Finite Group Databasebeta

← C11×#23159 #14600352

Subgroups — C11×#23159 #14600352

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#499C211yesmaximal, characteristic
2C11×#2370C212yesmaximal
3C11×#1989C212yesmaximal
4C11×#1941C212yesmaximal
5C11×#1921C212yesmaximal
6C11×#1918C212yesmaximal
7C4×C11×#106C211yesmaximal, characteristic
8C4×C11×#106C212yesmaximal
9C8×C11×C4⋊C4C211yesmaximal, characteristic
10C2×C11×#125C2212yes—
11C11×#499C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#106C2211yescharacteristic
15C2×C11×#106C2212yes—
16C2×C11×#106C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C4×C8×C11C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#389—22no—
21C11×#389C2212yes—
22C11×#389C2212yes—
23C11×#387—22no—
24C11×#387—22no—
25C4×C11×C4⋊C4—22no—
26C4×C11×C4⋊C4C2212yes—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C4⋊C4C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C11×#340C2212yes—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#336C2212yes—
36C22×C8×C11C2312yes—
37C22×C8×C11C2311yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C11×#125—24no—
40C11×#125C2×C418yes—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11C2312yes—
54C2×C42×C11C2311yescharacteristic
55C11×#107C2×C414yes—
56C11×#107C2×C414yes—
57C11×#106—22no—
58C11×#106C2×C418yes—
59C11×#106Q814yes—
60C11×C4⋊C8—22no—
61C4×C8×C11—24no—
62C4×C8×C11C2×C414yes—
63C11×#95—22no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95D411yescharacteristic
69C11×#95D411yescharacteristic
70#23159C1111yesmaximal, characteristic, direct product factor, Sylow
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2411yescharacteristic
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—22no—
85C2×C8×C11C22×C412yes—
86C2×C8×C11C22×C412yes—
87C2×C8×C11C2×Q812yes—
88C2×C8×C11#4112yes—
89C11×C4⋊C4—28no—
90C11×C4⋊C4—28no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—44no—
98C11×C4⋊C4—82no—
99C11×C4⋊C4C22×C414yes—
100C11×C4⋊C4C22×C414yes—
101C11×C4⋊C4C2×Q814yes—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—44no—
105C42×C11—82no—
106C42×C11—82no—
107C42×C11C22×C412yes—
108C42×C11#4112yes—
109C2×#499C2×C1111yescharacteristic
110#2370C2×C1112yes—
111#1989C2×C1112yes—
112#1941C2×C1112yes—
113#1921C2×C1112yes—
114#1918C2×C1112yes—
115C4×#106C2×C1111yescharacteristic
116C4×#106C2×C1112yes—
117C8×C4⋊C4C2×C1111yescharacteristic
118C23×C11C22×D411yescharacteristic
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C4×D412yes—
139C2×C4×C11C4×D412yes—
140C2×C4×C11#13514yes—
141C2×C4×C11C23×C411yescharacteristic
142C2×C4×C11C22×Q811yescharacteristic
143C2×C4×C11C2×#4111yescharacteristic
144C2×C4×C11C2×#4111yescharacteristic
145C2×C4×C112−1+411yescharacteristic
146C2×C4×C112−1+411yescharacteristic
147C8×C11—22no—
148C8×C11—42no—
149C8×C11C4×Q814yes—
150C2×#125C22×C1112yes—
151#499C4×C1118yescomplemented
152C2×#107C22×C1111yescharacteristic
153C2×#107C22×C1111yescharacteristic
154C2×#106C22×C1111yescharacteristic
155C2×#106C22×C1112yes—
156C2×#106C22×C1111yescharacteristic
157C2×C4⋊C8C22×C1111yescharacteristic
158C2×C4×C8C22×C1112yes—
159C2×C4×C8C22×C1111yescharacteristic
160#389—22no—
161#389C22×C1112yes—
162#389C22×C1112yes—
163#387—22no—
164#387—22no—
165C4×C4⋊C4—22no—
166C4×C4⋊C4C22×C1112yes—
167C4×C4⋊C4C22×C1112yes—
168C4×C4⋊C4C22×C1112yes—
169C4×C4⋊C4C22×C1111yescharacteristic
170#340C22×C1112yes—
171#340C22×C1112yes—
172#340C22×C1112yes—
173#340C22×C1112yes—
174#340C22×C1112yes—
175#336C22×C1112yes—
176C22×C11C2×C4×D411yescharacteristic
177C22×C11#54711yescharacteristic
178C22×C11D4×Q811yescharacteristic
179C22×C11C2×#13512yes—
180C22×C11#57712yes—
181C4×C11—24no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—42no—
185C4×C11—44no—
186C4×C11—44no—
187C4×C11—44no—
188C4×C11—82no—
189C4×C11C2×C4×Q811yescharacteristic
190C4×C11#51911yescharacteristic
191C4×C11#55611yescharacteristic
192C4×C11#55711yescharacteristic
193C22×C8C23×C1112yes—
194C22×C8C23×C1111yescharacteristic
195C22×C8C23×C1111yescharacteristic
196#125—24no—
197#125C2×C4×C1118yes—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4D4×C1112yes—
203C2×C4⋊C4C23×C1112yes—
204C2×C4⋊C4C23×C1112yes—
205C2×C4⋊C4C23×C1112yes—
206C2×C4⋊C4C23×C1112yes—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42C23×C1112yes—
211C2×C42C23×C1111yescharacteristic
212#107C2×C4×C1114yes—
213#107C2×C4×C1114yes—
214#106—22no—
215#106C2×C4×C1118yes—
216#106Q8×C1114yes—
217C4⋊C8—22no—
218C4×C8—24no—
219C4×C8C2×C4×C1114yes—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95D4×C1111yescharacteristic
226#95D4×C1111yescharacteristic
227C2×C11#236511yescharacteristic
228C2×C11C4×#13511yescharacteristic
229C2×C11#295211yescharacteristic
230C2×C11#333712yes—
231C2×C11#338112yes—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4C2×D4×C1112yes—
237C22×C4C2×D4×C1111yescharacteristic
238C22×C4C2×D4×C1111yescharacteristic
239C22×C4C2×D4×C1112yes—
240C22×C4C24×C1111yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8C22×C4×C1112yes—
247C2×C8C22×C4×C1112yes—
248C2×C8C2×Q8×C1112yes—
249C2×C8C11×#4112yes—
250C4⋊C4—28no—
251C4⋊C4—28no—
252C4⋊C4—24no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—44no—
259C4⋊C4—82no—
260C4⋊C4C22×C4×C1114yes—
261C4⋊C4C22×C4×C1114yes—
262C4⋊C4C2×Q8×C1114yes—
263C42—22no—
264C42—22no—
265C42—44no—
266C42—82no—
267C42—82no—
268C42C22×C4×C1112yes—
269C42C11×#4112yes—
270C11#2315911yescharacteristic, direct product factor, Sylow
271C23C22×D4×C1111yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4C4×D4×C1112yes—
292C2×C4C4×D4×C1112yes—
293C2×C4C11×#13514yes—
294C2×C4C23×C4×C1111yescharacteristic
295C2×C4C22×Q8×C1111yescharacteristic
296C2×C4C2×C11×#4111yescharacteristic
297C2×C4C2×C11×#4111yescharacteristic
298C2×C4C11×2−1+411yescharacteristic
299C2×C4C11×2−1+411yescharacteristic
300C8—22no—
301C8—42no—
302C8C4×Q8×C1114yes—
303C22C2×C4×D4×C1111yescharacteristic
304C22C11×#54711yescharacteristic
305C22D4×Q8×C1111yescharacteristic
306C22C2×C11×#13512yes—
307C22C11×#57712yes—
308C4—22no—
309C4—22no—
310C4—24no—
311C4—44no—
312C4—44no—
313C4—42no—
314C4—44no—
315C4—82no—
316C4C2×C4×Q8×C1111yescharacteristic
317C4C11×#51911yescharacteristic
318C4C11×#55611yescharacteristic
319C4C11×#55711yescharacteristic
320C2C11×#236511yescharacteristic
321C2C4×C11×#13511yescharacteristic
322C2C11×#295211yescharacteristic
323C2C11×#333712yes—
324C2C11×#338112yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
11. C11×#499C4semidirect
70. #23159C11direct (N × H)
151. #499C4×C11semidirect
270. C11#23159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4992
C11×#23702
C11×#19892
C11×#19412
C11×#19212
C11×#19182
C4×C11×#1062
C8×C11×C4⋊C42
#2315911