Finite Group Databasebeta

← C2×#13080434 #15630106

Subgroups — C2×#13080434 #15630106

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic
2#13080434C2116yesmaximal, direct product factor
3C2×#10622701C211yesmaximal, characteristic, complemented
4C2×#10622581C212yesmaximal, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622661C212yesmaximal, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622659C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C22×#66873C212yesmaximal, complemented
12C2×C11×#554C211yesmaximal, characteristic, complemented
13C22×D4×D11—21no—
14C23×D44C2212yes—
15C11×#554—24no—
16C11×#554C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#125—21no—
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yescomplemented
21C2×C4×Q8×C11C2211yescharacteristic, complemented
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yescomplemented
25C22×#4325C2211yescharacteristic
26C22×#4325C2212yescomplemented
27C2×#66983C2212yes—
28C23×C11⋊C8C2212yescomplemented
29D4×D44—24no—
30D4×D44C2218yes—
31C2×#66948—21no—
32C2×#66935—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×#66899C2211yescharacteristic, complemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37#10622701C2218yescomplemented
38#10622697C2218yescomplemented
39#10622661C22116yescomplemented
40#10622659C22116yescomplemented
41#10622640C2218yescomplemented
42C4×#4325C2218yescomplemented
43D4×C11⋊C8C2218yescomplemented
44#10622581C22116yescomplemented
45C2×#66873C2212yes—
46C2×#66873C2211yescharacteristic
47C2×#66873C22116yescomplemented
48C2×#66873C2212yescomplemented
49C2×#66873C2212yescomplemented
50C2×#66873C2212yescomplemented
51C2×#66872C2212yescomplemented
52C2×#66872C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C24×D11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—22no—
60C23×C4×C11C2312yes—
61C22×C22⋊D11—22no—
62C2×D4×D11—28no—
63C2×D4×D11—48no—
64C22×D44—28no—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—24no—
68C22×D44—21no—
69C22×D44—44no—
70C22×D44C2312yes—
71C22×D44C2318yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yescomplemented
76C11×#125—28no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—216no—
79C11×C22⋊Q8C2318yescomplemented
80C4×Q8×C11—22no—
81C4×Q8×C11C2314yescomplemented
82C4×D4×C11—28no—
83C4×D4×C11D414yes—
84C4×D4×C11C2314yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2318yescomplemented
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4D412yes—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×#4325—24no—
99C2×#4325—44no—
100C2×#4325C2314yes—
101C2×#4325C2318yescomplemented
102#66983—24no—
103#66983C2318yes—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—22no—
106C2×C4⋊Dic11C2311yescharacteristic
107C22×C11⋊C8—44no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111C22×C11⋊C8C2318yescomplemented
112#66948—28no—
113#66935—216no—
114#66927—22no—
115#66927C2314yes—
116C4×D44—22no—
117C4×D44C2314yes—
118#66899C2314yescomplemented
119C22⋊(C11⋊C8)C2318yescomplemented
120#66873C2314yes—
121#66873C2318yes—
122#66873C2318yescomplemented
123#66873C2318yescomplemented
124#66873C2318yescomplemented
125#66872C2314yescomplemented
126#66872C2318yescomplemented
127C4⋊(C11⋊C8)C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3295—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—28no—
134C23×D11—48no—
135C23×D11—48no—
136C23×D11—84no—
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—82no—
142C2×Q8×C11C2412yes—
143C2×D4×C11SD1618yescomplemented
144C2×D4×C11C2×D414yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—28no—
151C22×C4×C11—84no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—48no—
160C22×Dic11—21no—
161D4×D11—432no—
162C2×D44—216no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—24no—
166C2×D44—28no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—22no—
170C2×D44—24no—
171C2×D44—48no—
172C2×D44—48no—
173C2×D44—416no—
174C2×D44—44no—
175C2×D44—82no—
176C2×D44#4114yes—
177C2×D44C2414yes—
178C2×D44C2412yes—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4C2×D414yes—
188C11×C4⋊C4C2412yes—
189C11×C4⋊C4C2414yes—
190C11×C22⋊C4—28no—
191C11×C22⋊C4C2×D418yes—
192C42×C11—24no—
193C42×C11C2×D412yes—
194C42×C11C2412yes—
195#4325—28no—
196#4325—48no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2412yes—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8—48no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2414yes—
208C2×#554D1111yescharacteristic, complemented
209C2×D42—111no—
210#3295—1116no—
211C2×#486—111no—
212C2×#481—112no—
213C2×#476—111no—
214C2×#465—112no—
215C2×#460—111no—
216C2×#450—112no—
217C2×C4×SD16—111no—
218C2×C8×D4—111no—
219C22×#102—112no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11C2×SD1618yes—
223C23×C11C22×D414yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—416no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—416no—
234C22×D11—44no—
235C22×D11—88no—
236C22×D11—832no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—42no—
240Q8×C11—84no—
241D4×C11C2×SD16116yescomplemented
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11—88no—
254C2×C4×C11C2×SD1614yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—416no—
263C2×Dic11—22no—
264C2×Dic11—42no—
265D44—24no—
266D44—24no—
267D44—22no—
268D44—24no—
269D44—416no—
270D44—44no—
271D44—48no—
272D44—84no—
273D44C2×#4114yes—
274C4×D11—48no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—24no—
278C23×D4—112no—
279C23×D4—221no—
280C22×SD16—111no—
281C22×SD16—112no—
282C23×C8—112no—
283#554—24no—
284#554C2×D1118yescomplemented
285D42—118no—
286D42—224no—
287C2×C4⋊Q8C2×D1111yescharacteristic, complemented
288C2×#127—111no—
289C2×#125—21no—
290C2×C22⋊Q8—22no—
291C2×C22⋊Q8C2×D1112yescomplemented
292C2×#121—112no—
293C2×#121—221no—
294C2×#120—222no—
295C2×C4×Q8C2×D1111yescharacteristic, complemented
296C2×C4×D4—21no—
297C2×C4×D4—111no—
298C2×C4×D4C2×D1111yescharacteristic
299C22×C4⋊C4C2×D1112yescomplemented
300#486—118no—
301#481—1116no—
302#476—118no—
303#465—1116no—
304#460—118no—
305#450—1116no—
306C4×SD16—118no—
307C8×D4—118no—
308C2×#106—111no—
309C2×#106—112no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×#102—111no—
316C2×#102—112no—
317C2×#102—1116no—
318C2×C22⋊C8—112no—
319C2×C4×C8—111no—
320C22×C11—24no—
321C22×C11—216no—
322C22×C11—24no—
323C22×C11#54612yes—
324C22×C11C22×SD1618yes—
325C22×C11C22×SD1612yes—
326C22×C11#57612yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—24no—
329C2×D11—48no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—832no—
336C2×D11—88no—
337C4×C11—24no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—44no—
342C4×C11#54612yes—
343C4×C11C22×SD1614yes—
344C4×C11C22×#4111yescharacteristic
345C4×C11C2×H(5,𝔽2)11yescharacteristic
346Dic11—42no—
347C25—222no—
348C22×Q8—21no—
349C22×Q8C22×D1111yescharacteristic
350C22×D4—111no—
351C22×D4—112no—
352C22×D4—118no—
353C22×D4—228no—
354C22×D4—222no—
355C22×D4—228no—
356C22×D4—222no—
357C22×D4—221no—
358C22×D4—224no—
359C22×D4—221no—
360C22×D4—444no—
361C22×D4—448no—
362C22×D4C22⋊D1111yescharacteristic
363C23×C4—22no—
364C23×C4—221no—
365C23×C4C22×D1112yes—
366C2×SD16—114no—
367C2×SD16—118no—
368C2×SD16—224no—
369C2×SD16—444no—
370C22×C8—111no—
371C22×C8—112no—
372C22×C8—111no—
373C22×C8—118no—
374C22×C8—444no—
375C4⋊Q8—22no—
376C4⋊Q8C22×D1114yescomplemented
377#127—114no—
378#127—222no—
379#125—28no—
380C22⋊Q8—24no—
381C22⋊Q8—216no—
382C22⋊Q8C22×D1118yescomplemented
383#121—118no—
384#121—224no—
385#121—228no—
386#120—2216no—
387C4×Q8—22no—
388C4×Q8C22×D1114yescomplemented
389C4×D4—28no—
390C4×D4—114no—
391C4×D4—222no—
392C4×D4C22⋊D1114yes—
393C4×D4C22×D1114yes—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1118yescomplemented
404C2×C22⋊C4—22no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4C22⋊D1112yes—
408C2×C42—21no—
409C2×C42C22×D1111yescharacteristic
410#106—114no—
411#106—118no—
412C4⋊C8—114no—
413#103—114no—
414#102—114no—
415#102—118no—
416#102—118no—
417#102—118no—
418#102—118no—
419C22⋊C8—118no—
420C4×C8—114no—
421C2×C11—28no—
422C2×C11#329514yescomplemented
423C2×C11C2×#54611yescharacteristic
424C2×C11C23×SD1611yescharacteristic
425C2×C11C2×#57611yescharacteristic
426D11—44no—
427D11—84no—
428C24—221no—
429C24—222no—
430C24—228no—
431C24—448no—
432C24—448no—
433C24—884no—
434C24C2×C22⋊D1112yes—
435C2×Q8—21no—
436C2×Q8—24no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—82no—
440C2×Q8C23×D1112yes—
441C2×D4—114no—
442C2×D4—112no—
443C2×D4—114no—
444C2×D4—2216no—
445C2×D4—228no—
446C2×D4—224no—
447C2×D4—222no—
448C2×D4—224no—
449C2×D4—221no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—222no—
453C2×D4—224no—
454C2×D4—448no—
455C2×D4—4416no—
456C2×D4—448no—
457C2×D4—448no—
458C2×D4—4432no—
459C2×D4—444no—
460C2×D4—882no—
461C2×D4#432518yescomplemented
462C2×D4C2×C22⋊D1114yes—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—28no—
469C22×C4—84no—
470C22×C4—221no—
471C22×C4—224no—
472C22×C4—444no—
473C22×C4C2×C22⋊D1114yes—
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1112yes—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C23×D1114yes—
478C22×C4C23×D1111yescharacteristic
479SD16—228no—
480SD16—448no—
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—114no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—224no—
487C2×C8—448no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—28no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—28no—
494C4⋊C4—112no—
495C4⋊C4—221no—
496C4⋊C4C2×C22⋊D1114yes—
497C4⋊C4C23×D1112yes—
498C4⋊C4C23×D1114yes—
499C22⋊C4—28no—
500C22⋊C4—224no—
501C22⋊C4—228no—
502C22⋊C4C2×C22⋊D1118yes—
503C42—24no—
504C42C2×C22⋊D1112yes—
505C42C23×D1112yes—
506C11C2×#329511yescharacteristic, complemented, Sylow
507C23—24no—
508C23—24no—
509C23—224no—
510C23—222no—
511C23—224no—
512C23—4416no—
513C23—442no—
514C23—442no—
515C23—4416no—
516C23—444no—
517C23—444no—
518C23—444no—
519C23—888no—
520C23—8832no—
521C23C2×#432518yes—
522C23C22×C22⋊D1114yes—
523C23C22×C22⋊D1111yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—42no—
527Q8—84no—
528D4—114no—
529D4—224no—
530D4—224no—
531D4—222no—
532D4—224no—
533D4—4416no—
534D4—4416no—
535D4—448no—
536D4—444no—
537D4—884no—
538D4C2×#4325116yescomplemented
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—88no—
551C2×C4—222no—
552C2×C4—442no—
553C2×C4—448no—
554C2×C4C2×#432514yes—
555C2×C4#41×D1112yes—
556C2×C4#6704212yes—
557C2×C4C22×C22⋊D1112yes—
558C2×C4C22×C22⋊D1114yes—
559C2×C4C22×C22⋊D1112yes—
560C2×C4C22×C22⋊D1111yescharacteristic
561C2×C4C24×D1111yescharacteristic
562C8—222no—
563C8—222no—
564C8—224no—
565C22—216no—
566C22—24no—
567C22—24no—
568C22—224no—
569C22—448no—
570C22—442no—
571C22—442no—
572C22—444no—
573C22—444no—
574C22—444no—
575C22—8832no—
576C22—888no—
577C22C22×#432518yes—
578C22C22×#432512yes—
579C22#1062336012yes—
580C22#1062336612yes—
581C22C23×C22⋊D1111yescharacteristic
582C4—24no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—44no—
587C4—442no—
588C4C22×#432514yes—
589C4#1062336012yes—
590C4C2×#41×D1111yescharacteristic
591C4C2×#6704211yescharacteristic
592C2—28no—
593C2—444no—
594C2—884no—
595C2#1308043414yesdirect product factor
596C2C2×#1062336011yescharacteristic
597C2C23×#432511yescharacteristic
598C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenterC2×#554D11
hypocenterC11C2×#3295
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13080434C2direct (N × H)
3. C2×#10622701C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622661C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622659C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C22×#66873C2semidirect
12. C2×C11×#554C2semidirect
16. C11×#554C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
21. C2×C4×Q8×C11C22semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C22×#4325C22semidirect
28. C23×C11⋊C8C22semidirect
35. C2×#66899C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. #10622701C22semidirect
38. #10622697C22semidirect
39. #10622661C22semidirect
40. #10622659C22semidirect
41. #10622640C22semidirect
42. C4×#4325C22semidirect
43. D4×C11⋊C8C22semidirect
44. #10622581C22semidirect
47. C2×#66873C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66872C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
75. C11×C4⋊Q8C23semidirect
79. C11×C22⋊Q8C23semidirect
81. C4×Q8×C11C23semidirect
93. C2×C11×C4⋊C4C23semidirect
101. C2×#4325C23semidirect
111. C22×C11⋊C8C23semidirect
118. #66899C23semidirect
119. C22⋊(C11⋊C8)C23semidirect
122. #66873C23semidirect
123. #66873C23semidirect
124. #66873C23semidirect
125. #66872C23semidirect
126. #66872C23semidirect
127. C4⋊(C11⋊C8)C23semidirect
128. C4×C11⋊C8C23semidirect
143. C2×D4×C11SD16semidirect
208. C2×#554D11semidirect
241. D4×C11C2×SD16semidirect
284. #554C2×D11semidirect
287. C2×C4⋊Q8C2×D11semidirect
291. C2×C22⋊Q8C2×D11semidirect
295. C2×C4×Q8C2×D11semidirect
299. C22×C4⋊C4C2×D11semidirect
376. C4⋊Q8C22×D11semidirect
382. C22⋊Q8C22×D11semidirect
388. C4×Q8C22×D11semidirect
403. C2×C4⋊C4C22×D11semidirect
422. C2×C11#3295semidirect
461. C2×D4#4325semidirect
506. C11C2×#3295semidirect
538. D4C2×#4325semidirect
595. C2#13080434direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D442
#130804342
C2×#106227012
C2×#106225812
C2×#106226972
C2×#106226612
C2×#106226402
C2×#106226592
C2×C4×#43252
C2×D4×C11⋊C82
C22×#668732
C2×C11×#5542
C2×#329511