Finite Group Databasebeta

← C2×#13081624 #15634705

Subgroups — C2×#13081624 #15634705

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2#13081624C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622686C211yesmaximal, characteristic
5C2×#10622640C211yesmaximal, characteristic, complemented
6C2×#10622688C211yesmaximal, characteristic, complemented
7C2×#10622629C212yesmaximal, complemented
8C2×#10622670C212yesmaximal, complemented
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4326C211yesmaximal, characteristic, complemented
11C2×C4×#4323C212yesmaximal, complemented
12C2×C11×#559C211yesmaximal, characteristic, complemented
13C11×#559—24no—
14C11×#559C2218yescomplemented
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124—21no—
17C2×C11×#124C2212yes—
18C2×C11×#123—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2212yes—
23C2×#67000—21no—
24C22×#4326C2211yescharacteristic
25C22×#4325C2212yes—
26C22×#4324C2212yes—
27C22×#4323C2212yes—
28C22×#4323C2212yes—
29#10623116—24no—
30#10623116C2218yescomplemented
31C2×#66947—22no—
32C2×#66946—21no—
33C2×#66928C2212yes—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×C4×Dic22C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66896C2212yes—
39#10622688C2218yescomplemented
40#10622686C2218yes—
41#10622672C22116yescomplemented
42#10622670C22116yescomplemented
43C4×#4326C2218yescomplemented
44#10622640C2218yescomplemented
45Q8×C11⋊C8C2218yescomplemented
46#10622629C22116yescomplemented
47C4×#4323C22116yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66873C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4×C11⋊C8C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11C2312yes—
60C23×C4×C11—22no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44C2312yes—
64C22×C4×D11—22no—
65C22×Dic22C2311yescharacteristic
66C11×#127—22no—
67C11×#127C2314yes—
68C11×#124—28no—
69C11×#124—24no—
70C11×#124C2318yes—
71C11×#123—216no—
72C4×Q8×C11—22no—
73C4×Q8×C11D414yes—
74C4×Q8×C11C2314yes—
75C4×Q8×C11C2314yes—
76C4×D4×C11—28no—
77C4×D4×C11—24no—
78C4×D4×C11C2318yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89#67000—28no—
90C2×#4326—24no—
91C2×#4326C2314yes—
92C2×#4325—44no—
93C2×#4325C2318yes—
94C2×#4324—44no—
95C2×#4324C2318yes—
96C2×#4323—28no—
97C2×#4323—44no—
98C2×#4323C2318yes—
99C2×#4323C2318yes—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109#66947—216no—
110#66946—28no—
111#66928—24no—
112#66928C2318yes—
113#66927—22no—
114#66927C2314yes—
115C4×D44—24no—
116C4×D44C2318yes—
117C4×Dic22—22no—
118C4×Dic22C2314yes—
119#66899C2314yes—
120#66896C2318yes—
121#66874C2314yes—
122#66873C2318yes—
123#66871C2314yes—
124C4⋊(C11⋊C8)C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C4×C11⋊C8C2318yes—
127C4×C11⋊C8C2314yes—
128C2×#3396—111nomaximal, Sylow
129C24×C11—22no—
130C23×D11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2×D414yes—
136C2×Q8×C11C2412yes—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—44no—
143C2×D4×C11—82no—
144C2×D4×C11C2414yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—28no—
148C22×C4×C11—84no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C2×D44—22no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—44no—
162C2×D44—82no—
163C2×D44C2414yes—
164C2×C4×D11—28no—
165C2×C4×D11—84no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22C2412yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D414yes—
173C11×C4⋊C4C2×D418yes—
174C11×C4⋊C4C2412yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C42×C11—24no—
179C42×C11C2×D412yes—
180C42×C11C2×D414yes—
181C42×C11C2412yes—
182C42×C11C2414yes—
183#4326—28no—
184#4325—48no—
185#4324—48no—
186#4323—216no—
187#4323—48no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2412yes—
193Dic11⋊C4—24no—
194C4×Dic11—24no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—24no—
197C2×C11⋊C8#4114yes—
198C2×C11⋊C8C2414yes—
199C2×C11⋊C8C2412yes—
200C2×C11⋊C8C2412yes—
201C2×#559—111no—
202C2×#559D1111yescharacteristic, complemented
203#3396—1116no—
204C2×#495—112no—
205C2×#493—111no—
206C2×#460—111no—
207C2×#460—111no—
208C2×#463—112no—
209C2×#463—112no—
210C2×C8×Q8—111no—
211C2×C4×Q16—111no—
212C2×C4×D8—112no—
213C23×C11—24no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—44no—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222Q8×C11—28no—
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—44no—
229D4×C11—48no—
230D4×C11—84no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—88no—
239C2×C4×C11#13514yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C2×C4×C11C2511yescharacteristic
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252D44—24no—
253D44—24no—
254D44—44no—
255D44—48no—
256D44—84no—
257C4×D11—88no—
258Dic22—22no—
259Dic22—22no—
260Dic22—42no—
261C11⋊C8—22no—
262C11⋊C8—24no—
263C11⋊C8C2×#4114yes—
264C22×Q16—111no—
265C22×SD16—112no—
266C22×SD16—112no—
267C22×D8—112no—
268C22×D8—112no—
269#559—24no—
270#559—118no—
271#559—224no—
272#559C2×D1118yescomplemented
273C2×#127—111no—
274C2×#127C2×D1111yescharacteristic
275C2×#124—21no—
276C2×#124—112no—
277C2×#124—221no—
278C2×#124C2×D1112yes—
279C2×#123—22no—
280C2×#123—222no—
281C2×C4×Q8—111no—
282C2×C4×Q8C2×D1111yescharacteristic
283C2×C4×Q8C2×D1111yescharacteristic
284C2×C4×D4—21no—
285C2×C4×D4—112no—
286C2×C4×D4—221no—
287C2×C4×D4C2×D1112yes—
288#495—1116no—
289#493—118no—
290#463—1116no—
291#463—1116no—
292#460—118no—
293#460—118no—
294C8×Q8—118no—
295C4×Q16—118no—
296C4×D8—1116no—
297C2×#107—111no—
298C2×C4⋊C8—112no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#102—112no—
303C2×#102—112no—
304C2×C4×C8—111no—
305C2×C4×C8—112no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—88no—
310C22×C11#55012yes—
311C22×C11C2×#13512yes—
312C22×C11#57612yes—
313C22×C11C23×D411yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—88no—
318C4×C11—24no—
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11#55012yes—
324C4×C11C2×#13514yes—
325C4×C11C22×#4111yescharacteristic
326C4×C11C2×H(5,𝔽2)11yescharacteristic
327Dic11—42no—
328Dic11—42no—
329C22×Q8—111no—
330C22×Q8C22⋊D1111yescharacteristic
331C22×Q8C22×D1111yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—112no—
335C22×D4—221no—
336C22×D4—221no—
337C22×D4C22×D1112yes—
338C23×C4—22no—
339C23×C4—222no—
340C2×Q16—114no—
341C2×Q16—224no—
342C2×SD16—118no—
343C2×SD16—118no—
344C2×SD16—444no—
345C2×SD16—444no—
346C2×D8—118no—
347C2×D8—118no—
348C2×D8—228no—
349C2×D8—444no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—112no—
353#127—22no—
354#127—114no—
355#127—222no—
356#127C22×D1114yes—
357#124—28no—
358#124—24no—
359#124—118no—
360#124—228no—
361#124—224no—
362#124C22×D1118yes—
363#123—216no—
364#123—2216no—
365C4×Q8—22no—
366C4×Q8—114no—
367C4×Q8—222no—
368C4×Q8C22⋊D1114yes—
369C4×Q8C22×D1114yes—
370C4×Q8C22×D1114yes—
371C4×D4—28no—
372C4×D4—24no—
373C4×D4—118no—
374C4×D4—228no—
375C4×D4—224no—
376C4×D4C22×D1118yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22⋊D1112yes—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C42—21no—
390C2×C42—221no—
391C2×C42C22×D1112yes—
392C2×C42C22×D1111yescharacteristic
393#107—114no—
394C4⋊C8—114no—
395C4⋊C8—118no—
396#103—114no—
397#103—114no—
398#102—118no—
399#102—118no—
400C4×C8—118no—
401C4×C8—114no—
402C2×C11—84no—
403C2×C11#339614yescomplemented
404C2×C11C2×#55011yescharacteristic
405C2×C11C22×#13511yescharacteristic
406C2×C11C2×#57611yescharacteristic
407D11—84no—
408C24—22no—
409C24—222no—
410C2×Q8—24no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—112no—
415C2×Q8—221no—
416C2×Q8—222no—
417C2×Q8—222no—
418C2×Q8C2×C22⋊D1114yes—
419C2×Q8C23×D1112yes—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—44no—
426C2×D4—82no—
427C2×D4—114no—
428C2×D4—224no—
429C2×D4—224no—
430C2×D4—224no—
431C2×D4—222no—
432C2×D4—224no—
433C2×D4—444no—
434C2×D4—882no—
435C2×D4C23×D1114yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—28no—
439C22×C4—84no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—228no—
443C22×C4—884no—
444C22×C4C2×C22⋊D1112yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449Q16—228no—
450SD16—448no—
451SD16—448no—
452D8—2216no—
453D8—448no—
454C2×C8—114no—
455C2×C8—112no—
456C2×C8—114no—
457C2×C8—112no—
458C2×C8—222no—
459C2×C8—224no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—112no—
463C4⋊C4—221no—
464C4⋊C4—224no—
465C4⋊C4C2×C22⋊D1114yes—
466C4⋊C4C2×C22⋊D1118yes—
467C4⋊C4C23×D1112yes—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22⋊C4—28no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C42—24no—
475C42—224no—
476C42C2×C22⋊D1114yes—
477C42C2×C22⋊D1112yes—
478C42C23×D1114yes—
479C42C23×D1112yes—
480C11C2×#339611yescharacteristic, complemented, Sylow
481C23—24no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—224no—
486C23—444no—
487C23—444no—
488C23—444no—
489C23C22×C22⋊D1111yescharacteristic
490Q8—28no—
491Q8—22no—
492Q8—22no—
493Q8—42no—
494Q8—222no—
495Q8—222no—
496Q8—442no—
497D4—24no—
498D4—24no—
499D4—48no—
500D4—44no—
501D4—84no—
502D4—224no—
503D4—224no—
504D4—448no—
505D4—444no—
506D4—884no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—88no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—888no—
520C2×C4#6700314yes—
521C2×C4#41×D1112yes—
522C2×C4#6704212yes—
523C2×C4C22×C22⋊D1114yes—
524C2×C4C22×C22⋊D1114yes—
525C2×C4C22×C22⋊D1112yes—
526C2×C4C22×C22⋊D1112yes—
527C2×C4C22×C22⋊D1111yescharacteristic
528C2×C4C24×D1111yescharacteristic
529C8—114no—
530C8—222no—
531C8—224no—
532C22—44no—
533C22—44no—
534C22—44no—
535C22—88no—
536C22—444no—
537C22—444no—
538C22—444no—
539C22—888no—
540C22C2×#6700312yes—
541C22#1062336512yes—
542C22#1062336612yes—
543C22C23×C22⋊D1111yescharacteristic
544C4—24no—
545C4—24no—
546C4—22no—
547C4—42no—
548C4—42no—
549C4—442no—
550C4—442no—
551C4C2×#6700314yes—
552C4#1062336512yes—
553C4C2×#41×D1111yescharacteristic
554C4C2×#6704211yescharacteristic
555C2—84no—
556C2—884no—
557C2#1308162414yesdirect product factor
558C2C2×#1062336511yescharacteristic
559C2C22×#6700311yescharacteristic
560C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622686C2
hypercenterC2×#559D11
hypocenterC11C2×#3396
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081624C2direct (N × H)
3. C2×#10622672C2semidirect
5. C2×#10622640C2semidirect
6. C2×#10622688C2semidirect
7. C2×#10622629C2semidirect
8. C2×#10622670C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4326C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#559C2semidirect
14. C11×#559C22semidirect
30. #10623116C22semidirect
39. #10622688C22semidirect
41. #10622672C22semidirect
42. #10622670C22semidirect
43. C4×#4326C22semidirect
44. #10622640C22semidirect
45. Q8×C11⋊C8C22semidirect
46. #10622629C22semidirect
47. C4×#4323C22semidirect
202. C2×#559D11semidirect
272. #559C2×D11semidirect
403. C2×C11#3396semidirect
480. C11C2×#3396semidirect
557. C2#13081624direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130816242
C2×#106226722
C2×#106226862
C2×#106226402
C2×#106226882
C2×#106226292
C2×#106226702
C2×Q8×C11⋊C82
C2×C4×#43262
C2×C4×#43232
C2×C11×#5592
C2×#339611