Finite Group Databasebeta

← C2×#13081430 #15633508

Subgroups — C2×#13081430 #15633508

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2#13081430C2116yesmaximal, direct product factor
3C2×#10622702C212yesmaximal, complemented
4C2×#10622701C211yesmaximal, characteristic
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622700C212yesmaximal, complemented
7C2×#10622641C212yesmaximal, complemented
8C2×#10622640C211yesmaximal, characteristic
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×C4×#4326C211yesmaximal, characteristic, complemented
12C2×Q82×C11C211yesmaximal, characteristic, complemented
13Q82×C11—24no—
14Q82×C11C2218yescomplemented
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—22no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#67000—21no—
24C22×#4326C2211yescharacteristic
25C22×#4325C2212yes—
26#10623116—24no—
27#10623116C2218yes—
28C2×#66947—22no—
29C2×#66946—21no—
30C2×#66928C2212yes—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2212yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622704C2218yescomplemented
36#10622702C22116yescomplemented
37#10622701C2218yes—
38#10622700C22116yescomplemented
39C4×#4326C2218yescomplemented
40#10622641C22116yescomplemented
41#10622640C2218yes—
42#10622639C22116yescomplemented
43#10622637C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11D411yescharacteristic
58C22×Q8×C11C2311yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×C4×D11—22no—
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—28no—
65C11×C4⋊Q8—216no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8C2318yes—
69C11×C4⋊Q8C2314yes—
70C4×Q8×C11—28no—
71C4×Q8×C11—22no—
72C4×Q8×C11—24no—
73C4×Q8×C11D414yes—
74C4×Q8×C11C2318yes—
75C4×Q8×C11C2314yes—
76C4×Q8×C11C2314yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89#67000—28no—
90C2×#4326—24no—
91C2×#4326C2314yes—
92C2×#4325—28no—
93C2×#4325C2318yes—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66947—216no—
104#66946—28no—
105#66928—24no—
106#66928C2318yes—
107#66927—22no—
108#66927C2314yes—
109C4×D44—24no—
110C4×D44C2318yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113#66899C2314yes—
114#66874C2318yes—
115#66874C2314yes—
116#66873C2318yes—
117#66873C2318yes—
118#66873C2318yes—
119#66871C2318yes—
120#66871C2314yes—
121C4⋊(C11⋊C8)C2314yes—
122C4⋊(C11⋊C8)C2318yes—
123#66867C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3375—111nomaximal, Sylow
126C23×D11—22no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—28no—
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×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C2×D44—22no—
148C2×D44—24no—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—44no—
153C2×D44—82no—
154C2×D44C2414yes—
155C2×C4×D11—28no—
156C2×C4×D11—84no—
157C2×Dic22—21no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22C2412yes—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2×D418yes—
169C11×C4⋊C4C2414yes—
170C11×C4⋊C4C2412yes—
171C42×C11—28no—
172C42×C11—24no—
173C42×C11C2×D412yes—
174C42×C11C2×D414yes—
175C42×C11C2412yes—
176C42×C11C2414yes—
177#4326—28no—
178#4325—216no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182C4⋊Dic11—21no—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—24no—
185C4×Dic11—24no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2414yes—
192C2×#559—111no—
193C2×Q82D1111yescharacteristic, complemented
194#3375—1116no—
195C2×#489—112no—
196C2×#486—111no—
197C2×#477—111no—
198C2×#474—112no—
199C2×#464—112no—
200C2×#460—111no—
201C2×#446—111no—
202C2×#440—112no—
203C2×C4×Q16—111no—
204C23×C11C22×D411yescharacteristic
205C22×D11—24no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209Q8×C11—24no—
210Q8×C11—28no—
211Q8×C11—22no—
212Q8×C11—88no—
213Q8×C11—84no—
214Q8×C11C2×#4114yes—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11#13714yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D414yes—
227C2×C4×C11C22×D414yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D412yes—
230C2×C4×C11C2×#4112yes—
231C2×C4×C112−1+412yes—
232C2×C4×C11C2511yescharacteristic
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237D44—24no—
238D44—24no—
239D44—44no—
240D44—48no—
241D44—84no—
242C4×D11—88no—
243Dic22—22no—
244Dic22—22no—
245Dic22—42no—
246C11⋊C8—24no—
247C11⋊C8—22no—
248C11⋊C8—22no—
249C22×Q16—111no—
250C22×SD16—112no—
251#559—118no—
252#559—224no—
253Q82—24no—
254Q82C2×D1118yescomplemented
255C2×C4⋊Q8—21no—
256C2×C4⋊Q8—22no—
257C2×C4⋊Q8C2×D1111yescharacteristic
258C2×C4⋊Q8C2×D1112yes—
259C2×#127—111no—
260C2×#124—112no—
261C2×#124—221no—
262C2×#123—222no—
263C2×C4×Q8—21no—
264C2×C4×Q8—111no—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×Q8C2×D1112yes—
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—112no—
269C2×C4×D4—221no—
270#489—1116no—
271#486—118no—
272#477—118no—
273#474—1116no—
274#464—1116no—
275#460—118no—
276#446—118no—
277#440—1116no—
278C4×Q16—118no—
279C2×#107—112no—
280C2×#107—111no—
281C2×C4⋊C8—111no—
282C2×C4⋊C8—112no—
283C2×#103—111no—
284C2×#103—112no—
285C2×#103—111no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102—112no—
289C2×#97—112no—
290C2×C4×C8—111no—
291C22×C11#54812yes—
292C22×C11C2×#13712yes—
293C22×C11#57612yes—
294C22×C11C23×D411yescharacteristic
295C2×D11—44no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—88no—
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—24no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—44no—
305C4×C11#54812yes—
306C4×C11C2×#13714yes—
307C4×C11C22×#4111yescharacteristic
308C4×C11C2×2−1+411yescharacteristic
309Dic11—42no—
310Dic11—42no—
311C22×Q8—22no—
312C22×Q8—21no—
313C22×Q8—111no—
314C22×Q8C22⋊D1111yescharacteristic
315C22×Q8C22×D1111yescharacteristic
316C22×D4—112no—
317C22×D4—221no—
318C22×D4—221no—
319C23×C4—222no—
320C2×Q16—114no—
321C2×Q16—224no—
322C2×SD16—118no—
323C2×SD16—228no—
324C22×C8—112no—
325C22×C8—111no—
326C22×C8—111no—
327C4⋊Q8—28no—
328C4⋊Q8—216no—
329C4⋊Q8—24no—
330C4⋊Q8—22no—
331C4⋊Q8C22×D1118yes—
332C4⋊Q8C22×D1114yes—
333#127—114no—
334#127—222no—
335#124—118no—
336#124—228no—
337#124—224no—
338#123—2216no—
339C4×Q8—28no—
340C4×Q8—24no—
341C4×Q8—22no—
342C4×Q8—114no—
343C4×Q8—222no—
344C4×Q8C22⋊D1114yes—
345C4×Q8C22×D1114yes—
346C4×Q8C22×D1118yes—
347C4×Q8C22×D1114yes—
348C4×D4—118no—
349C4×D4—228no—
350C4×D4—224no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22⋊D1112yes—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42—221no—
367C2×C42C22×D1112yes—
368C2×C42C22×D1111yescharacteristic
369#107—114no—
370#107—118no—
371C4⋊C8—114no—
372C4⋊C8—118no—
373#103—114no—
374#103—114no—
375#103—118no—
376#102—118no—
377#102—118no—
378#102—118no—
379#97—118no—
380C4×C8—114no—
381C2×C11#337514yescomplemented
382C2×C11C2×#54811yescharacteristic
383C2×C11C22×#13711yescharacteristic
384C2×C11C2×#57611yescharacteristic
385D11—84no—
386C24—222no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—28no—
391C2×Q8—24no—
392C2×Q8—84no—
393C2×Q8—82no—
394C2×Q8—112no—
395C2×Q8—221no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8#434314yes—
399C2×Q8C2×C22⋊D1114yes—
400C2×Q8C23×D1112yes—
401C2×D4—114no—
402C2×D4—224no—
403C2×D4—224no—
404C2×D4—224no—
405C2×D4—222no—
406C2×D4—224no—
407C2×D4—444no—
408C2×D4—882no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—228no—
415C22×C4—884no—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1112yes—
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421Q16—228no—
422SD16—2216no—
423C2×C8—112no—
424C2×C8—112no—
425C2×C8—114no—
426C2×C8—224no—
427C2×C8—222no—
428C2×C8—222no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—28no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—112no—
436C4⋊C4—221no—
437C4⋊C4—224no—
438C4⋊C4C2×C22⋊D1114yes—
439C4⋊C4C2×C22⋊D1118yes—
440C4⋊C4C23×D1114yes—
441C4⋊C4C23×D1112yes—
442C22⋊C4—228no—
443C22⋊C4—228no—
444C22⋊C4—228no—
445C42—28no—
446C42—24no—
447C42—224no—
448C42C2×C22⋊D1114yes—
449C42C2×C22⋊D1112yes—
450C42C23×D1112yes—
451C42C23×D1114yes—
452C11C2×#337511yescharacteristic, complemented, Sylow
453C23—224no—
454C23—444no—
455C23—444no—
456C23—444no—
457C23C22×C22⋊D1111yescharacteristic
458Q8—28no—
459Q8—24no—
460Q8—22no—
461Q8—88no—
462Q8—84no—
463Q8—222no—
464Q8—222no—
465Q8—442no—
466Q8C2×#434314yes—
467D4—224no—
468D4—224no—
469D4—448no—
470D4—444no—
471D4—884no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—888no—
486C2×C4#6699514yes—
487C2×C4C2×#434312yes—
488C2×C4#6704012yes—
489C2×C4C22×C22⋊D1114yes—
490C2×C4C22×C22⋊D1114yes—
491C2×C4C22×C22⋊D1112yes—
492C2×C4C22×C22⋊D1112yes—
493C2×C4C22×C22⋊D1111yescharacteristic
494C2×C4C24×D1111yescharacteristic
495C8—224no—
496C8—222no—
497C8—222no—
498C22—444no—
499C22—444no—
500C22—444no—
501C22—888no—
502C22C2×#6699512yes—
503C22#1062334812yes—
504C22#1062336612yes—
505C22C23×C22⋊D1111yescharacteristic
506C4—24no—
507C4—24no—
508C4—24no—
509C4—22no—
510C4—42no—
511C4—44no—
512C4—442no—
513C4—442no—
514C4C2×#6699514yes—
515C4#1062334812yes—
516C4C22×#434311yescharacteristic
517C4C2×#6704011yescharacteristic
518C2—884no—
519C2#1308143014yesdirect product factor
520C2C2×#1062334811yescharacteristic
521C2C22×#6699511yescharacteristic
522C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×Q82×C11C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×Q82D11
hypocenterC11C2×#3375
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. #13081430C2direct (N × H)
3. C2×#10622702C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622641C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622639C2semidirect
11. C2×C4×#4326C2semidirect
12. C2×Q82×C11C2semidirect
14. Q82×C11C22semidirect
35. #10622704C22semidirect
36. #10622702C22semidirect
38. #10622700C22semidirect
39. C4×#4326C22semidirect
40. #10622641C22semidirect
42. #10622639C22semidirect
43. #10622637C22semidirect
193. C2×Q82D11semidirect
254. Q82C2×D11semidirect
381. C2×C11#3375semidirect
452. C11C2×#3375semidirect
519. C2#13081430direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130814302
C2×#106227022
C2×#106227012
C2×#106227042
C2×#106227002
C2×#106226412
C2×#106226402
C2×#106226372
C2×#106226392
C2×C4×#43262
C2×Q82×C112
C2×#337511