Finite Group Databasebeta

← C2×#13078467 #15621354

Subgroups — C2×#13078467 #15621354

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×#10623050C211yesmaximal, characteristic, complemented
2#13078467C2116yesmaximal, direct product factor
3C2×#10622635C212yesmaximal, complemented
4C2×#10622634C212yesmaximal, complemented
5C2×#10622622C212yesmaximal, complemented
6C2×#10622620C212yesmaximal, complemented
7C2×#10622577C211yesmaximal, characteristic, complemented
8C22×#66871C211yesmaximal, characteristic, complemented
9C2×#10622612C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic
11C2×#10622846C211yesmaximal, characteristic
12C2×C11×#520C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C11×#520—24no—
15C11×#520C2218yes—
16C2×C4×Q8×C11C2212yes—
17C2×C4×D4×C11—22no—
18C2×C4×D4×C11C2212yes—
19C2×C11×#117—21no—
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623050—24no—
28#10623050C2218yescomplemented
29C2×#66943—21no—
30C2×#66941—21no—
31C2×#66931—22no—
32C2×#66923C2212yes—
33C2×#66922C2212yes—
34#10622846C2218yes—
35#10622845C2218yes—
36C2×#66899C2211yescharacteristic
37C2×#66899C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2212yes—
41C2×#66896C2211yescharacteristic
42#10622635C22116yescomplemented
43#10622634C22116yescomplemented
44#10622622C22116yescomplemented
45#10622620C22116yescomplemented
46#10622612C2218yescomplemented
47#10622577C2218yescomplemented
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2218yescomplemented
53C2×C4⋊(C11⋊C8)C2212yes—
54C2×C4⋊(C11⋊C8)C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41Q818yescomplemented
58C2×C11×#41C2314yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C22×Dic22—22no—
68C4×Q8×C11—24no—
69C4×Q8×C11C2318yes—
70C4×D4×C11—216no—
71C4×D4×C11—24no—
72C4×D4×C11C2318yes—
73C11×#117—28no—
74C11×#117D414yes—
75C11×#117C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—22no—
87C2×C42×C11C2312yes—
88C2×C22⋊Dic11—21no—
89#66979—22no—
90#66979C2314yes—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—21no—
101C2×#4318—24no—
102C2×#4318C2314yes—
103C22×C11⋊C8—24no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2314yes—
108#66943—28no—
109#66941—28no—
110#66931—216no—
111#66923—24no—
112#66923C2318yes—
113#66922—24no—
114#66922C2318yes—
115#66899C2318yes—
116#66899C2314yes—
117#66899C2314yes—
118#66896C2318yes—
119#66896C2314yes—
120#66896C2314yes—
121#66872C2318yes—
122#66871C2318yes—
123#66871C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2318yes—
126C4⋊(C11⋊C8)C2318yes—
127C2×#3083—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C11×#41—216no—
131C11×#41—28no—
132C11×#41C2×Q8116yescomplemented
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2×Q814yes—
136C2×Q8×C11C2412yes—
137C2×D4×C11—28no—
138C2×D4×C11—24no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11C2×Q814yes—
142C2×D4×C11C2412yes—
143C22×C4×C11—21no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—28no—
149C22×C4×C11—84no—
150C22×C4×C11—82no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×Q814yes—
156C22×C4×C11#4114yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2412yes—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—82no—
164C2×Dic22—28no—
165C2×Dic22—84no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2414yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4C2×D418yes—
174C42×C11—28no—
175C42×C11C2×D414yes—
176C42×C11C2414yes—
177C22⋊Dic11—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11—22no—
180C4⋊Dic11—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11—24no—
183C4⋊Dic11C2412yes—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188C4×Dic11—24no—
189#4318—28no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2412yes—
196C2×C11⋊C8C2414yes—
197C2×#544—111no—
198C2×#520D1111yescharacteristic
199#3083—1116no—
200C2×#479—112no—
201C2×#477—112no—
202C2×#478—112no—
203C2×#474—112no—
204C2×#428—111no—
205C22×#107—111no—
206C2×#424—111no—
207C2×#417—111no—
208C2×#416—111no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C22⋊Q814yes—
216C23×C11C22×D412yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—24no—
219Q8×C11—22no—
220Q8×C11C22×Q814yes—
221D4×C11—216no—
222D4×C11—24no—
223D4×C11—22no—
224D4×C11C22×Q814yes—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—216no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—88no—
233C2×C4×C11—84no—
234C2×C4×C11C22⋊Q814yes—
235C2×C4×C11C22⋊Q818yes—
236C2×C4×C11C22×D414yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×Q812yes—
241C2×C4×C11C22×Q814yes—
242C2×C4×C11C2×#4112yes—
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2511yescharacteristic
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—84no—
252Dic22—88no—
253C11⋊C8—22no—
254C11⋊C8—22no—
255C11⋊C8—24no—
256C22×#41C2×D1111yescharacteristic
257C22×M16—111no—
258C23×C8—111no—
259#544—118no—
260#544—224no—
261C2×C4⋊Q8—112no—
262C2×C4⋊Q8—221no—
263C2×#125—112no—
264C2×#125—221no—
265C2×C22⋊Q8—222no—
266#520—24no—
267#520C2×D1118yes—
268C2×C4×Q8C2×D1112yes—
269C2×C4×D4—22no—
270C2×C4×D4C2×D1112yes—
271C2×#117—21no—
272C2×#117—111no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—21no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4C2×D1111yescharacteristic
277#479—1116no—
278#478—1116no—
279#477—1116no—
280#474—1116no—
281#428—118no—
282C2×#107—112no—
283C2×#107—112no—
284C2×#107—112no—
285C2×#107—118no—
286C2×#106—112no—
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×C11—24no—
302C22×C11—48no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C2×C22⋊Q814yes—
306C22×C11C2×C22⋊Q812yes—
307C22×C11#57612yes—
308C22×C11#57812yes—
309C22×C11C23×D411yescharacteristic
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—44no—
314C4×C11C2×C22⋊Q814yes—
315C4×C11C2×C22⋊Q812yes—
316C4×C11C23×Q811yescharacteristic
317C4×C11C22×#4111yescharacteristic
318Dic11—42no—
319Dic11—44no—
320Dic11—42no—
321C2×#41—24no—
322C2×#41—22no—
323C2×#41Dic2218yescomplemented
324C2×#41C22×D1114yes—
325C22×Q8—222no—
326C22×Q8C22×D1111yescharacteristic
327C22×D4—21no—
328C22×D4C22×D1111yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—22no—
332C23×C4—221no—
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—118no—
342C4⋊Q8—228no—
343C4⋊Q8—224no—
344#125—118no—
345#125—228no—
346#125—224no—
347C22⋊Q8—2216no—
348C4×Q8—24no—
349C4×Q8C22×D1118yes—
350C4×D4—216no—
351C4×D4—24no—
352C4×D4C22×D1118yes—
353#117—28no—
354#117—114no—
355#117—222no—
356#117C22⋊D1114yes—
357#117C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22×D1112yes—
374C2×C4⋊C4C22×D1114yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4C22⋊D1112yes—
378C2×C42—22no—
379C2×C42—221no—
380C2×C42C22×D1112yes—
381#107—118no—
382#107—118no—
383#107—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—44no—
395C2×C11#308314yescomplemented
396C2×C11C22×C22⋊Q811yescharacteristic
397C2×C11C2×#57611yescharacteristic
398C2×C11C2×#57811yescharacteristic
399C24—21no—
400C24C2×C22⋊D1111yescharacteristic
401#41—216no—
402#41—28no—
403#41C2×Dic22116yescomplemented
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—228no—
407C2×Q8—884no—
408C2×Q8C2×Dic2214yes—
409C2×Q8C23×D1112yes—
410C2×D4—28no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4C2×Dic2214yes—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—28no—
422C22×C4—84no—
423C22×C4—82no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—882no—
429C22×C4C2×Dic2214yes—
430C22×C4#433914yes—
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—114no—
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—228no—
444C2×C8—224no—
445C4⋊C4—24no—
446C4⋊C4—28no—
447C4⋊C4—22no—
448C4⋊C4—112no—
449C4⋊C4—114no—
450C4⋊C4—112no—
451C4⋊C4—224no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4C2×C22⋊D1114yes—
459C4⋊C4C2×C22⋊D1114yes—
460C4⋊C4C23×D1114yes—
461C22⋊C4—28no—
462C22⋊C4—224no—
463C22⋊C4C2×C22⋊D1118yes—
464C42—28no—
465C42—224no—
466C42C2×C22⋊D1114yes—
467C42C23×D1114yes—
468C11C2×#308311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—24no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23#6697714yes—
476C23C22×C22⋊D1112yes—
477C23C22×C22⋊D1111yescharacteristic
478Q8—24no—
479Q8—22no—
480Q8—888no—
481Q8C22×Dic2214yes—
482D4—216no—
483D4—24no—
484D4—22no—
485D4C22×Dic2214yes—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—216no—
491C2×C4—24no—
492C2×C4—44no—
493C2×C4—88no—
494C2×C4—84no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—444no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—884no—
502C2×C4#6697714yes—
503C2×C4#6697718yes—
504C2×C4C22×Dic2212yes—
505C2×C4C22×Dic2214yes—
506C2×C4C2×#433912yes—
507C2×C4C2×#433914yes—
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—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#6697714yes—
524C22C2×#6697712yes—
525C22#1062336612yes—
526C22#1062336912yes—
527C22C23×C22⋊D1111yescharacteristic
528C4—24no—
529C4—24no—
530C4—24no—
531C4—44no—
532C4—444no—
533C4—442no—
534C4—442no—
535C4C2×#6697714yes—
536C4C2×#6697712yes—
537C4C23×Dic2211yescharacteristic
538C4C22×#433911yescharacteristic
539C2—24no—
540C2—44no—
541C2#1307846714yesdirect product factor
542C2C22×#6697711yescharacteristic
543C2C2×#1062336611yescharacteristic
544C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#520D11
hypocenterC11C2×#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
2. #13078467C2direct (N × H)
3. C2×#10622635C2semidirect
4. C2×#10622634C2semidirect
5. C2×#10622622C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622577C2semidirect
8. C22×#66871C2semidirect
9. C2×#10622612C2semidirect
28. #10623050C22semidirect
42. #10622635C22semidirect
43. #10622634C22semidirect
44. #10622622C22semidirect
45. #10622620C22semidirect
46. #10622612C22semidirect
47. #10622577C22semidirect
52. C2×#66871C22semidirect
57. C2×C11×#41Q8semidirect
132. C11×#41C2×Q8semidirect
323. C2×#41Dic22semidirect
395. C2×C11#3083semidirect
403. #41C2×Dic22semidirect
468. C11C2×#3083semidirect
541. C2#13078467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130784672
C2×#106226352
C2×#106226342
C2×#106226222
C2×#106226202
C2×#106225772
C22×#668712
C2×#106226122
C2×#106228452
C2×#106228462
C2×C11×#5202
C2×#308311