Finite Group Databasebeta

← #27404473

Subgroups — #27404473

Order 13568.

1134 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
1C2×#16810724C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic
3#20277724C211yesmaximal, characteristic, complemented
4#20277545C211yesmaximal, characteristic
5#20275577C211yesmaximal, characteristic, complemented
6#20275407C211yesmaximal, characteristic, complemented
7#20275358C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275058C211yesmaximal, characteristic, complemented
10#20275051C211yesmaximal, characteristic, complemented
11#20274964C211yesmaximal, characteristic, complemented
12#20274905C211yesmaximal, characteristic, complemented
13#102×Dic53C211yesmaximal, characteristic, complemented
14#20274501C211yesmaximal, characteristic, complemented
15C2×C53×#452C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×Q8×Dic53C2211yescharacteristic
18C2×D4×Dic53C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21#16810724—24no—
22C2×#13133151C2211yescharacteristic
23C2×#13133151C2211yescharacteristic
24#16810624—24no—
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×C8×Dic53C2211yescharacteristic
33#16810530C2211yescharacteristic
34#16810530C2211yescharacteristic
35#16810530C2211yescharacteristic
36#16810522—21no—
37#16810522C2211yescharacteristic
38#16810509—21no—
39#16810503—21no—
40#16810503—21no—
41#16810498—21no—
42#16810486—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45C22⋊C4×Dic53—21no—
46C4×C22⋊Dic53C2211yescharacteristic
47C2×#13133124—21no—
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×#41×C53C2211yescharacteristic
55C22×Q16×C53C2211yescharacteristic
56C22×SD16×C53C2211yescharacteristic
57C2×C22⋊Q8×C53C2211yescharacteristic
58C53×#452C418yescomplemented
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C23×Dic53—21no—
63C23×Dic53—21no—
64C23×Dic53—21no—
65C2×#11719917—22no—
66C2×#11719917—22no—
67C2×#11719917—41no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70Q8×Dic53—22no—
71Q8×Dic53—41no—
72D4×Dic53—22no—
73D4×Dic53—22no—
74D4×Dic53—41no—
75D4×Dic53—41no—
76C2×C4⋊Dic53—21no—
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×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53D411yescharacteristic
89C2×C22⋊Dic53D411yescharacteristic
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53C2311yescharacteristic
93C2×C4×Dic53C2311yescharacteristic
94#13133151—22no—
95#13133151—41no—
96#13133141—22no—
97#13133141—22no—
98#13133141—22no—
99#13133141—41no—
100#13133138—22no—
101#13133138D414yes—
102#13133127—22no—
103C8×Dic53—41no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124D411yescharacteristic
114#13133124D411yescharacteristic
115C2×#41×C53—22no—
116C2×#41×C53—22no—
117C2×#41×C53—22no—
118C2×#41×C53—41no—
119C2×#41×C53—41no—
120C2×#41×C53C2×C414yes—
121C22×Q8×C53C2311yescharacteristic
122C22×Q8×C53C2311yescharacteristic
123C22×D4×C53—21no—
124C22×D4×C53C2311yescharacteristic
125C23×C4×C53—21no—
126C23×C4×C53C2311yescharacteristic
127C2×Q16×C53—41no—
128C2×Q16×C53—41no—
129C2×Q16×C53C2×C414yescomplemented
130C2×SD16×C53—22no—
131C2×SD16×C53—22no—
132C2×SD16×C53C2×C414yescomplemented
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C22⋊Q8×C53—22no—
136C22⋊Q8×C53C2×C414yescomplemented
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140#103×C53C2×C414yescomplemented
141#102×C53C2×C414yescomplemented
142C22⋊C8×C53C2×C414yescomplemented
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145#41×C53—28no—
146#41×C53—44no—
147#41×C53—44no—
148#41×C53—44no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53C22×C412yes—
160C2×Q8×C53C22×C412yes—
161C2×D4×C53—24no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—42no—
166C2×D4×C53—42no—
167C2×D4×C53C22×C412yes—
168C2×D4×C53C2×D412yes—
169C2×D4×C53#4112yes—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—24no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53#4112yes—
183C22×C4×C53C2411yescharacteristic
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—42no—
189C22×Dic53—42no—
190C22×Dic53—42no—
191C22×Dic53—42no—
192C22×Dic53—42no—
193C22×Dic53—42no—
194C22×Dic53—81no—
195C22×Dic53—81no—
196C22×Dic53—81no—
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201Q16×C53—44no—
202SD16×C53—28no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53C22×C412yes—
208C2×C8×C53C22×C412yes—
209C4⋊C4×C53—24no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53C22×C412yes—
212C22⋊C4×C53—24no—
213C22⋊Dic53—22no—
214C22⋊Dic53—41no—
215C22⋊Dic53—42no—
216C22⋊Dic53—42no—
217C22⋊Dic53—81no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—42no—
226C4⋊Dic53—42no—
227C4⋊Dic53—81no—
228C4⋊Dic53C2×D412yes—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53—21no—
232C4×Dic53—21no—
233C4×Dic53—42no—
234C4×Dic53—81no—
235#11719917—44no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322C2×D412yes—
242C23×C53—22no—
243C23×C53—21no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53C4×D412yes—
256C23×C53C22×D411yescharacteristic
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—41no—
262Q8×C53—41no—
263Q8×C53—41no—
264Q8×C53—41no—
265D4×C53—22no—
266D4×C53—22no—
267D4×C53—22no—
268D4×C53—48no—
269D4×C53C4×D414yes—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—48no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53C4×D412yes—
287C2×C4×C53C23×C411yescharacteristic
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53C2×#4111yescharacteristic
291C2×C4×C53H(5,𝔽2)11yescharacteristic
292C2×C4×C53H(5,𝔽2)11yescharacteristic
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—22no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—84no—
317C2×Dic53—84no—
318C2×Dic53—84no—
319C2×Dic53#13712yes—
320C8×C53—22no—
321C8×C53—22no—
322#88322—22no—
323#88322—41no—
324#22862—531nomaximal, Sylow
325C22×C53—22no—
326C22×C53—24no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—41no—
332C22×C53—42no—
333C22×C53—41no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—42no—
339C22×C53C2×C4×D411yescharacteristic
340C22×C53D4211yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53C2×#13711yescharacteristic
343C22×C53#57511yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57811yescharacteristic
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53C2×C4×D411yescharacteristic
351C4×C53#51811yescharacteristic
352C4×C53#54611yescharacteristic
353C4×C53#55111yescharacteristic
354Dic53—22no—
355Dic53—41no—
356Dic53—42no—
357Dic53—41no—
358Dic53—41no—
359Dic53—81no—
360Dic53—81no—
361Dic53—81no—
362C2×#452D5311yescharacteristic
363C2×#440—531no—
364C2×#417—531no—
365#2360—531no—
366#2339—531no—
367#1969—531no—
368#1935—531no—
369#1928—531no—
370#1894—531no—
371#1878—531no—
372#1877—531no—
373#1862—531no—
374#1852—531no—
375C4×#102—531no—
376#1753—531no—
377C2×C53—42no—
378C2×C53—44no—
379C2×C53#235811yescharacteristic
380C2×C53C4×#13711yescharacteristic
381C2×C53#295111yescharacteristic
382C2×C53#327311yescharacteristic
383C2×C53#327611yescharacteristic
384C2×C53#331411yescharacteristic
385C2×C53#331511yescharacteristic
386C22×#41C2×D5311yescharacteristic
387C22×Q16C2×D5311yescharacteristic
388C22×SD16C2×D5311yescharacteristic
389C22×M16—531no—
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×C4×Q8—531no—
392C2×C4×D4—531no—
393C2×C4×D4—531no—
394C22×C4⋊C4—531no—
395#452Dic5318yescomplemented
396#440—1064no—
397C2×#107—531no—
398C2×#107—531no—
399#417—1064no—
400C2×#103—531no—
401C2×#103—531no—
402C2×#103—531no—
403C2×#103—531no—
404C2×#103C2×D5311yescharacteristic
405C2×#102—531no—
406C2×#102—531no—
407C2×#102C2×D5311yescharacteristic
408C2×C22⋊C8C2×D5311yescharacteristic
409C2×#97—531no—
410C2×C4×C8—531no—
411#391—531no—
412#391—531no—
413#391—531no—
414#389—531no—
415#389—1061no—
416#387—1061no—
417#386—1061no—
418#386—1061no—
419#385—1061no—
420#381—1061no—
421#380—531no—
422C4×C4⋊C4—531no—
423C4×C22⋊C4—531no—
424C4×C22⋊C4—1061no—
425C2×#95—1061no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#336—531no—
431#336—531no—
432C53#2286211yescharacteristic, complemented, Sylow
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C2×#41C2×Dic5314yes—
439C22×Q8C22×D5311yescharacteristic
440C22×Q8C22×D5311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D5311yescharacteristic
443C23×C4—21no—
444C23×C4—1061no—
445C23×C4—1061no—
446C23×C4—1061no—
447C23×C4C22×D5311yescharacteristic
448C2×Q16—41no—
449C2×Q16—41no—
450C2×Q16C2×Dic5314yescomplemented
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16C2×Dic5314yescomplemented
454C2×M16—1062no—
455C2×M16—1062no—
456C2×M16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8C22×D5311yescharacteristic
460C22×C8C22×D5311yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8C2×Dic5314yescomplemented
463C4×Q8—1062no—
464C4×Q8—2121no—
465C4×D4—1062no—
466C4×D4—1062no—
467C4×D4—2121no—
468C4×D4—2121no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—531no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—531no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4—1061no—
485C2×C22⋊C4—1061no—
486C2×C42—531no—
487C2×C42—531no—
488C2×C42—1061no—
489C2×C42—1061no—
490#107—1062no—
491#107—2121no—
492#103—1062no—
493#103—1062no—
494#103—1062no—
495#103—2121no—
496#103C2×Dic5314yescomplemented
497#102—534no—
498#102—1062no—
499#102C2×Dic5314yescomplemented
500C22⋊C8C2×Dic5314yescomplemented
501#97—1062no—
502C4×C8—2121no—
503#95—531no—
504#95—531no—
505#95—1061no—
506#95—1061no—
507#95—1061no—
508#95—1061no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514C24—21no—
515C24D4×D5311yescharacteristic
516#41—28no—
517#41—44no—
518#41—44no—
519#41—44no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8C22×Dic5312yes—
531C2×Q8C22×Dic5312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4D4×D5312yes—
539C2×D4#1171994712yes—
540C2×D4C22×Dic5312yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—531no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—4241no—
560C22×C4—4241no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4—2122no—
565C22×C4—2122no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4D4×D5311yescharacteristic
569C22×C4#1171994712yes—
570C22×C4C22×Dic5312yes—
571C22×C4C23×D5311yescharacteristic
572Q16—44no—
573SD16—28no—
574M16—2124no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—532no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8C22×Dic5312yes—
586C2×C8C22×Dic5312yes—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—532no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—4241no—
598C4⋊C4—2122no—
599C4⋊C4—2122no—
600C4⋊C4C22×Dic5312yes—
601C22⋊C4—24no—
602C22⋊C4—1062no—
603C22⋊C4—4241no—
604C22⋊C4—2121no—
605C22⋊C4—2122no—
606C22⋊C4—2122no—
607C42—1061no—
608C42—1061no—
609C42—1061no—
610C42—1061no—
611C42—4241no—
612C42—2122no—
613C23—22no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23D4×Dic5312yes—
627C23C2×D4×D5311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4D4×Dic5314yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—532no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1062no—
669C2×C4—1061no—
670C2×C4—4244no—
671C2×C4—4244no—
672C2×C4—4244no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4D4×Dic5312yes—
685C2×C4C23×Dic5311yescharacteristic
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4C2×#1171994711yescharacteristic
688C2×C4C2×#1171994711yescharacteristic
689C2×C4#1313326211yescharacteristic
690C2×C4#1313326211yescharacteristic
691C8—22no—
692C8—22no—
693C8—1062no—
694C8—2121no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—22no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—42no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22C2×D4×Dic5311yescharacteristic
710C22#1681125511yescharacteristic
711C22#1681126011yescharacteristic
712C22#137×D5311yescharacteristic
713C22#1681142211yescharacteristic
714C22#1681142511yescharacteristic
715C22#1681143711yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—1062no—
721C4—4241no—
722C4—4241no—
723C4—4241no—
724C4—2121no—
725C4—2121no—
726C4—2122no—
727C4—2121no—
728C4C2×D4×Dic5311yescharacteristic
729C4#1681109811yescharacteristic
730C4#1681126011yescharacteristic
731C4#1681130411yescharacteristic
732C2—42no—
733C2—44no—
734C2#2027769911yescharacteristic
735C2#137×Dic5311yescharacteristic
736C2#2028359111yescharacteristic
737C2#2028631911yescharacteristic
738C2#2028635911yescharacteristic
739C2#2028678911yescharacteristic
740C2#2028680411yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#452D53
hypocenterC53#22862
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16810724C2semidirect
3. #20277724C2semidirect
5. #20275577C2semidirect
6. #20275407C2semidirect
7. #20275358C2semidirect
8. #20275149C2semidirect
9. #20275058C2semidirect
10. #20275051C2semidirect
11. #20274964C2semidirect
12. #20274905C2semidirect
13. #102×Dic53C2semidirect
14. #20274501C2semidirect
58. C53×#452C4semidirect
129. C2×Q16×C53C2×C4semidirect
132. C2×SD16×C53C2×C4semidirect
136. C22⋊Q8×C53C2×C4semidirect
140. #103×C53C2×C4semidirect
141. #102×C53C2×C4semidirect
142. C22⋊C8×C53C2×C4semidirect
395. #452Dic53semidirect
432. C53#22862semidirect
450. C2×Q16C2×Dic53semidirect
453. C2×SD16C2×Dic53semidirect
462. C22⋊Q8C2×Dic53semidirect
496. #103C2×Dic53semidirect
499. #102C2×Dic53semidirect
500. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107242
C2×#168106242
#202777242
#202775452
#202755772
#202754072
#202753582
#202751492
#202750582
#202750512
#202749642
#202749052
#102×Dic532
#202745012
C2×C53×#4522
#2286253