Finite Group Databasebeta

← C2×#13080970 #15632193

Subgroups — C2×#13080970 #15632193

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic
3#13080970C2116yesmaximal, direct product factor
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622390C212yesmaximal, complemented
6C2×#10622475C212yesmaximal, complemented
7C2×#10622464C211yesmaximal, characteristic, complemented
8C2×#10622391C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×D11×#106C212yesmaximal, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999—22no—
17C2×#66991C2212yes—
18C22×#4324C2211yescharacteristic
19C2×#66977—21no—
20C22×C8×D11C2212yes—
21#10623261—24no—
22#10623261C2218yescomplemented
23#10623082—24no—
24#10623082C2218yes—
25C2×#66950C2212yes—
26C2×#66946—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66943—21no—
30C2×#66936—22no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#476C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66881C2212yes—
41C2×#66880C2212yes—
42#10622692C2218yescomplemented
43C4×#4324C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622475C22116yescomplemented
50D11×#106C22116yescomplemented
51#10622464C2218yescomplemented
52#10622447C2218yescomplemented
53#10622391C22116yescomplemented
54#10622390C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4339—28no—
60C2×#4339—48no—
61C22×D44D411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11C2312yes—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C4×D4×C11—22no—
71C4×D4×C11C2314yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78#66999—216no—
79#66991—24no—
80#66991C2318yes—
81C2×#4324—24no—
82C2×#4324C2314yes—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4D412yes—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90#66977—28no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—28no—
98C2×C8×D11C2318yes—
99#66950—24no—
100#66950C2318yes—
101#66946—28no—
102C4⋊C4×D11—24no—
103C4⋊C4×D11—24no—
104C4⋊C4×D11C2318yes—
105C4⋊C4×D11C2318yes—
106#66943—28no—
107#66936—216no—
108C4×D44D414yes—
109C4×D44C2314yes—
110#66922—22no—
111#66922C2314yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#102C2318yes—
117#66896C2314yes—
118(C2×D11)⋊C8C2318yes—
119#66881C2318yes—
120#66880C2318yes—
121#66874C2314yes—
122#66872C2314yes—
123#66872C2318yes—
124#66872C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3335—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D412yes—
129C2×Q8×C11—24no—
130C2×Q8×C11—82no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11C2412yes—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
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—48no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11C2×D412yes—
148#4339—432no—
149C2×D44SD1618yescomplemented
150C2×D44C2×D414yes—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—48no—
156C2×C4×D11—84no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2414yes—
159C2×Dic22—21no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—44no—
164C2×Dic22C2412yes—
165C2×C8×C11—24no—
166C2×C8×C11C2414yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4C2414yes—
171C11×C4⋊C4C2412yes—
172C11×C22⋊C4—24no—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C22⋊Dic11—28no—
176#4324—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4C2×D418yes—
179C4⋊Dic11—28no—
180C4⋊Dic11—21no—
181C4⋊Dic11—22no—
182C4⋊Dic11—24no—
183C4⋊Dic11C2×D414yes—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—24no—
189C4×Dic11—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8#4114yescomplemented
192C2×C11⋊C8C2412yes—
193C2×C11⋊C8C2412yes—
194C8×D11—216no—
195C2×#554—111no—
196C2×#547—111no—
197#3335—1116no—
198C2×#498—111no—
199C2×#481—112no—
200C2×#483—112no—
201C2×#475—111no—
202C2×#476D1111yescharacteristic, complemented
203C2×#465—112no—
204C2×C4×SD16—111no—
205C2×C8×D4—111no—
206C22×#106—112no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—24no—
214C22×D11C2×SD1618yes—
215C22×D11C22×D414yes—
216Q8×C11—84no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—42no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—48no—
226C2×C4×C11C2×SD1614yes—
227C2×C4×C11C22×D412yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D412yes—
230C2×C4×C11C2×#4112yes—
231C2×C4×C112−1+412yes—
232C2×C4×C11C2511yescharacteristic
233C22⋊D11—416no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11C22×D414yes—
242D44C2×SD16116yescomplemented
243C4×D11—28no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—416no—
247C4×D11—88no—
248Dic22—22no—
249Dic22—22no—
250Dic22—42no—
251Dic22—48no—
252C8×C11—24no—
253C11⋊C8—22no—
254C11⋊C8C2×#4114yescomplemented
255C22×#41—221no—
256C22×SD16—111no—
257C23×C8—112no—
258#554—118no—
259#554—224no—
260#547—118no—
261#547—224no—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#125—221no—
265C2×#123—222no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—222no—
268C2×C22⋊Q8—221no—
269C2×#121—112no—
270C2×C4×Q8—111no—
271C2×C4×D4—111no—
272C2×C4×D4—221no—
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275C22×C4⋊C4—112no—
276#498—118no—
277#483—1116no—
278#481—1116no—
279#476C2×D1118yescomplemented
280#475—118no—
281#465—1116no—
282C4×SD16—118no—
283C8×D4—118no—
284C2×#106—112no—
285C2×#106—112no—
286C2×#106—112no—
287C2×#106—111no—
288C2×#106—1116no—
289C2×#106C2×D1112yes—
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×#103—112no—
292C2×#103—111no—
293C2×#102—111no—
294C2×#102C2×D1112yes—
295C2×C22⋊C8—112no—
296C2×C4×C8—111no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11#54712yes—
302C22×C11C22×SD1612yes—
303C22×C11#57712yes—
304C22×C11C23×D411yescharacteristic
305C2×D11—216no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11C22×SD1618yes—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11#54712yes—
313C4×C11C22×SD1614yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×2−1+411yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—44no—
319Dic11—42no—
320C2×#41—228no—
321C2×#41—448no—
322C22×Q8—21no—
323C22×Q8—111no—
324C22×Q8—221no—
325C22×D4—111no—
326C22×D4—222no—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4—112no—
330C23×C4—222no—
331C23×C4—222no—
332C2×SD16—114no—
333C2×SD16—224no—
334C22×C8—111no—
335C22×C8—111no—
336C22×C8—118no—
337C22×C8—228no—
338C22×C8C22×D1112yes—
339C4⋊Q8—22no—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342C4⋊Q8C22×D1114yes—
343#125—228no—
344#123—2216no—
345C22⋊Q8—118no—
346C22⋊Q8—2216no—
347C22⋊Q8—224no—
348C22⋊Q8—228no—
349#121—118no—
350#121—224no—
351C4×Q8—114no—
352C4×Q8—222no—
353C4×D4—22no—
354C4×D4—114no—
355C4×D4—114no—
356C4×D4—228no—
357C4×D4C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#106—118no—
380#106—114no—
381#106—118no—
382#106—118no—
383#106C22×D1118yes—
384C4⋊C8C22×D1114yes—
385#103—118no—
386#103—114no—
387#102—114no—
388#102C22×D1118yes—
389C22⋊C8—118no—
390C4×C8—114no—
391C2×C11—82no—
392C2×C11#333514yescomplemented
393C2×C11C2×#54711yescharacteristic
394C2×C11C23×SD1611yescharacteristic
395C2×C11C2×#57711yescharacteristic
396D11—28no—
397C24—21no—
398C24—112no—
399#41—4432no—
400C2×Q8—24no—
401C2×Q8—82no—
402C2×Q8—112no—
403C2×Q8—221no—
404C2×Q8—224no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—444no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—118no—
412C2×D4—114no—
413C2×D4—228no—
414C2×D4—448no—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—44no—
420C22×C4—112no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—228no—
424C22×C4—228no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—448no—
431C22×C4—884no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435SD16—228no—
436C2×C8—24no—
437C2×C8—114no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—2216no—
441C2×C8—222no—
442C2×C8C23×D1114yes—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—114no—
447C4⋊C4—112no—
448C4⋊C4—114no—
449C4⋊C4—228no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4C23×D1114yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—24no—
459C22⋊C4—118no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C42—224no—
463C42D4×D1112yes—
464C42C23×D1112yes—
465C11C2×#333511yescharacteristic, complemented, Sylow
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—118no—
471C23—114no—
472C23—224no—
473C23—224no—
474C23C2×D4×D1111yescharacteristic
475Q8—84no—
476Q8—222no—
477Q8—222no—
478Q8—448no—
479Q8—442no—
480D4—22no—
481D4—22no—
482D4—42no—
483D4—1116no—
484D4—4416no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—48no—
491C2×C4—114no—
492C2×C4—224no—
493C2×C4—228no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—4416no—
500C2×C4—444no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—888no—
504C2×C4SD16×D1114yes—
505C2×C4C2×D4×D1112yes—
506C2×C4C2×D4×D1112yes—
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4#6704012yes—
509C2×C4#41×D1112yes—
510C2×C4C24×D1111yescharacteristic
511C8—24no—
512C8—114no—
513C8—222no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22—118no—
519C22—2216no—
520C22—224no—
521C22—224no—
522C22#1062316212yes—
523C22C2×SD16×D1112yes—
524C22#1062330612yes—
525C22C22×D4×D1111yescharacteristic
526C4—22no—
527C4—42no—
528C4—44no—
529C4—224no—
530C4—444no—
531C4—442no—
532C4—442no—
533C4#1062316212yes—
534C4C2×SD16×D1114yes—
535C4C2×#6704011yescharacteristic
536C4C2×#41×D1111yescharacteristic
537C2—82no—
538C2—228no—
539C2#1308097014yesdirect product factor
540C2C2×#1062316211yescharacteristic
541C2C22×SD16×D1111yescharacteristic
542C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
hypercenterC2×#476D11
hypocenterC11C2×#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13080970C2direct (N × H)
4. C2×#10622692C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622475C2semidirect
7. C2×#10622464C2semidirect
8. C2×#10622391C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622447C2semidirect
11. C2×D11×#106C2semidirect
12. C2×C11×#476C2semidirect
22. #10623261C22semidirect
34. C11×#476C22semidirect
42. #10622692C22semidirect
43. C4×#4324C22semidirect
49. #10622475C22semidirect
50. D11×#106C22semidirect
51. #10622464C22semidirect
52. #10622447C22semidirect
53. #10622391C22semidirect
54. #10622390C22semidirect
149. C2×D44SD16semidirect
191. C2×C11⋊C8#41semidirect
202. C2×#476D11semidirect
242. D44C2×SD16semidirect
254. C11⋊C8C2×#41semidirect
279. #476C2×D11semidirect
392. C2×C11#3335semidirect
465. C11C2×#3335semidirect
539. C2#13080970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106230822
#130809702
C2×#106226922
C2×#106223902
C2×#106224752
C2×#106224642
C2×#106223912
C2×C4×#43242
C2×#106224472
C2×D11×#1062
C2×C11×#4762
C2×#333511