Finite Group Databasebeta

← C2×#13067144 #14721003

Subgroups — C2×#13067144 #14721003

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13067144C218yesmaximal, direct product factor
4C2×#10622089C214yesmaximal, complemented
5C2×C11×#381C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11—21no—
8C23×D44C411yescharacteristic, complemented
9C22×C11×C22⋊C4—21no—
10C2×#66983—21no—
11C2×#66983—22no—
12C2×#66983—21no—
13C2×#66983—22no—
14C2×#66983C412yescomplemented
15C2×#66983C414yescomplemented
16C2×#66983C2212yes—
17C2×#66983C2214yes—
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C411yescharacteristic, complemented
20C22×#4318—21no—
21C11×#381—22no—
22C11×#381C2214yescomplemented
23C2×C11×#95—21no—
24C2×C11×#95C2212yescomplemented
25#10622820—22no—
26#10622820C2214yescomplemented
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)C2212yescomplemented
29#10622089C22116yescomplemented
30C25×C11D411yescharacteristic
31C24×D11—21no—
32C23×C4×C11—22no—
33C23×C4×C11—44no—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C412yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D412yes—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D412yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C22×C22⋊D11—22no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11—22no—
47C22×C22⋊D11—24no—
48C22×C22⋊D11—48no—
49C23×Dic11—21no—
50C22×D44—22no—
51C22×D44—21no—
52C22×D44—44no—
53C22×D44C2×C412yes—
54C22×D44C2×C414yescomplemented
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—44no—
57#66983—24no—
58#66983—24no—
59#66983—24no—
60#66983—22no—
61#66983—24no—
62#66983—22no—
63#66983—24no—
64#66983C2×C414yes—
65#66983C2×C418yescomplemented
66#66983C2314yes—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2×C412yes—
74C2×C4⋊Dic11C2×C414yescomplemented
75C2×#4318—24no—
76C2×#4318—44no—
77C22×C11⋊C8—22no—
78C11×#95—24no—
79C11×#95—22no—
80C11×#95C2314yescomplemented
81C22⋊(C11⋊C8)—24no—
82C22⋊(C11⋊C8)—22no—
83C22⋊(C11⋊C8)C2314yescomplemented
84C2×#1510—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—42no—
88C24×C11C22⋊C411yescharacteristic
89C24×C11C22⋊C412yes—
90C24×C11C22⋊C411yescharacteristic
91C24×C11C2×D412yes—
92C24×C11C2×D411yescharacteristic
93C23×D11—22no—
94C23×D11—24no—
95C23×D11—44no—
96C23×D11—44no—
97C23×D11—44no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—44no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—44no—
105C22×C4×C11—42no—
106C22×C4×C11—44no—
107C22×C4×C11—42no—
108C22×C4×C11—44no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11C22⋊C412yes—
113C22×C4×C11C22⋊C411yescharacteristic
114C22×C4×C11C22⋊C412yes—
115C22×C4×C11C22⋊C411yescharacteristic
116C22×C4×C11C22⋊C412yes—
117C22×C4×C11C22⋊C412yes—
118C22×C4×C11C22⋊C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—28no—
132C2×C22⋊D11—24no—
133C2×C22⋊D11—416no—
134C2×C22⋊D11—416no—
135C2×C22⋊D11—48no—
136C2×C22⋊D11—48no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—44no—
140C2×D44—22no—
141C2×D44—24no—
142C2×D44—48no—
143C2×D44—44no—
144C2×D44—44no—
145C2×D44—48no—
146C2×D44C22×C414yes—
147C11×C22⋊C4—48no—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—24no—
153C4⋊Dic11C22×C414yes—
154#4318—48no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8—44no—
157C22×#121—111no—
158C2×#407—111no—
159C2×#381D1111yescharacteristic, complemented
160#1510—118no—
161C2×#327—114no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—416no—
176C23×C11#9914yes—
177C23×C11C2×C22⋊C412yes—
178C23×C11C2×C22⋊C412yes—
179C23×C11C2×C22⋊C411yescharacteristic
180C23×C11C2×C22⋊C411yescharacteristic
181C23×C11AGL(1,ℤ/8)14yes—
182C23×C11C22×D411yescharacteristic
183C22×D11—24no—
184C22×D11—48no—
185C22×D11—48no—
186C22×D11—48no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—816no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—88no—
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—416no—
220C22⋊D11—48no—
221C22⋊D11—48no—
222C2×Dic11—24no—
223C2×Dic11—48no—
224C2×Dic11—44no—
225D44—44no—
226D44—44no—
227D44—48no—
228C11⋊C8—44no—
229C23×D4—111no—
230C23×D4—221no—
231C24×C4C2×D1111yescharacteristic
232C22×M16—221no—
233C2×#121—112no—
234C2×#121—114no—
235C2×#121—112no—
236C2×#121—114no—
237C2×#121—221no—
238C2×#121—222no—
239C2×#121—221no—
240C2×#121—222no—
241C22×C4⋊C4—111no—
242C22×C22⋊C4—21no—
243C22×C22⋊C4—221no—
244#407—114no—
245#407—222no—
246C2×C22⋊C8—112no—
247C2×C22⋊C8—221no—
248#381—22no—
249#381C2×D1114yescomplemented
250C2×#95—21no—
251C2×#95C2×D1112yescomplemented
252#327—1116no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—22no—
256C22×C11—21no—
257C22×C11—22no—
258C22×C11—21no—
259C22×C11—28no—
260C22×C11—28no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—48no—
265C22×C11—48no—
266C22×C11—44no—
267C22×C11C2×#9914yes—
268C22×C11C2×#9912yes—
269C22×C11#41812yes—
270C22×C11#41812yes—
271C22×C11#42112yes—
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11C2×AGL(1,ℤ/8)12yes—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—816no—
278C2×D11—88no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—22no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—84no—
286Dic11—44no—
287C25—221no—
288C25C22⋊D1111yescharacteristic
289C22×D4—112no—
290C22×D4—114no—
291C22×D4—224no—
292C22×D4—222no—
293C22×D4—224no—
294C22×D4—222no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—444no—
298C22×D4—448no—
299C23×C4—22no—
300C23×C4—44no—
301C23×C4—221no—
302C23×C4C4×D1111yescharacteristic
303C23×C4C4×D1112yes—
304C23×C4C4×D1111yescharacteristic
305C23×C4D4411yescharacteristic
306C23×C4D4411yescharacteristic
307C23×C4D4412yes—
308C23×C4C22⋊D1111yescharacteristic
309C23×C4C22⋊D1112yes—
310C23×C4C22×D1111yescharacteristic
311C23×C4C22×D1112yes—
312C2×M16—224no—
313C2×M16—444no—
314C22×C8—222no—
315#121—114no—
316#121—118no—
317#121—114no—
318#121—224no—
319#121—224no—
320#121—224no—
321#121—222no—
322#121—224no—
323#121—222no—
324#121—224no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—224no—
334C2×C22⋊C4—222no—
335C22⋊C8—114no—
336C22⋊C8—222no—
337C22⋊C8—224no—
338#95—24no—
339#95—22no—
340#95C22×D1114yescomplemented
341C2×C11—22no—
342C2×C11—24no—
343C2×C11—22no—
344C2×C11—42no—
345C2×C11#151014yescomplemented
346C2×C11C22×#9911yescharacteristic
347C2×C11C2×#41811yescharacteristic
348C2×C11C2×#42111yescharacteristic
349D11—84no—
350C24—24no—
351C24—24no—
352C24—42no—
353C24—224no—
354C24—222no—
355C24—444no—
356C24—444no—
357C24—444no—
358C24(C2×D11)⋊C411yescharacteristic
359C24(C2×D11)⋊C412yes—
360C24(C2×D11)⋊C411yescharacteristic
361C24C2×C22⋊D1112yes—
362C24C2×C22⋊D1111yescharacteristic
363C2×D4—114no—
364C2×D4—228no—
365C2×D4—224no—
366C2×D4—224no—
367C2×D4—222no—
368C2×D4—224no—
369C2×D4—444no—
370C2×D4—448no—
371C2×D4—448no—
372C2×D4—444no—
373C2×D4—4416no—
374C2×D4—4416no—
375C2×D4—448no—
376C2×D4—448no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—42no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—44no—
386C22×C4—42no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—224no—
392C22×C4—222no—
393C22×C4—444no—
394C22×C4(C2×D11)⋊C412yes—
395C22×C4(C2×D11)⋊C412yes—
396C22×C4(C2×D11)⋊C411yescharacteristic
397C22×C4(C2×D11)⋊C411yescharacteristic
398C22×C4(C2×D11)⋊C412yes—
399C22×C4(C2×D11)⋊C412yes—
400C22×C4(C2×D11)⋊C412yes—
401C22×C4C2×C4×D1112yes—
402C22×C4C2×C4×D1111yescharacteristic
403C22×C4C2×C4×D1112yes—
404C22×C4C2×C4×D1111yescharacteristic
405C22×C4C2×D4412yes—
406C22×C4C2×D4411yescharacteristic
407C22×C4C2×D4412yes—
408C22×C4C2×D4411yescharacteristic
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C23×D1111yescharacteristic
412M16—448no—
413C2×C8—224no—
414C2×C8—444no—
415C4⋊C4—114no—
416C4⋊C4—222no—
417C4⋊C4—224no—
418C22⋊C4—48no—
419C22⋊C4—224no—
420C22⋊C4—228no—
421C22⋊C4—224no—
422C11C2×#151011yescharacteristic, complemented, Sylow
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23—24no—
429C23—22no—
430C23—24no—
431C23—24no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23—416no—
437C23—224no—
438C23—448no—
439C23—448no—
440C23—448no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—8816no—
445C23#6687014yes—
446C23C2×(C2×D11)⋊C412yes—
447C23C2×(C2×D11)⋊C412yes—
448C23C2×(C2×D11)⋊C411yescharacteristic
449C23C2×(C2×D11)⋊C411yescharacteristic
450C23#6700214yes—
451C23C22×C22⋊D1111yescharacteristic
452D4—444no—
453D4—444no—
454D4—448no—
455D4—4416no—
456D4—448no—
457D4—448no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—88no—
480C2×C4—224no—
481C2×C4—448no—
482C2×C4—444no—
483C2×C4C2×(C2×D11)⋊C411yescharacteristic
484C2×C4C2×(C2×D11)⋊C412yes—
485C2×C4C2×(C2×D11)⋊C411yescharacteristic
486C2×C4C2×(C2×D11)⋊C412yes—
487C2×C4C22×C4×D1111yescharacteristic
488C2×C4C22×D4411yescharacteristic
489C8—444no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—28no—
494C22—28no—
495C22—21no—
496C22—22no—
497C22—21no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—48no—
502C22—48no—
503C22—44no—
504C22—444no—
505C22—444no—
506C22—444no—
507C22—8816no—
508C22—888no—
509C22C2×#6687014yes—
510C22C2×#6687012yes—
511C22#1062261412yes—
512C22#1062261412yes—
513C22#1062261812yes—
514C22C22×(C2×D11)⋊C411yescharacteristic
515C22C2×#6700212yes—
516C4—21no—
517C4—21no—
518C4—22no—
519C4—21no—
520C4—22no—
521C4—21no—
522C4—84no—
523C4—444no—
524C2—22no—
525C2—24no—
526C2—22no—
527C2—42no—
528C2—884no—
529C2#1306714414yesdirect product factor
530C2C22×#6687011yescharacteristic
531C2C2×#1062261411yescharacteristic
532C2C2×#1062261811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#381C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#66983C2
cosocleC22×C4×C11C24
hypercenterC2×#381D11
hypocenterC11C2×#1510
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C2×#10622820C2semidirect
3. #13067144C2direct (N × H)
4. C2×#10622089C2semidirect
5. C2×C11×#381C2semidirect
8. C23×D44C4semidirect
14. C2×#66983C4semidirect
15. C2×#66983C4semidirect
19. C22×C4⋊Dic11C4semidirect
22. C11×#381C22semidirect
24. C2×C11×#95C22semidirect
26. #10622820C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622089C22semidirect
54. C22×D44C2×C4semidirect
65. #66983C2×C4semidirect
74. C2×C4⋊Dic11C2×C4semidirect
80. C11×#95C23semidirect
83. C22⋊(C11⋊C8)C23semidirect
159. C2×#381D11semidirect
249. #381C2×D11semidirect
251. C2×#95C2×D11semidirect
340. #95C22×D11semidirect
345. C2×C11#1510semidirect
422. C11C2×#1510semidirect
529. C2#13067144direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106228202
#130671442
C2×#106220892
C2×C11×#3812
C2×#151011