Finite Group Databasebeta

← C2×#13081310 #15633395

Subgroups — C2×#13081310 #15633395

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×#10623101C211yesmaximal, characteristic, complemented
3#13081310C2116yesmaximal, direct product factor
4C2×#10622413C212yesmaximal, complemented
5C2×#10622307C211yesmaximal, characteristic
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622504C212yesmaximal, complemented
8C2×#10622798C212yesmaximal, complemented
9C2×#10622640C211yesmaximal, characteristic
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622401C212yesmaximal, complemented
12C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4325C2212yes—
19#10623116—24no—
20#10623116C2218yes—
21#10623101—24no—
22#10623101C2218yescomplemented
23C2×#66947—22no—
24C2×#66946C2212yes—
25C2×#66943—22no—
26C2×#66943C2212yes—
27C2×#66928—21no—
28C2×#66927C2211yescharacteristic
29C2×C4×D44—21no—
30C2×#66922—21no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×Q16C2218yescomplemented
35C2×C11×#107C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40#10622798C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622640C2218yes—
46#10622633C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622504C22116yescomplemented
51#10622413C22116yescomplemented
52#10622401C22116yescomplemented
53#10622307C2218yes—
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×C4×D11—22no—
61C22×Dic22—21no—
62C22×Dic22D411yescharacteristic
63C2×C11×Q16—24no—
64C2×C11×Q16C2314yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C4×Q8×C11C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#67000—24no—
79#67000C2318yes—
80Q8×Dic11—24no—
81Q8×Dic11C2318yes—
82C2×#4325—28no—
83C2×#4325C2318yes—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4D412yes—
94C2×C4×Dic11—22no—
95C2×C4×Dic11C2312yes—
96C22×C11⋊C8C2312yes—
97#66947—216no—
98#66946—24no—
99#66946C2318yes—
100#66943—216no—
101#66943—24no—
102#66943C2318yes—
103#66928—28no—
104#66927—22no—
105#66927C2314yes—
106C4×D44—28no—
107#66922—28no—
108#66922—22no—
109#66922C2314yes—
110C4×Dic22—28no—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C11×#107C2314yes—
114C11×#103C2314yes—
115C11×#103C2314yes—
116C4×C8×C11C2314yes—
117#66899C2318yes—
118#66885C2318yes—
119#66885C2318yes—
120Dic11⋊C8C2318yes—
121C8×Dic11C2318yes—
122#66873C2318yes—
123#66872C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3365—111nomaximal, Sylow
126C23×D11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11#4114yes—
133C2×Q8×C11C2412yes—
134C2×Q8×C11C2412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—22no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C2×D44—24no—
146C2×D44—22no—
147C2×D44—24no—
148C2×D44—24no—
149C2×D44—24no—
150C2×D44—44no—
151C2×D44—82no—
152C2×D44C2414yes—
153C2×C4×D11—28no—
154C2×C4×D11—84no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22—44no—
158C2×Dic22C2×D414yes—
159C11×Q16—28no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11C2412yes—
163C2×C8×C11C2412yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4C2412yes—
169C11×C4⋊C4C2412yes—
170C42×C11—24no—
171C42×C11—24no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174#4325—216no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—28no—
179C4⋊Dic11—28no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11C2×D414yes—
183C4⋊Dic11C2414yes—
184Dic11⋊C4—28no—
185Dic11⋊C4C2×D418yes—
186C4×Dic11—28no—
187C4×Dic11C2×D414yes—
188C4×Dic11C2414yes—
189C2×C11⋊C8—24no—
190C2×C11⋊C8C2414yes—
191C2×#559—111no—
192C2×#557—111no—
193#3365—1116no—
194C2×#488—112no—
195C2×#486—111no—
196C2×#475—111no—
197C2×#478—112no—
198C2×#464—112no—
199C2×#460—111no—
200C2×C8×Q8—111no—
201C2×C4×Q16D1111yescharacteristic, complemented
202C2×C4×SD16—112no—
203C23×C11C22×D411yescharacteristic
204C22×D11—24no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—44no—
208Q8×C11—24no—
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213Q8×C11C2×#4114yes—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#13514yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—44no—
234C2×Dic11C22×D414yes—
235C2×Dic11C22×D414yes—
236D44—24no—
237D44—24no—
238D44—44no—
239D44—48no—
240D44—84no—
241C4×D11—88no—
242Dic22—28no—
243Dic22—48no—
244C8×C11—22no—
245C8×C11—22no—
246C11⋊C8—24no—
247C22×Q16C2×D1111yescharacteristic
248C22×SD16—112no—
249#559—118no—
250#559—224no—
251#557—118no—
252#557—224no—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8—221no—
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—221no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—112no—
267C2×C4×D4—221no—
268#488—1116no—
269#486—118no—
270#478—1116no—
271#475—118no—
272#464—1116no—
273#460—118no—
274C8×Q8—118no—
275C4×Q16C2×D1118yescomplemented
276C4×SD16—1116no—
277C2×#107C2×D1111yescharacteristic
278C2×#106—112no—
279C2×C4⋊C8—112no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103C2×D1111yescharacteristic
283C2×#103C2×D1111yescharacteristic
284C2×#102—112no—
285C2×#102—112no—
286C2×#102—112no—
287C2×C4×C8—112no—
288C2×C4×C8C2×D1111yescharacteristic
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—24no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11#54812yes—
303C4×C11C2×#13514yes—
304C4×C11C22×#4111yescharacteristic
305C4×C11C2×2−1+411yescharacteristic
306Dic11—24no—
307Dic11—24no—
308Dic11—44no—
309C22×Q8—111no—
310C22×Q8—221no—
311C22×Q8C22×D1111yescharacteristic
312C22×Q8C22×D1111yescharacteristic
313C22×D4—112no—
314C22×D4—221no—
315C22×D4—221no—
316C23×C4—222no—
317C2×Q16—24no—
318C2×Q16C22×D1114yes—
319C2×SD16—118no—
320C2×SD16—228no—
321C22×C8—112no—
322C22×C8C22×D1111yescharacteristic
323C22×C8C22×D1111yescharacteristic
324C4⋊Q8—114no—
325C4⋊Q8—228no—
326C4⋊Q8—222no—
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—22no—
338C4×Q8—114no—
339C4×Q8—114no—
340C4×Q8—118no—
341C4×Q8—228no—
342C4×Q8—224no—
343C4×Q8C22×D1114yes—
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—112no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—112no—
365C2×C42—222no—
366C2×C42C22×D1111yescharacteristic
367#107C22×D1114yes—
368#106—118no—
369C4⋊C8—118no—
370C4⋊C8—114no—
371#103—118no—
372#103C22×D1114yes—
373#103C22×D1114yes—
374#102—118no—
375#102—118no—
376#102—118no—
377C4×C8—118no—
378C4×C8C22×D1114yes—
379C2×C11#336514yescomplemented
380C2×C11C2×#54811yescharacteristic
381C2×C11C22×#13511yescharacteristic
382C2×C11C2×#57711yescharacteristic
383D11—84no—
384C24—222no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—114no—
391C2×Q8—224no—
392C2×Q8—224no—
393C2×Q8—444no—
394C2×Q8#433914yes—
395C2×Q8C23×D1112yes—
396C2×Q8C23×D1112yes—
397C2×D4—114no—
398C2×D4—224no—
399C2×D4—224no—
400C2×D4—222no—
401C2×D4—224no—
402C2×D4—224no—
403C2×D4—444no—
404C2×D4—882no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—228no—
412C22×C4—222no—
413C22×C4—884no—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417Q16—28no—
418SD16—2216no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—114no—
422C2×C8—224no—
423C2×C8C23×D1112yes—
424C2×C8C23×D1112yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—114no—
430C4⋊C4—118no—
431C4⋊C4—114no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—222no—
436C4⋊C4—224no—
437C4⋊C4C23×D1112yes—
438C4⋊C4C23×D1112yes—
439C22⋊C4—228no—
440C22⋊C4—228no—
441C22⋊C4—228no—
442C42—24no—
443C42—24no—
444C42—114no—
445C42—114no—
446C42—228no—
447C42D4×D1112yes—
448C42C23×D1112yes—
449C11C2×#336511yescharacteristic, complemented, Sylow
450C23—224no—
451C23—444no—
452C23—444no—
453C23—444no—
454C23C2×D4×D1111yescharacteristic
455Q8—24no—
456Q8—22no—
457Q8—22no—
458Q8—22no—
459Q8—42no—
460Q8—228no—
461Q8—448no—
462Q8C2×#433914yes—
463D4—224no—
464D4—224no—
465D4—448no—
466D4—444no—
467D4—884no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—114no—
478C2×C4—114no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—444no—
483C2×C4—888no—
484C2×C4#6697214yes—
485C2×C4C2×#433912yes—
486C2×C4C2×D4×D1112yes—
487C2×C4C2×D4×D1112yes—
488C2×C4C2×D4×D1111yescharacteristic
489C2×C4#6704312yes—
490C2×C4C24×D1111yescharacteristic
491C8—22no—
492C8—22no—
493C8—224no—
494C22—444no—
495C22—444no—
496C22—444no—
497C22—888no—
498C22#1062308312yes—
499C22C2×#6697212yes—
500C22#1062330112yes—
501C22C22×D4×D1111yescharacteristic
502C4—24no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—224no—
508C4—224no—
509C4—444no—
510C4#1062308312yes—
511C4C2×#6697214yes—
512C4C22×#433911yescharacteristic
513C4C2×#6704311yescharacteristic
514C2—884no—
515C2#1308131014yesdirect product factor
516C2C2×#1062308311yescharacteristic
517C2C22×#6697211yescharacteristic
518C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×C4×Q16D11
hypocenterC11C2×#3365
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#10623101C2semidirect
3. #13081310C2direct (N × H)
4. C2×#10622413C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622504C2semidirect
8. C2×#10622798C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622401C2semidirect
12. C2×C4×C11×Q16C2semidirect
22. #10623101C22semidirect
34. C4×C11×Q16C22semidirect
40. #10622798C22semidirect
46. #10622633C22semidirect
50. #10622504C22semidirect
51. #10622413C22semidirect
52. #10622401C22semidirect
54. C8×Dic22C22semidirect
201. C2×C4×Q16D11semidirect
275. C4×Q16C2×D11semidirect
379. C2×C11#3365semidirect
449. C11C2×#3365semidirect
515. C2#13081310direct (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×#106231012
#130813102
C2×#106224132
C2×#106223072
C2×#106226332
C2×#106225042
C2×#106227982
C2×#106226402
C2×C8×Dic222
C2×#106224012
C2×C4×C11×Q162
C2×#336511