Finite Group Databasebeta

← C2×#20286236 #28259085

Subgroups — C2×#20286236 #28259085

Order 13568.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133243C211yesmaximal, characteristic, complemented
2C22×#13133237C211yesmaximal, characteristic, complemented
3C2×#16811278C211yesmaximal, characteristic, complemented
4#20286236C2116yesmaximal, direct product factor
5C2×#16811018C211yesmaximal, characteristic, complemented
6C2×#16810879C211yesmaximal, characteristic, complemented
7C2×#16810850C211yesmaximal, characteristic, complemented
8C2×#16810835C211yesmaximal, characteristic, complemented
9C2×#16810828C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic, complemented
13C2×#16810774C211yesmaximal, characteristic, complemented
14C2×#16810733C211yesmaximal, characteristic, complemented
15C2×#16810695C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic, complemented
19C2×#13133243—28no—
20C2×#13133243C2218yescomplemented
21C2×#13133237—28no—
22C2×#13133237C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719925C2211yescharacteristic, complemented
25C22×#11719923C2211yescharacteristic
26C22×#11719923C2211yescharacteristic
27C22×#11719923C2211yescharacteristic
28C22×#11719923C2211yescharacteristic
29C22×#11719924C2211yescharacteristic, complemented
30C22×#11719922C2211yescharacteristic
31C22×#11719922C2211yescharacteristic
32C22×#11719917C2211yescharacteristic
33C23×#88322C2211yescharacteristic, complemented
34#16811278—24no—
35#16811278C2218yescomplemented
36C2×#13133217C2211yescharacteristic, complemented
37C2×#13133199—21no—
38C2×#13133199—21no—
39C2×#13133196C2211yescharacteristic
40C2×#13133196C2211yescharacteristic, complemented
41C2×#13133188—21no—
42C2×C4×D212C2211yescharacteristic, complemented
43C2×C4⋊C4×D53—21no—
44#16811018C2218yescomplemented
45#16810879C2218yescomplemented
46#16810850C2218yescomplemented
47#16810835C2218yescomplemented
48#16810828C2218yescomplemented
49#16810785C2218yescomplemented
50#16810783C2218yescomplemented
51#16810774C2218yescomplemented
52#16810766C2218yescomplemented
53#16810733C2218yescomplemented
54#16810695C2218yescomplemented
55C2×#13133148C2211yescharacteristic, complemented
56C2×C4⋊#88322C2211yescharacteristic, complemented
57C2×#13133141C2211yescharacteristic, complemented
58C2×#13133140C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133138C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133137C2211yescharacteristic, complemented
63C2×C22⋊#88322C2211yescharacteristic
64C2×C22⋊#88322C2211yescharacteristic, complemented
65C2×#13133128C2211yescharacteristic, complemented
66C22×#41×C53C2211yescharacteristic
67C23×D4×C53C2211yescharacteristic
68C53×#546—24no—
69C53×#546C2218yescomplemented
70C2×#124×C53C2211yescharacteristic
71C2×#123×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53—21no—
74C2×#121×C53C2211yescharacteristic
75C2×#120×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C2×C4×D4×C53C2211yescharacteristic
78C22×C22⋊C4×C53—21no—
79C2×#11719945—22no—
80C2×#11719945—22no—
81C2×#11719945—24no—
82C2×#11719945—24no—
83C2×#11719945—42no—
84C2×#11719945—42no—
85C2×#11719945C2314yes—
86C2×#11719945C2314yescomplemented
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95#13133243—232no—
96#13133237—232no—
97C2×#11719925—24no—
98C2×#11719925—42no—
99C2×#11719925C2314yescomplemented
100C2×#11719925C2314yescomplemented
101C2×#11719923—24no—
102C2×#11719923—24no—
103C2×#11719923—24no—
104C2×#11719923—42no—
105C2×#11719923C2314yes—
106C2×#11719923C2314yes—
107C2×#11719923C2314yes—
108C2×#11719923C2314yes—
109C2×#11719924—24no—
110C2×#11719924C2314yescomplemented
111C2×#11719922—24no—
112C2×#11719922D418yescomplemented
113C2×#11719922C2314yes—
114C2×#11719922C2314yes—
115C2×#11719917—24no—
116C2×#11719917C2314yes—
117C22×#88322—24no—
118C22×#88322C2311yescharacteristic
119C22×#88322C2311yescharacteristic
120C22×#88322C2311yescharacteristic
121C22×#88322C2311yescharacteristic
122C22×#88322C2314yescomplemented
123#13133217—22no—
124#13133217C2314yescomplemented
125#13133199—28no—
126#13133199—28no—
127#13133196—22no—
128#13133196—22no—
129#13133196C2314yes—
130#13133196C2314yescomplemented
131#13133188—28no—
132C4×D212—22no—
133C4×D212C2314yescomplemented
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C4⋊C4×D53—28no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143#13133148C2314yescomplemented
144C4⋊#88322C2314yescomplemented
145#13133141C2314yescomplemented
146#13133140C2314yescomplemented
147#13133140C2314yescomplemented
148#13133138C2314yes—
149#13133138C2314yes—
150#13133137C2314yescomplemented
151C22⋊#88322C2314yes—
152C22⋊#88322C2314yescomplemented
153#13133128C2314yescomplemented
154C25×C53—21no—
155C2×#41×C53—22no—
156C2×#41×C53—24no—
157C2×#41×C53—42no—
158C2×#41×C53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C22×D4×C53—24no—
161C22×D4×C53—21no—
162C22×D4×C53—21no—
163C22×D4×C53—21no—
164C22×D4×C53—22no—
165C22×D4×C53—42no—
166C22×D4×C53D411yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C22×D4×C53C2314yes—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C23×C4×C53C2311yescharacteristic
174#124×C53—22no—
175#124×C53C2314yes—
176#123×C53—28no—
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179#121×C53—28no—
180#121×C53—22no—
181#121×C53C2314yes—
182#120×C53—28no—
183C4×D4×C53—22no—
184C4×D4×C53D414yes—
185C4×D4×C53C2314yes—
186C4×D4×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53D411yescharacteristic
189C2×C4⋊C4×C53C2311yescharacteristic
190C2×C22⋊C4×C53—28no—
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53—21no—
194C2×C22⋊C4×C53—21no—
195C2×C22⋊C4×C53—21no—
196C2×C22⋊C4×C53D411yescharacteristic
197C2×C22⋊C4×C53D411yescharacteristic
198C2×C42×C53C2311yescharacteristic
199C24×C53—21no—
200C24×C53—21no—
201C24×C53—24no—
202C24×C53—44no—
203C24×C53—44no—
204C24×C53—82no—
205C24×C53C2×D411yescharacteristic
206C24×C53C2×D411yescharacteristic
207C23×D53—21no—
208#41×C53—28no—
209#41×C53—44no—
210#41×C53—48no—
211C2×Q8×C53—21no—
212C2×Q8×C53—22no—
213C2×Q8×C53—22no—
214C2×Q8×C53C2412yes—
215C2×D4×C53—28no—
216C2×D4×C53—24no—
217C2×D4×C53—24no—
218C2×D4×C53—21no—
219C2×D4×C53—22no—
220C2×D4×C53—24no—
221C2×D4×C53—21no—
222C2×D4×C53—22no—
223C2×D4×C53—22no—
224C2×D4×C53—44no—
225C2×D4×C53—48no—
226C2×D4×C53—42no—
227C2×D4×C53—44no—
228C2×D4×C53—44no—
229C2×D4×C53—82no—
230C2×D4×C53C2×D414yes—
231C2×D4×C53C2×D414yes—
232C2×D4×C53C2412yes—
233C2×D4×C53C2412yes—
234C22×C4×C53—22no—
235C22×C4×C53—22no—
236C22×C4×C53—22no—
237C22×C4×C53—22no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—24no—
241C22×C4×C53—24no—
242C22×C4×C53—44no—
243C22×C4×C53—82no—
244C22×C4×C53C2×D411yescharacteristic
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D412yes—
249C22×C4×C53C2×D412yes—
250C22×C4×C53C2412yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2411yescharacteristic
253C2×C22⋊D53—24no—
254C2×C22⋊D53—24no—
255C2×C22⋊D53—44no—
256C2×C22⋊D53—44no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260#11719945—28no—
261#11719945—28no—
262#11719945—44no—
263#11719945—44no—
264#11719945—48no—
265#11719945—48no—
266C2×D212—21no—
267C2×D212—22no—
268C2×D212C2×D414yes—
269C2×D212C2412yes—
270C2×C4×D53—24no—
271C2×C4×D53—24no—
272C2×C4×D53—24no—
273C2×C4×D53—44no—
274C2×C4×D53—44no—
275C2×C4×D53—44no—
276C2×Dic106—22no—
277C2×Dic106—22no—
278C2×Dic106—22no—
279C2×Dic106—22no—
280C2×Dic106—21no—
281C2×Dic106—21no—
282C2×Dic106C2412yes—
283C2×Dic106C2412yes—
284C4⋊C4×C53—24no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53C2×D414yes—
287C4⋊C4×C53C2412yes—
288C22⋊C4×C53—24no—
289C22⋊C4×C53—24no—
290C22⋊C4×C53—24no—
291C22⋊C4×C53—24no—
292C22⋊C4×C53—24no—
293C22⋊C4×C53C2×D414yes—
294C22⋊C4×C53C2×D414yes—
295C42×C53C2×D412yes—
296C42×C53C2412yes—
297C22⋊Dic53—24no—
298C22⋊Dic53—24no—
299#11719925—28no—
300#11719925—44no—
301#11719924—28no—
302#11719923—28no—
303#11719923—28no—
304#11719923—28no—
305#11719923—44no—
306#11719922—28no—
307#11719922C2×D4116yescomplemented
308#11719921—24no—
309C4⋊Dic53—24no—
310C4⋊Dic53—24no—
311C4⋊Dic53—21no—
312C4⋊Dic53C2412yes—
313#11719919—24no—
314#11719919—24no—
315#11719917—28no—
316C2×#88322—22no—
317C2×#88322—22no—
318C2×#88322—22no—
319C2×#88322—28no—
320C2×#88322C2×D414yes—
321C2×#88322C2412yes—
322C2×#88322C2412yes—
323C2×#88322C2412yes—
324C2×#88322C2412yes—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—24no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—48no—
335C23×C53—48no—
336C23×C53—42no—
337C23×C53—42no—
338C23×C53—42no—
339C23×C53—42no—
340C23×C53—42no—
341C23×C53—84no—
342C23×C53—816no—
343C23×C53C22×D412yes—
344C23×C53C22×D412yes—
345C23×C53C22×D411yescharacteristic
346C22×D53—24no—
347C22×D53—22no—
348C22×D53—42no—
349C22×D53—42no—
350Q8×C53—22no—
351Q8×C53—22no—
352Q8×C53—42no—
353D4×C53—24no—
354D4×C53—22no—
355D4×C53—22no—
356D4×C53—22no—
357D4×C53—44no—
358D4×C53—48no—
359D4×C53—48no—
360D4×C53—42no—
361D4×C53—84no—
362D4×C53C22×D414yes—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—24no—
368C2×C4×C53—24no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—48no—
376C2×C4×C53—42no—
377C2×C4×C53—42no—
378C2×C4×C53—84no—
379C2×C4×C53C22×D412yes—
380C2×C4×C53C22×D412yes—
381C2×C4×C53C22×D412yes—
382C2×C4×C53C22×D412yes—
383C2×C4×C53C22×D412yes—
384C2×C4×C53C22×D411yescharacteristic
385C2×C4×C53H(5,𝔽2)12yes—
386C2×C4×C53C2511yescharacteristic
387C22⋊D53—48no—
388C22⋊D53—48no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—42no—
393C2×Dic53—42no—
394C2×Dic53—42no—
395D212—24no—
396D212—22no—
397D212C22×D414yes—
398C4×D53—48no—
399C4×D53—48no—
400C4×D53—48no—
401Dic106—22no—
402Dic106—22no—
403Dic106—22no—
404Dic106—22no—
405Dic106—42no—
406Dic106—42no—
407#88322—22no—
408#88322—22no—
409#88322—22no—
410#88322C22×D414yes—
411C2×#3267—531nomaximal, Sylow
412C22×C53—22no—
413C22×C53—22no—
414C22×C53—24no—
415C22×C53—22no—
416C22×C53—22no—
417C22×C53—22no—
418C22×C53—22no—
419C22×C53—44no—
420C22×C53—44no—
421C22×C53—48no—
422C22×C53—42no—
423C22×C53—42no—
424C22×C53—42no—
425C22×C53—42no—
426C22×C53—42no—
427C22×C53—816no—
428C22×C53—84no—
429C22×C53D4212yes—
430C22×C53#57512yes—
431C22×C53#57712yes—
432C22×C53C23×D411yescharacteristic
433C2×D53—24no—
434C2×D53—48no—
435C2×D53—42no—
436C2×D53—42no—
437C4×C53—22no—
438C4×C53—22no—
439C4×C53—22no—
440C4×C53—22no—
441C4×C53—42no—
442C4×C53—42no—
443C4×C53D4212yes—
444C4×C53C23×D411yescharacteristic
445C4×C53C2×H(5,𝔽2)11yescharacteristic
446Dic53—42no—
447Dic53—42no—
448Dic53—42no—
449C22×AGL(1,ℤ/8)—531no—
450C22×#135—531no—
451C2×#547—531no—
452C2×#546D5311yescharacteristic, complemented
453#3267—5316no—
454C2×#497—531no—
455C2×#470—531no—
456C2×#465—531no—
457C2×#463—531no—
458C2×#461—531no—
459C2×#452—531no—
460C2×#452—531no—
461C2×#449—531no—
462C2×#450—531no—
463C2×#442—531no—
464C2×#435—531no—
465C2×C53—42no—
466C2×C53—42no—
467C2×C53—44no—
468C2×C53—82no—
469C2×C53#326714yescomplemented
470C2×C53C2×D4211yescharacteristic
471C2×C53C2×#57511yescharacteristic
472C2×C53C2×#57711yescharacteristic
473D53—44no—
474C22×#41—531no—
475C22×#41—531no—
476C22×#41C2×D5311yescharacteristic
477C23×D4C2×D5311yescharacteristic
478C2×AGL(1,ℤ/8)—538no—
479C2×AGL(1,ℤ/8)—1068no—
480C2×#135—538no—
481C2×#135—1068no—
482C22×Q16—531no—
483C22×Q16—531no—
484C22×SD16—531no—
485C22×SD16—531no—
486C22×SD16—531no—
487C22×SD16—531no—
488C22×SD16—531no—
489C22×D8—531no—
490C22×D8—531no—
491C22×M16—531no—
492C23×C8—531no—
493#547—538no—
494#547—1064no—
495#546—24no—
496#546C2×D5318yescomplemented
497C2×C4⋊Q8—531no—
498C2×#124C2×D5311yescharacteristic
499C2×#123—21no—
500C2×#123—1061no—
501C2×#123—1061no—
502C2×C22⋊Q8—531no—
503C2×C22⋊Q8—531no—
504C2×C22⋊Q8C2×D5311yescharacteristic
505C2×#121—21no—
506C2×#121—1061no—
507C2×#121C2×D5311yescharacteristic
508C2×#120—21no—
509C2×C4×D4—531no—
510C2×C4×D4C2×D5311yescharacteristic
511C2×C4×D4C2×D5311yescharacteristic
512C22×C4⋊C4—1061no—
513C22×C22⋊C4—21no—
514#497—538no—
515#470—538no—
516#465—538no—
517#463—538no—
518#461—538no—
519#452—538no—
520#452—538no—
521#450—538no—
522#449—538no—
523#442—538no—
524#435—538no—
525C2×#106—531no—
526C2×C4⋊C8—531no—
527C2×#103—531no—
528C2×#103—531no—
529C2×#103—531no—
530C2×#102—531no—
531C2×#102—531no—
532C2×#102—531no—
533C2×C22⋊C8—531no—
534C2×C22⋊C8—531no—
535C2×#97—531no—
536C53C2×#326711yescharacteristic, complemented, Sylow
537C25—21no—
538C2×#41—22no—
539C2×#41—24no—
540C2×#41—42no—
541C2×#41—534no—
542C2×#41—534no—
543C2×#41—1064no—
544C2×#41—1064no—
545C2×#41—1062no—
546C2×#41—1062no—
547C2×#41—2122no—
548C2×#41—2122no—
549C2×#41C22×D5314yes—
550C22×Q8—531no—
551C22×Q8—531no—
552C22×Q8C22×D5311yescharacteristic
553C22×D4—24no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—42no—
559C22×D4—531no—
560C22×D4—1061no—
561C22×D4—1061no—
562C22×D4C22⋊D5311yescharacteristic
563C22×D4C22×D5311yescharacteristic
564C22×D4C22×D5314yes—
565C22×D4C22×D5311yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—1061no—
569C23×C4—1061no—
570C23×C4—1061no—
571C23×C4C22×D5311yescharacteristic
572C23×C4C22×D5311yescharacteristic
573AGL(1,ℤ/8)—10632no—
574#135—10632no—
575C2×Q16—534no—
576C2×Q16—534no—
577C2×Q16—1064no—
578C2×Q16—2122no—
579C2×SD16—534no—
580C2×SD16—534no—
581C2×SD16—534no—
582C2×SD16—534no—
583C2×SD16—534no—
584C2×SD16—1064no—
585C2×SD16—1064no—
586C2×SD16—1064no—
587C2×SD16—1064no—
588C2×SD16—2122no—
589C2×D8—538no—
590C2×D8—534no—
591C2×D8—534no—
592C2×D8—1064no—
593C2×M16—534no—
594C2×M16—1064no—
595C22×C8—531no—
596C22×C8—531no—
597C22×C8—534no—
598C22×C8—531no—
599C22×C8—531no—
600C22×C8—1064no—
601C4⋊Q8—534no—
602C4⋊Q8—1062no—
603#124—22no—
604#124C22×D5314yes—
605#123—28no—
606#123—1068no—
607#123—1068no—
608C22⋊Q8—22no—
609C22⋊Q8—534no—
610C22⋊Q8—534no—
611C22⋊Q8—1062no—
612C22⋊Q8—1062no—
613C22⋊Q8C22×D5314yes—
614#121—22no—
615#121—28no—
616#121—1068no—
617#121C22×D5314yes—
618#120—28no—
619C4×D4—22no—
620C4×D4—534no—
621C4×D4—1062no—
622C4×D4C22⋊D5314yes—
623C4×D4C22×D5314yes—
624C4×D4C22×D5314yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—531no—
627C2×C4⋊C4—1061no—
628C2×C4⋊C4—1061no—
629C2×C4⋊C4—1061no—
630C2×C4⋊C4—1061no—
631C2×C4⋊C4—1068no—
632C2×C4⋊C4C22⋊D5311yescharacteristic
633C2×C4⋊C4C22×D5311yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—28no—
640C2×C22⋊C4—1061no—
641C2×C22⋊C4—1061no—
642C2×C22⋊C4—1061no—
643C2×C22⋊C4C22⋊D5311yescharacteristic
644C2×C22⋊C4C22⋊D5311yescharacteristic
645C2×C42C22×D5311yescharacteristic
646#106—534no—
647C4⋊C8—534no—
648#103—534no—
649#103—534no—
650#103—534no—
651#102—534no—
652#102—534no—
653#102—534no—
654C22⋊C8—534no—
655C22⋊C8—534no—
656#97—534no—
657C24—21no—
658C24—21no—
659C24—24no—
660C24—44no—
661C24—44no—
662C24—82no—
663C24—1061no—
664C24C2×C22⋊D5311yescharacteristic
665C24C2×C22⋊D5311yescharacteristic
666#41—28no—
667#41—44no—
668#41—48no—
669#41—1068no—
670#41—1068no—
671#41—2124no—
672#41—2124no—
673#41—2128no—
674#41—2128no—
675C2×Q8—21no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—532no—
679C2×Q8—532no—
680C2×Q8—1061no—
681C2×Q8—1061no—
682C2×Q8—1062no—
683C2×Q8—1062no—
684C2×Q8—1062no—
685C2×Q8—1062no—
686C2×Q8C23×D5312yes—
687C2×D4—28no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—24no—
693C2×D4—21no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—82no—
702C2×D4—534no—
703C2×D4—532no—
704C2×D4—1064no—
705C2×D4—1064no—
706C2×D4—1061no—
707C2×D4—1062no—
708C2×D4—2124no—
709C2×D4—2124no—
710C2×D4D4×D5314yes—
711C2×D4C2×C22⋊D5314yes—
712C2×D4C23×D5312yes—
713C2×D4C23×D5312yes—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—44no—
723C22×C4—82no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1064no—
728C22×C4—1064no—
729C22×C4—1064no—
730C22×C4—2124no—
731C22×C4—2124no—
732C22×C4—2124no—
733C22×C4C2×C22⋊D5312yes—
734C22×C4C2×C22⋊D5312yes—
735C22×C4C2×C22⋊D5311yescharacteristic
736C22×C4C2×C22⋊D5311yescharacteristic
737C22×C4C2×C22⋊D5311yescharacteristic
738C22×C4C2×C22⋊D5311yescharacteristic
739C22×C4C23×D5312yes—
740C22×C4C23×D5312yes—
741C22×C4C23×D5311yescharacteristic
742Q16—1068no—
743Q16—2124no—
744SD16—1068no—
745SD16—1068no—
746SD16—1068no—
747SD16—1068no—
748SD16—2124no—
749D8—5316no—
750D8—1068no—
751M16—1068no—
752C2×C8—534no—
753C2×C8—532no—
754C2×C8—532no—
755C2×C8—532no—
756C2×C8—532no—
757C2×C8—1068no—
758C2×C8—1062no—
759C2×C8—1062no—
760C2×C8—1062no—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—532no—
764C4⋊C4—1061no—
765C4⋊C4—1064no—
766C4⋊C4—1064no—
767C4⋊C4—1064no—
768C4⋊C4—1064no—
769C4⋊C4C2×C22⋊D5314yes—
770C4⋊C4C23×D5312yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—1064no—
777C22⋊C4—1064no—
778C22⋊C4—1064no—
779C22⋊C4C2×C22⋊D5314yes—
780C22⋊C4C2×C22⋊D5314yes—
781C42C2×C22⋊D5312yes—
782C42C23×D5312yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—22no—
792C23—48no—
793C23—48no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—84no—
800C23—816no—
801C23—1062no—
802C23—1064no—
803C23—2122no—
804C23—2122no—
805C23C22×C22⋊D5312yes—
806C23C22×C22⋊D5312yes—
807C23C22×C22⋊D5311yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—42no—
811Q8—1062no—
812Q8—1062no—
813Q8—1062no—
814Q8—1062no—
815Q8—2122no—
816Q8—2122no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—24no—
821D4—44no—
822D4—48no—
823D4—48no—
824D4—42no—
825D4—84no—
826D4—534no—
827D4—1062no—
828D4—1064no—
829D4—2128no—
830D4—2128no—
831D4C2×D4×D5314yes—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—48no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—84no—
848C2×C4—1062no—
849C2×C4—1062no—
850C2×C4—1062no—
851C2×C4—2128no—
852C2×C4—2128no—
853C2×C4—2128no—
854C2×C4—2122no—
855C2×C4—2122no—
856C2×C4—2122no—
857C2×C4C2×D4×D5312yes—
858C2×C4C22×C22⋊D5312yes—
859C2×C4C22×C22⋊D5312yes—
860C2×C4C22×C22⋊D5312yes—
861C2×C4C22×C22⋊D5312yes—
862C2×C4C22×C22⋊D5311yescharacteristic
863C2×C4#1313326212yes—
864C2×C4C24×D5311yescharacteristic
865C8—534no—
866C8—1062no—
867C8—1062no—
868C8—1062no—
869C22—22no—
870C22—22no—
871C22—24no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—44no—
877C22—44no—
878C22—48no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—84no—
886C22—1064no—
887C22—2128no—
888C22—2122no—
889C22—2122no—
890C22D4×C22⋊D5312yes—
891C22#1681142112yes—
892C22#1681143412yes—
893C22C23×C22⋊D5311yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—42no—
899C4—42no—
900C4—2122no—
901C4—2122no—
902C4—2122no—
903C4D4×C22⋊D5312yes—
904C4C22×D4×D5311yescharacteristic
905C4C2×#1313326211yescharacteristic
906C2—42no—
907C2—42no—
908C2—44no—
909C2—82no—
910C2—2124no—
911C2#2028623614yesdirect product factor
912C2C2×D4×C22⋊D5311yescharacteristic
913C2C2×#1681142111yescharacteristic
914C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3267
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. C22×#13133243C2semidirect
2. C22×#13133237C2semidirect
3. C2×#16811278C2semidirect
4. #20286236C2direct (N × H)
5. C2×#16811018C2semidirect
6. C2×#16810879C2semidirect
7. C2×#16810850C2semidirect
8. C2×#16810835C2semidirect
9. C2×#16810828C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810766C2semidirect
13. C2×#16810774C2semidirect
14. C2×#16810733C2semidirect
15. C2×#16810695C2semidirect
16. C2×C53×#546C2semidirect
18. C22×#11719945C22semidirect
20. C2×#13133243C22semidirect
22. C2×#13133237C22semidirect
23. C22×#11719925C22semidirect
24. C22×#11719925C22semidirect
29. C22×#11719924C22semidirect
33. C23×#88322C22semidirect
35. #16811278C22semidirect
36. C2×#13133217C22semidirect
40. C2×#13133196C22semidirect
42. C2×C4×D212C22semidirect
44. #16811018C22semidirect
45. #16810879C22semidirect
46. #16810850C22semidirect
47. #16810835C22semidirect
48. #16810828C22semidirect
49. #16810785C22semidirect
50. #16810783C22semidirect
51. #16810774C22semidirect
52. #16810766C22semidirect
53. #16810733C22semidirect
54. #16810695C22semidirect
55. C2×#13133148C22semidirect
56. C2×C4⋊#88322C22semidirect
57. C2×#13133141C22semidirect
58. C2×#13133140C22semidirect
59. C2×#13133140C22semidirect
62. C2×#13133137C22semidirect
64. C2×C22⋊#88322C22semidirect
65. C2×#13133128C22semidirect
69. C53×#546C22semidirect
86. C2×#11719945C23semidirect
99. C2×#11719925C23semidirect
100. C2×#11719925C23semidirect
110. C2×#11719924C23semidirect
112. C2×#11719922D4semidirect
122. C22×#88322C23semidirect
124. #13133217C23semidirect
130. #13133196C23semidirect
133. C4×D212C23semidirect
143. #13133148C23semidirect
144. C4⋊#88322C23semidirect
145. #13133141C23semidirect
146. #13133140C23semidirect
147. #13133140C23semidirect
150. #13133137C23semidirect
152. C22⋊#88322C23semidirect
153. #13133128C23semidirect
307. #11719922C2×D4semidirect
452. C2×#546D53semidirect
469. C2×C53#3267semidirect
496. #546C2×D53semidirect
536. C53C2×#3267semidirect
911. C2#20286236direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332432
C22×#131332372
C2×#168112782
#202862362
C2×#168110182
C2×#168108792
C2×#168108502
C2×#168108352
C2×#168108282
C2×#168107852
C2×#168107832
C2×#168107662
C2×#168107742
C2×#168107332
C2×#168106952
C2×C53×#5462
C2×#326753