Finite Group Databasebeta

← C2×#13081242 #15632523

Subgroups — C2×#13081242 #15632523

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2#13081242C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622580C212yesmaximal, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622697C211yesmaximal, characteristic, complemented
8C2×#10622662C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622577C212yesmaximal, complemented
12C2×C11×#554C211yesmaximal, characteristic, complemented
13C11×#554—24no—
14C11×#554C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C22×#4325C2211yescharacteristic
24C2×#66991—21no—
25C2×#66983C2212yes—
26C2×#66979C2212yes—
27C22×#4318C2212yes—
28#10623094—24no—
29#10623094C2218yes—
30C2×#66945—21no—
31C2×#66938—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622697C2218yescomplemented
38#10622691C2218yescomplemented
39#10622662C22116yescomplemented
40#10622658C22116yescomplemented
41C4×#4325C2218yescomplemented
42#10622634C2218yescomplemented
43#10622625C2218yescomplemented
44#10622580C22116yescomplemented
45C2×#66873C2212yes—
46C2×#66873C2211yescharacteristic
47#10622577C22116yescomplemented
48C2×#66872C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C22×C22⋊D11—22no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C11×#125—28no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—216no—
69C11×C22⋊Q8C2318yes—
70C4×Q8×C11—22no—
71C4×Q8×C11C2314yes—
72C4×D4×C11—28no—
73C4×D4×C11D414yes—
74C4×D4×C11C2314yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89C2×#4325—24no—
90C2×#4325C2314yes—
91#66991—28no—
92#66983—24no—
93#66983C2318yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96#66979—24no—
97#66979C2318yes—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4×Dic11—22no—
102C2×#4318—28no—
103C2×#4318C2318yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2311yescharacteristic
107#66945—28no—
108#66938—216no—
109C4×D44—22no—
110C4×D44C2314yes—
111#66922—22no—
112#66922C2314yes—
113#66899C2318yes—
114#66899C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66873C2314yes—
117#66873C2318yes—
118#66872C2314yes—
119#66872C2318yes—
120#66871C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3357—111nomaximal, Sylow
126C24×C11C2×D412yes—
127C23×D11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—82no—
133C2×Q8×C11C2412yes—
134C2×D4×C11—24no—
135C2×D4×C11C2×D414yes—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—28no—
142C22×C4×C11—84no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2414yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—28no—
150C2×C22⋊D11—84no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C2×D44—21no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44C2412yes—
157C2×C4×D11—24no—
158C2×C4×D11—44no—
159C2×Dic22—24no—
160C2×Dic22—82no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2412yes—
169C11×C4⋊C4C2414yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4C2×D418yes—
172C42×C11—24no—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C22⋊Dic11—28no—
176#4325—28no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—28no—
179C4⋊Dic11—22no—
180C4⋊Dic11—24no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2414yes—
183C4⋊Dic11C2412yes—
184C4×Dic11—28no—
185#4318—216no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8#4114yes—
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2414yes—
191C2×C11⋊C8C2412yes—
192C2×#555—111no—
193C2×#554D1111yescharacteristic, complemented
194#3357—1116no—
195C2×#500—111no—
196C2×#485—112no—
197C2×#480—112no—
198C2×#477—111no—
199C2×#476—111no—
200C2×#468—112no—
201C2×C4×SD16—111no—
202C2×#436—111no—
203C2×#428—112no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11C22×D414yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—84no—
217D4×C11—28no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—28no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11—88no—
230C2×C4×C11#13714yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C112−1+412yes—
237C2×C4×C11C2511yescharacteristic
238C22⋊D11—88no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—42no—
242C2×Dic11—44no—
243D44—22no—
244D44—22no—
245D44—42no—
246C4×D11—48no—
247Dic22—84no—
248C11⋊C8—24no—
249C11⋊C8—22no—
250C11⋊C8C2×#4114yes—
251C22×SD16—111no—
252C22×M16—112no—
253#555—118no—
254#555—224no—
255#554—24no—
256#554C2×D1118yescomplemented
257C2×C4⋊Q8—111no—
258C2×C4⋊Q8C2×D1111yescharacteristic
259C2×#125—21no—
260C2×#124—222no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8C2×D1112yes—
263C2×#121—112no—
264C2×#121—221no—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—21no—
267C2×C4×D4—111no—
268C2×C4×D4C2×D1111yescharacteristic
269C2×#117—112no—
270C2×#117—221no—
271C22×C4⋊C4C2×D1112yes—
272#500—118no—
273#485—1116no—
274#480—1116no—
275#477—118no—
276#476—118no—
277#468—1116no—
278C4×SD16—118no—
279#436—118no—
280#428—1116no—
281C2×#107—112no—
282C2×#107—112no—
283C2×#107—112no—
284C2×#106—112no—
285C2×#106—111no—
286C2×C4⋊C8—111no—
287C2×#103—112no—
288C2×#103—111no—
289C2×#102—111no—
290C2×#102—112no—
291C2×C22⋊C8—112no—
292C2×C4×C8—111no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—48no—
297C22×C11#54712yes—
298C22×C11C2×#13712yes—
299C22×C11#57612yes—
300C22×C11C23×D411yescharacteristic
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—84no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11#54712yes—
311C4×C11C2×#13714yes—
312C4×C11C22×#4111yescharacteristic
313C4×C11C2×2−1+411yescharacteristic
314Dic11—42no—
315Dic11—44no—
316C22×Q8—21no—
317C22×Q8—221no—
318C22×Q8C22×D1111yescharacteristic
319C22×D4—111no—
320C22×D4—222no—
321C22×D4C22⋊D1111yescharacteristic
322C23×C4—22no—
323C23×C4—221no—
324C23×C4C22×D1112yes—
325C2×SD16—114no—
326C2×SD16—224no—
327C2×M16—118no—
328C2×M16—228no—
329C22×C8—111no—
330C22×C8—112no—
331C22×C8—111no—
332C4⋊Q8—22no—
333C4⋊Q8—114no—
334C4⋊Q8—222no—
335C4⋊Q8C22×D1114yes—
336#125—28no—
337#124—2216no—
338C22⋊Q8—24no—
339C22⋊Q8—216no—
340C22⋊Q8C22×D1118yes—
341#121—118no—
342#121—228no—
343#121—224no—
344C4×Q8—22no—
345C4×Q8C22×D1114yes—
346C4×D4—28no—
347C4×D4—114no—
348C4×D4—222no—
349C4×D4C22⋊D1114yes—
350C4×D4C22×D1114yes—
351#117—118no—
352#117—224no—
353#117—228no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1118yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4C22⋊D1112yes—
371C2×C42—21no—
372C2×C42—222no—
373C2×C42C22×D1111yescharacteristic
374#107—118no—
375#107—118no—
376#107—118no—
377#106—114no—
378#106—118no—
379C4⋊C8—114no—
380#103—114no—
381#103—118no—
382#102—114no—
383#102—118no—
384C22⋊C8—118no—
385C4×C8—114no—
386C2×C11—44no—
387C2×C11#335714yescomplemented
388C2×C11C2×#54711yescharacteristic
389C2×C11C22×#13711yescharacteristic
390C2×C11C2×#57611yescharacteristic
391D11—82no—
392C24—221no—
393C24C2×C22⋊D1112yes—
394C2×Q8—21no—
395C2×Q8—24no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—82no—
399C2×Q8—224no—
400C2×Q8—882no—
401C2×Q8C23×D1112yes—
402C2×D4—24no—
403C2×D4—112no—
404C2×D4—228no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4—884no—
409C2×D4C2×C22⋊D1114yes—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—28no—
416C22×C4—84no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—444no—
421C22×C4C2×C22⋊D1114yes—
422C22×C4C2×C22⋊D1112yes—
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C23×D1114yes—
426C22×C4C23×D1111yescharacteristic
427SD16—228no—
428M16—2216no—
429C2×C8—114no—
430C2×C8—112no—
431C2×C8—112no—
432C2×C8—114no—
433C2×C8—224no—
434C2×C8—222no—
435C4⋊C4—21no—
436C4⋊C4—28no—
437C4⋊C4—22no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—28no—
441C4⋊C4—112no—
442C4⋊C4—114no—
443C4⋊C4—221no—
444C4⋊C4—222no—
445C4⋊C4—224no—
446C4⋊C4C2×C22⋊D1114yes—
447C4⋊C4C23×D1112yes—
448C4⋊C4C23×D1114yes—
449C22⋊C4—28no—
450C22⋊C4—228no—
451C22⋊C4—228no—
452C22⋊C4—224no—
453C22⋊C4C2×C22⋊D1118yes—
454C42—24no—
455C42—228no—
456C42C2×C22⋊D1112yes—
457C42C23×D1112yes—
458C11C2×#335711yescharacteristic, complemented, Sylow
459C23—24no—
460C23—24no—
461C23—24no—
462C23—222no—
463C23—442no—
464C23—442no—
465C23—442no—
466C23C22×C22⋊D1114yes—
467C23C22×C22⋊D1111yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—84no—
472Q8—884no—
473D4—28no—
474D4—222no—
475D4—222no—
476D4—442no—
477D4—888no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—28no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—88no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—442no—
493C2×C4—444no—
494C2×C4—448no—
495C2×C4#6699514yes—
496C2×C4#41×D1112yes—
497C2×C4#6704312yes—
498C2×C4C22×C22⋊D1114yes—
499C2×C4C22×C22⋊D1112yes—
500C2×C4C22×C22⋊D1112yes—
501C2×C4C22×C22⋊D1111yescharacteristic
502C2×C4C24×D1111yescharacteristic
503C8—114no—
504C8—224no—
505C8—222no—
506C22—24no—
507C22—24no—
508C22—24no—
509C22—48no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—884no—
514C22C2×#6699512yes—
515C22#1062335512yes—
516C22#1062336612yes—
517C22C23×C22⋊D1111yescharacteristic
518C4—24no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—44no—
523C4—442no—
524C4—444no—
525C4C2×#6699514yes—
526C4#1062335512yes—
527C4C2×#41×D1111yescharacteristic
528C4C2×#6704311yescharacteristic
529C2—44no—
530C2—882no—
531C2#1308124214yesdirect product factor
532C2C2×#1062335511yescharacteristic
533C2C22×#6699511yescharacteristic
534C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×#554D11
hypocenterC11C2×#3357
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13081242C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622634C2semidirect
7. C2×#10622697C2semidirect
8. C2×#10622662C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622577C2semidirect
12. C2×C11×#554C2semidirect
14. C11×#554C22semidirect
37. #10622697C22semidirect
38. #10622691C22semidirect
39. #10622662C22semidirect
40. #10622658C22semidirect
41. C4×#4325C22semidirect
42. #10622634C22semidirect
43. #10622625C22semidirect
44. #10622580C22semidirect
47. #10622577C22semidirect
193. C2×#554D11semidirect
256. #554C2×D11semidirect
387. C2×C11#3357semidirect
458. C11C2×#3357semidirect
531. C2#13081242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
#130812422
C2×#106226912
C2×#106226582
C2×#106225802
C2×#106226342
C2×#106226972
C2×#106226622
C2×C4×#43252
C2×#106226252
C2×#106225772
C2×C11×#5542
C2×#335711