Finite Group Databasebeta

← C2×#13067138 #14720897

Subgroups — C2×#13067138 #14720897

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3C2×#10622262C211yesmaximal, characteristic, complemented
4#13067138C218yesmaximal, direct product factor
5C2×#10622105C211yesmaximal, characteristic, complemented
6C2×#10622090C211yesmaximal, characteristic, complemented
7C2×#10622175C211yesmaximal, characteristic
8C2×C11×#327C211yesmaximal, characteristic
9C2×C11×#121C2211yescharacteristic
10C2×#66989C411yescharacteristic, complemented
11C2×#66988—21no—
12C2×D4×Dic11—21no—
13C2×D4×Dic11C411yescharacteristic, complemented
14C2×#66977C2211yescharacteristic
15C22×Dic11⋊C4—21no—
16C22×C4×Dic11—21no—
17C22×C4×Dic11C2211yescharacteristic
18#10623131—22no—
19#10623131—22no—
20#10623131C414yescomplemented
21#10623131C2214yes—
22C2×#66943C411yescharacteristic, complemented
23C2×#66940C411yescharacteristic, complemented
24C2×#66932—21no—
25C2×#66930—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66879—21no—
31C2×Dic11⋊C8—21no—
32#10622332—22no—
33#10622332C2214yescomplemented
34#10622262—22no—
35#10622262C2214yescomplemented
36C11×#327C2214yes—
37#10622175C2214yes—
38#10622105C2214yescomplemented
39#10622090C2214yescomplemented
40C22×D4×C11—21no—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
48C22×Dic22C2×C411yescharacteristic
49C22×C8×C11—21no—
50C11×#121—21no—
51C11×#121—21no—
52C11×#121C2×C412yes—
53C11×#121C2312yes—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60#66989—22no—
61#66989C2×C414yescomplemented
62#66988—24no—
63#66988—24no—
64D4×Dic11—24no—
65D4×Dic11—24no—
66D4×Dic11—22no—
67D4×Dic11C2×C414yescomplemented
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70#66977—21no—
71#66977—21no—
72#66977C2×C412yes—
73#66977C2312yes—
74C2×Dic11⋊C4—28no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—24no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—44no—
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11D412yes—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8—21no—
91#66943—22no—
92#66943C2×C414yescomplemented
93#66940—22no—
94#66940C2×C414yescomplemented
95#66932—24no—
96#66932—24no—
97#66930—24no—
98#66930—24no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8C2312yes—
101C11×#95—21no—
102C11×#95C2312yes—
103C11⋊#95—21no—
104C11⋊#95C2312yes—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)C2312yes—
107#66879—24no—
108Dic11⋊C8—24no—
109C2×#1509—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11C2×D411yescharacteristic
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—44no—
141C22×Dic11—42no—
142C22×Dic11C22⋊C411yescharacteristic
143C22×Dic11C22⋊C411yescharacteristic
144C22×Dic11C22⋊C411yescharacteristic
145C22×Dic11C22⋊C412yes—
146C22×Dic11C22⋊C412yes—
147C22×Dic11C22⋊C411yescharacteristic
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150C2×Dic22—21no—
151C2×Dic22—42no—
152C2×Dic22C22×C412yes—
153C2×C8×C11—22no—
154C2×C8×C11—42no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C22⋊Dic11—24no—
160C22⋊Dic11—24no—
161C22⋊Dic11—24no—
162C22⋊Dic11—22no—
163C22⋊Dic11—22no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—216no—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172C4×Dic11—24no—
173C4×Dic11—48no—
174C4×Dic11C22⋊C412yes—
175C4×Dic11C22⋊C412yes—
176C4×Dic11C22⋊C412yes—
177C4×Dic11C22⋊C412yes—
178C4×Dic11C22×C412yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C2×D412yes—
181C4×Dic11C2×D412yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—42no—
184C2×#529—111no—
185C2×#432—111no—
186C2×C4×C4⋊C4—111no—
187#1509—118no—
188C2×#328—111no—
189C2×#328—111no—
190C2×#327—111no—
191C2×#327D1111yescharacteristic
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11C2×C22⋊C411yescharacteristic
200C23×C11AGL(1,ℤ/8)12yes—
201C23×C11#13712yes—
202C23×C11C22×D411yescharacteristic
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—44no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—48no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11—48no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—48no—
241C2×Dic11#10414yes—
242C2×Dic11C2×C22⋊C412yes—
243C2×Dic11C2×C22⋊C412yes—
244C2×Dic11C2×C22⋊C412yes—
245C2×Dic11C2×C22⋊C412yes—
246Dic22—42no—
247Dic22—42no—
248C8×C11—42no—
249C11⋊C8—42no—
250#529—114no—
251#529—114no—
252#529—222no—
253#529—222no—
254C2×#126—221no—
255C2×#125—111no—
256C2×#124—111no—
257C2×#123—221no—
258C2×C22⋊Q8—111no—
259C2×#121C2×D1111yescharacteristic
260C2×C4×Q8—111no—
261C2×C4×D4—111no—
262C2×C4×D4—221no—
263C2×#117—221no—
264C22×C4⋊C4—221no—
265C22×C42—111no—
266C22×C42—221no—
267#432—114no—
268#432—222no—
269C2×C4⋊C8—221no—
270C2×C22⋊C8—111no—
271C2×C22⋊C8C2×D1111yescharacteristic
272C2×#97—221no—
273C4×C4⋊C4—114no—
274C4×C4⋊C4—222no—
275C2×#95—111no—
276C2×#95C2×D1111yescharacteristic
277#328—114no—
278#328—114no—
279#327—114no—
280#327C2×D1114yes—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—24no—
286C22×C11—24no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—84no—
291C22×C11#41012yes—
292C22×C11#41712yes—
293C22×C11#41712yes—
294C22×C11C2×#10412yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—44no—
303C4×C11—42no—
304Dic11—22no—
305Dic11—22no—
306Dic11—22no—
307Dic11—44no—
308Dic11—42no—
309Dic11—42no—
310Dic11C2×#10414yes—
311C22×Q8—111no—
312C22×D4—21no—
313C22×D4C4×D1111yescharacteristic
314C23×C4—21no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—221no—
318C23×C4—221no—
319C23×C4C22×D1111yescharacteristic
320C22×C8—21no—
321C22×C8—221no—
322#126—224no—
323#126—224no—
324#125—114no—
325#125—222no—
326#124—114no—
327#124—222no—
328#123—224no—
329#123—224no—
330C22⋊Q8—112no—
331C22⋊Q8—112no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334#121—21no—
335#121—21no—
336#121C4×D1112yes—
337#121C22×D1112yes—
338C4×Q8—114no—
339C4×Q8—222no—
340C4×D4—114no—
341C4×D4—222no—
342C4×D4—224no—
343C4×D4—224no—
344#117—224no—
345#117—224no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—228no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C4×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—112no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—112no—
365C2×C42—112no—
366C2×C42—112no—
367C2×C42—221no—
368C2×C42—224no—
369C2×C42—444no—
370C4⋊C8—224no—
371C22⋊C8—21no—
372C22⋊C8—112no—
373C22⋊C8—221no—
374C22⋊C8C22×D1112yes—
375#97—224no—
376#95—21no—
377#95—112no—
378#95—221no—
379#95C22×D1112yes—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—22no—
383C2×C11—82no—
384C2×C11#150914yescomplemented
385C2×C11C2×#41011yescharacteristic
386C2×C11C2×#41711yescharacteristic
387C2×C11C22×#10411yescharacteristic
388C24—21no—
389C24D4×D1111yescharacteristic
390C2×Q8—112no—
391C2×Q8—221no—
392C2×Q8—442no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4C2×C4×D1112yes—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—111no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—444no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4C2×C4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431C2×C8—22no—
432C2×C8—42no—
433C2×C8—222no—
434C2×C8—442no—
435C4⋊C4—21no—
436C4⋊C4—112no—
437C4⋊C4—224no—
438C4⋊C4—224no—
439C4⋊C4—224no—
440C4⋊C4—2216no—
441C4⋊C4—221no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4C2×C4×D1112yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C22⋊C4—222no—
451C22⋊C4—222no—
452C42—112no—
453C42—112no—
454C42—112no—
455C42—112no—
456C42—112no—
457C42—112no—
458C42—112no—
459C42—112no—
460C42—224no—
461C42—448no—
462C11C2×#150911yescharacteristic, complemented, Sylow
463C23—22no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23C22⋊C4×D1111yescharacteristic
470C23C22⋊C4×D1111yescharacteristic
471C23#6696412yes—
472C23#6696812yes—
473C23C2×D4×D1111yescharacteristic
474Q8—442no—
475Q8—442no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—44no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—112no—
494C2×C4—114no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—448no—
510C2×C4—442no—
511C2×C4—448no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4C22⋊C4×D1111yescharacteristic
516C2×C4C22⋊C4×D1111yescharacteristic
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C8—42no—
520C8—442no—
521C22—21no—
522C22—21no—
523C22—24no—
524C22—24no—
525C22—21no—
526C22—21no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22#1062235312yes—
532C22#1062238412yes—
533C22#1062238412yes—
534C22D11×#10412yes—
535C22C2×C22⋊C4×D1111yescharacteristic
536C22C2×#6696411yescharacteristic
537C22C2×#6696811yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—114no—
545C4—222no—
546C4—222no—
547C4—222no—
548C4—444no—
549C4—442no—
550C4—442no—
551C2—21no—
552C2—21no—
553C2—22no—
554C2—82no—
555C2#1306713814yesdirect product factor
556C2C2×#1062235311yescharacteristic
557C2C2×#1062238411yescharacteristic
558C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#327D11
hypocenterC11C2×#1509
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. C2×#10622262C2semidirect
4. #13067138C2direct (N × H)
5. C2×#10622105C2semidirect
6. C2×#10622090C2semidirect
10. C2×#66989C4semidirect
13. C2×D4×Dic11C4semidirect
20. #10623131C4semidirect
22. C2×#66943C4semidirect
23. C2×#66940C4semidirect
33. #10622332C22semidirect
35. #10622262C22semidirect
38. #10622105C22semidirect
39. #10622090C22semidirect
61. #66989C2×C4semidirect
67. D4×Dic11C2×C4semidirect
92. #66943C2×C4semidirect
94. #66940C2×C4semidirect
384. C2×C11#1509semidirect
462. C11C2×#1509semidirect
555. C2#13067138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231312
C2×#106223322
C2×#106222622
#130671382
C2×#106221052
C2×#106220902
C2×#106221752
C2×C11×#3272
C2×#150911