Finite Group Databasebeta

← C2×#13079784 #15625803

Subgroups — C2×#13079784 #15625803

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13079784C2116yesmaximal, direct product factor
3C2×#10622677C212yesmaximal, complemented
4C2×#10622681C212yesmaximal, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622581C211yesmaximal, characteristic
7C2×#10622584C211yesmaximal, characteristic, complemented
8C2×#10622580C211yesmaximal, characteristic
9C2×#10622676C212yesmaximal, complemented
10C2×#10622679C212yesmaximal, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C22×C11×#125C211yesmaximal, characteristic, complemented
13C2×C11×#125—21no—
14C2×C11×#125—21no—
15C2×C11×#125—24no—
16C2×C11×#125C2212yes—
17C2×C11×#125C2212yes—
18C2×C11×#125C2218yescomplemented
19C22×C11×C4⋊C4—21no—
20C22×C11×C4⋊C4—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66982—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66977C2211yescharacteristic
28#10623010—24no—
29#10623010C2218yes—
30C2×#66929—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×#66923C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622681C22116yescomplemented
39#10622679C22116yescomplemented
40#10622677C22116yescomplemented
41#10622676C22116yescomplemented
42#10622584C2218yescomplemented
43#10622583C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46#10622581C2218yes—
47#10622580C2218yes—
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66872C2212yes—
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53C2×#66871C2212yes—
54#10622538C2218yescomplemented
55C2×C4⋊(C11⋊C8)C2212yes—
56C2×C4×C11⋊C8C2212yes—
57C23×C4×C11—21no—
58C23×C4×C11—21no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C11×#125—24no—
67C11×#125—24no—
68C11×#125—28no—
69C11×#125—28no—
70C11×#125C2318yes—
71C11×#125C2318yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—28no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D414yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2314yes—
92C2×C22⋊Dic11—21no—
93#66983—22no—
94#66983C2314yes—
95#66982—28no—
96C4×C22⋊D11—28no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977C2314yes—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2312yes—
111C22×C11⋊C8C2312yes—
112#66929—28no—
113#66928—22no—
114#66928C2314yes—
115C4×D44—22no—
116C4×D44C2314yes—
117#66925—28no—
118#66923—22no—
119#66923C2314yes—
120C4×Dic22—22no—
121C4×Dic22C2314yes—
122C22⋊(C11⋊C8)C2314yes—
123C22⋊(C11⋊C8)C2314yes—
124#66874C2318yes—
125#66874C2318yes—
126#66873C2318yes—
127#66873C2318yes—
128#66872C2318yes—
129#66872C2318yes—
130#66871C2318yes—
131#66871C2318yes—
132C4⋊(C11⋊C8)C2318yes—
133C4×C11⋊C8C2318yes—
134C2×#3232—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—24no—
163C2×D44C2412yes—
164C2×C4×D11—24no—
165C2×C4×D11—44no—
166C2×Dic22—21no—
167C2×Dic22—24no—
168C2×Dic22C2412yes—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2414yes—
178C11×C4⋊C4C2414yes—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C42×C11C2×D414yes—
182C42×C11C2×D414yes—
183C42×C11C2412yes—
184C42×C11C2412yes—
185C22⋊Dic11—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2412yes—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198C4×Dic11—24no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2414yes—
202C2×C11⋊C8C2414yes—
203C2×#529—111no—
204C22×#125D1111yescharacteristic, complemented
205#3232—1116no—
206C2×#499—112no—
207C2×#488—112no—
208C2×#484—111no—
209C2×#481—111no—
210C2×#483—111no—
211C2×#480—111no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#431—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11#13514yes—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C2×C4×C11—22no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11—48no—
236C2×C4×C11—48no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C112−1+414yes—
246C2×C4×C11C2511yescharacteristic
247C22⋊D11—48no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254D44—24no—
255D44—42no—
256C4×D11—48no—
257Dic22—24no—
258Dic22—42no—
259C11⋊C8—24no—
260C11⋊C8—24no—
261#529—118no—
262#529—224no—
263C2×#126—221no—
264C2×#125—21no—
265C2×#125—21no—
266C2×#125—24no—
267C2×#125—111no—
268C2×#125C2×D1112yes—
269C2×#125C2×D1112yes—
270C2×#125C2×D1118yescomplemented
271C2×#124—111no—
272C2×#123—221no—
273C2×C22⋊Q8—111no—
274C2×#121—111no—
275C2×C4×Q8—111no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—221no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4—21no—
281C22×C4⋊C4C2×D1111yescharacteristic
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C42C2×D1111yescharacteristic
284#499—1116no—
285#488—1116no—
286#484—118no—
287#483—118no—
288#481—118no—
289#480—118no—
290#479—1116no—
291#478—1116no—
292#431—118no—
293C2×#107—112no—
294C2×#107—112no—
295C2×#106—112no—
296C2×#106—112no—
297C2×C4⋊C8—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—112no—
305C22×C11—22no—
306C22×C11—28no—
307C22×C11—22no—
308C22×C11#53612yes—
309C22×C11C2×#13514yes—
310C22×C11C2×#13512yes—
311C22×C11#57512yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—44no—
323C4×C11—44no—
324C4×C11#53612yes—
325C4×C11C2×2−1+412yes—
326Dic11—42no—
327Dic11—42no—
328Dic11—42no—
329C22×Q8—111no—
330C22×D4—111no—
331C22×D4—221no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—221no—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8—112no—
339C22×C8—112no—
340#126—228no—
341#125—24no—
342#125—24no—
343#125—28no—
344#125—28no—
345#125—114no—
346#125—222no—
347#125C22×D1118yes—
348#125C22×D1118yes—
349#124—114no—
350#124—222no—
351#123—228no—
352C22⋊Q8—114no—
353C22⋊Q8—222no—
354#121—114no—
355#121—222no—
356C4×Q8—114no—
357C4×Q8—222no—
358C4×D4—114no—
359C4×D4—228no—
360C4×D4—222no—
361#117—228no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1112yes—
379C2×C4⋊C4C22×D1112yes—
380C2×C4⋊C4C22×D1114yes—
381C2×C4⋊C4C22×D1114yes—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—221no—
388C2×C42C22⋊D1111yescharacteristic
389C2×C42C22⋊D1111yescharacteristic
390C2×C42C22⋊D1114yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1114yes—
394#107—118no—
395#107—118no—
396#106—118no—
397#106—118no—
398C4⋊C8—118no—
399#103—118no—
400#103—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—114no—
404C22⋊C8—114no—
405C4×C8—118no—
406C2×C11—24no—
407C2×C11#323214yescomplemented
408C2×C11C2×#53611yescharacteristic
409C2×C11C22×#13511yescharacteristic
410C2×C11C2×#57511yescharacteristic
411D11—82no—
412C24—221no—
413C24C2×C22⋊D1111yescharacteristic
414C2×Q8—112no—
415C2×Q8—221no—
416C2×Q8—224no—
417C2×D4—112no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—221no—
421C2×D4—444no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—224no—
435C22×C4—444no—
436C22×C4C2×C22⋊D1114yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C2×C8—114no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8—224no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4C23×D1114yes—
467C4⋊C4C23×D1114yes—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C42—224no—
474C42C2×C22⋊D1114yes—
475C42C2×C22⋊D1112yes—
476C42C2×C22⋊D1112yes—
477C42C2×C22⋊D1114yes—
478C42C23×D1112yes—
479C42C23×D1112yes—
480C11C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—222no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23#6700314yes—
488C23C22×C22⋊D1112yes—
489C23C22×C22⋊D1111yescharacteristic
490Q8—224no—
491Q8—442no—
492D4—224no—
493D4—448no—
494D4—442no—
495C2×C4—22no—
496C2×C4—28no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—448no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4#6704014yes—
518C2×C4C22×C22⋊D1112yes—
519C2×C4C22×C22⋊D1112yes—
520C2×C4C22×C22⋊D1112yes—
521C2×C4C22×C22⋊D1112yes—
522C2×C4C22×C22⋊D1112yes—
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C24×D1111yescharacteristic
525C8—224no—
526C8—224no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—884no—
534C22#1062334712yes—
535C22C2×#6700314yes—
536C22C2×#6700312yes—
537C22#1062335312yes—
538C22C23×C22⋊D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—44no—
545C4—44no—
546C4—442no—
547C4—442no—
548C4—442no—
549C4#1062334712yes—
550C4C2×#6704012yes—
551C2—24no—
552C2—882no—
553C2#1307978414yesdirect product factor
554C2C2×#1062334711yescharacteristic
555C2C22×#6700311yescharacteristic
556C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#125C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×#125D11
hypocenterC11C2×#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13079784C2direct (N × H)
3. C2×#10622677C2semidirect
4. C2×#10622681C2semidirect
5. C2×#10622583C2semidirect
7. C2×#10622584C2semidirect
9. C2×#10622676C2semidirect
10. C2×#10622679C2semidirect
11. C2×#10622538C2semidirect
12. C22×C11×#125C2semidirect
18. C2×C11×#125C22semidirect
38. #10622681C22semidirect
39. #10622679C22semidirect
40. #10622677C22semidirect
41. #10622676C22semidirect
42. #10622584C22semidirect
43. #10622583C22semidirect
54. #10622538C22semidirect
204. C22×#125D11semidirect
270. C2×#125C2×D11semidirect
407. C2×C11#3232semidirect
480. C11C2×#3232semidirect
553. C2#13079784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130797842
C2×#106226772
C2×#106226812
C2×#106225832
C2×#106225812
C2×#106225842
C2×#106225802
C2×#106226762
C2×#106226792
C2×#106225382
C22×C11×#1252
C2×#323211