Finite Group Databasebeta

← C11×#61697 #14638890

Subgroups — C11×#61697 #14638890

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C2×C11×#554C211yesmaximal, characteristic, complemented
3C11×#3335C218yesmaximal, complemented
4C11×#3295C218yesmaximal, complemented
5C11×#3227C212yesmaximal, complemented
6C11×#3187C214yesmaximal, complemented
7C11×#3103C212yesmaximal, complemented
8C2×C11×#481C214yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C11×#554—24no—
12C11×#554C2218yescomplemented
13C11×#547C2214yes—
14C11×#546—24no—
15D42×C11C2214yes—
16C11×#537—21no—
17C11×#534—22no—
18C11×#532C2212yes—
19C2×C11×C4⋊Q8C2211yescharacteristic, complemented
20C2×C11×#125—21no—
21C2×C11×C22⋊Q8—22no—
22C2×C11×C22⋊Q8C2212yescomplemented
23C2×C11×#121C2214yes—
24C2×C4×Q8×C11C2211yescharacteristic, complemented
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2212yescomplemented
28C11×#498C2214yescomplemented
29C11×#486C2214yescomplemented
30C11×#483C2218yescomplemented
31C11×#481C2218yescomplemented
32C11×#481C22116yescomplemented
33C11×#481C2214yescomplemented
34C11×#476C2218yescomplemented
35C11×#475C2214yescomplemented
36C11×#465C22116yescomplemented
37C11×#460C2214yescomplemented
38C11×#450C2218yescomplemented
39C11×#448C2214yescomplemented
40C4×C11×SD16C2218yescomplemented
41C8×D4×C11C2218yescomplemented
42C11×#431C2212yescomplemented
43C2×C11×#106C2218yescomplemented
44C2×C11×#102C2218yescomplemented
45C2×C11×C22⋊C8C2214yescomplemented
46C11×H(5,𝔽2)—48no—
47C2×C11×#41—24no—
48C2×C11×#41—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2314yes—
55C23×C4×C11—22no—
56C23×C4×C11C2312yes—
57C2×C11×SD16C2318yes—
58C22×C8×C11C2318yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8C2312yes—
61C11×C4⋊Q8C2314yes—
62C11×#127C2312yes—
63C11×#125—28no—
64C11×#124—22no—
65C11×#123—28no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—216no—
69C11×C22⋊Q8C2318yes—
70C11×#121—24no—
71C11×#121—24no—
72C11×#121—22no—
73C11×#121—24no—
74C11×#121C2314yes—
75C11×#121C2318yes—
76C11×#120—28no—
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yes—
79C4×D4×C11—28no—
80C4×D4×C11—22no—
81C4×D4×C11D414yes—
82C4×D4×C11C2314yes—
83C4×D4×C11C2314yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2318yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C11×#106C23116yes—
100C11×#106C2318yes—
101C11×C4⋊C8C2314yes—
102C11×#103C2318yes—
103C11×#102C2318yes—
104C11×#102C23116yes—
105C11×C22⋊C8C2314yes—
106C11×C22⋊C8C2318yes—
107C4×C8×C11C2314yes—
108#61697C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—24no—
110C24×C11C2×D412yes—
111C11×#41—416no—
112C11×#41—48no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—24no—
116C2×Q8×C11—42no—
117C2×Q8×C11—82no—
118C2×Q8×C11C2412yes—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—48no—
125C2×D4×C11—416no—
126C2×D4×C11—416no—
127C2×D4×C11SD1618yescomplemented
128C2×D4×C11C2×D414yes—
129C2×D4×C11C2414yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—28no—
135C22×C4×C11—24no—
136C22×C4×C11—44no—
137C22×C4×C11—84no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2414yes—
144C11×SD16—48no—
145C2×C8×C11—48no—
146C2×C8×C11C2418yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D414yes—
156C11×C4⋊C4C2412yes—
157C11×C4⋊C4C2414yes—
158C11×C4⋊C4C2414yes—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4C2×D418yes—
164C42×C11—24no—
165C42×C11C2×D412yes—
166C42×C11C2412yes—
167#3496C2×C1111yescharacteristic
168C2×#554C2×C1111yescharacteristic, complemented
169#3335C2×C1118yescomplemented
170#3295C2×C1118yescomplemented
171#3227C2×C1112yescomplemented
172#3187C2×C1114yescomplemented
173#3103C2×C1112yescomplemented
174C2×#481C2×C1114yescomplemented
175#2972C2×C1111yescharacteristic, complemented
176C23×C11—24no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—48no—
180C23×C11—84no—
181C23×C11—84no—
182C23×C11C2×SD1618yes—
183C23×C11C22×D414yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—24no—
186Q8×C11—42no—
187Q8×C11—44no—
188Q8×C11—84no—
189D4×C11—28no—
190D4×C11—416no—
191D4×C11—48no—
192D4×C11—44no—
193D4×C11—82no—
194D4×C11—84no—
195D4×C11C2×SD16116yes—
196C2×C4×C11—28no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—48no—
209C2×C4×C11—48no—
210C2×C4×C11—88no—
211C2×C4×C11C2×SD1614yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D412yes—
214C2×C4×C11C22×D414yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C2511yescharacteristic
217C8×C11—28no—
218C2×H(5,𝔽2)—21no—
219#554—24no—
220#554C22×C1118yescomplemented
221#547C22×C1114yes—
222#546—24no—
223D42C22×C1114yes—
224#537—21no—
225#534—22no—
226#532C22×C1112yes—
227C2×C4⋊Q8C22×C1111yescharacteristic, complemented
228C2×#125—21no—
229C2×C22⋊Q8—22no—
230C2×C22⋊Q8C22×C1112yescomplemented
231C2×#121C22×C1114yes—
232C2×C4×Q8C22×C1111yescharacteristic, complemented
233C2×C4×D4—21no—
234C2×C4×D4C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1112yescomplemented
236#498C22×C1114yescomplemented
237#486C22×C1114yescomplemented
238#483C22×C1118yescomplemented
239#481C22×C11116yescomplemented
240#481C22×C1114yescomplemented
241#481C22×C1118yescomplemented
242#476C22×C1118yescomplemented
243#475C22×C1114yescomplemented
244#465C22×C11116yescomplemented
245#460C22×C1114yescomplemented
246#450C22×C1118yescomplemented
247#448C22×C1114yescomplemented
248C4×SD16C22×C1118yescomplemented
249C8×D4C22×C1118yescomplemented
250#431C22×C1112yescomplemented
251C2×#106C22×C1118yescomplemented
252C2×#102C22×C1118yescomplemented
253C2×C22⋊C8C22×C1114yescomplemented
254C22×C11—21no—
255C22×C11—24no—
256C22×C11—21no—
257C22×C11—24no—
258C22×C11—48no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—168no—
263C22×C11C22×SD1618yes—
264C22×C11C22×SD1612yes—
265C22×C11C23×D411yescharacteristic
266C4×C11—22no—
267C4×C11—21no—
268C4×C11—24no—
269C4×C11—42no—
270C4×C11—44no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11C22×SD1614yes—
274C4×C11#58512yes—
275H(5,𝔽2)—48no—
276C2×#41—24no—
277C2×#41—22no—
278C22×Q8—21no—
279C22×Q8C23×C1111yescharacteristic
280C22×D4—24no—
281C22×D4—24no—
282C22×D4D4×C1111yescharacteristic
283C22×D4C23×C1114yes—
284C23×C4—22no—
285C23×C4C23×C1112yes—
286C2×SD16C23×C1118yes—
287C22×C8C23×C1118yes—
288C4⋊Q8—22no—
289C4⋊Q8C23×C1114yes—
290C4⋊Q8C23×C1112yes—
291#127C23×C1112yes—
292#125—28no—
293#124—22no—
294#123—28no—
295C22⋊Q8—24no—
296C22⋊Q8—24no—
297C22⋊Q8—216no—
298C22⋊Q8C23×C1118yes—
299#121—24no—
300#121—24no—
301#121—22no—
302#121—24no—
303#121C23×C1114yes—
304#121C23×C1118yes—
305#120—28no—
306C4×Q8—22no—
307C4×Q8C23×C1114yes—
308C4×D4—28no—
309C4×D4—22no—
310C4×D4D4×C1114yes—
311C4×D4C23×C1114yes—
312C4×D4C23×C1114yes—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4D4×C1111yescharacteristic
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1118yes—
322C2×C4⋊C4C23×C1114yes—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4D4×C1112yes—
326C2×C42—21no—
327C2×C42C23×C1111yescharacteristic
328#106C23×C1118yes—
329#106C23×C11116yes—
330C4⋊C8C23×C1114yes—
331#103C23×C1118yes—
332#102C23×C1118yes—
333#102C23×C11116yes—
334C22⋊C8C23×C1114yes—
335C22⋊C8C23×C1118yes—
336C4×C8C23×C1114yes—
337C2×C11—22no—
338C2×C11—28no—
339C2×C11—84no—
340C2×C11#348511yescharacteristic
341C2×C11C23×SD1611yescharacteristic
342C2×C11#358511yescharacteristic
343C24—24no—
344C24C2×D4×C1112yes—
345#41—416no—
346#41—48no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—24no—
350C2×Q8—42no—
351C2×Q8—82no—
352C2×Q8C24×C1112yes—
353C2×D4—28no—
354C2×D4—24no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—24no—
358C2×D4—48no—
359C2×D4—416no—
360C2×D4—416no—
361C2×D4C11×SD1618yescomplemented
362C2×D4C2×D4×C1114yes—
363C2×D4C24×C1114yes—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—28no—
369C22×C4—24no—
370C22×C4—44no—
371C22×C4—84no—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1114yes—
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C24×C1111yescharacteristic
377C22×C4C24×C1114yes—
378SD16—48no—
379C2×C8—48no—
380C2×C8C24×C1118yes—
381C4⋊C4—21no—
382C4⋊C4—28no—
383C4⋊C4—22no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—28no—
387C4⋊C4—24no—
388C4⋊C4—22no—
389C4⋊C4C2×D4×C1114yes—
390C4⋊C4C24×C1112yes—
391C4⋊C4C24×C1114yes—
392C4⋊C4C24×C1114yes—
393C22⋊C4—28no—
394C22⋊C4—24no—
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4C2×D4×C1118yes—
398C42—24no—
399C42C2×D4×C1112yes—
400C42C24×C1112yes—
401C11#6169711yescharacteristic, direct product factor, Sylow
402C23—24no—
403C23—42no—
404C23—42no—
405C23—48no—
406C23—84no—
407C23—84no—
408C23C2×C11×SD1618yes—
409C23C22×D4×C1114yes—
410C23C22×D4×C1111yescharacteristic
411Q8—24no—
412Q8—42no—
413Q8—44no—
414Q8—84no—
415D4—28no—
416D4—416no—
417D4—48no—
418D4—44no—
419D4—82no—
420D4—84no—
421D4C2×C11×SD16116yes—
422C2×C4—28no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—48no—
435C2×C4—48no—
436C2×C4—88no—
437C2×C4C2×C11×SD1614yes—
438C2×C4C22×D4×C1111yescharacteristic
439C2×C4C22×D4×C1112yes—
440C2×C4C22×D4×C1114yes—
441C2×C4C22×D4×C1112yes—
442C2×C4C25×C1111yescharacteristic
443C8—28no—
444C22—21no—
445C22—24no—
446C22—21no—
447C22—24no—
448C22—48no—
449C22—44no—
450C22—44no—
451C22—44no—
452C22—168no—
453C22C22×C11×SD1618yes—
454C22C22×C11×SD1612yes—
455C22C23×D4×C1111yescharacteristic
456C4—21no—
457C4—24no—
458C4—22no—
459C4—42no—
460C4—44no—
461C4—42no—
462C4—44no—
463C4C22×C11×SD1614yes—
464C4C11×#58512yes—
465C2—22no—
466C2—28no—
467C2—84no—
468C2C11×#348511yescharacteristic
469C2C23×C11×SD1611yescharacteristic
470C2C11×#358511yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3496C2
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
2. C2×C11×#554C2semidirect
3. C11×#3335C2semidirect
4. C11×#3295C2semidirect
5. C11×#3227C2semidirect
6. C11×#3187C2semidirect
7. C11×#3103C2semidirect
8. C2×C11×#481C2semidirect
9. C11×#2972C2semidirect
12. C11×#554C22semidirect
19. C2×C11×C4⋊Q8C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
24. C2×C4×Q8×C11C22semidirect
27. C22×C11×C4⋊C4C22semidirect
28. C11×#498C22semidirect
29. C11×#486C22semidirect
30. C11×#483C22semidirect
31. C11×#481C22semidirect
32. C11×#481C22semidirect
33. C11×#481C22semidirect
34. C11×#476C22semidirect
35. C11×#475C22semidirect
36. C11×#465C22semidirect
37. C11×#460C22semidirect
38. C11×#450C22semidirect
39. C11×#448C22semidirect
40. C4×C11×SD16C22semidirect
41. C8×D4×C11C22semidirect
42. C11×#431C22semidirect
43. C2×C11×#106C22semidirect
44. C2×C11×#102C22semidirect
45. C2×C11×C22⋊C8C22semidirect
108. #61697C11direct (N × H)
127. C2×D4×C11SD16semidirect
168. C2×#554C2×C11semidirect
169. #3335C2×C11semidirect
170. #3295C2×C11semidirect
171. #3227C2×C11semidirect
172. #3187C2×C11semidirect
173. #3103C2×C11semidirect
174. C2×#481C2×C11semidirect
175. #2972C2×C11semidirect
220. #554C22×C11semidirect
227. C2×C4⋊Q8C22×C11semidirect
230. C2×C22⋊Q8C22×C11semidirect
232. C2×C4×Q8C22×C11semidirect
235. C22×C4⋊C4C22×C11semidirect
236. #498C22×C11semidirect
237. #486C22×C11semidirect
238. #483C22×C11semidirect
239. #481C22×C11semidirect
240. #481C22×C11semidirect
241. #481C22×C11semidirect
242. #476C22×C11semidirect
243. #475C22×C11semidirect
244. #465C22×C11semidirect
245. #460C22×C11semidirect
246. #450C22×C11semidirect
247. #448C22×C11semidirect
248. C4×SD16C22×C11semidirect
249. C8×D4C22×C11semidirect
250. #431C22×C11semidirect
251. C2×#106C22×C11semidirect
252. C2×#102C22×C11semidirect
253. C2×C22⋊C8C22×C11semidirect
361. C2×D4C11×SD16semidirect
401. C11#61697direct (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×#5542
C11×#33352
C11×#32952
C11×#32272
C11×#31872
C11×#31032
C2×C11×#4812
C11×#29722
#6169711