Finite Group Databasebeta

← C2×#13078981 #15623021

Subgroups — C2×#13078981 #15623021

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2#13078981C2116yesmaximal, direct product factor
3C2×#10622695C212yesmaximal, complemented
4C2×#10622668C212yesmaximal, complemented
5C2×#10622669C212yesmaximal, complemented
6C2×#10622694C212yesmaximal, complemented
7C2×#10622845C211yesmaximal, characteristic
8C2×#10622838C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic
10C22×#66899C211yesmaximal, characteristic, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#536C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C11×#536—24no—
16C11×#536C2218yes—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×#124C2212yes—
19C2×C11×#123—22no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×#117C2211yescharacteristic
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—
36#10622838C2218yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2212yes—
42C2×#66899C2212yes—
43C2×#66899C2212yes—
44C2×#66899C2218yescomplemented
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2212yes—
48#10622695C22116yescomplemented
49#10622694C22116yescomplemented
50#10622669C22116yescomplemented
51#10622668C22116yescomplemented
52#10622610C2218yescomplemented
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41C2314yes—
59C22×Q8×C11—21no—
60C22×Q8×C11—22no—
61C22×Q8×C11—24no—
62C22×Q8×C11—24no—
63C22×Q8×C11C2312yes—
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2314yes—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11—21no—
72C22×Dic22—22no—
73C11×C4⋊Q8—24no—
74C11×C4⋊Q8C2318yes—
75C11×#124—24no—
76C11×#124C2318yes—
77C11×#123—216no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C11×#117D414yes—
81C11×#117C2314yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11C2312yes—
90C2×C22⋊Dic11—21no—
91#66979—22no—
92#66979C2314yes—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—21no—
103C2×#4318—24no—
104C2×#4318C2314yes—
105C22×C11⋊C8—24no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66943—28no—
111#66941—28no—
112#66931—216no—
113#66923—24no—
114#66923C2318yes—
115#66922—24no—
116#66922C2318yes—
117#66899C2318yes—
118#66899C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121#66899C2318yes—
122#66899C2314yes—
123#66899C2314yes—
124#66896C2318yes—
125#66896C2314yes—
126#66896C2314yes—
127#66867C2318yes—
128C4×C11⋊C8C2318yes—
129C2×#3137—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C11×#41—28no—
133C11×#41—28no—
134C11×#41—48no—
135C2×Q8×C11—24no—
136C2×Q8×C11—22no—
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11—24no—
140C2×Q8×C11—28no—
141C2×Q8×C11—28no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—44no—
145C2×Q8×C11—48no—
146C2×Q8×C11C2414yes—
147C2×Q8×C11C2412yes—
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—44no—
153C2×D4×C11C2412yes—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4114yes—
165C22×C4×C11#4114yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2412yes—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—24no—
172C22×Dic11—82no—
173C2×Dic22—28no—
174C2×Dic22—84no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4C2×D414yes—
178C11×C4⋊C4C2×D414yes—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4C2×D418yes—
182C42×C11C2×D414yes—
183C42×C11C2414yes—
184C22⋊Dic11—24no—
185C4⋊Dic11—21no—
186C4⋊Dic11—22no—
187C4⋊Dic11—28no—
188C4⋊Dic11—21no—
189C4⋊Dic11—24no—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2414yes—
192C4⋊Dic11C2412yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195C4×Dic11—24no—
196#4318—28no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—28no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×C11⋊C8C2412yes—
204C2×#544—111no—
205C2×#536D1111yescharacteristic
206#3137—1116no—
207C2×#491—112no—
208C2×#489—112no—
209C2×#488—112no—
210C2×#487—112no—
211C2×#417—111no—
212C2×#419—111no—
213C2×#416—111no—
214C22×#103—111no—
215C2×#405—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11#12414yes—
223C23×C11C22×D412yes—
224C23×C11C22×D411yescharacteristic
225Q8×C11—24no—
226Q8×C11—24no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—48no—
230Q8×C11—44no—
231Q8×C11—42no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—48no—
235D4×C11—42no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—42no—
241C2×C4×C11—48no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11#12414yes—
245C2×C4×C11#12418yes—
246C2×C4×C11C22×D414yes—
247C2×C4×C11C22×D414yes—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4114yes—
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2511yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—42no—
259C2×Dic11—44no—
260C2×Dic11—42no—
261C2×Dic11—84no—
262Dic22—88no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C11⋊C8—24no—
266C22×#41C2×D1111yescharacteristic
267C23×Q8C2×D1111yescharacteristic
268C22×M16—111no—
269C23×C8—111no—
270#544—118no—
271#544—224no—
272#536—24no—
273#536C2×D1118yes—
274C2×C4⋊Q8—112no—
275C2×C4⋊Q8—221no—
276C2×C4⋊Q8C2×D1112yes—
277C2×#125—112no—
278C2×#125—221no—
279C2×#124C2×D1112yes—
280C2×#123—22no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8—21no—
283C2×C22⋊Q8—222no—
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287#491—1116no—
288#489—1116no—
289#488—1116no—
290#487—1116no—
291#419—118no—
292#417—118no—
293#416—118no—
294C2×#103—111no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—111no—
301C2×#103—118no—
302C2×#102—111no—
303C2×#102—112no—
304C2×#102—111no—
305#405—118no—
306C2×#97—112no—
307C2×C4×C8—112no—
308C22×C11—28no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—84no—
315C22×C11C2×#12414yes—
316C22×C11C2×#12412yes—
317C22×C11#57712yes—
318C22×C11#57812yes—
319C22×C11C23×D411yescharacteristic
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—42no—
323C4×C11—44no—
324C4×C11C2×#12414yes—
325C4×C11C2×#12412yes—
326C4×C11C22×#4111yescharacteristic
327C4×C11C22×#4111yescharacteristic
328Dic11—42no—
329Dic11—44no—
330Dic11—42no—
331C2×#41—22no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41C22×D1114yes—
335C22×Q8—21no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8—222no—
340C22×Q8C22×D1112yes—
341C22×Q8C22×D1111yescharacteristic
342C22×Q8C22×D1114yes—
343C22×D4—21no—
344C22×D4C22×D1111yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C2×M16—114no—
350C2×M16—224no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—114no—
354C22×C8—112no—
355C22×C8—224no—
356C4⋊Q8—24no—
357C4⋊Q8—118no—
358C4⋊Q8—228no—
359C4⋊Q8—224no—
360C4⋊Q8C22×D1118yes—
361#125—118no—
362#125—228no—
363#125—224no—
364#124—24no—
365#124C22×D1118yes—
366#123—216no—
367C22⋊Q8—28no—
368C22⋊Q8—28no—
369C22⋊Q8—2216no—
370#117—114no—
371#117—222no—
372#117C22⋊D1114yes—
373#117C22×D1114yes—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4C22⋊D1111yescharacteristic
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4C22⋊D1112yes—
391C2×C42—221no—
392C2×C42C22×D1112yes—
393#103—118no—
394#103—118no—
395#103—114no—
396#103—114no—
397#103—118no—
398#103—118no—
399#103—118no—
400#102—114no—
401#102—114no—
402#102—118no—
403#97—118no—
404C4×C8—118no—
405C2×C11—24no—
406C2×C11—82no—
407C2×C11#313714yescomplemented
408C2×C11C22×#12411yescharacteristic
409C2×C11C2×#57711yescharacteristic
410C2×C11C2×#57811yescharacteristic
411C24—21no—
412C24C2×C22⋊D1111yescharacteristic
413#41—28no—
414#41—28no—
415#41—48no—
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—24no—
420C2×Q8—24no—
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—44no—
426C2×Q8—48no—
427C2×Q8—228no—
428C2×Q8—884no—
429C2×Q8C23×D1114yes—
430C2×Q8C23×D1112yes—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—44no—
436C2×D4C23×D1112yes—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—882no—
448C22×C4#434114yes—
449C22×C4#434114yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1112yes—
455C22×C4C23×D1111yescharacteristic
456M16—228no—
457C2×C8—112no—
458C2×C8—114no—
459C2×C8—112no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—228no—
463C2×C8—224no—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—114no—
467C4⋊C4—112no—
468C4⋊C4—112no—
469C4⋊C4—224no—
470C4⋊C4—222no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—228no—
474C4⋊C4—228no—
475C4⋊C4—228no—
476C4⋊C4C2×C22⋊D1114yes—
477C4⋊C4C2×C22⋊D1114yes—
478C22⋊C4—28no—
479C22⋊C4—28no—
480C22⋊C4—224no—
481C22⋊C4C2×C22⋊D1118yes—
482C42—224no—
483C42C2×C22⋊D1114yes—
484C42C23×D1114yes—
485C11C2×#313711yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23#6698914yes—
493C23C22×C22⋊D1112yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—24no—
496Q8—24no—
497Q8—22no—
498Q8—22no—
499Q8—48no—
500Q8—44no—
501Q8—42no—
502Q8—888no—
503D4—22no—
504D4—22no—
505D4—48no—
506D4—42no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—42no—
512C2×C4—48no—
513C2×C4—44no—
514C2×C4—48no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—884no—
522C2×C4#6698914yes—
523C2×C4#6698918yes—
524C2×C4C2×#434112yes—
525C2×C4C2×#434112yes—
526C2×C4C2×#434114yes—
527C2×C4C2×#434114yes—
528C2×C4C22×C22⋊D1114yes—
529C2×C4C22×C22⋊D1114yes—
530C2×C4C22×C22⋊D1112yes—
531C2×C4C22×C22⋊D1111yescharacteristic
532C2×C4C24×D1111yescharacteristic
533C8—222no—
534C8—222no—
535C8—224no—
536C22—28no—
537C22—22no—
538C22—22no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—84no—
543C22C2×#6698914yes—
544C22C2×#6698912yes—
545C22#1062336812yes—
546C22#1062336912yes—
547C22C23×C22⋊D1111yescharacteristic
548C4—24no—
549C4—24no—
550C4—42no—
551C4—44no—
552C4—444no—
553C4—442no—
554C4—442no—
555C4C2×#6698914yes—
556C4C2×#6698912yes—
557C4C22×#434111yescharacteristic
558C4C22×#434111yescharacteristic
559C2—24no—
560C2—82no—
561C2#1307898114yesdirect product factor
562C2C22×#6698911yescharacteristic
563C2C2×#1062336811yescharacteristic
564C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11C2×#3137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
2. #13078981C2direct (N × H)
3. C2×#10622695C2semidirect
4. C2×#10622668C2semidirect
5. C2×#10622669C2semidirect
6. C2×#10622694C2semidirect
8. C2×#10622838C2semidirect
10. C22×#66899C2semidirect
11. C2×#10622610C2semidirect
28. #10623050C22semidirect
36. #10622838C22semidirect
44. C2×#66899C22semidirect
48. #10622695C22semidirect
49. #10622694C22semidirect
50. #10622669C22semidirect
51. #10622668C22semidirect
52. #10622610C22semidirect
407. C2×C11#3137semidirect
485. C11C2×#3137semidirect
561. C2#13078981direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130789812
C2×#106226952
C2×#106226682
C2×#106226692
C2×#106226942
C2×#106228452
C2×#106228382
C2×#106228462
C22×#668992
C2×#106226102
C2×C11×#5362
C2×#313711