Finite Group Databasebeta

← C11×#23921 #14601114

Subgroups — C11×#23921 #14601114

Order 2816.

1908 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C212yesmaximal
2C2×C11×#451C214yesmaximal, complemented
3C11×#2001C214yesmaximal, complemented
4C11×#1872C214yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic
6C23×Q8×C11C2212yes—
7C24×C4×C11C2211yescharacteristic
8C22×C11×Q16C2214yescomplemented
9C2×C11×C22⋊Q8—22no—
10C2×C11×C22⋊Q8—22no—
11C2×C11×C22⋊Q8—216no—
12C2×C11×C22⋊Q8C2214yes—
13C2×C11×C22⋊Q8C2214yes—
14C22×C11×C4⋊C4—22no—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4—22no—
17C11×#451—216no—
18C2×C11×#103C2218yescomplemented
19C2×C11×C22⋊C8C2214yes—
20C2×C11×C22⋊C8C2212yes—
21C11×#340C2214yescomplemented
22C25×C11D411yescharacteristic
23C22×Q8×C11—28no—
24C22×Q8×C11—22no—
25C22×Q8×C11—28no—
26C22×Q8×C11—44no—
27C22×Q8×C11C2314yes—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—28no—
31C23×C4×C11—42no—
32C23×C4×C11D412yes—
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C2×C11×Q16—216no—
37C2×C11×Q16—44no—
38C22×C8×C11C2314yes—
39C11×C22⋊Q8—216no—
40C11×C22⋊Q8—216no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8D4116yes—
45C2×C11×C4⋊C4—216no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C22⋊C4—216no—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—24no—
54C11×#103—216no—
55C11×C22⋊C8—28no—
56C11×C22⋊C8—42no—
57#23921C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—24no—
59C24×C11—24no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11Q1614yescomplemented
63C24×C11C2×D411yescharacteristic
64C24×C11C2×D412yes—
65C2×Q8×C11—28no—
66C2×Q8×C11—24no—
67C2×Q8×C11—28no—
68C2×Q8×C11—28no—
69C2×Q8×C11—432no—
70C2×Q8×C11—44no—
71C2×Q8×C11—44no—
72C2×Q8×C11C2×D418yes—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—28no—
76C22×C4×C11—28no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—416no—
87C22×C4×C11—44no—
88C22×C4×C11—44no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D418yes—
94C22×C4×C11C2411yescharacteristic
95C11×Q16—416no—
96C2×C8×C11—28no—
97C2×C8×C11—24no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—216no—
100C11×C4⋊C4—216no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4C2×D418yes—
103C11×C22⋊C4—216no—
104C11×C22⋊C4—216no—
105C22×C22⋊Q8C2×C1112yes—
106C2×#451C2×C1114yescomplemented
107#2001C2×C1114yescomplemented
108#1872C2×C1114yescomplemented
109#1779C2×C1111yescharacteristic
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—21no—
116C23×C11—22no—
117C23×C11—21no—
118C23×C11—216no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11—44no—
122C23×C11—48no—
123C23×C11#12014yes—
124C23×C11C2×Q1612yes—
125C23×C11C2×Q1614yes—
126C23×C11#13714yes—
127C23×C11C22×D411yescharacteristic
128Q8×C11—216no—
129Q8×C11—416no—
130Q8×C11—48no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—216no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—44no—
139C2×C4×C11—48no—
140C2×C4×C11—416no—
141C2×C4×C11—416no—
142C2×C4×C11—44no—
143C2×C4×C11—44no—
144C2×C4×C11—44no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11#12014yes—
148C2×C4×C11C22×D414yes—
149C2×C4×C11H(5,𝔽2)12yes—
150C8×C11—44no—
151C23×Q8C22×C1112yes—
152C24×C4C22×C1111yescharacteristic
153C22×Q16C22×C1114yescomplemented
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—216no—
157C2×C22⋊Q8C22×C1114yes—
158C2×C22⋊Q8C22×C1114yes—
159C22×C4⋊C4—22no—
160C22×C4⋊C4C22×C1112yes—
161C22×C22⋊C4—22no—
162#451—216no—
163C2×#103C22×C1118yescomplemented
164C2×C22⋊C8C22×C1114yes—
165C2×C22⋊C8C22×C1112yes—
166#340C22×C1114yescomplemented
167C22×C11—24no—
168C22×C11—24no—
169C22×C11—24no—
170C22×C11—24no—
171C22×C11—24no—
172C22×C11—24no—
173C22×C11—22no—
174C22×C11—24no—
175C22×C11—416no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—42no—
179C22×C11#45118yescomplemented
180C22×C11C2×#12012yes—
181C22×C11#53411yescharacteristic
182C22×C11C22×Q1611yescharacteristic
183C22×C11C2×#13712yes—
184C22×C11#57511yescharacteristic
185C4×C11—24no—
186C4×C11—41no—
187C4×C11—48no—
188C4×C11—48no—
189C4×C11D4214yes—
190C25D4×C1111yescharacteristic
191C22×Q8—28no—
192C22×Q8—22no—
193C22×Q8—28no—
194C22×Q8—44no—
195C22×Q8C23×C1114yes—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—28no—
199C23×C4—42no—
200C23×C4D4×C1112yes—
201C23×C4D4×C1111yescharacteristic
202C23×C4C23×C1111yescharacteristic
203C23×C4C23×C1112yes—
204C2×Q16—216no—
205C2×Q16—44no—
206C22×C8C23×C1114yes—
207C22⋊Q8—216no—
208C22⋊Q8—216no—
209C22⋊Q8—28no—
210C22⋊Q8—28no—
211C22⋊Q8—28no—
212C22⋊Q8D4×C11116yes—
213C2×C4⋊C4—216no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—28no—
218C2×C4⋊C4C23×C1114yes—
219C2×C22⋊C4—216no—
220C2×C22⋊C4—24no—
221C2×C22⋊C4—24no—
222#103—216no—
223C22⋊C8—28no—
224C22⋊C8—42no—
225C2×C11—28no—
226C2×C11—42no—
227C2×C11#240311yescharacteristic
228C2×C11C2×#45112yes—
229C2×C11#300712yes—
230C2×C11#318911yescharacteristic
231C2×C11#319511yescharacteristic
232C24—24no—
233C24—24no—
234C24—41no—
235C24—41no—
236C24C11×Q1614yescomplemented
237C24C2×D4×C1111yescharacteristic
238C24C2×D4×C1112yes—
239C2×Q8—28no—
240C2×Q8—24no—
241C2×Q8—28no—
242C2×Q8—28no—
243C2×Q8—432no—
244C2×Q8—44no—
245C2×Q8—44no—
246C2×Q8C2×D4×C1118yes—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—416no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C2×D4×C1112yes—
267C22×C4C2×D4×C1118yes—
268C22×C4C24×C1111yescharacteristic
269Q16—416no—
270C2×C8—28no—
271C2×C8—24no—
272C4⋊C4—28no—
273C4⋊C4—216no—
274C4⋊C4—216no—
275C4⋊C4—24no—
276C4⋊C4C2×D4×C1118yes—
277C22⋊C4—216no—
278C22⋊C4—216no—
279C11#2392111yescharacteristic, direct product factor, Sylow
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—21no—
286C23—22no—
287C23—21no—
288C23—216no—
289C23—44no—
290C23—44no—
291C23—44no—
292C23—48no—
293C23C11×#12014yes—
294C23C2×C11×Q1612yes—
295C23C2×C11×Q1614yes—
296C23C11×#13714yes—
297C23C22×D4×C1111yescharacteristic
298Q8—216no—
299Q8—416no—
300Q8—48no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—216no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—44no—
309C2×C4—48no—
310C2×C4—416no—
311C2×C4—416no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4C11×#12014yes—
318C2×C4C22×D4×C1114yes—
319C2×C4C11×H(5,𝔽2)12yes—
320C8—44no—
321C22—24no—
322C22—24no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22—24no—
327C22—22no—
328C22—24no—
329C22—416no—
330C22—41no—
331C22—41no—
332C22—42no—
333C22C11×#45118yescomplemented
334C22C2×C11×#12012yes—
335C22C11×#53411yescharacteristic
336C22C22×C11×Q1611yescharacteristic
337C22C2×C11×#13712yes—
338C22C11×#57511yescharacteristic
339C4—24no—
340C4—41no—
341C4—48no—
342C4—48no—
343C4D42×C1114yes—
344C2—28no—
345C2—42no—
346C2C11×#240311yescharacteristic
347C2C2×C11×#45112yes—
348C2C11×#300712yes—
349C2C11×#318911yescharacteristic
350C2C11×#319511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
3. C11×#2001C2semidirect
4. C11×#1872C2semidirect
8. C22×C11×Q16C22semidirect
18. C2×C11×#103C22semidirect
21. C11×#340C22semidirect
57. #23921C11direct (N × H)
62. C24×C11Q16semidirect
106. C2×#451C2×C11semidirect
107. #2001C2×C11semidirect
108. #1872C2×C11semidirect
153. C22×Q16C22×C11semidirect
163. C2×#103C22×C11semidirect
166. #340C22×C11semidirect
179. C22×C11#451semidirect
236. C24C11×Q16semidirect
279. C11#23921direct (N × H)
333. C22C11×#451semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C2×C11×#4512
C11×#20012
C11×#18722
C11×#17792
#2392111