Finite Group Databasebeta

← C2×#13081345 #15633472

Subgroups — C2×#13081345 #15633472

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2#13081345C2116yesmaximal, direct product factor
3C2×#10622680C212yesmaximal, complemented
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622679C212yesmaximal, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622640C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×C4×#4325C211yesmaximal, characteristic, complemented
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C11×#557—24no—
15C11×#557C2218yescomplemented
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—22no—
19C2×C11×#125C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4325C2212yes—
26#10623108—24no—
27#10623108C2218yes—
28C2×#66948—21no—
29C2×#66948—22no—
30C2×#66927C2211yescharacteristic
31C2×#66927C2212yes—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2212yes—
34C2×#66899C2211yescharacteristic
35#10622701C2218yescomplemented
36#10622700C2218yescomplemented
37#10622680C22116yescomplemented
38#10622679C22116yescomplemented
39#10622640C22116yescomplemented
40#10622640C2218yescomplemented
41#10622639C22116yescomplemented
42C4×#4325C2218yescomplemented
43#10622637C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66873C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C2×#4343—28no—
59C2×#4343—48no—
60C22×D44—22no—
61C22×D44—21no—
62C22×D44—22no—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×D44C2312yes—
66C22×C4×D11—22no—
67C22×C4×D11—21no—
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×#125—216no—
72C11×#125—24no—
73C11×#125C2318yes—
74C4×Q8×C11—28no—
75C4×Q8×C11—24no—
76C4×Q8×C11—22no—
77C4×Q8×C11D414yes—
78C4×Q8×C11C2314yes—
79C4×Q8×C11C2318yes—
80C4×Q8×C11C2314yes—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4D412yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C42×C11—22no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2312yes—
94C2×#4325—24no—
95C2×#4325—28no—
96C2×#4325C2314yes—
97C2×#4325C2318yes—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66948—28no—
105#66948—216no—
106#66927—24no—
107#66927—22no—
108#66927C2318yes—
109#66927C2314yes—
110C4×D44—24no—
111C4×D44—22no—
112C4×D44C2314yes—
113C4×D44C2318yes—
114#66899C2314yes—
115#66873C2314yes—
116#66873C2318yes—
117#66873C2318yes—
118#66873C2318yes—
119#66873C2318yes—
120#66872C2314yes—
121#66871C2318yes—
122C4⋊(C11⋊C8)C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3368—111nomaximal, Sylow
127C23×D11—22no—
128C23×D11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—24no—
132C2×Q8×C11—22no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11#4114yescomplemented
136C2×Q8×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146#4343—432no—
147C2×D44—22no—
148C2×D44—21no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—28no—
152C2×D44—24no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—22no—
156C2×D44—24no—
157C2×D44—48no—
158C2×D44—44no—
159C2×D44—84no—
160C2×D44—82no—
161C2×D44C2412yes—
162C2×D44C2414yes—
163C2×C4×D11—28no—
164C2×C4×D11—24no—
165C2×C4×D11—48no—
166C2×C4×D11—44no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2×D418yes—
176C11×C4⋊C4C2414yes—
177C11×C4⋊C4C2412yes—
178C42×C11—28no—
179C42×C11—24no—
180C42×C11C2×D414yes—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183C42×C11C2414yes—
184#4325—28no—
185#4325—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2412yes—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—24no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2414yes—
196C2×#557D1111yescharacteristic, complemented
197C2×#550—111no—
198#3368—1116no—
199C2×#490—112no—
200C2×#486—111no—
201C2×#478—112no—
202C2×#474—111no—
203C2×#460—111no—
204C2×#460—112no—
205C2×#446—111no—
206C2×#440—112no—
207C2×C4×SD16—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—44no—
212C22×D11—42no—
213C22×D11—44no—
214C22×D11—42no—
215C22×D11—44no—
216C22×D11—42no—
217Q8×C11—24no—
218Q8×C11—28no—
219Q8×C11—22no—
220Q8×C11—48no—
221Q8×C11C2×#4114yescomplemented
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11AGL(1,ℤ/8)14yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D414yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C112−1+412yes—
239C2×C4×C11C2511yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—42no—
242D44—22no—
243D44—24no—
244D44—22no—
245D44—24no—
246D44—416no—
247D44—44no—
248D44—42no—
249D44—48no—
250D44—88no—
251D44—84no—
252C4×D11—416no—
253C4×D11—48no—
254C11⋊C8—22no—
255C11⋊C8—24no—
256C11⋊C8—22no—
257C22×#41—221no—
258C22×SD16—111no—
259C22×SD16—112no—
260#557—24no—
261#557C2×D1118yescomplemented
262#550—118no—
263#550—224no—
264C2×C4⋊Q8—21no—
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×#127—111no—
267C2×#127—112no—
268C2×#125—22no—
269C2×#125C2×D1112yes—
270C2×#121—221no—
271C2×#121—222no—
272C2×C4×Q8—21no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×Q8C2×D1112yes—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—112no—
277C2×C4×D4—111no—
278#490—1116no—
279#486—118no—
280#478—1116no—
281#474—118no—
282#460—1116no—
283#460—118no—
284#446—118no—
285#440—1116no—
286C4×SD16—118no—
287C2×#107—112no—
288C2×#106—111no—
289C2×C4⋊C8—112no—
290C2×C4⋊C8—111no—
291C2×#103—111no—
292C2×#102—112no—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—111no—
296C2×#102—112no—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11#54812yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57712yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—44no—
304C2×D11—42no—
305C2×D11—44no—
306C2×D11—42no—
307C2×D11—44no—
308C2×D11—42no—
309C2×D11—88no—
310C2×D11—84no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—24no—
314C4×C11—22no—
315C4×C11—44no—
316C4×C11—42no—
317C4×C11#54812yes—
318C4×C11C2×AGL(1,ℤ/8)14yes—
319C4×C11C22×#4111yescharacteristic
320C4×C11C2×2−1+411yescharacteristic
321Dic11—42no—
322C2×#41—228no—
323C2×#41—448no—
324C22×Q8—21no—
325C22×Q8C22⋊D1111yescharacteristic
326C22×Q8C22×D1111yescharacteristic
327C22×D4—112no—
328C22×D4—111no—
329C22×D4—222no—
330C22×D4—221no—
331C22×D4—222no—
332C22×D4—221no—
333C23×C4—222no—
334C23×C4—221no—
335C2×SD16—114no—
336C2×SD16—118no—
337C2×SD16—224no—
338C2×SD16—228no—
339C22×C8—111no—
340C22×C8—112no—
341C22×C8—111no—
342C4⋊Q8—28no—
343C4⋊Q8—22no—
344C4⋊Q8C22×D1114yes—
345#127—114no—
346#127—118no—
347#127—224no—
348#127—222no—
349#125—216no—
350#125—24no—
351#125C22×D1118yes—
352#121—228no—
353#121—2216no—
354C4×Q8—28no—
355C4×Q8—24no—
356C4×Q8—22no—
357C4×Q8C22⋊D1114yes—
358C4×Q8C22×D1114yes—
359C4×Q8C22×D1118yes—
360C4×Q8C22×D1114yes—
361C4×D4—114no—
362C4×D4—118no—
363C4×D4—224no—
364C4×D4—222no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1112yes—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1112yes—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—221no—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42C22×D1112yes—
380C2×C42C22×D1111yescharacteristic
381#107—118no—
382#106—114no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#102—114no—
387#102—118no—
388#102—118no—
389#102—118no—
390#102—118no—
391#97—118no—
392C4×C8—114no—
393C2×C11#336814yescomplemented
394C2×C11C2×#54811yescharacteristic
395C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
396C2×C11C2×#57711yescharacteristic
397D11—84no—
398D11—82no—
399C24—222no—
400C24—221no—
401#41—4432no—
402C2×Q8—24no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—24no—
406C2×Q8—44no—
407C2×Q8#434314yescomplemented
408C2×Q8C2×C22⋊D1114yes—
409C2×Q8C23×D1112yes—
410C2×D4—112no—
411C2×D4—114no—
412C2×D4—222no—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—221no—
418C2×D4—228no—
419C2×D4—224no—
420C2×D4—228no—
421C2×D4—224no—
422C2×D4—448no—
423C2×D4—444no—
424C2×D4—884no—
425C2×D4—882no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—221no—
430C22×C4—228no—
431C22×C4—224no—
432C22×C4—448no—
433C22×C4—444no—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—228no—
440SD16—2216no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—114no—
444C2×C8—222no—
445C2×C8—224no—
446C2×C8—222no—
447C4⋊C4—28no—
448C4⋊C4—24no—
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—28no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—112no—
455C4⋊C4—221no—
456C4⋊C4C2×C22⋊D1114yes—
457C4⋊C4C2×C22⋊D1118yes—
458C4⋊C4C23×D1112yes—
459C4⋊C4C23×D1114yes—
460C22⋊C4—228no—
461C22⋊C4—224no—
462C42—28no—
463C42—24no—
464C42C2×C22⋊D1114yes—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C42C23×D1114yes—
468C11C2×#336811yescharacteristic, complemented, Sylow
469C23—224no—
470C23—222no—
471C23—444no—
472C23—442no—
473C23—444no—
474C23—442no—
475C23—444no—
476C23—442no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—24no—
479Q8—28no—
480Q8—22no—
481Q8—48no—
482Q8C2×#434314yescomplemented
483D4—222no—
484D4—224no—
485D4—222no—
486D4—224no—
487D4—4416no—
488D4—442no—
489D4—444no—
490D4—448no—
491D4—888no—
492D4—884no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—222no—
503C2×C4—4416no—
504C2×C4—442no—
505C2×C4—448no—
506C2×C4#6700214yes—
507C2×C4C2×#434312yes—
508C2×C4#6704012yes—
509C2×C4C22×C22⋊D1114yes—
510C2×C4C22×C22⋊D1112yes—
511C2×C4C22×C22⋊D1114yes—
512C2×C4C22×C22⋊D1111yescharacteristic
513C2×C4C22×C22⋊D1112yes—
514C2×C4C24×D1111yescharacteristic
515C8—222no—
516C8—224no—
517C8—222no—
518C22—444no—
519C22—442no—
520C22—444no—
521C22—442no—
522C22—444no—
523C22—442no—
524C22—888no—
525C22—884no—
526C22#1062334812yes—
527C22C2×#6700212yes—
528C22#1062336812yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—24no—
531C4—24no—
532C4—24no—
533C4—22no—
534C4—44no—
535C4—42no—
536C4—442no—
537C4#1062334812yes—
538C4C2×#6700214yes—
539C4C22×#434311yescharacteristic
540C4C2×#6704011yescharacteristic
541C2—884no—
542C2—882no—
543C2#1308134514yesdirect product factor
544C2C2×#1062334811yescharacteristic
545C2C22×#6700211yescharacteristic
546C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×#557D11
hypocenterC11C2×#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081345C2direct (N × H)
3. C2×#10622680C2semidirect
4. C2×#10622701C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622640C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622639C2semidirect
11. C2×C4×#4325C2semidirect
12. C2×C11×#557C2semidirect
15. C11×#557C22semidirect
35. #10622701C22semidirect
36. #10622700C22semidirect
37. #10622680C22semidirect
38. #10622679C22semidirect
39. #10622640C22semidirect
40. #10622640C22semidirect
41. #10622639C22semidirect
42. C4×#4325C22semidirect
43. #10622637C22semidirect
135. C2×Q8×C11#41semidirect
196. C2×#557D11semidirect
221. Q8×C11C2×#41semidirect
261. #557C2×D11semidirect
393. C2×C11#3368semidirect
407. C2×Q8#4343semidirect
468. C11C2×#3368semidirect
482. Q8C2×#4343semidirect
543. C2#13081345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231082
#130813452
C2×#106226802
C2×#106227012
C2×#106226792
C2×#106227002
C2×#106226402
C2×#106226372
C2×#106226392
C2×C4×#43252
C2×C11×#5572
C2×#336811