect
272. C2×C4×C53C22⋊Q8semidirect
307. C2×Dic53C22⋊Q8semidirect
321. C22×C53#391semidirect
408. C53#14702semidirect
435. C23×C4Dic106semidirect
676. C2×C4#13133194semidirect
687. C22#16810527semidirect

Maximal subgroups

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

subgroupindex
C22×#131331942
C23×C4×Dic532
C2×#168105272
C2×#168104812
#202729492
#202729462
#202729432
#202729382
#202729372
C53×C22⋊#952
#1470253