Finite Group Databasebeta

← C11×#60064 #14637257

Subgroups — C11×#60064 #14637257

Order 2816.

5134 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×#41C211yesmaximal, characteristic
2C2×C11×#568C212yesmaximal, complemented
3C11×#2880C2116yesmaximal, complemented
4C11×#2879C216yesmaximal, complemented
5C2×C11×#407C216yesmaximal, complemented
6C22×C11×#41—216no—
7C22×C11×#41C418yes—
8C22×C11×#41C411yescharacteristic
9C22×C11×#41C413yes—
10C22×C11×#41C2213yes—
11C22×C11×#41C2218yes—
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C411yescharacteristic
14C23×D4×C11C413yes—
15C24×C4×C11C2213yes—
16C11×#568—216no—
17C2×C11×#131C22116yescomplemented
18C22×C11×M16C22112yescomplemented
19C11×#408C22148yescomplemented
20C11×#407C2214yes—
21C11×#407C22124yescomplemented
22C11×#407C22112yescomplemented
23C2×C11×C22⋊C8C22124yescomplemented
24C25×C11C2×C413yes—
25C2×C11×#41—264no—
26C2×C11×#41—264no—
27C2×C11×#41—28no—
28C2×C11×#41—224no—
29C2×C11×#41—224no—
30C2×C11×#41C2×C418yes—
31C2×C11×#41C2×C4124yes—
32C2×C11×#41C2×C4112yes—
33C2×C11×#41C2×C414yes—
34C2×C11×#41D4116yes—
35C2×C11×#41C23112yes—
36C2×C11×#41C2314yes—
37C22×Q8×C11—28no—
38C22×Q8×C11C2×C418yes—
39C22×Q8×C11C2×C413yes—
40C22×Q8×C11C2×C411yescharacteristic
41C22×D4×C11—224no—
42C22×D4×C11C2×C416yes—
43C22×D4×C11C2×C4124yes—
44C22×D4×C11C2×C413yes—
45C22×D4×C11C2×C413yes—
46C23×C4×C11—224no—
47C23×C4×C11C2×C413yes—
48C23×C4×C11C2×C413yes—
49C23×C4×C11C2×C4112yes—
50C23×C4×C11C2×C413yes—
51C23×C4×C11C23112yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2313yes—
54C23×C4×C11C2313yes—
55C11×#131—264no—
56C2×C11×M16—248no—
57C2×C11×M16C2318yes—
58C2×C11×M16C23124yescomplemented
59C22×C8×C11C23124yescomplemented
60C11×C22⋊C8C23116yes—
61C11×C22⋊C8C23148yescomplemented
62#60064C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—212no—
64C24×C11—412no—
65C24×C11C22×C411yescharacteristic
66C24×C11C22×C4112yes—
67C24×C11C22×C413yes—
68C24×C11C22×C413yes—
69C11×#41—232no—
70C11×#41—296no—
71C11×#41—248no—
72C11×#41—248no—
73C11×#41C22⋊C4132yes—
74C11×#41C2×D4132yes—
75C2×Q8×C11—232no—
76C2×Q8×C11—212no—
77C2×Q8×C11C22⋊C418yes—
78C2×Q8×C11C22×C4112yes—
79C2×Q8×C11C22×C414yes—
80C2×D4×C11—224no—
81C2×D4×C11—296no—
82C2×D4×C11—212no—
83C2×D4×C11C22⋊C4124yes—
84C2×D4×C11C22×C4124yes—
85C2×D4×C11C22×C4112yes—
86C2×D4×C11C22×C4112yes—
87C22×C4×C11—212no—
88C22×C4×C11—212no—
89C22×C4×C11—212no—
90C22×C4×C11—248no—
91C22×C4×C11—24no—
92C22×C4×C11—212no—
93C22×C4×C11—248no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C413yes—
97C22×C4×C11C22×C4112yes—
98C22×C4×C11C22×C4112yes—
99C22×C4×C11C22×C4112yes—
100C22×C4×C11C22×C416yes—
101C22×C4×C11C22×C413yes—
102C22×C4×C11C22×C416yes—
103C22×C4×C11C2×D4124yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2416yes—
106C22×C4×C11C2416yes—
107C22×C4×C11C2411yescharacteristic
108C11×M16—216no—
109C11×M16—248no—
110C2×C8×C11—248no—
111C2×C8×C11C24116yes—
112C23×#41C2×C1111yescharacteristic
113C2×#568C2×C1112yescomplemented
114#2880C2×C11116yescomplemented
115#2879C2×C1116yescomplemented
116C2×#407C2×C1116yescomplemented
117C23×C11—22no—
118C23×C11—24no—
119C23×C11—224no—
120C23×C11—26no—
121C23×C11—224no—
122C23×C11—46no—
123C23×C11—412no—
124C23×C11—46no—
125C23×C11—448no—
126C23×C11C2×C22⋊C4112yes—
127C23×C11C23×C416yes—
128C23×C11C23×C411yescharacteristic
129C23×C11C23×C416yes—
130C23×C11C23×C412yes—
131Q8×C11—224no—
132Q8×C11C2×C22⋊C4116yes—
133D4×C11—248no—
134D4×C11—224no—
135D4×C11C2×C22⋊C4148yes—
136C2×C4×C11—22no—
137C2×C4×C11—26no—
138C2×C4×C11—224no—
139C2×C4×C11—24no—
140C2×C4×C11—224no—
141C2×C4×C11—224no—
142C2×C4×C11—212no—
143C2×C4×C11—24no—
144C2×C4×C11—212no—
145C2×C4×C11C2×C22⋊C4112yes—
146C2×C4×C11C2×C22⋊C4124yes—
147C2×C4×C11C23×C412yes—
148C2×C4×C11C23×C416yes—
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C23×C416yes—
151C2×C4×C11C22×D4124yes—
152C2×C4×C11C22×D414yes—
153C2×C4×C11C2511yescharacteristic
154C8×C11—216no—
155C22×#41—216no—
156C22×#41C4×C1118yes—
157C22×#41C4×C1111yescharacteristic
158C22×#41C4×C1113yes—
159C22×#41C22×C1113yes—
160C22×#41C22×C1118yes—
161C22×#41C22×C1111yescharacteristic
162C23×Q8C4×C1111yescharacteristic
163C23×D4C4×C1113yes—
164C24×C4C22×C1113yes—
165#568—216no—
166C2×#131C22×C11116yescomplemented
167C22×M16C22×C11112yescomplemented
168#408C22×C11148yescomplemented
169#407C22×C1114yes—
170#407C22×C11124yescomplemented
171#407C22×C11112yescomplemented
172C2×C22⋊C8C22×C11124yescomplemented
173C22×C11—28no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—212no—
178C22×C11—26no—
179C22×C11—212no—
180C22×C11—412no—
181C22×C11—448no—
182C22×C11—412no—
183C22×C11C22×C22⋊C412yes—
184C22×C11C22×C22⋊C4112yes—
185C22×C11#56814yescomplemented
186C22×C11C24×C411yescharacteristic
187C4×C11—22no—
188C4×C11—26no—
189C4×C11C22×C22⋊C412yes—
190C4×C11C22×C22⋊C4112yes—
191C4×C11C23×D412yes—
192C25C2×C4×C1113yes—
193C2×#41—264no—
194C2×#41—264no—
195C2×#41—28no—
196C2×#41—224no—
197C2×#41—224no—
198C2×#41C2×C4×C1118yes—
199C2×#41C2×C4×C11124yes—
200C2×#41C2×C4×C11112yes—
201C2×#41C2×C4×C1114yes—
202C2×#41D4×C11116yes—
203C2×#41C23×C11112yes—
204C2×#41C23×C1114yes—
205C22×Q8—28no—
206C22×Q8C2×C4×C1118yes—
207C22×Q8C2×C4×C1113yes—
208C22×Q8C2×C4×C1111yescharacteristic
209C22×D4—224no—
210C22×D4C2×C4×C1116yes—
211C22×D4C2×C4×C11124yes—
212C22×D4C2×C4×C1113yes—
213C22×D4C2×C4×C1113yes—
214C23×C4—224no—
215C23×C4C2×C4×C1113yes—
216C23×C4C2×C4×C1113yes—
217C23×C4C2×C4×C11112yes—
218C23×C4C2×C4×C1113yes—
219C23×C4C23×C1111yescharacteristic
220C23×C4C23×C11112yes—
221C23×C4C23×C1113yes—
222C23×C4C23×C1113yes—
223#131—264no—
224C2×M16—248no—
225C2×M16C23×C1118yes—
226C2×M16C23×C11124yescomplemented
227C22×C8C23×C11124yescomplemented
228C22⋊C8C23×C11116yes—
229C22⋊C8C23×C11148yescomplemented
230C2×C11—22no—
231C2×C11—24no—
232C2×C11—212no—
233C2×C11—46no—
234C2×C11C23×C22⋊C411yescharacteristic
235C2×C11C2×#56812yes—
236C24—212no—
237C24—412no—
238C24C22×C4×C1111yescharacteristic
239C24C22×C4×C11112yes—
240C24C22×C4×C1113yes—
241C24C22×C4×C1113yes—
242#41—232no—
243#41—296no—
244#41—248no—
245#41—248no—
246#41C11×C22⋊C4132yes—
247#41C2×D4×C11132yes—
248C2×Q8—232no—
249C2×Q8—212no—
250C2×Q8C11×C22⋊C418yes—
251C2×Q8C22×C4×C11112yes—
252C2×Q8C22×C4×C1114yes—
253C2×D4—224no—
254C2×D4—296no—
255C2×D4—212no—
256C2×D4C11×C22⋊C4124yes—
257C2×D4C22×C4×C11124yes—
258C2×D4C22×C4×C11112yes—
259C2×D4C22×C4×C11112yes—
260C22×C4—212no—
261C22×C4—212no—
262C22×C4—212no—
263C22×C4—248no—
264C22×C4—24no—
265C22×C4—212no—
266C22×C4—248no—
267C22×C4C22×C4×C1111yescharacteristic
268C22×C4C22×C4×C1112yes—
269C22×C4C22×C4×C1113yes—
270C22×C4C22×C4×C11112yes—
271C22×C4C22×C4×C11112yes—
272C22×C4C22×C4×C11112yes—
273C22×C4C22×C4×C1116yes—
274C22×C4C22×C4×C1113yes—
275C22×C4C22×C4×C1116yes—
276C22×C4C2×D4×C11124yes—
277C22×C4C24×C1112yes—
278C22×C4C24×C1116yes—
279C22×C4C24×C1116yes—
280C22×C4C24×C1111yescharacteristic
281M16—216no—
282M16—248no—
283C2×C8—248no—
284C2×C8C24×C11116yes—
285C11#6006411yescharacteristic, direct product factor, Sylow
286C23—22no—
287C23—24no—
288C23—224no—
289C23—26no—
290C23—224no—
291C23—46no—
292C23—412no—
293C23—46no—
294C23—448no—
295C23C2×C11×C22⋊C4112yes—
296C23C23×C4×C1116yes—
297C23C23×C4×C1111yescharacteristic
298C23C23×C4×C1116yes—
299C23C23×C4×C1112yes—
300Q8—224no—
301Q8C2×C11×C22⋊C4116yes—
302D4—248no—
303D4—224no—
304D4C2×C11×C22⋊C4148yes—
305C2×C4—22no—
306C2×C4—26no—
307C2×C4—224no—
308C2×C4—24no—
309C2×C4—224no—
310C2×C4—224no—
311C2×C4—212no—
312C2×C4—24no—
313C2×C4—212no—
314C2×C4C2×C11×C22⋊C4112yes—
315C2×C4C2×C11×C22⋊C4124yes—
316C2×C4C23×C4×C1112yes—
317C2×C4C23×C4×C1116yes—
318C2×C4C23×C4×C1111yescharacteristic
319C2×C4C23×C4×C1116yes—
320C2×C4C22×D4×C11124yes—
321C2×C4C22×D4×C1114yes—
322C2×C4C25×C1111yescharacteristic
323C8—216no—
324C22—28no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—212no—
329C22—26no—
330C22—212no—
331C22—412no—
332C22—448no—
333C22—412no—
334C22C22×C11×C22⋊C412yes—
335C22C22×C11×C22⋊C4112yes—
336C22C11×#56814yescomplemented
337C22C24×C4×C1111yescharacteristic
338C4—22no—
339C4—26no—
340C4C22×C11×C22⋊C412yes—
341C4C22×C11×C22⋊C4112yes—
342C4C23×D4×C1112yes—
343C2—22no—
344C2—24no—
345C2—212no—
346C2—46no—
347C2C23×C11×C22⋊C411yescharacteristic
348C2C2×C11×#56812yes—
subgroupG/H
centerC2×C4×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C24×C4
prime radicalC23×C11×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#568C2semidirect
3. C11×#2880C2semidirect
4. C11×#2879C2semidirect
5. C2×C11×#407C2semidirect
17. C2×C11×#131C22semidirect
18. C22×C11×M16C22semidirect
19. C11×#408C22semidirect
21. C11×#407C22semidirect
22. C11×#407C22semidirect
23. C2×C11×C22⋊C8C22semidirect
58. C2×C11×M16C23semidirect
59. C22×C8×C11C23semidirect
61. C11×C22⋊C8C23semidirect
62. #60064C11direct (N × H)
113. C2×#568C2×C11semidirect
114. #2880C2×C11semidirect
115. #2879C2×C11semidirect
116. C2×#407C2×C11semidirect
166. C2×#131C22×C11semidirect
167. C22×M16C22×C11semidirect
168. #408C22×C11semidirect
170. #407C22×C11semidirect
171. #407C22×C11semidirect
172. C2×C22⋊C8C22×C11semidirect
185. C22×C11#568semidirect
226. C2×M16C23×C11semidirect
227. C22×C8C23×C11semidirect
229. C22⋊C8C23×C11semidirect
285. C11#60064direct (N × H)
336. C22C11×#568semidirect

Maximal subgroups

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

subgroupindex
C23×C11×#412
C2×C11×#5682
C11×#28802
C11×#28792
C2×C11×#4072
#6006411