Finite Group Databasebeta

← C2×#13081311 #15633396

Subgroups — C2×#13081311 #15633396

Order 2816.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×#10623252C211yesmaximal, characteristic, complemented
3#13081311C2116yesmaximal, direct product factor
4C2×#10622413C212yesmaximal, complemented
5C2×#10622701C211yesmaximal, characteristic
6C2×#10622484C212yesmaximal, complemented
7C2×#10622411C212yesmaximal, complemented
8C2×#10622461C211yesmaximal, characteristic
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4326C211yesmaximal, characteristic, complemented
11C2×#10622465C212yesmaximal, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2212yes—
16C2×Q8×Dic11—21no—
17C2×#66997—21no—
18C22×#4326C2211yescharacteristic
19C22×#4314C2212yes—
20#10623252—24no—
21#10623252C2218yescomplemented
22#10623116—24no—
23#10623116C2218yes—
24C2×#66947—22no—
25C2×#66946C2212yes—
26C2×#66943C2212yes—
27C2×#66942—22no—
28C2×#66940C2212yes—
29C2×#66928—21no—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#475C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66885C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622701C2218yes—
43C4×#4326C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622484C22116yescomplemented
50#10622465C22116yescomplemented
51#10622461C2218yes—
52#10622443C2218yescomplemented
53#10622413C22116yescomplemented
54#10622411C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×C4×D11—22no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C4×Q8×C11—22no—
67C4×Q8×C11C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74#67000—24no—
75#67000C2318yes—
76Q8×Dic11—28no—
77#66997—28no—
78C2×#4326—24no—
79C2×#4326C2314yes—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4D412yes—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4314—28no—
96C2×#4314C2318yes—
97#66947—216no—
98#66946—24no—
99#66946C2318yes—
100#66943—24no—
101#66943C2318yes—
102#66942—216no—
103#66940—24no—
104#66940C2318yes—
105#66928—28no—
106#66927—22no—
107#66927C2314yes—
108C4×D44—28no—
109C4×Dic22—22no—
110C4×Dic22D414yes—
111C4×Dic22C2314yes—
112C4×Dic22C2314yes—
113C11×#106C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#103C2318yes—
116#66899C2314yes—
117#66885C2318yes—
118Dic11⋊C8C2318yes—
119C8×Dic11C2318yes—
120#66874C2314yes—
121#66873C2318yes—
122#66873C2318yes—
123#66871C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3365—111nomaximal, Sylow
126C23×D11—22no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11C2412yes—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D412yes—
143C2×D44—24no—
144C2×D44—22no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—24no—
148C2×D44—44no—
149C2×D44—82no—
150C2×D44C2414yes—
151C2×C4×D11—28no—
152C2×C4×D11—84no—
153C2×Dic22—24no—
154C2×Dic22—21no—
155C2×Dic22—22no—
156C2×Dic22C2×D414yes—
157C2×Dic22#4114yes—
158C2×Dic22C2412yes—
159C2×C8×C11—24no—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4C2412yes—
166C11×C4⋊C4C2414yes—
167C42×C11—24no—
168C42×C11C2×D412yes—
169C42×C11C2412yes—
170#4326—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174C4⋊Dic11—28no—
175C4⋊Dic11—21no—
176C4⋊Dic11C2×D414yes—
177C4⋊Dic11C2412yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—24no—
181Dic11⋊C4C2×D418yes—
182C4×Dic11—28no—
183C4×Dic11—24no—
184C4×Dic11C2×D414yes—
185C4×Dic11C2414yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190#4314—216no—
191C2×#559—111no—
192C2×#557—111no—
193#3365—1116no—
194C2×#488—112no—
195C2×#486—111no—
196C2×#475D1111yescharacteristic, complemented
197C2×#478—112no—
198C2×#464—112no—
199C2×#460—111no—
200C2×C8×Q8—111no—
201C2×C4×Q16—111no—
202C2×C4×SD16—112no—
203C23×C11C22×D411yescharacteristic
204C22×D11—24no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—44no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11—48no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—42no—
219C2×C4×C11#13514yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D412yes—
223C2×C4×C11C2×#4112yes—
224C2×C4×C112−1+412yes—
225C2×C4×C11C2511yescharacteristic
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11C22×D414yes—
233C2×Dic11C22×D414yes—
234D44—24no—
235D44—24no—
236D44—44no—
237D44—48no—
238D44—84no—
239C4×D11—88no—
240Dic22—24no—
241Dic22—28no—
242Dic22—22no—
243Dic22C2×#4114yes—
244C8×C11—24no—
245C11⋊C8—22no—
246C11⋊C8—22no—
247C22×Q16—111no—
248C22×SD16—112no—
249#559—118no—
250#559—224no—
251#557—118no—
252#557—224no—
253C2×C4⋊Q8—221no—
254C2×C4⋊Q8C2×D1111yescharacteristic
255C2×#127—111no—
256C2×#125—112no—
257C2×#125—222no—
258C2×#124—112no—
259C2×#124—221no—
260C2×#123—222no—
261C2×C4×Q8—111no—
262C2×C4×Q8—112no—
263C2×C4×Q8—111no—
264C2×C4×Q8—221no—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—112no—
267C2×C4×D4—221no—
268#488—1116no—
269#486—118no—
270#478—1116no—
271#475C2×D1118yescomplemented
272#464—1116no—
273#460—118no—
274C8×Q8—118no—
275C4×Q16—118no—
276C4×SD16—1116no—
277C2×#107—111no—
278C2×#106C2×D1112yes—
279C2×C4⋊C8—112no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—111no—
282C2×#103—111no—
283C2×#103C2×D1112yes—
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×C4×C8—112no—
288C2×C4×C8—111no—
289C22×C11#54812yes—
290C22×C11C2×#13512yes—
291C22×C11#57712yes—
292C22×C11C23×D411yescharacteristic
293C2×D11—44no—
294C2×D11—44no—
295C2×D11—44no—
296C2×D11—88no—
297C4×C11—22no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11#54812yes—
302C4×C11C2×#13514yes—
303C4×C11C22×#4111yescharacteristic
304C4×C11C2×2−1+411yescharacteristic
305Dic11—24no—
306Dic11—24no—
307Dic11—24no—
308Dic11—42no—
309C22×Q8—21no—
310C22×Q8—111no—
311C22×Q8—111no—
312C22×Q8C22×D1111yescharacteristic
313C22×D4—112no—
314C22×D4—221no—
315C22×D4—221no—
316C23×C4—222no—
317C2×Q16—114no—
318C2×Q16—224no—
319C2×SD16—118no—
320C2×SD16—228no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8C22×D1112yes—
324C4⋊Q8—22no—
325C4⋊Q8—228no—
326C4⋊Q8C22×D1114yes—
327#127—114no—
328#127—222no—
329#125—118no—
330#125—224no—
331#125—2216no—
332#124—118no—
333#124—228no—
334#124—224no—
335#123—2216no—
336C4×Q8—22no—
337C4×Q8—114no—
338C4×Q8—114no—
339C4×Q8—118no—
340C4×Q8—114no—
341C4×Q8—224no—
342C4×Q8—228no—
343C4×Q8—222no—
344C4×Q8C22×D1114yes—
345C4×D4—118no—
346C4×D4—228no—
347C4×D4—224no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1112yes—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C42—21no—
363C2×C42—112no—
364C2×C42—222no—
365C2×C42—221no—
366C2×C42C22×D1111yescharacteristic
367#107—114no—
368#106C22×D1118yes—
369C4⋊C8—118no—
370C4⋊C8C22×D1114yes—
371#103—114no—
372#103—114no—
373#103C22×D1118yes—
374#102—118no—
375#102—118no—
376#102—118no—
377C4×C8—118no—
378C4×C8—114no—
379C2×C11#336514yescomplemented
380C2×C11C2×#54811yescharacteristic
381C2×C11C22×#13511yescharacteristic
382C2×C11C2×#57711yescharacteristic
383D11—84no—
384C24—222no—
385C2×Q8—21no—
386C2×Q8—24no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—44no—
390C2×Q8—114no—
391C2×Q8—114no—
392C2×Q8—112no—
393C2×Q8—224no—
394C2×Q8—221no—
395C2×Q8—222no—
396C2×Q8C23×D1112yes—
397C2×D4—114no—
398C2×D4—224no—
399C2×D4—222no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—444no—
404C2×D4—882no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—228no—
411C22×C4—221no—
412C22×C4—221no—
413C22×C4—884no—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417Q16—228no—
418SD16—2216no—
419C2×C8—24no—
420C2×C8—112no—
421C2×C8—112no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8C23×D1114yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—114no—
430C4⋊C4—118no—
431C4⋊C4—112no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—221no—
436C4⋊C4—224no—
437C4⋊C4C23×D1114yes—
438C4⋊C4C23×D1112yes—
439C22⋊C4—228no—
440C22⋊C4—228no—
441C22⋊C4—228no—
442C42—24no—
443C42—114no—
444C42—114no—
445C42—228no—
446C42—224no—
447C42D4×D1112yes—
448C42C23×D1112yes—
449C11C2×#336511yescharacteristic, complemented, Sylow
450C23—224no—
451C23—444no—
452C23—444no—
453C23—444no—
454C23C2×D4×D1111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—48no—
458Q8—42no—
459Q8—114no—
460Q8—228no—
461Q8—224no—
462Q8—222no—
463D4—224no—
464D4—224no—
465D4—448no—
466D4—444no—
467D4—884no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—114no—
476C2×C4—114no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—442no—
483C2×C4—888no—
484C2×C4#6696914yes—
485C2×C4C2×D4×D1112yes—
486C2×C4C2×D4×D1112yes—
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4#6704012yes—
489C2×C4#41×D1112yes—
490C2×C4C24×D1111yescharacteristic
491C8—24no—
492C8—222no—
493C8—222no—
494C22—444no—
495C22—444no—
496C22—444no—
497C22—888no—
498C22#1062316412yes—
499C22C2×#6696912yes—
500C22#1062330912yes—
501C22C22×D4×D1111yescharacteristic
502C4—22no—
503C4—44no—
504C4—42no—
505C4—42no—
506C4—224no—
507C4—224no—
508C4—224no—
509C4—442no—
510C4#1062316412yes—
511C4C2×#6696914yes—
512C4C2×#6704011yescharacteristic
513C4C2×#41×D1111yescharacteristic
514C2—884no—
515C2#1308131114yesdirect product factor
516C2C2×#1062316411yescharacteristic
517C2C22×#6696911yescharacteristic
518C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#475D11
hypocenterC11C2×#3365
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#10623252C2semidirect
3. #13081311C2direct (N × H)
4. C2×#10622413C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622411C2semidirect
9. C2×#10622443C2semidirect
10. C2×C4×#4326C2semidirect
11. C2×#10622465C2semidirect
12. C2×C11×#475C2semidirect
21. #10623252C22semidirect
34. C11×#475C22semidirect
43. C4×#4326C22semidirect
49. #10622484C22semidirect
50. #10622465C22semidirect
52. #10622443C22semidirect
53. #10622413C22semidirect
54. #10622411C22semidirect
196. C2×#475D11semidirect
271. #475C2×D11semidirect
379. C2×C11#3365semidirect
449. C11C2×#3365semidirect
515. C2#13081311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106232522
#130813112
C2×#106224132
C2×#106227012
C2×#106224842
C2×#106224112
C2×#106224612
C2×#106224432
C2×C4×#43262
C2×#106224652
C2×C11×#4752
C2×#336511