Finite Group Databasebeta

← C2×#13080852 #15630608

Subgroups — C2×#13080852 #15630608

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic, complemented
2#13080852C2116yesmaximal, direct product factor
3C2×#10622701C211yesmaximal, characteristic, complemented
4C2×#10622616C212yesmaximal, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622652C212yesmaximal, complemented
7C2×#10622628C211yesmaximal, characteristic, complemented
8C2×#10622649C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622614C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic, complemented
13C22×D4×D11—21no—
14C23×D44C2212yes—
15C11×#555—24no—
16C11×#555C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#124—22no—
19C2×C11×#121—21no—
20C2×C11×#121C2212yescomplemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C2×C11×#117—21no—
24C2×C11×#117C2212yescomplemented
25C22×#4323C2211yescharacteristic
26C22×#4323C2212yescomplemented
27C2×#66983C2212yes—
28C22×#4318C2212yescomplemented
29D4×D44—24no—
30D4×D44C2218yescomplemented
31C2×#66948—21no—
32C2×#66935—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×#66896C2211yescharacteristic, complemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37#10622701C2218yescomplemented
38#10622697C2218yescomplemented
39#10622652C22116yescomplemented
40#10622649C22116yescomplemented
41#10622628C2218yescomplemented
42C4×#4323C2218yescomplemented
43#10622625C2218yescomplemented
44#10622616C22116yescomplemented
45#10622614C22116yescomplemented
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66873C2212yescomplemented
49C2×#66873C2212yescomplemented
50C2×#66873C2212yescomplemented
51C2×#66872C2212yescomplemented
52C2×#66871C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C24×D11—22no—
56C22×Q8×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2312yes—
62C22×C22⋊D11—22no—
63C2×D4×D11—28no—
64C2×D4×D11—48no—
65C22×D44—28no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—24no—
69C22×D44—21no—
70C22×D44—44no—
71C22×D44C2312yes—
72C22×D44C2318yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yescomplemented
77C11×#124—216no—
78C11×#121—28no—
79C11×#121—24no—
80C11×#121C2318yescomplemented
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C4×D4×C11C2314yes—
84C4×D4×C11C2314yescomplemented
85C11×#117—24no—
86C11×#117—28no—
87C11×#117C2318yescomplemented
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D412yes—
96C2×C42×C11—22no—
97C2×C42×C11C2311yescharacteristic
98C2×#4323—24no—
99C2×#4323—44no—
100C2×#4323C2314yes—
101C2×#4323C2318yescomplemented
102#66983—24no—
103#66983C2318yes—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—22no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×#4318—44no—
108C2×#4318C2318yescomplemented
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66948—28no—
113#66935—216no—
114#66927—22no—
115#66927C2314yes—
116C4×D44—22no—
117C4×D44C2314yes—
118#66896C2314yescomplemented
119C22⋊(C11⋊C8)C2318yescomplemented
120#66873C2314yes—
121#66873C2318yes—
122#66873C2318yescomplemented
123#66873C2318yescomplemented
124#66873C2318yescomplemented
125#66872C2318yescomplemented
126#66871C2314yescomplemented
127C4⋊(C11⋊C8)C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3325—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D412yes—
132C23×D11—21no—
133C23×D11—22no—
134C23×D11—28no—
135C23×D11—48no—
136C23×D11—48no—
137C23×D11—84no—
138C2×Q8×C11—24no—
139C2×Q8×C11—82no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—84no—
146C2×D4×C11C2×D414yes—
147C2×D4×C11C2412yes—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2414yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—28no—
161C2×C22⋊D11—48no—
162C22×Dic11—21no—
163D4×D11—432no—
164C2×D44—216no—
165C2×D44—21no—
166C2×D44—22no—
167C2×D44—24no—
168C2×D44—28no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—22no—
172C2×D44—24no—
173C2×D44—48no—
174C2×D44—48no—
175C2×D44—416no—
176C2×D44—44no—
177C2×D44—82no—
178C2×D44#4114yes—
179C2×D44C2414yes—
180C2×D44C2412yes—
181C2×C4×D11—24no—
182C2×C4×D11—44no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2412yes—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4C2×D418yes—
193C42×C11—28no—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196#4323—28no—
197#4323—48no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—28no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2412yes—
202#4318—48no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2412yes—
208C2×C11⋊C8C2414yes—
209C2×#555D1111yescharacteristic, complemented
210C2×D42—111no—
211#3325—1116no—
212C2×#486—111no—
213C2×#482—112no—
214C2×#476—111no—
215C2×#469—112no—
216C2×#459—111no—
217C2×#447—112no—
218C2×C4×D8—111no—
219C2×#436—111no—
220C2×#418—112no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11C22×D414yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—24no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—416no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—416no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—88no—
241C22×D11—832no—
242Q8×C11—84no—
243D4×C11—28no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—42no—
247D4×C11—88no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—28no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—42no—
256C2×C4×C11—44no—
257C2×C4×C11—48no—
258C2×C4×C11AGL(1,ℤ/8)14yes—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—416no—
267C2×Dic11—22no—
268C2×Dic11—42no—
269D44—24no—
270D44—24no—
271D44—22no—
272D44—24no—
273D44—416no—
274D44—44no—
275D44—48no—
276D44—84no—
277D44C2×#4114yes—
278C4×D11—48no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—24no—
282C23×D4—112no—
283C23×D4—221no—
284C22×D8—111no—
285C22×D8—112no—
286C22×M16—112no—
287#555—24no—
288#555C2×D1118yescomplemented
289D42—118no—
290D42—224no—
291C2×C4⋊Q8C2×D1111yescharacteristic, complemented
292C2×#127—111no—
293C2×#124—22no—
294C2×#121—21no—
295C2×#121—112no—
296C2×#121—221no—
297C2×#121C2×D1112yescomplemented
298C2×#120—222no—
299C2×C4×D4—111no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×C4×D4C2×D1111yescharacteristic, complemented
302C2×#117—21no—
303C2×#117C2×D1112yescomplemented
304#486—118no—
305#482—1116no—
306#476—118no—
307#469—1116no—
308#459—118no—
309#447—1116no—
310C4×D8—118no—
311#436—118no—
312C2×#107—111no—
313C2×#106—112no—
314C2×C4⋊C8—111no—
315#418—1116no—
316C2×#102—111no—
317C2×#102—112no—
318C2×#102—112no—
319C2×#102—112no—
320C2×#102—111no—
321C2×#102—112no—
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—48no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—84no—
332C22×C11#54612yes—
333C22×C11C2×AGL(1,ℤ/8)12yes—
334C22×C11#57612yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—42no—
338C2×D11—48no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—832no—
344C2×D11—88no—
345C4×C11—24no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11#54612yes—
350C4×C11C2×AGL(1,ℤ/8)14yes—
351C4×C11C22×#4111yescharacteristic
352C4×C11C2×H(5,𝔽2)11yescharacteristic
353Dic11—42no—
354C25—222no—
355C22×Q8—21no—
356C22×D4—22no—
357C22×D4—111no—
358C22×D4—112no—
359C22×D4—118no—
360C22×D4—228no—
361C22×D4—222no—
362C22×D4—228no—
363C22×D4—222no—
364C22×D4—221no—
365C22×D4—224no—
366C22×D4—221no—
367C22×D4—444no—
368C22×D4—448no—
369C22×D4C22⋊D1111yescharacteristic
370C22×D4C22×D1111yescharacteristic
371C23×C4—21no—
372C23×C4—221no—
373C23×C4C22×D1112yes—
374C2×D8—114no—
375C2×D8—118no—
376C2×D8—224no—
377C2×D8—444no—
378C2×M16—118no—
379C2×M16—444no—
380C22×C8—111no—
381C22×C8—112no—
382C22×C8—111no—
383C4⋊Q8—22no—
384C4⋊Q8C22×D1114yescomplemented
385#127—114no—
386#127—222no—
387#124—216no—
388#121—28no—
389#121—24no—
390#121—118no—
391#121—224no—
392#121—228no—
393#121C22×D1118yescomplemented
394#120—2216no—
395C4×D4—22no—
396C4×D4—114no—
397C4×D4—222no—
398C4×D4C22⋊D1114yes—
399C4×D4C22×D1114yes—
400C4×D4C22×D1114yescomplemented
401#117—24no—
402#117—28no—
403#117C22×D1118yescomplemented
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1112yes—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4C22⋊D1112yes—
415C2×C42—22no—
416C2×C42C22×D1111yescharacteristic
417#107—114no—
418#106—118no—
419C4⋊C8—114no—
420#102—114no—
421#102—114no—
422#102—118no—
423#102—118no—
424#102—118no—
425#102—118no—
426C22⋊C8—118no—
427C4×C8—114no—
428C2×C11—44no—
429C2×C11—82no—
430C2×C11#332514yescomplemented
431C2×C11C2×#54611yescharacteristic
432C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
433C2×C11C2×#57611yescharacteristic
434D11—44no—
435D11—84no—
436C24—21no—
437C24—221no—
438C24—222no—
439C24—228no—
440C24—448no—
441C24—448no—
442C24—884no—
443C24C2×C22⋊D1112yes—
444C2×Q8—24no—
445C2×Q8—82no—
446C2×D4—28no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—84no—
452C2×D4—114no—
453C2×D4—112no—
454C2×D4—114no—
455C2×D4—2216no—
456C2×D4—228no—
457C2×D4—224no—
458C2×D4—222no—
459C2×D4—224no—
460C2×D4—221no—
461C2×D4—228no—
462C2×D4—224no—
463C2×D4—222no—
464C2×D4—224no—
465C2×D4—448no—
466C2×D4—4416no—
467C2×D4—448no—
468C2×D4—4432no—
469C2×D4—448no—
470C2×D4—444no—
471C2×D4—882no—
472C2×D4C2×C22⋊D1114yes—
473C2×D4C23×D1112yes—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—44no—
480C22×C4—221no—
481C22×C4—224no—
482C22×C4—444no—
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C23×D1114yes—
488C22×C4C23×D1111yescharacteristic
489D8—228no—
490D8—448no—
491M16—448no—
492C2×C8—112no—
493C2×C8—112no—
494C2×C8—114no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—224no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4C2×C22⋊D1114yes—
504C4⋊C4C23×D1114yes—
505C4⋊C4C23×D1112yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—24no—
509C22⋊C4—224no—
510C22⋊C4—228no—
511C22⋊C4C2×C22⋊D1118yes—
512C42—28no—
513C42C2×C22⋊D1112yes—
514C42C23×D1112yes—
515C11C2×#332511yescharacteristic, complemented, Sylow
516C23—24no—
517C23—24no—
518C23—24no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—224no—
524C23—222no—
525C23—224no—
526C23—4416no—
527C23—4416no—
528C23—442no—
529C23—442no—
530C23—444no—
531C23—444no—
532C23—444no—
533C23—888no—
534C23—8832no—
535C23C22×C22⋊D1114yes—
536C23C22×C22⋊D1111yescharacteristic
537Q8—84no—
538D4—28no—
539D4—22no—
540D4—22no—
541D4—42no—
542D4—88no—
543D4—114no—
544D4—224no—
545D4—224no—
546D4—222no—
547D4—224no—
548D4—4416no—
549D4—4416no—
550D4—448no—
551D4—444no—
552D4—884no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—222no—
564C2×C4—442no—
565C2×C4—448no—
566C2×C4#6700214yes—
567C2×C4#41×D1112yes—
568C2×C4#6704212yes—
569C2×C4C22×C22⋊D1114yes—
570C2×C4C22×C22⋊D1112yes—
571C2×C4C22×C22⋊D1112yes—
572C2×C4C22×C22⋊D1111yescharacteristic
573C2×C4C24×D1111yescharacteristic
574C8—222no—
575C8—222no—
576C8—224no—
577C22—24no—
578C22—24no—
579C22—24no—
580C22—48no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—84no—
585C22—224no—
586C22—448no—
587C22—442no—
588C22—442no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—8832no—
593C22—888no—
594C22C2×#6700212yes—
595C22#1062336012yes—
596C22#1062336612yes—
597C22C23×C22⋊D1111yescharacteristic
598C4—24no—
599C4—22no—
600C4—42no—
601C4—44no—
602C4—442no—
603C4C2×#6700214yes—
604C4#1062336012yes—
605C4C2×#41×D1111yescharacteristic
606C4C2×#6704211yescharacteristic
607C2—44no—
608C2—82no—
609C2—444no—
610C2—884no—
611C2#1308085214yesdirect product factor
612C2C2×#1062336011yescharacteristic
613C2C22×#6700211yescharacteristic
614C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×D4×D44C2semidirect
2. #13080852C2direct (N × H)
3. C2×#10622701C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622652C2semidirect
7. C2×#10622628C2semidirect
8. C2×#10622649C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622614C2semidirect
12. C2×C11×#555C2semidirect
16. C11×#555C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×#121C22semidirect
22. C2×C4×D4×C11C22semidirect
24. C2×C11×#117C22semidirect
26. C22×#4323C22semidirect
28. C22×#4318C22semidirect
30. D4×D44C22semidirect
35. C2×#66896C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. #10622701C22semidirect
38. #10622697C22semidirect
39. #10622652C22semidirect
40. #10622649C22semidirect
41. #10622628C22semidirect
42. C4×#4323C22semidirect
43. #10622625C22semidirect
44. #10622616C22semidirect
45. #10622614C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
76. C11×C4⋊Q8C23semidirect
80. C11×#121C23semidirect
84. C4×D4×C11C23semidirect
87. C11×#117C23semidirect
101. C2×#4323C23semidirect
108. C2×#4318C23semidirect
118. #66896C23semidirect
119. C22⋊(C11⋊C8)C23semidirect
122. #66873C23semidirect
123. #66873C23semidirect
124. #66873C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. C4⋊(C11⋊C8)C23semidirect
128. C4×C11⋊C8C23semidirect
209. C2×#555D11semidirect
288. #555C2×D11semidirect
291. C2×C4⋊Q8C2×D11semidirect
297. C2×#121C2×D11semidirect
301. C2×C4×D4C2×D11semidirect
303. C2×#117C2×D11semidirect
384. C4⋊Q8C22×D11semidirect
393. #121C22×D11semidirect
400. C4×D4C22×D11semidirect
403. #117C22×D11semidirect
430. C2×C11#3325semidirect
515. C11C2×#3325semidirect
611. C2#13080852direct (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
#130808522
C2×#106227012
C2×#106226162
C2×#106226972
C2×#106226522
C2×#106226282
C2×#106226492
C2×C4×#43232
C2×#106226252
C2×#106226142
C2×C11×#5552
C2×#332511