Finite Group Databasebeta

← C11×#60140 #14637333

Subgroups — C11×#60140 #14637333

Order 2816.

2722 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#131C212yesmaximal, complemented
2C11×#3449C211yesmaximal, characteristic
3C11×#2932C214yesmaximal, complemented
4C11×#2931C214yesmaximal, complemented
5C11×#2930C218yesmaximal, complemented
6C11×#2929C218yesmaximal, complemented
7C11×#2905C211yesmaximal, characteristic, complemented
8C11×#2879C212yesmaximal, complemented
9C2×C11×#405C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C2×C11×#131—216no—
12C2×C11×#131C2214yes—
13C2×C11×#131C2214yes—
14C2×C11×#131C2214yescomplemented
15C2×C11×#131C2214yescomplemented
16C22×C11×M16C2212yes—
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2214yescomplemented
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2214yescomplemented
21C11×#537C414yes—
22C11×#536C414yes—
23C11×#535C414yes—
24C11×#534C414yes—
25C11×#532C2214yes—
26C11×#525C2218yes—
27C2×C11×#117C2211yescharacteristic
28C11×#436C22116yescomplemented
29C11×#435C22132yescomplemented
30C8×D4×C11C22116yescomplemented
31C11×#424C2218yescomplemented
32C11×#423C2214yescomplemented
33C11×#408C2218yes—
34C11×#408C2218yescomplemented
35C11×#407C2218yescomplemented
36C11×#405C2214yescomplemented
37C11×#405C2214yescomplemented
38C2×C11×#97C2212yescomplemented
39C2×C4×C8×C11C2212yescomplemented
40C2×C11×#41—28no—
41C2×C11×#41—28no—
42C2×C11×#41C2×C414yes—
43C2×C11×#41C2×C414yes—
44C2×C11×#41C2314yes—
45C2×C11×#41C2314yes—
46C22×Q8×C11C2×C412yes—
47C22×D4×C11C2×C414yes—
48C22×D4×C11C2×C412yes—
49C23×C4×C11C2314yes—
50C23×C4×C11C2311yescharacteristic
51C11×#131—216no—
52C11×#131—216no—
53C11×#131—216no—
54C11×#131—216no—
55C2×C11×M16—28no—
56C2×C11×M16—24no—
57C2×C11×M16—216no—
58C2×C11×M16C2314yes—
59C2×C11×M16C2314yes—
60C2×C11×M16C2314yes—
61C2×C11×M16C2318yes—
62C2×C11×M16C2318yes—
63C22×C8×C11—216no—
64C22×C8×C11D418yescomplemented
65C22×C8×C11C2312yes—
66C22×C8×C11C2314yes—
67C22×C8×C11C2318yes—
68C22×C8×C11C2318yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2312yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2312yes—
73C11×C4⋊Q8C2×C414yes—
74C11×#127C2×C414yes—
75C11×#124C2×C418yes—
76C11×#123C2×C4116yes—
77C11×C22⋊Q8C2×C4116yes—
78C11×#121C2×C4116yes—
79C11×#121C2×C4116yes—
80C11×#120C2×C4116yes—
81C4×D4×C11C23116yes—
82C11×#117C2×C414yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4C2×C412yes—
85C2×C11×C22⋊C4C2×C412yes—
86C2×C42×C11C2312yes—
87C11×C4⋊C8C23116yes—
88C11×C22⋊C8C23132yes—
89C11×#97C2318yes—
90C4×C8×C11C2314yes—
91C4×C8×C11C2314yes—
92#60140C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C22×C414yes—
94C24×C11C22×C411yescharacteristic
95C11×#41—216no—
96C11×#41—216no—
97C11×#41—28no—
98C11×#41—28no—
99C11×#41—28no—
100C11×#41—28no—
101C2×Q8×C11—28no—
102C2×Q8×C11C22×C414yes—
103C2×Q8×C11C22×C414yes—
104C2×D4×C11—216no—
105C2×D4×C11—28no—
106C2×D4×C11C22×C418yes—
107C2×D4×C11C22×C418yes—
108C2×D4×C11C22×C414yes—
109C2×D4×C11C22×C414yes—
110C2×D4×C11C22×C4116yes—
111C22×C4×C11—28no—
112C22×C4×C11—28no—
113C22×C4×C11C22×C418yes—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11#4114yes—
120C22×C4×C11C2418yes—
121C22×C4×C11C2411yescharacteristic
122C22×C4×C11C2412yes—
123C11×M16—216no—
124C11×M16—216no—
125C11×M16—28no—
126C11×M16—28no—
127C11×M16—28no—
128C2×C8×C11—216no—
129C2×C8×C11—216no—
130C2×C8×C11—28no—
131C2×C8×C11—24no—
132C2×C8×C11C2×D418yes—
133C2×C8×C11C2×D418yes—
134C2×C8×C11C2×D414yes—
135C2×C8×C11C2×D414yes—
136C2×C8×C11C2414yes—
137C2×C8×C11C2418yes—
138C2×C8×C11C2411yescharacteristic
139C2×C8×C11C2412yes—
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4C22×C418yes—
142C11×C4⋊C4C22×C4116yes—
143C11×C22⋊C4C22×C418yes—
144C11×C22⋊C4C22×C4132yes—
145C42×C11C22×C414yes—
146C42×C11C2414yes—
147C22×#131C2×C1112yescomplemented
148#3449C2×C1111yescharacteristic
149#2932C2×C1114yescomplemented
150#2931C2×C1114yescomplemented
151#2930C2×C1118yescomplemented
152#2929C2×C1118yescomplemented
153#2905C2×C1111yescharacteristic, complemented
154#2879C2×C1112yescomplemented
155C2×#405C2×C1111yescharacteristic, complemented
156C23×C11—28no—
157C23×C11—42no—
158C23×C11—48no—
159C23×C11C4×D414yes—
160C23×C11C23×C418yes—
161C23×C11C23×C412yes—
162C23×C11C23×C411yescharacteristic
163Q8×C11—28no—
164Q8×C11—28no—
165D4×C11—216no—
166D4×C11—216no—
167D4×C11—28no—
168D4×C11—28no—
169D4×C11—416no—
170C2×C4×C11—28no—
171C2×C4×C11—216no—
172C2×C4×C11—28no—
173C2×C4×C11—28no—
174C2×C4×C11—44no—
175C2×C4×C11C4×D418yes—
176C2×C4×C11C4×D414yes—
177C2×C4×C11C23×C418yes—
178C2×C4×C11C23×C418yes—
179C2×C4×C11C23×C411yescharacteristic
180C2×C4×C11C23×C412yes—
181C2×C4×C11C22×D414yes—
182C2×C4×C11C22×D412yes—
183C2×C4×C11C2×#4112yes—
184C2×C4×C11C2×#4114yes—
185C2×C4×C11C2511yescharacteristic
186C8×C11—28no—
187C8×C11—24no—
188C8×C11C22×D412yes—
189C8×C11C22×D414yes—
190C8×C11C22×D412yes—
191C22×#41C22×C1112yes—
192C2×#131—216no—
193C2×#131C22×C1114yes—
194C2×#131C22×C1114yes—
195C2×#131C22×C1114yescomplemented
196C2×#131C22×C1114yescomplemented
197C22×M16C22×C1111yescharacteristic
198C22×M16C22×C1112yes—
199C22×M16C22×C1114yescomplemented
200C23×C8C22×C1111yescharacteristic
201C23×C8C22×C1114yescomplemented
202#537C4×C1114yes—
203#536C4×C1114yes—
204#535C4×C1114yes—
205#534C4×C1114yes—
206#532C22×C1114yes—
207#525C22×C1118yes—
208C2×#117C22×C1111yescharacteristic
209#436C22×C11116yescomplemented
210#435C22×C11132yescomplemented
211C8×D4C22×C11116yescomplemented
212#424C22×C1118yescomplemented
213#423C22×C1114yescomplemented
214#408C22×C1118yes—
215#408C22×C1118yescomplemented
216#407C22×C1118yescomplemented
217#405C22×C1114yescomplemented
218#405C22×C1114yescomplemented
219C2×#97C22×C1112yescomplemented
220C2×C4×C8C22×C1112yescomplemented
221C22×C11—22no—
222C22×C11—24no—
223C22×C11—28no—
224C22×C11—216no—
225C22×C11—44no—
226C22×C11—416no—
227C22×C11C2×C4×D414yes—
228C22×C11C2×C4×D412yes—
229C22×C11C24×C411yescharacteristic
230C4×C11—28no—
231C4×C11—28no—
232C4×C11C2×C4×D414yes—
233C4×C11C2×C4×D412yes—
234C4×C11C23×D411yescharacteristic
235C4×C11C22×#4111yescharacteristic
236C2×#41—28no—
237C2×#41—28no—
238C2×#41C2×C4×C1114yes—
239C2×#41C2×C4×C1114yes—
240C2×#41C23×C1114yes—
241C2×#41C23×C1114yes—
242C22×Q8C2×C4×C1112yes—
243C22×D4C2×C4×C1114yes—
244C22×D4C2×C4×C1112yes—
245C23×C4C23×C1114yes—
246C23×C4C23×C1111yescharacteristic
247#131—216no—
248#131—216no—
249#131—216no—
250#131—216no—
251C2×M16—28no—
252C2×M16—24no—
253C2×M16—216no—
254C2×M16C23×C1114yes—
255C2×M16C23×C1114yes—
256C2×M16C23×C1114yes—
257C2×M16C23×C1118yes—
258C2×M16C23×C1118yes—
259C22×C8—216no—
260C22×C8D4×C1118yescomplemented
261C22×C8C23×C1114yes—
262C22×C8C23×C1118yes—
263C22×C8C23×C1118yes—
264C22×C8C23×C1112yes—
265C22×C8C23×C1112yes—
266C22×C8C23×C1112yes—
267C22×C8C23×C1111yescharacteristic
268C22×C8C23×C1111yescharacteristic
269C4⋊Q8C2×C4×C1114yes—
270#127C2×C4×C1114yes—
271#124C2×C4×C1118yes—
272#123C2×C4×C11116yes—
273C22⋊Q8C2×C4×C11116yes—
274#121C2×C4×C11116yes—
275#121C2×C4×C11116yes—
276#120C2×C4×C11116yes—
277C4×D4C23×C11116yes—
278#117C2×C4×C1114yes—
279#117C23×C1114yes—
280C2×C4⋊C4C2×C4×C1112yes—
281C2×C22⋊C4C2×C4×C1112yes—
282C2×C42C23×C1112yes—
283C4⋊C8C23×C11116yes—
284C22⋊C8C23×C11132yes—
285#97C23×C1118yes—
286C4×C8C23×C1114yes—
287C4×C8C23×C1114yes—
288C2×C11—24no—
289C2×C11—22no—
290C2×C11—48no—
291C2×C11C22×C4×D411yescharacteristic
292C2×C11#357312yes—
293C24C22×C4×C1114yes—
294C24C22×C4×C1111yescharacteristic
295#41—216no—
296#41—216no—
297#41—28no—
298#41—28no—
299#41—28no—
300#41—28no—
301C2×Q8—28no—
302C2×Q8C22×C4×C1114yes—
303C2×Q8C22×C4×C1114yes—
304C2×D4—216no—
305C2×D4—28no—
306C2×D4C22×C4×C1118yes—
307C2×D4C22×C4×C1118yes—
308C2×D4C22×C4×C1114yes—
309C2×D4C22×C4×C1114yes—
310C2×D4C22×C4×C11116yes—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4C22×C4×C1118yes—
314C22×C4C22×C4×C1114yes—
315C22×C4C22×C4×C1114yes—
316C22×C4C22×C4×C1111yescharacteristic
317C22×C4C22×C4×C1112yes—
318C22×C4C2×D4×C1114yes—
319C22×C4C11×#4114yes—
320C22×C4C24×C1118yes—
321C22×C4C24×C1111yescharacteristic
322C22×C4C24×C1112yes—
323M16—28no—
324M16—28no—
325M16—28no—
326M16—216no—
327M16—216no—
328C2×C8—28no—
329C2×C8—24no—
330C2×C8—216no—
331C2×C8—216no—
332C2×C8C2×D4×C1118yes—
333C2×C8C2×D4×C1118yes—
334C2×C8C2×D4×C1114yes—
335C2×C8C2×D4×C1114yes—
336C2×C8C24×C1114yes—
337C2×C8C24×C1118yes—
338C2×C8C24×C1111yescharacteristic
339C2×C8C24×C1111yescharacteristic
340C2×C8C24×C1112yes—
341C4⋊C4C22×C4×C1118yes—
342C4⋊C4C22×C4×C11116yes—
343C22⋊C4C22×C4×C1118yes—
344C22⋊C4C22×C4×C11132yes—
345C42C22×C4×C1114yes—
346C42C24×C1114yes—
347C11#6014011yescharacteristic, direct product factor, Sylow
348C23—28no—
349C23—42no—
350C23—48no—
351C23C4×D4×C1114yes—
352C23C23×C4×C1118yes—
353C23C23×C4×C1112yes—
354C23C23×C4×C1111yescharacteristic
355Q8—28no—
356Q8—28no—
357D4—216no—
358D4—216no—
359D4—28no—
360D4—28no—
361D4—416no—
362C2×C4—28no—
363C2×C4—216no—
364C2×C4—28no—
365C2×C4—28no—
366C2×C4—44no—
367C2×C4C4×D4×C1118yes—
368C2×C4C4×D4×C1114yes—
369C2×C4C23×C4×C1118yes—
370C2×C4C23×C4×C1118yes—
371C2×C4C23×C4×C1111yescharacteristic
372C2×C4C23×C4×C1112yes—
373C2×C4C22×D4×C1114yes—
374C2×C4C22×D4×C1112yes—
375C2×C4C2×C11×#4112yes—
376C2×C4C2×C11×#4114yes—
377C2×C4C25×C1111yescharacteristic
378C8—28no—
379C8—24no—
380C8C22×D4×C1112yes—
381C8C22×D4×C1114yes—
382C8C22×D4×C1112yes—
383C22—22no—
384C22—24no—
385C22—28no—
386C22—216no—
387C22—44no—
388C22—416no—
389C22C2×C4×D4×C1114yes—
390C22C2×C4×D4×C1112yes—
391C22C24×C4×C1111yescharacteristic
392C4—28no—
393C4—28no—
394C4C2×C4×D4×C1114yes—
395C4C2×C4×D4×C1112yes—
396C4C23×D4×C1111yescharacteristic
397C4C22×C11×#4111yescharacteristic
398C2—24no—
399C2—22no—
400C2—48no—
401C2C22×C4×D4×C1111yescharacteristic
402C2C11×#357312yes—
subgroupG/H
centerC2×C8×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C24×C4
prime radicalC11×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#131C2semidirect
3. C11×#2932C2semidirect
4. C11×#2931C2semidirect
5. C11×#2930C2semidirect
6. C11×#2929C2semidirect
7. C11×#2905C2semidirect
8. C11×#2879C2semidirect
9. C2×C11×#405C2semidirect
14. C2×C11×#131C22semidirect
15. C2×C11×#131C22semidirect
18. C22×C11×M16C22semidirect
20. C23×C8×C11C22semidirect
28. C11×#436C22semidirect
29. C11×#435C22semidirect
30. C8×D4×C11C22semidirect
31. C11×#424C22semidirect
32. C11×#423C22semidirect
34. C11×#408C22semidirect
35. C11×#407C22semidirect
36. C11×#405C22semidirect
37. C11×#405C22semidirect
38. C2×C11×#97C22semidirect
39. C2×C4×C8×C11C22semidirect
64. C22×C8×C11D4semidirect
92. #60140C11direct (N × H)
147. C22×#131C2×C11semidirect
149. #2932C2×C11semidirect
150. #2931C2×C11semidirect
151. #2930C2×C11semidirect
152. #2929C2×C11semidirect
153. #2905C2×C11semidirect
154. #2879C2×C11semidirect
155. C2×#405C2×C11semidirect
195. C2×#131C22×C11semidirect
196. C2×#131C22×C11semidirect
199. C22×M16C22×C11semidirect
201. C23×C8C22×C11semidirect
209. #436C22×C11semidirect
210. #435C22×C11semidirect
211. C8×D4C22×C11semidirect
212. #424C22×C11semidirect
213. #423C22×C11semidirect
215. #408C22×C11semidirect
216. #407C22×C11semidirect
217. #405C22×C11semidirect
218. #405C22×C11semidirect
219. C2×#97C22×C11semidirect
220. C2×C4×C8C22×C11semidirect
260. C22×C8D4×C11semidirect
347. C11#60140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1312
C11×#34492
C11×#29322
C11×#29312
C11×#29302
C11×#29292
C11×#29052
C11×#28792
C2×C11×#4052
#6014011