Finite Group Databasebeta

← C11×#61694 #14638887

Subgroups — C11×#61694 #14638887

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C2×C11×#547C211yesmaximal, characteristic, complemented
3C11×#3334C218yesmaximal, complemented
4C11×#3294C218yesmaximal, complemented
5C11×#3226C212yesmaximal, complemented
6C11×#3186C214yesmaximal, complemented
7C11×#3100C212yesmaximal, complemented
8C2×C11×#480C214yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C22×C11×#41—21no—
12C11×#547—24no—
13C11×#547C2218yescomplemented
14C11×#547C2214yescomplemented
15C11×#546—24no—
16D42×C11C2214yescomplemented
17C11×#537—21no—
18C11×#534—22no—
19C11×#532C2212yes—
20C2×C11×C4⋊Q8C2211yescharacteristic, complemented
21C2×C11×#123—22no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×#121C2214yes—
24C2×C11×#121C2212yescomplemented
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2212yescomplemented
28C11×#500C2214yescomplemented
29C11×#486C2214yescomplemented
30C11×#480C2218yescomplemented
31C11×#480C2218yescomplemented
32C11×#480C22116yescomplemented
33C11×#480C2214yescomplemented
34C11×#474C2218yescomplemented
35C11×#474C2214yescomplemented
36C11×#466C22116yescomplemented
37C11×#459C2214yescomplemented
38C11×#447C2214yescomplemented
39C11×#447C2218yescomplemented
40C4×C11×D8C2218yescomplemented
41C8×D4×C11C2218yescomplemented
42C11×#431C2212yescomplemented
43C2×C11×#107C2218yescomplemented
44C2×C11×#102C2218yescomplemented
45C2×C11×C22⋊C8C2214yescomplemented
46C11×H(5,𝔽2)—48no—
47C2×C11×#41—24no—
48C2×C11×#41—28no—
49C2×C11×#41—22no—
50C2×C11×#41—48no—
51C22×Q8×C11—21no—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—24no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2314yes—
58C23×C4×C11—22no—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C2×C11×D8C2318yes—
62C22×C8×C11C2318yes—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2312yes—
65C11×C4⋊Q8C2314yes—
66C11×#127C2312yes—
67C11×#124—22no—
68C11×#123—216no—
69C11×#123—28no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—24no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—24no—
77C11×#121C2314yes—
78C11×#121C2318yes—
79C11×#121C2318yes—
80C11×#120—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11D414yes—
84C4×D4×C11C2314yes—
85C4×D4×C11C2314yes—
86C4×D4×C11C2314yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2318yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11C2311yescharacteristic
100C11×#107C23116yes—
101C11×#107C2318yes—
102C11×C4⋊C8C2314yes—
103C11×#102C2318yes—
104C11×#102C23116yes—
105C11×#102C2318yes—
106C11×C22⋊C8C2314yes—
107C11×C22⋊C8C2318yes—
108C4×C8×C11C2314yes—
109#61694C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11—24no—
112C24×C11C2×D412yes—
113C11×#41—432no—
114C11×#41—416no—
115C11×#41—48no—
116C2×Q8×C11—22no—
117C2×Q8×C11—24no—
118C2×Q8×C11—44no—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—28no—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—24no—
126C2×D4×C11—42no—
127C2×D4×C11—48no—
128C2×D4×C11—48no—
129C2×D4×C11—416no—
130C2×D4×C11—416no—
131C2×D4×C11D818yescomplemented
132C2×D4×C11C2×D414yes—
133C2×D4×C11C2414yes—
134C2×D4×C11C2412yes—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—28no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11—48no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2414yes—
150C11×D8—48no—
151C2×C8×C11—48no—
152C2×C8×C11C2418yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D414yes—
160C11×C4⋊C4C2412yes—
161C11×C4⋊C4C2414yes—
162C11×C4⋊C4C2414yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4C2×D418yes—
169C42×C11C2×D412yes—
170C42×C11C2412yes—
171#3496C2×C1111yescharacteristic, complemented
172C2×#547C2×C1111yescharacteristic, complemented
173#3334C2×C1118yescomplemented
174#3294C2×C1118yescomplemented
175#3226C2×C1112yescomplemented
176#3186C2×C1114yescomplemented
177#3100C2×C1112yescomplemented
178C2×#480C2×C1114yescomplemented
179#2972C2×C1111yescharacteristic, complemented
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—48no—
188C23×C11—84no—
189C23×C11—84no—
190C23×C11C2×D818yes—
191C23×C11C22×D414yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—48no—
194Q8×C11—44no—
195D4×C11—24no—
196D4×C11—28no—
197D4×C11—42no—
198D4×C11—48no—
199D4×C11—416no—
200D4×C11—416no—
201D4×C11—44no—
202D4×C11—82no—
203D4×C11—84no—
204D4×C11C2×D8116yes—
205C2×C4×C11—28no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—416no—
216C2×C4×C11—48no—
217C2×C4×C11—48no—
218C2×C4×C11—48no—
219C2×C4×C11C2×D814yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2511yescharacteristic
225C8×C11—28no—
226C2×H(5,𝔽2)—21no—
227C22×#41—21no—
228#547—24no—
229#547C22×C1114yescomplemented
230#547C22×C1118yescomplemented
231#546—24no—
232D42C22×C1114yescomplemented
233#537—21no—
234#534—22no—
235#532C22×C1112yes—
236C2×C4⋊Q8C22×C1111yescharacteristic, complemented
237C2×#123—22no—
238C2×C22⋊Q8—21no—
239C2×#121C22×C1114yes—
240C2×#121C22×C1112yescomplemented
241C2×C4×D4C22×C1111yescharacteristic
242C2×C4×D4C22×C1111yescharacteristic, complemented
243C22×C4⋊C4C22×C1112yescomplemented
244#500C22×C1114yescomplemented
245#486C22×C1114yescomplemented
246#480C22×C1118yescomplemented
247#480C22×C11116yescomplemented
248#480C22×C1114yescomplemented
249#480C22×C1118yescomplemented
250#474C22×C1114yescomplemented
251#474C22×C1118yescomplemented
252#466C22×C11116yescomplemented
253#459C22×C1114yescomplemented
254#447C22×C1114yescomplemented
255#447C22×C1118yescomplemented
256C4×D8C22×C1118yescomplemented
257C8×D4C22×C1118yescomplemented
258#431C22×C1112yescomplemented
259C2×#107C22×C1118yescomplemented
260C2×#102C22×C1118yescomplemented
261C2×C22⋊C8C22×C1114yescomplemented
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—21no—
265C22×C11—24no—
266C22×C11—48no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—44no—
273C22×C11—84no—
274C22×C11—168no—
275C22×C11C22×D812yes—
276C22×C11C22×D818yes—
277C22×C11C23×D411yescharacteristic
278C4×C11—22no—
279C4×C11—21no—
280C4×C11—24no—
281C4×C11—42no—
282C4×C11—44no—
283C4×C11—44no—
284C4×C11C22×D814yes—
285C4×C11#58512yes—
286H(5,𝔽2)—48no—
287C2×#41—24no—
288C2×#41—28no—
289C2×#41—22no—
290C2×#41—48no—
291C22×Q8—21no—
292C22×D4—24no—
293C22×D4—22no—
294C22×D4—24no—
295C22×D4D4×C1111yescharacteristic
296C22×D4C23×C1111yescharacteristic
297C22×D4C23×C1114yes—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4C23×C1112yes—
301C2×D8C23×C1118yes—
302C22×C8C23×C1118yes—
303C4⋊Q8—22no—
304C4⋊Q8C23×C1114yes—
305C4⋊Q8C23×C1112yes—
306#127C23×C1112yes—
307#124—22no—
308#123—216no—
309#123—28no—
310C22⋊Q8—28no—
311C22⋊Q8—24no—
312#121—24no—
313#121—24no—
314#121—24no—
315#121—22no—
316#121—24no—
317#121C23×C1114yes—
318#121C23×C1118yes—
319#121C23×C1118yes—
320#120—28no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4D4×C1114yes—
324C4×D4C23×C1114yes—
325C4×D4C23×C1114yes—
326C4×D4C23×C1114yes—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C4⋊C4C23×C1111yescharacteristic
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1118yes—
334C2×C4⋊C4C23×C1114yes—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4D4×C1112yes—
339C2×C42C23×C1111yescharacteristic
340#107C23×C1118yes—
341#107C23×C11116yes—
342C4⋊C8C23×C1114yes—
343#102C23×C1118yes—
344#102C23×C11116yes—
345#102C23×C1118yes—
346C22⋊C8C23×C1114yes—
347C22⋊C8C23×C1118yes—
348C4×C8C23×C1114yes—
349C2×C11—22no—
350C2×C11—28no—
351C2×C11—82no—
352C2×C11—84no—
353C2×C11#348511yescharacteristic
354C2×C11C23×D811yescharacteristic
355C2×C11#358611yescharacteristic
356C24—21no—
357C24—24no—
358C24C2×D4×C1112yes—
359#41—432no—
360#41—416no—
361#41—48no—
362C2×Q8—22no—
363C2×Q8—24no—
364C2×Q8—44no—
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—28no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—42no—
373C2×D4—48no—
374C2×D4—48no—
375C2×D4—416no—
376C2×D4—416no—
377C2×D4C11×D818yescomplemented
378C2×D4C2×D4×C1114yes—
379C2×D4C24×C1114yes—
380C2×D4C24×C1112yes—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—28no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—44no—
388C22×C4—48no—
389C22×C4—44no—
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1112yes—
392C22×C4C2×D4×C1114yes—
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C24×C1111yescharacteristic
395C22×C4C24×C1114yes—
396D8—48no—
397C2×C8—48no—
398C2×C8C24×C1118yes—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—28no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4C2×D4×C1114yes—
406C4⋊C4C24×C1112yes—
407C4⋊C4C24×C1114yes—
408C4⋊C4C24×C1114yes—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—24no—
414C22⋊C4C2×D4×C1118yes—
415C42C2×D4×C1112yes—
416C42C24×C1112yes—
417C11#6169411yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—24no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—48no—
426C23—84no—
427C23—84no—
428C23C2×C11×D818yes—
429C23C22×D4×C1114yes—
430C23C22×D4×C1111yescharacteristic
431Q8—48no—
432Q8—44no—
433D4—24no—
434D4—28no—
435D4—42no—
436D4—48no—
437D4—416no—
438D4—416no—
439D4—44no—
440D4—82no—
441D4—84no—
442D4C2×C11×D8116yes—
443C2×C4—28no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—416no—
454C2×C4—48no—
455C2×C4—48no—
456C2×C4—48no—
457C2×C4C2×C11×D814yes—
458C2×C4C22×D4×C1111yescharacteristic
459C2×C4C22×D4×C1112yes—
460C2×C4C22×D4×C1114yes—
461C2×C4C22×D4×C1112yes—
462C2×C4C25×C1111yescharacteristic
463C8—28no—
464C22—21no—
465C22—24no—
466C22—21no—
467C22—24no—
468C22—48no—
469C22—42no—
470C22—44no—
471C22—42no—
472C22—44no—
473C22—44no—
474C22—42no—
475C22—84no—
476C22—168no—
477C22C22×C11×D812yes—
478C22C22×C11×D818yes—
479C22C23×D4×C1111yescharacteristic
480C4—21no—
481C4—24no—
482C4—22no—
483C4—42no—
484C4—44no—
485C4—44no—
486C4C22×C11×D814yes—
487C4C11×#58512yes—
488C2—22no—
489C2—28no—
490C2—82no—
491C2—84no—
492C2C11×#348511yescharacteristic
493C2C23×C11×D811yescharacteristic
494C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3496C2semidirect
2. C2×C11×#547C2semidirect
3. C11×#3334C2semidirect
4. C11×#3294C2semidirect
5. C11×#3226C2semidirect
6. C11×#3186C2semidirect
7. C11×#3100C2semidirect
8. C2×C11×#480C2semidirect
9. C11×#2972C2semidirect
13. C11×#547C22semidirect
14. C11×#547C22semidirect
16. D42×C11C22semidirect
20. C2×C11×C4⋊Q8C22semidirect
24. C2×C11×#121C22semidirect
26. C2×C4×D4×C11C22semidirect
27. C22×C11×C4⋊C4C22semidirect
28. C11×#500C22semidirect
29. C11×#486C22semidirect
30. C11×#480C22semidirect
31. C11×#480C22semidirect
32. C11×#480C22semidirect
33. C11×#480C22semidirect
34. C11×#474C22semidirect
35. C11×#474C22semidirect
36. C11×#466C22semidirect
37. C11×#459C22semidirect
38. C11×#447C22semidirect
39. C11×#447C22semidirect
40. C4×C11×D8C22semidirect
41. C8×D4×C11C22semidirect
42. C11×#431C22semidirect
43. C2×C11×#107C22semidirect
44. C2×C11×#102C22semidirect
45. C2×C11×C22⋊C8C22semidirect
109. #61694C11direct (N × H)
131. C2×D4×C11D8semidirect
171. #3496C2×C11semidirect
172. C2×#547C2×C11semidirect
173. #3334C2×C11semidirect
174. #3294C2×C11semidirect
175. #3226C2×C11semidirect
176. #3186C2×C11semidirect
177. #3100C2×C11semidirect
178. C2×#480C2×C11semidirect
179. #2972C2×C11semidirect
229. #547C22×C11semidirect
230. #547C22×C11semidirect
232. D42C22×C11semidirect
236. C2×C4⋊Q8C22×C11semidirect
240. C2×#121C22×C11semidirect
242. C2×C4×D4C22×C11semidirect
243. C22×C4⋊C4C22×C11semidirect
244. #500C22×C11semidirect
245. #486C22×C11semidirect
246. #480C22×C11semidirect
247. #480C22×C11semidirect
248. #480C22×C11semidirect
249. #480C22×C11semidirect
250. #474C22×C11semidirect
251. #474C22×C11semidirect
252. #466C22×C11semidirect
253. #459C22×C11semidirect
254. #447C22×C11semidirect
255. #447C22×C11semidirect
256. C4×D8C22×C11semidirect
257. C8×D4C22×C11semidirect
258. #431C22×C11semidirect
259. C2×#107C22×C11semidirect
260. C2×#102C22×C11semidirect
261. C2×C22⋊C8C22×C11semidirect
377. C2×D4C11×D8semidirect
417. C11#61694direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C2×C11×#5472
C11×#33342
C11×#32942
C11×#32262
C11×#31862
C11×#31002
C2×C11×#4802
C11×#29722
#6169411