Finite Group Databasebeta

← C2×C11×#2502 #14611958

Subgroups — C2×C11×#2502 #14611958

Order 2816.

3094 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C23×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2502C2116yesmaximal, direct product factor
4C2×C11×#398C214yesmaximal, complemented
5C2×C11×#391C212yesmaximal, complemented
6C2×C11×#385C214yesmaximal
7C2×C11×#384C212yesmaximal, complemented
8C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×C4×C11C2212yes—
12C2×C11×C22⋊Q8—28no—
13C2×C11×C22⋊Q8C2218yes—
14C22×C11×C4⋊C4—28no—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2218yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2218yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2212yes—
23C22×C42×C11C2212yes—
24C11×#398C22132yescomplemented
25C11×#391C22116yescomplemented
26C11×#385C22132yes—
27C11×#384C22116yescomplemented
28C4×C11×C22⋊C4C2218yes—
29C2×C11×#95C2212yes—
30C2×C11×#95C2218yes—
31C25×C11C2311yescharacteristic
32C22×Q8×C11—24no—
33C22×Q8×C11—28no—
34C22×Q8×C11C2314yes—
35C23×C4×C11—28no—
36C23×C4×C11—28no—
37C23×C4×C11—48no—
38C23×C4×C11D418yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2314yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2314yes—
45C23×C4×C11C2318yes—
46C23×C4×C11C2311yescharacteristic
47C11×C22⋊Q8—232no—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—232no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—28no—
53C2×C11×C4⋊C4—416no—
54C2×C11×C4⋊C4C2318yes—
55C2×C11×C4⋊C4C2318yes—
56C2×C11×C4⋊C4C2314yes—
57C2×C11×C4⋊C4C2318yes—
58C2×C11×C4⋊C4C23132yes—
59C2×C11×C22⋊C4—28no—
60C2×C11×C22⋊C4Q8116yescomplemented
61C2×C11×C22⋊C4C2318yes—
62C2×C11×C22⋊C4C2318yes—
63C2×C42×C11—28no—
64C2×C42×C11C2318yes—
65C11×#95C2318yes—
66C11×#95C23132yes—
67C2×#2502C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—24no—
69C24×C11—24no—
70C24×C11C2×D414yes—
71C24×C11C2×Q818yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C2×Q8×C11—28no—
75C2×Q8×C11—216no—
76C2×Q8×C11—416no—
77C22×C4×C11—28no—
78C22×C4×C11—24no—
79C22×C4×C11—28no—
80C22×C4×C11—232no—
81C22×C4×C11—216no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—216no—
85C22×C4×C11—28no—
86C22×C4×C11—28no—
87C22×C4×C11—28no—
88C22×C4×C11—216no—
89C22×C4×C11—416no—
90C22×C4×C11—432no—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×D4116yes—
93C22×C4×C11C2×D414yes—
94C22×C4×C11C2×Q8116yes—
95C22×C4×C11#4118yes—
96C22×C4×C11C2414yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2412yes—
100C22×C4×C11C2418yes—
101C22×C4×C11C2412yes—
102C11×C4⋊C4—216no—
103C11×C4⋊C4—216no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—216no—
106C11×C4⋊C4—432no—
107C11×C22⋊C4—216no—
108C11×C22⋊C4C2×Q8132yescomplemented
109C42×C11—216no—
110C22×C22⋊Q8C2×C1111yescharacteristic
111C23×C4⋊C4C2×C1111yescharacteristic
112#2502C2×C11116yesdirect product factor
113C2×#398C2×C1114yescomplemented
114C2×#391C2×C1112yescomplemented
115C2×#385C2×C1114yes—
116C2×#384C2×C1112yescomplemented
117C2×C4×C22⋊C4C2×C1111yescharacteristic
118C23×C11—28no—
119C23×C11—28no—
120C23×C11—232no—
121C23×C11—24no—
122C23×C11—24no—
123C23×C11C4⋊Q8116yes—
124C23×C11C22×D414yes—
125C23×C11C22×D412yes—
126C23×C11C22×Q818yes—
127C23×C11C22×Q814yes—
128C23×C11C2×#4114yes—
129C23×C11H(5,𝔽2)14yes—
130C23×C11C2511yescharacteristic
131Q8×C11—416no—
132C2×C4×C11—28no—
133C2×C4×C11—232no—
134C2×C4×C11—28no—
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11—232no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—216no—
144C2×C4×C11—432no—
145C2×C4×C11—48no—
146C2×C4×C11—48no—
147C2×C4×C11—416no—
148C2×C4×C11#123116yes—
149C2×C4×C11C22×D414yes—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C22×Q8116yes—
152C2×C4×C11C2×#4118yes—
153C23×Q8C22×C1111yescharacteristic
154C24×C4C22×C1111yescharacteristic
155C24×C4C22×C1112yes—
156C2×C22⋊Q8—28no—
157C2×C22⋊Q8C22×C1118yes—
158C22×C4⋊C4—28no—
159C22×C4⋊C4C22×C1112yes—
160C22×C4⋊C4C22×C1112yes—
161C22×C4⋊C4C22×C1118yes—
162C22×C4⋊C4C22×C1112yes—
163C22×C4⋊C4C22×C1111yescharacteristic
164C22×C4⋊C4C22×C1118yes—
165C22×C22⋊C4C22×C1112yes—
166C22×C22⋊C4C22×C1112yes—
167C22×C42C22×C1112yes—
168#398C22×C11132yescomplemented
169#391C22×C11116yescomplemented
170#385C22×C11132yes—
171#384C22×C11116yescomplemented
172C4×C22⋊C4C22×C1118yes—
173C2×#95C22×C1112yes—
174C2×#95C22×C1118yes—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—216no—
178C22×C11—232no—
179C22×C11C2×#12314yes—
180C22×C11C2×C4⋊Q818yes—
181C22×C11C2×C4⋊Q814yes—
182C22×C11#53514yes—
183C22×C11#554116yes—
184C22×C11C23×D411yescharacteristic
185C22×C11C23×Q812yes—
186C22×C11C22×#4112yes—
187C22×C11C2×H(5,𝔽2)12yes—
188C4×C11—24no—
189C4×C11—216no—
190C4×C11—44no—
191C4×C11—44no—
192C4×C11—48no—
193C4×C11C2×#12318yes—
194C25C23×C1111yescharacteristic
195C22×Q8—24no—
196C22×Q8—28no—
197C22×Q8C23×C1114yes—
198C23×C4—28no—
199C23×C4—28no—
200C23×C4—48no—
201C23×C4D4×C1118yes—
202C23×C4C23×C1112yes—
203C23×C4C23×C1112yes—
204C23×C4C23×C1114yes—
205C23×C4C23×C1111yescharacteristic
206C23×C4C23×C1114yes—
207C23×C4C23×C1114yes—
208C23×C4C23×C1118yes—
209C23×C4C23×C1111yescharacteristic
210C22⋊Q8—232no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—232no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—416no—
217C2×C4⋊C4C23×C1118yes—
218C2×C4⋊C4C23×C1118yes—
219C2×C4⋊C4C23×C1114yes—
220C2×C4⋊C4C23×C1118yes—
221C2×C4⋊C4C23×C11132yes—
222C2×C22⋊C4—28no—
223C2×C22⋊C4Q8×C11116yescomplemented
224C2×C22⋊C4C23×C1118yes—
225C2×C22⋊C4C23×C1118yes—
226C2×C42—28no—
227C2×C42C23×C1118yes—
228#95C23×C1118yes—
229#95C23×C11132yes—
230C2×C11—28no—
231C2×C11#250218yesdirect product factor
232C2×C11C22×#12311yescharacteristic
233C2×C11C22×C4⋊Q811yescharacteristic
234C2×C11C2×#53511yescharacteristic
235C2×C11C2×#55414yes—
236C24—24no—
237C24—24no—
238C24C2×D4×C1114yes—
239C24C2×Q8×C1118yes—
240C24C24×C1112yes—
241C24C24×C1111yescharacteristic
242C2×Q8—28no—
243C2×Q8—216no—
244C2×Q8—416no—
245C22×C4—28no—
246C22×C4—24no—
247C22×C4—28no—
248C22×C4—232no—
249C22×C4—216no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—216no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—28no—
256C22×C4—216no—
257C22×C4—416no—
258C22×C4—432no—
259C22×C4C2×D4×C1114yes—
260C22×C4C2×D4×C11116yes—
261C22×C4C2×D4×C1114yes—
262C22×C4C2×Q8×C11116yes—
263C22×C4C11×#4118yes—
264C22×C4C24×C1114yes—
265C22×C4C24×C1118yes—
266C22×C4C24×C1114yes—
267C22×C4C24×C1112yes—
268C22×C4C24×C1118yes—
269C22×C4C24×C1112yes—
270C4⋊C4—216no—
271C4⋊C4—216no—
272C4⋊C4—28no—
273C4⋊C4—216no—
274C4⋊C4—432no—
275C22⋊C4—216no—
276C22⋊C4C2×Q8×C11132yescomplemented
277C42—216no—
278C11C2×#250211yescharacteristic, direct product factor, Sylow
279C23—28no—
280C23—28no—
281C23—232no—
282C23—24no—
283C23—24no—
284C23C11×C4⋊Q8116yes—
285C23C22×D4×C1114yes—
286C23C22×D4×C1112yes—
287C23C22×Q8×C1118yes—
288C23C22×Q8×C1114yes—
289C23C2×C11×#4114yes—
290C23C11×H(5,𝔽2)14yes—
291C23C25×C1111yescharacteristic
292Q8—416no—
293C2×C4—28no—
294C2×C4—232no—
295C2×C4—28no—
296C2×C4—24no—
297C2×C4—28no—
298C2×C4—232no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—28no—
304C2×C4—216no—
305C2×C4—432no—
306C2×C4—48no—
307C2×C4—48no—
308C2×C4—416no—
309C2×C4C11×#123116yes—
310C2×C4C22×D4×C1114yes—
311C2×C4C22×D4×C1114yes—
312C2×C4C22×Q8×C11116yes—
313C2×C4C2×C11×#4118yes—
314C22—24no—
315C22—24no—
316C22—216no—
317C22—232no—
318C22C2×C11×#12314yes—
319C22C2×C11×C4⋊Q818yes—
320C22C2×C11×C4⋊Q814yes—
321C22C11×#53514yes—
322C22C11×#554116yes—
323C22C23×D4×C1111yescharacteristic
324C22C23×Q8×C1112yes—
325C22C22×C11×#4112yes—
326C22C2×C11×H(5,𝔽2)12yes—
327C4—24no—
328C4—216no—
329C4—44no—
330C4—48no—
331C4—44no—
332C4C2×C11×#12318yes—
333C2—28no—
334C2C11×#250218yesdirect product factor
335C2C22×C11×#12311yescharacteristic
336C2C22×C11×C4⋊Q811yescharacteristic
337C2C2×C11×#53511yescharacteristic
338C2C2×C11×#55414yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2502C2direct (N × H)
4. C2×C11×#398C2semidirect
5. C2×C11×#391C2semidirect
7. C2×C11×#384C2semidirect
24. C11×#398C22semidirect
25. C11×#391C22semidirect
27. C11×#384C22semidirect
60. C2×C11×C22⋊C4Q8semidirect
67. C2×#2502C11direct (N × H)
108. C11×C22⋊C4C2×Q8semidirect
112. #2502C2×C11direct (N × H)
113. C2×#398C2×C11semidirect
114. C2×#391C2×C11semidirect
116. C2×#384C2×C11semidirect
168. #398C22×C11semidirect
169. #391C22×C11semidirect
171. #384C22×C11semidirect
223. C2×C22⋊C4Q8×C11semidirect
231. C2×C11#2502direct (N × H)
276. C22⋊C4C2×Q8×C11semidirect
278. C11C2×#2502direct (N × H)
334. C2C11×#2502direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C23×C11×C4⋊C42
C11×#25022
C2×C11×#3982
C2×C11×#3912
C2×C11×#3852
C2×C11×#3842
C2×C4×C11×C22⋊C42
C2×#250211