Finite Group Databasebeta

← C2×C11×#3215 #14637977

Subgroups — C2×C11×#3215 #14637977

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic, complemented
2C22×C11×#124C211yesmaximal, characteristic
3C11×#3215C2116yesmaximal, direct product factor
4C2×C11×#497C212yesmaximal, complemented
5C2×C11×#489C212yesmaximal, complemented
6C2×C11×#464C214yesmaximal, complemented
7C2×C11×#451C212yesmaximal, complemented
8C2×C11×#450C212yesmaximal
9C2×C11×#432C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×Q16C2214yescomplemented
13C22×C11×SD16C2214yes—
14C11×#533—24no—
15C11×#533C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#125—21no—
19C2×C11×#124—21no—
20C2×C11×#124—21no—
21C2×C11×#124—24no—
22C2×C11×#124C2212yes—
23C2×C11×#124C2218yes—
24C2×C11×#124C2212yes—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2212yes—
27C2×C4×Q8×C11—21no—
28C2×C4×Q8×C11C2212yescomplemented
29C2×C11×#117—21no—
30C22×C11×C22⋊C4—21no—
31C22×C11×C22⋊C4—21no—
32C22×C42×C11C2211yescharacteristic
33C11×#497C22116yescomplemented
34C11×#489C22116yescomplemented
35C11×#464C22132yescomplemented
36C11×#451C22116yescomplemented
37C11×#450C22116yes—
38C11×#432C2218yescomplemented
39C2×C11×C4⋊C8C2212yescomplemented
40C2×C11×#103C2214yescomplemented
41C2×C11×#102C2214yes—
42C2×C11×C22⋊C8C2212yes—
43C2×C11×#97C2212yescomplemented
44C25×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—21no—
48C22×Q8×C11—44no—
49C22×Q8×C11C2312yes—
50C22×Q8×C11C2312yes—
51C22×Q8×C11C2314yes—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—44no—
55C22×D4×C11C2312yes—
56C22×D4×C11C2314yes—
57C23×C4×C11—21no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C2×C11×Q16—48no—
62C2×C11×Q16C23116yescomplemented
63C2×C11×SD16—48no—
64C2×C11×SD16C23116yes—
65C22×C8×C11C2314yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yescomplemented
69C11×C4⋊Q8C2314yescomplemented
70C11×#125—28no—
71C11×#124—28no—
72C11×#124—24no—
73C11×#124—28no—
74C11×#124—24no—
75C11×#124C2318yes—
76C11×#124C2318yes—
77C11×C22⋊Q8—28no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8C2318yes—
80C4×Q8×C11—28no—
81C4×Q8×C11—24no—
82C4×Q8×C11C2318yescomplemented
83C11×#117—28no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—28no—
92C2×C11×C22⋊C4—28no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C42×C11—22no—
98C2×C42×C11D411yescharacteristic
99C2×C42×C11D411yescharacteristic
100C2×C42×C11D414yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2314yes—
104C11×C4⋊C8C2318yescomplemented
105C11×#103C23116yescomplemented
106C11×#102C23116yes—
107C11×C22⋊C8C2318yes—
108C11×#97C2318yescomplemented
109C2×#3215C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—44no—
113C24×C11—44no—
114C24×C11—44no—
115C24×C11C2×D411yescharacteristic
116C2×Q8×C11—22no—
117C2×Q8×C11—24no—
118C2×Q8×C11—24no—
119C2×Q8×C11—22no—
120C2×Q8×C11—28no—
121C2×Q8×C11—28no—
122C2×Q8×C11—48no—
123C2×Q8×C11—44no—
124C2×Q8×C11—44no—
125C2×Q8×C11—48no—
126C2×Q8×C11C2414yes—
127C2×Q8×C11C2414yes—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—28no—
131C2×D4×C11—48no—
132C2×D4×C11—44no—
133C2×D4×C11—48no—
134C2×D4×C11C2414yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—42no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C11×Q16—416no—
154C11×SD16—416no—
155C2×C8×C11—28no—
156C2×C8×C11C2418yes—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C2414yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C42×C11—28no—
170C42×C11C2×D414yes—
171C42×C11C2×D412yes—
172C42×C11C2×D414yes—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C42×C11C2412yes—
176C2×#533C2×C1111yescharacteristic, complemented
177C22×#124C2×C1111yescharacteristic
178#3215C2×C11116yesdirect product factor
179C2×#497C2×C1112yescomplemented
180C2×#489C2×C1112yescomplemented
181C2×#464C2×C1114yescomplemented
182C2×#451C2×C1112yescomplemented
183C2×#450C2×C1112yes—
184C2×#432C2×C1111yescharacteristic, complemented
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—48no—
189C23×C11—48no—
190C23×C11—44no—
191C23×C11—48no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—816no—
195C23×C11#13714yes—
196C23×C11C22×D412yes—
197C23×C11C22×D411yescharacteristic
198Q8×C11—28no—
199Q8×C11—28no—
200Q8×C11—48no—
201Q8×C11—48no—
202Q8×C11—44no—
203Q8×C11—44no—
204D4×C11—28no—
205D4×C11—48no—
206D4×C11—44no—
207C2×C4×C11—22no—
208C2×C4×C11—28no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11—48no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D412yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D412yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11H(5,𝔽2)14yes—
230C2×C4×C11C2511yescharacteristic
231C8×C11—28no—
232C23×Q8C22×C1111yescharacteristic
233C23×D4C22×C1111yescharacteristic
234C22×Q16C22×C1114yescomplemented
235C22×SD16C22×C1114yes—
236#533—24no—
237#533C22×C1118yescomplemented
238C2×C4⋊Q8C22×C1111yescharacteristic, complemented
239C2×C4⋊Q8C22×C1111yescharacteristic, complemented
240C2×#125—21no—
241C2×#124—21no—
242C2×#124—21no—
243C2×#124—24no—
244C2×#124C22×C1112yes—
245C2×#124C22×C1118yes—
246C2×#124C22×C1112yes—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8C22×C1112yes—
249C2×C4×Q8—21no—
250C2×C4×Q8C22×C1112yescomplemented
251C2×#117—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C22×C1111yescharacteristic
255#497C22×C11116yescomplemented
256#489C22×C11116yescomplemented
257#464C22×C11132yescomplemented
258#451C22×C11116yescomplemented
259#450C22×C11116yes—
260#432C22×C1118yescomplemented
261C2×C4⋊C8C22×C1112yescomplemented
262C2×#103C22×C1114yescomplemented
263C2×#102C22×C1114yes—
264C2×C22⋊C8C22×C1112yes—
265C2×#97C22×C1112yescomplemented
266C22×C11—22no—
267C22×C11—28no—
268C22×C11—22no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—816no—
273C22×C11—88no—
274C22×C11#53512yes—
275C22×C11C2×#13714yes—
276C22×C11C2×#13712yes—
277C22×C11#57512yes—
278C22×C11C23×D411yescharacteristic
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11—44no—
287C4×C11#53512yes—
288C4×C11C2×H(5,𝔽2)12yes—
289C25—21no—
290C22×Q8—21no—
291C22×Q8—21no—
292C22×Q8—22no—
293C22×Q8—44no—
294C22×Q8C23×C1112yes—
295C22×Q8C23×C1112yes—
296C22×Q8C23×C1114yes—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—44no—
300C22×D4C23×C1112yes—
301C22×D4C23×C1114yes—
302C23×C4—21no—
303C23×C4D4×C1111yescharacteristic
304C23×C4D4×C1111yescharacteristic
305C23×C4C23×C1111yescharacteristic
306C2×Q16—48no—
307C2×Q16C23×C11116yescomplemented
308C2×SD16—48no—
309C2×SD16C23×C11116yes—
310C22×C8C23×C1114yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8C23×C1114yescomplemented
314C4⋊Q8C23×C1114yescomplemented
315#125—28no—
316#124—28no—
317#124—24no—
318#124—28no—
319#124—24no—
320#124C23×C1118yes—
321#124C23×C1118yes—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8C23×C1118yes—
325C4×Q8—28no—
326C4×Q8—24no—
327C4×Q8C23×C1118yescomplemented
328#117—28no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4C23×C1112yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C42—22no—
343C2×C42D4×C1111yescharacteristic
344C2×C42D4×C1111yescharacteristic
345C2×C42D4×C1114yes—
346C2×C42C23×C1111yescharacteristic
347C2×C42C23×C1111yescharacteristic
348C2×C42C23×C1114yes—
349C4⋊C8C23×C1118yescomplemented
350#103C23×C11116yescomplemented
351#102C23×C11116yes—
352C22⋊C8C23×C1118yes—
353#97C23×C1118yescomplemented
354C2×C11—24no—
355C2×C11—84no—
356C2×C11#321514yesdirect product factor
357C2×C11C2×#53511yescharacteristic
358C2×C11C22×#13711yescharacteristic
359C2×C11C2×#57511yescharacteristic
360C24—24no—
361C24—22no—
362C24—44no—
363C24—44no—
364C24—44no—
365C24C2×D4×C1111yescharacteristic
366C2×Q8—22no—
367C2×Q8—24no—
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—28no—
371C2×Q8—28no—
372C2×Q8—48no—
373C2×Q8—44no—
374C2×Q8—48no—
375C2×Q8—44no—
376C2×Q8C24×C1114yes—
377C2×Q8C24×C1114yes—
378C2×D4—24no—
379C2×D4—22no—
380C2×D4—28no—
381C2×D4—48no—
382C2×D4—44no—
383C2×D4—48no—
384C2×D4C24×C1114yes—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1112yes—
396C22×C4C2×D4×C1111yescharacteristic
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1114yes—
400C22×C4C2×D4×C1114yes—
401C22×C4C24×C1112yes—
402C22×C4C24×C1111yescharacteristic
403Q16—416no—
404SD16—416no—
405C2×C8—28no—
406C2×C8C24×C1118yes—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—28no—
411C4⋊C4—28no—
412C4⋊C4—22no—
413C4⋊C4C24×C1114yes—
414C22⋊C4—28no—
415C22⋊C4—28no—
416C22⋊C4—28no—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C42—28no—
420C42C2×D4×C1114yes—
421C42C2×D4×C1112yes—
422C42C2×D4×C1114yes—
423C42C2×D4×C1112yes—
424C42C24×C1112yes—
425C42C24×C1112yes—
426C11C2×#321511yescharacteristic, direct product factor, Sylow
427C23—22no—
428C23—22no—
429C23—24no—
430C23—48no—
431C23—48no—
432C23—44no—
433C23—48no—
434C23—44no—
435C23—44no—
436C23—816no—
437C23C11×#13714yes—
438C23C22×D4×C1112yes—
439C23C22×D4×C1111yescharacteristic
440Q8—28no—
441Q8—28no—
442Q8—48no—
443Q8—48no—
444Q8—44no—
445Q8—44no—
446D4—28no—
447D4—48no—
448D4—44no—
449C2×C4—22no—
450C2×C4—28no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—48no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4C22×D4×C1112yes—
466C2×C4C22×D4×C1112yes—
467C2×C4C22×D4×C1112yes—
468C2×C4C22×D4×C1112yes—
469C2×C4C22×D4×C1112yes—
470C2×C4C22×D4×C1111yescharacteristic
471C2×C4C11×H(5,𝔽2)14yes—
472C2×C4C25×C1111yescharacteristic
473C8—28no—
474C22—22no—
475C22—28no—
476C22—22no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—816no—
481C22—88no—
482C22C11×#53512yes—
483C22C2×C11×#13714yes—
484C22C2×C11×#13712yes—
485C22C11×#57512yes—
486C22C23×D4×C1111yescharacteristic
487C4—22no—
488C4—22no—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—44no—
493C4—44no—
494C4—44no—
495C4C11×#53512yes—
496C4C2×C11×H(5,𝔽2)12yes—
497C2—24no—
498C2—84no—
499C2C11×#321514yesdirect product factor
500C2C2×C11×#53511yescharacteristic
501C2C22×C11×#13711yescharacteristic
502C2C2×C11×#57511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#533C2semidirect
3. C11×#3215C2direct (N × H)
4. C2×C11×#497C2semidirect
5. C2×C11×#489C2semidirect
6. C2×C11×#464C2semidirect
7. C2×C11×#451C2semidirect
9. C2×C11×#432C2semidirect
12. C22×C11×Q16C22semidirect
15. C11×#533C22semidirect
16. C2×C11×C4⋊Q8C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
33. C11×#497C22semidirect
34. C11×#489C22semidirect
35. C11×#464C22semidirect
36. C11×#451C22semidirect
38. C11×#432C22semidirect
39. C2×C11×C4⋊C8C22semidirect
40. C2×C11×#103C22semidirect
43. C2×C11×#97C22semidirect
62. C2×C11×Q16C23semidirect
68. C11×C4⋊Q8C23semidirect
69. C11×C4⋊Q8C23semidirect
82. C4×Q8×C11C23semidirect
104. C11×C4⋊C8C23semidirect
105. C11×#103C23semidirect
108. C11×#97C23semidirect
109. C2×#3215C11direct (N × H)
176. C2×#533C2×C11semidirect
178. #3215C2×C11direct (N × H)
179. C2×#497C2×C11semidirect
180. C2×#489C2×C11semidirect
181. C2×#464C2×C11semidirect
182. C2×#451C2×C11semidirect
184. C2×#432C2×C11semidirect
234. C22×Q16C22×C11semidirect
237. #533C22×C11semidirect
238. C2×C4⋊Q8C22×C11semidirect
239. C2×C4⋊Q8C22×C11semidirect
250. C2×C4×Q8C22×C11semidirect
255. #497C22×C11semidirect
256. #489C22×C11semidirect
257. #464C22×C11semidirect
258. #451C22×C11semidirect
260. #432C22×C11semidirect
261. C2×C4⋊C8C22×C11semidirect
262. C2×#103C22×C11semidirect
265. C2×#97C22×C11semidirect
307. C2×Q16C23×C11semidirect
313. C4⋊Q8C23×C11semidirect
314. C4⋊Q8C23×C11semidirect
327. C4×Q8C23×C11semidirect
349. C4⋊C8C23×C11semidirect
350. #103C23×C11semidirect
353. #97C23×C11semidirect
356. C2×C11#3215direct (N × H)
426. C11C2×#3215direct (N × H)
499. C2C11×#3215direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C22×C11×#1242
C11×#32152
C2×C11×#4972
C2×C11×#4892
C2×C11×#4642
C2×C11×#4512
C2×C11×#4502
C2×C11×#4322
C2×#321511