Finite Group Databasebeta

← C2×#13079677 #15625144

Subgroups — C2×#13079677 #15625144

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic, complemented
2#13079677C2116yesmaximal, direct product factor
3C2×#10622671C211yesmaximal, characteristic, complemented
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622695C211yesmaximal, characteristic, complemented
6C2×#10622669C211yesmaximal, characteristic, complemented
7C2×#10622670C212yesmaximal, complemented
8C2×#10622696C212yesmaximal, complemented
9C2×#10622851C212yesmaximal, complemented
10C2×#10622840C212yesmaximal, complemented
11C2×#10622613C211yesmaximal, characteristic, complemented
12C2×C11×#536C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C11×#536—24no—
16C11×#536C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—22no—
22C2×C11×C22⋊Q8—22no—
23C2×C11×#117C2211yescharacteristic
24C22×#4325C2212yes—
25C22×#4325C2212yes—
26C22×#4325C2212yes—
27C22×#4323C2212yes—
28C2×#66983C2212yes—
29#10623066—24no—
30#10623066C2218yescomplemented
31C2×#66947—22no—
32C2×#66937—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44C2212yes—
35C2×#66923C2211yescharacteristic
36#10622851C22116yescomplemented
37#10622840C22116yescomplemented
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622698C2218yescomplemented
44#10622696C22116yescomplemented
45#10622695C2218yescomplemented
46#10622671C2218yescomplemented
47#10622670C22116yescomplemented
48#10622669C2218yescomplemented
49#10622613C2218yescomplemented
50C2×C4⋊(C11⋊C8)C2212yes—
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53C2×C11×#41—22no—
54C2×C11×#41—44no—
55C2×C11×#41C2314yes—
56C22×Q8×C11—21no—
57C22×Q8×C11—22no—
58C22×Q8×C11—44no—
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2314yes—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×D44—22no—
70C22×D44C2312yes—
71C22×C4×D11—22no—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yes—
75C11×C4⋊Q8C2314yes—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124C2314yes—
79C11×#124C2314yes—
80C11×#123—216no—
81C11×C22⋊Q8—216no—
82C11×#117D414yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D412yes—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×#4325—44no—
93C2×#4325—44no—
94C2×#4325—44no—
95C2×#4325C2318yes—
96C2×#4325C2318yes—
97C2×#4325C2318yes—
98C2×#4323—44no—
99C2×#4323C2318yes—
100#66983—24no—
101#66983C2318yes—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4—22no—
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2312yes—
108#66947—216no—
109#66937—216no—
110#66927—22no—
111#66927C2314yes—
112C4×D44—24no—
113C4×D44C2318yes—
114#66923—22no—
115#66923C2314yes—
116#66899C2318yes—
117#66899C2318yes—
118#66899C2318yes—
119#66896C2318yes—
120C22⋊(C11⋊C8)C2318yes—
121C4⋊(C11⋊C8)C2318yes—
122#66867C2314yes—
123C4×C11⋊C8C2314yes—
124C2×#3221—111nomaximal, Sylow
125C24×C11—21no—
126C24×C11C2×D411yescharacteristic
127C23×D11—22no—
128C11×#41—48no—
129C11×#41—48no—
130C2×Q8×C11—24no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11—48no—
138C2×Q8×C11—44no—
139C2×Q8×C11—48no—
140C2×Q8×C11C2412yes—
141C2×Q8×C11C2412yes—
142C2×Q8×C11C2412yes—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11C2412yes—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—28no—
163C2×C22⋊D11—84no—
164C22×Dic11—22no—
165C2×D44—22no—
166C2×D44—28no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—84no—
170C2×D44C2414yes—
171C2×C4×D11—28no—
172C2×C4×D11—84no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4C2×D418yes—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4C2×D418yes—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182C42×C11C2412yes—
183#4325—48no—
184#4325—48no—
185#4325—48no—
186#4323—48no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—22no—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—28no—
192C2×C11⋊C8—24no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8C2414yes—
195C2×C11⋊C8C2414yes—
196C2×#540—111no—
197C2×#536D1111yescharacteristic, complemented
198#3221—1116no—
199C2×#496—111no—
200C2×#492—111no—
201C2×#491—111no—
202C2×#488—111no—
203C2×#463—112no—
204C2×#461—112no—
205C2×#449—112no—
206C2×#448—112no—
207C2×#433—111no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—42no—
212C23×C11—44no—
213C23×C11C22×D412yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—44no—
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—48no—
228D4×C11—42no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—48no—
238C2×C4×C11—48no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11H(5,𝔽2)14yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—88no—
249C2×Dic11—24no—
250C2×Dic11—44no—
251D44—24no—
252D44—24no—
253D44—44no—
254D44—88no—
255C4×D11—88no—
256C11⋊C8—24no—
257C11⋊C8—24no—
258C22×#41C2×D1111yescharacteristic
259C23×Q8C2×D1111yescharacteristic
260C22×SD16—112no—
261C22×SD16—112no—
262C22×SD16—112no—
263C22×D8—112no—
264#540—118no—
265#540—224no—
266#536—24no—
267#536C2×D1118yescomplemented
268C2×C4⋊Q8C2×D1111yescharacteristic
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#127—111no—
271C2×#125—111no—
272C2×#124C2×D1111yescharacteristic
273C2×#124C2×D1111yescharacteristic
274C2×#123—22no—
275C2×#123—222no—
276C2×C22⋊Q8—22no—
277C2×#121—112no—
278C2×#121—222no—
279C2×C4×D4—112no—
280C2×#117C2×D1111yescharacteristic
281#496—118no—
282#492—118no—
283#491—118no—
284#488—118no—
285#463—1116no—
286#461—1116no—
287#449—1116no—
288#448—1116no—
289#433—118no—
290C2×C4⋊C8—112no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103—112no—
294C2×#102—112no—
295C2×C22⋊C8—112no—
296C2×#97—111no—
297C2×C4×C8—111no—
298C22×C11—22no—
299C22×C11—24no—
300C22×C11—44no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—84no—
304C22×C11#53512yes—
305C22×C11#57714yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—44no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—88no—
311C4×C11—22no—
312C4×C11—24no—
313C4×C11—24no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11#53512yes—
318C4×C11C2×H(5,𝔽2)12yes—
319Dic11—44no—
320C2×#41—22no—
321C2×#41—44no—
322C2×#41C22×D1114yes—
323C22×Q8—21no—
324C22×Q8—22no—
325C22×Q8—44no—
326C22×Q8C22×D1111yescharacteristic
327C22×Q8C22×D1111yescharacteristic
328C22×Q8C22×D1111yescharacteristic
329C22×Q8C22×D1114yes—
330C22×D4—21no—
331C22×D4—112no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4C22×D1111yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—222no—
338C23×C4C22×D1111yescharacteristic
339C2×SD16—118no—
340C2×SD16—118no—
341C2×SD16—118no—
342C2×SD16—444no—
343C2×SD16—444no—
344C2×SD16—444no—
345C2×D8—118no—
346C2×D8—444no—
347C22×C8—112no—
348C22×C8—112no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8C22×D1114yes—
352C4⋊Q8C22×D1114yes—
353#127—114no—
354#127—222no—
355#125—114no—
356#125—222no—
357#124—22no—
358#124—22no—
359#124C22×D1114yes—
360#124C22×D1114yes—
361#123—216no—
362#123—2216no—
363C22⋊Q8—216no—
364#121—118no—
365#121—224no—
366#121—2216no—
367C4×D4—118no—
368C4×D4—224no—
369#117C22⋊D1114yes—
370#117C22×D1114yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4C22⋊D1112yes—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4C22⋊D1112yes—
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—118no—
384#103—118no—
385#103—118no—
386#103—118no—
387#102—118no—
388C22⋊C8—118no—
389#97—114no—
390C4×C8—114no—
391C2×C11—42no—
392C2×C11—82no—
393C2×C11#322114yescomplemented
394C2×C11C2×#53511yescharacteristic
395C2×C11C2×#57712yes—
396D11—84no—
397C24—21no—
398C24—222no—
399C24C2×C22⋊D1111yescharacteristic
400#41—48no—
401#41—48no—
402C2×Q8—24no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—48no—
410C2×Q8—44no—
411C2×Q8—48no—
412C2×Q8C23×D1112yes—
413C2×Q8C23×D1112yes—
414C2×Q8C23×D1112yes—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—21no—
418C2×D4—44no—
419C2×D4—114no—
420C2×D4—228no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—222no—
424C2×D4—228no—
425C2×D4—884no—
426C2×D4—884no—
427C2×D4C23×D1112yes—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—222no—
437C22×C4—228no—
438C22×C4—884no—
439C22×C4C2×C22⋊D1112yes—
440C22×C4C2×C22⋊D1112yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1112yes—
444C22×C4C23×D1111yescharacteristic
445SD16—448no—
446SD16—448no—
447SD16—448no—
448D8—448no—
449C2×C8—114no—
450C2×C8—114no—
451C2×C8—224no—
452C2×C8—224no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—114no—
456C4⋊C4—222no—
457C4⋊C4—228no—
458C4⋊C4C2×C22⋊D1118yes—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C22⋊C4C2×C22⋊D1118yes—
464C42C2×C22⋊D1112yes—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C42C23×D1112yes—
468C11C2×#322111yescharacteristic, complemented, Sylow
469C23—22no—
470C23—24no—
471C23—22no—
472C23—42no—
473C23—44no—
474C23—224no—
475C23—444no—
476C23—444no—
477C23—444no—
478C23C22×C22⋊D1112yes—
479C23C22×C22⋊D1111yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—24no—
483Q8—48no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487D4—24no—
488D4—48no—
489D4—42no—
490D4—224no—
491D4—224no—
492D4—444no—
493D4—888no—
494D4—888no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—48no—
504C2×C4—48no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—224no—
509C2×C4—444no—
510C2×C4—888no—
511C2×C4#6703714yes—
512C2×C4C22×C22⋊D1114yes—
513C2×C4C22×C22⋊D1114yes—
514C2×C4C22×C22⋊D1112yes—
515C2×C4C22×C22⋊D1111yescharacteristic
516C2×C4C24×D1111yescharacteristic
517C8—224no—
518C8—224no—
519C22—22no—
520C22—24no—
521C22—44no—
522C22—42no—
523C22—44no—
524C22—84no—
525C22—444no—
526C22—444no—
527C22—444no—
528C22—888no—
529C22#1062333612yes—
530C22#1062336814yes—
531C22C23×C22⋊D1111yescharacteristic
532C4—22no—
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—444no—
539C4#1062333612yes—
540C4C2×#6703712yes—
541C2—42no—
542C2—82no—
543C2—884no—
544C2#1307967714yesdirect product factor
545C2C2×#1062333611yescharacteristic
546C2C2×#1062336812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
hypercenterC2×#536D11
hypocenterC11C2×#3221
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×#10623066C2semidirect
2. #13079677C2direct (N × H)
3. C2×#10622671C2semidirect
4. C2×#10622698C2semidirect
5. C2×#10622695C2semidirect
6. C2×#10622669C2semidirect
7. C2×#10622670C2semidirect
8. C2×#10622696C2semidirect
9. C2×#10622851C2semidirect
10. C2×#10622840C2semidirect
11. C2×#10622613C2semidirect
12. C2×C11×#536C2semidirect
16. C11×#536C22semidirect
30. #10623066C22semidirect
36. #10622851C22semidirect
37. #10622840C22semidirect
43. #10622698C22semidirect
44. #10622696C22semidirect
45. #10622695C22semidirect
46. #10622671C22semidirect
47. #10622670C22semidirect
48. #10622669C22semidirect
49. #10622613C22semidirect
197. C2×#536D11semidirect
267. #536C2×D11semidirect
393. C2×C11#3221semidirect
468. C11C2×#3221semidirect
544. C2#13079677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230662
#130796772
C2×#106226712
C2×#106226982
C2×#106226952
C2×#106226692
C2×#106226702
C2×#106226962
C2×#106228512
C2×#106228402
C2×#106226132
C2×C11×#5362
C2×#322111