Finite Group Databasebeta

← C2×C11×#2852 #14613810

Subgroups — C2×C11×#2852 #14613810

Order 2816.

3354 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#126C211yesmaximal, characteristic, complemented
2C23×C42×C11C211yesmaximal, characteristic, complemented
3C11×#2852C2116yesmaximal, direct product factor
4C2×C11×#388C213yesmaximal, complemented
5C2×C11×#387C213yesmaximal, complemented
6C2×C11×#386C213yesmaximal
7C2×C11×#385C213yesmaximal, complemented
8C2×C11×#383C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2213yes—
11C2×C11×#126—28no—
12C2×C11×#126C2218yescomplemented
13C22×C11×C4⋊C4C2213yes—
14C22×C11×C4⋊C4C2213yes—
15C22×C11×C22⋊C4C2213yes—
16C22×C11×C22⋊C4C2213yes—
17C22×C11×C22⋊C4C2213yes—
18C22×C42×C11—28no—
19C22×C42×C11C2213yes—
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2218yescomplemented
22C11×#388C22124yescomplemented
23C11×#387C22124yescomplemented
24C11×#386C22124yes—
25C11×#385C22124yescomplemented
26C11×#383C2218yescomplemented
27C2×C11×#95C2213yes—
28C2×C11×#95C2213yes—
29C2×C11×#95C2213yes—
30C2×C11×#95C2213yes—
31C25×C11C2311yescharacteristic
32C25×C11C2311yescharacteristic
33C22×D4×C11—212no—
34C22×D4×C11C2314yes—
35C23×C4×C11—212no—
36C23×C4×C11—212no—
37C23×C4×C11—212no—
38C23×C4×C11C23112yes—
39C23×C4×C11C2313yes—
40C23×C4×C11C2313yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2313yes—
43C23×C4×C11C2313yes—
44C11×#126—232no—
45C2×C11×C4⋊C4—212no—
46C2×C11×C4⋊C4—212no—
47C2×C11×C4⋊C4C23112yes—
48C2×C11×C4⋊C4C23112yes—
49C2×C11×C22⋊C4—212no—
50C2×C11×C22⋊C4—212no—
51C2×C11×C22⋊C4—212no—
52C2×C11×C22⋊C4C23112yes—
53C2×C11×C22⋊C4C23112yes—
54C2×C11×C22⋊C4C23112yes—
55C2×C42×C11—212no—
56C2×C42×C11—232no—
57C2×C42×C11D418yescomplemented
58C2×C42×C11C23112yes—
59C2×C42×C11C2314yes—
60C11×#95C23112yes—
61C11×#95C23112yes—
62C11×#95C23112yes—
63C11×#95C23112yes—
64C2×#2852C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—22no—
66C24×C11—26no—
67C24×C11—22no—
68C24×C11—26no—
69C24×C11—26no—
70C24×C11#41112yes—
71C24×C11C2412yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C2×D4×C11—224no—
75C2×D4×C11—416no—
76C22×C4×C11—296no—
77C22×C4×C11—26no—
78C22×C4×C11—224no—
79C22×C4×C11—26no—
80C22×C4×C11—26no—
81C22×C4×C11—26no—
82C22×C4×C11—224no—
83C22×C4×C11—224no—
84C22×C4×C11—26no—
85C22×C4×C11—26no—
86C22×C4×C11—26no—
87C22×C4×C11—26no—
88C22×C4×C11—26no—
89C22×C4×C11—26no—
90C22×C4×C11—26no—
91C22×C4×C11C2×D4112yes—
92C22×C4×C11#41112yes—
93C22×C4×C11C2412yes—
94C22×C4×C11C2416yes—
95C22×C4×C11C2416yes—
96C22×C4×C11C2416yes—
97C22×C4×C11C2416yes—
98C11×C4⋊C4—224no—
99C11×C4⋊C4—224no—
100C11×C22⋊C4—224no—
101C11×C22⋊C4—224no—
102C11×C22⋊C4—224no—
103C42×C11—224no—
104C42×C11C2×D4116yescomplemented
105C22×#126C2×C1111yescharacteristic, complemented
106C23×C42C2×C1111yescharacteristic, complemented
107#2852C2×C11116yesdirect product factor
108C2×#388C2×C1113yescomplemented
109C2×#387C2×C1113yescomplemented
110C2×#386C2×C1113yes—
111C2×#385C2×C1113yescomplemented
112C2×#383C2×C1111yescharacteristic, complemented
113C23×C11—224no—
114C23×C11—224no—
115C23×C11—22no—
116C23×C11—26no—
117C23×C11—22no—
118C23×C11—26no—
119C23×C11—26no—
120C23×C11—412no—
121C23×C11—44no—
122C23×C11—412no—
123C23×C11#126116yescomplemented
124C23×C11C22×D412yes—
125C23×C11C2×#41112yes—
126C23×C11C2×#4116yes—
127C23×C11C2×#4116yes—
128C23×C11C2511yescharacteristic
129D4×C11—416no—
130C2×C4×C11—296no—
131C2×C4×C11—224no—
132C2×C4×C11—224no—
133C2×C4×C11—26no—
134C2×C4×C11—26no—
135C2×C4×C11—26no—
136C2×C4×C11—26no—
137C2×C4×C11—26no—
138C2×C4×C11—26no—
139C2×C4×C11—26no—
140C2×C4×C11—26no—
141C2×C4×C11—26no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—412no—
145C2×C4×C11—44no—
146C2×C4×C11—412no—
147C2×C4×C11C22×D4112yes—
148C2×C4×C11C2×#41112yes—
149C23×D4C22×C1111yescharacteristic
150C24×C4C22×C1113yes—
151C2×#126—28no—
152C2×#126C22×C1118yescomplemented
153C22×C4⋊C4C22×C1113yes—
154C22×C4⋊C4C22×C1113yes—
155C22×C22⋊C4C22×C1113yes—
156C22×C22⋊C4C22×C1113yes—
157C22×C22⋊C4C22×C1113yes—
158C22×C42—28no—
159C22×C42C22×C1113yes—
160C22×C42C22×C1111yescharacteristic
161C22×C42C22×C1118yescomplemented
162#388C22×C11124yescomplemented
163#387C22×C11124yescomplemented
164#386C22×C11124yes—
165#385C22×C11124yescomplemented
166#383C22×C1118yescomplemented
167C2×#95C22×C1113yes—
168C2×#95C22×C1113yes—
169C2×#95C22×C1113yes—
170C2×#95C22×C1113yes—
171C22×C11—232no—
172C22×C11—212no—
173C22×C11—212no—
174C22×C11—46no—
175C22×C11—42no—
176C22×C11—46no—
177C22×C11—88no—
178C22×C11#525112yes—
179C22×C11C2×#12614yes—
180C22×C11C2×#12618yescomplemented
181C22×C11#529112yes—
182C22×C11C23×D411yescharacteristic
183C22×C11C22×#4113yes—
184C22×C11C22×#4113yes—
185C4×C11—212no—
186C4×C11—212no—
187C4×C11—46no—
188C4×C11—42no—
189C4×C11—46no—
190C25C23×C1111yescharacteristic
191C25C23×C1111yescharacteristic
192C22×D4—212no—
193C22×D4C23×C1114yes—
194C23×C4—212no—
195C23×C4—212no—
196C23×C4—212no—
197C23×C4C23×C1113yes—
198C23×C4C23×C1113yes—
199C23×C4C23×C11112yes—
200C23×C4C23×C1111yescharacteristic
201C23×C4C23×C1113yes—
202C23×C4C23×C1113yes—
203#126—232no—
204C2×C4⋊C4—212no—
205C2×C4⋊C4—212no—
206C2×C4⋊C4C23×C11112yes—
207C2×C4⋊C4C23×C11112yes—
208C2×C22⋊C4—212no—
209C2×C22⋊C4—212no—
210C2×C22⋊C4—212no—
211C2×C22⋊C4C23×C11112yes—
212C2×C22⋊C4C23×C11112yes—
213C2×C22⋊C4C23×C11112yes—
214C2×C42—212no—
215C2×C42—232no—
216C2×C42D4×C1118yescomplemented
217C2×C42C23×C11112yes—
218C2×C42C23×C1114yes—
219#95C23×C11112yes—
220#95C23×C11112yes—
221#95C23×C11112yes—
222#95C23×C11112yes—
223C2×C11—28no—
224C2×C11—82no—
225C2×C11#285218yesdirect product factor
226C2×C11C2×#52513yes—
227C2×C11C22×#12611yescharacteristic
228C2×C11C2×#52913yes—
229C24—22no—
230C24—26no—
231C24—22no—
232C24—26no—
233C24—26no—
234C24C11×#41112yes—
235C24C24×C1112yes—
236C24C24×C1112yes—
237C24C24×C1111yescharacteristic
238C2×D4—224no—
239C2×D4—416no—
240C22×C4—296no—
241C22×C4—26no—
242C22×C4—224no—
243C22×C4—26no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4—26no—
253C22×C4—26no—
254C22×C4—26no—
255C22×C4C2×D4×C11112yes—
256C22×C4C11×#41112yes—
257C22×C4C24×C1112yes—
258C22×C4C24×C1116yes—
259C22×C4C24×C1116yes—
260C22×C4C24×C1116yes—
261C22×C4C24×C1116yes—
262C4⋊C4—224no—
263C4⋊C4—224no—
264C22⋊C4—224no—
265C22⋊C4—224no—
266C22⋊C4—224no—
267C42—224no—
268C42C2×D4×C11116yescomplemented
269C11C2×#285211yescharacteristic, direct product factor, Sylow
270C23—224no—
271C23—224no—
272C23—22no—
273C23—26no—
274C23—22no—
275C23—26no—
276C23—26no—
277C23—412no—
278C23—44no—
279C23—412no—
280C23C11×#126116yescomplemented
281C23C22×D4×C1112yes—
282C23C2×C11×#41112yes—
283C23C2×C11×#4116yes—
284C23C2×C11×#4116yes—
285C23C25×C1111yescharacteristic
286D4—416no—
287C2×C4—296no—
288C2×C4—224no—
289C2×C4—224no—
290C2×C4—26no—
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—412no—
302C2×C4—44no—
303C2×C4—412no—
304C2×C4C22×D4×C11112yes—
305C2×C4C2×C11×#41112yes—
306C22—212no—
307C22—212no—
308C22—232no—
309C22—46no—
310C22—42no—
311C22—46no—
312C22—88no—
313C22C11×#525112yes—
314C22C2×C11×#12614yes—
315C22C2×C11×#12618yescomplemented
316C22C11×#529112yes—
317C22C23×D4×C1111yescharacteristic
318C22C22×C11×#4113yes—
319C22C22×C11×#4113yes—
320C4—212no—
321C4—212no—
322C4—46no—
323C4—42no—
324C4—46no—
325C2—28no—
326C2—82no—
327C2C11×#285218yesdirect product factor
328C2C2×C11×#52513yes—
329C2C22×C11×#12611yescharacteristic
330C2C2×C11×#52913yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#126C2semidirect
2. C23×C42×C11C2semidirect
3. C11×#2852C2direct (N × H)
4. C2×C11×#388C2semidirect
5. C2×C11×#387C2semidirect
7. C2×C11×#385C2semidirect
8. C2×C11×#383C2semidirect
12. C2×C11×#126C22semidirect
21. C22×C42×C11C22semidirect
22. C11×#388C22semidirect
23. C11×#387C22semidirect
25. C11×#385C22semidirect
26. C11×#383C22semidirect
57. C2×C42×C11D4semidirect
64. C2×#2852C11direct (N × H)
104. C42×C11C2×D4semidirect
105. C22×#126C2×C11semidirect
106. C23×C42C2×C11semidirect
107. #2852C2×C11direct (N × H)
108. C2×#388C2×C11semidirect
109. C2×#387C2×C11semidirect
111. C2×#385C2×C11semidirect
112. C2×#383C2×C11semidirect
123. C23×C11#126semidirect
152. C2×#126C22×C11semidirect
161. C22×C42C22×C11semidirect
162. #388C22×C11semidirect
163. #387C22×C11semidirect
165. #385C22×C11semidirect
166. #383C22×C11semidirect
180. C22×C11C2×#126semidirect
216. C2×C42D4×C11semidirect
225. C2×C11#2852direct (N × H)
268. C42C2×D4×C11semidirect
269. C11C2×#2852direct (N × H)
280. C23C11×#126semidirect
315. C22C2×C11×#126semidirect
327. C2C11×#2852direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C23×C42×C112
C11×#28522
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C11×#3832
C2×#285211