Finite Group Databasebeta

← C11×#60143 #14637336

Subgroups — C11×#60143 #14637336

Order 2816.

2706 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C212yesmaximal, complemented
2C11×#3449C211yesmaximal, characteristic
3C11×#2933C2116yesmaximal, complemented
4C11×#2932C214yesmaximal, complemented
5C11×#2931C214yesmaximal, complemented
6C11×#2905C211yesmaximal, characteristic, complemented
7C2×C11×#408C212yesmaximal, complemented
8C2×C11×#405C211yesmaximal, characteristic, complemented
9C22×C11×#41C2212yes—
10C11×#568—216no—
11C2×C11×#131C2218yes—
12C2×C11×#131C2218yescomplemented
13C22×C11×M16C2212yes—
14C22×C11×M16C2211yescharacteristic
15C22×C11×M16C2218yescomplemented
16C23×C8×C11C2211yescharacteristic
17C11×#537C414yes—
18C11×#536C414yes—
19C11×#535C414yes—
20C11×#534C414yes—
21C11×#532C2214yes—
22C11×#525C2218yes—
23C2×C11×#117C2211yescharacteristic
24C11×#436C22116yescomplemented
25C11×#435C22132yescomplemented
26C8×D4×C11C22116yescomplemented
27C11×#424C2218yescomplemented
28C11×#423C2214yescomplemented
29C11×#408C2218yes—
30C11×#408C2214yescomplemented
31C11×#408C2214yescomplemented
32C2×C11×C22⋊C8C2218yescomplemented
33C11×#405C2218yescomplemented
34C2×C11×#97C2212yescomplemented
35C2×C4×C8×C11C2212yescomplemented
36C2×C11×#41—28no—
37C2×C11×#41—28no—
38C2×C11×#41C2×C414yes—
39C2×C11×#41C2×C414yes—
40C2×C11×#41C2314yes—
41C2×C11×#41C2314yes—
42C22×Q8×C11C2×C412yes—
43C22×D4×C11C2×C414yes—
44C22×D4×C11C2×C412yes—
45C23×C4×C11C2314yes—
46C23×C4×C11C2311yescharacteristic
47C11×#131—232no—
48C11×#131—232no—
49C2×C11×M16—28no—
50C2×C11×M16—232no—
51C2×C11×M16D418yescomplemented
52C2×C11×M16C2314yes—
53C2×C11×M16C2314yes—
54C2×C11×M16C23116yes—
55C2×C11×M16C2314yes—
56C22×C8×C11—24no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2314yes—
60C22×C8×C11C2314yes—
61C22×C8×C11C23116yes—
62C22×C8×C11C2312yes—
63C11×C4⋊Q8C2×C414yes—
64C11×#127C2×C414yes—
65C11×#124C2×C418yes—
66C11×#123C2×C4116yes—
67C11×C22⋊Q8C2×C4116yes—
68C11×#121C2×C4116yes—
69C11×#121C2×C4116yes—
70C11×#120C2×C4116yes—
71C4×D4×C11C23116yes—
72C11×#117C2×C414yes—
73C11×#117C2314yes—
74C2×C11×C4⋊C4C2×C412yes—
75C2×C11×C22⋊C4C2×C412yes—
76C2×C42×C11C2312yes—
77C11×C4⋊C8C23116yes—
78C11×C22⋊C8C23116yes—
79C11×C22⋊C8C23116yes—
80C11×#97C2318yes—
81C4×C8×C11C2318yes—
82#60143C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11C22×C414yes—
84C24×C11C22×C411yescharacteristic
85C11×#41—216no—
86C11×#41—216no—
87C11×#41—28no—
88C11×#41—28no—
89C11×#41—28no—
90C11×#41—28no—
91C2×Q8×C11—28no—
92C2×Q8×C11C22×C414yes—
93C2×Q8×C11C22×C414yes—
94C2×D4×C11—216no—
95C2×D4×C11—28no—
96C2×D4×C11C22×C418yes—
97C2×D4×C11C22×C418yes—
98C2×D4×C11C22×C414yes—
99C2×D4×C11C22×C414yes—
100C2×D4×C11C22×C4116yes—
101C22×C4×C11—28no—
102C22×C4×C11—28no—
103C22×C4×C11C22×C418yes—
104C22×C4×C11C22×C414yes—
105C22×C4×C11C22×C414yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D414yes—
109C22×C4×C11#4114yes—
110C22×C4×C11C2418yes—
111C22×C4×C11C2411yescharacteristic
112C22×C4×C11C2412yes—
113C11×M16—232no—
114C11×M16—28no—
115C11×M16—28no—
116C11×M16C2×D4116yes—
117C2×C8×C11—232no—
118C2×C8×C11—28no—
119C2×C8×C11—28no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C2×D418yes—
123C2×C8×C11C2412yes—
124C2×C8×C11C2412yes—
125C2×C8×C11C2418yes—
126C2×C8×C11C2414yes—
127C11×C4⋊C4C22×C418yes—
128C11×C4⋊C4C22×C4116yes—
129C11×C22⋊C4C22×C418yes—
130C11×C22⋊C4C22×C4132yes—
131C42×C11C22×C414yes—
132C42×C11C2414yes—
133C2×#568C2×C1112yescomplemented
134#3449C2×C1111yescharacteristic
135#2933C2×C11116yescomplemented
136#2932C2×C1114yescomplemented
137#2931C2×C1114yescomplemented
138#2905C2×C1111yescharacteristic, complemented
139C2×#408C2×C1112yescomplemented
140C2×#405C2×C1111yescharacteristic, complemented
141C23×C11—28no—
142C23×C11—42no—
143C23×C11—48no—
144C23×C11C4×D414yes—
145C23×C11C23×C418yes—
146C23×C11C23×C412yes—
147C23×C11C23×C411yescharacteristic
148Q8×C11—28no—
149Q8×C11—28no—
150D4×C11—216no—
151D4×C11—216no—
152D4×C11—28no—
153D4×C11—28no—
154D4×C11—416no—
155C2×C4×C11—28no—
156C2×C4×C11—216no—
157C2×C4×C11—28no—
158C2×C4×C11—28no—
159C2×C4×C11—44no—
160C2×C4×C11C4×D418yes—
161C2×C4×C11C4×D414yes—
162C2×C4×C11C23×C418yes—
163C2×C4×C11C23×C418yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C23×C412yes—
166C2×C4×C11C22×D414yes—
167C2×C4×C11C22×D412yes—
168C2×C4×C11C2×#4114yes—
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2511yescharacteristic
171C8×C11—28no—
172C8×C11—22no—
173C8×C11—22no—
174C8×C11C22×D418yes—
175C22×#41C22×C1112yes—
176#568—216no—
177C2×#131C22×C1118yes—
178C2×#131C22×C1118yescomplemented
179C22×M16C22×C1112yes—
180C22×M16C22×C1111yescharacteristic
181C22×M16C22×C1118yescomplemented
182C23×C8C22×C1111yescharacteristic
183#537C4×C1114yes—
184#536C4×C1114yes—
185#535C4×C1114yes—
186#534C4×C1114yes—
187#532C22×C1114yes—
188#525C22×C1118yes—
189C2×#117C22×C1111yescharacteristic
190#436C22×C11116yescomplemented
191#435C22×C11132yescomplemented
192C8×D4C22×C11116yescomplemented
193#424C22×C1118yescomplemented
194#423C22×C1114yescomplemented
195#408C22×C1118yes—
196#408C22×C1114yescomplemented
197#408C22×C1114yescomplemented
198C2×C22⋊C8C22×C1118yescomplemented
199#405C22×C1118yescomplemented
200C2×#97C22×C1112yescomplemented
201C2×C4×C8C22×C1112yescomplemented
202C22×C11—22no—
203C22×C11—24no—
204C22×C11—28no—
205C22×C11—216no—
206C22×C11—44no—
207C22×C11—88no—
208C22×C11C2×C4×D414yes—
209C22×C11C2×C4×D412yes—
210C22×C11C24×C411yescharacteristic
211C4×C11—28no—
212C4×C11—28no—
213C4×C11C2×C4×D414yes—
214C4×C11C2×C4×D412yes—
215C4×C11C23×D411yescharacteristic
216C4×C11C22×#4111yescharacteristic
217C2×#41—28no—
218C2×#41—28no—
219C2×#41C2×C4×C1114yes—
220C2×#41C2×C4×C1114yes—
221C2×#41C23×C1114yes—
222C2×#41C23×C1114yes—
223C22×Q8C2×C4×C1112yes—
224C22×D4C2×C4×C1114yes—
225C22×D4C2×C4×C1112yes—
226C23×C4C23×C1114yes—
227C23×C4C23×C1111yescharacteristic
228#131—232no—
229#131—232no—
230C2×M16—28no—
231C2×M16—232no—
232C2×M16D4×C1118yescomplemented
233C2×M16C23×C1114yes—
234C2×M16C23×C1114yes—
235C2×M16C23×C11116yes—
236C2×M16C23×C1114yes—
237C22×C8—24no—
238C22×C8C23×C1111yescharacteristic
239C22×C8C23×C1111yescharacteristic
240C22×C8C23×C1114yes—
241C22×C8C23×C1114yes—
242C22×C8C23×C11116yes—
243C22×C8C23×C1112yes—
244C4⋊Q8C2×C4×C1114yes—
245#127C2×C4×C1114yes—
246#124C2×C4×C1118yes—
247#123C2×C4×C11116yes—
248C22⋊Q8C2×C4×C11116yes—
249#121C2×C4×C11116yes—
250#121C2×C4×C11116yes—
251#120C2×C4×C11116yes—
252C4×D4C23×C11116yes—
253#117C2×C4×C1114yes—
254#117C23×C1114yes—
255C2×C4⋊C4C2×C4×C1112yes—
256C2×C22⋊C4C2×C4×C1112yes—
257C2×C42C23×C1112yes—
258C4⋊C8C23×C11116yes—
259C22⋊C8C23×C11116yes—
260C22⋊C8C23×C11116yes—
261#97C23×C1118yes—
262C4×C8C23×C1118yes—
263C2×C11—24no—
264C2×C11—22no—
265C2×C11—48no—
266C2×C11C22×C4×D411yescharacteristic
267C2×C11#357312yes—
268C24C22×C4×C1114yes—
269C24C22×C4×C1111yescharacteristic
270#41—216no—
271#41—216no—
272#41—28no—
273#41—28no—
274#41—28no—
275#41—28no—
276C2×Q8—28no—
277C2×Q8C22×C4×C1114yes—
278C2×Q8C22×C4×C1114yes—
279C2×D4—216no—
280C2×D4—28no—
281C2×D4C22×C4×C1118yes—
282C2×D4C22×C4×C1118yes—
283C2×D4C22×C4×C1114yes—
284C2×D4C22×C4×C1114yes—
285C2×D4C22×C4×C11116yes—
286C22×C4—28no—
287C22×C4—28no—
288C22×C4C22×C4×C1118yes—
289C22×C4C22×C4×C1114yes—
290C22×C4C22×C4×C1114yes—
291C22×C4C22×C4×C1111yescharacteristic
292C22×C4C22×C4×C1112yes—
293C22×C4C2×D4×C1114yes—
294C22×C4C11×#4114yes—
295C22×C4C24×C1118yes—
296C22×C4C24×C1111yescharacteristic
297C22×C4C24×C1112yes—
298M16—28no—
299M16—28no—
300M16—232no—
301M16C2×D4×C11116yes—
302C2×C8—28no—
303C2×C8—28no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—232no—
307C2×C8C2×D4×C1118yes—
308C2×C8C24×C1112yes—
309C2×C8C24×C1112yes—
310C2×C8C24×C1118yes—
311C2×C8C24×C1114yes—
312C4⋊C4C22×C4×C1118yes—
313C4⋊C4C22×C4×C11116yes—
314C22⋊C4C22×C4×C1118yes—
315C22⋊C4C22×C4×C11132yes—
316C42C22×C4×C1114yes—
317C42C24×C1114yes—
318C11#6014311yescharacteristic, direct product factor, Sylow
319C23—28no—
320C23—42no—
321C23—48no—
322C23C4×D4×C1114yes—
323C23C23×C4×C1118yes—
324C23C23×C4×C1112yes—
325C23C23×C4×C1111yescharacteristic
326Q8—28no—
327Q8—28no—
328D4—216no—
329D4—216no—
330D4—28no—
331D4—28no—
332D4—416no—
333C2×C4—28no—
334C2×C4—216no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—44no—
338C2×C4C4×D4×C1118yes—
339C2×C4C4×D4×C1114yes—
340C2×C4C23×C4×C1118yes—
341C2×C4C23×C4×C1118yes—
342C2×C4C23×C4×C1111yescharacteristic
343C2×C4C23×C4×C1112yes—
344C2×C4C22×D4×C1114yes—
345C2×C4C22×D4×C1112yes—
346C2×C4C2×C11×#4114yes—
347C2×C4C2×C11×#4112yes—
348C2×C4C25×C1111yescharacteristic
349C8—28no—
350C8—22no—
351C8—22no—
352C8C22×D4×C1118yes—
353C22—22no—
354C22—24no—
355C22—28no—
356C22—216no—
357C22—44no—
358C22—88no—
359C22C2×C4×D4×C1114yes—
360C22C2×C4×D4×C1112yes—
361C22C24×C4×C1111yescharacteristic
362C4—28no—
363C4—28no—
364C4C2×C4×D4×C1114yes—
365C4C2×C4×D4×C1112yes—
366C4C23×D4×C1111yescharacteristic
367C4C22×C11×#4111yescharacteristic
368C2—24no—
369C2—22no—
370C2—48no—
371C2C22×C4×D4×C1111yescharacteristic
372C2C11×#357312yes—
subgroupG/H
centerC2×C4×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C24×C4
prime radicalC11×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
3. C11×#2933C2semidirect
4. C11×#2932C2semidirect
5. C11×#2931C2semidirect
6. C11×#2905C2semidirect
7. C2×C11×#408C2semidirect
8. C2×C11×#405C2semidirect
12. C2×C11×#131C22semidirect
15. C22×C11×M16C22semidirect
24. C11×#436C22semidirect
25. C11×#435C22semidirect
26. C8×D4×C11C22semidirect
27. C11×#424C22semidirect
28. C11×#423C22semidirect
30. C11×#408C22semidirect
31. C11×#408C22semidirect
32. C2×C11×C22⋊C8C22semidirect
33. C11×#405C22semidirect
34. C2×C11×#97C22semidirect
35. C2×C4×C8×C11C22semidirect
51. C2×C11×M16D4semidirect
82. #60143C11direct (N × H)
133. C2×#568C2×C11semidirect
135. #2933C2×C11semidirect
136. #2932C2×C11semidirect
137. #2931C2×C11semidirect
138. #2905C2×C11semidirect
139. C2×#408C2×C11semidirect
140. C2×#405C2×C11semidirect
178. C2×#131C22×C11semidirect
181. C22×M16C22×C11semidirect
190. #436C22×C11semidirect
191. #435C22×C11semidirect
192. C8×D4C22×C11semidirect
193. #424C22×C11semidirect
194. #423C22×C11semidirect
196. #408C22×C11semidirect
197. #408C22×C11semidirect
198. C2×C22⋊C8C22×C11semidirect
199. #405C22×C11semidirect
200. C2×#97C22×C11semidirect
201. C2×C4×C8C22×C11semidirect
232. C2×M16D4×C11semidirect
318. C11#60143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C11×#34492
C11×#29332
C11×#29322
C11×#29312
C11×#29052
C2×C11×#4082
C2×C11×#4052
#6014311