Finite Group Databasebeta

← C2×#20286220 #28259068

Subgroups — C2×#20286220 #28259068

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×SD16×D53C211yesmaximal, characteristic, complemented
3C2×Q8×D212C211yesmaximal, characteristic, complemented
4C2×#16811266C211yesmaximal, characteristic
5#20286220C2116yesmaximal, direct product factor
6C2×#16811018C211yesmaximal, characteristic, complemented
7C2×#16810868C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810829C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810760C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×#16810693C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic, complemented
20C22×D4×D53C2211yescharacteristic
21C2×#13133249—28no—
22C2×#13133249C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719925C2211yescharacteristic, complemented
25C22×#11719913C2211yescharacteristic
26C22×#11719913C2211yescharacteristic
27C22×#11719923C2211yescharacteristic
28C22×#11719923C2211yescharacteristic
29C22×#11719924C2211yescharacteristic
30C2×SD16×D53—28no—
31C2×SD16×D53C2218yescomplemented
32C22×#11719912C2211yescharacteristic, complemented
33C22×C8×D53C2211yescharacteristic
34Q8×D212—24no—
35Q8×D212C2218yescomplemented
36#16811266—24no—
37#16811266C2218yes—
38C2×#13133217—21no—
39C2×#13133217C2211yescharacteristic, complemented
40C2×#13133199—21no—
41C2×#13133197—21no—
42C2×#13133197—21no—
43C2×#13133197C2211yescharacteristic
44C2×#13133197C2211yescharacteristic, complemented
45C2×#13133193C2211yescharacteristic
46C2×#13133190—21no—
47C2×#13133188C2211yescharacteristic
48C2×#13133187—21no—
49C2×C4×D212—21no—
50C2×C4×D212C2211yescharacteristic
51C2×C4×D212C2211yescharacteristic
52C2×C22⋊C4×D53—21no—
53#16811018C2218yescomplemented
54#16810868C2218yescomplemented
55#16810863C2218yescomplemented
56#16810829C2218yescomplemented
57#16810788C2218yescomplemented
58#16810777C2218yescomplemented
59#16810775C2218yescomplemented
60#16810760C2218yescomplemented
61#16810721C2218yescomplemented
62#16810693C2218yescomplemented
63C2×#13133150C2211yescharacteristic, complemented
64C2×#13133142C2211yescharacteristic, complemented
65C2×#13133142C2211yescharacteristic, complemented
66C2×#13133141C2211yescharacteristic, complemented
67C2×#13133137C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#13133129C2211yescharacteristic, complemented
70C2×#13133128C2211yescharacteristic, complemented
71C22×Q16×C53C2211yescharacteristic, complemented
72C22×SD16×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic, complemented
75C53×#464C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#102×C53C2211yescharacteristic
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—42no—
83C2×#11719949C2314yes—
84C22×Dic106—21no—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C2×Q8×D53—22no—
89C2×Q8×D53—22no—
90C2×Q8×D53—24no—
91C2×Q8×D53—24no—
92C2×Q8×D53—42no—
93C2×Q8×D53—42no—
94C2×Q8×D53C2314yes—
95C2×Q8×D53C2314yescomplemented
96C22×D212—21no—
97C22×D212D411yescharacteristic
98C22×D212C2311yescharacteristic
99C22×C22⋊D53—21no—
100C22×C22⋊D53—21no—
101C2×D4×D53—24no—
102C2×D4×D53—22no—
103C2×D4×D53—42no—
104C2×D4×D53C2314yes—
105C22×C4×D53—21no—
106C22×C4×D53—21no—
107C22×C4×D53—21no—
108C22×C4×D53—21no—
109C22×C4×D53C2311yescharacteristic
110C22×C4×D53C2311yescharacteristic
111#13133249—232no—
112C2×#11719925—24no—
113C2×#11719925—42no—
114C2×#11719925C2314yescomplemented
115C2×#11719925C2314yescomplemented
116C2×#11719913—24no—
117C2×#11719913—24no—
118C2×#11719913C2314yes—
119C2×#11719913C2314yes—
120C2×#11719923—24no—
121C2×#11719923—42no—
122C2×#11719923C2314yes—
123C2×#11719923C2314yes—
124C2×#11719924D418yescomplemented
125C2×#11719924C2314yes—
126SD16×D53—232no—
127C2×#11719912—24no—
128C2×#11719912C2314yescomplemented
129C22×#88322C2311yescharacteristic
130C22×#88322C2311yescharacteristic
131C2×C8×D53—24no—
132C2×C8×D53C2314yes—
133#13133217—22no—
134#13133217—28no—
135#13133217C2314yescomplemented
136#13133199—28no—
137#13133197—28no—
138#13133197—28no—
139#13133197—22no—
140#13133197—22no—
141#13133197C2314yes—
142#13133197C2314yescomplemented
143#13133193—22no—
144#13133193C2314yes—
145#13133190—28no—
146#13133188—22no—
147#13133188C2314yes—
148#13133187—28no—
149C4×D212—22no—
150C4×D212—28no—
151C4×D212D414yes—
152C4×D212C2314yes—
153C4×D212C2314yes—
154C2×C4⋊Dic53—21no—
155C2×C4⋊Dic53—21no—
156C2×C4⋊Dic53—21no—
157C2×C4⋊Dic53—21no—
158C2×C4⋊Dic53D411yescharacteristic
159C2×C4⋊Dic53C2311yescharacteristic
160C2×#11719919—21no—
161C2×C22⋊Dic53—21no—
162C2×#11719921—21no—
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921D411yescharacteristic
167C2×#11719921D411yescharacteristic
168C22⋊C4×D53—28no—
169#13133150C2314yescomplemented
170#13133142C2314yescomplemented
171#13133142C2314yescomplemented
172#13133141C2314yescomplemented
173#13133137C2314yes—
174#13133129C2314yes—
175#13133129C2314yescomplemented
176#13133128C2314yescomplemented
177C22×Q8×C53C2311yescharacteristic
178C22×Q8×C53C2311yescharacteristic
179C22×D4×C53C2311yescharacteristic
180C2×Q16×C53—24no—
181C2×Q16×C53C2314yescomplemented
182C2×SD16×C53—24no—
183C2×SD16×C53C2314yes—
184C22×C8×C53C2311yescharacteristic
185C22×C8×C53C2311yescharacteristic
186#124×C53—22no—
187#124×C53C2314yes—
188C4×Q8×C53—22no—
189C4×Q8×C53C2314yescomplemented
190C2×C4⋊C4×C53—21no—
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53—21no—
194C2×C42×C53—21no—
195C2×C42×C53C2311yescharacteristic
196C4⋊C8×C53C2314yescomplemented
197#103×C53C2314yescomplemented
198#102×C53C2314yes—
199C24×C53—21no—
200C23×D53—21no—
201C23×D53—24no—
202C23×D53—44no—
203C23×D53—44no—
204C23×D53—82no—
205C23×D53C2×D411yescharacteristic
206C23×D53C2×D411yescharacteristic
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53—22no—
210C2×Q8×C53—22no—
211C2×Q8×C53—22no—
212C2×Q8×C53C2×D414yes—
213C2×Q8×C53C2412yes—
214C2×Q8×C53C2412yes—
215C2×D4×C53—22no—
216C2×D4×C53—21no—
217C2×D4×C53—22no—
218C2×D4×C53C2412yes—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—82no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719949—28no—
235#11719949—44no—
236#11719949—48no—
237Q8×D53—28no—
238Q8×D53—28no—
239Q8×D53—44no—
240Q8×D53—44no—
241Q8×D53—48no—
242Q8×D53—48no—
243D4×D53—28no—
244D4×D53—44no—
245D4×D53—48no—
246C2×D212—24no—
247C2×D212—21no—
248C2×D212—22no—
249C2×D212—24no—
250C2×D212—44no—
251C2×D212C2×D414yes—
252C2×D212C2×D414yes—
253C2×D212C2412yes—
254C2×C4×D53—22no—
255C2×C4×D53—22no—
256C2×C4×D53—22no—
257C2×C4×D53—22no—
258C2×C4×D53—24no—
259C2×C4×D53—24no—
260C2×C4×D53—24no—
261C2×C4×D53—24no—
262C2×C4×D53—44no—
263C2×C4×D53—44no—
264C2×C4×D53—44no—
265C2×C4×D53—82no—
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D412yes—
268C2×C4×D53C2412yes—
269C2×C4×D53C2412yes—
270C2×Dic106—22no—
271C2×Dic106—22no—
272C2×Dic106—22no—
273C2×Dic106—22no—
274C2×Dic106—21no—
275C2×Dic106—21no—
276C2×Dic106—24no—
277C2×Dic106—24no—
278C2×Dic106—44no—
279C2×Dic106—44no—
280C2×Dic106C2412yes—
281C2×Dic106C2412yes—
282Q16×C53—28no—
283SD16×C53—28no—
284C2×C8×C53—22no—
285C2×C8×C53—22no—
286C2×C8×C53C2412yes—
287C2×C8×C53C2412yes—
288C4⋊C4×C53—24no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53C2412yes—
291C22⋊C4×C53—24no—
292C22⋊C4×C53—24no—
293C42×C53—24no—
294C42×C53C2×D412yes—
295C42×C53C2412yes—
296C22⋊Dic53—24no—
297#11719925—28no—
298#11719925—44no—
299#11719924C2×D4116yescomplemented
300#11719923—28no—
301#11719923—44no—
302#11719921—24no—
303#11719921—24no—
304#11719921—24no—
305#11719921—24no—
306#11719921C2×D414yes—
307#11719921C2×D414yes—
308C4⋊Dic53—24no—
309C4⋊Dic53—24no—
310C4⋊Dic53—21no—
311C4⋊Dic53—24no—
312C4⋊Dic53—24no—
313C4⋊Dic53C2×D414yes—
314C4⋊Dic53C2412yes—
315#11719919—24no—
316C2×#88322—22no—
317C2×#88322C2×D414yes—
318C2×#88322C2412yes—
319C2×#88322C2412yes—
320#11719913—28no—
321#11719913—28no—
322#11719912—28no—
323C8×D53—28no—
324C23×C53—22no—
325C23×C53—42no—
326C23×C53—42no—
327C23×C53—42no—
328C23×C53C22×D411yescharacteristic
329C22×D53—22no—
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—24no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—48no—
337C22×D53—42no—
338C22×D53—42no—
339C22×D53—48no—
340C22×D53—84no—
341C22×D53—816no—
342C22×D53#13714yescomplemented
343C22×D53C22×D412yes—
344C22×D53C22×D412yes—
345Q8×C53—24no—
346Q8×C53—22no—
347Q8×C53—22no—
348Q8×C53—22no—
349Q8×C53—42no—
350Q8×C53C22×D414yes—
351D4×C53—22no—
352D4×C53—22no—
353D4×C53—42no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—42no—
361C2×C4×C53—42no—
362C2×C4×C53C22×D412yes—
363C2×C4×C53C22×D412yes—
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C22×D412yes—
366C2×C4×C53H(5,𝔽2)12yes—
367C2×C4×C53C2511yescharacteristic
368C22⋊D53—48no—
369C22⋊D53—84no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—42no—
376C2×Dic53—42no—
377C2×Dic53—42no—
378C2×Dic53C22×D412yes—
379C2×Dic53C22×D412yes—
380D212—28no—
381D212—24no—
382D212—22no—
383D212—48no—
384D212C22×D414yes—
385C4×D53—24no—
386C4×D53—24no—
387C4×D53—22no—
388C4×D53—22no—
389C4×D53—22no—
390C4×D53—22no—
391C4×D53—48no—
392C4×D53—48no—
393C4×D53—48no—
394C4×D53—84no—
395Dic106—22no—
396Dic106—22no—
397Dic106—22no—
398Dic106—22no—
399Dic106—48no—
400Dic106—48no—
401Dic106—42no—
402Dic106—42no—
403C8×C53—22no—
404C8×C53—22no—
405#88322—22no—
406#88322C22×D414yes—
407C2×#3266—531nomaximal, Sylow
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—84no—
412C22×C53D4212yes—
413C22×C53C2×#13712yes—
414C22×C53#57712yes—
415C22×C53C23×D411yescharacteristic
416C2×D53—22no—
417C2×D53—28no—
418C2×D53—22no—
419C2×D53—22no—
420C2×D53—24no—
421C2×D53—22no—
422C2×D53—22no—
423C2×D53—44no—
424C2×D53—48no—
425C2×D53—42no—
426C2×D53—42no—
427C2×D53—816no—
428C2×D53C2×#13714yescomplemented
429C4×C53—24no—
430C4×C53—22no—
431C4×C53—22no—
432C4×C53—42no—
433C4×C53—42no—
434C4×C53D4212yes—
435C4×C53C23×D411yescharacteristic
436C4×C53C2×H(5,𝔽2)11yescharacteristic
437Dic53—22no—
438Dic53—22no—
439Dic53—42no—
440Dic53—42no—
441Dic53—42no—
442C22×#137—531no—
443C23×SD16—531no—
444C2×D4×Q8—531no—
445C2×#546—531no—
446#3266—5316no—
447C2×#497—531no—
448C2×#468—531no—
449C2×#467—531no—
450C2×#464D5311yescharacteristic, complemented
451C2×#461—531no—
452C2×#452—531no—
453C2×#451—531no—
454C2×#448—531no—
455C2×#450—531no—
456C2×#440—531no—
457C2×#435—531no—
458C2×C53—82no—
459C2×C53#326614yescomplemented
460C2×C53C2×D4211yescharacteristic
461C2×C53C22×#13711yescharacteristic
462C2×C53C2×#57711yescharacteristic
463D53—24no—
464D53—42no—
465D53—44no—
466C22×#41—531no—
467C23×Q8—531no—
468C23×Q8—531no—
469C23×D4—531no—
470C2×#137—538no—
471C2×#137—1068no—
472C22×Q16—531no—
473C22×Q16—531no—
474C22×Q16C2×D5311yescharacteristic, complemented
475C22×SD16—531no—
476C22×SD16—531no—
477C22×SD16—531no—
478C22×SD16—538no—
479C22×SD16—531no—
480C22×SD16—531no—
481C22×SD16—1068no—
482C22×SD16C2×D5311yescharacteristic
483C22×M16—531no—
484C23×C8—531no—
485D4×Q8—538no—
486D4×Q8—1064no—
487#546—538no—
488#546—1064no—
489C2×C4⋊Q8—531no—
490C2×C4⋊Q8—1061no—
491C2×#124C2×D5311yescharacteristic
492C2×#123—1061no—
493C2×C22⋊Q8—531no—
494C2×C22⋊Q8—531no—
495C2×C22⋊Q8—531no—
496C2×C22⋊Q8—1061no—
497C2×C22⋊Q8—1061no—
498C2×#121—531no—
499C2×#121—1061no—
500C2×#120—1061no—
501C2×C4×Q8C2×D5311yescharacteristic, complemented
502C2×C4×D4—531no—
503C2×C4×D4—531no—
504C2×C4×D4—1061no—
505C22×C22⋊C4—1061no—
506#497—538no—
507#468—538no—
508#467—538no—
509#464C2×D5318yescomplemented
510#461—538no—
511#452—538no—
512#451—538no—
513#450—538no—
514#448—538no—
515#440—538no—
516#435—538no—
517C2×#107—531no—
518C2×C4⋊C8C2×D5311yescharacteristic, complemented
519C2×#103—531no—
520C2×#103—531no—
521C2×#103—531no—
522C2×#103C2×D5311yescharacteristic, complemented
523C2×#102—531no—
524C2×#102C2×D5311yescharacteristic
525C2×C22⋊C8—531no—
526C2×C22⋊C8—531no—
527C2×#97—531no—
528C53C2×#326611yescharacteristic, complemented, Sylow
529C25—1061no—
530C2×#41—534no—
531C2×#41—1062no—
532C2×#41—1064no—
533C2×#41—2122no—
534C22×Q8—534no—
535C22×Q8—534no—
536C22×Q8—531no—
537C22×Q8—531no—
538C22×Q8—1061no—
539C22×Q8—1061no—
540C22×Q8—1062no—
541C22×Q8—1062no—
542C22×Q8—1064no—
543C22×Q8—1064no—
544C22×Q8—2122no—
545C22×Q8—2122no—
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5311yescharacteristic
548C22×D4—534no—
549C22×D4—531no—
550C22×D4—531no—
551C22×D4—1061no—
552C22×D4—1062no—
553C22×D4—1061no—
554C22×D4—1064no—
555C22×D4—1061no—
556C22×D4—2122no—
557C22×D4C22×D5311yescharacteristic
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—1061no—
561C23×C4—1061no—
562C23×C4—1061no—
563C23×C4—1061no—
564#137—10632no—
565C2×Q16—24no—
566C2×Q16—534no—
567C2×Q16—534no—
568C2×Q16—1064no—
569C2×Q16—2122no—
570C2×Q16C22×D5314yescomplemented
571C2×SD16—24no—
572C2×SD16—538no—
573C2×SD16—534no—
574C2×SD16—534no—
575C2×SD16—534no—
576C2×SD16—534no—
577C2×SD16—534no—
578C2×SD16—1064no—
579C2×SD16—1064no—
580C2×SD16—1064no—
581C2×SD16—10632no—
582C2×SD16—2122no—
583C2×SD16C22×D5314yes—
584C2×M16—534no—
585C2×M16—1064no—
586C22×C8—531no—
587C22×C8—531no—
588C22×C8—534no—
589C22×C8—1064no—
590C22×C8C22×D5311yescharacteristic
591C22×C8C22×D5311yescharacteristic
592C4⋊Q8—534no—
593C4⋊Q8—1068no—
594C4⋊Q8—1062no—
595#124—22no—
596#124C22×D5314yes—
597#123—1068no—
598C22⋊Q8—534no—
599C22⋊Q8—534no—
600C22⋊Q8—534no—
601C22⋊Q8—1068no—
602C22⋊Q8—1068no—
603C22⋊Q8—1062no—
604C22⋊Q8—1062no—
605C22⋊Q8—1062no—
606#121—534no—
607#121—1068no—
608#121—1062no—
609#120—1068no—
610C4×Q8—22no—
611C4×Q8C22×D5314yescomplemented
612C4×D4—534no—
613C4×D4—534no—
614C4×D4—534no—
615C4×D4—1068no—
616C4×D4—1062no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—531no—
619C2×C4⋊C4—531no—
620C2×C4⋊C4—1061no—
621C2×C4⋊C4—1061no—
622C2×C4⋊C4—1061no—
623C2×C4⋊C4—1061no—
624C2×C4⋊C4—1061no—
625C2×C4⋊C4C22×D5311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—531no—
629C2×C22⋊C4—531no—
630C2×C22⋊C4—1068no—
631C2×C22⋊C4—1061no—
632C2×C22⋊C4—1061no—
633C2×C22⋊C4—1061no—
634C2×C22⋊C4—1061no—
635C2×C22⋊C4—1061no—
636C2×C42—21no—
637C2×C42C22×D5311yescharacteristic
638#107—534no—
639C4⋊C8C22×D5314yescomplemented
640#103—534no—
641#103—534no—
642#103—534no—
643#103C22×D5314yescomplemented
644#102—534no—
645#102C22×D5314yes—
646C22⋊C8—534no—
647C22⋊C8—534no—
648#97—534no—
649C24—21no—
650C24—531no—
651C24—531no—
652C24—1064no—
653C24—1061no—
654C24—4242no—
655C24—2124no—
656C24—2124no—
657#41—1068no—
658#41—2124no—
659#41—2128no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—532no—
666C2×Q8—532no—
667C2×Q8—1064no—
668C2×Q8—1064no—
669C2×Q8—1061no—
670C2×Q8—1061no—
671C2×Q8—1068no—
672C2×Q8—1068no—
673C2×Q8—1062no—
674C2×Q8—1062no—
675C2×Q8—1062no—
676C2×Q8—1062no—
677C2×Q8—2124no—
678C2×Q8—2124no—
679C2×Q8—2124no—
680C2×Q8—2124no—
681C2×Q8—2128no—
682C2×Q8—2128no—
683C2×Q8D4×D5314yes—
684C2×Q8C23×D5312yes—
685C2×Q8C23×D5312yes—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—534no—
690C2×D4—534no—
691C2×D4—532no—
692C2×D4—1064no—
693C2×D4—1064no—
694C2×D4—1064no—
695C2×D4—1068no—
696C2×D4—1064no—
697C2×D4—1061no—
698C2×D4—1062no—
699C2×D4—4242no—
700C2×D4—2124no—
701C2×D4—2124no—
702C2×D4—2128no—
703C2×D4—2124no—
704C2×D4C23×D5312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—531no—
709C22×C4—531no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—1064no—
715C22×C4—1064no—
716C22×C4—1064no—
717C22×C4—1062no—
718C22×C4—1062no—
719C22×C4—1062no—
720C22×C4—1062no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1064no—
725C22×C4—4242no—
726C22×C4—2124no—
727C22×C4—2124no—
728C22×C4—2124no—
729C22×C4D4×D5311yescharacteristic
730C22×C4D4×D5311yescharacteristic
731C22×C4C23×D5311yescharacteristic
732Q16—28no—
733Q16—1068no—
734Q16—2124no—
735SD16—28no—
736SD16—5316no—
737SD16—1068no—
738SD16—1068no—
739SD16—1068no—
740SD16—2124no—
741M16—1068no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—534no—
745C2×C8—532no—
746C2×C8—532no—
747C2×C8—1068no—
748C2×C8—1062no—
749C2×C8C23×D5312yes—
750C2×C8C23×D5312yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—534no—
754C4⋊C4—532no—
755C4⋊C4—1064no—
756C4⋊C4—1064no—
757C4⋊C4—1064no—
758C4⋊C4—1061no—
759C4⋊C4—1064no—
760C4⋊C4—1064no—
761C4⋊C4C23×D5312yes—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—534no—
765C22⋊C4—534no—
766C22⋊C4—1064no—
767C22⋊C4—1064no—
768C22⋊C4—1064no—
769C22⋊C4—1064no—
770C22⋊C4—1064no—
771C42—24no—
772C42D4×D5312yes—
773C42C23×D5312yes—
774C23—22no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—534no—
779C23—532no—
780C23—532no—
781C23—1062no—
782C23—1062no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—1062no—
787C23—1064no—
788C23—4244no—
789C23—42416no—
790C23—2128no—
791C23—2128no—
792C23—2122no—
793C23—2122no—
794C23C2×D4×D5311yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—22no—
798Q8—22no—
799Q8—42no—
800Q8—1062no—
801Q8—1062no—
802Q8—1062no—
803Q8—1062no—
804Q8—2128no—
805Q8—2128no—
806Q8—2122no—
807Q8—2122no—
808Q8C2×D4×D5314yes—
809D4—22no—
810D4—22no—
811D4—42no—
812D4—534no—
813D4—1068no—
814D4—1062no—
815D4—1064no—
816D4—4244no—
817D4—2128no—
818D4—2128no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—532no—
828C2×C4—532no—
829C2×C4—1062no—
830C2×C4—1062no—
831C2×C4—1062no—
832C2×C4—1062no—
833C2×C4—1062no—
834C2×C4—1062no—
835C2×C4—1064no—
836C2×C4—1064no—
837C2×C4—1062no—
838C2×C4—1062no—
839C2×C4—1062no—
840C2×C4—4244no—
841C2×C4—2128no—
842C2×C4—2128no—
843C2×C4—2128no—
844C2×C4—2122no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4C2×D4×D5312yes—
848C2×C4C2×D4×D5312yes—
849C2×C4C2×D4×D5312yes—
850C2×C4C2×D4×D5311yescharacteristic
851C2×C4#1313326312yes—
852C2×C4C24×D5311yescharacteristic
853C8—22no—
854C8—22no—
855C8—534no—
856C8—1062no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—84no—
861C22—534no—
862C22—1068no—
863C22—1062no—
864C22—1062no—
865C22—1062no—
866C22—1064no—
867C22—1062no—
868C22—1062no—
869C22—42416no—
870C22—2124no—
871C22—2128no—
872C22—2122no—
873C22—2122no—
874C22#1681125712yes—
875C22#137×D5312yes—
876C22#1681143012yes—
877C22C22×D4×D5311yescharacteristic
878C4—24no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—1062no—
884C4—1062no—
885C4—2122no—
886C4—2122no—
887C4—2122no—
888C4#1681125712yes—
889C4C22×D4×D5311yescharacteristic
890C4C2×#1313326311yescharacteristic
891C2—82no—
892C2—1064no—
893C2—2122no—
894C2—2124no—
895C2#2028622014yesdirect product factor
896C2C2×#1681125711yescharacteristic
897C2C2×#137×D5311yescharacteristic
898C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC2×#16811266C2
hypercenterC2×#464D53
hypocenterC53C2×#3266
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×SD16×D53C2semidirect
3. C2×Q8×D212C2semidirect
5. #20286220C2direct (N × H)
6. C2×#16811018C2semidirect
7. C2×#16810868C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810829C2semidirect
10. C2×#16810788C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810760C2semidirect
13. C2×#16810775C2semidirect
14. C2×#16810721C2semidirect
15. C2×#16810693C2semidirect
16. C2×C53×#464C2semidirect
19. C22×Q8×D53C22semidirect
22. C2×#13133249C22semidirect
23. C22×#11719925C22semidirect
24. C22×#11719925C22semidirect
31. C2×SD16×D53C22semidirect
32. C22×#11719912C22semidirect
35. Q8×D212C22semidirect
39. C2×#13133217C22semidirect
44. C2×#13133197C22semidirect
53. #16811018C22semidirect
54. #16810868C22semidirect
55. #16810863C22semidirect
56. #16810829C22semidirect
57. #16810788C22semidirect
58. #16810777C22semidirect
59. #16810775C22semidirect
60. #16810760C22semidirect
61. #16810721C22semidirect
62. #16810693C22semidirect
63. C2×#13133150C22semidirect
64. C2×#13133142C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133141C22semidirect
69. C2×#13133129C22semidirect
70. C2×#13133128C22semidirect
71. C22×Q16×C53C22semidirect
74. C2×C4×Q8×C53C22semidirect
75. C53×#464C22semidirect
76. C2×C4⋊C8×C53C22semidirect
77. C2×#103×C53C22semidirect
95. C2×Q8×D53C23semidirect
114. C2×#11719925C23semidirect
115. C2×#11719925C23semidirect
124. C2×#11719924D4semidirect
128. C2×#11719912C23semidirect
135. #13133217C23semidirect
142. #13133197C23semidirect
169. #13133150C23semidirect
170. #13133142C23semidirect
171. #13133142C23semidirect
172. #13133141C23semidirect
175. #13133129C23semidirect
176. #13133128C23semidirect
181. C2×Q16×C53C23semidirect
189. C4×Q8×C53C23semidirect
196. C4⋊C8×C53C23semidirect
197. #103×C53C23semidirect
299. #11719924C2×D4semidirect
342. C22×D53#137semidirect
428. C2×D53C2×#137semidirect
450. C2×#464D53semidirect
459. C2×C53#3266semidirect
474. C22×Q16C2×D53semidirect
501. C2×C4×Q8C2×D53semidirect
509. #464C2×D53semidirect
518. C2×C4⋊C8C2×D53semidirect
522. C2×#103C2×D53semidirect
528. C53C2×#3266semidirect
570. C2×Q16C22×D53semidirect
611. C4×Q8C22×D53semidirect
639. C4⋊C8C22×D53semidirect
643. #103C22×D53semidirect
895. C2#20286220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C22×SD16×D532
C2×Q8×D2122
C2×#168112662
#202862202
C2×#168110182
C2×#168108682
C2×#168108632
C2×#168108292
C2×#168107882
C2×#168107772
C2×#168107602
C2×#168107752
C2×#168107212
C2×#168106932
C2×C53×#4642
C2×#326653