Finite Group Databasebeta

← #27441271

Subgroups — #27441271

Order 13568.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810911C211yesmaximal, characteristic, complemented
2C22×#13133138C211yesmaximal, characteristic
3#20278418C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic53C211yesmaximal, characteristic
5#20276246C211yesmaximal, characteristic, complemented
6#20276087C211yesmaximal, characteristic, complemented
7#20276085C211yesmaximal, characteristic, complemented
8#20275849C211yesmaximal, characteristic, complemented
9#20274978C211yesmaximal, characteristic, complemented
10#20274974C211yesmaximal, characteristic, complemented
11#20274910C211yesmaximal, characteristic, complemented
12#20274892C211yesmaximal, characteristic, complemented
13#20274738C211yesmaximal, characteristic, complemented
14#20274713C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C2×#13133216C2211yescharacteristic, complemented
18C2×#13133194—21no—
19C2×D4×Dic53C2211yescharacteristic
20C2×D4×Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53—21no—
23#16810911—24no—
24C2×#13133149C2211yescharacteristic, complemented
25C2×#13133149C2211yescharacteristic, complemented
26C2×#13133148C2211yescharacteristic, complemented
27C2×#13133148C2211yescharacteristic, complemented
28C2×#13133146C2211yescharacteristic, complemented
29C2×#13133146C2211yescharacteristic, complemented
30C2×#13133138—24no—
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35#16810557—21no—
36#16810544—21no—
37#16810526C2211yescharacteristic
38#16810526C2211yescharacteristic
39#16810522C2211yescharacteristic, complemented
40#16810519C2211yescharacteristic, complemented
41#16810503—21no—
42#16810503—21no—
43#16810495—21no—
44#16810492C2211yescharacteristic, complemented
45#16810483C2211yescharacteristic
46#16810479—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic, complemented
49#16810386C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C23×D4×C53C2211yescharacteristic
55C2×#102×C53C2211yescharacteristic
56C2×#102×C53C2211yescharacteristic
57C2×#102×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C22×Dic106—21no—
62C23×Dic53—21no—
63C23×Dic53—21no—
64C23×Dic53—21no—
65C22×#88322—22no—
66C22×#88322—22no—
67C22×#88322—41no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133216—22no—
71#13133216—41no—
72#13133194—44no—
73D4×Dic53—22no—
74D4×Dic53—22no—
75D4×Dic53—41no—
76D4×Dic53—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53—22no—
80C2×C4⋊Dic53—41no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×#11719919—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C22⋊Dic53—21no—
96C2×C22⋊Dic53—44no—
97C2×C22⋊Dic53D411yescharacteristic
98C2×C22⋊Dic53D411yescharacteristic
99C2×C4×Dic53C2311yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101#13133149—22no—
102#13133149—41no—
103#13133148—22no—
104#13133148—41no—
105#13133146—22no—
106#13133146—41no—
107#13133138—22no—
108#13133138—22no—
109#13133138—22no—
110#13133138D414yes—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124D411yescharacteristic
115#13133124D411yescharacteristic
116C25×C53—21no—
117C22×D4×C53—22no—
118C22×D4×C53—22no—
119C22×D4×C53—21no—
120C22×D4×C53—22no—
121C22×D4×C53—41no—
122C22×D4×C53—41no—
123C22×D4×C53Q814yescomplemented
124C22×D4×C53C2311yescharacteristic
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C22⋊C4×C53—21no—
132#102×C53—22no—
133#102×C53—22no—
134#102×C53—41no—
135#102×C53—41no—
136C22⋊C8×C53—22no—
137#95×C53—21no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—24no—
141C24×C53—42no—
142C24×C53—42no—
143C24×C53—42no—
144C24×C53—42no—
145C24×C53—81no—
146C24×C53—81no—
147C24×C53C2×D411yescharacteristic
148C2×D4×C53—28no—
149C2×D4×C53—24no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—44no—
159C2×D4×C53—44no—
160C2×D4×C53—44no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53C2×D412yes—
164C2×D4×C53C2×Q812yes—
165C2×D4×C53C2×Q812yes—
166C2×D4×C53#4112yes—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×Q812yes—
175C22×C4×C53#4112yes—
176C22×C4×C53C2411yescharacteristic
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—42no—
182C22×Dic53—42no—
183C22×Dic53—42no—
184C22×Dic53—42no—
185C22×Dic53—42no—
186C22×Dic53—42no—
187C22×Dic53—81no—
188C22×Dic53—81no—
189C22×Dic53—81no—
190C22×Dic53C2×D411yescharacteristic
191C22×Dic53C2×D411yescharacteristic
192C22×Dic53C2×D411yescharacteristic
193C22×Dic53C2×D411yescharacteristic
194C2×Dic106—42no—
195C2×Dic106—42no—
196C2×Dic106—81no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C22⋊C4×C53—42no—
208C22⋊Dic53—22no—
209C22⋊Dic53—42no—
210C22⋊Dic53—42no—
211C22⋊Dic53—42no—
212C22⋊Dic53—42no—
213C22⋊Dic53—42no—
214C22⋊Dic53—81no—
215C22⋊Dic53—81no—
216C22⋊Dic53SD1614yes—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—42no—
225C4⋊Dic53—42no—
226C4⋊Dic53C2×D412yes—
227#11719919—42no—
228#11719919—42no—
229#11719919—42no—
230#11719919—81no—
231C4×Dic53—21no—
232C4×Dic53—21no—
233C4×Dic53—21no—
234C4×Dic53—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—44no—
241C2×#88322C2×D412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—48no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—48no—
262C23×C53—84no—
263C23×C53—84no—
264C23×C53—84no—
265C23×C53—84no—
266C23×C53—84no—
267C23×C53C22⋊Q812yes—
268C23×C53C2×SD1612yes—
269C23×C53AGL(1,ℤ/8)12yes—
270C23×C53C22×D411yescharacteristic
271D4×C53—22no—
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—22no—
275D4×C53—22no—
276D4×C53—48no—
277D4×C53—41no—
278D4×C53—41no—
279D4×C53C22⋊Q814yescomplemented
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53C22⋊Q812yes—
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C22×Q811yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—22no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—84no—
322C2×Dic53—84no—
323C2×Dic53—84no—
324C2×Dic53C2×SD1612yes—
325C2×Dic53C2×SD1612yes—
326Dic106—84no—
327C8×C53—41no—
328C8×C53—41no—
329#88322—22no—
330#88322—41no—
331#25958—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—24no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—816no—
349C22×C53—81no—
350C22×C53—81no—
351C22×C53—81no—
352C22×C53—81no—
353C22×C53#47614yescomplemented
354C22×C53C2×C22⋊Q811yescharacteristic
355C22×C53D4211yescharacteristic
356C22×C53#54611yescharacteristic
357C22×C53C22×SD1611yescharacteristic
358C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C53#57611yescharacteristic
360C22×C53#57711yescharacteristic
361C4×C53—22no—
362C4×C53—81no—
363C4×C53—81no—
364C4×C53C2×C22⋊Q811yescharacteristic
365C4×C53#54311yescharacteristic
366C4×C53#54611yescharacteristic
367C4×C53#55111yescharacteristic
368Dic53—22no—
369Dic53—22no—
370Dic53—41no—
371Dic53—42no—
372Dic53—41no—
373Dic53—81no—
374Dic53—81no—
375Dic53—81no—
376C2×#476—531no—
377C22×#102—531no—
378#2440—531no—
379D4×C22⋊C4—531no—
380#2094—531no—
381#2065—531no—
382#2065—531no—
383#2023—531no—
384#1864—531no—
385#1864—531no—
386#1853—531no—
387#1850—531no—
388#1807—531no—
389#1802—531no—
390#1786D5311yescharacteristic
391C2×C53—24no—
392C2×C53—44no—
393C2×C53—82no—
394C2×C53#243711yescharacteristic
395C2×C53C2×#47611yescharacteristic
396C2×C53#308111yescharacteristic
397C2×C53#326411yescharacteristic
398C2×C53D4×SD1611yescharacteristic
399C2×C53#329511yescharacteristic
400C2×C53#330611yescharacteristic
401C23×D4C2×D5311yescharacteristic
402C23×C8—531no—
403C2×C4⋊Q8—531no—
404C2×C22⋊Q8—1061no—
405C2×C4×D4—531no—
406C2×C4×D4—531no—
407C22×C4⋊C4—531no—
408C22×C22⋊C4—1061no—
409#476—1064no—
410C2×#106—531no—
411C2×#106—531no—
412C2×#106—531no—
413C2×#106—531no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×#102—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×#102—531no—
420C2×#102—1064no—
421C2×#102C2×D5311yescharacteristic
422C2×#102C2×D5311yescharacteristic
423C2×#102C2×D5311yescharacteristic
424C2×#102C2×D5311yescharacteristic
425C2×C22⋊C8C2×D5311yescharacteristic
426#398—1061no—
427#395—1061no—
428#390—531no—
429#390—531no—
430#389—531no—
431#389—531no—
432#386—1061no—
433#386—1061no—
434#385—1061no—
435#384—531no—
436#380—531no—
437#380C2×D5311yescharacteristic
438#379—1061no—
439C4×C22⋊C4—531no—
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#336—531no—
445#336—531no—
446C53#2595811yescharacteristic, complemented, Sylow
447C25—21no—
448C22×Q8—1061no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4Dic10614yescomplemented
456C22×D4C22×D5311yescharacteristic
457C22×D4C22×D5311yescharacteristic
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4C22×D5311yescharacteristic
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—1062no—
465C22×C8—1062no—
466C22×C8—2121no—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C4⋊Q8—1062no—
470C4⋊Q8—2121no—
471C22⋊Q8—2124no—
472C4×D4—1062no—
473C4×D4—1062no—
474C4×D4—2121no—
475C4×D4—2121no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—1062no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—2121no—
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—2124no—
501C2×C42—531no—
502C2×C42—531no—
503#106—1062no—
504#106—1062no—
505#106—2121no—
506#106—2121no—
507C4⋊C8—1062no—
508C4⋊C8—2121no—
509#102—22no—
510#102—22no—
511#102—41no—
512#102—41no—
513#102—534no—
514#102—1062no—
515#102—1062no—
516#102—1062no—
517C22⋊C8—22no—
518#95—21no—
519#95—531no—
520#95—531no—
521#95—1061no—
522#95—1061no—
523#95—1061no—
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24D4×D5311yescharacteristic
534C2×Q8—4241no—
535C2×Q8—2122no—
536C2×Q8—2122no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic10612yes—
553C2×D4C2×Dic10612yes—
554C2×D4D4×D5312yes—
555C2×D4#1171994712yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—531no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—531no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—4241no—
571C22×C4—4241no—
572C22×C4—4241no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4—2122no—
576C22×C4—2122no—
577C22×C4—2122no—
578C22×C4—2122no—
579C22×C4C2×Dic10612yes—
580C22×C4D4×D5311yescharacteristic
581C22×C4#1171994712yes—
582C22×C4C23×D5311yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—532no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—2124no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—532no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—4241no—
609C4⋊C4—2122no—
610C4⋊C4—2122no—
611C4⋊C4—2122no—
612C4⋊C4—2122no—
613C4⋊C4—2122no—
614C22⋊C4—42no—
615C22⋊C4—534no—
616C22⋊C4—1062no—
617C22⋊C4—4241no—
618C22⋊C4—4241no—
619C22⋊C4—2122no—
620C22⋊C4—2122no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C22⋊C4—2122no—
624C42—1061no—
625C42—1061no—
626C42—1061no—
627C42—1061no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1313319412yes—
654C23SD16×D5312yes—
655C23#1313324112yes—
656C23C2×D4×D5311yescharacteristic
657Q8—4244no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1313319414yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—1062no—
691C2×C4—1061no—
692C2×C4—4244no—
693C2×C4—4244no—
694C2×C4—4244no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4#1313319412yes—
707C2×C4C2×D4×D5311yescharacteristic
708C2×C4C22×Dic10611yescharacteristic
709C2×C4C2×#1171994711yescharacteristic
710C2×C4C2×#1171994711yescharacteristic
711C2×C4#1313326211yescharacteristic
712C2×C4#1313326211yescharacteristic
713C8—41no—
714C8—41no—
715C8—1062no—
716C8—2121no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1681091114yescomplemented
739C22C2×#1313319411yescharacteristic
740C22#1681125511yescharacteristic
741C22#1681126011yescharacteristic
742C22C2×SD16×D5311yescharacteristic
743C22C2×#1313324111yescharacteristic
744C22#1681142711yescharacteristic
745C22#1681143311yescharacteristic
746C4—22no—
747C4—81no—
748C4—81no—
749C4—1062no—
750C4—1062no—
751C4—4241no—
752C4—4241no—
753C4—4241no—
754C4—2121no—
755C4—2121no—
756C4—2122no—
757C4C2×#1313319411yescharacteristic
758C4#1681124911yescharacteristic
759C4#1681126011yescharacteristic
760C4#1681130411yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#2027838111yescharacteristic
765C2C2×#1681091111yescharacteristic
766C2#2028454811yescharacteristic
767C2#2028618811yescharacteristic
768C2#2028640911yescharacteristic
769C2#2028653211yescharacteristic
770C2#2028668011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#1786C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
hypercenter#1786D53
hypocenterC53#25958
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#16810911C2semidirect
3. #20278418C2semidirect
5. #20276246C2semidirect
6. #20276087C2semidirect
7. #20276085C2semidirect
8. #20275849C2semidirect
9. #20274978C2semidirect
10. #20274974C2semidirect
11. #20274910C2semidirect
12. #20274892C2semidirect
13. #20274738C2semidirect
14. #20274713C2semidirect
17. C2×#13133216C22semidirect
24. C2×#13133149C22semidirect
25. C2×#13133149C22semidirect
26. C2×#13133148C22semidirect
27. C2×#13133148C22semidirect
28. C2×#13133146C22semidirect
29. C2×#13133146C22semidirect
39. #16810522C22semidirect
40. #16810519C22semidirect
44. #16810492C22semidirect
48. #16810386C22semidirect
49. #16810386C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
123. C22×D4×C53Q8semidirect
279. D4×C53C22⋊Q8semidirect
353. C22×C53#476semidirect
446. C53#25958semidirect
455. C22×D4Dic106semidirect
666. D4#13133194semidirect
738. C22#16810911semidirect

Maximal subgroups

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

subgroupindex
C2×#168109112
C22×#131331382
#202784182
D4×C22⋊Dic532
#202762462
#202760872
#202760852
#202758492
#202749782
#202749742
#202749102
#202748922
#202747382
#202747132
C53×#17862
#2595853