Finite Group Databasebeta

← C2×#13078552 #15621566

Subgroups — C2×#13078552 #15621566

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×#66979C211yesmaximal, characteristic, complemented
2#13078552C2116yesmaximal, direct product factor
3C2×#10622647C212yesmaximal, complemented
4C2×#10622648C214yesmaximal, complemented
5C2×#10622646C212yesmaximal, complemented
6C2×#10622577C212yesmaximal, complemented
7C2×#10622828C212yesmaximal, complemented
8C2×#10622820C211yesmaximal, characteristic, complemented
9C22×C11×#121C211yesmaximal, characteristic
10C23×D4×C11—21no—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C2×C11×#121—21no—
14C2×C11×#121—21no—
15C2×C11×#121—24no—
16C2×C11×#121C2218yes—
17C2×C11×#121C2212yes—
18C2×C11×#121C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C22×C22⋊Dic11—21no—
22C2×#66979—21no—
23C2×#66979—24no—
24C2×#66979—21no—
25C2×#66979C2212yes—
26C2×#66979C2212yescomplemented
27C2×#66979C2218yescomplemented
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×C4×Dic11—21no—
31C22×#4318C2212yes—
32#10622828C22116yescomplemented
33C2×#66896C2214yescomplemented
34C2×#66896C2214yescomplemented
35#10622820C2218yescomplemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37C2×C22⋊(C11⋊C8)C2212yescomplemented
38#10622648C22132yescomplemented
39#10622647C22116yescomplemented
40#10622646C22116yescomplemented
41#10622577C22116yescomplemented
42C2×#66872C2214yescomplemented
43C2×#66871C2214yescomplemented
44C25×C11—21no—
45C25×C11D411yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—28no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—28no—
52C22×D4×C11—48no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—28no—
56C23×C4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D414yes—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C11×#121—28no—
68C11×#121—24no—
69C11×#121—28no—
70C11×#121—24no—
71C11×#121C2318yes—
72C11×#121C2318yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—28no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—22no—
83#66979—24no—
84#66979—28no—
85#66979—24no—
86#66979—28no—
87#66979C2318yes—
88#66979C2318yescomplemented
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2314yescomplemented
96C2×C4⋊Dic11C2314yescomplemented
97C2×C4×Dic11—22no—
98C2×C4×Dic11—28no—
99C2×C4×Dic11—22no—
100C2×#4318—28no—
101C2×#4318C2318yes—
102C22×C11⋊C8C2314yes—
103#66896C23116yescomplemented
104#66896C23116yescomplemented
105C22⋊(C11⋊C8)C2318yescomplemented
106C22⋊(C11⋊C8)C2318yescomplemented
107#66872C23116yescomplemented
108#66871C23116yescomplemented
109C2×#3094—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—42no—
115C24×C11—44no—
116C24×C11—44no—
117C24×C11—44no—
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D414yes—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—28no—
127C2×D4×C11—216no—
128C2×D4×C11—432no—
129C2×D4×C11—48no—
130C2×D4×C11—48no—
131C2×D4×C11—48no—
132C2×D4×C11—44no—
133C2×D4×C11C2414yes—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—216no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—216no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4118yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2412yes—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—44no—
163C22×Dic11—44no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C2414yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C22⋊Dic11—28no—
170C22⋊Dic11—28no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—24no—
174C4⋊Dic11—24no—
175C4⋊Dic11C2414yes—
176C4⋊Dic11C2414yes—
177C4×Dic11—28no—
178C4×Dic11—28no—
179#4318—216no—
180C2×C11⋊C8—28no—
181C2×C11⋊C8C2418yes—
182C22×#121D1111yescharacteristic
183C22×#117—111no—
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—24no—
201C23×C11—44no—
202C23×C11—416no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—44no—
209C23×C11—816no—
210C23×C11#12314yes—
211C23×C11AGL(1,ℤ/8)14yes—
212C23×C11C22×D412yes—
213C23×C11C22×D412yes—
214C23×C11C22×D412yes—
215C23×C11C22×D411yescharacteristic
216D4×C11—28no—
217D4×C11—416no—
218D4×C11—416no—
219D4×C11—48no—
220D4×C11—44no—
221C2×C4×C11—28no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—28no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—28no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11#12318yes—
234C2×C4×C11#12314yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4114yes—
240C2×C4×C11C2×#4118yes—
241C2×C4×C11C2511yescharacteristic
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—48no—
245C2×Dic11—48no—
246C2×Dic11—44no—
247C2×Dic11—44no—
248C11⋊C8—28no—
249C23×D4—21no—
250C23×D4C2×D1111yescharacteristic
251C24×C4C2×D1111yescharacteristic
252C22×M16—112no—
253C2×#121—24no—
254C2×#121—21no—
255C2×#121—21no—
256C2×#121C2×D1112yes—
257C2×#121C2×D1112yes—
258C2×#121C2×D1118yes—
259C2×#117—112no—
260C2×#117—118no—
261C2×#117—112no—
262C2×#117—221no—
263C2×#117—224no—
264C2×#117—221no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4—21no—
269C22×C22⋊C4—221no—
270C22×C42—221no—
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×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—816no—
298C22×C11—88no—
299C22×C11C2×#12314yes—
300C22×C11C2×#12312yes—
301C22×C11C2×AGL(1,ℤ/8)14yes—
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57512yes—
304C22×C11C23×D411yescharacteristic
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—44no—
308C4×C11C2×#12314yes—
309C4×C11C2×#12312yes—
310C4×C11C22×#4112yes—
311Dic11—44no—
312Dic11—44no—
313C25—21no—
314C25C22⋊D1111yescharacteristic
315C22×D4—28no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—28no—
319C22×D4—22no—
320C22×D4—21no—
321C22×D4—48no—
322C22×D4C22×D1112yes—
323C22×D4C22×D1114yes—
324C23×C4—28no—
325C23×C4—21no—
326C23×C4—221no—
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—28no—
340#121—24no—
341#121—24no—
342#121—28no—
343#121C22×D1118yes—
344#121C22×D1118yes—
345#117—118no—
346#117—118no—
347#117—228no—
348#117—224no—
349#117—228no—
350#117—224no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22×D1112yes—
362C2×C4⋊C4C22×D1114yes—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—228no—
370C2×C42—222no—
371C2×C42—222no—
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—84no—
382C2×C11#309414yescomplemented
383C2×C11C22×#12311yescharacteristic
384C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
385C2×C11C2×#57511yescharacteristic
386C24—24no—
387C24—24no—
388C24—24no—
389C24—22no—
390C24—42no—
391C24—44no—
392C24—44no—
393C24—44no—
394C24C2×C22⋊D1111yescharacteristic
395C24C2×C22⋊D1114yes—
396C24C2×C22⋊D1111yescharacteristic
397C24C2×C22⋊D1111yescharacteristic
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—216no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—432no—
405C2×D4—48no—
406C2×D4—48no—
407C2×D4—48no—
408C2×D4—44no—
409C2×D4C23×D1114yes—
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—22no—
419C22×C4—44no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4#434118yes—
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—24no—
444C4⋊C4—22no—
445C4⋊C4—114no—
446C4⋊C4—114no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4C23×D1114yes—
452C22⋊C4—28no—
453C22⋊C4—28no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C42—228no—
457C42—228no—
458C11C2×#309411yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—28no—
464C23—22no—
465C23—28no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—44no—
470C23—416no—
471C23—48no—
472C23—48no—
473C23—44no—
474C23—48no—
475C23—44no—
476C23—44no—
477C23—816no—
478C23#6698514yes—
479C23#6698814yes—
480C23C22×C22⋊D1112yes—
481C23C22×C22⋊D1112yes—
482C23C22×C22⋊D1112yes—
483C23C22×C22⋊D1111yescharacteristic
484D4—28no—
485D4—416no—
486D4—416no—
487D4—44no—
488D4—48no—
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—48no—
500C2×C4—44no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—448no—
504C2×C4—448no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4#6698818yes—
508C2×C4#6698814yes—
509C2×C4C2×#434114yes—
510C2×C4C2×#434118yes—
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—44no—
529C22—44no—
530C22—44no—
531C22—816no—
532C22—88no—
533C22C2×#6698514yes—
534C22C2×#6698512yes—
535C22C2×#6698814yes—
536C22C2×#6698812yes—
537C22#1062335312yes—
538C22C23×C22⋊D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—44no—
542C4—444no—
543C4—444no—
544C4C2×#6698812yes—
545C4C2×#6698814yes—
546C4C22×#434112yes—
547C2—24no—
548C2—24no—
549C2—42no—
550C2—84no—
551C2#1307855214yesdirect product factor
552C2C22×#6698811yescharacteristic
553C2C22×#6698511yescharacteristic
554C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C22×D4
hypercenterC22×#121D11
hypocenterC11C2×#3094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. #13078552C2direct (N × H)
3. C2×#10622647C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622577C2semidirect
7. C2×#10622828C2semidirect
8. C2×#10622820C2semidirect
26. C2×#66979C22semidirect
27. C2×#66979C22semidirect
28. C22×C4⋊Dic11C22semidirect
29. C22×C4⋊Dic11C22semidirect
32. #10622828C22semidirect
33. C2×#66896C22semidirect
34. C2×#66896C22semidirect
35. #10622820C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. C2×C22⋊(C11⋊C8)C22semidirect
38. #10622648C22semidirect
39. #10622647C22semidirect
40. #10622646C22semidirect
41. #10622577C22semidirect
42. C2×#66872C22semidirect
43. C2×#66871C22semidirect
88. #66979C23semidirect
95. C2×C4⋊Dic11C23semidirect
96. C2×C4⋊Dic11C23semidirect
103. #66896C23semidirect
104. #66896C23semidirect
105. C22⋊(C11⋊C8)C23semidirect
106. C22⋊(C11⋊C8)C23semidirect
107. #66872C23semidirect
108. #66871C23semidirect
382. C2×C11#3094semidirect
458. C11C2×#3094semidirect
551. C2#13078552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
#130785522
C2×#106226472
C2×#106226482
C2×#106226462
C2×#106225772
C2×#106228282
C2×#106228202
C22×C11×#1212
C2×#309411