Finite Group Databasebeta

← C2×#13081514 #15634249

Subgroups — C2×#13081514 #15634249

Order 2816.

2082 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×#10623261C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081514C2116yesmaximal, direct product factor
4C2×#10622469C212yesmaximal, complemented
5C2×#10622692C211yesmaximal, characteristic, complemented
6C2×#10622379C212yesmaximal, complemented
7C2×#10622483C212yesmaximal, complemented
8C2×#10622459C211yesmaximal, characteristic, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622398C212yesmaximal
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C23×Dic22—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999—22no—
17C2×D4×Dic11C2212yes—
18C22×#4323C2211yescharacteristic
19C2×#66977—21no—
20#10623261—24no—
21#10623261C2218yescomplemented
22D4×Dic22—24no—
23D4×Dic22C2218yescomplemented
24C2×#66950—21no—
25C2×#66946C2212yes—
26C2×C4⋊C4×D11—21no—
27C2×#66943C2212yes—
28C2×#66941C2212yes—
29C2×#66931—22no—
30C2×C4×D44C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#476C2218yescomplemented
34C2×C11×#106C2212yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×#66896C2211yescharacteristic
38C2×#66885C2212yes—
39C2×#66882C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622692C2218yescomplemented
43C4×#4323C2218yes—
44C2×#66873C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622483C22116yescomplemented
50#10622469C22116yescomplemented
51#10622459C2218yescomplemented
52#10622444C2218yescomplemented
53#10622398C22116yes—
54#10622379C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×Dic22—28no—
65C22×Dic22—48no—
66C22×Dic22D411yescharacteristic
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C4×D4×C11—22no—
71C4×D4×C11C2314yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78#66999—216no—
79D4×Dic11—24no—
80D4×Dic11C2318yes—
81C2×#4323Q818yescomplemented
82C2×#4323C2314yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—28no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4D412yes—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66950—28no—
98#66946—24no—
99#66946C2318yes—
100C4⋊C4×D11—28no—
101#66943—24no—
102#66943C2318yes—
103#66941—24no—
104#66941C2318yes—
105#66931—216no—
106C4×D44—22no—
107C4×D44C2314yes—
108#66922—22no—
109#66922C2314yes—
110C4×Dic22D414yes—
111C4×Dic22C2314yes—
112C11×#106C2318yes—
113C11×C4⋊C8C2314yes—
114C11×#102C2318yes—
115#66896C2314yes—
116#66885C2318yes—
117#66882C2318yes—
118#66879C2318yes—
119Dic11⋊C8C2318yes—
120#66873C2314yes—
121#66872C2318yes—
122#66872C2318yes—
123#66871C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3384—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—82no—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11C2×Q814yes—
133C2×D4×C11C2412yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—28no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—48no—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44C2×Q814yescomplemented
150C2×D44C2412yes—
151C2×C4×D11—28no—
152C2×C4×D11—24no—
153C2×C4×D11—44no—
154C2×C4×D11—84no—
155C2×Dic22—28no—
156C2×Dic22—24no—
157C2×Dic22—24no—
158C2×Dic22—432no—
159C2×Dic22—48no—
160C2×Dic22—44no—
161C2×Dic22C2×D414yes—
162C2×C8×C11—24no—
163C2×C8×C11C2414yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4C2412yes—
168C11×C4⋊C4C2414yes—
169C11×C22⋊C4—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C22⋊Dic11—28no—
173#4323C2×Q8116yescomplemented
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—28no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—21no—
180C4⋊Dic11C2×D414yes—
181C4⋊Dic11C2412yes—
182C4⋊Dic11C2414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4C2×D418yes—
186C4×Dic11C2×D414yes—
187C4×Dic11C2414yes—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C2×Q814yescomplemented
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2412yes—
192C2×#554—111no—
193C2×D4×Q8—111no—
194#3384—1116no—
195C2×#501—112no—
196C2×#498—111no—
197C2×#478—112no—
198C2×#476—112no—
199C2×#476D1111yescharacteristic, complemented
200C2×#474—111no—
201C2×#446—111no—
202C2×#442—112no—
203C2×C4×D8—111no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—42no—
212C22×D11—42no—
213Q8×C11—84no—
214D4×C11—24no—
215D4×C11—22no—
216D4×C11C22×Q814yes—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—48no—
223C2×C4×C11AGL(1,ℤ/8)14yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×Q812yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—416no—
235C2×Dic11—44no—
236C2×Dic11—42no—
237C2×Dic11C22×D414yes—
238C2×Dic11C22×D414yes—
239D44—24no—
240D44—22no—
241D44C22×Q814yescomplemented
242C4×D11—48no—
243C4×D11—88no—
244Dic22—28no—
245Dic22—416no—
246Dic22—48no—
247C8×C11—24no—
248C11⋊C8—22no—
249C11⋊C8C22×Q814yescomplemented
250C23×Q8—221no—
251C22×D8—111no—
252#554—118no—
253#554—224no—
254D4×Q8—118no—
255D4×Q8—224no—
256C2×C4⋊Q8—112no—
257C2×C4⋊Q8—111no—
258C2×C4⋊Q8C2×D1111yescharacteristic
259C2×#125—112no—
260C2×C22⋊Q8—222no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—221no—
263C2×C22⋊Q8—222no—
264C2×C4×Q8—111no—
265C2×C4×D4—112no—
266C2×C4×D4—112no—
267C2×C4×D4—111no—
268C2×C4×D4C2×D1111yescharacteristic
269C22×C4⋊C4—221no—
270#501—1116no—
271#498—118no—
272#478—1116no—
273#476—1116no—
274#476C2×D1118yescomplemented
275#474—118no—
276#446—118no—
277#442—1116no—
278C4×D8—118no—
279C2×#107—112no—
280C2×#107—111no—
281C2×#106—112no—
282C2×#106—112no—
283C2×#106C2×D1112yes—
284C2×C4⋊C8—112no—
285C2×C4⋊C8C2×D1111yescharacteristic
286C2×#102—111no—
287C2×#102—112no—
288C2×#102—111no—
289C2×#102C2×D1112yes—
290C2×#97—112no—
291C2×C4×C8—111no—
292C22×C11—24no—
293C22×C11—48no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11D4×Q812yes—
297C22×C11C2×AGL(1,ℤ/8)12yes—
298C22×C11#57712yes—
299C22×C11C23×D411yescharacteristic
300C2×D11—24no—
301C2×D11—48no—
302C2×D11—42no—
303C2×D11—42no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11D4×Q812yes—
308C4×C11C2×AGL(1,ℤ/8)14yes—
309C4×C11C23×Q811yescharacteristic
310C4×C11C2×2−1+411yescharacteristic
311Dic11—24no—
312Dic11—24no—
313Dic11—44no—
314Dic11—42no—
315C22×Q8—21no—
316C22×Q8—111no—
317C22×Q8—222no—
318C22×Q8—228no—
319C22×Q8—221no—
320C22×Q8—448no—
321C22×D4—111no—
322C22×D4C22×D1111yescharacteristic
323C23×C4—21no—
324C23×C4—222no—
325C23×C4—222no—
326C23×C4—221no—
327C2×D8—118no—
328C2×D8—114no—
329C22×C8—111no—
330C22×C8—111no—
331C22×C8C22×D1112yes—
332C4⋊Q8—22no—
333C4⋊Q8—118no—
334C4⋊Q8—114no—
335C4⋊Q8—224no—
336C4⋊Q8—222no—
337C4⋊Q8C22×D1114yes—
338#125—118no—
339#125—224no—
340C22⋊Q8—2216no—
341C22⋊Q8—228no—
342C22⋊Q8—228no—
343C22⋊Q8—2216no—
344C4×Q8—114no—
345C4×Q8—114no—
346C4×D4—22no—
347C4×D4—118no—
348C4×D4—118no—
349C4×D4—114no—
350C4×D4—224no—
351C4×D4—224no—
352C4×D4—222no—
353C4×D4C22×D1114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—221no—
370C2×C42—112no—
371C2×C42C22×D1111yescharacteristic
372#107—118no—
373#107—114no—
374#106—118no—
375#106—118no—
376#106C22×D1118yes—
377C4⋊C8—118no—
378C4⋊C8C22×D1114yes—
379#102—114no—
380#102—118no—
381#102—114no—
382#102C22×D1118yes—
383#97—118no—
384C4×C8—114no—
385C2×C11—44no—
386C2×C11#338414yescomplemented
387C2×C11C2×D4×Q811yescharacteristic
388C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
389C2×C11C2×#57711yescharacteristic
390D11—44no—
391C24—21no—
392C24—221no—
393C2×Q8—24no—
394C2×Q8—82no—
395C2×Q8—114no—
396C2×Q8—228no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—448no—
400C2×Q8—4432no—
401C2×Q8—444no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—114no—
405C2×D4—112no—
406C2×D4—221no—
407C2×D4—222no—
408C2×D4Q8×D1114yes—
409C2×D4C23×D1112yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—44no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—228no—
417C22×C4—228no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—224no—
421C22×C4—448no—
422C22×C4—444no—
423C22×C4—884no—
424C22×C4D4×D1111yescharacteristic
425C22×C4D4×D1111yescharacteristic
426C22×C4C23×D1111yescharacteristic
427D8—1116no—
428C2×C8—24no—
429C2×C8—114no—
430C2×C8—112no—
431C2×C8—112no—
432C2×C8—222no—
433C2×C8C23×D1114yes—
434C4⋊C4—24no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—114no—
438C4⋊C4—118no—
439C4⋊C4—114no—
440C4⋊C4—112no—
441C4⋊C4—228no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C4⋊C4—221no—
445C4⋊C4—222no—
446C4⋊C4—224no—
447C4⋊C4C23×D1112yes—
448C4⋊C4C23×D1114yes—
449C22⋊C4—24no—
450C22⋊C4—228no—
451C22⋊C4—228no—
452C22⋊C4—224no—
453C42—114no—
454C42—114no—
455C42D4×D1112yes—
456C42C23×D1112yes—
457C11C2×#338411yescharacteristic, complemented, Sylow
458C23—24no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23—224no—
463C23—222no—
464C23—442no—
465C23—442no—
466C23C2×D4×D1111yescharacteristic
467Q8—84no—
468Q8—228no—
469Q8—4416no—
470Q8—448no—
471D4—24no—
472D4—22no—
473D4—114no—
474D4—224no—
475D4—222no—
476D4C2×Q8×D1114yes—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—48no—
483C2×C4—114no—
484C2×C4—114no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—4416no—
490C2×C4—444no—
491C2×C4—442no—
492C2×C4—448no—
493C2×C4—888no—
494C2×C4#6696714yes—
495C2×C4C2×D4×D1112yes—
496C2×C4C2×D4×D1112yes—
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×Q8×D1112yes—
499C2×C4#6704312yes—
500C2×C4C24×D1111yescharacteristic
501C8—24no—
502C8—114no—
503C8—222no—
504C22—24no—
505C22—48no—
506C22—42no—
507C22—42no—
508C22—224no—
509C22—448no—
510C22—442no—
511C22—442no—
512C22#1062316312yes—
513C22C2×#6696712yes—
514C22#1062330612yes—
515C22C22×D4×D1111yescharacteristic
516C4—22no—
517C4—42no—
518C4—44no—
519C4—224no—
520C4—224no—
521C4—444no—
522C4—442no—
523C4#1062316312yes—
524C4C2×#6696714yes—
525C4C22×Q8×D1111yescharacteristic
526C4C2×#6704311yescharacteristic
527C2—44no—
528C2—444no—
529C2#1308151414yesdirect product factor
530C2C2×#1062316311yescharacteristic
531C2C22×#6696711yescharacteristic
532C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#476D11
hypocenterC11C2×#3384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081514C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622692C2semidirect
6. C2×#10622379C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622459C2semidirect
9. C2×#10622444C2semidirect
12. C2×C11×#476C2semidirect
21. #10623261C22semidirect
23. D4×Dic22C22semidirect
33. C11×#476C22semidirect
42. #10622692C22semidirect
49. #10622483C22semidirect
50. #10622469C22semidirect
51. #10622459C22semidirect
52. #10622444C22semidirect
54. #10622379C22semidirect
81. C2×#4323Q8semidirect
149. C2×D44C2×Q8semidirect
173. #4323C2×Q8semidirect
189. C2×C11⋊C8C2×Q8semidirect
199. C2×#476D11semidirect
241. D44C22×Q8semidirect
249. C11⋊C8C22×Q8semidirect
274. #476C2×D11semidirect
386. C2×C11#3384semidirect
457. C11C2×#3384semidirect
529. C2#13081514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×D4×Dic222
#130815142
C2×#106224692
C2×#106226922
C2×#106223792
C2×#106224832
C2×#106224592
C2×#106224442
C2×#106223982
C2×C4×#43232
C2×C11×#4762
C2×#338411