Finite Group Databasebeta

← C11×#21829 #14599022

Subgroups — C11×#21829 #14599022

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C11×#2920C212yesmaximal
3C11×#1997C218yesmaximal, complemented
4C11×#1821C214yesmaximal
5C23×Q8×C11C412yes—
6C2×C11×C4⋊Q8—22no—
7C2×C11×C4⋊Q8—22no—
8C2×C11×C4⋊Q8—22no—
9C2×C11×C4⋊Q8—22no—
10C2×C11×C4⋊Q8C414yes—
11C2×C11×C4⋊Q8C2214yes—
12C22×C11×C4⋊C4C412yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C11×#432—22no—
16C11×#432—22no—
17C11×#431—22no—
18C11×#431—22no—
19C11×#423C2214yes—
20C11×#407C2214yes—
21C4×C11×M16C2214yes—
22C11×#343C22116yes—
23C22×Q8×C11—24no—
24C22×Q8×C11—22no—
25C22×Q8×C11—22no—
26C22×Q8×C11—48no—
27C22×Q8×C11C2×C418yes—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C414yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16C2318yes—
33C11×C4⋊Q8—24no—
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—24no—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8—24no—
40C11×C4⋊Q8—24no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—24no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4C2×C418yes—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C11×C4⋊C4C2314yes—
49C2×C42×C11C2×C412yes—
50C2×C42×C11D412yes—
51C2×C42×C11D412yes—
52C2×C42×C11D412yes—
53C2×C42×C11D412yes—
54C2×C42×C11C2312yes—
55C11×C4⋊C8—24no—
56C11×C4⋊C8—24no—
57C11×C22⋊C8—24no—
58C11×C22⋊C8—24no—
59C11×#97—24no—
60C4×C8×C11—24no—
61#21829C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11C22×C411yescharacteristic
63C2×Q8×C11—28no—
64C2×Q8×C11—28no—
65C2×Q8×C11—48no—
66C2×Q8×C11—416no—
67C2×Q8×C11—416no—
68C2×Q8×C11—48no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—48no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C412yes—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C412yes—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C418yes—
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2411yescharacteristic
88C11×M16—216no—
89C2×C8×C11—28no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—28no—
92C11×C4⋊C4—28no—
93C11×C4⋊C4—28no—
94C42×C11C22⋊C412yes—
95C42×C11C22⋊C412yes—
96C42×C11C22⋊C412yes—
97C42×C11C22⋊C412yes—
98C42×C11C2×D412yes—
99C42×C11C2×D412yes—
100C42×C11C2×D412yes—
101C42×C11C2×D412yes—
102C22×C4⋊Q8C2×C1111yescharacteristic
103#2920C2×C1112yes—
104#1997C2×C1118yescomplemented
105#1821C2×C1114yes—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11C23×C411yescharacteristic
112Q8×C11—416no—
113Q8×C11—416no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—28no—
124C2×C4×C11—48no—
125C2×C4×C11—48no—
126C2×C4×C11—48no—
127C2×C4×C11#10014yes—
128C2×C4×C11#10114yes—
129C2×C4×C11C2×C22⋊C412yes—
130C2×C4×C11C2×C22⋊C412yes—
131C2×C4×C11C2×C22⋊C412yes—
132C2×C4×C11C2×C22⋊C412yes—
133C2×C4×C11C2×C22⋊C412yes—
134C2×C4×C11C22×D412yes—
135C2×C4×C112−1+414yes—
136C8×C11—48no—
137C23×Q8C4×C1112yes—
138C2×C4⋊Q8—22no—
139C2×C4⋊Q8—22no—
140C2×C4⋊Q8—22no—
141C2×C4⋊Q8—22no—
142C2×C4⋊Q8C4×C1114yes—
143C2×C4⋊Q8C22×C1114yes—
144C22×C4⋊C4C4×C1112yes—
145C22×C4⋊C4C22×C1112yes—
146C22×C42C22×C1111yescharacteristic
147#432—22no—
148#432—22no—
149#431—22no—
150#431—22no—
151#423C22×C1114yes—
152#407C22×C1114yes—
153C4×M16C22×C1114yes—
154#343C22×C11116yes—
155C22×C11—28no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11C2×#10012yes—
163C22×C11C2×#10112yes—
164C22×C11C22×C22⋊C411yescharacteristic
165C22×C11#51912yes—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—48no—
170C4×C11C2×#10014yes—
171C4×C11C2×#10114yes—
172C4×C11#53614yes—
173C22×Q8—24no—
174C22×Q8—22no—
175C22×Q8—22no—
176C22×Q8—48no—
177C22×Q8C2×C4×C1118yes—
178C23×C4C2×C4×C1111yescharacteristic
179C23×C4C2×C4×C1111yescharacteristic
180C23×C4C2×C4×C1114yes—
181C23×C4C23×C1111yescharacteristic
182C2×M16C23×C1118yes—
183C4⋊Q8—24no—
184C4⋊Q8—24no—
185C4⋊Q8—24no—
186C4⋊Q8—24no—
187C4⋊Q8—24no—
188C4⋊Q8—24no—
189C4⋊Q8—24no—
190C4⋊Q8—24no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4C2×C4×C1118yes—
197C2×C4⋊C4C2×C4×C1114yes—
198C2×C4⋊C4C23×C1114yes—
199C2×C42C2×C4×C1112yes—
200C2×C42D4×C1112yes—
201C2×C42D4×C1112yes—
202C2×C42D4×C1112yes—
203C2×C42D4×C1112yes—
204C2×C42C23×C1112yes—
205C4⋊C8—24no—
206C4⋊C8—24no—
207C22⋊C8—24no—
208C22⋊C8—24no—
209#97—24no—
210C4×C8—24no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11—22no—
214C2×C11#231011yescharacteristic
215C2×C11C22×#10011yescharacteristic
216C2×C11C22×#10111yescharacteristic
217C24C22×C4×C1111yescharacteristic
218C2×Q8—28no—
219C2×Q8—28no—
220C2×Q8—416no—
221C2×Q8—48no—
222C2×Q8—416no—
223C2×Q8—48no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—48no—
230C22×C4C11×C22⋊C411yescharacteristic
231C22×C4C11×C22⋊C412yes—
232C22×C4C11×C22⋊C411yescharacteristic
233C22×C4C11×C22⋊C412yes—
234C22×C4C11×C22⋊C411yescharacteristic
235C22×C4C11×C22⋊C411yescharacteristic
236C22×C4C22×C4×C1111yescharacteristic
237C22×C4C22×C4×C1112yes—
238C22×C4C22×C4×C1112yes—
239C22×C4C22×C4×C1118yes—
240C22×C4C2×D4×C1112yes—
241C22×C4C2×D4×C1112yes—
242C22×C4C24×C1111yescharacteristic
243M16—216no—
244C2×C8—28no—
245C4⋊C4—28no—
246C4⋊C4—28no—
247C4⋊C4—28no—
248C4⋊C4—28no—
249C42C11×C22⋊C412yes—
250C42C11×C22⋊C412yes—
251C42C11×C22⋊C412yes—
252C42C11×C22⋊C412yes—
253C42C2×D4×C1112yes—
254C42C2×D4×C1112yes—
255C42C2×D4×C1112yes—
256C42C2×D4×C1112yes—
257C11#2182911yescharacteristic, direct product factor, Sylow
258C23—22no—
259C23—22no—
260C23—22no—
261C23C2×C11×C22⋊C411yescharacteristic
262C23C2×C11×C22⋊C411yescharacteristic
263C23C23×C4×C1111yescharacteristic
264Q8—416no—
265Q8—416no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—28no—
276C2×C4—48no—
277C2×C4—48no—
278C2×C4—48no—
279C2×C4C11×#10014yes—
280C2×C4C11×#10114yes—
281C2×C4C2×C11×C22⋊C412yes—
282C2×C4C2×C11×C22⋊C412yes—
283C2×C4C2×C11×C22⋊C412yes—
284C2×C4C2×C11×C22⋊C412yes—
285C2×C4C2×C11×C22⋊C412yes—
286C2×C4C22×D4×C1112yes—
287C2×C4C11×2−1+414yes—
288C8—48no—
289C22—28no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22C2×C11×#10012yes—
297C22C2×C11×#10112yes—
298C22C22×C11×C22⋊C411yescharacteristic
299C22C11×#51912yes—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—48no—
304C4C2×C11×#10014yes—
305C4C2×C11×#10114yes—
306C4C11×#53614yes—
307C2—22no—
308C2—22no—
309C2—22no—
310C2C11×#231011yescharacteristic
311C2C22×C11×#10011yescharacteristic
312C2C22×C11×#10111yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1997C2semidirect
61. #21829C11direct (N × H)
104. #1997C2×C11semidirect
257. C11#21829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C11×#29202
C11×#19972
C11×#18212
#2182911