Finite Group Databasebeta

← C2×#13081233 #15632513

Subgroups — C2×#13081233 #15632513

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10623110C211yesmaximal, characteristic
3#13081233C2116yesmaximal, direct product factor
4C2×#10622293C211yesmaximal, characteristic, complemented
5C2×#10622428C212yesmaximal, complemented
6C2×#10622418C212yesmaximal, complemented
7C2×#10622634C211yesmaximal, characteristic, complemented
8C2×#10622633C211yesmaximal, characteristic, complemented
9C2×#10622802C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic
11C2×#10622494C212yesmaximal, complemented
12C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999C2212yes—
17C2×#66999C2212yes—
18C22×#4313C2212yes—
19#10623115—24no—
20#10623115C2218yes—
21#10623110—24no—
22#10623110C2218yes—
23C2×#66951—22no—
24C2×#66949—22no—
25C2×#66945C2212yes—
26C2×C4⋊C4×D11C2212yes—
27C2×#66928—21no—
28C2×C4×D44—21no—
29C2×C4×D44C2211yescharacteristic
30C2×#66923—21no—
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22—21no—
34C4×C11×Q16C2218yescomplemented
35C2×C11×#107C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41#10622802C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66881C2212yes—
44C2×#66881C2212yes—
45#10622634C2218yescomplemented
46#10622633C2218yescomplemented
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622494C22116yescomplemented
51#10622428C22116yescomplemented
52#10622418C22116yescomplemented
53#10622301C2218yes—
54#10622293C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D44D411yescharacteristic
58C22×C4×D11—22no—
59C22×C4×D11C2312yes—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C2×C11×Q16—24no—
63C2×C11×Q16C2314yes—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11C2314yes—
69C4×Q8×C11C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#66999—24no—
78#66999—24no—
79#66999C2318yes—
80#66999C2318yes—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4D412yes—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×C4×Dic11—22no—
94C22×C11⋊C8C2312yes—
95C2×#4313—28no—
96C2×#4313C2318yes—
97#66951—216no—
98#66949—216no—
99#66945—24no—
100#66945C2318yes—
101C4⋊C4×D11—24no—
102C4⋊C4×D11C2318yes—
103#66928—28no—
104C4×D44—28no—
105C4×D44D414yes—
106C4×D44C2314yes—
107#66923—28no—
108#66922—22no—
109#66922—22no—
110#66922C2314yes—
111#66922C2314yes—
112C4×Dic22—28no—
113C11×#107C2314yes—
114C11×#103C2314yes—
115C11×#103C2314yes—
116C4×C8×C11C2314yes—
117#66899C2318yes—
118#66899C2318yes—
119(C2×D11)⋊C8C2318yes—
120#66881C2318yes—
121#66881C2318yes—
122#66872C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3356—111nomaximal, Sylow
126C23×D11C2×D412yes—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
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×Dic11—22no—
144C22×Dic11C2×D412yes—
145C2×D44—24no—
146C2×D44C2×D414yes—
147C2×C4×D11—28no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—84no—
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2414yes—
153C2×Dic22—24no—
154C2×Dic22—24no—
155C2×Dic22—44no—
156C2×Dic22—82no—
157C11×Q16—28no—
158C2×C8×C11—22no—
159C2×C8×C11#4114yes—
160C2×C8×C11C2412yes—
161C2×C8×C11C2412yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4C2412yes—
167C11×C4⋊C4C2412yes—
168C42×C11—24no—
169C42×C11—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4C2×D418yes—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11C2×D414yes—
181C4⋊Dic11C2414yes—
182C4⋊Dic11C2414yes—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186C4×Dic11—28no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8C2414yes—
189#4313—216no—
190C2×#556—111no—
191C2×#554—111no—
192#3356—1116no—
193C2×#498—111no—
194C2×#485—112no—
195C2×#483—112no—
196C2×#477—111no—
197C2×#475—111no—
198C2×#470—112no—
199C2×C4×Q16D1111yescharacteristic, complemented
200C2×#436—111no—
201C2×#428—112no—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11C22×D414yes—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—42no—
212Q8×C11—42no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11#13714yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C112−1+412yes—
228C2×C4×C11C2511yescharacteristic
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—44no—
233C2×Dic11—44no—
234C2×Dic11C22×D414yes—
235D44—28no—
236C4×D11—28no—
237C4×D11—24no—
238C4×D11—24no—
239C4×D11—88no—
240Dic22—48no—
241Dic22—84no—
242C8×C11—22no—
243C8×C11C2×#4114yes—
244C11⋊C8—24no—
245C22×Q16C2×D1111yescharacteristic
246C22×M16—112no—
247#556—118no—
248#556—224no—
249#554—118no—
250#554—224no—
251C2×C4⋊Q8—111no—
252C2×C4⋊Q8—111no—
253C2×#126—222no—
254C2×#125—221no—
255C2×#124—221no—
256C2×C22⋊Q8—112no—
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8—222no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—111no—
263C2×C4×D4—221no—
264C2×#117—112no—
265C22×C4⋊C4—112no—
266#498—118no—
267#485—1116no—
268#483—1116no—
269#477—118no—
270#475—118no—
271#470—1116no—
272C4×Q16C2×D1118yescomplemented
273#436—118no—
274#428—1116no—
275C2×#107—112no—
276C2×#107C2×D1111yescharacteristic
277C2×#106—112no—
278C2×#106—112no—
279C2×#106—112no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103C2×D1111yescharacteristic
284C2×#103C2×D1111yescharacteristic
285C2×C22⋊C8—112no—
286C2×C4×C8C2×D1111yescharacteristic
287C22×C11#54712yes—
288C22×C11C2×#13712yes—
289C22×C11#57712yes—
290C22×C11C23×D411yescharacteristic
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—48no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11#54712yes—
301C4×C11C2×#13714yes—
302C4×C11C22×#4111yescharacteristic
303C4×C11C2×2−1+411yescharacteristic
304Dic11—24no—
305Dic11—44no—
306Dic11—44no—
307C22×Q8—221no—
308C22×Q8—221no—
309C22×Q8C22×D1111yescharacteristic
310C22×Q8C22×D1111yescharacteristic
311C22×D4—111no—
312C23×C4—112no—
313C23×C4—222no—
314C2×Q16—24no—
315C2×Q16C22×D1114yes—
316C2×M16—118no—
317C2×M16—228no—
318C22×C8—112no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—114no—
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324C4⋊Q8—222no—
325#126—2216no—
326#125—228no—
327#124—228no—
328C22⋊Q8—118no—
329C22⋊Q8—118no—
330C22⋊Q8—2216no—
331C22⋊Q8—224no—
332C22⋊Q8—224no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—228no—
336C4×Q8C22×D1114yes—
337C4×Q8C22×D1114yes—
338C4×D4—114no—
339C4×D4—114no—
340C4×D4—228no—
341#117—118no—
342#117—224no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C22⋊C4—112no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—222no—
364C2×C42C22×D1111yescharacteristic
365#107—118no—
366#107C22×D1114yes—
367#106—118no—
368#106—118no—
369#106—118no—
370C4⋊C8—114no—
371#103—118no—
372#103—118no—
373#103C22×D1114yes—
374#103C22×D1114yes—
375C22⋊C8—118no—
376C4×C8C22×D1114yes—
377C2×C11#335614yescomplemented
378C2×C11C2×#54711yescharacteristic
379C2×C11C22×#13711yescharacteristic
380C2×C11C2×#57711yescharacteristic
381D11—44no—
382C24—112no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—224no—
390C2×Q8—224no—
391C2×Q8—444no—
392C2×Q8—882no—
393C2×Q8C23×D1112yes—
394C2×Q8C23×D1112yes—
395C2×D4—114no—
396C2×D4—224no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—228no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—884no—
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413Q16—28no—
414M16—2216no—
415C2×C8—22no—
416C2×C8—114no—
417C2×C8—224no—
418C2×C8#433914yes—
419C2×C8C23×D1112yes—
420C2×C8C23×D1112yes—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—114no—
426C4⋊C4—114no—
427C4⋊C4—114no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—228no—
431C4⋊C4—222no—
432C4⋊C4—222no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4C23×D1112yes—
436C4⋊C4C23×D1112yes—
437C22⋊C4—118no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C22⋊C4—228no—
441C42—24no—
442C42—24no—
443C42—228no—
444C42D4×D1112yes—
445C42C23×D1112yes—
446C11C2×#335611yescharacteristic, complemented, Sylow
447C23—114no—
448C23—224no—
449C23—224no—
450C23—224no—
451C23C2×D4×D1111yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—22no—
455Q8—22no—
456Q8—42no—
457Q8—42no—
458Q8—448no—
459Q8—884no—
460D4—228no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—114no—
471C2×C4—224no—
472C2×C4—228no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—444no—
478C2×C4—444no—
479C2×C4—888no—
480C2×C4#6697114yes—
481C2×C4C2×#433912yes—
482C2×C4C2×D4×D1112yes—
483C2×C4C2×D4×D1112yes—
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4#6704312yes—
486C2×C4C24×D1111yescharacteristic
487C8—22no—
488C8—224no—
489C8C2×#433914yes—
490C22—224no—
491C22—224no—
492C22—224no—
493C22—448no—
494C22#1062308212yes—
495C22C2×#6697112yes—
496C22#1062330112yes—
497C22C22×D4×D1111yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—224no—
504C4—444no—
505C4—444no—
506C4#1062308212yes—
507C4C2×#6697114yes—
508C4C22×#433911yescharacteristic
509C4C2×#6704311yescharacteristic
510C2—444no—
511C2#1308123314yesdirect product factor
512C2C2×#1062308211yescharacteristic
513C2C22×#6697111yescharacteristic
514C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×C4×Q16D11
hypocenterC11C2×#3356
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
3. #13081233C2direct (N × H)
4. C2×#10622293C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622634C2semidirect
8. C2×#10622633C2semidirect
9. C2×#10622802C2semidirect
11. C2×#10622494C2semidirect
12. C2×C4×C11×Q16C2semidirect
34. C4×C11×Q16C22semidirect
41. #10622802C22semidirect
45. #10622634C22semidirect
46. #10622633C22semidirect
50. #10622494C22semidirect
51. #10622428C22semidirect
52. #10622418C22semidirect
54. #10622293C22semidirect
199. C2×C4×Q16D11semidirect
272. C4×Q16C2×D11semidirect
377. C2×C11#3356semidirect
446. C11C2×#3356semidirect
511. C2#13081233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106231102
#130812332
C2×#106222932
C2×#106224282
C2×#106224182
C2×#106226342
C2×#106226332
C2×#106228022
C2×#106223012
C2×#106224942
C2×C4×C11×Q162
C2×#335611