Finite Group Databasebeta

← #27399692

Subgroups — #27399692

Order 13568.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810701C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3C2×#16810628C211yesmaximal, characteristic, complemented
4#20277644C211yesmaximal, characteristic, complemented
5#20275648C211yesmaximal, characteristic, complemented
6#20275527C211yesmaximal, characteristic, complemented
7#20275154C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275033C211yesmaximal, characteristic, complemented
10#20275028C211yesmaximal, characteristic, complemented
11#20274725C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274646C211yesmaximal, characteristic, complemented
14C4×#13133138C211yesmaximal, characteristic, complemented
15C2×C53×#546C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic, complemented
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic, complemented
20#16810701—24no—
21C2×C4⋊#88322C2211yescharacteristic, complemented
22#16810628—24no—
23#16810624—24no—
24C2×#13133141C2211yescharacteristic, complemented
25C2×#13133141C2211yescharacteristic, complemented
26C2×#13133141C2211yescharacteristic, complemented
27C2×#13133141C2211yescharacteristic, complemented
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic, complemented
38C2×C4×#88322C2211yescharacteristic, complemented
39#16810516—21no—
40#16810509—21no—
41#16810503—21no—
42#16810489C2211yescharacteristic, complemented
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic, complemented
45C4×C4⋊Dic53C2211yescharacteristic, complemented
46C22⋊C4×Dic53—21no—
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—
65C2×#11719917—22no—
66C2×#11719917—22no—
67C2×#11719917—22no—
68C2×#11719917—22no—
69C2×#11719917—41no—
70C2×#11719917—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133176—22no—
76#13133176—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89C4⋊#88322—22no—
90#13133141—22no—
91#13133141—22no—
92#13133141—41no—
93#13133141—41no—
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138—22no—
98#13133138—22no—
99#13133138—41no—
100#13133138—41no—
101#13133138D414yescomplemented
102C22⋊#88322—22no—
103C22⋊#88322—22no—
104C4×#88322—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C25×C53—21no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53—41no—
115C2×#41×C53—41no—
116C2×#41×C53C2×C414yes—
117C22×Q8×C53C2311yescharacteristic
118C22×D4×C53—22no—
119C22×D4×C53—22no—
120C22×D4×C53—21no—
121C22×D4×C53—21no—
122C22×D4×C53—21no—
123C22×D4×C53—22no—
124C22×D4×C53—41no—
125C22×D4×C53—41no—
126C22×D4×C53C2×C414yescomplemented
127C22×D4×C53D411yescharacteristic
128C22×D4×C53C2311yescharacteristic
129C22×D4×C53C2311yescharacteristic
130C23×C4×C53—21no—
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134#124×C53—22no—
135#124×C53C2×C414yescomplemented
136#123×C53—28no—
137C22⋊Q8×C53—22no—
138C22⋊Q8×C53C2×C414yescomplemented
139#121×C53—28no—
140#121×C53—22no—
141#121×C53C2×C414yes—
142#120×C53—28no—
143C4×D4×C53—22no—
144C4×D4×C53C2×C414yes—
145C4×D4×C53C2×C414yescomplemented
146C4×D4×C53D414yes—
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53D411yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C22⋊C4×C53—28no—
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53—21no—
156C2×C22⋊C4×C53D411yescharacteristic
157C2×C22⋊C4×C53D411yescharacteristic
158C2×C42×C53C2311yescharacteristic
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—24no—
162C24×C53—42no—
163C24×C53—42no—
164C24×C53—42no—
165C24×C53—42no—
166C24×C53—81no—
167C24×C53—81no—
168C24×C53C2×D411yescharacteristic
169C24×C53C2×D411yescharacteristic
170#41×C53—28no—
171#41×C53—44no—
172#41×C53—44no—
173#41×C53—44no—
174C2×Q8×C53—21no—
175C2×Q8×C53—21no—
176C2×Q8×C53—21no—
177C2×Q8×C53—21no—
178C2×Q8×C53—21no—
179C2×Q8×C53C22×C412yes—
180C2×D4×C53—28no—
181C2×D4×C53—24no—
182C2×D4×C53—24no—
183C2×D4×C53—24no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—41no—
196C2×D4×C53—41no—
197C2×D4×C53—42no—
198C2×D4×C53—42no—
199C2×D4×C53—42no—
200C2×D4×C53—42no—
201C2×D4×C53—81no—
202C2×D4×C53—81no—
203C2×D4×C53C22⋊C414yes—
204C2×D4×C53C22×C412yes—
205C2×D4×C53C22×C412yes—
206C2×D4×C53C2×D412yes—
207C2×D4×C53#4112yes—
208C22×C4×C53—21no—
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—24no—
219C22×C4×C53—24no—
220C22×C4×C53—42no—
221C22×C4×C53—42no—
222C22×C4×C53—81no—
223C22×C4×C53—81no—
224C22×C4×C53C22×C412yes—
225C22×C4×C53C22×C412yes—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2411yescharacteristic
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—42no—
238C22×Dic53—42no—
239C22×Dic53—81no—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53C22⋊C414yes—
243C4⋊C4×C53C22×C412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53—24no—
249C22⋊C4×C53C22⋊C414yes—
250C22⋊C4×C53C22⋊C414yes—
251C42×C53C22×C412yes—
252C42×C53C2×D412yes—
253C22⋊Dic53—42no—
254C22⋊Dic53—42no—
255C22⋊Dic53—81no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—42no—
264C4⋊Dic53C2×D412yes—
265C4×Dic53—42no—
266C4×Dic53—81no—
267#11719917—44no—
268#11719917—44no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322C2×D412yes—
281C23×C53—22no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—22no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—22no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—21no—
296C23×C53—22no—
297C23×C53—48no—
298C23×C53—48no—
299C23×C53—41no—
300C23×C53—41no—
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—84no—
310C23×C53—84no—
311C23×C53—84no—
312C23×C53—84no—
313C23×C53—84no—
314C23×C53C2×C22⋊C412yes—
315C23×C53C2×C22⋊C412yes—
316C23×C53C22×D411yescharacteristic
317Q8×C53—22no—
318Q8×C53—22no—
319Q8×C53—41no—
320Q8×C53—41no—
321D4×C53—22no—
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—44no—
327D4×C53—48no—
328D4×C53—48no—
329D4×C53—41no—
330D4×C53—41no—
331D4×C53—84no—
332D4×C53C4×D414yes—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—48no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—84no—
357C2×C4×C53C2×C22⋊C412yes—
358C2×C4×C53C2×C22⋊C412yes—
359C2×C4×C53C2×C22⋊C412yes—
360C2×C4×C53C2×C22⋊C412yes—
361C2×C4×C53C23×C411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C2×#4111yescharacteristic
365C2×C4×C53H(5,𝔽2)11yescharacteristic
366C2×C4×C53H(5,𝔽2)11yescharacteristic
367C2×Dic53—22no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—41no—
377C2×Dic53—41no—
378C2×Dic53—41no—
379C2×Dic53—84no—
380#88322—22no—
381#88322—41no—
382#88322—41no—
383#88322—41no—
384#22427—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—24no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—22no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—42no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—42no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—42no—
403C22×C53—41no—
404C22×C53—41no—
405C22×C53—42no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—816no—
410C22×C53—81no—
411C22×C53—81no—
412C22×C53—81no—
413C22×C53—81no—
414C22×C53C22×C22⋊C411yescharacteristic
415C22×C53D4211yescharacteristic
416C22×C53#54611yescharacteristic
417C22×C53#57511yescharacteristic
418C22×C53#57511yescharacteristic
419C22×C53#57611yescharacteristic
420C22×C53#57711yescharacteristic
421C4×C53—22no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—22no—
425C4×C53—42no—
426C4×C53—42no—
427C4×C53C2×C4×D411yescharacteristic
428C4×C53#51811yescharacteristic
429C4×C53D4211yescharacteristic
430C4×C53#54611yescharacteristic
431Dic53—42no—
432Dic53—81no—
433Dic53—81no—
434Dic53—81no—
435C2×#546D5311yescharacteristic
436C2×#436—531no—
437C2×#417—531no—
438C2×#418—531no—
439#2352—531no—
440#1983—531no—
441#1958—531no—
442#1895—531no—
443#1894—531no—
444#1874—531no—
445#1873—531no—
446#1804—531no—
447#1788—531no—
448#1786—531no—
449C4×#102—531no—
450C2×C53—42no—
451C2×C53—42no—
452C2×C53—44no—
453C2×C53—82no—
454C2×C53D4×C22⋊C411yescharacteristic
455C2×C53#289611yescharacteristic
456C2×C53#289711yescharacteristic
457C2×C53#327311yescharacteristic
458C2×C53#327511yescharacteristic
459C2×C53#332211yescharacteristic
460C2×C53#332311yescharacteristic
461C22×#41C2×D5311yescharacteristic
462C23×D4C2×D5311yescharacteristic
463C22×M16—531no—
464C22×M16—531no—
465#546—24no—
466#546Dic5318yescomplemented
467C2×#124C2×D5311yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D5311yescharacteristic
470C2×#121—21no—
471C2×#121C2×D5311yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D5311yescharacteristic
474C2×C4×D4C2×D5311yescharacteristic
475C2×#117—531no—
476C22×C4⋊C4—531no—
477C22×C22⋊C4—21no—
478#436—1064no—
479C2×C4⋊C8—531no—
480#418—1064no—
481#417—1064no—
482C2×#103—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#102—531no—
487C2×#102—531no—
488C2×#102—531no—
489C2×#102—531no—
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×C22⋊C8—531no—
495C2×C22⋊C8—531no—
496C2×C4×C8—531no—
497#388—1061no—
498#387—1061no—
499#386—1061no—
500#382—531no—
501#380—531no—
502#380—531no—
503C4×C4⋊C4—531no—
504C4×C22⋊C4—1061no—
505#340—531no—
506#340—531no—
507#340—531no—
508#340—531no—
509C53#2242711yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×Dic5314yes—
517C22×Q8C22×D5311yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×Dic5314yescomplemented
527C22×D4C22⋊D5311yescharacteristic
528C22×D4C22×D5311yescharacteristic
529C22×D4C22×D5311yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C23×C4C22×D5311yescharacteristic
535C2×M16—1062no—
536C2×M16—1062no—
537C2×M16—1062no—
538C2×M16—1062no—
539C2×M16—2121no—
540C2×M16—2121no—
541C22×C8—531no—
542C22×C8—531no—
543C22×C8—531no—
544C22×C8—531no—
545#124—22no—
546#124C2×Dic5314yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×Dic5314yescomplemented
550#121—22no—
551#121—28no—
552#121C2×Dic5314yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×Dic5314yes—
556C4×D4C2×Dic5314yescomplemented
557C4×D4C22⋊D5314yes—
558#117—1062no—
559#117—2121no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—1062no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—2121no—
568C2×C4⋊C4C22⋊D5311yescharacteristic
569C2×C4⋊C4C22×D5311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C22⋊C4C22⋊D5311yescharacteristic
580C2×C22⋊C4C22⋊D5311yescharacteristic
581C2×C42—1061no—
582C2×C42—1061no—
583C2×C42C22×D5311yescharacteristic
584C4⋊C8—1062no—
585#103—1062no—
586#103—1062no—
587#103—2121no—
588#103—2121no—
589#102—534no—
590#102—1062no—
591#102—1062no—
592#102—1062no—
593#102—1062no—
594#102—1062no—
595#102—2121no—
596#102—2121no—
597C22⋊C8—1062no—
598C22⋊C8—1062no—
599C4×C8—1062no—
600#95—1061no—
601#95—1061no—
602#95—1061no—
603#95—1061no—
604#95—1061no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D5311yescharacteristic
615C24C2×C22⋊D5311yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic5312yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic5314yes—
650C2×D4D4×D5312yes—
651C2×D4#1171994712yes—
652C2×D4C22×Dic5312yes—
653C2×D4C22×Dic5312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—1061no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4—1061no—
674C22×C4—4241no—
675C22×C4—2122no—
676C22×C4—2122no—
677C22×C4C22×Dic5312yes—
678C22×C4C22×Dic5312yes—
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5312yes—
684C22×C4C2×C22⋊D5312yes—
685C22×C4C23×D5311yescharacteristic
686M16—2124no—
687M16—2124no—
688C2×C8—532no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—1061no—
697C2×C8—1061no—
698C2×C8—1061no—
699C2×C8—1061no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—532no—
703C4⋊C4—1061no—
704C4⋊C4—1061no—
705C4⋊C4—1061no—
706C4⋊C4—1061no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1061no—
710C4⋊C4—2122no—
711C4⋊C4C22⋊Dic5314yes—
712C4⋊C4C22×Dic5312yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—4241no—
719C22⋊C4—2122no—
720C22⋊C4—2122no—
721C22⋊C4C22⋊Dic5314yes—
722C22⋊C4C22⋊Dic5314yes—
723C42—4241no—
724C42—2122no—
725C42C22×Dic5312yes—
726C42C2×C22⋊D5312yes—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic5312yes—
761C23C2×C22⋊Dic5312yes—
762C23C22×C22⋊D5311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic5314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—1062no—
804C2×C4—4244no—
805C2×C4—2121no—
806C2×C4—2121no—
807C2×C4—2121no—
808C2×C4—2121no—
809C2×C4—2121no—
810C2×C4—2121no—
811C2×C4—2121no—
812C2×C4—2121no—
813C2×C4—2121no—
814C2×C4—2121no—
815C2×C4—2121no—
816C2×C4C2×C22⋊Dic5312yes—
817C2×C4C2×C22⋊Dic5312yes—
818C2×C4C2×C22⋊Dic5312yes—
819C2×C4C2×C22⋊Dic5312yes—
820C2×C4C23×Dic5311yescharacteristic
821C2×C4C2×D4×D5311yescharacteristic
822C2×C4C22×C22⋊D5311yescharacteristic
823C2×C4C2×#1171994711yescharacteristic
824C2×C4#1313326211yescharacteristic
825C2×C4#1313326211yescharacteristic
826C8—1062no—
827C8—2121no—
828C8—2121no—
829C8—2121no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊Dic5311yescharacteristic
860C22D4×C22⋊D5311yescharacteristic
861C22#1681126711yescharacteristic
862C22#1681142111yescharacteristic
863C22#1681142111yescharacteristic
864C22#1681142611yescharacteristic
865C22#1681143411yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—4241no—
873C4—4241no—
874C4—4241no—
875C4—2122no—
876C4C2×D4×Dic5311yescharacteristic
877C4#1681109811yescharacteristic
878C4D4×C22⋊D5311yescharacteristic
879C4#1681126711yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic5311yescharacteristic
885C2#2028323411yescharacteristic
886C2#2028324111yescharacteristic
887C2#2028632211yescharacteristic
888C2#2028634211yescharacteristic
889C2#2028691611yescharacteristic
890C2#2028693111yescharacteristic
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#22427
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×#16810701C2semidirect
2. C2×#16810624C2semidirect
3. C2×#16810628C2semidirect
4. #20277644C2semidirect
5. #20275648C2semidirect
6. #20275527C2semidirect
7. #20275154C2semidirect
8. #20275149C2semidirect
9. #20275033C2semidirect
10. #20275028C2semidirect
11. #20274725C2semidirect
12. #20274655C2semidirect
13. #20274646C2semidirect
14. C4×#13133138C2semidirect
17. C22×#11719917C22semidirect
19. C22×C4⋊Dic53C22semidirect
21. C2×C4⋊#88322C22semidirect
24. C2×#13133141C22semidirect
25. C2×#13133141C22semidirect
26. C2×#13133141C22semidirect
27. C2×#13133141C22semidirect
37. C2×C22⋊#88322C22semidirect
38. C2×C4×#88322C22semidirect
42. #16810489C22semidirect
44. #16810483C22semidirect
45. C4×C4⋊Dic53C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
54. C53×#546C4semidirect
101. #13133138D4semidirect
126. C22×D4×C53C2×C4semidirect
135. #124×C53C2×C4semidirect
138. C22⋊Q8×C53C2×C4semidirect
145. C4×D4×C53C2×C4semidirect
466. #546Dic53semidirect
509. C53#22427semidirect
526. C22×D4C2×Dic53semidirect
546. #124C2×Dic53semidirect
549. C22⋊Q8C2×Dic53semidirect
556. C4×D4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107012
C2×#168106242
C2×#168106282
#202776442
#202756482
#202755272
#202751542
#202751492
#202750332
#202750282
#202747252
#202746552
#202746462
C4×#131331382
C2×C53×#5462
#2242753