Finite Group Databasebeta

← C2×C11×#2537 #14612115

Subgroups — C2×C11×#2537 #14612115

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C214yesmaximal, complemented
2C22×C4×D4×C11C212yesmaximal, complemented
3C11×#2537C2116yesmaximal, direct product factor
4C2×C11×#394C214yesmaximal, complemented
5C2×C11×#384C211yesmaximal, characteristic, complemented
6C2×C11×#380C214yesmaximal, complemented
7C23×D4×C11C2214yes—
8C23×D4×C11C2212yes—
9C24×C4×C11C2214yes—
10C2×C11×#121—232no—
11C2×C11×#121C22132yescomplemented
12C2×C4×D4×C11—216no—
13C2×C4×D4×C11C22116yescomplemented
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2214yes—
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2214yes—
18C22×C11×C22⋊C4C2218yes—
19C22×C42×C11C2211yescharacteristic
20C11×#394C22132yescomplemented
21C11×#384C2218yescomplemented
22C11×#380C22132yescomplemented
23C2×C11×#95C2214yes—
24C25×C11C2314yes—
25C22×D4×C11—232no—
26C22×D4×C11—28no—
27C22×D4×C11—28no—
28C22×D4×C11—48no—
29C22×D4×C11D4116yescomplemented
30C22×D4×C11C23116yes—
31C22×D4×C11C2318yes—
32C23×C4×C11—216no—
33C23×C4×C11—216no—
34C23×C4×C11—216no—
35C23×C4×C11C23116yes—
36C23×C4×C11C2314yes—
37C23×C4×C11C2314yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C11×#121—2128no—
41C4×D4×C11—264no—
42C2×C11×C4⋊C4—28no—
43C2×C11×C4⋊C4—216no—
44C2×C11×C4⋊C4—44no—
45C2×C11×C4⋊C4C2318yes—
46C2×C11×C4⋊C4C23116yes—
47C2×C11×C4⋊C4C2318yes—
48C2×C11×C22⋊C4—232no—
49C2×C11×C22⋊C4—216no—
50C2×C11×C22⋊C4C23116yes—
51C2×C11×C22⋊C4C23132yes—
52C2×C42×C11D418yescomplemented
53C2×C42×C11C2314yes—
54C11×#95C23116yes—
55C2×#2537C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11—28no—
57C24×C11—28no—
58C24×C11—28no—
59C24×C11—28no—
60C24×C11—28no—
61C24×C11—28no—
62C24×C11C2×D4116yes—
63C24×C11C2418yes—
64C24×C11C2411yescharacteristic
65C2×D4×C11—264no—
66C2×D4×C11—264no—
67C2×D4×C11—216no—
68C2×D4×C11—216no—
69C2×D4×C11—416no—
70C2×D4×C11—464no—
71C2×D4×C11C2×D4132yescomplemented
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—28no—
75C22×C4×C11—28no—
76C22×C4×C11—216no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11—232no—
80C22×C4×C11—232no—
81C22×C4×C11—232no—
82C22×C4×C11—464no—
83C22×C4×C11C2×D414yes—
84C22×C4×C11C2×D418yes—
85C22×C4×C11C2×D418yes—
86C22×C4×C11#4118yes—
87C22×C4×C11C2418yes—
88C22×C4×C11C2418yes—
89C22×C4×C11C2412yes—
90C22×C4×C11C2414yes—
91C11×C4⋊C4—216no—
92C11×C4⋊C4—232no—
93C11×C4⋊C4—48no—
94C11×C22⋊C4—264no—
95C11×C22⋊C4—232no—
96C42×C11C2×D4116yescomplemented
97C22×#121C2×C1114yescomplemented
98C22×C4×D4C2×C1112yescomplemented
99#2537C2×C11116yesdirect product factor
100C2×#394C2×C1114yescomplemented
101C2×#384C2×C1111yescharacteristic, complemented
102C2×#380C2×C1114yescomplemented
103C23×C11—232no—
104C23×C11—232no—
105C23×C11—232no—
106C23×C11—28no—
107C23×C11—28no—
108C23×C11—28no—
109C23×C11—28no—
110C23×C11—28no—
111C23×C11—28no—
112C23×C11—416no—
113C23×C11—416no—
114C23×C11—416no—
115C23×C11—416no—
116C23×C11C22×D4116yes—
117C23×C11C22×D412yes—
118C23×C11C22×D414yes—
119C23×C11C2×#4114yes—
120C23×C11H(5,𝔽2)12yes—
121C23×C112−1+412yes—
122C23×C11C2511yescharacteristic
123D4×C11—264no—
124D4×C11—464no—
125C2×C4×C11—28no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—28no—
129C2×C4×C11—28no—
130C2×C4×C11—216no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—416no—
134C2×C4×C11—416no—
135C2×C4×C11—464no—
136C2×C4×C11#121132yescomplemented
137C2×C4×C11C22×D414yes—
138C2×C4×C11C22×D418yes—
139C2×C4×C11C22×D418yes—
140C2×C4×C11C2×#4118yes—
141C23×D4C22×C1114yes—
142C23×D4C22×C1112yes—
143C24×C4C22×C1114yes—
144C2×#121—232no—
145C2×#121C22×C11132yescomplemented
146C2×C4×D4—216no—
147C2×C4×D4C22×C11116yescomplemented
148C22×C4⋊C4C22×C1112yes—
149C22×C4⋊C4C22×C1114yes—
150C22×C4⋊C4C22×C1112yes—
151C22×C22⋊C4C22×C1114yes—
152C22×C22⋊C4C22×C1118yes—
153C22×C42C22×C1111yescharacteristic
154#394C22×C11132yescomplemented
155#384C22×C1118yescomplemented
156#380C22×C11132yescomplemented
157C2×#95C22×C1114yes—
158C22×C11—216no—
159C22×C11—216no—
160C22×C11—216no—
161C22×C11—48no—
162C22×C11—48no—
163C22×C11—48no—
164C22×C11—48no—
165C22×C11—464no—
166C22×C11C2×#12118yes—
167C22×C11#53714yes—
168C22×C11D4214yes—
169C22×C11#54718yes—
170C22×C11#55514yes—
171C22×C11C23×D411yescharacteristic
172C22×C11C23×D412yes—
173C22×C11C22×#4112yes—
174C22×C11C2×H(5,𝔽2)11yescharacteristic
175C22×C11C2×2−1+411yescharacteristic
176C4×C11—24no—
177C4×C11—48no—
178C4×C11—48no—
179C4×C11C2×#121116yescomplemented
180C25C23×C1114yes—
181C22×D4—232no—
182C22×D4—28no—
183C22×D4—28no—
184C22×D4—48no—
185C22×D4D4×C11116yescomplemented
186C22×D4C23×C11116yes—
187C22×D4C23×C1118yes—
188C23×C4—216no—
189C23×C4—216no—
190C23×C4—216no—
191C23×C4C23×C1114yes—
192C23×C4C23×C1114yes—
193C23×C4C23×C11116yes—
194C23×C4C23×C1111yescharacteristic
195C23×C4C23×C1112yes—
196#121—2128no—
197C4×D4—264no—
198C2×C4⋊C4—28no—
199C2×C4⋊C4—216no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4C23×C1118yes—
202C2×C4⋊C4C23×C11116yes—
203C2×C4⋊C4C23×C1118yes—
204C2×C22⋊C4—232no—
205C2×C22⋊C4—216no—
206C2×C22⋊C4C23×C11116yes—
207C2×C22⋊C4C23×C11132yes—
208C2×C42D4×C1118yescomplemented
209C2×C42C23×C1114yes—
210#95C23×C11116yes—
211C2×C11—416no—
212C2×C11#253718yesdirect product factor
213C2×C11C22×#12112yes—
214C2×C11C2×#53711yescharacteristic
215C2×C11C2×D4211yescharacteristic
216C2×C11C2×#54712yes—
217C2×C11C2×#55511yescharacteristic
218C24—28no—
219C24—28no—
220C24—28no—
221C24—28no—
222C24—28no—
223C24—28no—
224C24C2×D4×C11116yes—
225C24C24×C1118yes—
226C24C24×C1111yescharacteristic
227C2×D4—264no—
228C2×D4—264no—
229C2×D4—216no—
230C2×D4—216no—
231C2×D4—416no—
232C2×D4—464no—
233C2×D4C2×D4×C11132yescomplemented
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—28no—
237C22×C4—28no—
238C22×C4—216no—
239C22×C4—28no—
240C22×C4—28no—
241C22×C4—232no—
242C22×C4—232no—
243C22×C4—232no—
244C22×C4—464no—
245C22×C4C2×D4×C1114yes—
246C22×C4C2×D4×C1118yes—
247C22×C4C2×D4×C1118yes—
248C22×C4C11×#4118yes—
249C22×C4C24×C1118yes—
250C22×C4C24×C1118yes—
251C22×C4C24×C1112yes—
252C22×C4C24×C1114yes—
253C4⋊C4—216no—
254C4⋊C4—232no—
255C4⋊C4—48no—
256C22⋊C4—264no—
257C22⋊C4—232no—
258C42C2×D4×C11116yescomplemented
259C11C2×#253711yescharacteristic, direct product factor, Sylow
260C23—232no—
261C23—232no—
262C23—232no—
263C23—28no—
264C23—28no—
265C23—28no—
266C23—28no—
267C23—28no—
268C23—28no—
269C23—416no—
270C23—416no—
271C23—416no—
272C23—416no—
273C23C22×D4×C11116yes—
274C23C22×D4×C1112yes—
275C23C22×D4×C1114yes—
276C23C2×C11×#4114yes—
277C23C11×H(5,𝔽2)12yes—
278C23C11×2−1+412yes—
279C23C25×C1111yescharacteristic
280D4—264no—
281D4—464no—
282C2×C4—28no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—216no—
288C2×C4—28no—
289C2×C4—28no—
290C2×C4—416no—
291C2×C4—416no—
292C2×C4—464no—
293C2×C4C11×#121132yescomplemented
294C2×C4C22×D4×C1114yes—
295C2×C4C22×D4×C1118yes—
296C2×C4C22×D4×C1118yes—
297C2×C4C2×C11×#4118yes—
298C22—216no—
299C22—216no—
300C22—216no—
301C22—48no—
302C22—48no—
303C22—48no—
304C22—48no—
305C22—464no—
306C22C2×C11×#12118yes—
307C22C11×#53714yes—
308C22D42×C1114yes—
309C22C11×#54718yes—
310C22C11×#55514yes—
311C22C23×D4×C1111yescharacteristic
312C22C23×D4×C1112yes—
313C22C22×C11×#4112yes—
314C22C2×C11×H(5,𝔽2)11yescharacteristic
315C22C2×C11×2−1+411yescharacteristic
316C4—24no—
317C4—48no—
318C4—48no—
319C4C2×C11×#121116yescomplemented
320C2—416no—
321C2C11×#253718yesdirect product factor
322C2C22×C11×#12112yes—
323C2C2×C11×#53711yescharacteristic
324C2C2×D42×C1111yescharacteristic
325C2C2×C11×#54712yes—
326C2C2×C11×#55511yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#121C2semidirect
2. C22×C4×D4×C11C2semidirect
3. C11×#2537C2direct (N × H)
4. C2×C11×#394C2semidirect
5. C2×C11×#384C2semidirect
6. C2×C11×#380C2semidirect
11. C2×C11×#121C22semidirect
13. C2×C4×D4×C11C22semidirect
20. C11×#394C22semidirect
21. C11×#384C22semidirect
22. C11×#380C22semidirect
29. C22×D4×C11D4semidirect
52. C2×C42×C11D4semidirect
55. C2×#2537C11direct (N × H)
71. C2×D4×C11C2×D4semidirect
96. C42×C11C2×D4semidirect
97. C22×#121C2×C11semidirect
98. C22×C4×D4C2×C11semidirect
99. #2537C2×C11direct (N × H)
100. C2×#394C2×C11semidirect
101. C2×#384C2×C11semidirect
102. C2×#380C2×C11semidirect
136. C2×C4×C11#121semidirect
145. C2×#121C22×C11semidirect
147. C2×C4×D4C22×C11semidirect
154. #394C22×C11semidirect
155. #384C22×C11semidirect
156. #380C22×C11semidirect
179. C4×C11C2×#121semidirect
185. C22×D4D4×C11semidirect
208. C2×C42D4×C11semidirect
212. C2×C11#2537direct (N × H)
233. C2×D4C2×D4×C11semidirect
258. C42C2×D4×C11semidirect
259. C11C2×#2537direct (N × H)
293. C2×C4C11×#121semidirect
319. C4C2×C11×#121semidirect
321. C2C11×#2537direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C4×D4×C112
C11×#25372
C2×C11×#3942
C2×C11×#3842
C2×C11×#3802
C2×#253711