Finite Group Databasebeta

← C11×#23943 #14601136

Subgroups — C11×#23943 #14601136

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C211yesmaximal, characteristic
2C2×C11×#451C212yesmaximal
3C11×#2310C211yesmaximal, characteristic
4C11×#2026C212yesmaximal, complemented
5C11×#2016C212yesmaximal, complemented
6C11×#1878C214yesmaximal, complemented
7C11×#1873C212yesmaximal
8C11×#1818C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×Q16C2214yes—
11C11×#541—28no—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#126—22no—
14C2×C11×#125—22no—
15C2×C11×#125C2211yescharacteristic
16C2×C11×C22⋊Q8C2212yes—
17C2×C4×Q8×C11C2212yes—
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#451—28no—
21C2×C11×#103C2214yes—
22C2×C11×#103C2214yes—
23C2×C11×C22⋊C8C2212yes—
24C11×#391—22no—
25C11×#391C2212yes—
26C11×#391C2212yes—
27C11×#381—22no—
28C11×#340C2214yes—
29C11×#336C2212yes—
30C11×#336C2212yes—
31C22×Q8×C11—24no—
32C22×Q8×C11—21no—
33C22×Q8×C11—24no—
34C22×Q8×C11—42no—
35C22×Q8×C11C2312yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C2×C11×Q16—28no—
40C2×C11×Q16—28no—
41C2×C11×Q16—44no—
42C22×C8×C11C2314yes—
43C11×C4⋊Q8—24no—
44C11×#126—216no—
45C11×#125—216no—
46C11×#125—24no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8D418yes—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C11×#117—24no—
52C11×#117—42no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11—22no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C11×#103—28no—
68C11×#103—44no—
69C11×C22⋊C8—24no—
70C11×#95—24no—
71C11×#95—24no—
72#23943C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—24no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—24no—
78C2×Q8×C11—24no—
79C2×Q8×C11—24no—
80C2×Q8×C11—24no—
81C2×Q8×C11—416no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11C2×D414yes—
85C2×Q8×C11#4114yes—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D414yes—
99C22×C4×C11C2411yescharacteristic
100C11×Q16—416no—
101C2×C8×C11—24no—
102C2×C8×C11—24no—
103C2×C8×C11—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4C2×D414yes—
112C11×C22⋊C4—28no—
113C11×C22⋊C4—24no—
114C11×C22⋊C4—42no—
115C42×C11—28no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—42no—
119C2×#541C2×C1111yescharacteristic
120C2×#451C2×C1112yes—
121#2310C2×C1111yescharacteristic
122#2026C2×C1112yescomplemented
123#2016C2×C1112yescomplemented
124#1878C2×C1114yescomplemented
125#1873C2×C1112yes—
126#1818C2×C1111yescharacteristic
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—24no—
130C23×C11#12012yes—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—28no—
134Q8×C11—48no—
135Q8×C11—44no—
136Q8×C11—44no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—28no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—48no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11#12012yes—
156C2×C4×C11C22×D412yes—
157C2×C4×C11C2×#4112yes—
158C2×C4×C11H(5,𝔽2)12yes—
159C8×C11—44no—
160C23×Q8C22×C1111yescharacteristic
161C22×Q16C22×C1114yes—
162#541—28no—
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×#126—22no—
165C2×#125—22no—
166C2×#125C22×C1111yescharacteristic
167C2×C22⋊Q8C22×C1112yes—
168C2×C4×Q8C22×C1112yes—
169C2×#117C22×C1111yescharacteristic
170C2×#117C22×C1111yescharacteristic
171#451—28no—
172C2×#103C22×C1114yes—
173C2×#103C22×C1114yes—
174C2×C22⋊C8C22×C1112yes—
175#391—22no—
176#391C22×C1112yes—
177#391C22×C1112yes—
178#381—22no—
179#340C22×C1114yes—
180#336C22×C1112yes—
181#336C22×C1112yes—
182C22×C11—22no—
183C22×C11—24no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11C2×#12011yescharacteristic
187C22×C11#52511yescharacteristic
188C22×C11#53511yescharacteristic
189C22×C11#57814yes—
190C4×C11—22no—
191C4×C11—44no—
192C4×C11—44no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11—44no—
196C4×C11—82no—
197C4×C11#54614yes—
198C22×Q8—24no—
199C22×Q8—21no—
200C22×Q8—24no—
201C22×Q8—42no—
202C22×Q8C23×C1112yes—
203C22×Q8C23×C1112yes—
204C23×C4—21no—
205C23×C4C23×C1111yescharacteristic
206C2×Q16—28no—
207C2×Q16—28no—
208C2×Q16—44no—
209C22×C8C23×C1114yes—
210C4⋊Q8—24no—
211#126—216no—
212#125—216no—
213#125—24no—
214C22⋊Q8—24no—
215C22⋊Q8D4×C1118yes—
216C4×Q8—24no—
217C4×Q8—24no—
218#117—24no—
219#117—42no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4D4×C1112yes—
225C2×C4⋊C4C23×C1112yes—
226C2×C4⋊C4C23×C1112yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4D4×C1112yes—
230C2×C42—22no—
231C2×C42—21no—
232C2×C42C23×C1111yescharacteristic
233C2×C42C23×C1111yescharacteristic
234#103—28no—
235#103—44no—
236C22⋊C8—24no—
237#95—24no—
238#95—24no—
239C2×C11—42no—
240C2×C11#240411yescharacteristic
241C2×C11#301112yes—
242C2×C11#312712yes—
243C2×C11#322312yes—
244C24C2×D4×C1111yescharacteristic
245C2×Q8—24no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—24no—
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—416no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8C2×D4×C1114yes—
256C2×Q8C11×#4114yes—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C2×D4×C1112yes—
267C22×C4C2×D4×C1112yes—
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1114yes—
270C22×C4C24×C1111yescharacteristic
271Q16—416no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C4⋊C4—28no—
276C4⋊C4—28no—
277C4⋊C4—28no—
278C4⋊C4—28no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—24no—
282C4⋊C4C2×D4×C1114yes—
283C22⋊C4—28no—
284C22⋊C4—24no—
285C22⋊C4—42no—
286C42—28no—
287C42—22no—
288C42—22no—
289C42—42no—
290C11#2394311yescharacteristic, direct product factor, Sylow
291C23—21no—
292C23—21no—
293C23—24no—
294C23C11×#12012yes—
295C23C22×D4×C1111yescharacteristic
296Q8—28no—
297Q8—28no—
298Q8—48no—
299Q8—44no—
300Q8—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—28no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—48no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4C11×#12012yes—
320C2×C4C22×D4×C1112yes—
321C2×C4C2×C11×#4112yes—
322C2×C4C11×H(5,𝔽2)12yes—
323C8—44no—
324C22—22no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22C2×C11×#12011yescharacteristic
329C22C11×#52511yescharacteristic
330C22C11×#53511yescharacteristic
331C22C11×#57814yes—
332C4—22no—
333C4—44no—
334C4—44no—
335C4—42no—
336C4—42no—
337C4—44no—
338C4—82no—
339C4C11×#54614yes—
340C2—42no—
341C2C11×#240411yescharacteristic
342C2C11×#301112yes—
343C2C11×#312712yes—
344C2C11×#322312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2026C2semidirect
5. C11×#2016C2semidirect
6. C11×#1878C2semidirect
72. #23943C11direct (N × H)
122. #2026C2×C11semidirect
123. #2016C2×C11semidirect
124. #1878C2×C11semidirect
290. C11#23943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C2×C11×#4512
C11×#23102
C11×#20262
C11×#20162
C11×#18782
C11×#18732
C11×#18182
#2394311