Finite Group Databasebeta

← #27389827

Subgroups — #27389827

Order 13568.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811098C211yesmaximal, characteristic
2C2×#16810724C211yesmaximal, characteristic, complemented
3C2×SD16×Dic53C211yesmaximal, characteristic, complemented
4#20277399C211yesmaximal, characteristic, complemented
5#20275051C211yesmaximal, characteristic, complemented
6#20275051C211yesmaximal, characteristic, complemented
7#20275028C211yesmaximal, characteristic, complemented
8#20274978C211yesmaximal, characteristic, complemented
9#20274964C211yesmaximal, characteristic, complemented
10#20274916C211yesmaximal, characteristic, complemented
11#20274646C211yesmaximal, characteristic
12#20274542C211yesmaximal, characteristic, complemented
13#102×Dic53C211yesmaximal, characteristic, complemented
14#20274483C211yesmaximal, characteristic, complemented
15C2×C53×#450C211yesmaximal, characteristic
16#16811098—24no—
17#16811098—24no—
18C2×Q8×Dic53C2211yescharacteristic, complemented
19C2×D4×Dic53—21no—
20C2×D4×Dic53—21no—
21C2×D4×Dic53C2211yescharacteristic
22C2×D4×Dic53C2211yescharacteristic
23C2×D4×Dic53C2211yescharacteristic
24C2×D4×Dic53C2211yescharacteristic
25C2×#13133176C2211yescharacteristic
26C2×#13133176C2211yescharacteristic
27C22×C22⋊Dic53—21no—
28C22×C22⋊Dic53—21no—
29#16810724—24no—
30SD16×Dic53—24no—
31C2×#13133151C2211yescharacteristic, complemented
32C2×#13133149C2211yescharacteristic, complemented
33C2×#13133141C2211yescharacteristic, complemented
34C2×#13133141C2211yescharacteristic, complemented
35C2×#13133138C2211yescharacteristic
36C2×#13133138C2211yescharacteristic
37C2×#13133138C2211yescharacteristic
38C2×#13133138C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic
40C2×#13133127C2211yescharacteristic, complemented
41C2×C8×Dic53C2211yescharacteristic, complemented
42#16810530C2211yescharacteristic, complemented
43#16810522—21no—
44#16810522C2211yescharacteristic, complemented
45#16810516—21no—
46#16810516—21no—
47#16810509—21no—
48#16810483C2211yescharacteristic
49C4⋊C4×Dic53C2211yescharacteristic, complemented
50#16810386C2211yescharacteristic, complemented
51#16810386C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53#16810385C2211yescharacteristic, complemented
54#16810377C2211yescharacteristic, complemented
55#16810377C2211yescharacteristic, complemented
56C23×D4×C53C2211yescharacteristic
57C22×SD16×C53C2211yescharacteristic
58C22×SD16×C53C2211yescharacteristic
59C2×C22⋊Q8×C53C2211yescharacteristic
60C53×#450C418yescomplemented
61C2×#102×C53C2211yescharacteristic
62C2×#102×C53C2211yescharacteristic
63C2×C22⋊C8×C53C2211yescharacteristic
64C23×Dic53—21no—
65C23×Dic53—21no—
66C23×Dic53—21no—
67C23×Dic53—21no—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70Q8×Dic53—22no—
71Q8×Dic53—22no—
72D4×Dic53—28no—
73D4×Dic53—28no—
74D4×Dic53—22no—
75D4×Dic53—22no—
76D4×Dic53—22no—
77D4×Dic53—22no—
78D4×Dic53—22no—
79D4×Dic53—22no—
80D4×Dic53D414yes—
81D4×Dic53D414yes—
82#13133176—22no—
83#13133176—22no—
84#13133176—22no—
85#13133176—22no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53D411yescharacteristic
89C2×C4⋊Dic53D411yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C22⋊Dic53—28no—
95C2×C22⋊Dic53—28no—
96C2×C22⋊Dic53—21no—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×C22⋊Dic53—21no—
102C2×C22⋊Dic53D411yescharacteristic
103C2×C22⋊Dic53D411yescharacteristic
104C2×C4×Dic53—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53C2311yescharacteristic
108C2×C4×Dic53C2311yescharacteristic
109#13133151—22no—
110#13133149—22no—
111#13133141—22no—
112#13133141—22no—
113#13133138—22no—
114#13133138—22no—
115#13133138—22no—
116#13133138—22no—
117C22⋊#88322—22no—
118#13133127—22no—
119C8×Dic53—22no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123#13133124—21no—
124#13133124—21no—
125C25×C53—21no—
126C22×Q8×C53C2311yescharacteristic
127C22×D4×C53—22no—
128C22×D4×C53—22no—
129C22×D4×C53—22no—
130C22×D4×C53—22no—
131C22×D4×C53—21no—
132C22×D4×C53—22no—
133C22×D4×C53C2×C414yes—
134C22×D4×C53C2311yescharacteristic
135C22×D4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C2×SD16×C53—22no—
138C2×SD16×C53—22no—
139C2×SD16×C53—22no—
140C2×SD16×C53—22no—
141C2×SD16×C53C2×C414yescomplemented
142C2×SD16×C53C2×C414yescomplemented
143C22×C8×C53C2311yescharacteristic
144C22×C8×C53C2311yescharacteristic
145C22⋊Q8×C53—22no—
146C22⋊Q8×C53C2×C414yescomplemented
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C22⋊C4×C53—21no—
150#102×C53C2×C414yescomplemented
151#102×C53C2×C414yescomplemented
152C22⋊C8×C53C2×C414yescomplemented
153C24×C53—24no—
154C24×C53—24no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—24no—
158C24×C53—81no—
159C24×C53—81no—
160C24×C53—81no—
161C24×C53—81no—
162C24×C53C2×D411yescharacteristic
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53C22×C412yes—
169C2×D4×C53—24no—
170C2×D4×C53—28no—
171C2×D4×C53—28no—
172C2×D4×C53—24no—
173C2×D4×C53—28no—
174C2×D4×C53—28no—
175C2×D4×C53—24no—
176C2×D4×C53—21no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53C22×C412yes—
183C2×D4×C53C22×C412yes—
184C2×D4×C53C2×D412yes—
185C2×D4×C53C2×D412yes—
186C2×D4×C53#4112yes—
187C2×D4×C53#4112yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53#4112yes—
197C22×C4×C53C2411yescharacteristic
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—24no—
201C22×Dic53—24no—
202C22×Dic53—24no—
203C22×Dic53—24no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—81no—
207C22×Dic53—81no—
208C22×Dic53—81no—
209C22×Dic53—81no—
210C22×Dic53—81no—
211C22×Dic53—81no—
212C22×Dic53—81no—
213C22×Dic53—81no—
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218SD16×C53—28no—
219SD16×C53—28no—
220C2×C8×C53—21no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53C22×C412yes—
225C2×C8×C53C22×C412yes—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53C22×C412yes—
229C22⋊C4×C53—24no—
230C22⋊Dic53—24no—
231C22⋊Dic53—24no—
232C22⋊Dic53—24no—
233C22⋊Dic53—22no—
234C22⋊Dic53—22no—
235C22⋊Dic53—24no—
236C22⋊Dic53—24no—
237C22⋊Dic53—81no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53—22no—
241C4⋊Dic53—22no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—42no—
247C4⋊Dic53—81no—
248C4⋊Dic53C2×D412yes—
249C4⋊Dic53C2×D412yes—
250C4×Dic53—24no—
251C4×Dic53—21no—
252C4×Dic53—21no—
253C4×Dic53—42no—
254C4×Dic53—81no—
255C4×Dic53C2×D412yes—
256C4×Dic53C2×D412yes—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C23×C53—216no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—84no—
285C23×C53—84no—
286C23×C53—84no—
287C23×C53—84no—
288C23×C53—84no—
289C23×C53—84no—
290C23×C53C4×D412yes—
291C23×C53C22×D411yescharacteristic
292Q8×C53—22no—
293Q8×C53—22no—
294Q8×C53—41no—
295Q8×C53—41no—
296D4×C53—216no—
297D4×C53—22no—
298D4×C53—22no—
299D4×C53—22no—
300D4×C53—22no—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53C4×D414yes—
304D4×C53C4×D414yes—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53C4×D412yes—
318C2×C4×C53C23×C411yescharacteristic
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4111yescharacteristic
322C2×C4×C53C2×#4111yescharacteristic
323C2×C4×C53C2×#4111yescharacteristic
324C2×Dic53—21no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—21no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—21no—
331C2×Dic53—21no—
332C2×Dic53—21no—
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—84no—
347C2×Dic53—84no—
348C2×Dic53—84no—
349C2×Dic53—84no—
350C2×Dic53#12012yes—
351C2×Dic53#12012yes—
352C8×C53—22no—
353C8×C53—22no—
354#88322—41no—
355#88322—41no—
356#21459—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—24no—
361C22×C53—24no—
362C22×C53—41no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—41no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—41no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—41no—
378C22×C53—816no—
379C22×C53C2×C4×D411yescharacteristic
380C22×C53C2×#12011yescharacteristic
381C22×C53#52511yescharacteristic
382C22×C53#57611yescharacteristic
383C22×C53#57711yescharacteristic
384C22×C53#57711yescharacteristic
385C22×C53#57711yescharacteristic
386C4×C53—22no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53C2×C4×D411yescharacteristic
390C4×C53C2×C4×D411yescharacteristic
391C4×C53#52511yescharacteristic
392C4×C53#52511yescharacteristic
393Dic53—22no—
394Dic53—22no—
395Dic53—41no—
396Dic53—42no—
397Dic53—41no—
398Dic53—42no—
399Dic53—81no—
400Dic53—81no—
401C2×#518—531no—
402C2×#450D5311yescharacteristic
403C2×#440—531no—
404C2×C4×SD16—531no—
405#2323—531no—
406#1877—531no—
407#1877—531no—
408#1873—531no—
409#1864—531no—
410#1862—531no—
411#1854—531no—
412#1786—531no—
413#1762—531no—
414C4×#102—531no—
415#1750—531no—
416C2×C53—42no—
417C2×C53—44no—
418C2×C53—44no—
419C2×C53C4×#12011yescharacteristic
420C2×C53#294611yescharacteristic
421C2×C53#294911yescharacteristic
422C2×C53#300911yescharacteristic
423C2×C53#301211yescharacteristic
424C2×C53#311811yescharacteristic
425C2×C53#312311yescharacteristic
426C23×D4C2×D5311yescharacteristic
427C22×SD16C2×D5311yescharacteristic
428C22×SD16C2×D5311yescharacteristic
429C2×C22⋊Q8C2×D5311yescharacteristic
430#518—1064no—
431#518—1064no—
432C2×C4×Q8—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×C4×D4—1061no—
438C2×C4×D4—1061no—
439C2×#117—531no—
440C2×#117—531no—
441C22×C22⋊C4—1061no—
442C22×C22⋊C4—1061no—
443#450Dic5318yescomplemented
444#440—1064no—
445C4×SD16—1064no—
446C2×#107—531no—
447C2×#106—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102C2×D5311yescharacteristic
455C2×#102C2×D5311yescharacteristic
456C2×C22⋊C8—531no—
457C2×C22⋊C8C2×D5311yescharacteristic
458C2×#97—531no—
459C2×C4×C8—531no—
460#391—531no—
461#389—531no—
462#389—1061no—
463#388—1061no—
464#388—1061no—
465#387—1061no—
466#380—531no—
467C4×C4⋊C4—531no—
468#340—531no—
469#340—531no—
470#340—531no—
471#340—531no—
472#336—531no—
473#336—531no—
474C53#2145911yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8C22×D5311yescharacteristic
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—22no—
483C22×D4C2×Dic5314yes—
484C22×D4C22×D5311yescharacteristic
485C22×D4C22×D5311yescharacteristic
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4C22×D5311yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16C2×Dic5314yescomplemented
496C2×SD16C2×Dic5314yescomplemented
497C22×C8—531no—
498C22×C8—531no—
499C22×C8C22×D5311yescharacteristic
500C22×C8C22×D5311yescharacteristic
501C22⋊Q8—22no—
502C22⋊Q8C2×Dic5314yescomplemented
503C4×Q8—1062no—
504C4×Q8—1062no—
505C4×D4—534no—
506C4×D4—534no—
507C4×D4—1062no—
508C4×D4—1062no—
509C4×D4—1062no—
510C4×D4—1062no—
511C4×D4—1068no—
512C4×D4—1068no—
513C4×D4—1062no—
514C4×D4—1062no—
515#117—1062no—
516#117—1062no—
517#117—1062no—
518#117—1062no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4C22×D5311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1068no—
537C2×C22⋊C4—1068no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C42—531no—
541C2×C42—531no—
542C2×C42—1061no—
543C2×C42—1061no—
544C2×C42—1061no—
545#107—1062no—
546#106—1062no—
547#103—1062no—
548#103—1062no—
549#102—1062no—
550#102—1062no—
551#102—1062no—
552#102—1062no—
553#102C2×Dic5314yescomplemented
554#102C2×Dic5314yescomplemented
555C22⋊C8—1062no—
556C22⋊C8C2×Dic5314yescomplemented
557#97—1062no—
558C4×C8—1062no—
559#95—1061no—
560#95—1061no—
561#95—1061no—
562#95—1061no—
563#95—1061no—
564C24—24no—
565C24—24no—
566C24—21no—
567C24—21no—
568C24—24no—
569C24—81no—
570C24—81no—
571C24—81no—
572C24—81no—
573C24D4×D5311yescharacteristic
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C22×Dic5312yes—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4D4×D5312yes—
594C2×D4D4×D5312yes—
595C2×D4#1171994712yes—
596C2×D4#1171994712yes—
597C2×D4C22×Dic5312yes—
598C2×D4C22×Dic5312yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—531no—
606C22×C4—531no—
607C22×C4—531no—
608C22×C4—531no—
609C22×C4—1064no—
610C22×C4—1064no—
611C22×C4—1064no—
612C22×C4—1064no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—4241no—
618C22×C4—4241no—
619C22×C4—4241no—
620C22×C4—4241no—
621C22×C4—4241no—
622C22×C4—4241no—
623C22×C4—4241no—
624C22×C4—4241no—
625C22×C4D4×D5311yescharacteristic
626C22×C4#1171994712yes—
627C22×C4C22×Dic5312yes—
628C22×C4C23×D5311yescharacteristic
629SD16—28no—
630SD16—28no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8C22×Dic5312yes—
642C2×C8C22×Dic5312yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—532no—
646C4⋊C4—532no—
647C4⋊C4—1062no—
648C4⋊C4—1062no—
649C4⋊C4—1061no—
650C4⋊C4—1061no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—4241no—
656C4⋊C4—2122no—
657C4⋊C4C22×Dic5312yes—
658C22⋊C4—24no—
659C22⋊C4—1062no—
660C22⋊C4—1062no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4—4241no—
667C42—532no—
668C42—532no—
669C42—1064no—
670C42—1061no—
671C42—1061no—
672C42—4241no—
673C42—2122no—
674C23—216no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23D4×Dic5312yes—
702C23C2×D4×D5311yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4D4×Dic5314yes—
715D4D4×Dic5314yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—532no—
729C2×C4—532no—
730C2×C4—1061no—
731C2×C4—1061no—
732C2×C4—1061no—
733C2×C4—1061no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1061no—
737C2×C4—1061no—
738C2×C4—1061no—
739C2×C4—1061no—
740C2×C4—1061no—
741C2×C4—1061no—
742C2×C4—4244no—
743C2×C4—4244no—
744C2×C4—4244no—
745C2×C4—4244no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2121no—
756C2×C4D4×Dic5312yes—
757C2×C4C23×Dic5311yescharacteristic
758C2×C4C2×D4×D5311yescharacteristic
759C2×C4C2×D4×D5311yescharacteristic
760C2×C4C2×#1171994711yescharacteristic
761C2×C4C2×#1171994711yescharacteristic
762C2×C4C2×#1171994711yescharacteristic
763C8—22no—
764C8—22no—
765C8—2121no—
766C8—2121no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—24no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—816no—
789C22C2×D4×Dic5311yescharacteristic
790C22#120×D5311yescharacteristic
791C22#1681112911yescharacteristic
792C22#1681142711yescharacteristic
793C22#1681142911yescharacteristic
794C22#1681142911yescharacteristic
795C22#1681143311yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—1062no—
800C4—1062no—
801C4—4241no—
802C4—4241no—
803C4—2121no—
804C4—2122no—
805C4—2121no—
806C4—2122no—
807C4C2×D4×Dic5311yescharacteristic
808C4C2×D4×Dic5311yescharacteristic
809C4#1681112911yescharacteristic
810C4#1681112911yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2#120×Dic5311yescharacteristic
815C2#2028354811yescharacteristic
816C2#2028357511yescharacteristic
817C2#2028398711yescharacteristic
818C2#2028402011yescharacteristic
819C2#2028490011yescharacteristic
820C2#2028496111yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#450C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
cosocleC22×C4×C53C24
hypercenterC2×#450D53
hypocenterC53#21459
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×#16810724C2semidirect
3. C2×SD16×Dic53C2semidirect
4. #20277399C2semidirect
5. #20275051C2semidirect
6. #20275051C2semidirect
7. #20275028C2semidirect
8. #20274978C2semidirect
9. #20274964C2semidirect
10. #20274916C2semidirect
12. #20274542C2semidirect
13. #102×Dic53C2semidirect
14. #20274483C2semidirect
18. C2×Q8×Dic53C22semidirect
31. C2×#13133151C22semidirect
32. C2×#13133149C22semidirect
33. C2×#13133141C22semidirect
34. C2×#13133141C22semidirect
40. C2×#13133127C22semidirect
41. C2×C8×Dic53C22semidirect
42. #16810530C22semidirect
44. #16810522C22semidirect
49. C4⋊C4×Dic53C22semidirect
50. #16810386C22semidirect
51. #16810386C22semidirect
52. #16810385C22semidirect
53. #16810385C22semidirect
54. #16810377C22semidirect
55. #16810377C22semidirect
60. C53×#450C4semidirect
141. C2×SD16×C53C2×C4semidirect
142. C2×SD16×C53C2×C4semidirect
146. C22⋊Q8×C53C2×C4semidirect
150. #102×C53C2×C4semidirect
151. #102×C53C2×C4semidirect
152. C22⋊C8×C53C2×C4semidirect
443. #450Dic53semidirect
474. C53#21459semidirect
495. C2×SD16C2×Dic53semidirect
496. C2×SD16C2×Dic53semidirect
502. C22⋊Q8C2×Dic53semidirect
553. #102C2×Dic53semidirect
554. #102C2×Dic53semidirect
556. C22⋊C8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168110982
C2×#168107242
C2×SD16×Dic532
#202773992
#202750512
#202750282
#202749782
#202749642
#202749162
#202746462
#202745422
#102×Dic532
#202744832
C2×C53×#4502
#2145953