Finite Group Databasebeta

← #27399566

Subgroups — #27399566

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×#16811269C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic, complemented
4C22×#13133137C211yesmaximal, characteristic, complemented
5#20275647C211yesmaximal, characteristic, complemented
6#20275529C211yesmaximal, characteristic, complemented
7#20275151C211yesmaximal, characteristic, complemented
8#20275136C211yesmaximal, characteristic, complemented
9#20275032C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274712C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic, complemented
13#20274645C211yesmaximal, characteristic, complemented
14#20274543C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18C22×#11719917C2211yescharacteristic, complemented
19C23×#88322C2211yescharacteristic
20#16811269—24no—
21#16811269C418yescomplemented
22C2×#13133205C2211yescharacteristic
23C2×#13133202—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133191C2211yescharacteristic
26C2×#13133190—21no—
27C2×#13133185—21no—
28C2×C4×D212C2211yescharacteristic
29C2×C22⋊C4×D53—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic, complemented
32#16810622—24no—
33C2×#13133140C2211yescharacteristic, complemented
34C2×#13133140C2211yescharacteristic, complemented
35C2×#13133140C2211yescharacteristic, complemented
36C2×#13133140C2211yescharacteristic, complemented
37C2×#13133137—24no—
38C2×#13133137C2211yescharacteristic
39C2×#13133137C2211yescharacteristic
40C2×#13133137C2211yescharacteristic
41C2×#13133137C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×#13133137C2211yescharacteristic
44C2×#13133137C2211yescharacteristic
45C2×#13133137C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic, complemented
48C2×#13133128C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53C2×C4×D4×C53—21no—
54C2×C4×D4×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic, complemented
57C53×#389—21no—
58C53×#385—21no—
59C53×#385—21no—
60C53×#384C2211yescharacteristic, complemented
61C53×#380C2211yescharacteristic
62C53×#380C2211yescharacteristic, complemented
63C4×C4⋊C4×C53C2211yescharacteristic, complemented
64C24×D53—21no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—22no—
68C2×#11719945—41no—
69C2×#11719945—41no—
70C2×#11719945C2×C414yescomplemented
71C22×Dic106C2311yescharacteristic
72C22×D212—22no—
73C22×D212—22no—
74C22×D212—22no—
75C22×D212—21no—
76C22×D212—41no—
77C22×D212—41no—
78C22×D212C2×C414yescomplemented
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C2×#11719917—22no—
86C2×#11719917—22no—
87C2×#11719917—41no—
88C22×#88322—22no—
89C22×#88322—22no—
90C22×#88322—41no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95#13133205—22no—
96#13133205C2×C414yescomplemented
97#13133202—28no—
98#13133196—22no—
99#13133196C2×C414yescomplemented
100#13133191—22no—
101#13133191C2×C414yescomplemented
102#13133190—28no—
103#13133185—28no—
104C4×D212—22no—
105C4×D212C2×C414yescomplemented
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×C22⋊Dic53—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C22⋊C4×D53—28no—
114C4⋊#88322—22no—
115#13133140—22no—
116#13133140—22no—
117#13133140—41no—
118#13133140—41no—
119#13133137—22no—
120#13133137—22no—
121#13133137—22no—
122#13133137—22no—
123#13133137—22no—
124#13133137—41no—
125#13133137—41no—
126#13133137D414yescomplemented
127C22⋊#88322—22no—
128C22⋊#88322—22no—
129#13133128—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53—21no—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C4×D4×C53—44no—
136C4×D4×C53C2×C414yes—
137C4×D4×C53D414yes—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53—21no—
142C2×C4⋊C4×C53—22no—
143C2×C4⋊C4×C53—22no—
144C2×C4⋊C4×C53—41no—
145C2×C4⋊C4×C53—41no—
146C2×C4⋊C4×C53D411yescharacteristic
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C4⋊C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53D411yescharacteristic
154C2×C22⋊C4×C53D411yescharacteristic
155C2×C42×C53—21no—
156C2×C42×C53C2311yescharacteristic
157#95×C53—21no—
158#95×C53—21no—
159#95×C53—21no—
160C24×C53C2×D411yescharacteristic
161C24×C53C2×D411yescharacteristic
162C23×D53—21no—
163C23×D53—21no—
164C23×D53—24no—
165C23×D53—42no—
166C23×D53—42no—
167C23×D53—42no—
168C23×D53—42no—
169C23×D53—81no—
170C23×D53—81no—
171C2×D4×C53—22no—
172C2×D4×C53—22no—
173C2×D4×C53C22⋊C414yes—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—42no—
187C22×C4×C53—42no—
188C22×C4×C53—42no—
189C22×C4×C53—42no—
190C22×C4×C53—81no—
191C22×C4×C53—81no—
192C22×C4×C53C22×C412yes—
193C22×C4×C53C22×C412yes—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—42no—
204C2×C22⋊D53—42no—
205C2×C22⋊D53—81no—
206C2×C22⋊D53—81no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209#11719945—28no—
210#11719945—44no—
211#11719945—44no—
212#11719945—44no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212—28no—
221C2×D212—24no—
222C2×D212—21no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212—44no—
226C2×D212—42no—
227C2×D212—42no—
228C2×D212C22×C412yes—
229C2×D212C22×C412yes—
230C2×D212C2×D412yes—
231C2×D212#4112yes—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—42no—
235C2×C4×D53—42no—
236C2×C4×D53—81no—
237C2×C4×D53—81no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106C22×C412yes—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—42no—
252C4⋊C4×C53—42no—
253C4⋊C4×C53—42no—
254C4⋊C4×C53—81no—
255C4⋊C4×C53C22⋊C414yes—
256C4⋊C4×C53C2×D412yes—
257C22⋊C4×C53—42no—
258C22⋊C4×C53—42no—
259C22⋊C4×C53C22⋊C414yes—
260C22⋊C4×C53C22⋊C414yes—
261C42×C53—42no—
262C42×C53C22×C412yes—
263C42×C53C2×D412yes—
264C22⋊Dic53—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53C22×C412yes—
271#11719919—24no—
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—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—21no—
296C23×C53C2×C22⋊C412yes—
297C23×C53C2×C22⋊C412yes—
298C23×C53AGL(1,ℤ/8)12yes—
299C23×C53#13712yes—
300C23×C53C22×D411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—48no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—48no—
317C22×D53—84no—
318C22×D53—84no—
319C22×D53—84no—
320C22×D53—84no—
321C22×D53—84no—
322D4×C53—28no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—84no—
352C2×C4×C53—84no—
353C2×C4×C53C2×C22⋊C412yes—
354C2×C4×C53C2×C22⋊C412yes—
355C2×C4×C53C2×C22⋊C412yes—
356C2×C4×C53C2×C22⋊C412yes—
357C2×C4×C53C23×C411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53C2×#4111yescharacteristic
361C2×C4×C53H(5,𝔽2)11yescharacteristic
362C2×C4×C53H(5,𝔽2)11yescharacteristic
363C22⋊D53—48no—
364C22⋊D53—84no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—22no—
376D212—48no—
377D212—41no—
378D212—41no—
379D212C4×D414yescomplemented
380C4×D53—48no—
381C4×D53—84no—
382Dic106—22no—
383Dic106—22no—
384Dic106—41no—
385Dic106—41no—
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—22no—
399C22×C53—22no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—41no—
403C22×C53—41no—
404C22×C53#41714yescomplemented
405C22×C53C22×C22⋊C411yescharacteristic
406C22×C53D4211yescharacteristic
407C22×C53#54611yescharacteristic
408C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C53C2×#13711yescharacteristic
410C22×C53#57611yescharacteristic
411C22×C53#57711yescharacteristic
412C2×D53—24no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—816no—
423C2×D53—81no—
424C2×D53—81no—
425C2×D53—81no—
426C2×D53—81no—
427C4×C53—22no—
428C4×C53—22no—
429C4×C53—22no—
430C4×C53—22no—
431C4×C53—42no—
432C4×C53—81no—
433C4×C53—81no—
434C4×C53—81no—
435C4×C53C2×C4×D411yescharacteristic
436C4×C53#51811yescharacteristic
437C4×C53D4211yescharacteristic
438C4×C53#54611yescharacteristic
439Dic53—42no—
440Dic53—42no—
441C2×#546—531no—
442C2×#435—531no—
443C2×#417—531no—
444C22×#102—531no—
445D4×C4⋊C4D5311yescharacteristic, complemented
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×C53D4×C22⋊C411yescharacteristic
459C2×C53C2×#41711yescharacteristic
460C2×C53#289711yescharacteristic
461C2×C53#326411yescharacteristic
462C2×C53#326611yescharacteristic
463C2×C53#330611yescharacteristic
464C2×C53#331411yescharacteristic
465D53—44no—
466D53—82no—
467C22×#41—531no—
468C23×D4—531no—
469C22×M16—531no—
470C23×C8—531no—
471#546—538no—
472#546—1064no—
473C2×#124—531no—
474C2×#123—1061no—
475C2×C22⋊Q8—531no—
476C2×#121—531no—
477C2×#121—1061no—
478C2×#120—1061no—
479C2×C4×D4—21no—
480C2×C4×D4—531no—
481C2×C4×D4C2×D5311yescharacteristic
482C22×C4⋊C4C2×D5311yescharacteristic
483C22×C4⋊C4C2×D5311yescharacteristic, complemented
484C22×C22⋊C4—1061no—
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—21no—
505#385—21no—
506#385—21no—
507#384C2×D5311yescharacteristic, complemented
508#380C2×D5311yescharacteristic
509#380C2×D5311yescharacteristic, complemented
510C4×C4⋊C4C2×D5311yescharacteristic, complemented
511#340—531no—
512#340—531no—
513#340—531no—
514#340—531no—
515C53#2241911yescharacteristic, complemented, Sylow
516C25—1061no—
517C2×#41—534no—
518C2×#41—1062no—
519C2×#41—1062no—
520C2×#41—1062no—
521C2×#41—2121no—
522C2×#41—2121no—
523C22×Q8—531no—
524C22×D4—534no—
525C22×D4—531no—
526C22×D4—531no—
527C22×D4—1062no—
528C22×D4—1062no—
529C22×D4—1061no—
530C22×D4—1061no—
531C22×D4—1062no—
532C22×D4—1061no—
533C22×D4—2121no—
534C22×D4—2121no—
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—534no—
553#124—1062no—
554#123—1068no—
555C22⋊Q8—534no—
556C22⋊Q8—1062no—
557#121—534no—
558#121—1062no—
559#121—1068no—
560#120—1068no—
561C4×D4—44no—
562C4×D4—534no—
563C4×D4—1062no—
564C4×D4C4×D5314yes—
565C4×D4D21214yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—531no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4C22⋊D5311yescharacteristic
577C2×C4⋊C4C22×D5311yescharacteristic
578C2×C4⋊C4C22×D5311yescharacteristic
579C2×C4⋊C4C22×D5311yescharacteristic
580C2×C4⋊C4C22×D5311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C22⋊C4—1061no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1068no—
589C2×C22⋊C4C22⋊D5311yescharacteristic
590C2×C22⋊C4C22⋊D5311yescharacteristic
591C2×C42—21no—
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—21no—
610#95—21no—
611#95—21no—
612C24—1061no—
613C24—1064no—
614C24—1061no—
615C24—4241no—
616C24—4241no—
617C24—2122no—
618C24—2122no—
619C24—2122no—
620C24—2122no—
621C24C2×C22⋊D5311yescharacteristic
622C24C2×C22⋊D5311yescharacteristic
623#41—1068no—
624#41—2124no—
625#41—2124no—
626#41—2124no—
627C2×Q8—532no—
628C2×Q8—1061no—
629C2×Q8—1061no—
630C2×Q8—1061no—
631C2×Q8—1061no—
632C2×Q8—1061no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—532no—
636C2×D4—532no—
637C2×D4—532no—
638C2×D4—532no—
639C2×D4—1068no—
640C2×D4—1064no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—1061no—
649C2×D4—1061no—
650C2×D4—1061no—
651C2×D4—4241no—
652C2×D4—4241no—
653C2×D4—2124no—
654C2×D4—2124no—
655C2×D4—2124no—
656C2×D4—2122no—
657C2×D4—2122no—
658C2×D4—2122no—
659C2×D4—2122no—
660C2×D4#1171992114yes—
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—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—1061no—
680C22×C4—1061no—
681C22×C4—1064no—
682C22×C4—1064no—
683C22×C4—4241no—
684C22×C4—4241no—
685C22×C4—2122no—
686C22×C4—2122no—
687C22×C4C2×C4×D5312yes—
688C22×C4C2×C4×D5312yes—
689C22×C4C2×D21212yes—
690C22×C4C2×D21212yes—
691C22×C4C2×C22⋊D5311yescharacteristic
692C22×C4C2×C22⋊D5311yescharacteristic
693C22×C4C2×C22⋊D5311yescharacteristic
694C22×C4C2×C22⋊D5311yescharacteristic
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—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—81no—
721C4⋊C4—532no—
722C4⋊C4—1064no—
723C4⋊C4—1061no—
724C4⋊C4#1171992114yes—
725C4⋊C4D4×D5312yes—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—1064no—
729C22⋊C4—1064no—
730C22⋊C4—1064no—
731C22⋊C4—1064no—
732C22⋊C4—1064no—
733C22⋊C4#1171992114yes—
734C22⋊C4#1171992114yes—
735C42—42no—
736C42C2×C4×D5312yes—
737C42C2×D21212yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—1062no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—4244no—
753C23—4244no—
754C23—4244no—
755C23—4244no—
756C23—4244no—
757C23—2128no—
758C23—2128no—
759C23—2121no—
760C23—2121no—
761C23—2121no—
762C23—2121no—
763C23—2121no—
764C23—2121no—
765C23—2121no—
766C23—2121no—
767C23—2121no—
768C23—2121no—
769C23C2×#1171992112yes—
770C23C2×#1171992112yes—
771C23#1313324312yes—
772C23#1313324812yes—
773C23C22×C22⋊D5311yescharacteristic
774Q8—1062no—
775Q8—1062no—
776Q8—2121no—
777Q8—2121no—
778D4—28no—
779D4—534no—
780D4—1062no—
781D4—1062no—
782D4—1062no—
783D4—1062no—
784D4—1062no—
785D4—4244no—
786D4—2128no—
787D4—2128no—
788D4—2121no—
789D4—2121no—
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—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—4244no—
823C2×C4—2128no—
824C2×C4—2121no—
825C2×C4—2121no—
826C2×C4—2121no—
827C2×C4—2121no—
828C2×C4C2×#1171992112yes—
829C2×C4C2×#1171992112yes—
830C2×C4C2×#1171992112yes—
831C2×C4C2×#1171992112yes—
832C2×C4C22×C4×D5311yescharacteristic
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4C22×D21211yescharacteristic
835C2×C4#41×D5311yescharacteristic
836C2×C4#1313326211yescharacteristic
837C2×C4#1313326311yescharacteristic
838C8—1062no—
839C8—2121no—
840C8—2121no—
841C8—2121no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—1064no—
856C22—42416no—
857C22—4241no—
858C22—4241no—
859C22—4241no—
860C22—4241no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2122no—
865C22—2122no—
866C22—2122no—
867C22—2122no—
868C22—2122no—
869C22—2122no—
870C22#1681062214yescomplemented
871C22C22×#1171992111yescharacteristic
872C22D4×C22⋊D5311yescharacteristic
873C22#1681126111yescharacteristic
874C22C2×#1313324311yescharacteristic
875C22C2×#1313324811yescharacteristic
876C22#1681142611yescharacteristic
877C22#1681143111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—2122no—
887C4—2122no—
888C4C4×D4×D5311yescharacteristic
889C4#1681109511yescharacteristic
890C4D4×D21211yescharacteristic
891C4#1681126811yescharacteristic
892C2—24no—
893C2—42no—
894C2—4242no—
895C2—2124no—
896C2D4×#1171992111yescharacteristic
897C2C2×#1681062211yescharacteristic
898C2#2028323811yescharacteristic
899C2#2028619111yescharacteristic
900C2#2028622611yescharacteristic
901C2#2028667011yescharacteristic
902C2#2028679011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×C4⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenterD4×C4⋊C4D53
hypocenterC53#22419
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. C2×#16810622C2semidirect
4. C22×#13133137C2semidirect
5. #20275647C2semidirect
6. #20275529C2semidirect
7. #20275151C2semidirect
8. #20275136C2semidirect
9. #20275032C2semidirect
10. #20275022C2semidirect
11. #20274712C2semidirect
12. #20274653C2semidirect
13. #20274645C2semidirect
14. #20274543C2semidirect
15. D4×C4⋊C4×C53C2semidirect
18. C22×#11719917C22semidirect
21. #16811269C4semidirect
31. C2×C4⋊#88322C22semidirect
33. C2×#13133140C22semidirect
34. C2×#13133140C22semidirect
35. C2×#13133140C22semidirect
36. C2×#13133140C22semidirect
47. C2×C22⋊#88322C22semidirect
48. C2×#13133128C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
56. C22×C4⋊C4×C53C22semidirect
60. C53×#384C22semidirect
62. C53×#380C22semidirect
63. C4×C4⋊C4×C53C22semidirect
70. C2×#11719945C2×C4semidirect
78. C22×D212C2×C4semidirect
96. #13133205C2×C4semidirect
99. #13133196C2×C4semidirect
101. #13133191C2×C4semidirect
105. C4×D212C2×C4semidirect
126. #13133137D4semidirect
379. D212C4×D4semidirect
404. C22×C53#417semidirect
445. D4×C4⋊C4D53semidirect
483. C22×C4⋊C4C2×D53semidirect
507. #384C2×D53semidirect
509. #380C2×D53semidirect
510. C4×C4⋊C4C2×D53semidirect
515. C53#22419semidirect
870. C22#16810622semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
C2×#168106952
C2×#168106222
C22×#131331372
#202756472
#202755292
#202751512
#202751362
#202750322
#202750222
#202747122
#202746532
#202746452
#202745432
D4×C4⋊C4×C532
#2241953