Finite Group Databasebeta

← C2×#13078556 #15621570

Subgroups — C2×#13078556 #15621570

Order 2816.

2670 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2#13078556C2116yesmaximal, direct product factor
3C2×#10622581C212yesmaximal, complemented
4C2×#10622616C214yesmaximal, complemented
5C2×#10622580C212yesmaximal, complemented
6C2×#10622608C212yesmaximal, complemented
7C2×#10622614C212yesmaximal, complemented
8C2×#10622820C211yesmaximal, characteristic, complemented
9C22×C11×#117C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11—21no—
12C23×D44C2211yescharacteristic
13C2×C11×#117—21no—
14C2×C11×#117—21no—
15C2×C11×#117—24no—
16C2×C11×#117C2212yes—
17C2×C11×#117C2212yescomplemented
18C2×C11×#117C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C22×C11×C22⋊C4—21no—
22C22×C42×C11—21no—
23C2×#66983—21no—
24C2×#66983—21no—
25C2×#66983—24no—
26C2×#66983C2218yes—
27C2×#66983C2212yes—
28C2×#66983C2212yes—
29C22×(C2×D11)⋊C4—21no—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×#4318C2212yes—
32#10622820C2218yescomplemented
33C2×C22⋊(C11⋊C8)C2212yescomplemented
34C2×C22⋊(C11⋊C8)C2212yescomplemented
35#10622616C22132yescomplemented
36#10622614C22116yescomplemented
37#10622608C22116yescomplemented
38#10622581C22116yescomplemented
39#10622580C22116yescomplemented
40C2×#66873C2214yescomplemented
41C2×#66873C2214yescomplemented
42C2×#66872C2214yescomplemented
43C2×#66871C2214yescomplemented
44C25×C11D411yescharacteristic
45C24×D11—21no—
46C23×C4×C11—28no—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D414yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—22no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—48no—
61C23×Dic11—21no—
62C22×D44—28no—
63C22×D44—21no—
64C22×D44—22no—
65C22×D44C2312yes—
66C22×D44C2314yes—
67C11×#117—24no—
68C11×#117—28no—
69C11×#117—28no—
70C11×#117—24no—
71C11×#117C2318yes—
72C11×#117C2318yescomplemented
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yescomplemented
80C2×C11×C4⋊C4C2314yescomplemented
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11—22no—
85C2×C42×C11—28no—
86C2×C42×C11—22no—
87#66983—28no—
88#66983—24no—
89#66983—28no—
90#66983—24no—
91#66983C2318yes—
92#66983C2318yes—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—28no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×#4318—28no—
101C2×#4318C2318yes—
102C22×C11⋊C8C2314yes—
103C22⋊(C11⋊C8)C2318yescomplemented
104C22⋊(C11⋊C8)C2318yescomplemented
105#66873C23116yescomplemented
106#66873C23116yescomplemented
107#66872C23116yescomplemented
108#66871C23116yescomplemented
109C2×#3094—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—42no—
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D414yes—
115C24×C11C2×D411yescharacteristic
116C24×C11C2×D411yescharacteristic
117C23×D11—24no—
118C23×D11—22no—
119C23×D11—44no—
120C23×D11—44no—
121C23×D11—44no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—216no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—216no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—44no—
134C22×C4×C11—44no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4118yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2412yes—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—432no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—44no—
157C2×D44—24no—
158C2×D44—22no—
159C2×D44—28no—
160C2×D44—216no—
161C2×D44—48no—
162C2×D44—44no—
163C2×D44C2414yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2414yes—
169C11×C4⋊C4C2414yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C42×C11—28no—
173C42×C11—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—28no—
176C4⋊Dic11—24no—
177C4⋊Dic11—22no—
178C4⋊Dic11C2414yes—
179#4318—216no—
180C2×C11⋊C8—28no—
181C2×C11⋊C8C2418yes—
182C22×#121—111no—
183C22×#117D1111yescharacteristic, complemented
184#3094—1116no—
185C2×#481—112no—
186C2×#482—114no—
187C2×#480—112no—
188C2×#428—112no—
189C2×#418—112no—
190C2×#407—111no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—28no—
196C23×C11—22no—
197C23×C11—28no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—44no—
201C23×C11—416no—
202C23×C11#12314yes—
203C23×C11AGL(1,ℤ/8)14yes—
204C23×C11C22×D412yes—
205C23×C11C22×D412yes—
206C23×C11C22×D412yes—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—48no—
210C22×D11—48no—
211C22×D11—48no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—816no—
216C2×C4×C11—28no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—28no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—48no—
228C2×C4×C11—48no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11#12318yes—
232C2×C4×C11#12314yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4114yes—
238C2×C4×C11C2×#4118yes—
239C2×C4×C11C2511yescharacteristic
240C22⋊D11—416no—
241C22⋊D11—416no—
242C2×Dic11—24no—
243C2×Dic11—48no—
244C2×Dic11—44no—
245D44—28no—
246D44—48no—
247D44—44no—
248C11⋊C8—28no—
249C23×D4—111no—
250C23×D4—221no—
251C24×C4C2×D1111yescharacteristic
252C22×M16—112no—
253C2×#121—112no—
254C2×#121—112no—
255C2×#121—118no—
256C2×#121—224no—
257C2×#121—221no—
258C2×#121—221no—
259C2×#117—21no—
260C2×#117—21no—
261C2×#117—24no—
262C2×#117C2×D1112yes—
263C2×#117C2×D1112yescomplemented
264C2×#117C2×D1118yescomplemented
265C22×C4⋊C4—111no—
266C22×C4⋊C4C2×D1111yescharacteristic, complemented
267C22×C4⋊C4C2×D1111yescharacteristic, complemented
268C22×C22⋊C4—21no—
269C22×C22⋊C4—221no—
270C22×C42—21no—
271#482—1132no—
272#481—1116no—
273#480—1116no—
274#428—1116no—
275C2×#107—114no—
276C2×#106—114no—
277#418—1116no—
278C2×#102—114no—
279C2×#102—114no—
280#407—118no—
281C2×C22⋊C8—112no—
282C2×C22⋊C8—112no—
283C22×C11—28no—
284C22×C11—28no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—416no—
293C22×C11—44no—
294C22×C11C2×#12314yes—
295C22×C11C2×#12312yes—
296C22×C11C2×AGL(1,ℤ/8)14yes—
297C22×C11C2×AGL(1,ℤ/8)12yes—
298C22×C11#57512yes—
299C22×C11C23×D411yescharacteristic
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—816no—
304C2×D11—88no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—44no—
308C4×C11—44no—
309C4×C11C2×#12314yes—
310C4×C11C2×#12312yes—
311C4×C11C22×#4112yes—
312Dic11—44no—
313C25—221no—
314C25C22⋊D1111yescharacteristic
315C22×D4—112no—
316C22×D4—114no—
317C22×D4—228no—
318C22×D4—222no—
319C22×D4—222no—
320C22×D4—228no—
321C22×D4—222no—
322C22×D4—221no—
323C22×D4—448no—
324C23×C4—28no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—221no—
328C23×C4C22⋊D1111yescharacteristic
329C23×C4C22⋊D1114yes—
330C23×C4C22⋊D1111yescharacteristic
331C23×C4C22⋊D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1114yes—
335C23×C4C22×D1111yescharacteristic
336C2×M16—118no—
337C2×M16—228no—
338C22×C8—114no—
339#121—118no—
340#121—118no—
341#121—228no—
342#121—224no—
343#121—224no—
344#121—228no—
345#117—24no—
346#117—28no—
347#117—28no—
348#117—24no—
349#117C22×D1118yes—
350#117C22×D1118yescomplemented
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1112yes—
360C2×C4⋊C4C22×D1112yes—
361C2×C4⋊C4C22×D1114yescomplemented
362C2×C4⋊C4C22×D1114yescomplemented
363C2×C22⋊C4—22no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—22no—
370C2×C42—28no—
371C2×C42—22no—
372#107—1116no—
373#106—1116no—
374#102—1116no—
375#102—1116no—
376C22⋊C8—118no—
377C22⋊C8—118no—
378C2×C11—24no—
379C2×C11—24no—
380C2×C11—42no—
381C2×C11#309414yescomplemented
382C2×C11C22×#12311yescharacteristic
383C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C11C2×#57511yescharacteristic
385D11—84no—
386C24—24no—
387C24—24no—
388C24—42no—
389C24—224no—
390C24—222no—
391C24—444no—
392C24—444no—
393C24—444no—
394C24C2×C22⋊D1111yescharacteristic
395C24C2×C22⋊D1114yes—
396C24C2×C22⋊D1111yescharacteristic
397C24C2×C22⋊D1111yescharacteristic
398C2×D4—114no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—228no—
402C2×D4—2216no—
403C2×D4—224no—
404C2×D4—222no—
405C2×D4—4432no—
406C2×D4—448no—
407C2×D4—448no—
408C2×D4—448no—
409C2×D4—444no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—216no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—216no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—444no—
426C22×C4#433918yes—
427C22×C4C2×C22⋊D1114yes—
428C22×C4C2×C22⋊D1114yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1114yes—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C23×D1112yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1111yescharacteristic
440M16—2216no—
441C2×C8—118no—
442C2×C8—228no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—114no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4C23×D1114yes—
451C4⋊C4C23×D1114yes—
452C22⋊C4—28no—
453C22⋊C4—28no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C42—28no—
457C42—28no—
458C11C2×#309411yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—28no—
464C23—22no—
465C23—28no—
466C23—22no—
467C23—22no—
468C23—44no—
469C23—416no—
470C23—224no—
471C23—448no—
472C23—448no—
473C23—448no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23—8816no—
478C23#6698214yes—
479C23#6700214yes—
480C23C22×C22⋊D1112yes—
481C23C22×C22⋊D1112yes—
482C23C22×C22⋊D1112yes—
483C23C22×C22⋊D1111yescharacteristic
484D4—228no—
485D4—4416no—
486D4—4416no—
487D4—444no—
488D4—448no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—28no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—28no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—224no—
505C2×C4—448no—
506C2×C4—444no—
507C2×C4#6698218yes—
508C2×C4#6698214yes—
509C2×C4C2×#433914yes—
510C2×C4C2×#433918yes—
511C2×C4C22×C22⋊D1112yes—
512C2×C4C22×C22⋊D1112yes—
513C2×C4C22×C22⋊D1112yes—
514C2×C4C22×C22⋊D1111yescharacteristic
515C2×C4C24×D1111yescharacteristic
516C8—228no—
517C22—28no—
518C22—28no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—416no—
527C22—44no—
528C22—444no—
529C22—444no—
530C22—444no—
531C22—8816no—
532C22—888no—
533C22C2×#6698214yes—
534C22C2×#6698212yes—
535C22C2×#6700214yes—
536C22C2×#6700212yes—
537C22#1062335312yes—
538C22C23×C22⋊D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—44no—
542C4—44no—
543C4—444no—
544C4C2×#6698212yes—
545C4C2×#6698214yes—
546C4C22×#433912yes—
547C2—24no—
548C2—24no—
549C2—42no—
550C2—884no—
551C2#1307855614yesdirect product factor
552C2C22×#6698211yescharacteristic
553C2C22×#6700211yescharacteristic
554C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#117C2
socleC23×C11C22×D4
prime radicalC22×#66983C2
hypercenterC22×#117D11
hypocenterC11C2×#3094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13078556C2direct (N × H)
3. C2×#10622581C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622608C2semidirect
7. C2×#10622614C2semidirect
8. C2×#10622820C2semidirect
9. C22×C11×#117C2semidirect
17. C2×C11×#117C22semidirect
18. C2×C11×#117C22semidirect
19. C22×C11×C4⋊C4C22semidirect
20. C22×C11×C4⋊C4C22semidirect
32. #10622820C22semidirect
33. C2×C22⋊(C11⋊C8)C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
35. #10622616C22semidirect
36. #10622614C22semidirect
37. #10622608C22semidirect
38. #10622581C22semidirect
39. #10622580C22semidirect
40. C2×#66873C22semidirect
41. C2×#66873C22semidirect
42. C2×#66872C22semidirect
43. C2×#66871C22semidirect
72. C11×#117C23semidirect
79. C2×C11×C4⋊C4C23semidirect
80. C2×C11×C4⋊C4C23semidirect
103. C22⋊(C11⋊C8)C23semidirect
104. C22⋊(C11⋊C8)C23semidirect
105. #66873C23semidirect
106. #66873C23semidirect
107. #66872C23semidirect
108. #66871C23semidirect
183. C22×#117D11semidirect
263. C2×#117C2×D11semidirect
264. C2×#117C2×D11semidirect
266. C22×C4⋊C4C2×D11semidirect
267. C22×C4⋊C4C2×D11semidirect
350. #117C22×D11semidirect
361. C2×C4⋊C4C22×D11semidirect
362. C2×C4⋊C4C22×D11semidirect
381. C2×C11#3094semidirect
458. C11C2×#3094semidirect
551. C2#13078556direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
#130785562
C2×#106225812
C2×#106226162
C2×#106225802
C2×#106226082
C2×#106226142
C2×#106228202
C22×C11×#1172
C2×#309411