Finite Group Databasebeta

← C2×C11×#1621 #14595697

Subgroups — C2×C11×#1621 #14595697

Order 2816.

1438 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic, complemented
2C2×C11×#493C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C2×C11×#459C211yesmaximal, characteristic, complemented
5C11×#1621C218yesmaximal, direct product factor
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C22×C11×SD16—21no—
11C22×C11×D8—21no—
12C22×C11×D8—22no—
13C11×#550—22no—
14C11×#550—22no—
15C11×#550—22no—
16C11×#550C2214yescomplemented
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#121—22no—
21C2×C11×#121—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#493—22no—
26C11×#493C2214yescomplemented
27C11×#460—22no—
28C11×#460C2214yescomplemented
29C11×#459—22no—
30C11×#459C2214yescomplemented
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×#102—21no—
34C2×C11×#102—21no—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#331C2214yescomplemented
37C11×Q8⋊C8C2214yescomplemented
38C11×D4⋊C8C2214yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—44no—
42C2×C11×#41—44no—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11D411yescharacteristic
52C22×D4×C11D412yes—
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C2×C11×SD16—24no—
56C2×C11×SD16—44no—
57C2×C11×D8—28no—
58C2×C11×D8—24no—
59C2×C11×D8—48no—
60C2×C11×D8—44no—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C11×#127—24no—
65C11×#127—24no—
66C11×#127—21no—
67C11×#127—21no—
68C11×#127—21no—
69C11×#127—21no—
70C11×#127—21no—
71C11×#127D412yes—
72C11×#127C2312yes—
73C11×#127C2312yes—
74C11×#121—24no—
75C11×#121—28no—
76C11×#121—28no—
77C11×#121—24no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×Q8×C11C2312yes—
82C4×D4×C11—24no—
83C4×D4×C11—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2312yes—
98C11×C4⋊C8C2312yes—
99C11×#102—24no—
100C11×#102—24no—
101C4×C8×C11—21no—
102C4×C8×C11C2312yes—
103C2×#1621C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—41no—
107C11×#41—48no—
108C11×#41—416no—
109C11×#41—48no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11D814yescomplemented
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—48no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—84no—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×D414yes—
144C22×C4×C11—21no—
145C22×C4×C11—28no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—48no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C11×SD16—48no—
157C11×D8—48no—
158C11×D8—416no—
159C2×C8×C11—24no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—42no—
164C2×C8×C11—42no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2411yescharacteristic
180C2×#550C2×C1111yescharacteristic, complemented
181C2×#493C2×C1111yescharacteristic, complemented
182C2×#460C2×C1111yescharacteristic, complemented
183C2×#459C2×C1111yescharacteristic, complemented
184#1621C2×C1118yesdirect product factor
185C2×#331C2×C1111yescharacteristic, complemented
186C2×Q8⋊C8C2×C1111yescharacteristic, complemented
187C2×D4⋊C8C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—44no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—82no—
198C23×C11—82no—
199C23×C11—82no—
200C23×C11#12011yescharacteristic
201Q8×C11—22no—
202Q8×C11—24no—
203Q8×C11C2×D814yescomplemented
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—44no—
207D4×C11—416no—
208D4×C11—44no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—44no—
218D4×C11—42no—
219D4×C11—44no—
220D4×C11—82no—
221D4×C11—82no—
222D4×C11—88no—
223D4×C11—82no—
224D4×C11—82no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—416no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11C2×D812yes—
240C2×C4×C11#13512yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11AGL(1,ℤ/8)12yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C8×C11—24no—
247C8×C11—42no—
248C8×C11—42no—
249C22×#41—21no—
250C22×SD16—21no—
251C22×D8—22no—
252C22×D8—21no—
253#550—22no—
254#550—22no—
255#550—22no—
256#550C22×C1114yescomplemented
257C2×#127—21no—
258C2×#127C22×C1111yescharacteristic
259C2×#127C22×C1111yescharacteristic
260C2×#121—22no—
261C2×#121—21no—
262C2×C4×Q8C22×C1111yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C22×C1111yescharacteristic
265#493—22no—
266#493C22×C1114yescomplemented
267#460—22no—
268#460C22×C1114yescomplemented
269#459—22no—
270#459C22×C1114yescomplemented
271C2×C4⋊C8C22×C1111yescharacteristic
272C2×C4⋊C8C22×C1111yescharacteristic
273C2×#102—21no—
274C2×#102—21no—
275C2×C4×C8C22×C1111yescharacteristic
276#331C22×C1114yescomplemented
277Q8⋊C8C22×C1114yescomplemented
278D4⋊C8C22×C1114yescomplemented
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—84no—
286C22×C11—88no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—164no—
291C22×C11#44712yes—
292C22×C11#44912yes—
293C22×C11#45312yes—
294C22×C11C2×#12011yescharacteristic
295C4×C11—24no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11#44712yes—
301C4×C11#44912yes—
302C4×C11C22×D811yescharacteristic
303C4×C11C2×#13511yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—44no—
309C2×#41—44no—
310C22×Q8D4×C1111yescharacteristic
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4D4×C1111yescharacteristic
319C22×D4D4×C1112yes—
320C23×C4—22no—
321C23×C4—21no—
322C2×SD16—24no—
323C2×SD16—44no—
324C2×D8—24no—
325C2×D8—28no—
326C2×D8—48no—
327C2×D8—44no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331#127—24no—
332#127—24no—
333#127—21no—
334#127—21no—
335#127—21no—
336#127—21no—
337#127—21no—
338#127D4×C1112yes—
339#127C23×C1112yes—
340#127C23×C1112yes—
341#121—24no—
342#121—28no—
343#121—28no—
344#121—24no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8D4×C1112yes—
348C4×Q8C23×C1112yes—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4D4×C1112yes—
354C4×D4C23×C1112yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C1111yescharacteristic
357C2×C4⋊C4D4×C1111yescharacteristic
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C42—21no—
361C2×C42C23×C1111yescharacteristic
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8C23×C1112yes—
365C4⋊C8C23×C1112yes—
366#102—24no—
367#102—24no—
368C4×C8—21no—
369C4×C8C23×C1112yes—
370C2×C11—82no—
371C2×C11—84no—
372C2×C11—162no—
373C2×C11#162114yesdirect product factor
374C2×C11C2×#44711yescharacteristic
375C2×C11C2×#44911yescharacteristic
376C2×C11C2×#45311yescharacteristic
377C24—21no—
378C24—22no—
379C24—41no—
380#41—48no—
381#41—416no—
382#41—48no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8C11×D814yescomplemented
386C2×Q8C2×D4×C1112yes—
387C2×D4—28no—
388C2×D4—28no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—48no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—84no—
415C2×D4C2×D4×C1112yes—
416C2×D4C2×D4×C1114yes—
417C22×C4—21no—
418C22×C4—28no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—48no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429SD16—48no—
430D8—416no—
431D8—48no—
432C2×C8—24no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—42no—
437C2×C8—42no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4C2×D4×C1112yes—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—28no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C42C2×D4×C1111yescharacteristic
450C42C2×D4×C1111yescharacteristic
451C42C2×D4×C1111yescharacteristic
452C42C24×C1111yescharacteristic
453C11C2×#162111yescharacteristic, direct product factor, Sylow
454C23—22no—
455C23—24no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—44no—
460C23—44no—
461C23—42no—
462C23—42no—
463C23—82no—
464C23—82no—
465C23—82no—
466C23C11×#12011yescharacteristic
467Q8—22no—
468Q8—24no—
469Q8C2×C11×D814yescomplemented
470D4—22no—
471D4—22no—
472D4—44no—
473D4—416no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—44no—
484D4—42no—
485D4—44no—
486D4—82no—
487D4—82no—
488D4—88no—
489D4—82no—
490D4—82no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4C11×#12011yescharacteristic
503C2×C4C11×#12011yescharacteristic
504C2×C4C11×#12011yescharacteristic
505C2×C4C2×C11×D812yes—
506C2×C4C11×#13512yes—
507C2×C4C11×AGL(1,ℤ/8)12yes—
508C2×C4C11×AGL(1,ℤ/8)12yes—
509C2×C4C22×D4×C1111yescharacteristic
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C22×D4×C1111yescharacteristic
512C8—24no—
513C8—42no—
514C8—42no—
515C22—44no—
516C22—42no—
517C22—42no—
518C22—44no—
519C22—44no—
520C22—42no—
521C22—84no—
522C22—88no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22—164no—
527C22C11×#44712yes—
528C22C11×#44912yes—
529C22C11×#45312yes—
530C22C2×C11×#12011yescharacteristic
531C4—24no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—42no—
536C4C11×#44712yes—
537C4C11×#44912yes—
538C4C22×C11×D811yescharacteristic
539C4C2×C11×#13511yescharacteristic
540C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
541C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
542C2—82no—
543C2—84no—
544C2—162no—
545C2C11×#162114yesdirect product factor
546C2C2×C11×#44711yescharacteristic
547C2C2×C11×#44911yescharacteristic
548C2C2×C11×#45311yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#550C2semidirect
2. C2×C11×#493C2semidirect
3. C2×C11×#460C2semidirect
4. C2×C11×#459C2semidirect
5. C11×#1621C2direct (N × H)
6. C2×C11×#331C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
8. C2×C11×D4⋊C8C2semidirect
16. C11×#550C22semidirect
26. C11×#493C22semidirect
28. C11×#460C22semidirect
30. C11×#459C22semidirect
36. C11×#331C22semidirect
37. C11×Q8⋊C8C22semidirect
38. C11×D4⋊C8C22semidirect
103. C2×#1621C11direct (N × H)
112. C2×Q8×C11D8semidirect
180. C2×#550C2×C11semidirect
181. C2×#493C2×C11semidirect
182. C2×#460C2×C11semidirect
183. C2×#459C2×C11semidirect
184. #1621C2×C11direct (N × H)
185. C2×#331C2×C11semidirect
186. C2×Q8⋊C8C2×C11semidirect
187. C2×D4⋊C8C2×C11semidirect
203. Q8×C11C2×D8semidirect
256. #550C22×C11semidirect
266. #493C22×C11semidirect
268. #460C22×C11semidirect
270. #459C22×C11semidirect
276. #331C22×C11semidirect
277. Q8⋊C8C22×C11semidirect
278. D4⋊C8C22×C11semidirect
373. C2×C11#1621direct (N × H)
385. C2×Q8C11×D8semidirect
453. C11C2×#1621direct (N × H)
469. Q8C2×C11×D8semidirect
545. C2C11×#1621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4932
C2×C11×#4602
C2×C11×#4592
C11×#16212
C2×C11×#3312
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C2×#162111