Finite Group Databasebeta

← C11×#11886 #14589079

Subgroups — C11×#11886 #14589079

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic
2C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
3C11×#1808C211yesmaximal, characteristic, complemented
4C11×#1347C214yesmaximal, complemented
5C22×C11×D8C411yescharacteristic, complemented
6C23×C8×C11C2211yescharacteristic
7C2×C11×#121—21no—
8C22×C11×C16—21no—
9C11×#466—21no—
10C11×#466—21no—
11C11×#466C412yescomplemented
12C11×#466C2212yes—
13C2×C11×#107—21no—
14C2×C11×#107C411yescharacteristic, complemented
15C2×C11×#102—21no—
16C11×#380—21no—
17C11×C22⋊C16—21no—
18C11×C22⋊C16C2212yescomplemented
19C11×#340C2212yescomplemented
20C22×D4×C11—21no—
21C22×D4×C11—41no—
22C23×C4×C11D411yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—42no—
25C2×C11×D8C2×C412yes—
26C22×C8×C11—42no—
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×#121—22no—
34C11×#121—22no—
35C11×#121—41no—
36C11×#121—41no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C22⋊C4—41no—
41C2×C11×C16—22no—
42C2×C11×C16—42no—
43C11×#107—21no—
44C11×#107—42no—
45C11×#107C2×C412yes—
46C11×#102—22no—
47C11×#102—22no—
48C11×#95—41no—
49#11886C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—41no—
51C24×C11D811yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—42no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—41no—
58C2×D4×C11—82no—
59C2×D4×C11—82no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11D811yescharacteristic
67C22×C4×C11SD1611yescharacteristic
68C22×C4×C11SD1611yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C11×D8—42no—
71C11×D8—42no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11C22⋊C411yescharacteristic
79C2×C8×C11C22⋊C411yescharacteristic
80C2×C8×C11C22×C411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C11×C4⋊C4—22no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—82no—
89C11×C16—42no—
90C2×#466C2×C1111yescharacteristic
91C2×C22⋊C16C2×C1111yescharacteristic, complemented
92#1808C2×C1111yescharacteristic, complemented
93#1347C2×C1114yescomplemented
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—42no—
97C23×C11—82no—
98C23×C11—82no—
99C23×C11—82no—
100C23×C11#10211yescharacteristic
101C23×C11#10211yescharacteristic
102C23×C11D1612yes—
103C23×C11SD3212yes—
104C23×C11C2×D811yescharacteristic
105D4×C11—42no—
106D4×C11—42no—
107D4×C11—82no—
108D4×C11—84no—
109D4×C11—82no—
110D4×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11#10211yescharacteristic
126C2×C4×C11#10211yescharacteristic
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C8×C11—21no—
130C8×C11—21no—
131C8×C11—21no—
132C8×C11#9912yes—
133C22×D8C4×C1111yescharacteristic, complemented
134C23×C8C22×C1111yescharacteristic
135C2×#121—21no—
136C22×C16—21no—
137#466—21no—
138#466—21no—
139#466C4×C1112yescomplemented
140#466C22×C1112yes—
141C2×#107—21no—
142C2×#107C4×C1111yescharacteristic, complemented
143C2×#102—21no—
144#380—21no—
145C22⋊C16—21no—
146C22⋊C16C22×C1112yescomplemented
147#340C22×C1112yescomplemented
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—42no—
155C22×C11—42no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—164no—
160C22×C11#35712yes—
161C22×C11#35712yes—
162C22×C11C2×#10211yescharacteristic
163C22×C11C2×D1611yescharacteristic
164C22×C11C2×SD3211yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—82no—
169C4×C11—162no—
170C4×C11C2×#9911yescharacteristic
171C4×C11#42111yescharacteristic
172C22×D4—21no—
173C22×D4—41no—
174C23×C4D4×C1111yescharacteristic
175C2×D8—21no—
176C2×D8—42no—
177C2×D8C2×C4×C1112yes—
178C22×C8—42no—
179C22×C8C2×C4×C1111yescharacteristic
180C22×C8C2×C4×C1111yescharacteristic
181C22×C8D4×C1111yescharacteristic
182C22×C8D4×C1111yescharacteristic
183C22×C8D4×C1111yescharacteristic
184C22×C8C23×C1111yescharacteristic
185#121—22no—
186#121—22no—
187#121—41no—
188#121—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C16—22no—
194C2×C16—42no—
195#107—21no—
196#107—42no—
197#107C2×C4×C1112yes—
198#102—22no—
199#102—22no—
200#95—41no—
201C2×C11—21no—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11—21no—
205C2×C11—162no—
206C2×C11#151911yescharacteristic
207C2×C11C2×#35711yescharacteristic
208C2×C11#214511yescharacteristic
209C24—41no—
210C24C11×D811yescharacteristic
211C2×D4—22no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—41no—
217C2×D4—82no—
218C2×D4—82no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4C11×C22⋊C411yescharacteristic
224C22×C4C11×C22⋊C411yescharacteristic
225C22×C4C11×D811yescharacteristic
226C22×C4C11×SD1611yescharacteristic
227C22×C4C11×SD1611yescharacteristic
228C22×C4C2×D4×C1111yescharacteristic
229D8—42no—
230D8—42no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8C11×C22⋊C411yescharacteristic
238C2×C8C11×C22⋊C411yescharacteristic
239C2×C8C22×C4×C1111yescharacteristic
240C2×C8C2×D4×C1111yescharacteristic
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—82no—
248C16—42no—
249C11#1188611yescharacteristic, direct product factor, Sylow
250C23—41no—
251C23—41no—
252C23—42no—
253C23—82no—
254C23—82no—
255C23—82no—
256C23C11×#10211yescharacteristic
257C23C11×#10211yescharacteristic
258C23C11×D1612yes—
259C23C11×SD3212yes—
260C23C2×C11×D811yescharacteristic
261D4—42no—
262D4—42no—
263D4—82no—
264D4—82no—
265D4—82no—
266D4—84no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4C11×#10211yescharacteristic
282C2×C4C11×#10211yescharacteristic
283C2×C4C2×C11×C22⋊C411yescharacteristic
284C2×C4C2×C11×SD1611yescharacteristic
285C8—21no—
286C8—21no—
287C8—21no—
288C8C11×#9912yes—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—42no—
296C22—42no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—164no—
301C22C11×#35712yes—
302C22C11×#35712yes—
303C22C2×C11×#10211yescharacteristic
304C22C2×C11×D1611yescharacteristic
305C22C2×C11×SD3211yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—162no—
311C4C2×C11×#9911yescharacteristic
312C4C11×#42111yescharacteristic
313C2—21no—
314C2—22no—
315C2—21no—
316C2—22no—
317C2—162no—
318C2C11×#151911yescharacteristic
319C2C2×C11×#35711yescharacteristic
320C2C11×#214511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#102
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#466C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×C22⋊C16C2semidirect
3. C11×#1808C2semidirect
4. C11×#1347C2semidirect
5. C22×C11×D8C4semidirect
11. C11×#466C4semidirect
14. C2×C11×#107C4semidirect
18. C11×C22⋊C16C22semidirect
19. C11×#340C22semidirect
49. #11886C11direct (N × H)
91. C2×C22⋊C16C2×C11semidirect
92. #1808C2×C11semidirect
93. #1347C2×C11semidirect
133. C22×D8C4×C11semidirect
139. #466C4×C11semidirect
142. C2×#107C4×C11semidirect
146. C22⋊C16C22×C11semidirect
147. #340C22×C11semidirect
249. C11#11886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C11×C22⋊C162
C11×#18082
C11×#13472
#1188611