Finite Group Databasebeta

← C11×#21912 #14599105

Subgroups — C11×#21912 #14599105

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
2C11×#1916C218yesmaximal, complemented
3C11×#1817C212yesmaximal
4C11×#1797C212yesmaximal
5C4×C11×C22⋊C8C212yesmaximal
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C11×C4⋊C4C411yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C2×C11×C4⋊C8C2214yes—
12C2×C11×C22⋊C8C2214yes—
13C2×C4×C8×C11C2214yes—
14C4×C11×C4⋊C4C414yes—
15C4×C11×C4⋊C4C2214yes—
16C2×C11×#95C411yescharacteristic
17C2×C11×#95C411yescharacteristic
18C11×#336C2214yes—
19C11×#336C2214yes—
20C11×#336C2218yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C8×C11C2318yes—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4C818yescomplemented
31C2×C11×C4⋊C4C2×C414yes—
32C2×C11×C4⋊C4C2×C414yes—
33C2×C42×C11—24no—
34C2×C42×C11—42no—
35C2×C42×C11—42no—
36C2×C42×C11C2×C412yes—
37C2×C42×C11C2×C412yes—
38C2×C42×C11C2×C412yes—
39C2×C42×C11C2312yes—
40C2×C42×C11C2312yes—
41C2×C42×C11C2312yes—
42C11×C4⋊C8—44no—
43C11×C22⋊C8—28no—
44C4×C8×C11—44no—
45C11×#95C2×C414yes—
46C11×#95C2×C414yes—
47#21912C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11C22×C411yescharacteristic
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2×C814yes—
66C22×C4×C11C2×C814yes—
67C22×C4×C11C2×C814yes—
68C22×C4×C11M1614yes—
69C22×C4×C11C22×C412yes—
70C22×C4×C11C22×C412yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11#4114yes—
77C22×C4×C11C2411yescharacteristic
78C2×C8×C11—28no—
79C2×C8×C11—28no—
80C2×C8×C11—28no—
81C11×C4⋊C4—28no—
82C11×C4⋊C4C2×C8116yes—
83C42×C11—24no—
84C42×C11—24no—
85C42×C11—24no—
86C42×C11—24no—
87C42×C11—42no—
88C42×C11—42no—
89C2×C4×C4⋊C4C2×C1111yescharacteristic
90#1916C2×C1118yescomplemented
91#1817C2×C1112yes—
92#1797C2×C1112yes—
93C4×C22⋊C8C2×C1112yes—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11#11712yes—
99C23×C11C22×C812yes—
100C23×C11C2×M1612yes—
101C23×C11C23×C411yescharacteristic
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—28no—
113C2×C4×C11—28no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—44no—
125C2×C4×C11#11712yes—
126C2×C4×C11C22×C814yes—
127C2×C4×C11C22×C814yes—
128C2×C4×C11C22×C814yes—
129C2×C4×C11C2×M1614yes—
130C2×C4×C11C2×#4112yes—
131C2×C4×C11H(5,𝔽2)12yes—
132C2×C4×C112−1+412yes—
133C8×C11—48no—
134C22×C4⋊C4C4×C1111yescharacteristic
135C22×C4⋊C4C4×C1111yescharacteristic
136C22×C42C22×C1111yescharacteristic
137C22×C42C22×C1111yescharacteristic
138C22×C42C22×C1111yescharacteristic
139C2×C4⋊C8C22×C1114yes—
140C2×C22⋊C8C22×C1114yes—
141C2×C4×C8C22×C1114yes—
142C4×C4⋊C4C4×C1114yes—
143C4×C4⋊C4C22×C1114yes—
144C2×#95C4×C1111yescharacteristic
145C2×#95C4×C1111yescharacteristic
146#336C22×C1114yes—
147#336C22×C1118yes—
148#336C22×C1114yes—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11#43114yes—
156C22×C11C2×#11711yescharacteristic
157C22×C11#51811yescharacteristic
158C22×C11#51911yescharacteristic
159C22×C11C23×C811yescharacteristic
160C22×C11C22×M1611yescharacteristic
161C22×C11#56811yescharacteristic
162C22×C11#56811yescharacteristic
163C4×C11—22no—
164C4×C11—24no—
165C4×C11—24no—
166C4×C11—24no—
167C4×C11—24no—
168C4×C11—42no—
169C4×C11—42no—
170C4×C11#53914yes—
171C23×C4C2×C4×C1111yescharacteristic
172C23×C4C2×C4×C1111yescharacteristic
173C23×C4C2×C4×C1111yescharacteristic
174C23×C4C2×C4×C1111yescharacteristic
175C23×C4C2×C4×C1111yescharacteristic
176C23×C4C2×C4×C1111yescharacteristic
177C23×C4C23×C1111yescharacteristic
178C22×C8C23×C1118yes—
179C2×C4⋊C4—24no—
180C2×C4⋊C4C8×C1118yescomplemented
181C2×C4⋊C4C2×C4×C1114yes—
182C2×C4⋊C4C2×C4×C1114yes—
183C2×C42—24no—
184C2×C42—42no—
185C2×C42—42no—
186C2×C42C2×C4×C1112yes—
187C2×C42C2×C4×C1112yes—
188C2×C42C2×C4×C1112yes—
189C2×C42C23×C1112yes—
190C2×C42C23×C1112yes—
191C2×C42C23×C1112yes—
192C4⋊C8—44no—
193C22⋊C8—28no—
194C4×C8—44no—
195#95C2×C4×C1114yes—
196#95C2×C4×C1114yes—
197C2×C11—24no—
198C2×C11#231311yescharacteristic
199C2×C11C2×#43111yescharacteristic
200C2×C11#292111yescharacteristic
201C2×C11#297211yescharacteristic
202C2×C11#297311yescharacteristic
203C2×C11#298211yescharacteristic
204C2×C11#298311yescharacteristic
205C24C22×C4×C1111yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4C2×C8×C1114yes—
223C22×C4C2×C8×C1114yes—
224C22×C4C2×C8×C1114yes—
225C22×C4C11×M1614yes—
226C22×C4C22×C4×C1112yes—
227C22×C4C22×C4×C1112yes—
228C22×C4C22×C4×C1111yescharacteristic
229C22×C4C22×C4×C1112yes—
230C22×C4C22×C4×C1112yes—
231C22×C4C22×C4×C1112yes—
232C22×C4C22×C4×C1112yes—
233C22×C4C11×#4114yes—
234C22×C4C24×C1111yescharacteristic
235C2×C8—28no—
236C2×C8—28no—
237C2×C8—28no—
238C4⋊C4—28no—
239C4⋊C4C2×C8×C11116yes—
240C42—24no—
241C42—24no—
242C42—24no—
243C42—24no—
244C42—42no—
245C42—42no—
246C11#2191211yescharacteristic, direct product factor, Sylow
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23C11×#11712yes—
252C23C22×C8×C1112yes—
253C23C2×C11×M1612yes—
254C23C23×C4×C1111yescharacteristic
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4C11×#11712yes—
279C2×C4C22×C8×C1114yes—
280C2×C4C22×C8×C1114yes—
281C2×C4C22×C8×C1114yes—
282C2×C4C2×C11×M1614yes—
283C2×C4C2×C11×#4112yes—
284C2×C4C11×H(5,𝔽2)12yes—
285C2×C4C11×2−1+412yes—
286C8—48no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22C11×#43114yes—
294C22C2×C11×#11711yescharacteristic
295C22C11×#51811yescharacteristic
296C22C11×#51911yescharacteristic
297C22C23×C8×C1111yescharacteristic
298C22C22×C11×M1611yescharacteristic
299C22C11×#56811yescharacteristic
300C22C11×#56811yescharacteristic
301C4—24no—
302C4—24no—
303C4—24no—
304C4—24no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4C11×#53914yes—
309C2—24no—
310C2C11×#231311yescharacteristic
311C2C2×C11×#43111yescharacteristic
312C2C11×#292111yescharacteristic
313C2C11×#297211yescharacteristic
314C2C11×#297311yescharacteristic
315C2C11×#298211yescharacteristic
316C2C11×#298311yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC22C23×C8×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1916C2semidirect
30. C2×C11×C4⋊C4C8semidirect
47. #21912C11direct (N × H)
90. #1916C2×C11semidirect
180. C2×C4⋊C4C8×C11semidirect
246. C11#21912direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×C4⋊C42
C11×#19162
C11×#18172
C11×#17972
C4×C11×C22⋊C82
#2191211