Finite Group Databasebeta

← #27399572

Subgroups — #27399572

Order 13568.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810695C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3C22×#13133138C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic53C211yesmaximal, characteristic, complemented
5#20275648C211yesmaximal, characteristic, complemented
6#20275532C211yesmaximal, characteristic, complemented
7#20275154C211yesmaximal, characteristic, complemented
8#20275139C211yesmaximal, characteristic, complemented
9#20275033C211yesmaximal, characteristic, complemented
10#20275023C211yesmaximal, characteristic, complemented
11#20274715C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14#20274540C211yesmaximal, characteristic, complemented
15C2×C53×#546C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic, complemented
17C23×#88322C2211yescharacteristic
18C2×D4×Dic53—21no—
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic, complemented
21#16810695—24no—
22C2×C4⋊#88322C2211yescharacteristic, complemented
23#16810624—24no—
24C2×#13133141C2211yescharacteristic, complemented
25C2×#13133141C2211yescharacteristic, complemented
26C2×#13133141C2211yescharacteristic, complemented
27C2×#13133141C2211yescharacteristic, complemented
28C2×#13133138—24no—
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×#13133138C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×C22⋊#88322C2211yescharacteristic, complemented
39C2×#13133128C2211yescharacteristic, complemented
40#16810522—21no—
41#16810498—21no—
42#16810498—21no—
43#16810493C2211yescharacteristic, complemented
44#16810483C2211yescharacteristic
45#16810483C2211yescharacteristic, complemented
46C4×C4⋊Dic53C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51C22×#41×C53C2211yescharacteristic
52C23×D4×C53C2211yescharacteristic
53C53×#546—24no—
54C53×#546C418yescomplemented
55C2×#124×C53C2211yescharacteristic
56C2×#123×C53—21no—
57C2×C22⋊Q8×C53C2211yescharacteristic
58C2×#121×C53—21no—
59C2×#121×C53C2211yescharacteristic
60C2×#120×C53—21no—
61C2×C4×D4×C53C2211yescharacteristic
62C2×C4×D4×C53C2211yescharacteristic
63C22×C22⋊C4×C53—21no—
64C23×Dic53—21no—
65C23×Dic53—21no—
66C2×#11719917—22no—
67C2×#11719917—22no—
68C2×#11719917—41no—
69C22×#88322—22no—
70C22×#88322—22no—
71C22×#88322—41no—
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76D4×Dic53—44no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—41no—
84C2×C4⋊Dic53—41no—
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C4×Dic53—21no—
92C4⋊#88322—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141—41no—
96#13133141—41no—
97#13133138—22no—
98#13133138—22no—
99#13133138—22no—
100#13133138—22no—
101#13133138—22no—
102#13133138—41no—
103#13133138—41no—
104#13133138D414yescomplemented
105C22⋊#88322—22no—
106C22⋊#88322—22no—
107#13133128—22no—
108#13133124—21no—
109#13133124—21no—
110#13133124—21no—
111C25×C53—21no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53—22no—
115C2×#41×C53—41no—
116C2×#41×C53—41no—
117C2×#41×C53C2×C414yescomplemented
118C22×Q8×C53C2311yescharacteristic
119C22×D4×C53—22no—
120C22×D4×C53—22no—
121C22×D4×C53—21no—
122C22×D4×C53—21no—
123C22×D4×C53—21no—
124C22×D4×C53—22no—
125C22×D4×C53—41no—
126C22×D4×C53—41no—
127C22×D4×C53C2×C414yescomplemented
128C22×D4×C53D411yescharacteristic
129C22×D4×C53C2311yescharacteristic
130C22×D4×C53C2311yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53—21no—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135#124×C53—22no—
136#124×C53C2×C414yescomplemented
137#123×C53—28no—
138C22⋊Q8×C53—22no—
139C22⋊Q8×C53C2×C414yescomplemented
140#121×C53—28no—
141#121×C53—22no—
142#121×C53C2×C414yescomplemented
143#120×C53—28no—
144C4×D4×C53—22no—
145C4×D4×C53C2×C414yes—
146C4×D4×C53C2×C414yescomplemented
147C4×D4×C53D414yes—
148C2×C4⋊C4×C53—21no—
149C2×C4⋊C4×C53D411yescharacteristic
150C2×C4⋊C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—28no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53—21no—
156C2×C22⋊C4×C53—21no—
157C2×C22⋊C4×C53D411yescharacteristic
158C2×C22⋊C4×C53D411yescharacteristic
159C2×C42×C53C2311yescharacteristic
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—24no—
163C24×C53—42no—
164C24×C53—42no—
165C24×C53—42no—
166C24×C53—42no—
167C24×C53—81no—
168C24×C53—81no—
169C24×C53C2×D411yescharacteristic
170C24×C53C2×D411yescharacteristic
171#41×C53—28no—
172#41×C53—44no—
173#41×C53—44no—
174#41×C53—44no—
175C2×Q8×C53—21no—
176C2×Q8×C53—21no—
177C2×Q8×C53—21no—
178C2×Q8×C53—21no—
179C2×Q8×C53—21no—
180C2×Q8×C53C22×C412yes—
181C2×D4×C53—22no—
182C2×D4×C53—22no—
183C2×D4×C53—28no—
184C2×D4×C53—24no—
185C2×D4×C53—24no—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—44no—
196C2×D4×C53—44no—
197C2×D4×C53—44no—
198C2×D4×C53—42no—
199C2×D4×C53—42no—
200C2×D4×C53—42no—
201C2×D4×C53—42no—
202C2×D4×C53—81no—
203C2×D4×C53—81no—
204C2×D4×C53C22⋊C414yes—
205C2×D4×C53C22×C412yes—
206C2×D4×C53C22×C412yes—
207C2×D4×C53C2×D412yes—
208C2×D4×C53#4112yes—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—24no—
220C22×C4×C53—24no—
221C22×C4×C53—42no—
222C22×C4×C53—42no—
223C22×C4×C53—81no—
224C22×C4×C53—81no—
225C22×C4×C53C22×C412yes—
226C22×C4×C53C22×C412yes—
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2411yescharacteristic
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—42no—
239C22×Dic53—42no—
240C22×Dic53—42no—
241C22×Dic53—42no—
242C22×Dic53—81no—
243C22×Dic53—81no—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53C22⋊C414yes—
247C4⋊C4×C53C22×C412yes—
248C22⋊C4×C53—24no—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53C22⋊C414yes—
254C22⋊C4×C53C22⋊C414yes—
255C42×C53C22×C412yes—
256C42×C53C2×D412yes—
257C22⋊Dic53—42no—
258C22⋊Dic53—42no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—42no—
267C4⋊Dic53—42no—
268C4⋊Dic53—42no—
269C4⋊Dic53—81no—
270C4⋊Dic53C2×D412yes—
271C4×Dic53—42no—
272#11719917—44no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—44no—
285C2×#88322C2×D412yes—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—22no—
291C23×C53—21no—
292C23×C53—22no—
293C23×C53—21no—
294C23×C53—22no—
295C23×C53—21no—
296C23×C53—21no—
297C23×C53—21no—
298C23×C53—21no—
299C23×C53—22no—
300C23×C53—48no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—48no—
312C23×C53—84no—
313C23×C53—84no—
314C23×C53—84no—
315C23×C53—84no—
316C23×C53—84no—
317C23×C53C2×C22⋊C412yes—
318C23×C53C2×C22⋊C412yes—
319C23×C53AGL(1,ℤ/8)12yes—
320C23×C53#13712yes—
321C23×C53C22×D411yescharacteristic
322Q8×C53—22no—
323Q8×C53—22no—
324Q8×C53—41no—
325Q8×C53—41no—
326D4×C53—28no—
327D4×C53—22no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—22no—
331D4×C53—22no—
332D4×C53—48no—
333D4×C53—48no—
334D4×C53—41no—
335D4×C53—41no—
336D4×C53—84no—
337D4×C53C4×D414yescomplemented
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—21no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—48no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—84no—
362C2×C4×C53C2×C22⋊C412yes—
363C2×C4×C53C2×C22⋊C412yes—
364C2×C4×C53C2×C22⋊C412yes—
365C2×C4×C53C2×C22⋊C412yes—
366C2×C4×C53C23×C411yescharacteristic
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C2×#4111yescharacteristic
370C2×C4×C53H(5,𝔽2)11yescharacteristic
371C2×C4×C53H(5,𝔽2)11yescharacteristic
372C2×Dic53—22no—
373C2×Dic53—41no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—41no—
379C2×Dic53—41no—
380C2×Dic53—41no—
381C2×Dic53—41no—
382C2×Dic53—41no—
383C2×Dic53—41no—
384C2×Dic53—84no—
385C2×Dic53—84no—
386#88322—22no—
387#88322—41no—
388#88322—41no—
389#88322—41no—
390#22419—531nomaximal, Sylow
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—22no—
394C22×C53—22no—
395C22×C53—22no—
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—24no—
399C22×C53—22no—
400C22×C53—22no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—41no—
404C22×C53—42no—
405C22×C53—41no—
406C22×C53—42no—
407C22×C53—41no—
408C22×C53—42no—
409C22×C53—41no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—42no—
413C22×C53—42no—
414C22×C53—816no—
415C22×C53—81no—
416C22×C53—81no—
417C22×C53—81no—
418C22×C53—81no—
419C22×C53#41714yescomplemented
420C22×C53C22×C22⋊C411yescharacteristic
421C22×C53D4211yescharacteristic
422C22×C53#54611yescharacteristic
423C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C53C2×#13711yescharacteristic
425C22×C53#57611yescharacteristic
426C22×C53#57711yescharacteristic
427C4×C53—22no—
428C4×C53—22no—
429C4×C53—22no—
430C4×C53—22no—
431C4×C53—42no—
432C4×C53—42no—
433C4×C53C2×C4×D411yescharacteristic
434C4×C53#51811yescharacteristic
435C4×C53D4211yescharacteristic
436C4×C53#54611yescharacteristic
437Dic53—42no—
438Dic53—81no—
439Dic53—81no—
440Dic53—81no—
441C2×#546D5311yescharacteristic
442C2×#435—531no—
443C2×#417—531no—
444C22×#102—531no—
445D4×C4⋊C4—531no—
446#1983—531no—
447#1959—531no—
448#1895—531no—
449#1892—531no—
450#1874—531no—
451#1872—531no—
452#1802—531no—
453#1788—531no—
454#1786—531no—
455#1762—531no—
456C2×C53—24no—
457C2×C53—42no—
458C2×C53—44no—
459C2×C53—82no—
460C2×C53D4×C22⋊C411yescharacteristic
461C2×C53C2×#41711yescharacteristic
462C2×C53#289711yescharacteristic
463C2×C53#326411yescharacteristic
464C2×C53#326611yescharacteristic
465C2×C53#330611yescharacteristic
466C2×C53#331411yescharacteristic
467C22×#41C2×D5311yescharacteristic
468C23×D4C2×D5311yescharacteristic
469C22×M16—531no—
470C23×C8—531no—
471#546—24no—
472#546Dic5318yescomplemented
473C2×#124C2×D5311yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C2×D5311yescharacteristic
476C2×#121—21no—
477C2×#121C2×D5311yescharacteristic
478C2×#120—21no—
479C2×C4×D4—1061no—
480C2×C4×D4C2×D5311yescharacteristic
481C2×C4×D4C2×D5311yescharacteristic
482C22×C4⋊C4—531no—
483C22×C4⋊C4—531no—
484C22×C22⋊C4—21no—
485#435—1064no—
486C2×C4⋊C8—531no—
487#417—1064no—
488C2×#103—531no—
489C2×#103—531no—
490C2×#103—531no—
491C2×#103—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×#102—531no—
495C2×#102—531no—
496C2×#102—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—1064no—
501C2×C22⋊C8—531no—
502C2×C22⋊C8—531no—
503C2×#97—531no—
504#389—1061no—
505#385—1061no—
506#385—1061no—
507#384—531no—
508#380—531no—
509#380—531no—
510C4×C4⋊C4—531no—
511#340—531no—
512#340—531no—
513#340—531no—
514#340—531no—
515C53#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×Dic5314yescomplemented
523C22×Q8C22×D5311yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×Dic5314yescomplemented
533C22×D4C22⋊D5311yescharacteristic
534C22×D4C22×D5311yescharacteristic
535C22×D4C22×D5311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—1061no—
539C23×C4—1061no—
540C23×C4C22×D5311yescharacteristic
541C23×C4C22×D5311yescharacteristic
542C2×M16—1062no—
543C2×M16—1062no—
544C2×M16—2121no—
545C22×C8—531no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—531no—
549C22×C8—1062no—
550C22×C8—1062no—
551C22×C8—2121no—
552#124—22no—
553#124C2×Dic5314yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×Dic5314yescomplemented
557#121—22no—
558#121—28no—
559#121C2×Dic5314yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—2124no—
563C4×D4C2×Dic5314yes—
564C4×D4C2×Dic5314yescomplemented
565C4×D4C22⋊D5314yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—531no—
568C2×C4⋊C4—531no—
569C2×C4⋊C4—531no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—1062no—
572C2×C4⋊C4—1062no—
573C2×C4⋊C4—1061no—
574C2×C4⋊C4—1061no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—2121no—
578C2×C4⋊C4—2121no—
579C2×C4⋊C4C22⋊D5311yescharacteristic
580C2×C4⋊C4C22×D5311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4C22⋊D5311yescharacteristic
590C2×C22⋊C4C22⋊D5311yescharacteristic
591C2×C42—1061no—
592C2×C42C22×D5311yescharacteristic
593C4⋊C8—1062no—
594#103—1062no—
595#103—1062no—
596#103—2121no—
597#103—2121no—
598#102—534no—
599#102—1062no—
600#102—1062no—
601#102—1062no—
602#102—1062no—
603#102—1062no—
604#102—2121no—
605#102—2121no—
606C22⋊C8—1062no—
607C22⋊C8—1062no—
608#97—1062no—
609#95—1061no—
610#95—1061no—
611#95—1061no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D5311yescharacteristic
622C24C2×C22⋊D5311yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×Dic5312yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic5314yes—
657C2×D4D4×D5312yes—
658C2×D4#1171994712yes—
659C2×D4C22×Dic5312yes—
660C2×D4C22×Dic5312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—1061no—
681C22×C4—4241no—
682C22×C4—4241no—
683C22×C4—2122no—
684C22×C4—2122no—
685C22×C4—2122no—
686C22×C4—2122no—
687C22×C4C22×Dic5312yes—
688C22×C4C22×Dic5312yes—
689C22×C4C2×C22⋊D5311yescharacteristic
690C22×C4C2×C22⋊D5311yescharacteristic
691C22×C4C2×C22⋊D5311yescharacteristic
692C22×C4C2×C22⋊D5311yescharacteristic
693C22×C4C2×C22⋊D5312yes—
694C22×C4C2×C22⋊D5312yes—
695C22×C4C23×D5311yescharacteristic
696M16—2124no—
697C2×C8—532no—
698C2×C8—1061no—
699C2×C8—1061no—
700C2×C8—1061no—
701C2×C8—1061no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—2124no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—532no—
713C4⋊C4—1061no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—4241no—
721C4⋊C4—2122no—
722C4⋊C4—2122no—
723C4⋊C4—2122no—
724C4⋊C4C22⋊Dic5314yes—
725C4⋊C4C22×Dic5312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—2122no—
732C22⋊C4—2122no—
733C22⋊C4C22⋊Dic5314yes—
734C22⋊C4C22⋊Dic5314yes—
735C42—2122no—
736C42C22×Dic5312yes—
737C42C2×C22⋊D5312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—48no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊Dic5312yes—
770C23C2×C22⋊Dic5312yes—
771C23#1313324212yes—
772C23#1313324712yes—
773C23C22×C22⋊D5311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic5314yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—1062no—
815C2×C4—4244no—
816C2×C4—4244no—
817C2×C4—2121no—
818C2×C4—2121no—
819C2×C4—2121no—
820C2×C4—2121no—
821C2×C4—2121no—
822C2×C4—2121no—
823C2×C4—2121no—
824C2×C4—2121no—
825C2×C4—2121no—
826C2×C4—2121no—
827C2×C4—2121no—
828C2×C4C2×C22⋊Dic5312yes—
829C2×C4C2×C22⋊Dic5312yes—
830C2×C4C2×C22⋊Dic5312yes—
831C2×C4C2×C22⋊Dic5312yes—
832C2×C4C23×Dic5311yescharacteristic
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4C22×C22⋊D5311yescharacteristic
835C2×C4C2×#1171994711yescharacteristic
836C2×C4#1313326211yescharacteristic
837C2×C4#1313326211yescharacteristic
838C8—1062no—
839C8—2121no—
840C8—2121no—
841C8—2121no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1681062414yescomplemented
871C22C22×C22⋊Dic5311yescharacteristic
872C22D4×C22⋊D5311yescharacteristic
873C22#1681126711yescharacteristic
874C22C2×#1313324211yescharacteristic
875C22C2×#1313324711yescharacteristic
876C22#1681142611yescharacteristic
877C22#1681143411yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—4241no—
885C4—4241no—
886C4—4241no—
887C4—2122no—
888C4C2×D4×Dic5311yescharacteristic
889C4#1681109811yescharacteristic
890C4D4×C22⋊D5311yescharacteristic
891C4#1681126711yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic5311yescharacteristic
897C2C2×#1681062411yescharacteristic
898C2#2028324111yescharacteristic
899C2#2028619611yescharacteristic
900C2#2028622111yescharacteristic
901C2#2028667611yescharacteristic
902C2#2028679611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#546C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#546D53
hypocenterC53#22419
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16810695C2semidirect
2. C2×#16810624C2semidirect
3. C22×#13133138C2semidirect
4. D4×C4⋊Dic53C2semidirect
5. #20275648C2semidirect
6. #20275532C2semidirect
7. #20275154C2semidirect
8. #20275139C2semidirect
9. #20275033C2semidirect
10. #20275023C2semidirect
11. #20274715C2semidirect
12. #20274655C2semidirect
13. #20274646C2semidirect
14. #20274540C2semidirect
16. C22×#11719917C22semidirect
20. C22×C4⋊Dic53C22semidirect
22. C2×C4⋊#88322C22semidirect
24. C2×#13133141C22semidirect
25. C2×#13133141C22semidirect
26. C2×#13133141C22semidirect
27. C2×#13133141C22semidirect
38. C2×C22⋊#88322C22semidirect
39. C2×#13133128C22semidirect
43. #16810493C22semidirect
45. #16810483C22semidirect
46. C4×C4⋊Dic53C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
54. C53×#546C4semidirect
104. #13133138D4semidirect
117. C2×#41×C53C2×C4semidirect
127. C22×D4×C53C2×C4semidirect
136. #124×C53C2×C4semidirect
139. C22⋊Q8×C53C2×C4semidirect
142. #121×C53C2×C4semidirect
146. C4×D4×C53C2×C4semidirect
337. D4×C53C4×D4semidirect
419. C22×C53#417semidirect
472. #546Dic53semidirect
515. C53#22419semidirect
522. C2×#41C2×Dic53semidirect
532. C22×D4C2×Dic53semidirect
553. #124C2×Dic53semidirect
556. C22⋊Q8C2×Dic53semidirect
559. #121C2×Dic53semidirect
564. C4×D4C2×Dic53semidirect
789. D4D4×Dic53semidirect
870. C22#16810624semidirect

Maximal subgroups

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

subgroupindex
C2×#168106952
C2×#168106242
C22×#131331382
D4×C4⋊Dic532
#202756482
#202755322
#202751542
#202751392
#202750332
#202750232
#202747152
#202746552
#202746462
#202745402
C2×C53×#5462
#2241953