Finite Group Databasebeta

← C2×#13078474 #15621362

Subgroups — C2×#13078474 #15621362

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2#13078474C2116yesmaximal, direct product factor
3C2×#10622676C212yesmaximal, complemented
4C2×#10622707C212yesmaximal, complemented
5C2×#10622679C212yesmaximal, complemented
6C2×#10622697C212yesmaximal, complemented
7C2×#10622608C211yesmaximal, characteristic, complemented
8C22×#66872C211yesmaximal, characteristic, complemented
9C2×#10622612C211yesmaximal, characteristic, complemented
10C2×#10622579C211yesmaximal, characteristic
11C2×#10622615C211yesmaximal, characteristic
12C2×C11×#544C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C11×#544—24no—
15C11×#544C2218yescomplemented
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×#125—21no—
19C2×C11×#125C2212yes—
20C2×C11×C22⋊Q8—22no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623054—24no—
28#10623054C2218yes—
29C2×#66945—21no—
30C2×C4⋊C4×D11—21no—
31C2×(C22⋊D11)⋊C4—22no—
32C2×C4×D44C2212yes—
33C2×C4×Dic22C2212yes—
34#10622707C22116yescomplemented
35#10622697C22116yescomplemented
36#10622679C22116yescomplemented
37#10622676C22116yescomplemented
38#10622615C2218yes—
39#10622612C2218yescomplemented
40#10622608C2218yescomplemented
41C2×#66874C2211yescharacteristic
42C2×#66874C2212yes—
43C2×#66874C2211yescharacteristic
44#10622579C2218yes—
45C2×#66873C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66872C2218yescomplemented
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2212yes—
54C2×C4⋊(C11⋊C8)C2212yes—
55C22×Q8×C11—22no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C23×Dic11—21no—
60C2×#4339—22no—
61C2×#4339—24no—
62C2×#4339Q818yescomplemented
63C2×#4339C2314yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—22no—
67C22×Dic22C2311yescharacteristic
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—24no—
70C11×C4⋊Q8C2318yes—
71C11×#125—28no—
72C11×#125—24no—
73C11×#125C2318yes—
74C11×C22⋊Q8—216no—
75C11×#117—22no—
76C11×#117D414yes—
77C11×#117C2314yes—
78C11×#117C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11—21no—
93C2×C42×C11C2312yes—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—22no—
101C2×#4318—24no—
102C2×#4318C2314yes—
103C22×C11⋊C8—24no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2314yes—
108#66945—28no—
109C4⋊C4×D11—28no—
110(C22⋊D11)⋊C4—216no—
111C4×D44—24no—
112C4×D44C2318yes—
113C4×Dic22—24no—
114C4×Dic22C2318yes—
115#66874C2318yes—
116#66874C2314yes—
117#66874C2314yes—
118#66873C2318yes—
119#66873C2314yes—
120#66873C2314yes—
121#66872C2318yes—
122#66872C2318yes—
123#66872C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2318yes—
126C4⋊(C11⋊C8)C2318yes—
127C2×#3084—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×Q8×C11—28no—
131C2×Q8×C11—84no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—82no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×Q814yes—
142C22×C4×C11#4114yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2412yes—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—24no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—82no—
151#4339—216no—
152#4339—28no—
153#4339C2×Q8116yescomplemented
154C2×D44—21no—
155C2×D44—22no—
156C2×D44C2×Q814yes—
157C2×D44C2412yes—
158C2×C4×D11—28no—
159C2×C4×D11—24no—
160C2×C4×D11—28no—
161C2×C4×D11—84no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22C2×Q814yes—
165C2×Dic22C2412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D414yes—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2412yes—
176C11×C4⋊C4C2414yes—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4C2×D418yes—
180C42×C11—24no—
181C42×C11C2×D414yes—
182C42×C11C2414yes—
183(C2×D11)⋊C4—28no—
184C4⋊Dic11—22no—
185C4⋊Dic11—24no—
186C4⋊Dic11C2414yes—
187Dic11⋊C4—28no—
188C4×Dic11—28no—
189#4318—28no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8C2414yes—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2412yes—
197C2×#544D1111yescharacteristic, complemented
198C2×#520—111no—
199#3084—1116no—
200C2×#479—112no—
201C2×#475—112no—
202C2×#478—112no—
203C2×#476—112no—
204C2×#428—111no—
205C22×#106—111no—
206C2×#424—111no—
207C2×#417—111no—
208C2×#416—111no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11C22⋊Q814yes—
212C23×C11C22×D412yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—22no—
216C22×D11—42no—
217C22×D11—42no—
218Q8×C11—88no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—42no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—84no—
228C2×C4×C11C22⋊Q814yes—
229C2×C4×C11C22⋊Q818yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D414yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×Q812yes—
235C2×C4×C11C22×Q814yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C11C2×#4114yes—
238C2×C4×C11C2511yescharacteristic
239C22⋊D11—216no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—44no—
244C2×Dic11—84no—
245D44—24no—
246D44—22no—
247D44C22×Q814yes—
248C4×D11—216no—
249C4×D11—88no—
250Dic22—24no—
251Dic22—22no—
252Dic22C22×Q814yes—
253C11⋊C8—22no—
254C11⋊C8—22no—
255C11⋊C8—24no—
256C22×#41—111no—
257C22×M16—111no—
258C23×C8—111no—
259#544—24no—
260#544C2×D1118yescomplemented
261C2×C4⋊Q8—21no—
262C2×C4⋊Q8C2×D1112yes—
263C2×#125—21no—
264C2×#125C2×D1112yes—
265C2×C22⋊Q8—22no—
266#520—118no—
267#520—224no—
268C2×C4×Q8—112no—
269C2×C4×D4—112no—
270C2×C4×D4—222no—
271C2×#117—221no—
272C2×#117C2×D1111yescharacteristic
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C4⋊C4—221no—
276C22×C4⋊C4C2×D1111yescharacteristic
277#479—1116no—
278#478—1116no—
279#476—1116no—
280#475—1116no—
281#428—118no—
282C2×#107—112no—
283C2×#106—112no—
284C2×#106—112no—
285C2×#106—112no—
286C2×#106—118no—
287#424—118no—
288C2×C4⋊C8—112no—
289C2×C4⋊C8—112no—
290#417—118no—
291#416—118no—
292C2×#103—111no—
293C2×#103—112no—
294C2×#103—111no—
295C2×#102—111no—
296C2×#102—112no—
297C2×#102—111no—
298C22×C11—28no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11C2×C22⋊Q814yes—
302C22×C11C2×C22⋊Q812yes—
303C22×C11#57712yes—
304C22×C11#57712yes—
305C22×C11C23×D411yescharacteristic
306C2×D11—24no—
307C2×D11—48no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—42no—
315C4×C11C2×C22⋊Q812yes—
316C4×C11C2×C22⋊Q814yes—
317C4×C11C23×Q811yescharacteristic
318C4×C11C22×#4111yescharacteristic
319Dic11—24no—
320Dic11—44no—
321C2×#41—118no—
322C2×#41—114no—
323C2×#41—224no—
324C2×#41—222no—
325C22×Q8—22no—
326C22×Q8—111no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—21no—
330C23×C4—221no—
331C23×C4—221no—
332C23×C4—222no—
333C23×C4C22×D1111yescharacteristic
334C2×M16—114no—
335C2×M16—224no—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8—114no—
339C22×C8—112no—
340C22×C8—224no—
341C4⋊Q8—28no—
342C4⋊Q8—24no—
343C4⋊Q8C22×D1118yes—
344#125—28no—
345#125—24no—
346#125C22×D1118yes—
347C22⋊Q8—216no—
348C4×Q8—118no—
349C4×Q8—224no—
350C4×D4—118no—
351C4×D4—2216no—
352C4×D4—224no—
353#117—22no—
354#117—228no—
355#117C22⋊D1114yes—
356#117C22×D1114yes—
357#117C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—228no—
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22×D1112yes—
372C2×C4⋊C4C22×D1114yes—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4C22⋊D1112yes—
378C2×C42—21no—
379C2×C42—222no—
380C2×C42C22×D1112yes—
381#107—118no—
382#106—118no—
383#106—118no—
384#106—118no—
385C4⋊C8—118no—
386C4⋊C8—118no—
387#103—114no—
388#103—114no—
389#103—118no—
390#102—114no—
391#102—114no—
392#102—118no—
393C2×C11—24no—
394C2×C11#308414yescomplemented
395C2×C11C22×C22⋊Q811yescharacteristic
396C2×C11C2×#57711yescharacteristic
397C2×C11C2×#57711yescharacteristic
398D11—44no—
399C24—221no—
400C24C2×C22⋊D1111yescharacteristic
401#41—1116no—
402#41—2216no—
403#41—228no—
404C2×Q8—28no—
405C2×Q8—84no—
406C2×Q8—114no—
407C2×Q8—112no—
408C2×Q8—222no—
409C2×Q8—221no—
410C2×D4—114no—
411C2×D4—112no—
412C2×D4—228no—
413C2×D4—224no—
414C2×D4—222no—
415C2×D4—221no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—82no—
421C22×C4—221no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—228no—
427C22×C4—884no—
428C22×C4—882no—
429C22×C4Q8×D1114yes—
430C22×C4#434314yes—
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—228no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—114no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—228no—
444C2×C8—224no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—28no—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—114no—
453C4⋊C4—224no—
454C4⋊C4—222no—
455C4⋊C4—228no—
456C4⋊C4C2×C22⋊D1114yes—
457C4⋊C4C2×C22⋊D1114yes—
458C4⋊C4C23×D1114yes—
459C4⋊C4C23×D1112yes—
460C4⋊C4C23×D1112yes—
461C22⋊C4—24no—
462C22⋊C4—228no—
463C22⋊C4C2×C22⋊D1118yes—
464C42—24no—
465C42—228no—
466C42C2×C22⋊D1114yes—
467C42C23×D1114yes—
468C11C2×#308411yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—224no—
472C23—222no—
473C23—442no—
474C23—442no—
475C23#6699914yes—
476C23C22×C22⋊D1112yes—
477C23C22×C22⋊D1111yescharacteristic
478Q8—88no—
479Q8—114no—
480Q8—224no—
481Q8—222no—
482D4—114no—
483D4—2216no—
484D4—224no—
485D4—222no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—2216no—
498C2×C4—224no—
499C2×C4—444no—
500C2×C4—888no—
501C2×C4—884no—
502C2×C4#6699914yes—
503C2×C4#6699918yes—
504C2×C4C2×Q8×D1112yes—
505C2×C4C2×Q8×D1114yes—
506C2×C4C2×#434312yes—
507C2×C4C2×#434314yes—
508C2×C4C22×C22⋊D1114yes—
509C2×C4C22×C22⋊D1114yes—
510C2×C4C22×C22⋊D1112yes—
511C2×C4C22×C22⋊D1111yescharacteristic
512C2×C4C24×D1111yescharacteristic
513C8—222no—
514C8—222no—
515C8—224no—
516C22—28no—
517C22—22no—
518C22—22no—
519C22—224no—
520C22—448no—
521C22—442no—
522C22—442no—
523C22C2×#6699914yes—
524C22C2×#6699912yes—
525C22#1062336712yes—
526C22#1062336812yes—
527C22C23×C22⋊D1111yescharacteristic
528C4—24no—
529C4—24no—
530C4—42no—
531C4—44no—
532C4—42no—
533C4—224no—
534C4—444no—
535C4C2×#6699914yes—
536C4C2×#6699912yes—
537C4C22×Q8×D1111yescharacteristic
538C4C22×#434311yescharacteristic
539C2—24no—
540C2—444no—
541C2#1307847414yesdirect product factor
542C2C22×#6699911yescharacteristic
543C2C2×#1062336811yescharacteristic
544C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#544D11
hypocenterC11C2×#3084
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13078474C2direct (N × H)
3. C2×#10622676C2semidirect
4. C2×#10622707C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622608C2semidirect
8. C22×#66872C2semidirect
9. C2×#10622612C2semidirect
12. C2×C11×#544C2semidirect
15. C11×#544C22semidirect
34. #10622707C22semidirect
35. #10622697C22semidirect
36. #10622679C22semidirect
37. #10622676C22semidirect
39. #10622612C22semidirect
40. #10622608C22semidirect
51. C2×#66872C22semidirect
62. C2×#4339Q8semidirect
153. #4339C2×Q8semidirect
197. C2×#544D11semidirect
260. #544C2×D11semidirect
394. C2×C11#3084semidirect
468. C11C2×#3084semidirect
541. C2#13078474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230542
#130784742
C2×#106226762
C2×#106227072
C2×#106226792
C2×#106226972
C2×#106226082
C22×#668722
C2×#106226122
C2×#106225792
C2×#106226152
C2×C11×#5442
C2×#308411