Finite Group Databasebeta

← C11×#61695 #14638888

Subgroups — C11×#61695 #14638888

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C2×C11×#547C211yesmaximal, characteristic
3C11×#3335C218yesmaximal, complemented
4C11×#3298C218yesmaximal, complemented
5C11×#3229C212yesmaximal, complemented
6C11×#3187C214yesmaximal, complemented
7C11×#3101C212yesmaximal, complemented
8C2×C11×#483C214yesmaximal, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C22×C11×#41—21no—
11C11×#554—24no—
12C11×#554C2214yescomplemented
13D4×Q8×C11C2214yescomplemented
14C11×#547—24no—
15C11×#547C2218yes—
16C11×#544—21no—
17C11×#543—22no—
18C11×#533C2212yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#123—22no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8C2214yes—
23C2×C11×#121C2212yes—
24C11×#518—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C22×C11×C4⋊C4C2212yes—
28C11×#498C2214yescomplemented
29C11×#487C2214yescomplemented
30C11×#483C2218yes—
31C11×#483C2214yes—
32C11×#483C22116yescomplemented
33C11×#481C2218yescomplemented
34C11×#476C2214yescomplemented
35C11×#475C2218yescomplemented
36C11×#465C22116yescomplemented
37C11×#461C2214yescomplemented
38C11×#450C2214yes—
39C11×#448C2218yescomplemented
40C4×C11×SD16C2218yescomplemented
41C8×D4×C11C2218yescomplemented
42C11×#431C2212yes—
43C2×C11×#106C2218yescomplemented
44C2×C11×#103C2218yescomplemented
45C2×C11×C22⋊C8C2214yes—
46C2×C11×#41—28no—
47C2×C11×#41—48no—
48C22×Q8×C11—21no—
49C22×Q8×C11C2314yes—
50C22×D4×C11—22no—
51C22×D4×C11D411yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11—21no—
55C23×C4×C11C2312yes—
56C2×C11×SD16C2318yes—
57C22×C8×C11C2318yes—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8C2312yes—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2314yes—
63C11×#125—24no—
64C11×#125—22no—
65C11×#123—216no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—28no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8C2314yes—
73C11×C22⋊Q8C2318yes—
74C11×#121—24no—
75C11×#121C2318yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C4×D4×C11—22no—
81C4×D4×C11D414yes—
82C4×D4×C11C2314yes—
83C4×D4×C11C2314yes—
84C11×#117—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2318yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11C2311yescharacteristic
99C11×#106C23116yes—
100C11×#106C2318yes—
101C11×C4⋊C8C2314yes—
102C11×#103C2318yes—
103C11×#103C23116yes—
104C11×#102C2318yes—
105C11×C22⋊C8C2314yes—
106C11×C22⋊C8C2318yes—
107C4×C8×C11C2314yes—
108#61695C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—21no—
110C24×C11C2×D412yes—
111C11×#41—432no—
112C2×Q8×C11—24no—
113C2×Q8×C11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—48no—
116C2×Q8×C11—44no—
117C2×Q8×C11C2414yes—
118C2×D4×C11—28no—
119C2×D4×C11—21no—
120C2×D4×C11—42no—
121C2×D4×C11—48no—
122C2×D4×C11SD1618yescomplemented
123C2×D4×C11C2×D414yes—
124C2×D4×C11C2412yes—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—28no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—44no—
132C22×C4×C11—48no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×C4×C11C2414yes—
140C11×SD16—48no—
141C2×C8×C11—48no—
142C2×C8×C11C2418yes—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4C2×D414yes—
155C11×C4⋊C4C2414yes—
156C11×C4⋊C4C2412yes—
157C11×C4⋊C4C2414yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—28no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4C2×D418yes—
163C42×C11—24no—
164C42×C11C2×D412yes—
165C42×C11C2412yes—
166#3501C2×C1111yescharacteristic, complemented
167C2×#547C2×C1111yescharacteristic
168#3335C2×C1118yescomplemented
169#3298C2×C1118yescomplemented
170#3229C2×C1112yescomplemented
171#3187C2×C1114yescomplemented
172#3101C2×C1112yescomplemented
173C2×#483C2×C1114yescomplemented
174#2972C2×C1111yescharacteristic, complemented
175C23×C11—22no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C2×SD1618yes—
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D414yes—
184Q8×C11—28no—
185Q8×C11—48no—
186Q8×C11—82no—
187Q8×C11—84no—
188D4×C11—24no—
189D4×C11—42no—
190D4×C11—416no—
191D4×C11C2×SD16116yes—
192C2×C4×C11—28no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—416no—
204C2×C4×C11—48no—
205C2×C4×C11—84no—
206C2×C4×C11—84no—
207C2×C4×C11C2×SD1614yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D412yes—
210C2×C4×C11C22×D414yes—
211C2×C4×C11C22×D412yes—
212C2×C4×C11C2511yescharacteristic
213C8×C11—28no—
214C22×#41—21no—
215#554—24no—
216#554C22×C1114yescomplemented
217D4×Q8C22×C1114yescomplemented
218#547—24no—
219#547C22×C1118yes—
220#544—21no—
221#543—22no—
222#533C22×C1112yes—
223C2×C4⋊Q8C22×C1111yescharacteristic
224C2×#123—22no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C22×C1114yes—
227C2×#121C22×C1112yes—
228#518—21no—
229C2×C4×D4C22×C1111yescharacteristic
230C2×C4×D4C22×C1111yescharacteristic
231C22×C4⋊C4C22×C1112yes—
232#498C22×C1114yescomplemented
233#487C22×C1114yescomplemented
234#483C22×C1114yes—
235#483C22×C1118yes—
236#483C22×C11116yescomplemented
237#481C22×C1118yescomplemented
238#476C22×C1114yescomplemented
239#475C22×C1118yescomplemented
240#465C22×C11116yescomplemented
241#461C22×C1114yescomplemented
242#450C22×C1114yes—
243#448C22×C1118yescomplemented
244C4×SD16C22×C1118yescomplemented
245C8×D4C22×C1118yescomplemented
246#431C22×C1112yes—
247C2×#106C22×C1118yescomplemented
248C2×#103C22×C1118yescomplemented
249C2×C22⋊C8C22×C1114yes—
250C22×C11—21no—
251C22×C11—24no—
252C22×C11—21no—
253C22×C11—24no—
254C22×C11—48no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—84no—
259C22×C11C22×SD1612yes—
260C22×C11C22×SD1618yes—
261C22×C11C23×D411yescharacteristic
262C4×C11—22no—
263C4×C11—21no—
264C4×C11—24no—
265C4×C11—44no—
266C4×C11—44no—
267C4×C11—42no—
268C4×C11—44no—
269C4×C11C22×SD1614yes—
270C4×C11#58512yes—
271C2×#41—28no—
272C2×#41—48no—
273C22×Q8—21no—
274C22×Q8C23×C1114yes—
275C22×D4—22no—
276C22×D4D4×C1111yescharacteristic
277C22×D4C23×C1111yescharacteristic
278C23×C4—22no—
279C23×C4—21no—
280C23×C4C23×C1112yes—
281C2×SD16C23×C1118yes—
282C22×C8C23×C1118yes—
283C4⋊Q8—24no—
284C4⋊Q8—22no—
285C4⋊Q8C23×C1112yes—
286C4⋊Q8C23×C1114yes—
287C4⋊Q8C23×C1112yes—
288#125—24no—
289#125—22no—
290#123—216no—
291C22⋊Q8—24no—
292C22⋊Q8—24no—
293C22⋊Q8—22no—
294C22⋊Q8—28no—
295C22⋊Q8—28no—
296C22⋊Q8—28no—
297C22⋊Q8C23×C1114yes—
298C22⋊Q8C23×C1118yes—
299#121—24no—
300#121C23×C1118yes—
301C4×Q8—22no—
302C4×Q8C23×C1114yes—
303C4×D4—24no—
304C4×D4—24no—
305C4×D4—22no—
306C4×D4D4×C1114yes—
307C4×D4C23×C1114yes—
308C4×D4C23×C1114yes—
309#117—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C1111yescharacteristic
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1112yes—
317C2×C4⋊C4C23×C1118yes—
318C2×C4⋊C4C23×C1114yes—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4D4×C1112yes—
323C2×C42C23×C1111yescharacteristic
324#106C23×C1118yes—
325#106C23×C11116yes—
326C4⋊C8C23×C1114yes—
327#103C23×C1118yes—
328#103C23×C11116yes—
329#102C23×C1118yes—
330C22⋊C8C23×C1114yes—
331C22⋊C8C23×C1118yes—
332C4×C8C23×C1114yes—
333C2×C11—22no—
334C2×C11—28no—
335C2×C11—82no—
336C2×C11#348511yescharacteristic
337C2×C11C23×SD1611yescharacteristic
338C2×C11#358611yescharacteristic
339C24—21no—
340C24C2×D4×C1112yes—
341#41—432no—
342C2×Q8—24no—
343C2×Q8—22no—
344C2×Q8—24no—
345C2×Q8—48no—
346C2×Q8—44no—
347C2×Q8C24×C1114yes—
348C2×D4—28no—
349C2×D4—21no—
350C2×D4—42no—
351C2×D4—48no—
352C2×D4C11×SD1618yescomplemented
353C2×D4C2×D4×C1114yes—
354C2×D4C24×C1112yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—28no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—44no—
362C22×C4—48no—
363C22×C4—44no—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C2×D4×C1112yes—
366C22×C4C2×D4×C1114yes—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C24×C1111yescharacteristic
369C22×C4C24×C1114yes—
370SD16—48no—
371C2×C8—48no—
372C2×C8C24×C1118yes—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—28no—
376C4⋊C4—24no—
377C4⋊C4—28no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—24no—
384C4⋊C4C2×D4×C1114yes—
385C4⋊C4C24×C1114yes—
386C4⋊C4C24×C1112yes—
387C4⋊C4C24×C1114yes—
388C22⋊C4—24no—
389C22⋊C4—28no—
390C22⋊C4—24no—
391C22⋊C4—28no—
392C22⋊C4C2×D4×C1118yes—
393C42—24no—
394C42C2×D4×C1112yes—
395C42C24×C1112yes—
396C11#6169511yescharacteristic, direct product factor, Sylow
397C23—22no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23C2×C11×SD1618yes—
404C23C22×D4×C1111yescharacteristic
405C23C22×D4×C1114yes—
406Q8—28no—
407Q8—48no—
408Q8—82no—
409Q8—84no—
410D4—24no—
411D4—42no—
412D4—416no—
413D4C2×C11×SD16116yes—
414C2×C4—28no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—416no—
426C2×C4—48no—
427C2×C4—84no—
428C2×C4—84no—
429C2×C4C2×C11×SD1614yes—
430C2×C4C22×D4×C1111yescharacteristic
431C2×C4C22×D4×C1112yes—
432C2×C4C22×D4×C1114yes—
433C2×C4C22×D4×C1112yes—
434C2×C4C25×C1111yescharacteristic
435C8—28no—
436C22—21no—
437C22—24no—
438C22—21no—
439C22—24no—
440C22—48no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—84no—
445C22C22×C11×SD1612yes—
446C22C22×C11×SD1618yes—
447C22C23×D4×C1111yescharacteristic
448C4—21no—
449C4—24no—
450C4—22no—
451C4—44no—
452C4—42no—
453C4—44no—
454C4—44no—
455C4C22×C11×SD1614yes—
456C4C11×#58512yes—
457C2—22no—
458C2—28no—
459C2—82no—
460C2C11×#348511yescharacteristic
461C2C23×C11×SD1611yescharacteristic
462C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#547C2
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×#3501C2semidirect
3. C11×#3335C2semidirect
4. C11×#3298C2semidirect
5. C11×#3229C2semidirect
6. C11×#3187C2semidirect
7. C11×#3101C2semidirect
8. C2×C11×#483C2semidirect
9. C11×#2972C2semidirect
12. C11×#554C22semidirect
13. D4×Q8×C11C22semidirect
28. C11×#498C22semidirect
29. C11×#487C22semidirect
32. C11×#483C22semidirect
33. C11×#481C22semidirect
34. C11×#476C22semidirect
35. C11×#475C22semidirect
36. C11×#465C22semidirect
37. C11×#461C22semidirect
39. C11×#448C22semidirect
40. C4×C11×SD16C22semidirect
41. C8×D4×C11C22semidirect
43. C2×C11×#106C22semidirect
44. C2×C11×#103C22semidirect
108. #61695C11direct (N × H)
122. C2×D4×C11SD16semidirect
166. #3501C2×C11semidirect
168. #3335C2×C11semidirect
169. #3298C2×C11semidirect
170. #3229C2×C11semidirect
171. #3187C2×C11semidirect
172. #3101C2×C11semidirect
173. C2×#483C2×C11semidirect
174. #2972C2×C11semidirect
216. #554C22×C11semidirect
217. D4×Q8C22×C11semidirect
232. #498C22×C11semidirect
233. #487C22×C11semidirect
236. #483C22×C11semidirect
237. #481C22×C11semidirect
238. #476C22×C11semidirect
239. #475C22×C11semidirect
240. #465C22×C11semidirect
241. #461C22×C11semidirect
243. #448C22×C11semidirect
244. C4×SD16C22×C11semidirect
245. C8×D4C22×C11semidirect
247. C2×#106C22×C11semidirect
248. C2×#103C22×C11semidirect
352. C2×D4C11×SD16semidirect
396. C11#61695direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C2×C11×#5472
C11×#33352
C11×#32982
C11×#32292
C11×#31872
C11×#31012
C2×C11×#4832
C11×#29722
#6169511