Finite Group Databasebeta

← C2×#13067080 #14720402

Subgroups — C2×#13067080 #14720402

Order 2816.

1066 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
1C2×#10623111C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3C2×#10622450C211yesmaximal, characteristic, complemented
4#13067080C218yesmaximal, direct product factor
5C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67000C411yescharacteristic
11C2×#66999C411yescharacteristic
12C22×#4313—21no—
13#10623111—22no—
14#10623111—22no—
15#10623111C414yes—
16#10623111C2214yes—
17C2×#66951—21no—
18C2×#66948C411yescharacteristic
19C2×#66947—21no—
20C2×#66943C411yescharacteristic
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66925—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622450—22no—
33#10622450C2214yescomplemented
34#10622298—22no—
35#10622298C2214yescomplemented
36C11×Q8⋊C8C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38#10622121C2214yescomplemented
39#10622097C2214yescomplemented
40C22×Q8×C11C2×C411yescharacteristic
41C22×D44—21no—
42C22×D44C2×C411yescharacteristic
43C22×C4×D11—21no—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11C2×C412yes—
52C4×Q8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2×C411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#67000—22no—
58#67000C2×C414yes—
59#66999—22no—
60#66999C2×C414yes—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2×C411yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C2×#4313—24no—
76C2×#4313—44no—
77#66951—24no—
78#66951—24no—
79#66948—22no—
80#66948C2×C414yes—
81#66947—24no—
82#66947—24no—
83#66943—22no—
84#66943C2×C414yes—
85C4×D44—24no—
86C4×D44—24no—
87C4×D44—21no—
88C4×D44—21no—
89C4×D44C2×C412yes—
90C4×D44C2312yes—
91#66925—24no—
92#66925—24no—
93C42×D11C2×C412yes—
94C42×D11D412yes—
95C42×D11D412yes—
96C42×D11C2312yes—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2312yes—
99C4×C8×C11—21no—
100C4×C8×C11C2312yes—
101(C2×D11)⋊C8—24no—
102Dic11⋊C8—24no—
103Dic11⋊C8—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8—21no—
107C4×C11⋊C8C2312yes—
108C2×#1495—111nomaximal, Sylow
109C23×D11—21no—
110C23×D11C22⋊C411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C2×D44—24no—
125C2×D44—21no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—44no—
129C2×D44C22×C412yes—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C4×D11C22⋊C412yes—
140C2×C4×D11C22⋊C412yes—
141C2×C4×D11C22⋊C412yes—
142C2×C4×D11C22×C412yes—
143C2×C4×D11C2×D412yes—
144C2×C4×D11C2×D412yes—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—42no—
148C2×C8×C11—42no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C22×C412yes—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11C22×C411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2411yescharacteristic
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165C4⋊Dic11—24no—
166C4⋊Dic11—21no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170C4×Dic11C22⋊C412yes—
171C4×Dic11C22⋊C412yes—
172C4×Dic11C22⋊C412yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C4×Dic11C2×D412yes—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—42no—
179C2×C11⋊C8—42no—
180#4313—48no—
181C2×#529—111no—
182C2×#431—111no—
183C2×#423—111no—
184#1495—118no—
185C2×Q8⋊C8—111no—
186C2×Q8⋊C8D1111yescharacteristic, complemented
187C2×D4⋊C8—111no—
188C2×D4⋊C8—111no—
189C23×C11C2×C22⋊C411yescharacteristic
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11C2×C22⋊C412yes—
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—42no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11#13112yes—
210C2×C4×C11#13112yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—42no—
221C2×Dic11C2×C22⋊C412yes—
222C2×Dic11C2×C22⋊C412yes—
223C2×Dic11C2×C22⋊C412yes—
224D44—22no—
225D44—22no—
226D44—48no—
227D44—42no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—24no—
233C4×D11—24no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—42no—
238C4×D11—44no—
239C8×C11—42no—
240C8×C11—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C22×M16—221no—
244#529—114no—
245#529—114no—
246#529—222no—
247#529—222no—
248C2×#126—221no—
249C2×#125—111no—
250C2×#124—111no—
251C2×#123—221no—
252C2×C22⋊Q8—111no—
253C2×#121—111no—
254C2×C4×Q8C2×D1111yescharacteristic
255C2×C4×D4—111no—
256C2×C4×D4—221no—
257C2×#117—221no—
258C22×C42—111no—
259#431—114no—
260#431—222no—
261#423—114no—
262#423—222no—
263C2×C4⋊C8—111no—
264C2×C4⋊C8—221no—
265C2×C4⋊C8—221no—
266C2×C4⋊C8C2×D1111yescharacteristic
267C2×C22⋊C8—221no—
268C2×C4×C8—111no—
269C2×C4×C8C2×D1111yescharacteristic
270Q8⋊C8—114no—
271Q8⋊C8C2×D1114yescomplemented
272D4⋊C8—114no—
273D4⋊C8—114no—
274C22×C11#40812yes—
275C22×C11#41712yes—
276C22×C11#42112yes—
277C22×C11C22×C22⋊C411yescharacteristic
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—44no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—84no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—42no—
289C4×C11—42no—
290C4×C11#40812yes—
291C4×C11#41712yes—
292C4×C11C2×#13111yescharacteristic
293C4×C11C2×#13111yescharacteristic
294C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C11C2×#13711yescharacteristic
296Dic11—22no—
297Dic11—22no—
298Dic11—22no—
299Dic11—42no—
300C22×Q8C4×D1111yescharacteristic
301C22×D4—111no—
302C22×D4—221no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—221no—
307C2×M16—224no—
308C2×M16—444no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—221no—
312C22×C8—221no—
313#126—224no—
314#126—224no—
315#125—114no—
316#125—222no—
317#124—114no—
318#124—222no—
319#123—224no—
320#123—224no—
321C22⋊Q8—114no—
322C22⋊Q8—222no—
323#121—114no—
324#121—222no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8C4×D1112yes—
328C4×Q8C22×D1112yes—
329C4×D4—112no—
330C4×D4—112no—
331C4×D4—224no—
332C4×D4—224no—
333C4×D4—221no—
334C4×D4—221no—
335#117—224no—
336#117—224no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C4×D1111yescharacteristic
343C2×C22⋊C4—221no—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C42—21no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—112no—
353C2×C42—112no—
354C2×C42—112no—
355C2×C42—112no—
356C2×C42C22×D1111yescharacteristic
357C4⋊C8—21no—
358C4⋊C8—112no—
359C4⋊C8—224no—
360C4⋊C8—224no—
361C4⋊C8—221no—
362C4⋊C8C22×D1112yes—
363C22⋊C8—224no—
364C4×C8—21no—
365C4×C8—112no—
366C4×C8—221no—
367C4×C8C22×D1112yes—
368C2×C11#149514yescomplemented
369C2×C11C2×#40811yescharacteristic
370C2×C11C2×#41711yescharacteristic
371C2×C11C2×#42111yescharacteristic
372D11—42no—
373D11—82no—
374C24—111no—
375C24—221no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8C2×C4×D1112yes—
380C2×D4—112no—
381C2×D4—224no—
382C2×D4—221no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—444no—
386C22×C4—21no—
387C22×C4—21no—
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—222no—
403C22×C4—222no—
404C22×C4—442no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4C2×C4×D1111yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410M16—448no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—442no—
418C2×C8—442no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—112no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—221no—
427C4⋊C4C2×C4×D1112yes—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—222no—
433C22⋊C4—222no—
434C42—22no—
435C42—22no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—112no—
442C42C2×C4×D1111yescharacteristic
443C42D4×D1111yescharacteristic
444C42D4×D1111yescharacteristic
445C42C23×D1111yescharacteristic
446C11C2×#149511yescharacteristic, complemented, Sylow
447C23—112no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—442no—
453C23—442no—
454C23—442no—
455C23C22⋊C4×D1111yescharacteristic
456Q8—22no—
457Q8—22no—
458Q8—42no—
459D4—222no—
460D4—222no—
461D4—448no—
462D4—442no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—112no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—444no—
487C2×C4C22⋊C4×D1111yescharacteristic
488C2×C4C22⋊C4×D1111yescharacteristic
489C2×C4C22⋊C4×D1111yescharacteristic
490C2×C4#6695412yes—
491C2×C4#6696012yes—
492C2×C4#6696712yes—
493C2×C4#6697112yes—
494C2×C4C22×C4×D1111yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C8—42no—
498C8—42no—
499C8—442no—
500C8—442no—
501C22—222no—
502C22—222no—
503C22—222no—
504C22—444no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—884no—
509C22#1062234012yes—
510C22#1062241612yes—
511C22#1062243412yes—
512C22C2×C22⋊C4×D1111yescharacteristic
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—222no—
518C4—222no—
519C4—222no—
520C4—442no—
521C4#1062234012yes—
522C4#1062241612yes—
523C4C2×#6695411yescharacteristic
524C4C2×#6696011yescharacteristic
525C4C2×#6696711yescharacteristic
526C4C2×#6697111yescharacteristic
527C2—442no—
528C2—882no—
529C2#1306708014yesdirect product factor
530C2C2×#1062234011yescharacteristic
531C2C2×#1062241611yescharacteristic
532C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66948C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1495
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. C2×#10622450C2semidirect
4. #13067080C2direct (N × H)
5. C2×Q8⋊(C11⋊C8)C2semidirect
6. C2×#10622097C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
33. #10622450C22semidirect
35. #10622298C22semidirect
36. C11×Q8⋊C8C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. #10622121C22semidirect
39. #10622097C22semidirect
186. C2×Q8⋊C8D11semidirect
271. Q8⋊C8C2×D11semidirect
368. C2×C11#1495semidirect
446. C11C2×#1495semidirect
529. C2#13067080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×#106222982
C2×#106224502
#130670802
C2×Q8⋊(C11⋊C8)2
C2×#106220972
C2×#106221212
C2×C11×Q8⋊C82
C2×#149511