Finite Group Databasebeta

← C2×#13081236 #15632517

Subgroups — C2×#13081236 #15632517

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×#10623074C211yesmaximal, characteristic, complemented
2#13081236C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622646C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622655C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622608C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic
13C11×#555—24no—
14C11×#555C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×C11×#117C2212yes—
23C2×D4×Dic11—21no—
24C22×#4324C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C2×#66977C2212yes—
27C22×#4318C2212yes—
28#10623074—24no—
29#10623074C2218yescomplemented
30C2×#66943—21no—
31C2×#66931—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622704C2218yescomplemented
38#10622691C2218yescomplemented
39#10622655C22116yescomplemented
40#10622646C22116yescomplemented
41C4×#4324C2218yescomplemented
42#10622625C2218yescomplemented
43#10622621C2218yescomplemented
44#10622609C22116yescomplemented
45#10622608C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C23×Dic11—22no—
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C11×#124—216no—
67C11×#121—28no—
68C11×#121—24no—
69C11×#121C2318yes—
70C4×D4×C11—22no—
71C4×D4×C11D414yes—
72C4×D4×C11C2314yes—
73C4×D4×C11C2314yes—
74C11×#117—24no—
75C11×#117—28no—
76C11×#117C2318yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—22no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—22no—
88D4×Dic11—28no—
89C2×#4324—24no—
90C2×#4324C2314yes—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2318yes—
97#66977—24no—
98#66977C2318yes—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C2×#4318—28no—
103C2×#4318C2318yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2311yescharacteristic
107#66943—28no—
108#66931—216no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113#66896C2318yes—
114#66896C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66874C2314yes—
117#66874C2318yes—
118#66872C2314yes—
119#66872C2318yes—
120#66871C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3357—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D412yes—
128C2×Q8×C11—24no—
129C2×Q8×C11—82no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—84no—
136C2×D4×C11C2×D414yes—
137C2×D4×C11C2412yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—28no—
154C22×Dic11—84no—
155C2×Dic22—21no—
156C2×Dic22—24no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—82no—
160C2×Dic22C2412yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D414yes—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4C2×D418yes—
171C42×C11—28no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174C22⋊Dic11—28no—
175#4324—28no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—28no—
180C4⋊Dic11C2412yes—
181C4⋊Dic11C2414yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—28no—
184C4×Dic11—24no—
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×#555D1111yescharacteristic
193C2×#554—111no—
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×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D414yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—84no—
214D4×C11—28no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—88no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—28no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11#13714yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C112−1+412yes—
236C2×C4×C11C2511yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11—88no—
244Dic22—22no—
245Dic22—22no—
246Dic22—42no—
247Dic22—84no—
248C11⋊C8—24no—
249C11⋊C8—22no—
250C11⋊C8C2×#4114yes—
251C22×SD16—111no—
252C22×M16—112no—
253#555—24no—
254#555C2×D1118yes—
255#554—118no—
256#554—224no—
257C2×C4⋊Q8—111no—
258C2×C4⋊Q8C2×D1111yescharacteristic
259C2×#125—221no—
260C2×#124—22no—
261C2×C22⋊Q8—112no—
262C2×C22⋊Q8—222no—
263C2×#121—21no—
264C2×#121C2×D1112yes—
265C2×C4×Q8—111no—
266C2×C4×D4—221no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×C4×D4C2×D1111yescharacteristic
269C2×#117—21no—
270C2×#117C2×D1112yes—
271C22×C4⋊C4—112no—
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—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11#54712yes—
302C22×C11C2×#13712yes—
303C22×C11#57612yes—
304C22×C11C23×D411yescharacteristic
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11#54712yes—
310C4×C11C2×#13714yes—
311C4×C11C22×#4111yescharacteristic
312C4×C11C2×2−1+411yescharacteristic
313Dic11—42no—
314Dic11—44no—
315Dic11—42no—
316C22×Q8—21no—
317C22×Q8—111no—
318C22×Q8—221no—
319C22×D4—22no—
320C22×D4C22⋊D1111yescharacteristic
321C22×D4C22×D1111yescharacteristic
322C23×C4—21no—
323C23×C4—222no—
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—228no—
337#124—216no—
338C22⋊Q8—118no—
339C22⋊Q8—224no—
340C22⋊Q8—2216no—
341#121—28no—
342#121—24no—
343#121C22×D1118yes—
344C4×Q8—114no—
345C4×Q8—222no—
346C4×D4—22no—
347C4×D4—228no—
348C4×D4C22⋊D1114yes—
349C4×D4C22×D1114yes—
350C4×D4C22×D1114yes—
351#117—24no—
352#117—28no—
353#117C22×D1118yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4C22⋊D1112yes—
371C2×C42—22no—
372C2×C42—221no—
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—82no—
388C2×C11#335714yescomplemented
389C2×C11C2×#54711yescharacteristic
390C2×C11C22×#13711yescharacteristic
391C2×C11C2×#57611yescharacteristic
392C24—21no—
393C24C2×C22⋊D1112yes—
394C2×Q8—24no—
395C2×Q8—82no—
396C2×Q8—112no—
397C2×Q8—221no—
398C2×Q8—224no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—882no—
402C2×D4—28no—
403C2×D4—24no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—84no—
408C2×D4C2×C22⋊D1114yes—
409C2×D4C23×D1112yes—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—44no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—228no—
420C22×C4—884no—
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—24no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—112no—
439C4⋊C4—114no—
440C4⋊C4—221no—
441C4⋊C4—228no—
442C4⋊C4—222no—
443C4⋊C4—224no—
444C4⋊C4—224no—
445C4⋊C4—228no—
446C4⋊C4C2×C22⋊D1114yes—
447C4⋊C4C23×D1112yes—
448C4⋊C4C23×D1114yes—
449C22⋊C4—28no—
450C22⋊C4—28no—
451C22⋊C4—24no—
452C22⋊C4—228no—
453C22⋊C4C2×C22⋊D1118yes—
454C42—28no—
455C42—224no—
456C42C2×C22⋊D1112yes—
457C42C23×D1112yes—
458C11C2×#335711yescharacteristic, complemented, Sylow
459C23—24no—
460C23—24no—
461C23—24no—
462C23—22no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23C22×C22⋊D1114yes—
467C23C22×C22⋊D1111yescharacteristic
468Q8—84no—
469Q8—222no—
470Q8—222no—
471Q8—442no—
472Q8—884no—
473D4—28no—
474D4—22no—
475D4—22no—
476D4—42no—
477D4—88no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—28no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—48no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—224no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—444no—
494C2×C4—888no—
495C2×C4#6700414yes—
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—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22C2×#6700412yes—
515C22#1062335512yes—
516C22#1062336612yes—
517C22C23×C22⋊D1111yescharacteristic
518C4—24no—
519C4—22no—
520C4—42no—
521C4—44no—
522C4—442no—
523C4—442no—
524C4—444no—
525C4C2×#6700414yes—
526C4#1062335512yes—
527C4C2×#41×D1111yescharacteristic
528C4C2×#6704311yescharacteristic
529C2—44no—
530C2—82no—
531C2#1308123614yesdirect product factor
532C2C2×#1062335511yescharacteristic
533C2C22×#6700411yescharacteristic
534C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3357
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13081236C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622621C2semidirect
8. C2×#10622655C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622608C2semidirect
29. #10623074C22semidirect
37. #10622704C22semidirect
38. #10622691C22semidirect
39. #10622655C22semidirect
40. #10622646C22semidirect
41. C4×#4324C22semidirect
42. #10622625C22semidirect
43. #10622621C22semidirect
44. #10622609C22semidirect
45. #10622608C22semidirect
388. C2×C11#3357semidirect
458. C11C2×#3357semidirect
531. C2#13081236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130812362
C2×#106226912
C2×#106226092
C2×#106226462
C2×#106227042
C2×#106226212
C2×#106226552
C2×C4×#43242
C2×#106226252
C2×#106226082
C2×C11×#5552
C2×#335711