Finite Group Databasebeta

← C2×#13081344 #15633471

Subgroups — C2×#13081344 #15633471

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×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081344C2116yesmaximal, direct product factor
4C2×#10622377C212yesmaximal, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622504C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622375C212yesmaximal, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×Q8×Dic11—21no—
17C2×#66997—21no—
18C2×#66993C2212yes—
19C22×#4324C2211yescharacteristic
20C2×#66983—21no—
21C22×#4314C2212yes—
22#10623252—24no—
23#10623252C2218yescomplemented
24#10623084—24no—
25#10623084C2218yes—
26C2×#66946C2212yes—
27C2×#66943C2212yes—
28C2×#66942—22no—
29C2×#66940C2212yes—
30C2×#66937—22no—
31C2×#66927C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#474C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66885C2212yes—
40C2×#66879C2212yes—
41C2×Dic11⋊C8C2212yes—
42#10622701C2218yescomplemented
43C4×#4324C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622504C22116yescomplemented
50#10622502C22116yescomplemented
51#10622461C2218yescomplemented
52#10622444C2218yescomplemented
53#10622377C22116yescomplemented
54#10622375C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×C4×D11—22no—
66C22×Dic22D411yescharacteristic
67C22×Dic22C2311yescharacteristic
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78Q8×Dic11—28no—
79#66997—28no—
80#66993—24no—
81#66993C2318yes—
82C2×#4324—24no—
83C2×#4324C2314yes—
84#66983—28no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4D412yes—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11C2312yes—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×#4314—28no—
99C2×#4314C2318yes—
100#66946—24no—
101#66946C2318yes—
102#66943—24no—
103#66943C2318yes—
104#66942—216no—
105#66940—24no—
106#66940C2318yes—
107#66937—216no—
108#66927—22no—
109#66927C2314yes—
110C4×Dic22—22no—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C4×Dic22C2314yes—
114C11×#107C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#102C2318yes—
117#66896C2314yes—
118#66885C2318yes—
119#66879C2318yes—
120Dic11⋊C8C2318yes—
121#66874C2314yes—
122#66873C2318yes—
123#66873C2318yes—
124#66872C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3368—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—44no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11C2412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—44no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—28no—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—84no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150#4339—432no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—44no—
157C2×D44—82no—
158C2×D44C2414yes—
159C2×C4×D11—28no—
160C2×C4×D11—48no—
161C2×Dic22—24no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22C2×D414yes—
165C2×Dic22#4114yescomplemented
166C2×Dic22C2412yes—
167C2×C8×C11—24no—
168C2×C8×C11C2414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2412yes—
173C11×C4⋊C4C2414yes—
174C11×C22⋊C4—24no—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177#4324—28no—
178(C2×D11)⋊C4—28no—
179C4⋊Dic11—28no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2412yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—24no—
186Dic11⋊C4C2×D418yes—
187C4×Dic11—28no—
188C4×Dic11—24no—
189C4×Dic11C2×D414yes—
190C4×Dic11C2414yes—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195#4314—216no—
196C2×#557—111no—
197C2×#550—111no—
198#3368—1116no—
199C2×#490—112no—
200C2×#486—111no—
201C2×#478—112no—
202C2×#474D1111yescharacteristic, complemented
203C2×#460—111no—
204C2×#460—112no—
205C2×#446—111no—
206C2×#440—112no—
207C2×C4×SD16—111no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—44no—
217Q8×C11—48no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—48no—
227C2×C4×C11AGL(1,ℤ/8)14yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C112−1+412yes—
233C2×C4×C11C2511yescharacteristic
234C22⋊D11—416no—
235C22⋊D11—88no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—42no—
242C2×Dic11C22×D414yes—
243C2×Dic11C22×D414yes—
244D44—24no—
245D44—24no—
246D44—44no—
247D44—48no—
248D44—84no—
249C4×D11—416no—
250Dic22—24no—
251Dic22—28no—
252Dic22—22no—
253Dic22C2×#4114yescomplemented
254C8×C11—24no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C22×#41—221no—
258C22×SD16—111no—
259C22×SD16—112no—
260#557—118no—
261#557—224no—
262#550—118no—
263#550—224no—
264C2×C4⋊Q8—221no—
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×#127—112no—
267C2×#127—111no—
268C2×#125—112no—
269C2×#125—222no—
270C2×#121—222no—
271C2×#121—221no—
272C2×C4×Q8—111no—
273C2×C4×Q8—112no—
274C2×C4×Q8—111no—
275C2×C4×Q8—221no—
276C2×C4×D4—112no—
277C2×C4×D4C2×D1111yescharacteristic
278#490—1116no—
279#486—118no—
280#478—1116no—
281#474C2×D1118yescomplemented
282#460—118no—
283#460—1116no—
284#446—118no—
285#440—1116no—
286C4×SD16—118no—
287C2×#107C2×D1112yes—
288C2×#106—111no—
289C2×C4⋊C8—112no—
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×#103—111no—
292C2×#102—111no—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102C2×D1112yes—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—84no—
303C22×C11#54812yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57712yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—88no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11#54812yes—
315C4×C11C2×AGL(1,ℤ/8)14yes—
316C4×C11C22×#4111yescharacteristic
317C4×C11C2×2−1+411yescharacteristic
318Dic11—24no—
319Dic11—24no—
320Dic11—24no—
321Dic11—42no—
322C2×#41—228no—
323C2×#41—448no—
324C22×Q8—21no—
325C22×Q8—111no—
326C22×Q8—111no—
327C22×D4—112no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4C22×D1111yescharacteristic
333C23×C4—21no—
334C23×C4—222no—
335C2×SD16—114no—
336C2×SD16—118no—
337C2×SD16—228no—
338C2×SD16—224no—
339C22×C8—111no—
340C22×C8—111no—
341C22×C8C22×D1112yes—
342C4⋊Q8—22no—
343C4⋊Q8—228no—
344C4⋊Q8C22×D1114yes—
345#127—118no—
346#127—114no—
347#127—224no—
348#127—222no—
349#125—118no—
350#125—224no—
351#125—2216no—
352#121—2216no—
353#121—228no—
354C4×Q8—114no—
355C4×Q8—114no—
356C4×Q8—118no—
357C4×Q8—114no—
358C4×Q8—224no—
359C4×Q8—228no—
360C4×Q8—222no—
361C4×D4—22no—
362C4×D4—118no—
363C4×D4—224no—
364C4×D4C22×D1114yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1112yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—222no—
377C2×C42—112no—
378C2×C42—222no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107C22×D1118yes—
382#106—114no—
383C4⋊C8—118no—
384C4⋊C8C22×D1114yes—
385#103—114no—
386#102—114no—
387#102—118no—
388#102—118no—
389#102—118no—
390#102C22×D1118yes—
391#97—118no—
392C4×C8—114no—
393C2×C11—82no—
394C2×C11#336814yescomplemented
395C2×C11C2×#54811yescharacteristic
396C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C11C2×#57711yescharacteristic
398D11—84no—
399C24—21no—
400C24—222no—
401#41—4432no—
402C2×Q8—24no—
403C2×Q8—44no—
404C2×Q8—114no—
405C2×Q8—114no—
406C2×Q8—112no—
407C2×Q8—224no—
408C2×Q8—221no—
409C2×Q8—222no—
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—114no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—222no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—224no—
421C2×D4—448no—
422C2×D4—444no—
423C2×D4—882no—
424C2×D4—884no—
425C2×D4C23×D1112yes—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—44no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—228no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—448no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—2216no—
440SD16—228no—
441C2×C8—24no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8C23×D1114yes—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—114no—
451C4⋊C4—118no—
452C4⋊C4—112no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—221no—
457C4⋊C4—224no—
458C4⋊C4C23×D1114yes—
459C4⋊C4C23×D1112yes—
460C22⋊C4—24no—
461C22⋊C4—228no—
462C42—114no—
463C42—114no—
464C42—228no—
465C42—224no—
466C42D4×D1112yes—
467C42C23×D1112yes—
468C11C2×#336811yescharacteristic, complemented, Sylow
469C23—22no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—224no—
474C23—444no—
475C23—444no—
476C23—444no—
477C23C2×D4×D1111yescharacteristic
478Q8—48no—
479Q8—114no—
480Q8—228no—
481Q8—224no—
482Q8—222no—
483D4—22no—
484D4—22no—
485D4—42no—
486D4—224no—
487D4—224no—
488D4—4416no—
489D4—448no—
490D4—444no—
491D4—884no—
492D4—888no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—48no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—4416no—
507C2×C4—442no—
508C2×C4#6696414yes—
509C2×C4C2×D4×D1112yes—
510C2×C4C2×D4×D1112yes—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6704012yes—
513C2×C4#41×D1112yes—
514C2×C4C24×D1111yescharacteristic
515C8—24no—
516C8—222no—
517C8—222no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—84no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—888no—
526C22#1062316412yes—
527C22C2×#6696412yes—
528C22#1062330912yes—
529C22C22×D4×D1111yescharacteristic
530C4—22no—
531C4—42no—
532C4—44no—
533C4—224no—
534C4—224no—
535C4—224no—
536C4—442no—
537C4#1062316412yes—
538C4C2×#6696414yes—
539C4C2×#6704011yescharacteristic
540C4C2×#41×D1111yescharacteristic
541C2—82no—
542C2—884no—
543C2#1308134414yesdirect product factor
544C2C2×#1062316411yescharacteristic
545C2C22×#6696411yescharacteristic
546C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#474D11
hypocenterC11C2×#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081344C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622502C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#474C2semidirect
23. #10623252C22semidirect
34. C11×#474C22semidirect
42. #10622701C22semidirect
43. C4×#4324C22semidirect
49. #10622504C22semidirect
50. #10622502C22semidirect
51. #10622461C22semidirect
52. #10622444C22semidirect
53. #10622377C22semidirect
54. #10622375C22semidirect
165. C2×Dic22#41semidirect
202. C2×#474D11semidirect
253. Dic22C2×#41semidirect
281. #474C2×D11semidirect
394. C2×C11#3368semidirect
468. C11C2×#3368semidirect
543. C2#13081344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106230842
#130813442
C2×#106223772
C2×#106227012
C2×#106225042
C2×#106224612
C2×#106223752
C2×#106224442
C2×#106225022
C2×C4×#43242
C2×C11×#4742
C2×#336811