Finite Group Databasebeta

← C2×#13081612 #15634691

Subgroups — C2×#13081612 #15634691

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2#13081612C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622641C212yesmaximal, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622670C212yesmaximal, complemented
8C2×#10622628C211yesmaximal, characteristic
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4325C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C11×#556—24no—
14C11×#556C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×#67000—21no—
24C22×#4326C2212yes—
25C22×#4325C2212yes—
26C22×#4325C2212yes—
27C22×#4324C2211yescharacteristic
28C22×#4323C2212yes—
29#10623116—24no—
30#10623116C2218yescomplemented
31C2×#66947—22no—
32C2×#66946—21no—
33C2×#66928C2212yes—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×C4×Dic22C2211yescharacteristic
37C2×#66899C2212yes—
38C2×#66896C2211yescharacteristic
39#10622703C2218yescomplemented
40#10622698C2218yescomplemented
41#10622672C22116yescomplemented
42#10622670C22116yescomplemented
43#10622641C22116yescomplemented
44C4×#4325C22116yescomplemented
45Q8×C11⋊C8C2218yescomplemented
46C4×#4324C2218yescomplemented
47#10622628C2218yes—
48C2×#66874C2211yescharacteristic
49C2×#66873C2212yes—
50C2×#66872C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×C4×D11—22no—
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C11×#126—216no—
67C11×#124—24no—
68C11×#124C2318yes—
69C11×C22⋊Q8—28no—
70C4×Q8×C11—24no—
71C4×Q8×C11D414yes—
72C4×Q8×C11C2318yes—
73C4×Q8×C11C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C11×#117—28no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
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—21no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—22no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89#67000—28no—
90C2×#4326—44no—
91C2×#4326C2318yes—
92C2×#4325—28no—
93C2×#4325—44no—
94C2×#4325C2318yes—
95C2×#4325C2318yes—
96C2×#4324—24no—
97C2×#4324C2314yes—
98C2×#4323—44no—
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⋊C8C2312yes—
107C22×C11⋊C8C2311yescharacteristic
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#66899C2318yes—
120#66896C2314yes—
121#66874C2314yes—
122#66873C2318yes—
123#66872C2314yes—
124C4⋊(C11⋊C8)C2314yes—
125C4⋊(C11⋊C8)C2318yes—
126C4×C11⋊C8C2314yes—
127C4×C11⋊C8C2318yes—
128C2×#3394—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11C2×D414yes—
136C2×Q8×C11C2414yes—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11C2412yes—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×D44—22no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—44no—
158C2×D44—82no—
159C2×D44C2414yes—
160C2×C4×D11—28no—
161C2×C4×D11—84no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22C2412yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C2×D414yes—
171C11×C4⋊C4C2×D418yes—
172C11×C4⋊C4C2412yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—28no—
176C42×C11—28no—
177C42×C11C2×D412yes—
178C42×C11C2×D414yes—
179C42×C11C2412yes—
180C42×C11C2414yes—
181#4326—48no—
182#4325—216no—
183#4325—48no—
184#4324—28no—
185#4323—48no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2412yes—
191Dic11⋊C4—24no—
192C4×Dic11—24no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8#4114yes—
196C2×C11⋊C8C2414yes—
197C2×C11⋊C8C2412yes—
198C2×C11⋊C8C2412yes—
199C2×#559—111no—
200C2×#556D1111yescharacteristic, complemented
201#3394—1116no—
202C2×#495—112no—
203C2×#492—111no—
204C2×#464—112no—
205C2×#462—111no—
206C2×#463—112no—
207C2×#459—111no—
208C2×C8×Q8—111no—
209C2×C4×SD16—112no—
210C2×C4×SD16—111no—
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C22×D411yescharacteristic
216C22×D11—24no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—44no—
220Q8×C11—28no—
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—44no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—42no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—48no—
235C2×C4×C11#13514yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C2×C4×C11C2511yescharacteristic
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248D44—24no—
249D44—24no—
250D44—44no—
251D44—48no—
252D44—84no—
253C4×D11—88no—
254Dic22—22no—
255Dic22—22no—
256Dic22—42no—
257C11⋊C8—24no—
258C11⋊C8—22no—
259C11⋊C8C2×#4114yes—
260C22×Q16—112no—
261C22×SD16—112no—
262C22×SD16—111no—
263C22×SD16—112no—
264C22×D8—112no—
265#559—118no—
266#559—224no—
267#556—24no—
268#556C2×D1118yescomplemented
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#127—111no—
271C2×#126—22no—
272C2×#124—112no—
273C2×#124—221no—
274C2×#124C2×D1112yes—
275C2×#123—222no—
276C2×C22⋊Q8—21no—
277C2×C4×Q8—111no—
278C2×C4×Q8C2×D1112yes—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—112no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—21no—
284#495—1116no—
285#492—118no—
286#464—1116no—
287#463—1116no—
288#462—118no—
289#459—118no—
290C8×Q8—118no—
291C4×SD16—1116no—
292C4×SD16—118no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—112no—
296C2×#103—112no—
297C2×#103—111no—
298C2×#102—111no—
299C2×#102—112no—
300C2×C4×C8—111no—
301C2×C4×C8—112no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—84no—
306C22×C11#55012yes—
307C22×C11C2×#13512yes—
308C22×C11#57712yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—88no—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—22no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11#55012yes—
320C4×C11C2×#13514yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C2×H(5,𝔽2)11yescharacteristic
323Dic11—42no—
324Dic11—42no—
325C22×Q8—111no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×Q8C22×D1112yes—
328C22×D4—112no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—222no—
334C2×Q16—118no—
335C2×Q16—444no—
336C2×SD16—118no—
337C2×SD16—114no—
338C2×SD16—118no—
339C2×SD16—224no—
340C2×SD16—228no—
341C2×SD16—444no—
342C2×D8—118no—
343C2×D8—444no—
344C22×C8—111no—
345C22×C8—112no—
346C22×C8—111no—
347C4⋊Q8—22no—
348C4⋊Q8C22×D1114yes—
349#127—114no—
350#127—222no—
351#126—216no—
352#124—24no—
353#124—118no—
354#124—228no—
355#124—224no—
356#124C22×D1118yes—
357#123—2216no—
358C22⋊Q8—28no—
359C4×Q8—24no—
360C4×Q8—114no—
361C4×Q8—222no—
362C4×Q8C22⋊D1114yes—
363C4×Q8C22×D1118yes—
364C4×Q8C22×D1114yes—
365C4×D4—22no—
366C4×D4—118no—
367C4×D4—228no—
368C4×D4—224no—
369C4×D4C22×D1114yes—
370#117—28no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22⋊D1111yescharacteristic
377C2×C4⋊C4C22⋊D1112yes—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—22no—
386C2×C42—221no—
387C2×C42C22×D1112yes—
388C2×C42C22×D1111yescharacteristic
389#106—114no—
390C4⋊C8—114no—
391C4⋊C8—118no—
392#103—118no—
393#103—114no—
394#102—114no—
395#102—118no—
396C4×C8—114no—
397C4×C8—118no—
398C2×C11—82no—
399C2×C11#339414yescomplemented
400C2×C11C2×#55011yescharacteristic
401C2×C11C22×#13511yescharacteristic
402C2×C11C2×#57711yescharacteristic
403D11—84no—
404C24—21no—
405C24—222no—
406C2×Q8—24no—
407C2×Q8—22no—
408C2×Q8—24no—
409C2×Q8—24no—
410C2×Q8—112no—
411C2×Q8—221no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8C2×C22⋊D1114yes—
415C2×Q8C23×D1114yes—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—114no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—222no—
424C2×D4—224no—
425C2×D4—444no—
426C2×D4—882no—
427C2×D4C23×D1112yes—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—44no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—228no—
435C22×C4—884no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441Q16—448no—
442SD16—228no—
443SD16—2216no—
444SD16—448no—
445D8—448no—
446C2×C8—114no—
447C2×C8—112no—
448C2×C8—114no—
449C2×C8—112no—
450C2×C8—224no—
451C2×C8—222no—
452C4⋊C4—24no—
453C4⋊C4—28no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—112no—
457C4⋊C4—221no—
458C4⋊C4—224no—
459C4⋊C4C2×C22⋊D1114yes—
460C4⋊C4C2×C22⋊D1118yes—
461C4⋊C4C23×D1112yes—
462C22⋊C4—28no—
463C22⋊C4—24no—
464C22⋊C4—28no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C42—28no—
469C42—224no—
470C42C2×C22⋊D1112yes—
471C42C2×C22⋊D1114yes—
472C42C23×D1114yes—
473C42C23×D1112yes—
474C11C2×#339411yescharacteristic, complemented, Sylow
475C23—22no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—224no—
480C23—444no—
481C23—444no—
482C23—444no—
483C23C22×C22⋊D1111yescharacteristic
484Q8—28no—
485Q8—24no—
486Q8—24no—
487Q8—44no—
488Q8—222no—
489Q8—222no—
490Q8—442no—
491D4—22no—
492D4—22no—
493D4—42no—
494D4—224no—
495D4—224no—
496D4—448no—
497D4—444no—
498D4—884no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—48no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—888no—
512C2×C4#6700314yes—
513C2×C4#41×D1112yes—
514C2×C4#6704212yes—
515C2×C4C22×C22⋊D1114yes—
516C2×C4C22×C22⋊D1114yes—
517C2×C4C22×C22⋊D1112yes—
518C2×C4C22×C22⋊D1112yes—
519C2×C4C22×C22⋊D1111yescharacteristic
520C2×C4C24×D1111yescharacteristic
521C8—114no—
522C8—224no—
523C8—222no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—84no—
528C22—444no—
529C22—444no—
530C22—444no—
531C22—888no—
532C22C2×#6700312yes—
533C22#1062336512yes—
534C22#1062336812yes—
535C22C23×C22⋊D1111yescharacteristic
536C4—24no—
537C4—24no—
538C4—22no—
539C4—42no—
540C4—44no—
541C4—442no—
542C4—442no—
543C4C2×#6700314yes—
544C4#1062336512yes—
545C4C2×#41×D1111yescharacteristic
546C4C2×#6704211yescharacteristic
547C2—82no—
548C2—884no—
549C2#1308161214yesdirect product factor
550C2C2×#1062336511yescharacteristic
551C2C22×#6700311yescharacteristic
552C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×#556D11
hypocenterC11C2×#3394
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081612C2direct (N × H)
3. C2×#10622672C2semidirect
4. C2×#10622698C2semidirect
5. C2×#10622641C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622670C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#556C2semidirect
14. C11×#556C22semidirect
30. #10623116C22semidirect
39. #10622703C22semidirect
40. #10622698C22semidirect
41. #10622672C22semidirect
42. #10622670C22semidirect
43. #10622641C22semidirect
44. C4×#4325C22semidirect
45. Q8×C11⋊C8C22semidirect
46. C4×#4324C22semidirect
200. C2×#556D11semidirect
268. #556C2×D11semidirect
399. C2×C11#3394semidirect
474. C11C2×#3394semidirect
549. C2#13081612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130816122
C2×#106226722
C2×#106226982
C2×#106226412
C2×#106227032
C2×#106226702
C2×#106226282
C2×Q8×C11⋊C82
C2×C4×#43252
C2×C4×#43242
C2×C11×#5562
C2×#339411