Finite Group Databasebeta

← C2×#13081608 #15634687

Subgroups — C2×#13081608 #15634687

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×#10623115C211yesmaximal, characteristic, complemented
2#13081608C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622689C211yesmaximal, characteristic, complemented
5C2×#10622667C212yesmaximal, complemented
6C2×#10622644C211yesmaximal, characteristic, complemented
7C2×#10622629C212yesmaximal, complemented
8C2×#10622685C211yesmaximal, characteristic
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4325C211yesmaximal, characteristic, complemented
11C2×C4×#4324C212yesmaximal, 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×#66999—21no—
24C22×#4326C2212yes—
25C22×#4325C2211yescharacteristic
26C22×#4324C2212yes—
27C22×#4324C2212yes—
28C22×#4323C2212yes—
29#10623115—24no—
30#10623115C2218yescomplemented
31C2×#66951—22no—
32C2×#66945—21no—
33C2×#66928C2212yes—
34C2×C4×D44C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×#66899C2211yescharacteristic
38C2×#66896C2212yes—
39#10622689C2218yescomplemented
40#10622685C2218yes—
41#10622672C22116yescomplemented
42#10622667C22116yescomplemented
43#10622644C2218yescomplemented
44C4×#4325C2218yescomplemented
45Q8×C11⋊C8C2218yescomplemented
46C4×#4324C22116yescomplemented
47#10622629C22116yescomplemented
48C2×#66874C2212yes—
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
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×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22C2312yes—
64C11×#127—22no—
65C11×#127C2314yes—
66C11×#124—28no—
67C11×#124—24no—
68C11×#124C2318yes—
69C11×#123—216no—
70C4×Q8×C11—22no—
71C4×Q8×C11D414yes—
72C4×Q8×C11C2314yes—
73C4×Q8×C11C2314yes—
74C4×D4×C11—28no—
75C4×D4×C11—24no—
76C4×D4×C11C2318yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D412yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11—21no—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87#66999—28no—
88C2×#4326—44no—
89C2×#4326C2318yes—
90C2×#4325—24no—
91C2×#4325C2314yes—
92C2×#4324—28no—
93C2×#4324—44no—
94C2×#4324C2318yes—
95C2×#4324C2318yes—
96C2×#4323—44no—
97C2×#4323C2318yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—22no—
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66951—216no—
110#66945—28no—
111#66928—24no—
112#66928C2318yes—
113C4×D44—22no—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117C4×Dic22—24no—
118C4×Dic22C2318yes—
119#66899C2314yes—
120#66896C2318yes—
121#66874C2318yes—
122#66873C2314yes—
123#66872C2314yes—
124C4⋊(C11⋊C8)C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C4×C11⋊C8C2318yes—
127C4×C11⋊C8C2314yes—
128C2×#3394—111nomaximal, Sylow
129C24×C11—22no—
130C23×D11—21no—
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×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—22no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44C2412yes—
160C2×C4×D11—24no—
161C2×C4×D11—44no—
162C2×Dic22—22no—
163C2×Dic22—24no—
164C2×Dic22—24no—
165C2×Dic22C2414yes—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C2×D414yes—
169C11×C4⋊C4C2×D418yes—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C42×C11—24no—
175C42×C11C2×D414yes—
176C42×C11C2×D412yes—
177C42×C11C2414yes—
178C42×C11C2412yes—
179#4326—48no—
180#4325—28no—
181#4324—216no—
182#4324—48no—
183#4323—48no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187C4⋊Dic11—21no—
188C4⋊Dic11—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11C2412yes—
191Dic11⋊C4—28no—
192C4×Dic11—28no—
193C2×C11⋊C8—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8#4114yes—
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2414yes—
198C2×C11⋊C8C2412yes—
199C2×#559D1111yescharacteristic, complemented
200C2×#556—111no—
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—111no—
210C2×C4×SD16—112no—
211C23×C11—24no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220Q8×C11—28no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—42no—
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—44no—
227D4×C11—48no—
228D4×C11—84no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—88no—
237C2×C4×C11#13514yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D414yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11C2511yescharacteristic
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—42no—
250D44—22no—
251D44—22no—
252D44—42no—
253C4×D11—48no—
254Dic22—24no—
255Dic22—24no—
256Dic22—44no—
257C11⋊C8—24no—
258C11⋊C8—22no—
259C11⋊C8C2×#4114yes—
260C22×Q16—112no—
261C22×SD16—111no—
262C22×SD16—112no—
263C22×SD16—112no—
264C22×D8—112no—
265#559—24no—
266#559C2×D1118yescomplemented
267#556—118no—
268#556—224no—
269C2×C4⋊Q8—111no—
270C2×#127C2×D1111yescharacteristic
271C2×#126—222no—
272C2×#124—21no—
273C2×#124—112no—
274C2×#124C2×D1112yes—
275C2×#123—22no—
276C2×C22⋊Q8—221no—
277C2×C4×Q8—112no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—21no—
281C2×C4×D4—111no—
282C2×C4×D4C2×D1112yes—
283C2×#117—221no—
284#495—1116no—
285#492—118no—
286#464—1116no—
287#463—1116no—
288#462—118no—
289#459—118no—
290C8×Q8—118no—
291C4×SD16—118no—
292C4×SD16—1116no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—112no—
296C2×#103—111no—
297C2×#103—112no—
298C2×#102—112no—
299C2×#102—111no—
300C2×C4×C8—111no—
301C2×C4×C8—112no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—88no—
306C22×C11#55012yes—
307C22×C11C2×#13512yes—
308C22×C11#57712yes—
309C22×C11C23×D411yescharacteristic
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—84no—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#55012yes—
320C4×C11C2×#13514yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C2×H(5,𝔽2)11yescharacteristic
323Dic11—44no—
324Dic11—42no—
325C22×Q8—112no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×Q8C22×D1111yescharacteristic
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—111no—
331C22×D4C22×D1112yes—
332C23×C4—22no—
333C23×C4—221no—
334C2×Q16—118no—
335C2×Q16—444no—
336C2×SD16—114no—
337C2×SD16—118no—
338C2×SD16—118no—
339C2×SD16—228no—
340C2×SD16—224no—
341C2×SD16—444no—
342C2×D8—118no—
343C2×D8—444no—
344C22×C8—111no—
345C22×C8—112no—
346C22×C8—111no—
347C4⋊Q8—114no—
348C4⋊Q8—222no—
349#127—22no—
350#127C22×D1114yes—
351#126—2216no—
352#124—28no—
353#124—24no—
354#124—118no—
355#124—224no—
356#124C22×D1118yes—
357#123—216no—
358C22⋊Q8—228no—
359C4×Q8—22no—
360C4×Q8—118no—
361C4×Q8—224no—
362C4×Q8C22⋊D1114yes—
363C4×Q8C22×D1114yes—
364C4×Q8C22×D1114yes—
365C4×D4—28no—
366C4×D4—24no—
367C4×D4—114no—
368C4×D4—222no—
369C4×D4C22×D1118yes—
370#117—228no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22⋊D1111yescharacteristic
377C2×C4⋊C4C22⋊D1112yes—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—222no—
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1112yes—
389#106—114no—
390C4⋊C8—114no—
391C4⋊C8—118no—
392#103—114no—
393#103—118no—
394#102—118no—
395#102—114no—
396C4×C8—114no—
397C4×C8—118no—
398C2×C11—84no—
399C2×C11#339414yescomplemented
400C2×C11C2×#55011yescharacteristic
401C2×C11C22×#13511yescharacteristic
402C2×C11C2×#57711yescharacteristic
403D11—82no—
404C24—22no—
405C24—221no—
406C2×Q8—24no—
407C2×Q8—21no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—114no—
411C2×Q8—222no—
412C2×Q8—224no—
413C2×Q8—224no—
414C2×Q8C2×C22⋊D1114yes—
415C2×Q8C23×D1112yes—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—44no—
422C2×D4—82no—
423C2×D4—112no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—221no—
427C2×D4C23×D1114yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—28no—
431C22×C4—84no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—224no—
435C22×C4—444no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441Q16—448no—
442SD16—2216no—
443SD16—228no—
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—21no—
454C4⋊C4—112no—
455C4⋊C4—221no—
456C4⋊C4—224no—
457C4⋊C4—228no—
458C4⋊C4—224no—
459C4⋊C4C2×C22⋊D1114yes—
460C4⋊C4C2×C22⋊D1118yes—
461C4⋊C4C23×D1112yes—
462C22⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—28no—
465C22⋊C4—228no—
466C22⋊C4—224no—
467C22⋊C4—228no—
468C42—24no—
469C42—228no—
470C42C2×C22⋊D1114yes—
471C42C2×C22⋊D1112yes—
472C42C23×D1112yes—
473C42C23×D1114yes—
474C11C2×#339411yescharacteristic, complemented, Sylow
475C23—24no—
476C23—44no—
477C23—44no—
478C23—44no—
479C23—222no—
480C23—442no—
481C23—442no—
482C23—442no—
483C23C22×C22⋊D1111yescharacteristic
484Q8—28no—
485Q8—22no—
486Q8—22no—
487Q8—42no—
488Q8—224no—
489Q8—224no—
490Q8—444no—
491D4—24no—
492D4—24no—
493D4—48no—
494D4—44no—
495D4—84no—
496D4—222no—
497D4—222no—
498D4—442no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—88no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—442no—
510C2×C4—444no—
511C2×C4—448no—
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—44no—
525C22—44no—
526C22—44no—
527C22—88no—
528C22—442no—
529C22—442no—
530C22—442no—
531C22—884no—
532C22C2×#6700312yes—
533C22#1062336512yes—
534C22#1062336712yes—
535C22C23×C22⋊D1111yescharacteristic
536C4—24no—
537C4—24no—
538C4—22no—
539C4—42no—
540C4—42no—
541C4—442no—
542C4—444no—
543C4C2×#6700314yes—
544C4#1062336512yes—
545C4C2×#41×D1111yescharacteristic
546C4C2×#6704211yescharacteristic
547C2—84no—
548C2—882no—
549C2#1308160814yesdirect product factor
550C2C2×#1062336511yescharacteristic
551C2C22×#6700311yescharacteristic
552C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#559D11
hypocenterC11C2×#3394
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×#10623115C2semidirect
2. #13081608C2direct (N × H)
3. C2×#10622672C2semidirect
4. C2×#10622689C2semidirect
5. C2×#10622667C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622629C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#559C2semidirect
14. C11×#559C22semidirect
30. #10623115C22semidirect
39. #10622689C22semidirect
41. #10622672C22semidirect
42. #10622667C22semidirect
43. #10622644C22semidirect
44. C4×#4325C22semidirect
45. Q8×C11⋊C8C22semidirect
46. C4×#4324C22semidirect
47. #10622629C22semidirect
199. C2×#559D11semidirect
266. #559C2×D11semidirect
399. C2×C11#3394semidirect
474. C11C2×#3394semidirect
549. C2#13081608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130816082
C2×#106226722
C2×#106226892
C2×#106226672
C2×#106226442
C2×#106226292
C2×#106226852
C2×Q8×C11⋊C82
C2×C4×#43252
C2×C4×#43242
C2×C11×#5592
C2×#339411