Finite Group Databasebeta

← C11×#60685 #14637878

Subgroups — C11×#60685 #14637878

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3455C212yesmaximal, complemented
2C11×#3179C218yesmaximal, complemented
3C11×#3178C218yesmaximal, complemented
4C11×#3162C211yesmaximal, characteristic, complemented
5C11×#3150C211yesmaximal, characteristic, complemented
6C11×#3131C212yesmaximal, complemented
7C11×#3054C212yesmaximal, complemented
8C11×#3050C212yesmaximal, complemented
9C11×#2943C212yesmaximal, complemented
10C4×C11×#135C212yesmaximal, complemented
11C2×C11×#405C211yesmaximal, characteristic, complemented
12C2×C11×#135C2212yes—
13C2×C11×#135C2212yes—
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C11×#542C2218yes—
17C11×#541C2214yes—
18C11×#540C2214yes—
19C11×#539—24no—
20C11×#538—24no—
21C11×#533C2212yes—
22C11×#532C2212yes—
23C11×#529—28no—
24C11×#525C2214yes—
25C4×C11×#41C2214yes—
26C2×C11×#117C2211yescharacteristic
27C11×#501C2218yescomplemented
28C11×#497C2214yescomplemented
29C11×#496C2214yescomplemented
30C11×#488C2218yescomplemented
31C11×#487C2214yescomplemented
32C11×#486C2214yescomplemented
33C11×#470C2214yes—
34C11×#469C2214yes—
35C11×#468C2218yes—
36C11×#467C2214yes—
37C11×#466C2214yes—
38C11×#465C2218yes—
39C11×#442C2214yescomplemented
40C11×#441C2214yescomplemented
41C11×#440C2218yescomplemented
42C4×C11×Q16C2214yescomplemented
43C4×C11×SD16C2218yescomplemented
44C4×C11×D8C2214yescomplemented
45C11×#427C2212yes—
46C11×#427C2212yes—
47C11×#416C2214yes—
48C11×#416C2214yes—
49C11×#405C2218yes—
50C2×C11×#97C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52C2×C4×C8×C11C2211yescharacteristic
53C2×C4×C8×C11C2211yescharacteristic
54C2×C11×#41C2314yes—
55C23×C4×C11C2311yescharacteristic
56C11×#135—28no—
57C11×#135—28no—
58C2×C11×Q16C2312yes—
59C2×C11×Q16C2312yes—
60C2×C11×SD16C2314yes—
61C2×C11×SD16C2314yes—
62C2×C11×D8C2312yes—
63C2×C11×D8C2312yes—
64C2×C11×M16—24no—
65C2×C11×M16C2314yes—
66C22×C8×C11—24no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8C2312yes—
73C11×C4⋊Q8C2314yes—
74C11×#127C2312yes—
75C11×#126—28no—
76C11×#126—28no—
77C11×#125—28no—
78C11×#125C2314yes—
79C11×#124—28no—
80C11×#124C2314yes—
81C11×#123—24no—
82C11×#123—28no—
83C11×#123—28no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8C2318yes—
87C11×#121—24no—
88C11×#121—28no—
89C11×#121C2318yes—
90C11×#120—24no—
91C4×Q8×C11—24no—
92C4×Q8×C11C2318yes—
93C4×D4×C11—28no—
94C4×D4×C11—28no—
95C4×D4×C11—24no—
96C4×D4×C11C2318yes—
97C11×#117—24no—
98C11×#117D414yes—
99C11×#117C2314yes—
100C11×#117C2314yes—
101C2×C11×C4⋊C4D412yes—
102C2×C11×C22⋊C4D412yes—
103C2×C42×C11—24no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C11×#107C2314yes—
107C11×#107C2314yes—
108C11×#106C2314yes—
109C11×#106C2314yes—
110C11×#103C2318yes—
111C11×#103C2318yes—
112C11×#102C2318yes—
113C11×#102C2318yes—
114C11×#97C2314yes—
115C11×#97C2314yes—
116C4×C8×C11C2314yes—
117C4×C8×C11C2314yes—
118#60685C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11C2×D411yescharacteristic
120C11×#41—28no—
121C11×#41—28no—
122C2×Q8×C11—24no—
123C2×Q8×C11C2414yes—
124C2×D4×C11—24no—
125C2×D4×C11—28no—
126C2×D4×C11—24no—
127C2×D4×C11C2414yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—28no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2411yescharacteristic
138C11×Q16—24no—
139C11×Q16—24no—
140C11×SD16—28no—
141C11×SD16—28no—
142C11×D8—24no—
143C11×D8—24no—
144C11×M16—28no—
145C2×C8×C11—28no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11#4114yes—
149C2×C8×C11#4114yes—
150C2×C8×C11C2412yes—
151C2×C8×C11C2412yes—
152C2×C8×C11C2412yes—
153C2×C8×C11C2412yes—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4C2×D418yes—
160C11×C4⋊C4C2418yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4C2×D418yes—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C42×C11C2412yes—
173#3455C2×C1112yescomplemented
174#3179C2×C1118yescomplemented
175#3178C2×C1118yescomplemented
176#3162C2×C1111yescharacteristic, complemented
177#3150C2×C1111yescharacteristic, complemented
178#3131C2×C1112yescomplemented
179#3054C2×C1112yescomplemented
180#3050C2×C1112yescomplemented
181#2943C2×C1112yescomplemented
182C4×#135C2×C1112yescomplemented
183C2×#405C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—42no—
187C23×C11C22×D412yes—
188C23×C11C22×D411yescharacteristic
189Q8×C11—24no—
190Q8×C11—24no—
191Q8×C11—84no—
192D4×C11—24no—
193D4×C11—24no—
194D4×C11—48no—
195D4×C11—84no—
196D4×C11—88no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—48no—
206C2×C4×C11—88no—
207C2×C4×C11C22×D414yes—
208C2×C4×C11C22×D414yes—
209C2×C4×C11C22×D412yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4112yes—
212C2×C4×C11C2×#4112yes—
213C2×C4×C11C2511yescharacteristic
214C8×C11—22no—
215C8×C11—22no—
216C8×C11C2×#4114yes—
217C8×C11C2×#4114yes—
218C2×#135C22×C1112yes—
219C2×#135C22×C1112yes—
220C22×M16C22×C1111yescharacteristic
221C23×C8C22×C1111yescharacteristic
222#542C22×C1118yes—
223#541C22×C1114yes—
224#540C22×C1114yes—
225#539—24no—
226#538—24no—
227#533C22×C1112yes—
228#532C22×C1112yes—
229#529—28no—
230#525C22×C1114yes—
231C4×#41C22×C1114yes—
232C2×#117C22×C1111yescharacteristic
233#501C22×C1118yescomplemented
234#497C22×C1114yescomplemented
235#496C22×C1114yescomplemented
236#488C22×C1118yescomplemented
237#487C22×C1114yescomplemented
238#486C22×C1114yescomplemented
239#470C22×C1114yes—
240#469C22×C1114yes—
241#468C22×C1118yes—
242#467C22×C1114yes—
243#466C22×C1114yes—
244#465C22×C1118yes—
245#442C22×C1114yescomplemented
246#441C22×C1114yescomplemented
247#440C22×C1118yescomplemented
248C4×Q16C22×C1114yescomplemented
249C4×SD16C22×C1118yescomplemented
250C4×D8C22×C1114yescomplemented
251#427C22×C1112yes—
252#427C22×C1112yes—
253#416C22×C1114yes—
254#416C22×C1114yes—
255#405C22×C1118yes—
256C2×#97C22×C1111yescharacteristic
257C2×#97C22×C1111yescharacteristic
258C2×C4×C8C22×C1111yescharacteristic
259C2×C4×C8C22×C1111yescharacteristic
260C22×C11—22no—
261C22×C11—24no—
262C22×C11—22no—
263C22×C11—44no—
264C22×C11—48no—
265C22×C11—44no—
266C22×C11#53212yes—
267C22×C11C23×D411yescharacteristic
268C4×C11—24no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—48no—
272C4×C11—44no—
273C4×C11#53212yes—
274C4×C11C22×#4111yescharacteristic
275C4×C11C22×#4111yescharacteristic
276C2×#41C23×C1114yes—
277C23×C4C23×C1111yescharacteristic
278#135—28no—
279#135—28no—
280C2×Q16C23×C1112yes—
281C2×Q16C23×C1112yes—
282C2×SD16C23×C1114yes—
283C2×SD16C23×C1114yes—
284C2×D8C23×C1112yes—
285C2×D8C23×C1112yes—
286C2×M16—24no—
287C2×M16C23×C1114yes—
288C22×C8—24no—
289C22×C8C23×C1111yescharacteristic
290C22×C8C23×C1114yes—
291C22×C8C23×C1111yescharacteristic
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C4⋊Q8C23×C1112yes—
295C4⋊Q8C23×C1114yes—
296#127C23×C1112yes—
297#126—28no—
298#126—28no—
299#125—28no—
300#125C23×C1114yes—
301#124—28no—
302#124C23×C1114yes—
303#123—24no—
304#123—28no—
305#123—28no—
306C22⋊Q8—24no—
307C22⋊Q8—28no—
308C22⋊Q8C23×C1118yes—
309#121—24no—
310#121—28no—
311#121C23×C1118yes—
312#120—24no—
313C4×Q8—24no—
314C4×Q8C23×C1118yes—
315C4×D4—28no—
316C4×D4—28no—
317C4×D4—24no—
318C4×D4C23×C1118yes—
319#117—24no—
320#117D4×C1114yes—
321#117C23×C1114yes—
322#117C23×C1114yes—
323C2×C4⋊C4D4×C1112yes—
324C2×C22⋊C4D4×C1112yes—
325C2×C42—24no—
326C2×C42C23×C1111yescharacteristic
327C2×C42C23×C1111yescharacteristic
328#107C23×C1114yes—
329#107C23×C1114yes—
330#106C23×C1114yes—
331#106C23×C1114yes—
332#103C23×C1118yes—
333#103C23×C1118yes—
334#102C23×C1118yes—
335#102C23×C1118yes—
336#97C23×C1114yes—
337#97C23×C1114yes—
338C4×C8C23×C1114yes—
339C4×C8C23×C1114yes—
340C2×C11—22no—
341C2×C11—42no—
342C2×C11—84no—
343C2×C11C2×#53211yescharacteristic
344C2×C11#358412yes—
345C24C2×D4×C1111yescharacteristic
346#41—28no—
347#41—28no—
348C2×Q8—24no—
349C2×Q8C24×C1114yes—
350C2×D4—24no—
351C2×D4—28no—
352C2×D4—24no—
353C2×D4C24×C1114yes—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—28no—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C2×D4×C1112yes—
360C22×C4C2×D4×C1112yes—
361C22×C4C2×D4×C1112yes—
362C22×C4C24×C1112yes—
363C22×C4C24×C1111yescharacteristic
364Q16—24no—
365Q16—24no—
366SD16—28no—
367SD16—28no—
368D8—24no—
369D8—24no—
370M16—28no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—28no—
374C2×C8C11×#4114yes—
375C2×C8C11×#4114yes—
376C2×C8C24×C1112yes—
377C2×C8C24×C1112yes—
378C2×C8C24×C1112yes—
379C2×C8C24×C1112yes—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—24no—
385C4⋊C4C2×D4×C1118yes—
386C4⋊C4C24×C1118yes—
387C22⋊C4—24no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4C2×D4×C1118yes—
393C42—24no—
394C42—28no—
395C42C2×D4×C1112yes—
396C42C2×D4×C1112yes—
397C42C24×C1112yes—
398C42C24×C1112yes—
399C11#6068511yescharacteristic, direct product factor, Sylow
400C23—22no—
401C23—24no—
402C23—42no—
403C23C22×D4×C1112yes—
404C23C22×D4×C1111yescharacteristic
405Q8—24no—
406Q8—24no—
407Q8—84no—
408D4—24no—
409D4—24no—
410D4—48no—
411D4—84no—
412D4—88no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—28no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—48no—
422C2×C4—88no—
423C2×C4C22×D4×C1114yes—
424C2×C4C22×D4×C1114yes—
425C2×C4C22×D4×C1112yes—
426C2×C4C22×D4×C1111yescharacteristic
427C2×C4C2×C11×#4112yes—
428C2×C4C2×C11×#4112yes—
429C2×C4C25×C1111yescharacteristic
430C8—22no—
431C8—22no—
432C8C2×C11×#4114yes—
433C8C2×C11×#4114yes—
434C22—22no—
435C22—22no—
436C22—24no—
437C22—44no—
438C22—44no—
439C22—48no—
440C22C11×#53212yes—
441C22C23×D4×C1111yescharacteristic
442C4—22no—
443C4—24no—
444C4—24no—
445C4—44no—
446C4—48no—
447C4C11×#53212yes—
448C4C22×C11×#4111yescharacteristic
449C4C22×C11×#4111yescharacteristic
450C2—22no—
451C2—42no—
452C2—84no—
453C2C2×C11×#53211yescharacteristic
454C2C11×#358412yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3455C2semidirect
2. C11×#3179C2semidirect
3. C11×#3178C2semidirect
4. C11×#3162C2semidirect
5. C11×#3150C2semidirect
6. C11×#3131C2semidirect
7. C11×#3054C2semidirect
8. C11×#3050C2semidirect
9. C11×#2943C2semidirect
10. C4×C11×#135C2semidirect
11. C2×C11×#405C2semidirect
27. C11×#501C22semidirect
28. C11×#497C22semidirect
29. C11×#496C22semidirect
30. C11×#488C22semidirect
31. C11×#487C22semidirect
32. C11×#486C22semidirect
39. C11×#442C22semidirect
40. C11×#441C22semidirect
41. C11×#440C22semidirect
42. C4×C11×Q16C22semidirect
43. C4×C11×SD16C22semidirect
44. C4×C11×D8C22semidirect
118. #60685C11direct (N × H)
173. #3455C2×C11semidirect
174. #3179C2×C11semidirect
175. #3178C2×C11semidirect
176. #3162C2×C11semidirect
177. #3150C2×C11semidirect
178. #3131C2×C11semidirect
179. #3054C2×C11semidirect
180. #3050C2×C11semidirect
181. #2943C2×C11semidirect
182. C4×#135C2×C11semidirect
183. C2×#405C2×C11semidirect
233. #501C22×C11semidirect
234. #497C22×C11semidirect
235. #496C22×C11semidirect
236. #488C22×C11semidirect
237. #487C22×C11semidirect
238. #486C22×C11semidirect
245. #442C22×C11semidirect
246. #441C22×C11semidirect
247. #440C22×C11semidirect
248. C4×Q16C22×C11semidirect
249. C4×SD16C22×C11semidirect
250. C4×D8C22×C11semidirect
399. C11#60685direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34552
C11×#31792
C11×#31782
C11×#31622
C11×#31502
C11×#31312
C11×#30542
C11×#30502
C11×#29432
C4×C11×#1352
C2×C11×#4052
#6068511