Finite Group Databasebeta

← C2×#13081194 #15632471

Subgroups — C2×#13081194 #15632471

Order 2816.

2082 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×#10623086C211yesmaximal, characteristic
2#13081194C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622657C212yesmaximal, complemented
5C2×#10622616C212yesmaximal, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622700C211yesmaximal, characteristic, complemented
8C2×#10622662C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622608C212yesmaximal, complemented
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C11×#556—24no—
15C11×#556C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2212yes—
24C22×#4325C2211yescharacteristic
25C2×#66983C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×#4318C2212yes—
28#10623086—24no—
29#10623086C2218yes—
30C2×#66950—21no—
31C2×#66939—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622700C2218yescomplemented
38#10622691C2218yescomplemented
39#10622662C22116yescomplemented
40#10622657C22116yescomplemented
41C4×#4325C2218yescomplemented
42#10622633C2218yescomplemented
43#10622625C2218yescomplemented
44#10622616C22116yescomplemented
45#10622608C22116yescomplemented
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11C2312yes—
59C22×C22⋊D11—22no—
60C23×Dic11—22no—
61C2×#4341—28no—
62C2×#4341—48no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C11×#126—216no—
69C11×#124—28no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8C2318yes—
72C4×Q8×C11—28no—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×D4×C11D414yes—
76C4×D4×C11C2314yes—
77C11×#117—24no—
78C11×#117C2318yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×#4325—24no—
92C2×#4325C2314yes—
93#66983—24no—
94#66983C2318yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2318yes—
103C2×#4318—28no—
104C2×#4318C2318yes—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2311yescharacteristic
108#66950—28no—
109#66939—216no—
110C4×D44—22no—
111C4×D44C2314yes—
112#66922—22no—
113#66922C2314yes—
114#66899C2318yes—
115#66899C2314yes—
116C22⋊(C11⋊C8)C2318yes—
117#66873C2314yes—
118#66873C2318yes—
119#66872C2314yes—
120#66872C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3353—111nomaximal, Sylow
127C24×C11C2×D412yes—
128C23×D11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—44no—
134C2×Q8×C11C2412yes—
135C2×D4×C11—24no—
136C2×D4×C11C2×D414yes—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—28no—
149C2×C22⋊D11—48no—
150C22×Dic11—28no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—48no—
154#4341—432no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44C2412yes—
159C2×C4×D11—24no—
160C2×C4×D11—44no—
161C2×Dic22—24no—
162C2×Dic22—44no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D414yes—
169C11×C4⋊C4C2414yes—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4C2×D418yes—
174C42×C11—28no—
175C42×C11—24no—
176C42×C11C2×D412yes—
177C42×C11C2412yes—
178#4325—28no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11—28no—
185C4⋊Dic11C2414yes—
186C4⋊Dic11C2412yes—
187#4318—216no—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8#4114yescomplemented
191C2×C11⋊C8C2412yes—
192C2×C11⋊C8C2414yes—
193C2×C11⋊C8C2412yes—
194C2×#556D1111yescharacteristic, complemented
195C2×#547—111no—
196#3353—1116no—
197C2×#500—111no—
198C2×#484—112no—
199C2×#482—112no—
200C2×#475—111no—
201C2×#474—111no—
202C2×#468—112no—
203C2×C4×SD16—111no—
204C2×#436—111no—
205C2×#428—112no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11C22×D414yes—
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—42no—
218Q8×C11—48no—
219D4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—28no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11AGL(1,ℤ/8)14yes—
232C2×C4×C11C22×D414yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C112−1+412yes—
238C2×C4×C11C2511yescharacteristic
239C22⋊D11—416no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—416no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245D44—22no—
246D44—22no—
247D44—42no—
248C4×D11—48no—
249Dic22—48no—
250C11⋊C8—24no—
251C11⋊C8—22no—
252C11⋊C8C2×#4114yescomplemented
253C22×#41—221no—
254C22×SD16—111no—
255C22×M16—112no—
256#556—24no—
257#556C2×D1118yescomplemented
258#547—118no—
259#547—224no—
260C2×C4⋊Q8—111no—
261C2×C4⋊Q8C2×D1111yescharacteristic
262C2×#126—22no—
263C2×#124—21no—
264C2×#123—222no—
265C2×C22⋊Q8—221no—
266C2×C22⋊Q8C2×D1112yes—
267C2×#121—112no—
268C2×C4×Q8—21no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4C2×D1111yescharacteristic
272C2×#117C2×D1112yes—
273C22×C4⋊C4—112no—
274#500—118no—
275#484—1116no—
276#482—1116no—
277#475—118no—
278#474—118no—
279#468—1116no—
280C4×SD16—118no—
281#436—118no—
282#428—1116no—
283C2×#107—112no—
284C2×#107—112no—
285C2×#107—112no—
286C2×#106—112no—
287C2×#106—111no—
288C2×C4⋊C8—111no—
289C2×#103—112no—
290C2×#103—111no—
291C2×#102—111no—
292C2×#102—112no—
293C2×C22⋊C8—112no—
294C2×C4×C8—111no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—48no—
299C22×C11#54712yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—84no—
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11#54712yes—
313C4×C11C2×AGL(1,ℤ/8)14yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×2−1+411yescharacteristic
316Dic11—44no—
317Dic11—42no—
318C2×#41—228no—
319C2×#41—448no—
320C22×Q8—21no—
321C22×Q8—221no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—111no—
324C22×D4—222no—
325C22×D4C22⋊D1111yescharacteristic
326C23×C4—222no—
327C23×C4—221no—
328C23×C4C22×D1112yes—
329C2×SD16—114no—
330C2×SD16—224no—
331C2×M16—118no—
332C2×M16—228no—
333C22×C8—111no—
334C22×C8—112no—
335C22×C8—111no—
336C4⋊Q8—22no—
337C4⋊Q8—114no—
338C4⋊Q8—222no—
339C4⋊Q8C22×D1114yes—
340#126—216no—
341#124—28no—
342#123—2216no—
343C22⋊Q8—24no—
344C22⋊Q8—228no—
345C22⋊Q8C22×D1118yes—
346#121—118no—
347#121—224no—
348C4×Q8—28no—
349C4×Q8—22no—
350C4×Q8C22×D1114yes—
351C4×D4—114no—
352C4×D4—222no—
353C4×D4C22⋊D1114yes—
354C4×D4C22×D1114yes—
355#117—24no—
356#117C22×D1118yes—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—118no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4C22⋊D1112yes—
374C2×C42—22no—
375C2×C42—21no—
376C2×C42C22×D1111yescharacteristic
377#107—118no—
378#107—118no—
379#107—118no—
380#106—114no—
381#106—118no—
382C4⋊C8—114no—
383#103—114no—
384#103—118no—
385#102—114no—
386#102—118no—
387C22⋊C8—118no—
388C4×C8—114no—
389C2×C11—44no—
390C2×C11#335314yescomplemented
391C2×C11C2×#54711yescharacteristic
392C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C11C2×#57811yescharacteristic
394D11—82no—
395C24—221no—
396C24C2×C22⋊D1112yes—
397#41—4432no—
398C2×Q8—21no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—224no—
404C2×Q8—444no—
405C2×Q8C23×D1112yes—
406C2×D4—24no—
407C2×D4—112no—
408C2×D4—228no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—221no—
412C2×D4—448no—
413C2×D4C2×C22⋊D1114yes—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—228no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—448no—
424C22×C4—444no—
425C22×C4C2×C22⋊D1114yes—
426C22×C4C2×C22⋊D1112yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C23×D1114yes—
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432M16—2216no—
433C2×C8—114no—
434C2×C8—112no—
435C2×C8—112no—
436C2×C8—114no—
437C2×C8—224no—
438C2×C8—222no—
439C4⋊C4—28no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—112no—
445C4⋊C4—114no—
446C4⋊C4—221no—
447C4⋊C4—222no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4C2×C22⋊D1114yes—
451C4⋊C4C23×D1112yes—
452C4⋊C4C23×D1114yes—
453C22⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—224no—
456C22⋊C4—228no—
457C22⋊C4C2×C22⋊D1118yes—
458C42—28no—
459C42—24no—
460C42C2×C22⋊D1112yes—
461C42C23×D1112yes—
462C11C2×#335311yescharacteristic, complemented, Sylow
463C23—24no—
464C23—24no—
465C23—24no—
466C23—222no—
467C23—442no—
468C23—442no—
469C23—442no—
470C23C22×C22⋊D1114yes—
471C23C22×C22⋊D1111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—48no—
475Q8—42no—
476Q8—448no—
477D4—28no—
478D4—222no—
479D4—222no—
480D4—4416no—
481D4—442no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—28no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—44no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—4416no—
496C2×C4—442no—
497C2×C4—444no—
498C2×C4—448no—
499C2×C4#6700214yes—
500C2×C4#41×D1112yes—
501C2×C4#6704312yes—
502C2×C4C22×C22⋊D1114yes—
503C2×C4C22×C22⋊D1112yes—
504C2×C4C22×C22⋊D1112yes—
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C24×D1111yescharacteristic
507C8—114no—
508C8—224no—
509C8—222no—
510C22—24no—
511C22—24no—
512C22—24no—
513C22—48no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—884no—
518C22C2×#6700212yes—
519C22#1062335512yes—
520C22#1062336912yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—24no—
523C4—22no—
524C4—44no—
525C4—42no—
526C4—42no—
527C4—442no—
528C4—444no—
529C4C2×#6700214yes—
530C4#1062335512yes—
531C4C2×#41×D1111yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—44no—
534C2—882no—
535C2#1308119414yesdirect product factor
536C2C2×#1062335511yescharacteristic
537C2C22×#6700211yescharacteristic
538C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenterC2×#556D11
hypocenterC11C2×#3353
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13081194C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622657C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622700C2semidirect
8. C2×#10622662C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622608C2semidirect
12. C2×C11×#556C2semidirect
15. C11×#556C22semidirect
37. #10622700C22semidirect
38. #10622691C22semidirect
39. #10622662C22semidirect
40. #10622657C22semidirect
41. C4×#4325C22semidirect
42. #10622633C22semidirect
43. #10622625C22semidirect
44. #10622616C22semidirect
45. #10622608C22semidirect
190. C2×C11⋊C8#41semidirect
194. C2×#556D11semidirect
252. C11⋊C8C2×#41semidirect
257. #556C2×D11semidirect
390. C2×C11#3353semidirect
462. C11C2×#3353semidirect
535. C2#13081194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
#130811942
C2×#106226912
C2×#106226572
C2×#106226162
C2×#106226332
C2×#106227002
C2×#106226622
C2×C4×#43252
C2×#106226252
C2×#106226082
C2×C11×#5562
C2×#335311