Finite Group Databasebeta

← C11×#60619 #14637812

Subgroups — C11×#60619 #14637812

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3458C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic
3C11×#3140C214yesmaximal, complemented
4C11×#3138C214yesmaximal, complemented
5C11×#3136C2116yesmaximal, complemented
6C11×#2896C212yesmaximal, complemented
7C2×C11×#418C212yesmaximal, complemented
8C11×#2873C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×M16C2212yes—
12C11×#544—22no—
13C11×#544C2218yescomplemented
14C11×#543—22no—
15C11×#535—24no—
16C11×#535C2218yes—
17C11×#533—24no—
18C11×#533C2214yescomplemented
19C2×C11×#127C2212yes—
20C2×C11×#124C2212yes—
21C2×C11×#121—22no—
22C2×C11×#120—22no—
23C2×C11×#117C2212yes—
24C2×C11×#117C2211yescharacteristic
25C11×#490C22116yescomplemented
26C11×#489C22116yescomplemented
27C11×#488C22116yescomplemented
28C11×#486C22116yescomplemented
29C11×#419C2214yescomplemented
30C11×#418C2218yes—
31C11×#418C2218yescomplemented
32C11×#418C2214yescomplemented
33C11×#417C2218yescomplemented
34C11×#416C2218yescomplemented
35C2×C11×#102C2218yescomplemented
36C11×#405C2218yescomplemented
37C4×C11×M16C2214yescomplemented
38C25×C11—21no—
39C2×C11×#41—22no—
40C2×C11×#41—28no—
41C2×C11×#41C2314yes—
42C22×Q8×C11C2311yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11—28no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C22×D4×C11C2314yes—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16—28no—
54C2×C11×M16C2314yes—
55C2×C11×M16C2314yes—
56C22×C8×C11C2314yes—
57C11×C4⋊Q8—28no—
58C11×C4⋊Q8C2318yescomplemented
59C11×#127—24no—
60C11×#127C2318yes—
61C11×#125—28no—
62C11×#125C2318yescomplemented
63C11×#124—24no—
64C11×#124C2318yes—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8—216no—
67C11×#121—216no—
68C11×#120—216no—
69C4×Q8×C11—28no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117D414yes—
73C11×#117C2314yes—
74C11×#117C2314yes—
75C11×#117C2314yes—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4D412yes—
81C2×C42×C11—22no—
82C2×C42×C11C2312yes—
83C11×#103C23116yescomplemented
84C11×#102C23132yes—
85C11×#102C23116yescomplemented
86C11×#97C2318yescomplemented
87C4×C8×C11C2318yescomplemented
88#60619C1111yesmaximal, characteristic, direct product factor, Sylow
89C24×C11—22no—
90C24×C11—21no—
91C24×C11—24no—
92C24×C11—44no—
93C24×C11—84no—
94C24×C11C2×D411yescharacteristic
95C11×#41—28no—
96C11×#41—28no—
97C11×#41—48no—
98C2×Q8×C11—21no—
99C2×Q8×C11—28no—
100C2×Q8×C11—24no—
101C2×Q8×C11C2412yes—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—216no—
107C2×D4×C11—28no—
108C2×D4×C11—28no—
109C2×D4×C11—28no—
110C2×D4×C11—24no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11—48no—
114C2×D4×C11—88no—
115C2×D4×C11C2414yes—
116C2×D4×C11C2412yes—
117C22×C4×C11—21no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—44no—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4118yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2412yes—
127C11×M16—28no—
128C11×M16—28no—
129C2×C8×C11—28no—
130C2×C8×C11C2418yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—216no—
134C11×C4⋊C4C2×D418yes—
135C11×C4⋊C4C2418yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—216no—
139C11×C22⋊C4C2×D418yes—
140C42×C11—24no—
141C42×C11—24no—
142C42×C11C2×D414yes—
143C42×C11C2414yes—
144#3458C2×C1111yescharacteristic, complemented
145C2×#535C2×C1111yescharacteristic
146#3140C2×C1114yescomplemented
147#3138C2×C1114yescomplemented
148#3136C2×C11116yescomplemented
149#2896C2×C1112yescomplemented
150C2×#418C2×C1112yescomplemented
151#2873C2×C1111yescharacteristic, complemented
152C23×C11—24no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11—48no—
157C23×C11—42no—
158C23×C11—44no—
159C23×C11—48no—
160C23×C11—88no—
161C23×C11—816no—
162C23×C11#12414yes—
163C23×C11C22×D411yescharacteristic
164C23×C11C22×D412yes—
165Q8×C11—24no—
166Q8×C11—42no—
167Q8×C11—88no—
168D4×C11—28no—
169D4×C11—24no—
170D4×C11—48no—
171D4×C11—48no—
172D4×C11—44no—
173D4×C11—42no—
174D4×C11—816no—
175C2×C4×C11—28no—
176C2×C4×C11—22no—
177C2×C4×C11—44no—
178C2×C4×C11—42no—
179C2×C4×C11—48no—
180C2×C4×C11—84no—
181C2×C4×C11#12414yes—
182C2×C4×C11#12418yes—
183C2×C4×C11C22×D418yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D412yes—
186C2×C4×C11C2×#4114yes—
187C2×C4×C11C2×#4114yes—
188C2×C4×C11C2×#4114yes—
189C2×C4×C11C2511yescharacteristic
190C8×C11—28no—
191C22×#41C22×C1111yescharacteristic
192C23×D4C22×C1111yescharacteristic
193C22×M16C22×C1112yes—
194#544—22no—
195#544C22×C1118yescomplemented
196#543—22no—
197#535—24no—
198#535C22×C1118yes—
199#533—24no—
200#533C22×C1114yescomplemented
201C2×#127C22×C1112yes—
202C2×#124C22×C1112yes—
203C2×#121—22no—
204C2×#120—22no—
205C2×#117C22×C1112yes—
206C2×#117C22×C1111yescharacteristic
207#490C22×C11116yescomplemented
208#489C22×C11116yescomplemented
209#488C22×C11116yescomplemented
210#486C22×C11116yescomplemented
211#419C22×C1114yescomplemented
212#418C22×C1118yes—
213#418C22×C1118yescomplemented
214#418C22×C1114yescomplemented
215#417C22×C1118yescomplemented
216#416C22×C1118yescomplemented
217C2×#102C22×C1118yescomplemented
218#405C22×C1118yescomplemented
219C4×M16C22×C1114yescomplemented
220C22×C11—22no—
221C22×C11—24no—
222C22×C11—44no—
223C22×C11—44no—
224C22×C11—48no—
225C22×C11—42no—
226C22×C11—44no—
227C22×C11—84no—
228C22×C11—88no—
229C22×C11—816no—
230C22×C11C2×#12412yes—
231C22×C11C2×#12414yes—
232C22×C11C23×D411yescharacteristic
233C4×C11—28no—
234C4×C11—48no—
235C4×C11—42no—
236C4×C11C2×#12414yes—
237C4×C11C2×#12412yes—
238C4×C11C22×#4112yes—
239C25—21no—
240C2×#41—22no—
241C2×#41—28no—
242C2×#41C23×C1114yes—
243C22×Q8C23×C1111yescharacteristic
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—28no—
249C22×D4C23×C1112yes—
250C22×D4C23×C1111yescharacteristic
251C22×D4C23×C1114yes—
252C23×C4—21no—
253C23×C4C23×C1111yescharacteristic
254C2×M16—28no—
255C2×M16C23×C1114yes—
256C2×M16C23×C1114yes—
257C22×C8C23×C1114yes—
258C4⋊Q8—28no—
259C4⋊Q8C23×C1118yescomplemented
260#127—24no—
261#127C23×C1118yes—
262#125—28no—
263#125C23×C1118yescomplemented
264#124—24no—
265#124C23×C1118yes—
266C22⋊Q8—28no—
267C22⋊Q8—216no—
268#121—216no—
269#120—216no—
270C4×Q8—28no—
271#117—22no—
272#117—22no—
273#117D4×C1114yes—
274#117C23×C1114yes—
275#117C23×C1114yes—
276#117C23×C1114yes—
277C2×C4⋊C4D4×C1112yes—
278C2×C4⋊C4C23×C1114yes—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4D4×C1112yes—
282C2×C42—22no—
283C2×C42C23×C1112yes—
284#103C23×C11116yescomplemented
285#102C23×C11132yes—
286#102C23×C11116yescomplemented
287#97C23×C1118yescomplemented
288C4×C8C23×C1118yescomplemented
289C2×C11—22no—
290C2×C11—24no—
291C2×C11—82no—
292C2×C11—84no—
293C2×C11C22×#12411yescharacteristic
294C2×C11#358512yes—
295C24—22no—
296C24—21no—
297C24—24no—
298C24—44no—
299C24—84no—
300C24C2×D4×C1111yescharacteristic
301#41—28no—
302#41—28no—
303#41—48no—
304C2×Q8—21no—
305C2×Q8—28no—
306C2×Q8—24no—
307C2×Q8C24×C1112yes—
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4—216no—
313C2×D4—28no—
314C2×D4—28no—
315C2×D4—28no—
316C2×D4—24no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—48no—
320C2×D4—88no—
321C2×D4C24×C1114yes—
322C2×D4C24×C1112yes—
323C22×C4—21no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—44no—
327C22×C4C2×D4×C1114yes—
328C22×C4C2×D4×C1112yes—
329C22×C4C2×D4×C1111yescharacteristic
330C22×C4C11×#4118yes—
331C22×C4C24×C1111yescharacteristic
332C22×C4C24×C1112yes—
333M16—28no—
334M16—28no—
335C2×C8—28no—
336C2×C8C24×C1118yes—
337C4⋊C4—24no—
338C4⋊C4—28no—
339C4⋊C4—216no—
340C4⋊C4C2×D4×C1118yes—
341C4⋊C4C24×C1118yes—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—216no—
345C22⋊C4C2×D4×C1118yes—
346C42—24no—
347C42—24no—
348C42C2×D4×C1114yes—
349C42C24×C1114yes—
350C11#6061911yescharacteristic, direct product factor, Sylow
351C23—24no—
352C23—22no—
353C23—42no—
354C23—44no—
355C23—48no—
356C23—42no—
357C23—44no—
358C23—48no—
359C23—88no—
360C23—816no—
361C23C11×#12414yes—
362C23C22×D4×C1111yescharacteristic
363C23C22×D4×C1112yes—
364Q8—24no—
365Q8—42no—
366Q8—88no—
367D4—28no—
368D4—24no—
369D4—48no—
370D4—48no—
371D4—44no—
372D4—42no—
373D4—816no—
374C2×C4—28no—
375C2×C4—22no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4—48no—
379C2×C4—84no—
380C2×C4C11×#12414yes—
381C2×C4C11×#12418yes—
382C2×C4C22×D4×C1118yes—
383C2×C4C22×D4×C1111yescharacteristic
384C2×C4C22×D4×C1112yes—
385C2×C4C2×C11×#4114yes—
386C2×C4C2×C11×#4114yes—
387C2×C4C2×C11×#4114yes—
388C2×C4C25×C1111yescharacteristic
389C8—28no—
390C22—22no—
391C22—24no—
392C22—44no—
393C22—42no—
394C22—44no—
395C22—44no—
396C22—48no—
397C22—88no—
398C22—84no—
399C22—816no—
400C22C2×C11×#12412yes—
401C22C2×C11×#12414yes—
402C22C23×D4×C1111yescharacteristic
403C4—28no—
404C4—42no—
405C4—48no—
406C4C2×C11×#12414yes—
407C4C2×C11×#12412yes—
408C4C22×C11×#4112yes—
409C2—22no—
410C2—24no—
411C2—84no—
412C2—82no—
413C2C22×C11×#12411yescharacteristic
414C2C11×#358512yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3458C2semidirect
3. C11×#3140C2semidirect
4. C11×#3138C2semidirect
5. C11×#3136C2semidirect
6. C11×#2896C2semidirect
7. C2×C11×#418C2semidirect
8. C11×#2873C2semidirect
13. C11×#544C22semidirect
18. C11×#533C22semidirect
25. C11×#490C22semidirect
26. C11×#489C22semidirect
27. C11×#488C22semidirect
28. C11×#486C22semidirect
29. C11×#419C22semidirect
31. C11×#418C22semidirect
32. C11×#418C22semidirect
33. C11×#417C22semidirect
34. C11×#416C22semidirect
35. C2×C11×#102C22semidirect
36. C11×#405C22semidirect
37. C4×C11×M16C22semidirect
58. C11×C4⋊Q8C23semidirect
62. C11×#125C23semidirect
83. C11×#103C23semidirect
85. C11×#102C23semidirect
86. C11×#97C23semidirect
87. C4×C8×C11C23semidirect
88. #60619C11direct (N × H)
144. #3458C2×C11semidirect
146. #3140C2×C11semidirect
147. #3138C2×C11semidirect
148. #3136C2×C11semidirect
149. #2896C2×C11semidirect
150. C2×#418C2×C11semidirect
151. #2873C2×C11semidirect
195. #544C22×C11semidirect
200. #533C22×C11semidirect
207. #490C22×C11semidirect
208. #489C22×C11semidirect
209. #488C22×C11semidirect
210. #486C22×C11semidirect
211. #419C22×C11semidirect
213. #418C22×C11semidirect
214. #418C22×C11semidirect
215. #417C22×C11semidirect
216. #416C22×C11semidirect
217. C2×#102C22×C11semidirect
218. #405C22×C11semidirect
219. C4×M16C22×C11semidirect
259. C4⋊Q8C23×C11semidirect
263. #125C23×C11semidirect
284. #103C23×C11semidirect
286. #102C23×C11semidirect
287. #97C23×C11semidirect
288. C4×C8C23×C11semidirect
350. C11#60619direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C2×C11×#5352
C11×#31402
C11×#31382
C11×#31362
C11×#28962
C2×C11×#4182
C11×#28732
#6061911