Finite Group Databasebeta

← C2×#13081330 #15633444

Subgroups — C2×#13081330 #15633444

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic, complemented
2#13081330C2116yesmaximal, direct product factor
3C2×#10622668C212yesmaximal, complemented
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622634C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622670C212yesmaximal
8C2×#10622696C211yesmaximal, characteristic, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C11×#556—24no—
15C11×#556C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C22×#4325C2212yes—
25C22×#4323C2211yescharacteristic
26Q8×D44—24no—
27Q8×D44C2218yescomplemented
28C2×#66950—21no—
29C2×#66950—22no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×#66922C2211yescharacteristic
33C2×#66922C2212yes—
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39#10622696C2218yescomplemented
40#10622694C2218yescomplemented
41#10622670C22116yes—
42#10622668C22116yescomplemented
43#10622639C22116yescomplemented
44#10622637C2218yescomplemented
45#10622634C22116yescomplemented
46C4×#4323C2218yes—
47#10622620C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66871C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C2×Q8×D11—28no—
60C2×Q8×D11—48no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—21no—
64C22×Dic22—22no—
65C22×Dic22—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C11×#126—216no—
69C11×#124—24no—
70C11×#124C2318yes—
71C11×C22⋊Q8—28no—
72C4×Q8×C11—24no—
73C4×Q8×C11D414yes—
74C4×Q8×C11C2318yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C11×#117—28no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11—22no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×#4325—28no—
92C2×#4325C2318yes—
93C2×#4323—24no—
94C2×#4323C2314yes—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66950—28no—
105#66950—216no—
106C4×D44—22no—
107C4×D44—24no—
108C4×D44C2314yes—
109C4×D44C2318yes—
110#66922—22no—
111#66922—24no—
112#66922C2314yes—
113#66922C2318yes—
114#66899C2318yes—
115#66899C2318yes—
116#66899C2318yes—
117#66896C2318yes—
118#66896C2314yes—
119#66873C2314yes—
120#66871C2318yes—
121#66871C2314yes—
122C4⋊(C11⋊C8)C2314yes—
123C4⋊(C11⋊C8)C2318yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3367—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—24no—
133C2×Q8×C11C2×D414yes—
134C2×Q8×C11C2414yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—22no—
150Q8×D11—432no—
151C2×D44—21no—
152C2×D44—22no—
153C2×D44#4114yes—
154C2×D44C2412yes—
155C2×C4×D11—28no—
156C2×C4×D11—24no—
157C2×C4×D11—48no—
158C2×C4×D11—44no—
159C2×Dic22—28no—
160C2×Dic22—24no—
161C2×Dic22—48no—
162C2×Dic22—44no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2×D418yes—
169C11×C4⋊C4C2412yes—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—28no—
173C42×C11—28no—
174C42×C11C2×D412yes—
175C42×C11C2×D414yes—
176C42×C11C2412yes—
177C42×C11C2414yes—
178#4325—216no—
179#4323—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—24no—
182C4⋊Dic11—22no—
183C4⋊Dic11—21no—
184C4⋊Dic11—28no—
185C4⋊Dic11—24no—
186C4⋊Dic11C2414yes—
187C4⋊Dic11C2412yes—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8C2412yes—
192C2×C11⋊C8C2412yes—
193C2×C11⋊C8C2414yes—
194C2×#556D1111yescharacteristic, complemented
195C2×D4×Q8—111no—
196#3367—1116no—
197C2×#489—112no—
198C2×#487—111no—
199C2×#477—112no—
200C2×#474—111no—
201C2×#463—112no—
202C2×#461—111no—
203C2×#446—111no—
204C2×#440—112no—
205C2×C4×D8—111no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D411yescharacteristic
211C22×D11—24no—
212C22×D11—22no—
213C22×D11—42no—
214C22×D11—42no—
215Q8×C11—28no—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—44no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—48no—
230C2×C4×C11AGL(1,ℤ/8)14yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D414yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C112−1+412yes—
238C2×C4×C11C2511yescharacteristic
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—42no—
242C2×Dic11—44no—
243D44—24no—
244D44—22no—
245D44C2×#4114yes—
246C4×D11—416no—
247C4×D11—48no—
248Dic22—416no—
249Dic22—48no—
250C11⋊C8—22no—
251C11⋊C8—24no—
252C11⋊C8—22no—
253C23×Q8—221no—
254C22×SD16—112no—
255C22×D8—111no—
256#556—24no—
257#556C2×D1118yescomplemented
258D4×Q8—118no—
259D4×Q8—224no—
260C2×C4⋊Q8—112no—
261C2×C4⋊Q8—111no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263C2×#126—22no—
264C2×#124C2×D1112yes—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8—221no—
267C2×C22⋊Q8—222no—
268C2×C4×Q8C2×D1112yes—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4—112no—
272C2×C4×D4C2×D1111yescharacteristic
273C2×#117—21no—
274#489—1116no—
275#487—118no—
276#477—1116no—
277#474—118no—
278#463—1116no—
279#461—118no—
280#446—118no—
281#440—1116no—
282C4×D8—118no—
283C2×#107—111no—
284C2×#107—112no—
285C2×C4⋊C8—112no—
286C2×C4⋊C8—111no—
287C2×#103—112no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#102—111no—
291C2×#102—112no—
292C2×#102—111no—
293C2×#97—112no—
294C2×C4×C8—111no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11#54812yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—24no—
304C2×D11—48no—
305C2×D11—42no—
306C2×D11—42no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11#54812yes—
313C4×C11C2×AGL(1,ℤ/8)14yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×2−1+411yescharacteristic
316Dic11—42no—
317Dic11—44no—
318C22×Q8—228no—
319C22×Q8—222no—
320C22×Q8—221no—
321C22×Q8—448no—
322C22×Q8C22⋊D1111yescharacteristic
323C22×Q8C22×D1112yes—
324C22×D4—111no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—222no—
328C23×C4—221no—
329C2×SD16—118no—
330C2×SD16—228no—
331C2×D8—114no—
332C2×D8—224no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C4⋊Q8—22no—
337C4⋊Q8—114no—
338C4⋊Q8—118no—
339C4⋊Q8—222no—
340C4⋊Q8—224no—
341C4⋊Q8C22×D1114yes—
342#126—216no—
343#124—24no—
344#124C22×D1118yes—
345C22⋊Q8—28no—
346C22⋊Q8—228no—
347C22⋊Q8—2216no—
348C4×Q8—24no—
349C4×Q8C22⋊D1114yes—
350C4×Q8C22×D1118yes—
351C4×Q8C22×D1114yes—
352C4×D4—22no—
353C4×D4—114no—
354C4×D4—118no—
355C4×D4—222no—
356C4×D4—224no—
357C4×D4C22×D1114yes—
358#117—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1112yes—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—221no—
374C2×C42—22no—
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1112yes—
377#107—114no—
378#107—118no—
379C4⋊C8—114no—
380C4⋊C8—118no—
381#103—118no—
382#103—118no—
383#103—118no—
384#102—114no—
385#102—118no—
386#102—114no—
387#97—118no—
388C4×C8—114no—
389C2×C11—82no—
390C2×C11#336714yescomplemented
391C2×C11C2×#54811yescharacteristic
392C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C11C2×#57811yescharacteristic
394D11—44no—
395C24—21no—
396C24—221no—
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—228no—
402C2×Q8—224no—
403C2×Q8—448no—
404C2×Q8—4432no—
405C2×Q8—444no—
406C2×Q8C2×C22⋊D1114yes—
407C2×Q8C23×D1114yes—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—114no—
412C2×D4—112no—
413C2×D4—222no—
414C2×D4—221no—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—44no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—448no—
425C22×C4—444no—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—2216no—
432D8—228no—
433C2×C8—112no—
434C2×C8—112no—
435C2×C8—114no—
436C2×C8—222no—
437C2×C8—224no—
438C2×C8—222no—
439C4⋊C4—24no—
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—21no—
443C4⋊C4—112no—
444C4⋊C4—114no—
445C4⋊C4—221no—
446C4⋊C4—222no—
447C4⋊C4—228no—
448C4⋊C4—224no—
449C4⋊C4C2×C22⋊D1114yes—
450C4⋊C4C2×C22⋊D1118yes—
451C4⋊C4C23×D1112yes—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—28no—
455C22⋊C4—228no—
456C22⋊C4—224no—
457C42—28no—
458C42C2×C22⋊D1112yes—
459C42C2×C22⋊D1114yes—
460C42C23×D1112yes—
461C42C23×D1114yes—
462C11C2×#336711yescharacteristic, complemented, Sylow
463C23—22no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—224no—
468C23—222no—
469C23—442no—
470C23—442no—
471C23C22×C22⋊D1111yescharacteristic
472Q8—28no—
473Q8—24no—
474Q8—24no—
475Q8—44no—
476Q8—4416no—
477Q8—448no—
478D4—22no—
479D4—22no—
480D4—42no—
481D4—114no—
482D4—224no—
483D4—222no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—4416no—
495C2×C4—444no—
496C2×C4—442no—
497C2×C4—448no—
498C2×C4#6700214yes—
499C2×C4#41×D1112yes—
500C2×C4#6704312yes—
501C2×C4C22×C22⋊D1114yes—
502C2×C4C22×C22⋊D1112yes—
503C2×C4C22×C22⋊D1114yes—
504C2×C4C22×C22⋊D1112yes—
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C24×D1111yescharacteristic
507C8—222no—
508C8—224no—
509C8—222no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22—224no—
515C22—442no—
516C22—448no—
517C22—442no—
518C22C2×#6700212yes—
519C22#1062336212yes—
520C22#1062336912yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—24no—
523C4—24no—
524C4—22no—
525C4—42no—
526C4—44no—
527C4—444no—
528C4—442no—
529C4C2×#6700214yes—
530C4#1062336212yes—
531C4C2×#41×D1111yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—82no—
534C2—444no—
535C2#1308133014yesdirect product factor
536C2C2×#1062336211yescharacteristic
537C2C22×#6700211yescharacteristic
538C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#556D11
hypocenterC11C2×#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D44C2semidirect
2. #13081330C2direct (N × H)
3. C2×#10622668C2semidirect
4. C2×#10622694C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622620C2semidirect
8. C2×#10622696C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622639C2semidirect
12. C2×C11×#556C2semidirect
15. C11×#556C22semidirect
27. Q8×D44C22semidirect
39. #10622696C22semidirect
40. #10622694C22semidirect
42. #10622668C22semidirect
43. #10622639C22semidirect
44. #10622637C22semidirect
45. #10622634C22semidirect
47. #10622620C22semidirect
194. C2×#556D11semidirect
257. #556C2×D11semidirect
390. C2×C11#3367semidirect
462. C11C2×#3367semidirect
535. C2#13081330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130813302
C2×#106226682
C2×#106226942
C2×#106226342
C2×#106226202
C2×#106226702
C2×#106226962
C2×#106226372
C2×#106226392
C2×C4×#43232
C2×C11×#5562
C2×#336711