Finite Group Databasebeta

← C2×#13067026 #14720299

Subgroups — C2×#13067026 #14720299

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
3C2×C4×#4313C211yesmaximal, characteristic, complemented
4#13067026C218yesmaximal, direct product factor
5C2×#10622094C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66991C411yescharacteristic
11C2×#66989C411yescharacteristic
12C2×C4×C22⋊D11—21no—
13C2×#66979—21no—
14C22×#4313—21no—
15C22×C8×D11—21no—
16#10623088—22no—
17#10623088—22no—
18#10623088C414yes—
19#10623088C2214yes—
20C2×#66950C411yescharacteristic
21C2×#66943C411yescharacteristic
22C2×#66936—21no—
23C2×#66932—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66879—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32D11×C4⋊C8—22no—
33D11×C4⋊C8C2214yescomplemented
34C4×#4313—22no—
35C4×#4313C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38#10622122C2214yescomplemented
39#10622094C2214yescomplemented
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—21no—
43C22×C4×D11C2×C411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×Dic22C2×C411yescharacteristic
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11C2×C412yes—
52C4×D4×C11C2312yes—
53C2×C11×C4⋊C4C2×C411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59#66991—22no—
60#66991C2×C414yes—
61#66989—22no—
62#66989C2×C414yes—
63C4×C22⋊D11—24no—
64C4×C22⋊D11—24no—
65C2×(C2×D11)⋊C4—21no—
66#66979—24no—
67#66979—24no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79C2×#4313—28no—
80C2×#4313—24no—
81C2×C8×D11—24no—
82C2×C8×D11—44no—
83#66950—22no—
84#66950C2×C414yes—
85#66943—22no—
86#66943C2×C414yes—
87#66936—24no—
88#66936—24no—
89#66932—24no—
90#66932—24no—
91C42×D11C2×C412yes—
92C42×D11D412yes—
93C42×D11D412yes—
94C42×D11C2312yes—
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2×C412yes—
98C4×Dic22C2312yes—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2312yes—
101C4×C8×C11—21no—
102C4×C8×C11C2312yes—
103#66879—24no—
104Dic11⋊C8—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109C2×#1483—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C22⋊C411yescharacteristic
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—24no—
125C2×C22⋊D11—44no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11C22⋊C411yescharacteristic
129C22×Dic11C22⋊C411yescharacteristic
130C22×Dic11C22⋊C411yescharacteristic
131C2×C4×D11—24no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11C22⋊C412yes—
137C2×C4×D11C22⋊C412yes—
138C2×C4×D11C22⋊C412yes—
139C2×C4×D11C22×C412yes—
140C2×C4×D11C2×D412yes—
141C2×C4×D11C2×D412yes—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22C22×C412yes—
146C2×C8×C11—24no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C22×C412yes—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11C22×C411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2411yescharacteristic
158C22⋊Dic11—24no—
159C22⋊Dic11—24no—
160C22⋊Dic11—24no—
161(C2×D11)⋊C4—24no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11C22×C412yes—
166Dic11⋊C4—24no—
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11C22⋊C412yes—
172C4×Dic11C22⋊C412yes—
173C4×Dic11C22⋊C412yes—
174C4×Dic11C22×C412yes—
175C4×Dic11C2×D412yes—
176C4×Dic11C2×D412yes—
177C2×C11⋊C8—24no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—42no—
181#4313—216no—
182C8×D11—48no—
183C2×#529—111no—
184C22×C4⋊C8—111no—
185C2×C4×M16—111no—
186#1483—118no—
187C2×Q8⋊C8—111no—
188C2×Q8⋊C8—111no—
189C2×D4⋊C8—111no—
190C2×D4⋊C8D1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C2×C22⋊C411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11#10414yes—
199C22×D11C2×C22⋊C412yes—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—42no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—44no—
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11#13112yes—
213C2×C4×C11#13112yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—48no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230C4×D11—24no—
231C4×D11—24no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—22no—
236C4×D11—24no—
237C4×D11—24no—
238Dic22—22no—
239Dic22—22no—
240Dic22—42no—
241C8×C11—24no—
242C8×C11—42no—
243C11⋊C8—24no—
244C11⋊C8—42no—
245C22×M16—221no—
246C23×C8—221no—
247#529—114no—
248#529—114no—
249#529—222no—
250#529—222no—
251C2×#126—221no—
252C2×#125—111no—
253C2×#124—111no—
254C2×#123—221no—
255C2×C22⋊Q8—111no—
256C2×#121—111no—
257C2×C4×Q8—111no—
258C2×C4×D4—221no—
259C2×C4×D4C2×D1111yescharacteristic
260C2×#117—221no—
261C22×C42—111no—
262C2×C4⋊C8—111no—
263C2×C4⋊C8—114no—
264C2×C4⋊C8—222no—
265C2×C4⋊C8—221no—
266C2×C4⋊C8C2×D1111yescharacteristic
267C4×M16—114no—
268C4×M16—222no—
269C2×#97—221no—
270C2×C4×C8—111no—
271C2×C4×C8C2×D1111yescharacteristic
272Q8⋊C8—114no—
273Q8⋊C8—114no—
274D4⋊C8—114no—
275D4⋊C8C2×D1114yescomplemented
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—84no—
280C22×C11#40812yes—
281C22×C11#41712yes—
282C22×C11C2×#10412yes—
283C22×C11C22×C22⋊C411yescharacteristic
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—28no—
287C2×D11C2×#10414yes—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—42no—
291C4×C11#40812yes—
292C4×C11#41712yes—
293C4×C11C2×#13111yescharacteristic
294C4×C11C2×#13111yescharacteristic
295C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C11C2×#13711yescharacteristic
297Dic11—22no—
298Dic11—22no—
299Dic11—22no—
300Dic11—42no—
301Dic11—42no—
302C22×Q8—111no—
303C22×D4—221no—
304C22×D4C4×D1111yescharacteristic
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—111no—
309C2×M16—224no—
310C2×M16—228no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—224no—
314C22×C8—221no—
315C22×C8—221no—
316C22×C8—444no—
317#126—224no—
318#126—224no—
319#125—114no—
320#125—222no—
321#124—114no—
322#124—222no—
323#123—224no—
324#123—224no—
325C22⋊Q8—114no—
326C22⋊Q8—222no—
327#121—114no—
328#121—222no—
329C4×Q8—112no—
330C4×Q8—112no—
331C4×Q8—221no—
332C4×Q8—221no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—224no—
336C4×D4—224no—
337C4×D4C4×D1112yes—
338C4×D4C22×D1112yes—
339#117—224no—
340#117—224no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4C4×D1111yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—112no—
356C2×C42—112no—
357C2×C42—112no—
358C2×C42—112no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—21no—
362C4⋊C8—112no—
363C4⋊C8—224no—
364C4⋊C8—221no—
365C4⋊C8C22×D1112yes—
366#97—224no—
367C4×C8—21no—
368C4×C8—112no—
369C4×C8—221no—
370C4×C8C22×D1112yes—
371C2×C11—82no—
372C2×C11#148314yescomplemented
373C2×C11C2×#40811yescharacteristic
374C2×C11C2×#41711yescharacteristic
375C2×C11C22×#10411yescharacteristic
376D11—24no—
377C24—21no—
378C24—111no—
379C2×Q8—112no—
380C2×Q8—221no—
381C2×Q8—222no—
382C2×Q8—222no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—224no—
387C2×D4—444no—
388C2×D4C2×C4×D1112yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—224no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413M16—2216no—
414C2×C8—24no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—42no—
418C2×C8—224no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—448no—
422C2×C8—442no—
423C4⋊C4—21no—
424C4⋊C4—112no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—221no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4C2×C4×D1112yes—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C22⋊C4—224no—
437C22⋊C4—224no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—112no—
442C42—112no—
443C42—112no—
444C42—222no—
445C42—222no—
446C42C2×C4×D1111yescharacteristic
447C42D4×D1111yescharacteristic
448C42D4×D1111yescharacteristic
449C42C23×D1111yescharacteristic
450C11C2×#148311yescharacteristic, complemented, Sylow
451C23—22no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—112no—
456C23—114no—
457C23—222no—
458C23—222no—
459C23C22⋊C4×D1111yescharacteristic
460Q8—222no—
461Q8—222no—
462Q8—442no—
463D4—22no—
464D4—22no—
465D4—42no—
466D4—448no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4C22⋊C4×D1111yescharacteristic
492C2×C4C22⋊C4×D1111yescharacteristic
493C2×C4C22⋊C4×D1111yescharacteristic
494C2×C4#6695412yes—
495C2×C4#6696012yes—
496C2×C4#6696412yes—
497C2×C4#6696812yes—
498C2×C4C22×C4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4C2×D4×D1111yescharacteristic
501C8—24no—
502C8—42no—
503C8—224no—
504C8—442no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—84no—
509C22—114no—
510C22—228no—
511C22—222no—
512C22—222no—
513C22#1062234012yes—
514C22#1062238412yes—
515C22D11×#10412yes—
516C22C2×C22⋊C4×D1111yescharacteristic
517C4—21no—
518C4—21no—
519C4—42no—
520C4—222no—
521C4—222no—
522C4—222no—
523C4—442no—
524C4—442no—
525C4#1062234012yes—
526C4#1062238412yes—
527C4C2×#6695411yescharacteristic
528C4C2×#6696011yescharacteristic
529C4C2×#6696411yescharacteristic
530C4C2×#6696811yescharacteristic
531C2—82no—
532C2—224no—
533C2#1306702614yesdirect product factor
534C2C2×#1062234011yescharacteristic
535C2C2×#1062238411yescharacteristic
536C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66991C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1483
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊C8C2semidirect
3. C2×C4×#4313C2semidirect
4. #13067026C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. D11×C4⋊C8C22semidirect
35. C4×#4313C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
190. C2×D4⋊C8D11semidirect
275. D4⋊C8C2×D11semidirect
372. C2×C11#1483semidirect
450. C11C2×#1483semidirect
533. C2#13067026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×D11×C4⋊C82
C2×C4×#43132
#130670262
C2×#106220942
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×D4⋊C82
C2×#148311