Finite Group Databasebeta

← C2×C11×#2920 #14637310

Subgroups — C2×C11×#2920 #14637310

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C11C211yesmaximal, characteristic
2C11×#2920C2116yesmaximal, direct product factor
3C2×C11×#432C214yesmaximal, complemented
4C2×C11×#431C214yesmaximal, complemented
5C2×C11×#423C212yesmaximal, complemented
6C2×C11×#407C212yesmaximal
7C2×C4×C11×M16C212yesmaximal, complemented
8C24×C4×C11C412yes—
9C24×C4×C11C2211yescharacteristic
10C22×C11×M16C2214yes—
11C22×C42×C11C418yes—
12C22×C42×C11C412yes—
13C22×C42×C11C412yes—
14C22×C42×C11C412yes—
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2212yes—
17C22×C42×C11C2218yes—
18C22×C42×C11C2212yes—
19C22×C42×C11C2211yescharacteristic
20C11×#432C22132yescomplemented
21C11×#431C22132yescomplemented
22C11×#423C22116yescomplemented
23C2×C11×C4⋊C8C2218yescomplemented
24C11×#407C22116yes—
25C2×C11×C22⋊C8C2218yes—
26C4×C11×M16C22116yescomplemented
27C2×C11×#97C2214yescomplemented
28C2×C4×C8×C11C2214yescomplemented
29C25×C11C2×C411yescharacteristic
30C23×C4×C11—216no—
31C23×C4×C11—28no—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C414yes—
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2×C412yes—
36C23×C4×C11C2×C412yes—
37C23×C4×C11C2×C412yes—
38C23×C4×C11C2×C412yes—
39C23×C4×C11C2×C412yes—
40C23×C4×C11C2×C4116yes—
41C23×C4×C11C2×C412yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2314yes—
44C23×C4×C11C2311yescharacteristic
45C2×C11×M16—216no—
46C2×C11×M16C23116yes—
47C22×C8×C11C2318yes—
48C2×C42×C11C2×C412yes—
49C2×C42×C11C2×C418yes—
50C2×C42×C11C2×C4116yes—
51C2×C42×C11C2×C4116yes—
52C2×C42×C11C2×C412yes—
53C2×C42×C11C2×C412yes—
54C2×C42×C11C2×C4116yes—
55C2×C42×C11C2×C412yes—
56C2×C42×C11C2×C411yescharacteristic
57C2×C42×C11C2×C414yes—
58C2×C42×C11C2×C412yes—
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2×C418yes—
61C2×C42×C11C2×C414yes—
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2314yes—
64C2×C42×C11C2312yes—
65C2×C42×C11C2314yes—
66C2×C42×C11C2318yes—
67C2×C42×C11C2318yes—
68C2×C42×C11C2311yescharacteristic
69C11×C4⋊C8C23132yescomplemented
70C11×C22⋊C8C23132yes—
71C11×#97C23116yescomplemented
72C4×C8×C11C23116yescomplemented
73C2×#2920C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—24no—
75C24×C11—28no—
76C24×C11C22×C414yes—
77C24×C11C22×C411yescharacteristic
78C24×C11C22×C412yes—
79C22×C4×C11—24no—
80C22×C4×C11—28no—
81C22×C4×C11—216no—
82C22×C4×C11—28no—
83C22×C4×C11—28no—
84C22×C4×C11—28no—
85C22×C4×C11—28no—
86C22×C4×C11—28no—
87C22×C4×C11—264no—
88C22×C4×C11—28no—
89C22×C4×C11—216no—
90C22×C4×C11M16116yescomplemented
91C22×C4×C11C22×C414yes—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C414yes—
94C22×C4×C11C22×C418yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C418yes—
99C22×C4×C11C22×C418yes—
100C22×C4×C11C22×C418yes—
101C22×C4×C11C22×C418yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C418yes—
107C22×C4×C11#4118yes—
108C22×C4×C11C2414yes—
109C22×C4×C11C2412yes—
110C22×C4×C11C2411yescharacteristic
111C11×M16—232no—
112C2×C8×C11—216no—
113C2×C8×C11C24116yes—
114C42×C11C22×C418yes—
115C42×C11C22×C418yes—
116C42×C11C22×C418yes—
117C42×C11C22×C418yes—
118C42×C11C22×C412yes—
119C42×C11C22×C414yes—
120C42×C11C22×C418yes—
121C42×C11C22×C414yes—
122C42×C11C22×C414yes—
123C42×C11C22×C412yes—
124C42×C11C2412yes—
125C42×C11C2412yes—
126C42×C11C2414yes—
127C23×C42C2×C1111yescharacteristic
128#2920C2×C11116yesdirect product factor
129C2×#432C2×C1114yescomplemented
130C2×#431C2×C1114yescomplemented
131C2×#423C2×C1112yescomplemented
132C2×#407C2×C1112yes—
133C2×C4×M16C2×C1112yescomplemented
134C23×C11—232no—
135C23×C11—28no—
136C23×C11—24no—
137C23×C11—216no—
138C23×C11—24no—
139C23×C11—24no—
140C23×C11#11714yes—
141C23×C11C2×M1618yes—
142C23×C11C23×C412yes—
143C23×C11C23×C414yes—
144C23×C11C23×C411yescharacteristic
145C2×C4×C11—28no—
146C2×C4×C11—24no—
147C2×C4×C11—216no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—28no—
151C2×C4×C11—216no—
152C2×C4×C11—216no—
153C2×C4×C11—216no—
154C2×C4×C11—216no—
155C2×C4×C11—216no—
156C2×C4×C11—28no—
157C2×C4×C11#11718yes—
158C2×C4×C11#11714yes—
159C2×C4×C11C2×M1618yes—
160C2×C4×C11C2×M1618yes—
161C2×C4×C11C2×M16132yescomplemented
162C2×C4×C11C23×C414yes—
163C2×C4×C11C23×C414yes—
164C2×C4×C11C23×C414yes—
165C2×C4×C11C23×C412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C23×C414yes—
168C2×C4×C11C23×C414yes—
169C2×C4×C11C2×#4114yes—
170C2×C4×C11C2×#4118yes—
171C2×C4×C11C2511yescharacteristic
172C8×C11—216no—
173C24×C4C4×C1112yes—
174C24×C4C22×C1111yescharacteristic
175C22×M16C22×C1114yes—
176C22×C42C4×C1118yes—
177C22×C42C4×C1112yes—
178C22×C42C4×C1112yes—
179C22×C42C4×C1112yes—
180C22×C42C22×C1111yescharacteristic
181C22×C42C22×C1111yescharacteristic
182C22×C42C22×C1112yes—
183C22×C42C22×C1112yes—
184C22×C42C22×C1118yes—
185#432C22×C11132yescomplemented
186#431C22×C11132yescomplemented
187#423C22×C11116yescomplemented
188C2×C4⋊C8C22×C1118yescomplemented
189#407C22×C11116yes—
190C2×C22⋊C8C22×C1118yes—
191C4×M16C22×C11116yescomplemented
192C2×#97C22×C1114yescomplemented
193C2×C4×C8C22×C1114yescomplemented
194C22×C11—232no—
195C22×C11—24no—
196C22×C11—28no—
197C22×C11—216no—
198C22×C11—24no—
199C22×C11—24no—
200C22×C11C2×#11714yes—
201C22×C11C2×#11712yes—
202C22×C11C22×M1618yes—
203C22×C11C22×M1614yes—
204C22×C11C24×C411yescharacteristic
205C4×C11—24no—
206C4×C11—24no—
207C4×C11—24no—
208C4×C11C2×#11712yes—
209C4×C11C2×#11714yes—
210C4×C11C22×M1618yes—
211C4×C11C22×M1618yes—
212C4×C11C22×#4112yes—
213C25C2×C4×C1111yescharacteristic
214C23×C4—216no—
215C23×C4—28no—
216C23×C4C2×C4×C1112yes—
217C23×C4C2×C4×C1112yes—
218C23×C4C2×C4×C1112yes—
219C23×C4C2×C4×C1112yes—
220C23×C4C2×C4×C1112yes—
221C23×C4C2×C4×C11116yes—
222C23×C4C2×C4×C1111yescharacteristic
223C23×C4C2×C4×C1114yes—
224C23×C4C2×C4×C1112yes—
225C23×C4C2×C4×C1112yes—
226C23×C4C23×C1112yes—
227C23×C4C23×C1114yes—
228C23×C4C23×C1111yescharacteristic
229C2×M16—216no—
230C2×M16C23×C11116yes—
231C22×C8C23×C1118yes—
232C2×C42C2×C4×C1112yes—
233C2×C42C2×C4×C1118yes—
234C2×C42C2×C4×C11116yes—
235C2×C42C2×C4×C11116yes—
236C2×C42C2×C4×C1112yes—
237C2×C42C2×C4×C1112yes—
238C2×C42C2×C4×C1118yes—
239C2×C42C2×C4×C11116yes—
240C2×C42C2×C4×C1112yes—
241C2×C42C2×C4×C1114yes—
242C2×C42C2×C4×C1111yescharacteristic
243C2×C42C2×C4×C1114yes—
244C2×C42C2×C4×C1112yes—
245C2×C42C2×C4×C1111yescharacteristic
246C2×C42C23×C1111yescharacteristic
247C2×C42C23×C1111yescharacteristic
248C2×C42C23×C1114yes—
249C2×C42C23×C1112yes—
250C2×C42C23×C1114yes—
251C2×C42C23×C1118yes—
252C2×C42C23×C1118yes—
253C4⋊C8C23×C11132yescomplemented
254C22⋊C8C23×C11132yes—
255#97C23×C11116yescomplemented
256C4×C8C23×C11116yescomplemented
257C2×C11—24no—
258C2×C11—28no—
259C2×C11#292014yesdirect product factor
260C2×C11C22×#11711yescharacteristic
261C2×C11C23×M1612yes—
262C24—24no—
263C24—28no—
264C24C22×C4×C1114yes—
265C24C22×C4×C1111yescharacteristic
266C24C22×C4×C1112yes—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—216no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—28no—
273C22×C4—28no—
274C22×C4—28no—
275C22×C4—264no—
276C22×C4—28no—
277C22×C4—216no—
278C22×C4C11×M16116yescomplemented
279C22×C4C22×C4×C1114yes—
280C22×C4C22×C4×C1112yes—
281C22×C4C22×C4×C1114yes—
282C22×C4C22×C4×C1118yes—
283C22×C4C22×C4×C1118yes—
284C22×C4C22×C4×C1112yes—
285C22×C4C22×C4×C1112yes—
286C22×C4C22×C4×C1118yes—
287C22×C4C22×C4×C1118yes—
288C22×C4C22×C4×C1118yes—
289C22×C4C22×C4×C1118yes—
290C22×C4C22×C4×C1112yes—
291C22×C4C22×C4×C1111yescharacteristic
292C22×C4C22×C4×C1112yes—
293C22×C4C22×C4×C1112yes—
294C22×C4C22×C4×C1118yes—
295C22×C4C11×#4118yes—
296C22×C4C24×C1114yes—
297C22×C4C24×C1111yescharacteristic
298C22×C4C24×C1112yes—
299M16—232no—
300C2×C8—216no—
301C2×C8C24×C11116yes—
302C42C22×C4×C1118yes—
303C42C22×C4×C1118yes—
304C42C22×C4×C1118yes—
305C42C22×C4×C1118yes—
306C42C22×C4×C1112yes—
307C42C22×C4×C1114yes—
308C42C22×C4×C1118yes—
309C42C22×C4×C1114yes—
310C42C22×C4×C1112yes—
311C42C22×C4×C1114yes—
312C42C24×C1112yes—
313C42C24×C1112yes—
314C42C24×C1114yes—
315C11C2×#292011yescharacteristic, direct product factor, Sylow
316C23—232no—
317C23—28no—
318C23—24no—
319C23—216no—
320C23—24no—
321C23—24no—
322C23C11×#11714yes—
323C23C2×C11×M1618yes—
324C23C23×C4×C1112yes—
325C23C23×C4×C1114yes—
326C23C23×C4×C1111yescharacteristic
327C2×C4—28no—
328C2×C4—24no—
329C2×C4—216no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—216no—
334C2×C4—216no—
335C2×C4—216no—
336C2×C4—216no—
337C2×C4—216no—
338C2×C4—28no—
339C2×C4C11×#11718yes—
340C2×C4C11×#11714yes—
341C2×C4C2×C11×M1618yes—
342C2×C4C2×C11×M1618yes—
343C2×C4C2×C11×M16132yescomplemented
344C2×C4C23×C4×C1114yes—
345C2×C4C23×C4×C1114yes—
346C2×C4C23×C4×C1114yes—
347C2×C4C23×C4×C1111yescharacteristic
348C2×C4C23×C4×C1112yes—
349C2×C4C23×C4×C1114yes—
350C2×C4C23×C4×C1114yes—
351C2×C4C2×C11×#4114yes—
352C2×C4C2×C11×#4118yes—
353C2×C4C25×C1111yescharacteristic
354C8—216no—
355C22—232no—
356C22—24no—
357C22—28no—
358C22—216no—
359C22—24no—
360C22—24no—
361C22C2×C11×#11714yes—
362C22C2×C11×#11712yes—
363C22C22×C11×M1618yes—
364C22C22×C11×M1614yes—
365C22C24×C4×C1111yescharacteristic
366C4—24no—
367C4—24no—
368C4—24no—
369C4C2×C11×#11712yes—
370C4C2×C11×#11714yes—
371C4C22×C11×M1618yes—
372C4C22×C11×M1618yes—
373C4C22×C11×#4112yes—
374C2—24no—
375C2—28no—
376C2C11×#292014yesdirect product factor
377C2C22×C11×#11711yescharacteristic
378C2C23×C11×M1612yes—
subgroupG/H
centerC2×C42×C11C23
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2920C2direct (N × H)
3. C2×C11×#432C2semidirect
4. C2×C11×#431C2semidirect
5. C2×C11×#423C2semidirect
7. C2×C4×C11×M16C2semidirect
20. C11×#432C22semidirect
21. C11×#431C22semidirect
22. C11×#423C22semidirect
23. C2×C11×C4⋊C8C22semidirect
26. C4×C11×M16C22semidirect
27. C2×C11×#97C22semidirect
28. C2×C4×C8×C11C22semidirect
69. C11×C4⋊C8C23semidirect
71. C11×#97C23semidirect
72. C4×C8×C11C23semidirect
73. C2×#2920C11direct (N × H)
90. C22×C4×C11M16semidirect
128. #2920C2×C11direct (N × H)
129. C2×#432C2×C11semidirect
130. C2×#431C2×C11semidirect
131. C2×#423C2×C11semidirect
133. C2×C4×M16C2×C11semidirect
161. C2×C4×C11C2×M16semidirect
185. #432C22×C11semidirect
186. #431C22×C11semidirect
187. #423C22×C11semidirect
188. C2×C4⋊C8C22×C11semidirect
191. C4×M16C22×C11semidirect
192. C2×#97C22×C11semidirect
193. C2×C4×C8C22×C11semidirect
253. C4⋊C8C23×C11semidirect
255. #97C23×C11semidirect
256. C4×C8C23×C11semidirect
259. C2×C11#2920direct (N × H)
278. C22×C4C11×M16semidirect
315. C11C2×#2920direct (N × H)
343. C2×C4C2×C11×M16semidirect
376. C2C11×#2920direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C42×C112
C11×#29202
C2×C11×#4322
C2×C11×#4312
C2×C11×#4232
C2×C11×#4072
C2×C4×C11×M162
C2×#292011