Finite Group Databasebeta

← C2×#13081404 #15633456

Subgroups — C2×#13081404 #15633456

Order 2816.

2134 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×Q8×D44C211yesmaximal, characteristic, complemented
2#13081404C2116yesmaximal, direct product factor
3C2×#10622668C212yesmaximal, complemented
4C2×#10622683C211yesmaximal, characteristic, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622621C212yesmaximal, complemented
7C2×#10622670C212yesmaximal, complemented
8C2×#10622685C211yesmaximal, characteristic
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622627C212yesmaximal, complemented
11C2×C4×#4325C211yesmaximal, characteristic, complemented
12C2×C11×#559C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C11×#559—24no—
15C11×#559C2218yescomplemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#124C2212yes—
19C2×C11×#123—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2212yes—
24C22×#4325C2211yescharacteristic
25C22×#4323C2212yes—
26Q8×D44—24no—
27Q8×D44C2218yescomplemented
28C2×#66950—21no—
29C2×#66950—22no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×#66922C2212yes—
33C2×#66922C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×#66896C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2212yes—
39#10622685C2218yes—
40#10622683C2218yescomplemented
41#10622670C22116yescomplemented
42#10622668C22116yescomplemented
43C4×#4325C2218yescomplemented
44#10622637C2218yescomplemented
45#10622633C2218yescomplemented
46#10622627C22116yescomplemented
47#10622621C22116yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
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—
61C2×Q8×D11—28no—
62C2×Q8×D11—48no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—21no—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C11×#127—22no—
69C11×#127C2314yes—
70C11×#124—28no—
71C11×#124—24no—
72C11×#124C2318yes—
73C11×#123—216no—
74C4×Q8×C11—22no—
75C4×Q8×C11D414yes—
76C4×Q8×C11C2314yes—
77C4×Q8×C11C2314yes—
78C4×D4×C11—28no—
79C4×D4×C11—24no—
80C4×D4×C11C2318yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D412yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×#4325—24no—
92C2×#4325C2314yes—
93C2×#4323—28no—
94C2×#4323C2318yes—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2312yes—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104#66950—28no—
105#66950—216no—
106C4×D44—24no—
107C4×D44—22no—
108C4×D44C2318yes—
109C4×D44C2314yes—
110#66922—24no—
111#66922—22no—
112#66922C2318yes—
113#66922C2314yes—
114#66899C2318yes—
115#66899C2314yes—
116#66896C2318yes—
117#66896C2318yes—
118#66896C2318yes—
119#66873C2314yes—
120#66872C2314yes—
121#66872C2318yes—
122C4⋊(C11⋊C8)C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124#66867C2318yes—
125C4×C11⋊C8C2314yes—
126C2×#3373—111nomaximal, Sylow
127C24×C11—22no—
128C23×D11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11C2×D414yes—
134C2×Q8×C11C2412yes—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—44no—
141C2×D4×C11—82no—
142C2×D4×C11C2414yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—28no—
146C22×C4×C11—84no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—22no—
154Q8×D11—432no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44#4114yes—
158C2×D44C2412yes—
159C2×C4×D11—28no—
160C2×C4×D11—24no—
161C2×C4×D11—48no—
162C2×C4×D11—44no—
163C2×Dic22—28no—
164C2×Dic22—24no—
165C2×Dic22—48no—
166C2×Dic22—44no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2×D418yes—
171C11×C4⋊C4C2412yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C42×C11—24no—
176C42×C11C2×D414yes—
177C42×C11C2×D412yes—
178C42×C11C2412yes—
179C42×C11C2414yes—
180#4325—28no—
181#4323—216no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—22no—
186C4⋊Dic11—28no—
187C4⋊Dic11—24no—
188C4⋊Dic11C2412yes—
189C4⋊Dic11C2414yes—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2414yes—
196C2×#559D1111yescharacteristic, complemented
197C2×D4×Q8—111no—
198#3373—1116no—
199C2×#489—112no—
200C2×#486—111no—
201C2×#475—111no—
202C2×#476—112no—
203C2×#463—112no—
204C2×#459—111no—
205C2×#446—111no—
206C2×#442—112no—
207C2×C4×SD16—111no—
208C23×C11—24no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—42no—
216C22×D11—42no—
217Q8×C11—28no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—42no—
221D4×C11—24no—
222D4×C11—24no—
223D4×C11—44no—
224D4×C11—48no—
225D4×C11—84no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—88no—
234C2×C4×C11AGL(1,ℤ/8)14yes—
235C2×C4×C11C22×D414yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C112−1+412yes—
242C2×C4×C11C2511yescharacteristic
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—42no—
246C2×Dic11—44no—
247D44—24no—
248D44—22no—
249D44C2×#4114yes—
250C4×D11—416no—
251C4×D11—48no—
252Dic22—416no—
253Dic22—48no—
254C11⋊C8—24no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C23×Q8—221no—
258C22×SD16—111no—
259C22×D8—112no—
260#559—24no—
261#559C2×D1118yescomplemented
262D4×Q8—118no—
263D4×Q8—224no—
264C2×C4⋊Q8—111no—
265C2×C4⋊Q8—112no—
266C2×#127C2×D1111yescharacteristic
267C2×#124—21no—
268C2×#124C2×D1112yes—
269C2×#123—22no—
270C2×C22⋊Q8—221no—
271C2×C22⋊Q8—222no—
272C2×C4×Q8C2×D1111yescharacteristic
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4—21no—
275C2×C4×D4—111no—
276C2×C4×D4—112no—
277C2×C4×D4C2×D1112yes—
278#489—1116no—
279#486—118no—
280#476—1116no—
281#475—118no—
282#463—1116no—
283#459—118no—
284#446—118no—
285#442—1116no—
286C4×SD16—118no—
287C2×#106—112no—
288C2×#106—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—112no—
291C2×#103—112no—
292C2×#103—111no—
293C2×#102—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—111no—
297C2×#97—112no—
298C2×C4×C8—111no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—88no—
303C22×C11#54812yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57712yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—24no—
308C2×D11—48no—
309C2×D11—42no—
310C2×D11—42no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11#54812yes—
317C4×C11C2×AGL(1,ℤ/8)14yes—
318C4×C11C22×#4111yescharacteristic
319C4×C11C2×2−1+411yescharacteristic
320Dic11—42no—
321Dic11—44no—
322C22×Q8—228no—
323C22×Q8—222no—
324C22×Q8—221no—
325C22×Q8—448no—
326C22×Q8C22⋊D1111yescharacteristic
327C22×Q8C22×D1111yescharacteristic
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—111no—
331C22×D4C22×D1112yes—
332C23×C4—22no—
333C23×C4—222no—
334C23×C4—221no—
335C2×SD16—114no—
336C2×SD16—224no—
337C2×D8—118no—
338C2×D8—228no—
339C22×C8—112no—
340C22×C8—111no—
341C22×C8—111no—
342C4⋊Q8—114no—
343C4⋊Q8—118no—
344C4⋊Q8—224no—
345C4⋊Q8—222no—
346#127—22no—
347#127C22×D1114yes—
348#124—28no—
349#124—24no—
350#124C22×D1118yes—
351#123—216no—
352C22⋊Q8—228no—
353C22⋊Q8—2216no—
354C4×Q8—22no—
355C4×Q8C22⋊D1114yes—
356C4×Q8C22×D1114yes—
357C4×Q8C22×D1114yes—
358C4×D4—28no—
359C4×D4—24no—
360C4×D4—114no—
361C4×D4—118no—
362C4×D4—224no—
363C4×D4—222no—
364C4×D4C22×D1118yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22⋊D1112yes—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—221no—
378C2×C42—21no—
379C2×C42C22×D1112yes—
380C2×C42C22×D1111yescharacteristic
381#106—114no—
382#106—118no—
383C4⋊C8—114no—
384C4⋊C8—118no—
385#103—114no—
386#103—118no—
387#102—118no—
388#102—118no—
389#102—118no—
390#102—114no—
391#97—118no—
392C4×C8—114no—
393C2×C11—84no—
394C2×C11#337314yescomplemented
395C2×C11C2×#54811yescharacteristic
396C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C11C2×#57711yescharacteristic
398D11—44no—
399C24—22no—
400C24—221no—
401C2×Q8—24no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—228no—
406C2×Q8—224no—
407C2×Q8—448no—
408C2×Q8—4432no—
409C2×Q8—444no—
410C2×Q8C2×C22⋊D1114yes—
411C2×Q8C23×D1112yes—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—44no—
418C2×D4—82no—
419C2×D4—114no—
420C2×D4—112no—
421C2×D4—222no—
422C2×D4—221no—
423C2×D4C23×D1114yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—28no—
427C22×C4—84no—
428C22×C4—222no—
429C22×C4—221no—
430C22×C4—228no—
431C22×C4—224no—
432C22×C4—448no—
433C22×C4—444no—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439SD16—228no—
440D8—2216no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—114no—
444C2×C8—224no—
445C2×C8—222no—
446C2×C8—222no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—114no—
450C4⋊C4—112no—
451C4⋊C4—221no—
452C4⋊C4—222no—
453C4⋊C4—228no—
454C4⋊C4—224no—
455C4⋊C4C2×C22⋊D1114yes—
456C4⋊C4C2×C22⋊D1118yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C42—24no—
464C42C2×C22⋊D1114yes—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C42C23×D1114yes—
468C11C2×#337311yescharacteristic, complemented, Sylow
469C23—24no—
470C23—44no—
471C23—44no—
472C23—44no—
473C23—224no—
474C23—222no—
475C23—442no—
476C23—442no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—28no—
479Q8—22no—
480Q8—22no—
481Q8—42no—
482Q8—4416no—
483Q8—448no—
484D4—24no—
485D4—24no—
486D4—48no—
487D4—44no—
488D4—84no—
489D4—114no—
490D4—224no—
491D4—222no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—88no—
500C2×C4—224no—
501C2×C4—222no—
502C2×C4—4416no—
503C2×C4—444no—
504C2×C4—442no—
505C2×C4—448no—
506C2×C4#6700214yes—
507C2×C4#41×D1112yes—
508C2×C4#6704312yes—
509C2×C4C22×C22⋊D1114yes—
510C2×C4C22×C22⋊D1114yes—
511C2×C4C22×C22⋊D1112yes—
512C2×C4C22×C22⋊D1112yes—
513C2×C4C22×C22⋊D1111yescharacteristic
514C2×C4C24×D1111yescharacteristic
515C8—224no—
516C8—222no—
517C8—222no—
518C22—44no—
519C22—44no—
520C22—44no—
521C22—88no—
522C22—224no—
523C22—448no—
524C22—442no—
525C22—442no—
526C22C2×#6700212yes—
527C22#1062336212yes—
528C22#1062336712yes—
529C22C23×C22⋊D1111yescharacteristic
530C4—24no—
531C4—24no—
532C4—22no—
533C4—42no—
534C4—42no—
535C4—444no—
536C4—442no—
537C4C2×#6700214yes—
538C4#1062336212yes—
539C4C2×#41×D1111yescharacteristic
540C4C2×#6704311yescharacteristic
541C2—84no—
542C2—444no—
543C2#1308140414yesdirect product factor
544C2C2×#1062336211yescharacteristic
545C2C22×#6700211yescharacteristic
546C2C2×#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×#3373
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×Q8×D44C2semidirect
2. #13081404C2direct (N × H)
3. C2×#10622668C2semidirect
4. C2×#10622683C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622670C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622627C2semidirect
11. C2×C4×#4325C2semidirect
12. C2×C11×#559C2semidirect
15. C11×#559C22semidirect
27. Q8×D44C22semidirect
40. #10622683C22semidirect
41. #10622670C22semidirect
42. #10622668C22semidirect
43. C4×#4325C22semidirect
44. #10622637C22semidirect
45. #10622633C22semidirect
46. #10622627C22semidirect
47. #10622621C22semidirect
196. C2×#559D11semidirect
261. #559C2×D11semidirect
394. C2×C11#3373semidirect
468. C11C2×#3373semidirect
543. C2#13081404direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130814042
C2×#106226682
C2×#106226832
C2×#106226332
C2×#106226212
C2×#106226702
C2×#106226852
C2×#106226372
C2×#106226272
C2×C4×#43252
C2×C11×#5592
C2×#337311