Finite Group Databasebeta

← C2×#13081356 #15633496

Subgroups — C2×#13081356 #15633496

Order 2816.

1842 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2#13081356C2116yesmaximal, direct product factor
3C2×#10622702C212yesmaximal
4C2×#10622706C211yesmaximal, characteristic, complemented
5C2×#10622707C212yesmaximal, complemented
6C2×#10622697C211yesmaximal, characteristic
7C2×#10622641C212yesmaximal
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622643C212yesmaximal, complemented
11C2×C4×#4325C211yesmaximal, characteristic
12C2×Q82×C11C211yesmaximal, characteristic, complemented
13Q82×C11—24no—
14Q82×C11C2218yescomplemented
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—22no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C4⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66999—21no—
24C22×#4326C2212yes—
25C22×#4325C2211yescharacteristic
26#10623115—24no—
27#10623115C2218yes—
28C2×#66951—22no—
29C2×#66945—21no—
30C2×#66928C2212yes—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×#66899C2211yescharacteristic
35#10622707C22116yescomplemented
36#10622706C2218yescomplemented
37#10622702C22116yes—
38#10622697C2218yes—
39#10622644C2218yescomplemented
40#10622643C22116yescomplemented
41#10622641C22116yes—
42C4×#4325C2218yes—
43#10622637C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2211yescharacteristic
49C2×#66872C2212yes—
50C2×#66872C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2312yes—
62C11×C4⋊Q8—28no—
63C11×C4⋊Q8—216no—
64C11×C4⋊Q8—24no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C11×C4⋊Q8C2318yes—
68C4×Q8×C11—28no—
69C4×Q8×C11—24no—
70C4×Q8×C11—22no—
71C4×Q8×C11D414yes—
72C4×Q8×C11C2314yes—
73C4×Q8×C11C2318yes—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87#66999—28no—
88C2×#4326—28no—
89C2×#4326C2318yes—
90C2×#4325—24no—
91C2×#4325C2314yes—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66951—216no—
104#66945—28no—
105#66928—24no—
106#66928C2318yes—
107C4×D44—22no—
108C4×D44C2314yes—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—24no—
112C4×Dic22C2318yes—
113#66899C2314yes—
114#66874C2318yes—
115#66874C2318yes—
116#66874C2318yes—
117#66873C2314yes—
118#66873C2318yes—
119#66872C2314yes—
120#66872C2318yes—
121C4⋊(C11⋊C8)C2318yes—
122C4⋊(C11⋊C8)C2314yes—
123#66867C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3369—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—28no—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—84no—
133C2×Q8×C11—82no—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11#4114yes—
136C2×Q8×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—22no—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44C2412yes—
151C2×C4×D11—24no—
152C2×C4×D11—44no—
153C2×Dic22—22no—
154C2×Dic22—24no—
155C2×Dic22—24no—
156C2×Dic22C2414yes—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D418yes—
165C11×C4⋊C4C2412yes—
166C11×C4⋊C4C2414yes—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11C2×D414yes—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C42×C11C2414yes—
173#4326—216no—
174#4325—28no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—21no—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11C2412yes—
182Dic11⋊C4—28no—
183C4×Dic11—28no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2412yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2414yes—
190C2×Q82D1111yescharacteristic, complemented
191C2×#556—111no—
192#3369—1116no—
193C2×#489—112no—
194C2×#487—111no—
195C2×#475—112no—
196C2×#476—111no—
197C2×#464—112no—
198C2×#462—111no—
199C2×#446—111no—
200C2×#441—112no—
201C2×C4×SD16—111no—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207Q8×C11—24no—
208Q8×C11—28no—
209Q8×C11—22no—
210Q8×C11—88no—
211Q8×C11—84no—
212Q8×C11C2×#4114yes—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11#13714yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D412yes—
228C2×C4×C11C2×#4112yes—
229C2×C4×C112−1+412yes—
230C2×C4×C11C2511yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235D44—22no—
236D44—22no—
237D44—42no—
238C4×D11—48no—
239Dic22—24no—
240Dic22—24no—
241Dic22—44no—
242C11⋊C8—22no—
243C11⋊C8—24no—
244C11⋊C8—22no—
245C22×Q16—112no—
246C22×SD16—111no—
247Q82—24no—
248Q82C2×D1118yescomplemented
249#556—118no—
250#556—224no—
251C2×C4⋊Q8—21no—
252C2×C4⋊Q8—22no—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8C2×D1112yes—
255C2×C4⋊Q8C2×D1111yescharacteristic
256C2×#126—222no—
257C2×#124—112no—
258C2×C22⋊Q8—221no—
259C2×C4×Q8—21no—
260C2×C4×Q8—112no—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×Q8C2×D1112yes—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×D4—111no—
265C2×#117—221no—
266#489—1116no—
267#487—118no—
268#476—118no—
269#475—1116no—
270#464—1116no—
271#462—118no—
272#446—118no—
273#441—1116no—
274C4×SD16—118no—
275C2×#106—111no—
276C2×#106—112no—
277C2×C4⋊C8—112no—
278C2×C4⋊C8—111no—
279C2×#103—111no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#102—111no—
284C2×#102—112no—
285C2×#97—112no—
286C2×C4×C8—111no—
287C22×C11#54812yes—
288C22×C11C2×#13712yes—
289C22×C11#57712yes—
290C22×C11C23×D411yescharacteristic
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—84no—
295C4×C11—24no—
296C4×C11—24no—
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11#54812yes—
302C4×C11C2×#13714yes—
303C4×C11C22×#4111yescharacteristic
304C4×C11C2×2−1+411yescharacteristic
305Dic11—44no—
306Dic11—42no—
307C22×Q8—22no—
308C22×Q8—21no—
309C22×Q8—112no—
310C22×Q8C22⋊D1111yescharacteristic
311C22×Q8C22×D1111yescharacteristic
312C22×D4—111no—
313C23×C4—221no—
314C2×Q16—118no—
315C2×Q16—228no—
316C2×SD16—114no—
317C2×SD16—224no—
318C22×C8—111no—
319C22×C8—112no—
320C22×C8—111no—
321C4⋊Q8—28no—
322C4⋊Q8—216no—
323C4⋊Q8—22no—
324C4⋊Q8—24no—
325C4⋊Q8—114no—
326C4⋊Q8—222no—
327C4⋊Q8C22×D1118yes—
328C4⋊Q8C22×D1114yes—
329#126—2216no—
330#124—118no—
331#124—224no—
332C22⋊Q8—228no—
333C4×Q8—28no—
334C4×Q8—22no—
335C4×Q8—24no—
336C4×Q8—118no—
337C4×Q8—224no—
338C4×Q8C22⋊D1114yes—
339C4×Q8C22×D1114yes—
340C4×Q8C22×D1118yes—
341C4×Q8C22×D1114yes—
342C4×D4—114no—
343C4×D4—222no—
344#117—228no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22⋊D1112yes—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—222no—
360C2×C42—22no—
361C2×C42—21no—
362C2×C42—222no—
363C2×C42C22×D1111yescharacteristic
364C2×C42C22×D1112yes—
365#106—114no—
366#106—118no—
367C4⋊C8—114no—
368C4⋊C8—118no—
369#103—114no—
370#103—118no—
371#103—118no—
372#103—118no—
373#102—114no—
374#102—118no—
375#97—118no—
376C4×C8—114no—
377C2×C11#336914yescomplemented
378C2×C11C2×#54811yescharacteristic
379C2×C11C22×#13711yescharacteristic
380C2×C11C2×#57711yescharacteristic
381D11—82no—
382C24—221no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—28no—
387C2×Q8—24no—
388C2×Q8—84no—
389C2×Q8—82no—
390C2×Q8—114no—
391C2×Q8—222no—
392C2×Q8—224no—
393C2×Q8—224no—
394C2×Q8#434314yes—
395C2×Q8C2×C22⋊D1114yes—
396C2×Q8C23×D1112yes—
397C2×D4—112no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—221no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—224no—
407C22×C4—444no—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1112yes—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413Q16—2216no—
414SD16—228no—
415C2×C8—112no—
416C2×C8—112no—
417C2×C8—114no—
418C2×C8—222no—
419C2×C8—224no—
420C2×C8—222no—
421C4⋊C4—28no—
422C4⋊C4—24no—
423C4⋊C4—28no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—112no—
428C4⋊C4—221no—
429C4⋊C4—224no—
430C4⋊C4—228no—
431C4⋊C4—224no—
432C4⋊C4C2×C22⋊D1114yes—
433C4⋊C4C2×C22⋊D1118yes—
434C4⋊C4C23×D1112yes—
435C4⋊C4C23×D1114yes—
436C22⋊C4—228no—
437C22⋊C4—224no—
438C22⋊C4—228no—
439C42—28no—
440C42—24no—
441C42—228no—
442C42C2×C22⋊D1112yes—
443C42C2×C22⋊D1114yes—
444C42C23×D1112yes—
445C42C23×D1114yes—
446C11C2×#336911yescharacteristic, complemented, Sylow
447C23—222no—
448C23—442no—
449C23—442no—
450C23—442no—
451C23C22×C22⋊D1111yescharacteristic
452Q8—28no—
453Q8—24no—
454Q8—22no—
455Q8—88no—
456Q8—84no—
457Q8—224no—
458Q8—224no—
459Q8—444no—
460Q8C2×#434314yes—
461D4—222no—
462D4—222no—
463D4—442no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—442no—
476C2×C4—444no—
477C2×C4—448no—
478C2×C4#6699514yes—
479C2×C4C2×#434312yes—
480C2×C4#6704012yes—
481C2×C4C22×C22⋊D1114yes—
482C2×C4C22×C22⋊D1114yes—
483C2×C4C22×C22⋊D1112yes—
484C2×C4C22×C22⋊D1112yes—
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C24×D1111yescharacteristic
487C8—222no—
488C8—224no—
489C8—222no—
490C22—442no—
491C22—442no—
492C22—442no—
493C22—884no—
494C22C2×#6699512yes—
495C22#1062334812yes—
496C22#1062336712yes—
497C22C23×C22⋊D1111yescharacteristic
498C4—24no—
499C4—24no—
500C4—24no—
501C4—22no—
502C4—44no—
503C4—42no—
504C4—442no—
505C4—444no—
506C4C2×#6699514yes—
507C4#1062334812yes—
508C4C22×#434311yescharacteristic
509C4C2×#6704011yescharacteristic
510C2—882no—
511C2#1308135614yesdirect product factor
512C2C2×#1062334811yescharacteristic
513C2C22×#6699511yescharacteristic
514C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×Q82×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×Q82D11
hypocenterC11C2×#3369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
2. #13081356C2direct (N × H)
4. C2×#10622706C2semidirect
5. C2×#10622707C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622643C2semidirect
12. C2×Q82×C11C2semidirect
14. Q82×C11C22semidirect
35. #10622707C22semidirect
36. #10622706C22semidirect
39. #10622644C22semidirect
40. #10622643C22semidirect
43. #10622637C22semidirect
190. C2×Q82D11semidirect
248. Q82C2×D11semidirect
377. C2×C11#3369semidirect
446. C11C2×#3369semidirect
511. C2#13081356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130813562
C2×#106227022
C2×#106227062
C2×#106227072
C2×#106226972
C2×#106226412
C2×#106226442
C2×#106226372
C2×#106226432
C2×C4×#43252
C2×Q82×C112
C2×#336911