Finite Group Databasebeta

← C2×#13080861 #15630617

Subgroups — C2×#13080861 #15630617

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×#10623094C211yesmaximal, characteristic, complemented
2C2×#10623248C211yesmaximal, characteristic, complemented
3#13080861C2116yesmaximal, direct product factor
4C2×#10622683C211yesmaximal, characteristic, complemented
5C2×#10622392C212yesmaximal, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622772C212yesmaximal, complemented
8C2×#10622769C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622383C212yesmaximal, complemented
12C2×C11×#459C211yesmaximal, characteristic, complemented
13C22×D4×D11—21no—
14C22×D4×D11C2212yes—
15C22×C11×D8C2212yescomplemented
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic, complemented
18C2×#66991—21no—
19C2×#66991C2212yes—
20C2×#66991C2212yescomplemented
21C2×#66990—22no—
22C22×#4323C2211yescharacteristic
23C2×#66983—21no—
24C2×#66979—21no—
25C22×#4313C2212yescomplemented
26#10623248—24no—
27#10623248C2218yescomplemented
28#10623094—24no—
29#10623094C2218yescomplemented
30C2×#66945C2212yescomplemented
31C2×#66938—22no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic, complemented
35C11×#459C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic, complemented
37C2×C11×#102C2212yescomplemented
38C2×#66896C2212yescomplemented
39C2×#66896C2211yescharacteristic, complemented
40C2×#66896C2212yescomplemented
41#10622772C22116yescomplemented
42#10622769C22116yescomplemented
43C2×#66885C2212yes—
44C2×(C2×D11)⋊C8C2212yescomplemented
45C2×#66881C2212yescomplemented
46#10622683C2218yescomplemented
47C4×#4323C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic, complemented
50C2×C4×C11⋊C8C2211yescharacteristic, complemented
51#10622455C2218yescomplemented
52#10622451C2218yescomplemented
53#10622392C22116yescomplemented
54#10622383C22116yescomplemented
55C24×D11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11—21no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C22×C22⋊D11—22no—
64C2×D4×D11—28no—
65C2×D4×D11—28no—
66C2×D4×D11—24no—
67C2×D4×D11—44no—
68C2×D4×D11—48no—
69C2×D4×D11C2318yes—
70C22×D44D411yescharacteristic
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11C2312yes—
74C22×Dic22—21no—
75C2×C11×D8—44no—
76C2×C11×D8C2318yescomplemented
77C22×C8×C11C2312yes—
78C11×#127—22no—
79C11×#127C2314yes—
80C4×D4×C11—22no—
81C4×D4×C11C2314yescomplemented
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87#66991—24no—
88#66991—24no—
89#66991—28no—
90#66991C2318yes—
91#66991C2318yescomplemented
92#66990—216no—
93C2×#4323—24no—
94C2×#4323C2314yes—
95#66983—28no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4D412yes—
99#66979—28no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4×Dic11—22no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4313—44no—
108C2×#4313C2318yescomplemented
109#66945—24no—
110#66945C2318yescomplemented
111#66938—216no—
112C4×D44—22no—
113C4×D44D414yes—
114C4×D44C2314yes—
115C4×D44C2314yes—
116#66922—22no—
117#66922C2314yescomplemented
118C11×C4⋊C8C2314yescomplemented
119C11×#102C2318yescomplemented
120#66896C2318yescomplemented
121#66896C2314yescomplemented
122#66896C2318yescomplemented
123#66885C2318yes—
124(C2×D11)⋊C8C2318yescomplemented
125#66881C2318yescomplemented
126#66873C2314yes—
127#66871C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3325—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11—22no—
132C23×D11—21no—
133C23×D11—28no—
134C23×D11—48no—
135C23×D11—48no—
136C23×D11—84no—
137C23×D11C2×D412yes—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11—82no—
148C2×D4×C11C2414yes—
149C2×D4×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—84no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11C2×D412yes—
165D4×D11—216no—
166D4×D11—48no—
167D4×D11—416no—
168D4×D11—432no—
169C2×D44—24no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44C2×D414yes—
173C2×D44#4114yes—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—44no—
179C2×C4×D11C2×D414yes—
180C2×C4×D11C2414yes—
181C2×Dic22—24no—
182C2×Dic22—82no—
183C11×D8—48no—
184C2×C8×C11—24no—
185C2×C8×C11C2414yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189C42×C11C2×D412yes—
190C42×C11C2412yes—
191C22⋊Dic11—28no—
192C22⋊Dic11—28no—
193#4323—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4C2×D418yes—
197C4⋊Dic11—22no—
198C4⋊Dic11—24no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D414yes—
201C4⋊Dic11C2412yes—
202C4⋊Dic11C2414yes—
203C4×Dic11—28no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8C2412yes—
207C2×C11⋊C8C2412yes—
208#4313—48no—
209C2×#555—111no—
210C2×D42—111no—
211#3325—1116no—
212C2×#486—111no—
213C2×#482—112no—
214C2×#476—111no—
215C2×#469—112no—
216C2×#459D1111yescharacteristic, complemented
217C2×#447—112no—
218C2×C4×D8—111no—
219C2×#436—111no—
220C2×#418—112no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—44no—
224C23×C11—42no—
225C23×C11—44no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—44no—
229C23×C11C22×D411yescharacteristic
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—416no—
236C22×D11—416no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—88no—
240C22×D11—832no—
241C22×D11C22×D414yes—
242D4×C11—22no—
243D4×C11—24no—
244D4×C11—22no—
245D4×C11—24no—
246D4×C11—44no—
247D4×C11—42no—
248D4×C11—48no—
249D4×C11—84no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—42no—
253C2×C4×C11—48no—
254C2×C4×C11AGL(1,ℤ/8)14yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4112yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—416no—
262C22⋊D11—416no—
263C22⋊D11—88no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11C22×D414yes—
270D44—24no—
271D44—28no—
272D44—22no—
273D44C2×#4114yes—
274C4×D11—28no—
275C4×D11—24no—
276C4×D11—24no—
277C4×D11—48no—
278Dic22—84no—
279C8×C11—24no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C23×D4—112no—
283C23×D4—221no—
284C22×D8—111no—
285C22×D8C2×D1112yescomplemented
286C22×M16—112no—
287#555—118no—
288#555—224no—
289D42—118no—
290D42—224no—
291C2×C4⋊Q8—111no—
292C2×#127C2×D1111yescharacteristic
293C2×#124—222no—
294C2×#121—112no—
295C2×#121—112no—
296C2×#121—221no—
297C2×#121—221no—
298C2×#120—222no—
299C2×C4×D4—111no—
300C2×C4×D4—111no—
301C2×C4×D4C2×D1111yescharacteristic, complemented
302C2×#117—112no—
303C2×#117—221no—
304#486—118no—
305#482—1116no—
306#476—118no—
307#469—1116no—
308#459C2×D1118yescomplemented
309#447—1116no—
310C4×D8—118no—
311#436—118no—
312C2×#107—111no—
313C2×#106—112no—
314C2×C4⋊C8C2×D1111yescharacteristic, complemented
315#418—1116no—
316C2×#102—112no—
317C2×#102—112no—
318C2×#102—111no—
319C2×#102—112no—
320C2×#102—111no—
321C2×#102C2×D1112yescomplemented
322C2×C22⋊C8—112no—
323C2×C4×C8—111no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—42no—
330C22×C11—88no—
331C22×C11—84no—
332C22×C11#54612yes—
333C22×C11C2×AGL(1,ℤ/8)12yes—
334C22×C11#57612yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—42no—
341C2×D11—48no—
342C2×D11—48no—
343C2×D11—42no—
344C2×D11—832no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11#54612yes—
348C4×C11C2×AGL(1,ℤ/8)14yes—
349C4×C11C22×#4111yescharacteristic
350C4×C11C2×H(5,𝔽2)11yescharacteristic
351Dic11—24no—
352Dic11—42no—
353Dic11—44no—
354C25—222no—
355C22×Q8—221no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—118no—
359C22×D4—111no—
360C22×D4—111no—
361C22×D4—224no—
362C22×D4—222no—
363C22×D4—228no—
364C22×D4—228no—
365C22×D4—222no—
366C22×D4—222no—
367C22×D4—444no—
368C22×D4—448no—
369C22×D4C22×D1111yescharacteristic
370C22×D4C22×D1112yes—
371C23×C4—21no—
372C23×C4—112no—
373C23×C4—221no—
374C2×D8—44no—
375C2×D8—114no—
376C2×D8—224no—
377C2×D8C22×D1118yescomplemented
378C2×M16—118no—
379C2×M16—444no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8C22×D1112yes—
383C4⋊Q8—114no—
384C4⋊Q8—222no—
385#127—22no—
386#127C22×D1114yes—
387#124—2216no—
388#121—118no—
389#121—118no—
390#121—228no—
391#121—228no—
392#121—224no—
393#121—224no—
394#120—2216no—
395C4×D4—22no—
396C4×D4—114no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—222no—
400C4×D4C22×D1114yescomplemented
401#117—118no—
402#117—224no—
403#117—228no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417#107—114no—
418#106—118no—
419C4⋊C8C22×D1114yescomplemented
420#102—118no—
421#102—114no—
422#102—118no—
423#102—118no—
424#102—114no—
425#102C22×D1118yescomplemented
426C22⋊C8—118no—
427C4×C8—114no—
428C2×C11—84no—
429C2×C11—82no—
430C2×C11#332514yescomplemented
431C2×C11C2×#54611yescharacteristic
432C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
433C2×C11C2×#57611yescharacteristic
434D11—44no—
435D11—44no—
436C24—21no—
437C24—22no—
438C24—112no—
439C24—228no—
440C24—221no—
441C24—448no—
442C24—448no—
443C24—884no—
444C2×Q8—224no—
445C2×Q8—882no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—24no—
454C2×D4—44no—
455C2×D4—82no—
456C2×D4—114no—
457C2×D4—114no—
458C2×D4—112no—
459C2×D4—228no—
460C2×D4—2216no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—224no—
464C2×D4—221no—
465C2×D4—222no—
466C2×D4—448no—
467C2×D4—4416no—
468C2×D4—448no—
469C2×D4—4432no—
470C2×D4—448no—
471C2×D4—884no—
472C2×D4C23×D1114yes—
473C2×D4C23×D1112yes—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—44no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4—224no—
485C22×C4—444no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489D8—48no—
490D8—228no—
491M16—448no—
492C2×C8—24no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8C23×D1114yes—
498C4⋊C4—21no—
499C4⋊C4—114no—
500C4⋊C4—114no—
501C4⋊C4—112no—
502C4⋊C4—222no—
503C4⋊C4—221no—
504C4⋊C4—224no—
505C4⋊C4C23×D1112yes—
506C22⋊C4—24no—
507C22⋊C4—118no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—228no—
511C22⋊C4—224no—
512C42—228no—
513C42D4×D1112yes—
514C42C23×D1112yes—
515C11C2×#332511yescharacteristic, complemented, Sylow
516C23—22no—
517C23—24no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—42no—
522C23—44no—
523C23—42no—
524C23—114no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—222no—
530C23—4416no—
531C23—4416no—
532C23—442no—
533C23—442no—
534C23—888no—
535C23—8832no—
536C23C2×D4×D1111yescharacteristic
537Q8—884no—
538D4—22no—
539D4—24no—
540D4—22no—
541D4—24no—
542D4—48no—
543D4—42no—
544D4—44no—
545D4—84no—
546D4—114no—
547D4—228no—
548D4—224no—
549D4—222no—
550D4—4416no—
551D4—4416no—
552D4—888no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—114no—
558C2×C4—224no—
559C2×C4—228no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—442no—
565C2×C4—444no—
566C2×C4—448no—
567C2×C4#6696414yes—
568C2×C4C2×D4×D1112yes—
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4#6703712yes—
572C2×C4#41×D1112yes—
573C2×C4C24×D1111yescharacteristic
574C8—24no—
575C8—222no—
576C8—222no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—44no—
582C22—42no—
583C22—88no—
584C22—84no—
585C22—224no—
586C22—224no—
587C22—224no—
588C22—224no—
589C22—448no—
590C22—448no—
591C22—442no—
592C22—442no—
593C22—8832no—
594C22#1062314312yes—
595C22C2×#6696412yes—
596C22#1062330512yes—
597C22C22×D4×D1111yescharacteristic
598C4—22no—
599C4—42no—
600C4—224no—
601C4—442no—
602C4—444no—
603C4#1062314312yes—
604C4C2×#6696414yes—
605C4C2×#6703711yescharacteristic
606C4C2×#41×D1111yescharacteristic
607C2—84no—
608C2—82no—
609C2—444no—
610C2—444no—
611C2#1308086114yesdirect product factor
612C2C2×#1062314311yescharacteristic
613C2C22×#6696411yescharacteristic
614C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. C2×#10623248C2semidirect
3. #13080861C2direct (N × H)
4. C2×#10622683C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622769C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622383C2semidirect
12. C2×C11×#459C2semidirect
15. C22×C11×D8C22semidirect
17. C2×C4×D4×C11C22semidirect
20. C2×#66991C22semidirect
25. C22×#4313C22semidirect
27. #10623248C22semidirect
29. #10623094C22semidirect
30. C2×#66945C22semidirect
34. C2×#66922C22semidirect
35. C11×#459C22semidirect
36. C2×C11×C4⋊C8C22semidirect
37. C2×C11×#102C22semidirect
38. C2×#66896C22semidirect
39. C2×#66896C22semidirect
40. C2×#66896C22semidirect
41. #10622772C22semidirect
42. #10622769C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. C2×#66881C22semidirect
46. #10622683C22semidirect
47. C4×#4323C22semidirect
49. C2×#66871C22semidirect
50. C2×C4×C11⋊C8C22semidirect
51. #10622455C22semidirect
52. #10622451C22semidirect
53. #10622392C22semidirect
54. #10622383C22semidirect
76. C2×C11×D8C23semidirect
81. C4×D4×C11C23semidirect
91. #66991C23semidirect
108. C2×#4313C23semidirect
110. #66945C23semidirect
117. #66922C23semidirect
118. C11×C4⋊C8C23semidirect
119. C11×#102C23semidirect
120. #66896C23semidirect
121. #66896C23semidirect
122. #66896C23semidirect
124. (C2×D11)⋊C8C23semidirect
125. #66881C23semidirect
127. #66871C23semidirect
128. C4×C11⋊C8C23semidirect
216. C2×#459D11semidirect
285. C22×D8C2×D11semidirect
301. C2×C4×D4C2×D11semidirect
308. #459C2×D11semidirect
314. C2×C4⋊C8C2×D11semidirect
321. C2×#102C2×D11semidirect
377. C2×D8C22×D11semidirect
400. C4×D4C22×D11semidirect
419. C4⋊C8C22×D11semidirect
425. #102C22×D11semidirect
430. C2×C11#3325semidirect
515. C11C2×#3325semidirect
611. C2#13080861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106232482
#130808612
C2×#106226832
C2×#106223922
C2×#106224552
C2×#106227722
C2×#106227692
C2×C4×#43232
C2×#106224512
C2×#106223832
C2×C11×#4592
C2×#332511