Finite Group Databasebeta

← C11×#23928 #14601121

Subgroups — C11×#23928 #14601121

Order 2816.

1696 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C212yesmaximal
2C2×C11×#451C214yesmaximal, complemented
3C11×#2001C214yesmaximal, complemented
4C11×#1873C214yesmaximal, complemented
5C11×#1780C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Q8×C11C2212yes—
8C22×C11×Q16C2214yes—
9C11×#536—216no—
10C2×C11×C4⋊Q8—22no—
11C2×C11×#124—22no—
12C2×C11×#123—22no—
13C2×C11×#123—22no—
14C2×C11×C22⋊Q8C2214yes—
15C2×C11×C22⋊Q8C2214yes—
16C2×C11×#117C2212yes—
17C11×#451—216no—
18C2×C11×#103C2218yes—
19C2×C11×C22⋊C8C2214yes—
20C2×C11×C22⋊C8C2212yes—
21C11×#340C2214yes—
22C2×C11×#41—28no—
23C2×C11×#41—42no—
24C22×Q8×C11—28no—
25C22×Q8×C11—22no—
26C22×Q8×C11—28no—
27C22×Q8×C11—44no—
28C22×Q8×C11D411yescharacteristic
29C22×Q8×C11C2314yes—
30C22×D4×C11D411yescharacteristic
31C22×D4×C11D412yes—
32C23×C4×C11—22no—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2312yes—
35C2×C11×Q16—216no—
36C2×C11×Q16—44no—
37C22×C8×C11C2314yes—
38C11×C4⋊Q8—216no—
39C11×#124—216no—
40C11×#123—216no—
41C11×#123—216no—
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8D4116yes—
46C11×#117—28no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—24no—
53C2×C42×C11—22no—
54C11×#103—216no—
55C11×C22⋊C8—28no—
56C11×C22⋊C8—42no—
57#23928C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C2×D411yescharacteristic
59C24×C11C2×D412yes—
60C11×#41—416no—
61C2×Q8×C11—28no—
62C2×Q8×C11—24no—
63C2×Q8×C11—24no—
64C2×Q8×C11—28no—
65C2×Q8×C11—28no—
66C2×Q8×C11—41no—
67C2×Q8×C11—432no—
68C2×Q8×C11—44no—
69C2×Q8×C11—44no—
70C2×Q8×C11C2×D418yes—
71C2×D4×C11—24no—
72C2×D4×C11—24no—
73C2×D4×C11—24no—
74C2×D4×C11—42no—
75C2×D4×C11—41no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—28no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—44no—
84C22×C4×C11—44no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D418yes—
88C22×C4×C11C2411yescharacteristic
89C11×Q16—416no—
90C2×C8×C11—28no—
91C2×C8×C11—24no—
92C11×C4⋊C4—216no—
93C11×C4⋊C4—216no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4C2×D418yes—
96C11×C22⋊C4—28no—
97C11×C22⋊C4—216no—
98C11×C22⋊C4—216no—
99C42×C11—28no—
100C2×#536C2×C1112yes—
101C2×#451C2×C1114yescomplemented
102#2001C2×C1114yescomplemented
103#1873C2×C1114yescomplemented
104#1780C2×C1111yescharacteristic
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—28no—
108C23×C11—22no—
109C23×C11—21no—
110C23×C11—24no—
111C23×C11#12014yes—
112C23×C11C22×D411yescharacteristic
113Q8×C11—216no—
114Q8×C11—44no—
115Q8×C11—416no—
116Q8×C11—48no—
117D4×C11—48no—
118D4×C11—44no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—216no—
122C2×C4×C11—28no—
123C2×C4×C11—28no—
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—416no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—48no—
130C2×C4×C11—44no—
131C2×C4×C11#12014yes—
132C2×C4×C11C22×D414yes—
133C2×C4×C11H(5,𝔽2)12yes—
134C8×C11—44no—
135C22×#41C22×C1111yescharacteristic
136C23×Q8C22×C1112yes—
137C22×Q16C22×C1114yes—
138#536—216no—
139C2×C4⋊Q8—22no—
140C2×#124—22no—
141C2×#123—22no—
142C2×#123—22no—
143C2×C22⋊Q8C22×C1114yes—
144C2×C22⋊Q8C22×C1114yes—
145C2×#117C22×C1112yes—
146#451—216no—
147C2×#103C22×C1118yes—
148C2×C22⋊C8C22×C1114yes—
149C2×C22⋊C8C22×C1112yes—
150#340C22×C1114yes—
151C22×C11—24no—
152C22×C11—28no—
153C22×C11—44no—
154C22×C11—44no—
155C22×C11—41no—
156C22×C11—42no—
157C22×C11—44no—
158C22×C11C2×#12012yes—
159C22×C11#53411yescharacteristic
160C22×C11#57814yes—
161C4×C11—24no—
162C4×C11—41no—
163C4×C11—48no—
164C4×C11—48no—
165C4×C11D4214yes—
166C2×#41—28no—
167C2×#41—42no—
168C22×Q8—28no—
169C22×Q8—22no—
170C22×Q8—28no—
171C22×Q8—44no—
172C22×Q8D4×C1111yescharacteristic
173C22×Q8C23×C1114yes—
174C22×D4D4×C1111yescharacteristic
175C22×D4D4×C1112yes—
176C23×C4—22no—
177C23×C4C23×C1111yescharacteristic
178C23×C4C23×C1112yes—
179C2×Q16—216no—
180C2×Q16—44no—
181C22×C8C23×C1114yes—
182C4⋊Q8—216no—
183#124—216no—
184#123—216no—
185#123—216no—
186C22⋊Q8—28no—
187C22⋊Q8—28no—
188C22⋊Q8—28no—
189C22⋊Q8D4×C11116yes—
190#117—28no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4C23×C1114yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—24no—
197C2×C42—22no—
198#103—216no—
199C22⋊C8—28no—
200C22⋊C8—42no—
201C2×C11—44no—
202C2×C11—81no—
203C2×C11#240311yescharacteristic
204C2×C11#301114yes—
205C2×C11#320212yes—
206C24C2×D4×C1111yescharacteristic
207C24C2×D4×C1112yes—
208#41—416no—
209C2×Q8—28no—
210C2×Q8—24no—
211C2×Q8—24no—
212C2×Q8—28no—
213C2×Q8—28no—
214C2×Q8—41no—
215C2×Q8—432no—
216C2×Q8—44no—
217C2×Q8—44no—
218C2×Q8C2×D4×C1118yes—
219C2×D4—24no—
220C2×D4—24no—
221C2×D4—24no—
222C2×D4—42no—
223C2×D4—41no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—28no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1112yes—
235C22×C4C2×D4×C1118yes—
236C22×C4C24×C1111yescharacteristic
237Q16—416no—
238C2×C8—28no—
239C2×C8—24no—
240C4⋊C4—216no—
241C4⋊C4—216no—
242C4⋊C4—24no—
243C4⋊C4C2×D4×C1118yes—
244C22⋊C4—28no—
245C22⋊C4—216no—
246C22⋊C4—216no—
247C42—28no—
248C11#2392811yescharacteristic, direct product factor, Sylow
249C23—22no—
250C23—22no—
251C23—28no—
252C23—22no—
253C23—21no—
254C23—24no—
255C23C11×#12014yes—
256C23C22×D4×C1111yescharacteristic
257Q8—216no—
258Q8—44no—
259Q8—416no—
260Q8—48no—
261D4—48no—
262D4—44no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—216no—
266C2×C4—28no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—416no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—44no—
275C2×C4C11×#12014yes—
276C2×C4C22×D4×C1114yes—
277C2×C4C11×H(5,𝔽2)12yes—
278C8—44no—
279C22—24no—
280C22—28no—
281C22—44no—
282C22—44no—
283C22—41no—
284C22—42no—
285C22—44no—
286C22C2×C11×#12012yes—
287C22C11×#53411yescharacteristic
288C22C11×#57814yes—
289C4—24no—
290C4—41no—
291C4—48no—
292C4—48no—
293C4D42×C1114yes—
294C2—44no—
295C2—81no—
296C2C11×#240311yescharacteristic
297C2C11×#301114yes—
298C2C11×#320212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#451C2semidirect
3. C11×#2001C2semidirect
4. C11×#1873C2semidirect
57. #23928C11direct (N × H)
101. C2×#451C2×C11semidirect
102. #2001C2×C11semidirect
103. #1873C2×C11semidirect
248. C11#23928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4512
C11×#20012
C11×#18732
C11×#17802
#2392811