Finite Group Databasebeta

← C2×#20286427 #28259325

Subgroups — C2×#20286427 #28259325

Order 13568.

2934 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×#13133239C211yesmaximal, characteristic, complemented
2C23×#11719913C211yesmaximal, characteristic, complemented
3C2×#16811282C211yesmaximal, characteristic, complemented
4C2×#16811269C211yesmaximal, characteristic, complemented
5#20286427C2116yesmaximal, direct product factor
6C2×#16811007C211yesmaximal, characteristic, complemented
7C2×#16810852C211yesmaximal, characteristic, complemented
8C2×#16810852C211yesmaximal, characteristic, complemented
9C2×#16810846C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810770C211yesmaximal, characteristic, complemented
13C2×#16810781C211yesmaximal, characteristic, complemented
14C2×#16810759C211yesmaximal, characteristic, complemented
15C2×C4×#11719913C211yesmaximal, characteristic, complemented
16C2×C8×D4×C53C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic, complemented
19C23×Dic106C2211yescharacteristic
20C23×D212C2211yescharacteristic
21C2×#13133239—28no—
22C2×#13133239C2218yescomplemented
23C22×Dic212C2211yescharacteristic, complemented
24C22×Dic212C2211yescharacteristic, complemented
25C22×#11719913—28no—
26C22×#11719913C2211yescharacteristic
27C22×#11719913C2211yescharacteristic
28C22×#11719913C2211yescharacteristic
29C22×#11719913C2211yescharacteristic
30C22×#11719913C2218yescomplemented
31C22×#11719913C2211yescharacteristic, complemented
32C22×D424C2211yescharacteristic
33C22×D424C2211yescharacteristic
34#16811282—24no—
35#16811282C2218yescomplemented
36#16811269—24no—
37#16811269C2218yescomplemented
38C2×#13133205C2211yescharacteristic
39C2×#13133205C2211yescharacteristic, complemented
40C2×#13133203—21no—
41C2×#13133202—21no—
42C2×#13133196C2211yescharacteristic
43C2×#13133196C2211yescharacteristic, complemented
44C2×#13133195—21no—
45C2×#13133191C2211yescharacteristic
46C2×#13133191C2211yescharacteristic
47C2×#13133190—21no—
48C2×#13133189—21no—
49C2×#13133185—21no—
50C2×C4×Dic106C2211yescharacteristic, complemented
51C2×C4×D212C2211yescharacteristic
52C2×#13133177—21no—
53C2×C22⋊C4×D53—21no—
54#16811007C2218yescomplemented
55#16810852C2218yescomplemented
56#16810852C2218yescomplemented
57#16810846C2218yescomplemented
58#16810839C2218yescomplemented
59#16810787C2218yescomplemented
60#16810781C2218yescomplemented
61#16810770C2218yescomplemented
62#16810759C2218yescomplemented
63C4×#11719913C2218yescomplemented
64C2×#13133149C2211yescharacteristic, complemented
65C2×#13133142C2211yescharacteristic, complemented
66C2×#13133142C2211yescharacteristic, complemented
67C2×#13133142C2211yescharacteristic, complemented
68C2×#13133139C2211yescharacteristic
69C2×#13133139C2211yescharacteristic
70C2×#13133139C2211yescharacteristic, complemented
71C23×C8×C53C2211yescharacteristic
72C23×C8×C53C2211yescharacteristic, complemented
73C2×C4×D4×C53C2211yescharacteristic
74C8×D4×C53C2218yescomplemented
75C2×C4⋊C8×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×C22⋊C8×C53C2211yescharacteristic, complemented
78C2×C4×C8×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719945—22no—
81C2×#11719945—22no—
82C2×#11719945—24no—
83C2×#11719945—24no—
84C2×#11719945—42no—
85C2×#11719945—42no—
86C2×#11719945C2314yes—
87C2×#11719945C2314yescomplemented
88C22×Dic106—24no—
89C22×Dic106—22no—
90C22×Dic106—21no—
91C22×Dic106—42no—
92C22×Dic106C2311yescharacteristic
93C22×Dic106C2311yescharacteristic
94C22×Dic106C2314yes—
95C22×Dic106C2311yescharacteristic
96C22×D212—24no—
97C22×D212—22no—
98C22×D212—21no—
99C22×D212—42no—
100C22×D212C2311yescharacteristic
101C22×D212C2311yescharacteristic
102C22×D212C2314yes—
103C22×D212C2311yescharacteristic
104C22×C22⋊D53—21no—
105C22×C22⋊D53—21no—
106C22×C22⋊D53—21no—
107C22×C22⋊D53—21no—
108C23×Dic53—21no—
109C22×C4×D53—21no—
110C22×C4×D53—21no—
111C22×C4×D53—21no—
112#13133239—232no—
113C2×Dic212—24no—
114C2×Dic212—42no—
115C2×Dic212C2314yescomplemented
116C2×Dic212C2314yescomplemented
117C2×#11719913—24no—
118C2×#11719913—24no—
119C2×#11719913—232no—
120C2×#11719913—24no—
121C2×#11719913—24no—
122C2×#11719913D418yescomplemented
123C2×#11719913C2314yes—
124C2×#11719913C2314yes—
125C2×#11719913C2314yes—
126C2×#11719913C2314yes—
127C2×#11719913C2314yescomplemented
128C2×D424—24no—
129C2×D424—42no—
130C2×D424C2314yes—
131C2×D424C2314yes—
132#13133205—22no—
133#13133205—22no—
134#13133205C2314yes—
135#13133205C2314yescomplemented
136#13133203—28no—
137#13133202—28no—
138#13133196—22no—
139#13133196—22no—
140#13133196C2314yes—
141#13133196C2314yescomplemented
142#13133195—28no—
143#13133191—22no—
144#13133191—22no—
145#13133191C2314yes—
146#13133191C2314yes—
147#13133190—28no—
148#13133189—28no—
149#13133185—28no—
150C4×Dic106—22no—
151C4×Dic106C2314yescomplemented
152C4×D212—22no—
153C4×D212C2314yes—
154#13133177—28no—
155C2×C4⋊Dic53C2311yescharacteristic
156C2×C4⋊Dic53C2311yescharacteristic
157C2×#11719919—21no—
158C2×#11719919—21no—
159C2×#11719919—21no—
160C2×C22⋊Dic53—21no—
161C2×C22⋊Dic53—21no—
162C2×#11719921—21no—
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C22⋊C4×D53—28no—
170C2×C4×Dic53—21no—
171#13133149C2314yescomplemented
172#13133142C2314yescomplemented
173#13133142C2314yescomplemented
174#13133142C2314yescomplemented
175#13133139C2314yes—
176#13133139C2314yes—
177#13133139C2314yescomplemented
178C22×D4×C53D411yescharacteristic
179C23×C4×C53C2311yescharacteristic
180C23×C4×C53C2311yescharacteristic
181C22×C8×C53—24no—
182C22×C8×C53—24no—
183C22×C8×C53C2314yes—
184C22×C8×C53C2311yescharacteristic
185C22×C8×C53C2311yescharacteristic
186C22×C8×C53C2311yescharacteristic
187C22×C8×C53C2311yescharacteristic
188C22×C8×C53C2314yescomplemented
189C4×D4×C53D414yes—
190C4×D4×C53C2314yes—
191C2×C4⋊C4×C53D411yescharacteristic
192C2×C22⋊C4×C53D411yescharacteristic
193C2×C22⋊C4×C53D411yescharacteristic
194C2×C42×C53C2311yescharacteristic
195C4⋊C8×C53C2314yescomplemented
196C22⋊C8×C53C2314yes—
197C22⋊C8×C53C2314yescomplemented
198C4×C8×C53C2314yescomplemented
199C24×C53C2×D411yescharacteristic
200C24×C53C2×D411yescharacteristic
201C23×D53—21no—
202C23×D53—21no—
203C23×D53—21no—
204C23×D53—24no—
205C23×D53—44no—
206C23×D53—44no—
207C23×D53—82no—
208C2×D4×C53—24no—
209C2×D4×C53C2×D414yes—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—22no—
213C22×C4×C53—22no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D412yes—
219C22×C4×C53C2×D412yes—
220C22×C4×C53C2412yes—
221C22×C4×C53C2412yes—
222C22×C4×C53C2411yescharacteristic
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—44no—
229C2×C22⋊D53—44no—
230C2×C22⋊D53—82no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—24no—
237C22×Dic53—44no—
238#11719945—28no—
239#11719945—28no—
240#11719945—44no—
241#11719945—44no—
242#11719945—48no—
243#11719945—48no—
244C2×D212—21no—
245C2×D212—22no—
246C2×D212—22no—
247C2×D212—22no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—28no—
251C2×D212—24no—
252C2×D212—21no—
253C2×D212—21no—
254C2×D212—44no—
255C2×D212—48no—
256C2×D212—44no—
257C2×D212C2×D414yes—
258C2×D212C2412yes—
259C2×D212C2412yes—
260C2×D212C2412yes—
261C2×C4×D53—24no—
262C2×C4×D53—24no—
263C2×C4×D53—24no—
264C2×C4×D53—44no—
265C2×C4×D53—44no—
266C2×C4×D53—82no—
267C2×Dic106—21no—
268C2×Dic106—22no—
269C2×Dic106—22no—
270C2×Dic106—22no—
271C2×Dic106—22no—
272C2×Dic106—22no—
273C2×Dic106—28no—
274C2×Dic106—24no—
275C2×Dic106—21no—
276C2×Dic106—21no—
277C2×Dic106—44no—
278C2×Dic106—48no—
279C2×Dic106—44no—
280C2×Dic106C2×D414yes—
281C2×Dic106C2412yes—
282C2×Dic106C2412yes—
283C2×Dic106C2412yes—
284C2×C8×C53—22no—
285C2×C8×C53—22no—
286C2×C8×C53—22no—
287C2×C8×C53—28no—
288C2×C8×C53—28no—
289C2×C8×C53C2×D414yes—
290C2×C8×C53C2412yes—
291C2×C8×C53C2412yes—
292C2×C8×C53C2412yes—
293C2×C8×C53C2412yes—
294C4⋊C4×C53C2×D414yes—
295C22⋊C4×C53C2×D414yes—
296C22⋊C4×C53C2×D414yes—
297C42×C53C2×D412yes—
298C42×C53C2412yes—
299C22⋊Dic53—24no—
300C22⋊Dic53—24no—
301#11719921—24no—
302#11719921—24no—
303#11719921—24no—
304#11719921—24no—
305#11719921—24no—
306#11719921—24no—
307#11719921—24no—
308C4⋊Dic53—21no—
309C4⋊Dic53—21no—
310C4⋊Dic53C2412yes—
311C4⋊Dic53C2412yes—
312#11719919—24no—
313#11719919—24no—
314#11719919—24no—
315C4×Dic53—24no—
316Dic212—28no—
317Dic212—44no—
318D424—28no—
319D424—44no—
320#11719913—28no—
321#11719913—28no—
322#11719913—28no—
323#11719913—28no—
324#11719913C2×D4116yescomplemented
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53#13514yescomplemented
331C23×C53C22×D412yes—
332C23×C53C22×D412yes—
333C23×C53C22×D411yescharacteristic
334C22×D53—24no—
335C22×D53—22no—
336C22×D53—22no—
337C22×D53—22no—
338C22×D53—48no—
339C22×D53—42no—
340C22×D53—42no—
341C22×D53—42no—
342C22×D53—42no—
343C22×D53—42no—
344C22×D53—42no—
345C22×D53—48no—
346C22×D53—42no—
347C22×D53—42no—
348C22×D53—84no—
349C22×D53—816no—
350D4×C53—28no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53C22×D412yes—
362C2×C4×C53C22×D412yes—
363C2×C4×C53C22×D412yes—
364C2×C4×C53C22×D412yes—
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D411yescharacteristic
367C2×C4×C53H(5,𝔽2)12yes—
368C2×C4×C53C2511yescharacteristic
369C22⋊D53—48no—
370C22⋊D53—48no—
371C22⋊D53—48no—
372C22⋊D53—84no—
373C2×Dic53—24no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—48no—
380C2×Dic53—42no—
381C2×Dic53—42no—
382C2×Dic53—42no—
383C2×Dic53—42no—
384D212—24no—
385D212—22no—
386D212—22no—
387D212—22no—
388D212—22no—
389D212—22no—
390D212—48no—
391D212—42no—
392D212—42no—
393D212C22×D414yes—
394C4×D53—48no—
395C4×D53—48no—
396C4×D53—84no—
397Dic106—24no—
398Dic106—22no—
399Dic106—22no—
400Dic106—22no—
401Dic106—22no—
402Dic106—22no—
403Dic106—48no—
404Dic106—42no—
405Dic106—42no—
406Dic106C22×D414yes—
407C8×C53—22no—
408C8×C53—22no—
409C8×C53—22no—
410C8×C53C22×D414yes—
411C2×#3282—531nomaximal, Sylow
412C22×C53—22no—
413C22×C53—28no—
414C22×C53—22no—
415C22×C53—22no—
416C22×C53—22no—
417C22×C53—22no—
418C22×C53—44no—
419C22×C53D4212yes—
420C22×C53C2×#13512yes—
421C22×C53C2×#13514yescomplemented
422C22×C53#57712yes—
423C22×C53C23×D411yescharacteristic
424C2×D53—24no—
425C2×D53—48no—
426C2×D53—42no—
427C2×D53—42no—
428C2×D53—42no—
429C2×D53—42no—
430C2×D53—42no—
431C2×D53—42no—
432C2×D53—42no—
433C2×D53—42no—
434C2×D53—816no—
435C2×D53—84no—
436C2×D53—84no—
437C4×C53—22no—
438C4×C53—22no—
439C4×C53—22no—
440C4×C53—22no—
441C4×C53D4212yes—
442C4×C53C23×D411yescharacteristic
443C4×C53C2×H(5,𝔽2)11yescharacteristic
444Dic53—24no—
445Dic53—42no—
446Dic53—42no—
447Dic53—42no—
448Dic53—42no—
449C22×#135—531no—
450C23×SD16—531no—
451C2×#548—531no—
452C2×#546—531no—
453#3282—5316no—
454C2×#495—531no—
455C2×#465—531no—
456C2×#465—531no—
457C2×#464—531no—
458C2×#463—531no—
459C2×#452—531no—
460C2×#449—531no—
461C2×#451—531no—
462C2×#447—531no—
463C2×C4×SD16—531no—
464C2×C8×D4D5311yescharacteristic, complemented
465C2×C53—24no—
466C2×C53—42no—
467C2×C53#328214yescomplemented
468C2×C53C2×D4211yescharacteristic
469C2×C53C22×#13511yescharacteristic
470C2×C53C2×#57711yescharacteristic
471D53—44no—
472D53—82no—
473D53—82no—
474C22×#41—531no—
475C22×#41—531no—
476C23×Q8—531no—
477C23×D4—531no—
478C2×#135—538no—
479C2×#135—1068no—
480C22×Q16—531no—
481C22×Q16—531no—
482C22×SD16—531no—
483C22×SD16—531no—
484C22×SD16—531no—
485C22×SD16—531no—
486C22×SD16—531no—
487C22×SD16—538no—
488C22×SD16—1068no—
489C22×D8—531no—
490C22×D8—531no—
491C23×C8C2×D5311yescharacteristic
492C23×C8C2×D5311yescharacteristic, complemented
493#548—538no—
494#548—1064no—
495#546—538no—
496#546—1064no—
497C2×#124—531no—
498C2×#124—531no—
499C2×#124—1061no—
500C2×#123—1061no—
501C2×C22⋊Q8—531no—
502C2×C22⋊Q8—531no—
503C2×C22⋊Q8—1061no—
504C2×#121—531no—
505C2×#121—531no—
506C2×#121—1061no—
507C2×#121—1061no—
508C2×#120—1061no—
509C2×C4×Q8—531no—
510C2×C4×D4—531no—
511C2×C4×D4—1061no—
512C2×C4×D4C2×D5311yescharacteristic
513C22×C22⋊C4—1061no—
514#495—538no—
515#465—538no—
516#465—538no—
517#464—538no—
518#463—538no—
519#452—538no—
520#451—538no—
521#449—538no—
522#447—538no—
523C4×SD16—538no—
524C8×D4C2×D5318yescomplemented
525C2×#106—531no—
526C2×C4⋊C8C2×D5311yescharacteristic, complemented
527C2×#103—531no—
528C2×#103—531no—
529C2×#103—531no—
530C2×#102—531no—
531C2×#102—531no—
532C2×#102—531no—
533C2×C22⋊C8C2×D5311yescharacteristic
534C2×C22⋊C8C2×D5311yescharacteristic, complemented
535C2×C4×C8C2×D5311yescharacteristic, complemented
536C53C2×#328211yescharacteristic, complemented, Sylow
537C25—1061no—
538C2×#41—534no—
539C2×#41—534no—
540C2×#41—1064no—
541C2×#41—1064no—
542C2×#41—1062no—
543C2×#41—1062no—
544C2×#41—2122no—
545C2×#41—2122no—
546C22×Q8—531no—
547C22×Q8—531no—
548C22×Q8—531no—
549C22×Q8—534no—
550C22×Q8—1064no—
551C22×Q8—1061no—
552C22×Q8—1062no—
553C22×Q8—2122no—
554C22×D4—531no—
555C22×D4—531no—
556C22×D4—531no—
557C22×D4—534no—
558C22×D4—1064no—
559C22×D4—1061no—
560C22×D4—1061no—
561C22×D4—1061no—
562C22×D4—1061no—
563C22×D4—1061no—
564C22×D4—1062no—
565C22×D4—2122no—
566C22×D4D21211yescharacteristic
567C23×C4—1061no—
568C23×C4—1061no—
569C23×C4—1061no—
570C23×C4—1061no—
571C23×C4C22×D5311yescharacteristic
572C23×C4C22×D5311yescharacteristic
573#135—10632no—
574C2×Q16—534no—
575C2×Q16—534no—
576C2×Q16—1064no—
577C2×Q16—2122no—
578C2×SD16—538no—
579C2×SD16—534no—
580C2×SD16—534no—
581C2×SD16—534no—
582C2×SD16—534no—
583C2×SD16—534no—
584C2×SD16—10632no—
585C2×SD16—1064no—
586C2×SD16—1064no—
587C2×SD16—1064no—
588C2×SD16—1064no—
589C2×D8—534no—
590C2×D8—534no—
591C2×D8—1064no—
592C2×D8—2122no—
593C22×C8—24no—
594C22×C8—24no—
595C22×C8C22×D5311yescharacteristic
596C22×C8C22×D5314yes—
597C22×C8C22×D5311yescharacteristic
598C22×C8C22×D5311yescharacteristic
599C22×C8C22×D5311yescharacteristic
600C22×C8C22×D5314yescomplemented
601#124—534no—
602#124—534no—
603#124—1068no—
604#124—1062no—
605#124—1062no—
606#123—1068no—
607C22⋊Q8—534no—
608C22⋊Q8—534no—
609C22⋊Q8—1062no—
610C22⋊Q8—1062no—
611C22⋊Q8—1068no—
612#121—534no—
613#121—534no—
614#121—1068no—
615#121—1062no—
616#121—1062no—
617#121—1068no—
618#120—1068no—
619C4×Q8—534no—
620C4×Q8—1062no—
621C4×D4—534no—
622C4×D4—1068no—
623C4×D4—1062no—
624C4×D4D21214yes—
625C4×D4C22×D5314yes—
626C2×C4⋊C4—531no—
627C2×C4⋊C4—531no—
628C2×C4⋊C4—1061no—
629C2×C4⋊C4—1061no—
630C2×C4⋊C4—1061no—
631C2×C4⋊C4D21211yescharacteristic
632C2×C22⋊C4—1061no—
633C2×C22⋊C4—1061no—
634C2×C22⋊C4—1061no—
635C2×C22⋊C4—1061no—
636C2×C22⋊C4—1061no—
637C2×C22⋊C4—1061no—
638C2×C22⋊C4—1061no—
639C2×C22⋊C4—1061no—
640C2×C22⋊C4—1061no—
641C2×C22⋊C4—1068no—
642C2×C22⋊C4D21211yescharacteristic
643C2×C22⋊C4D21211yescharacteristic
644C2×C42—1061no—
645C2×C42C22×D5311yescharacteristic
646#106—534no—
647C4⋊C8C22×D5314yescomplemented
648#103—534no—
649#103—534no—
650#103—534no—
651#102—534no—
652#102—534no—
653#102—534no—
654C22⋊C8C22×D5314yes—
655C22⋊C8C22×D5314yescomplemented
656C4×C8C22×D5314yescomplemented
657C24—1061no—
658C24—1064no—
659C24—1061no—
660C24—1061no—
661C24—4242no—
662C24—2124no—
663C24—2124no—
664C24C2×D21211yescharacteristic
665C24C2×D21211yescharacteristic
666#41—1068no—
667#41—1068no—
668#41—2124no—
669#41—2124no—
670#41—2128no—
671#41—2128no—
672C2×Q8—534no—
673C2×Q8—532no—
674C2×Q8—532no—
675C2×Q8—532no—
676C2×Q8—1068no—
677C2×Q8—1061no—
678C2×Q8—1064no—
679C2×Q8—1061no—
680C2×Q8—1061no—
681C2×Q8—1062no—
682C2×Q8—1062no—
683C2×Q8—1062no—
684C2×Q8—1062no—
685C2×Q8—1062no—
686C2×Q8—2124no—
687C2×Q8—2124no—
688C2×Q8—2128no—
689C2×D4—24no—
690C2×D4—534no—
691C2×D4—532no—
692C2×D4—532no—
693C2×D4—532no—
694C2×D4—1068no—
695C2×D4—1064no—
696C2×D4—1064no—
697C2×D4—1064no—
698C2×D4—1064no—
699C2×D4—1062no—
700C2×D4—1062no—
701C2×D4—1061no—
702C2×D4—1064no—
703C2×D4—1061no—
704C2×D4—1061no—
705C2×D4—1062no—
706C2×D4—1062no—
707C2×D4—1062no—
708C2×D4—4242no—
709C2×D4—2124no—
710C2×D4—2128no—
711C2×D4—2124no—
712C2×D4—2124no—
713C2×D4—2124no—
714C2×D4—2124no—
715C2×D4C2×D21214yes—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—1061no—
721C22×C4—1064no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1064no—
727C22×C4—1064no—
728C22×C4—1064no—
729C22×C4—4242no—
730C22×C4—2124no—
731C22×C4—2124no—
732C22×C4—2124no—
733C22×C4C2×D21212yes—
734C22×C4C2×D21212yes—
735C22×C4C2×D21211yescharacteristic
736C22×C4C2×D21211yescharacteristic
737C22×C4C2×D21211yescharacteristic
738C22×C4C2×D21211yescharacteristic
739C22×C4C23×D5312yes—
740C22×C4C23×D5312yes—
741C22×C4C23×D5311yescharacteristic
742Q16—1068no—
743Q16—2124no—
744SD16—5316no—
745SD16—1068no—
746SD16—1068no—
747SD16—1068no—
748SD16—1068no—
749D8—1068no—
750D8—2124no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—28no—
755C2×C8—28no—
756C2×C8D4×D5314yes—
757C2×C8C23×D5312yes—
758C2×C8C23×D5312yes—
759C2×C8C23×D5312yes—
760C2×C8C23×D5312yes—
761C4⋊C4—532no—
762C4⋊C4—532no—
763C4⋊C4—1061no—
764C4⋊C4—1061no—
765C4⋊C4—1064no—
766C4⋊C4—1064no—
767C4⋊C4—1064no—
768C4⋊C4C2×D21214yes—
769C22⋊C4—1064no—
770C22⋊C4—1064no—
771C22⋊C4—1064no—
772C22⋊C4—1064no—
773C22⋊C4—1064no—
774C22⋊C4—1064no—
775C22⋊C4—1064no—
776C22⋊C4—1064no—
777C22⋊C4—1064no—
778C22⋊C4C2×D21214yes—
779C22⋊C4C2×D21214yes—
780C42—1064no—
781C42C2×D21212yes—
782C42C23×D5312yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—1062no—
789C23—1064no—
790C23—1062no—
791C23—1062no—
792C23—42416no—
793C23—4244no—
794C23—2128no—
795C23—2122no—
796C23—2122no—
797C23—2128no—
798C23—2122no—
799C23—2122no—
800C23—2122no—
801C23—2122no—
802C23—2122no—
803C23—2122no—
804C23#1313323914yescomplemented
805C23C22×D21212yes—
806C23C22×D21212yes—
807C23C22×D21211yescharacteristic
808Q8—534no—
809Q8—1062no—
810Q8—1064no—
811Q8—1062no—
812Q8—1062no—
813Q8—1062no—
814Q8—1062no—
815Q8—2128no—
816Q8—2122no—
817Q8—2122no—
818D4—28no—
819D4—534no—
820D4—1062no—
821D4—1062no—
822D4—1062no—
823D4—1062no—
824D4—1062no—
825D4—1064no—
826D4—4244no—
827D4—2128no—
828D4—2128no—
829D4—2128no—
830D4—2128no—
831D4—2122no—
832D4—2122no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—1062no—
844C2×C4—1064no—
845C2×C4—1062no—
846C2×C4—1062no—
847C2×C4—1062no—
848C2×C4—1062no—
849C2×C4—4244no—
850C2×C4—2128no—
851C2×C4—2128no—
852C2×C4—2128no—
853C2×C4—2122no—
854C2×C4—2122no—
855C2×C4—2122no—
856C2×C4—2122no—
857C2×C4C2×D4×D5312yes—
858C2×C4C22×D21212yes—
859C2×C4C22×D21212yes—
860C2×C4C22×D21212yes—
861C2×C4C22×D21212yes—
862C2×C4C22×D21211yescharacteristic
863C2×C4#1313326312yes—
864C2×C4C24×D5311yescharacteristic
865C8—22no—
866C8—22no—
867C8—22no—
868C8C2×D4×D5314yes—
869C22—22no—
870C22—22no—
871C22—28no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—1064no—
877C22—42416no—
878C22—4244no—
879C22—4244no—
880C22—2122no—
881C22—2122no—
882C22—2122no—
883C22—2122no—
884C22—2122no—
885C22—2122no—
886C22—2122no—
887C22—2122no—
888C22—2128no—
889C22D4×D21212yes—
890C22C2×#1313323912yes—
891C22C2×#1313323914yescomplemented
892C22#1681143512yes—
893C22C23×D21211yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—1064no—
899C4—2122no—
900C4—2122no—
901C4—2122no—
902C4—2122no—
903C4D4×D21212yes—
904C4C22×D4×D5311yescharacteristic
905C4C2×#1313326311yescharacteristic
906C2—24no—
907C2—42no—
908C2—4242no—
909C2—4242no—
910C2—2124no—
911C2#2028642714yesdirect product factor
912C2C2×D4×D21211yescharacteristic
913C2C22×#1313323911yescharacteristic
914C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C8×D4×C53C2
socleC23×C53C22×D4
hypercenterC2×C8×D4D53
hypocenterC53C2×#3282
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13133239C2semidirect
2. C23×#11719913C2semidirect
3. C2×#16811282C2semidirect
4. C2×#16811269C2semidirect
5. #20286427C2direct (N × H)
6. C2×#16811007C2semidirect
7. C2×#16810852C2semidirect
8. C2×#16810852C2semidirect
9. C2×#16810846C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810770C2semidirect
13. C2×#16810781C2semidirect
14. C2×#16810759C2semidirect
15. C2×C4×#11719913C2semidirect
16. C2×C8×D4×C53C2semidirect
18. C22×#11719945C22semidirect
22. C2×#13133239C22semidirect
23. C22×Dic212C22semidirect
24. C22×Dic212C22semidirect
30. C22×#11719913C22semidirect
31. C22×#11719913C22semidirect
35. #16811282C22semidirect
37. #16811269C22semidirect
39. C2×#13133205C22semidirect
43. C2×#13133196C22semidirect
50. C2×C4×Dic106C22semidirect
54. #16811007C22semidirect
55. #16810852C22semidirect
56. #16810852C22semidirect
57. #16810846C22semidirect
58. #16810839C22semidirect
59. #16810787C22semidirect
60. #16810781C22semidirect
61. #16810770C22semidirect
62. #16810759C22semidirect
63. C4×#11719913C22semidirect
64. C2×#13133149C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133142C22semidirect
67. C2×#13133142C22semidirect
70. C2×#13133139C22semidirect
72. C23×C8×C53C22semidirect
74. C8×D4×C53C22semidirect
75. C2×C4⋊C8×C53C22semidirect
77. C2×C22⋊C8×C53C22semidirect
78. C2×C4×C8×C53C22semidirect
87. C2×#11719945C23semidirect
115. C2×Dic212C23semidirect
116. C2×Dic212C23semidirect
122. C2×#11719913D4semidirect
127. C2×#11719913C23semidirect
135. #13133205C23semidirect
141. #13133196C23semidirect
151. C4×Dic106C23semidirect
171. #13133149C23semidirect
172. #13133142C23semidirect
173. #13133142C23semidirect
174. #13133142C23semidirect
177. #13133139C23semidirect
188. C22×C8×C53C23semidirect
195. C4⋊C8×C53C23semidirect
197. C22⋊C8×C53C23semidirect
198. C4×C8×C53C23semidirect
324. #11719913C2×D4semidirect
330. C23×C53#135semidirect
421. C22×C53C2×#135semidirect
464. C2×C8×D4D53semidirect
467. C2×C53#3282semidirect
492. C23×C8C2×D53semidirect
524. C8×D4C2×D53semidirect
526. C2×C4⋊C8C2×D53semidirect
534. C2×C22⋊C8C2×D53semidirect
535. C2×C4×C8C2×D53semidirect
536. C53C2×#3282semidirect
600. C22×C8C22×D53semidirect
647. C4⋊C8C22×D53semidirect
655. C22⋊C8C22×D53semidirect
656. C4×C8C22×D53semidirect
804. C23#13133239semidirect
891. C22C2×#13133239semidirect
911. C2#20286427direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332392
C23×#117199132
C2×#168112822
C2×#168112692
#202864272
C2×#168110072
C2×#168108522
C2×#168108462
C2×#168108392
C2×#168107872
C2×#168107702
C2×#168107812
C2×#168107592
C2×C4×#117199132
C2×C8×D4×C532
C2×#328253