Finite Group Databasebeta

← C2×#13067021 #14720276

Subgroups — C2×#13067021 #14720276

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3C2×#10622298C211yesmaximal, characteristic, complemented
4#13067021C218yesmaximal, 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—
14#10623088—22no—
15#10623088—22no—
16#10623088C414yes—
17#10623088C2214yes—
18C2×#66950C411yescharacteristic
19C2×#66943C411yescharacteristic
20C2×#66936—21no—
21C2×#66932—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×(C2×D11)⋊C8—21no—
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×C8×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622446—22no—
33#10622446C2214yescomplemented
34#10622298—22no—
35#10622298C2214yescomplemented
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—
79#66950—22no—
80#66950C2×C414yes—
81#66943—22no—
82#66943C2×C414yes—
83#66936—24no—
84#66936—24no—
85#66932—24no—
86#66932—24no—
87C42×D11C2×C412yes—
88C42×D11D412yes—
89C42×D11D412yes—
90C42×D11C2312yes—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C4×Dic22C2×C412yes—
94C4×Dic22C2312yes—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2312yes—
97C4×C8×C11—21no—
98C4×C8×C11C2312yes—
99(C2×D11)⋊C8—24no—
100(C2×D11)⋊C8—24no—
101Dic11⋊C8—24no—
102C8×Dic11—24no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—21no—
106C4×C11⋊C8C2312yes—
107C2×#1482—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11C22⋊C411yescharacteristic
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11C22×C412yes—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—24no—
123C2×C22⋊D11—44no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11C22⋊C411yescharacteristic
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11C22⋊C411yescharacteristic
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—42no—
134C2×C4×D11C22⋊C412yes—
135C2×C4×D11C22⋊C412yes—
136C2×C4×D11C22⋊C412yes—
137C2×C4×D11C22×C412yes—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×D412yes—
140C2×Dic22—21no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22C22×C412yes—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—42no—
147C2×C8×C11—42no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C22×C412yes—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11C22×C411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2411yescharacteristic
156C22⋊Dic11—24no—
157C22⋊Dic11—24no—
158C22⋊Dic11—24no—
159(C2×D11)⋊C4—24no—
160C4⋊Dic11—24no—
161C4⋊Dic11—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11C22×C412yes—
164Dic11⋊C4—24no—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11C22⋊C412yes—
170C4×Dic11C22⋊C412yes—
171C4×Dic11C22⋊C412yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—42no—
178C2×C11⋊C8—42no—
179C2×#529—111no—
180C2×#431—111no—
181C2×#431—111no—
182#1482—118no—
183C2×Q8⋊C8—111no—
184C2×Q8⋊C8—111no—
185C2×D4⋊C8—111no—
186C2×D4⋊C8D1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11C2×C22⋊C411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11C2×C22⋊C412yes—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—42no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11#13112yes—
209C2×C4×C11#13112yes—
210C2×C4×C11#13512yes—
211C2×C4×C11#13512yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—48no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11C2×C22⋊C412yes—
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—24no—
231C4×D11—24no—
232C4×D11—42no—
233C4×D11—42no—
234Dic22—22no—
235Dic22—22no—
236Dic22—42no—
237C8×C11—42no—
238C8×C11—42no—
239C11⋊C8—42no—
240C11⋊C8—42no—
241#529—114no—
242#529—114no—
243#529—222no—
244#529—222no—
245C2×#126—221no—
246C2×#125—111no—
247C2×#124—111no—
248C2×#123—221no—
249C2×C22⋊Q8—111no—
250C2×#121—111no—
251C2×C4×Q8—111no—
252C2×C4×D4—221no—
253C2×C4×D4C2×D1111yescharacteristic
254C2×#117—221no—
255C22×C42—111no—
256#431—114no—
257#431—114no—
258#431—222no—
259#431—222no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8—221no—
262C2×C4⋊C8C2×D1111yescharacteristic
263C2×C22⋊C8—221no—
264C2×C22⋊C8—221no—
265C2×C4×C8—111no—
266C2×C4×C8—221no—
267C2×C4×C8C2×D1111yescharacteristic
268Q8⋊C8—114no—
269Q8⋊C8—114no—
270D4⋊C8—114no—
271D4⋊C8C2×D1114yescomplemented
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—84no—
276C22×C11#40812yes—
277C22×C11#41612yes—
278C22×C11#42112yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—44no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11#40812yes—
288C4×C11#41612yes—
289C4×C11C2×#13111yescharacteristic
290C4×C11C2×#13111yescharacteristic
291C4×C11C2×#13511yescharacteristic
292C4×C11C2×#13511yescharacteristic
293Dic11—22no—
294Dic11—22no—
295Dic11—22no—
296Dic11—42no—
297Dic11—42no—
298C22×Q8—111no—
299C22×D4—221no—
300C22×D4C4×D1111yescharacteristic
301C23×C4—21no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—221no—
308C22×C8—221no—
309#126—224no—
310#126—224no—
311#125—114no—
312#125—222no—
313#124—114no—
314#124—222no—
315#123—224no—
316#123—224no—
317C22⋊Q8—114no—
318C22⋊Q8—222no—
319#121—114no—
320#121—222no—
321C4×Q8—112no—
322C4×Q8—112no—
323C4×Q8—221no—
324C4×Q8—221no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—224no—
328C4×D4—224no—
329C4×D4C4×D1112yes—
330C4×D4C22×D1112yes—
331#117—224no—
332#117—224no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4C4×D1111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—112no—
348C2×C42—112no—
349C2×C42—112no—
350C2×C42—112no—
351C2×C42—221no—
352C2×C42C22×D1111yescharacteristic
353C4⋊C8—21no—
354C4⋊C8—112no—
355C4⋊C8—224no—
356C4⋊C8—221no—
357C4⋊C8C22×D1112yes—
358C22⋊C8—224no—
359C22⋊C8—224no—
360C4×C8—21no—
361C4×C8—112no—
362C4×C8—224no—
363C4×C8—221no—
364C4×C8C22×D1112yes—
365C2×C11—82no—
366C2×C11#148214yescomplemented
367C2×C11C2×#40811yescharacteristic
368C2×C11C2×#41611yescharacteristic
369C2×C11C2×#42111yescharacteristic
370D11—42no—
371C24—21no—
372C24—111no—
373C2×Q8—112no—
374C2×Q8—221no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—224no—
381C2×D4—444no—
382C2×D4C2×C4×D1112yes—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—111no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—442no—
404C22×C4C2×C4×D1111yescharacteristic
405C22×C4D4×D1111yescharacteristic
406C22×C4D4×D1111yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—42no—
410C2×C8—42no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—442no—
414C2×C8—442no—
415C4⋊C4—21no—
416C4⋊C4—112no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—221no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4C2×C4×D1112yes—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—224no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C42—112no—
431C42—112no—
432C42—112no—
433C42—112no—
434C42—112no—
435C42—112no—
436C42—222no—
437C42—222no—
438C42C2×C4×D1111yescharacteristic
439C42D4×D1111yescharacteristic
440C42D4×D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11C2×#148211yescharacteristic, complemented, Sylow
443C23—22no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—112no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23C22⋊C4×D1111yescharacteristic
452Q8—222no—
453Q8—222no—
454Q8—442no—
455D4—22no—
456D4—22no—
457D4—42no—
458D4—448no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4C22⋊C4×D1111yescharacteristic
484C2×C4C22⋊C4×D1111yescharacteristic
485C2×C4C22⋊C4×D1111yescharacteristic
486C2×C4#6695412yes—
487C2×C4#6696012yes—
488C2×C4#6696512yes—
489C2×C4#6696912yes—
490C2×C4C22×C4×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C8—42no—
494C8—42no—
495C8—442no—
496C8—442no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—84no—
501C22—222no—
502C22—222no—
503C22—222no—
504C22—444no—
505C22#1062234012yes—
506C22#1062238512yes—
507C22#1062243412yes—
508C22C2×C22⋊C4×D1111yescharacteristic
509C4—21no—
510C4—21no—
511C4—42no—
512C4—222no—
513C4—222no—
514C4—222no—
515C4—442no—
516C4—442no—
517C4#1062234012yes—
518C4#1062238512yes—
519C4C2×#6695411yescharacteristic
520C4C2×#6696011yescharacteristic
521C4C2×#6696511yescharacteristic
522C4C2×#6696911yescharacteristic
523C2—82no—
524C2—442no—
525C2#1306702114yesdirect product factor
526C2C2×#1062234011yescharacteristic
527C2C2×#1062238511yescharacteristic
528C2C2×#1062243411yescharacteristic
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×#1482
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×#10622446C2semidirect
3. C2×#10622298C2semidirect
4. #13067021C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. #10622446C22semidirect
35. #10622298C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
186. C2×D4⋊C8D11semidirect
271. D4⋊C8C2×D11semidirect
366. C2×C11#1482semidirect
442. C11C2×#1482semidirect
525. C2#13067021direct (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×#106224462
C2×#106222982
#130670212
C2×#106220942
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×D4⋊C82
C2×#148211