Finite Group Databasebeta

← C11×#12109 #14589302

Subgroups — C11×#12109 #14589302

Order 2816.

410 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3202C211yesmaximal, characteristic, complemented
2C11×#2187C212yesmaximal, complemented
3C11×#2018C211yesmaximal, characteristic
4C11×#1350C212yesmaximal, complemented
5C11×#1315C211yesmaximal, characteristic, complemented
6C2×C11×AGL(1,ℤ/8)—21no—
7C22×C11×D8C2211yescharacteristic
8C11×#536—21no—
9C2×C11×SD32—22no—
10C11×#485—22no—
11C11×#470—21no—
12C11×#467C2212yes—
13C11×#451—22no—
14C2×C11×#100—21no—
15C11×#408C2211yescharacteristic
16C11×#357—22no—
17C11×C22⋊C16C2212yes—
18C11×#341C2211yescharacteristic
19C2×C11×#41D411yescharacteristic
20C22×Q8×C11—21no—
21C22×D4×C11—21no—
22C11×AGL(1,ℤ/8)—42no—
23C11×AGL(1,ℤ/8)—42no—
24C2×C11×Q16—21no—
25C2×C11×Q16D412yes—
26C2×C11×SD16—41no—
27C2×C11×D8—22no—
28C2×C11×D8—42no—
29C2×C11×D8—41no—
30C2×C11×M16—21no—
31C2×C11×M16D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C11×C4⋊Q8—41no—
34C11×#124—41no—
35C11×#123—41no—
36C11×#123—41no—
37C11×C22⋊Q8—22no—
38C11×C22⋊Q8—22no—
39C11×#117—21no—
40C11×SD32—44no—
41C2×C11×C16—22no—
42C11×#107D412yes—
43C11×#106—21no—
44C11×#103—22no—
45C11×#103—22no—
46C11×#100—42no—
47C11×C22⋊C8—22no—
48#12109C1111yesmaximal, characteristic, direct product factor, Sylow
49C24×C11—41no—
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C2×Q8×C11—81no—
55C2×Q8×C11—81no—
56C2×Q8×C11D811yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11D811yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C11×Q16—42no—
69C11×Q16—81no—
70C11×SD16—44no—
71C11×D8—24no—
72C11×D8—42no—
73C11×D8—44no—
74C11×M16—22no—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11C2×D412yes—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—41no—
88C11×C16—42no—
89#3202C2×C1111yescharacteristic, complemented
90#2187C2×C1112yescomplemented
91#2018C2×C1111yescharacteristic
92#1350C2×C1112yescomplemented
93#1315C2×C1111yescharacteristic, complemented
94C23×C11—21no—
95C23×C11—42no—
96C23×C11—81no—
97C23×C11—81no—
98C23×C11—162no—
99C23×C11AGL(1,ℤ/8)11yescharacteristic
100Q8×C11—41no—
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—82no—
104D4×C11—41no—
105D4×C11—42no—
106D4×C11—42no—
107D4×C11—81no—
108D4×C11—81no—
109D4×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C8×C11—22no—
121C8×C11—42no—
122C8×C11—41no—
123C2×AGL(1,ℤ/8)—21no—
124C22×D8C22×C1111yescharacteristic
125#536—21no—
126C2×SD32—22no—
127#485—22no—
128#470—21no—
129#467C22×C1112yes—
130#451—22no—
131C2×#100—21no—
132#408C22×C1111yescharacteristic
133#357—22no—
134C22⋊C16C22×C1112yes—
135#341C22×C1111yescharacteristic
136C22×C11—21no—
137C22×C11—22no—
138C22×C11—41no—
139C22×C11—42no—
140C22×C11—82no—
141C22×C11—162no—
142C22×C11—162no—
143C22×C11—162no—
144C22×C11#44711yescharacteristic
145C4×C11—21no—
146C4×C11—41no—
147C4×C11—82no—
148C4×C11—82no—
149C4×C11#45311yescharacteristic
150C4×C11B(4,𝔽2)11yescharacteristic
151C2×#41D4×C1111yescharacteristic
152C22×Q8—21no—
153C22×D4—21no—
154AGL(1,ℤ/8)—42no—
155AGL(1,ℤ/8)—42no—
156C2×Q16—21no—
157C2×Q16D4×C1112yes—
158C2×SD16—41no—
159C2×D8—22no—
160C2×D8—42no—
161C2×D8—41no—
162C2×M16—21no—
163C2×M16D4×C1111yescharacteristic
164C22×C8C23×C1111yescharacteristic
165C4⋊Q8—41no—
166#124—41no—
167#123—41no—
168#123—41no—
169C22⋊Q8—22no—
170C22⋊Q8—22no—
171#117—21no—
172SD32—44no—
173C2×C16—22no—
174#107D4×C1112yes—
175#106—21no—
176#103—22no—
177#103—22no—
178#100—42no—
179C22⋊C8—22no—
180C2×C11—41no—
181C2×C11—81no—
182C2×C11—162no—
183C2×C11#159511yescharacteristic
184C2×C11#219312yes—
185C24—41no—
186#41—41no—
187#41—41no—
188C2×Q8—22no—
189C2×Q8—41no—
190C2×Q8—81no—
191C2×Q8—81no—
192C2×Q8C11×D811yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4C11×D811yescharacteristic
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C1111yescharacteristic
204Q16—42no—
205Q16—81no—
206SD16—44no—
207D8—24no—
208D8—42no—
209D8—44no—
210M16—22no—
211M16—41no—
212M16—41no—
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8C2×D4×C1112yes—
217C4⋊C4—22no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C42—41no—
224C16—42no—
225C11#1210911yescharacteristic, direct product factor, Sylow
226C23—21no—
227C23—42no—
228C23—81no—
229C23—81no—
230C23—162no—
231C23C11×AGL(1,ℤ/8)11yescharacteristic
232Q8—41no—
233Q8—42no—
234Q8—42no—
235Q8—82no—
236D4—41no—
237D4—42no—
238D4—42no—
239D4—81no—
240D4—81no—
241D4—81no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4C11×#12011yescharacteristic
251C2×C4C2×C11×D811yescharacteristic
252C8—22no—
253C8—42no—
254C8—41no—
255C22—22no—
256C22—21no—
257C22—42no—
258C22—41no—
259C22—82no—
260C22—162no—
261C22—162no—
262C22—162no—
263C22C11×#44711yescharacteristic
264C4—21no—
265C4—41no—
266C4—82no—
267C4—82no—
268C4C11×#45311yescharacteristic
269C4C11×B(4,𝔽2)11yescharacteristic
270C2—41no—
271C2—81no—
272C2—162no—
273C2C11×#159511yescharacteristic
274C2C11×#219312yes—
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC11×#2018C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#408 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3202C2semidirect
2. C11×#2187C2semidirect
4. C11×#1350C2semidirect
5. C11×#1315C2semidirect
48. #12109C11direct (N × H)
89. #3202C2×C11semidirect
90. #2187C2×C11semidirect
92. #1350C2×C11semidirect
93. #1315C2×C11semidirect
225. C11#12109direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32022
C11×#21872
C11×#20182
C11×#13502
C11×#13152
#1210911