Finite Group Databasebeta

← C11×#9991 #14587184

Subgroups — C11×#9991 #14587184

Order 2816.

698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C11×#3195C211yesmaximal, characteristic
2C2×C11×#451C212yesmaximal
3C11×#1784C211yesmaximal, characteristic
4C11×#1472C212yesmaximal
5C11×#1298C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C22×C11×Q16—22no—
8C2×C11×C22⋊Q8C2212yes—
9C11×#483—22no—
10C11×#470—22no—
11C11×#451—22no—
12C11×#451—24no—
13C11×#451—24no—
14C2×C11×#103—22no—
15C2×C11×#101—22no—
16C11×#407C2211yescharacteristic
17C11×#407C2211yescharacteristic
18C2×C11×C22⋊C8C2212yes—
19C11×#324—24no—
20C22×Q8×C11—21no—
21C22×Q8×C11—22no—
22C22×Q8×C11—22no—
23C22×Q8×C11—44no—
24C22×Q8×C11D412yes—
25C22×Q8×C11D412yes—
26C23×C4×C11—21no—
27C23×C4×C11C2311yescharacteristic
28C2×C11×Q16—28no—
29C2×C11×Q16—22no—
30C2×C11×Q16—48no—
31C2×C11×M16—21no—
32C2×C11×M16D412yes—
33C22×C8×C11—22no—
34C11×C22⋊Q8—22no—
35C11×C22⋊Q8—22no—
36C11×C22⋊Q8—22no—
37C11×C22⋊Q8—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4D412yes—
40C2×C11×C22⋊C4—22no—
41C11×#106—22no—
42C11×#103—28no—
43C11×#103—24no—
44C11×#101—44no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8D414yes—
49#9991C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11#4111yescharacteristic
51C2×Q8×C11—24no—
52C2×Q8×C11—28no—
53C2×Q8×C11—24no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11—44no—
57C2×Q8×C11—44no—
58C2×Q8×C11—42no—
59C2×Q8×C11—44no—
60C2×Q8×C11—48no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—42no—
67C22×C4×C11—44no—
68C22×C4×C11—42no—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C11×Q16—416no—
74C11×Q16—82no—
75C11×M16—42no—
76C11×M16—42no—
77C2×C8×C11—22no—
78C2×C8×C11—24no—
79C2×C8×C11—44no—
80C2×C8×C11—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87#3195C2×C1111yescharacteristic
88C2×#451C2×C1112yes—
89#1784C2×C1111yescharacteristic
90#1472C2×C1112yes—
91#1298C2×C1111yescharacteristic
92C23×C11—24no—
93C23×C11—41no—
94C23×C11#12111yescharacteristic
95C23×C11#12112yes—
96Q8×C11—28no—
97Q8×C11—44no—
98Q8×C11—44no—
99Q8×C11—44no—
100Q8×C11—44no—
101Q8×C11—44no—
102C2×C4×C11—24no—
103C2×C4×C11—22no—
104C2×C4×C11—24no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—48no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—44no—
113C2×C4×C11—82no—
114C2×C4×C11#12012yes—
115C2×C4×C11#12011yescharacteristic
116C2×C4×C11#12711yescharacteristic
117C8×C11—44no—
118C8×C11—42no—
119C8×C11—81no—
120C23×Q8C22×C1111yescharacteristic
121C22×Q16—22no—
122C2×C22⋊Q8C22×C1112yes—
123#483—22no—
124#470—22no—
125#451—22no—
126#451—24no—
127#451—24no—
128C2×#103—22no—
129C2×#101—22no—
130#407C22×C1111yescharacteristic
131#407C22×C1111yescharacteristic
132C2×C22⋊C8C22×C1112yes—
133#324—24no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—21no—
138C22×C11—44no—
139C22×C11#39211yescharacteristic
140C22×C11#47314yes—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—44no—
144C4×C11—82no—
145C4×C11—82no—
146C4×C11B(4,𝔽2)12yes—
147C22×Q8—21no—
148C22×Q8—22no—
149C22×Q8—22no—
150C22×Q8—44no—
151C22×Q8D4×C1112yes—
152C22×Q8D4×C1112yes—
153C23×C4—21no—
154C23×C4C23×C1111yescharacteristic
155C2×Q16—28no—
156C2×Q16—22no—
157C2×Q16—48no—
158C2×M16—21no—
159C2×M16D4×C1112yes—
160C22×C8—22no—
161C22⋊Q8—22no—
162C22⋊Q8—22no—
163C22⋊Q8—22no—
164C22⋊Q8—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4D4×C1112yes—
167C2×C22⋊C4—22no—
168#106—22no—
169#103—28no—
170#103—24no—
171#101—44no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8D4×C1114yes—
176C2×C11—24no—
177C2×C11—41no—
178C2×C11#202012yes—
179C2×C11#202111yescharacteristic
180C24C11×#4111yescharacteristic
181C2×Q8—24no—
182C2×Q8—28no—
183C2×Q8—24no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—44no—
187C2×Q8—44no—
188C2×Q8—42no—
189C2×Q8—44no—
190C2×Q8—48no—
191C2×Q8—41no—
192C2×Q8—41no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—44no—
198C22×C4—42no—
199C22×C4C2×D4×C1112yes—
200C22×C4C2×D4×C1111yescharacteristic
201C22×C4C2×D4×C1111yescharacteristic
202C22×C4C2×D4×C1112yes—
203Q16—416no—
204Q16—82no—
205M16—42no—
206M16—42no—
207C2×C8—22no—
208C2×C8—24no—
209C2×C8—44no—
210C2×C8—41no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C11#999111yescharacteristic, direct product factor, Sylow
218C23—24no—
219C23—41no—
220C23C11×#12111yescharacteristic
221C23C11×#12112yes—
222Q8—28no—
223Q8—44no—
224Q8—44no—
225Q8—44no—
226Q8—44no—
227Q8—44no—
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—48no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—82no—
240C2×C4C11×#12012yes—
241C2×C4C11×#12011yescharacteristic
242C2×C4C11×#12711yescharacteristic
243C8—44no—
244C8—42no—
245C8—81no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—21no—
250C22—44no—
251C22C11×#39211yescharacteristic
252C22C11×#47314yes—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—82no—
257C4—82no—
258C4C11×B(4,𝔽2)12yes—
259C2—24no—
260C2—41no—
261C2C11×#202012yes—
262C2C11×#202111yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
49. #9991C11direct (N × H)
217. C11#9991direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31952
C2×C11×#4512
C11×#17842
C11×#14722
C11×#12982
#999111