Finite Group Databasebeta

← C11×#11838 #14589031

Subgroups — C11×#11838 #14589031

Order 2816.

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3185C211yesmaximal, characteristic
2C11×#2165C211yesmaximal, characteristic
3C11×#1841C211yesmaximal, characteristic
4C11×#1342C212yesmaximal
5C11×#1340C212yesmaximal
6C11×#533—21no—
7C11×#498C411yescharacteristic, complemented
8C11×#494C411yescharacteristic, complemented
9C11×#487—21no—
10C11×#470—21no—
11C11×#470C2212yes—
12C11×#441—21no—
13C11×#441C412yescomplemented
14C4×C11×M16C2211yescharacteristic
15C11×#364—21no—
16C11×#349C2212yes—
17C11×#347—21no—
18C11×#344—21no—
19C11×#339—21no—
20C11×#338C2211yescharacteristic
21C11×H(3,ℤ/4)C2211yescharacteristic
22C2×C11×Q16—21no—
23C2×C11×Q16C2×C412yes—
24C2×C11×M16—21no—
25C2×C11×M16D411yescharacteristic
26C2×C11×M16C2311yescharacteristic
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×#125—41no—
30C11×C22⋊Q8—22no—
31C11×C22⋊Q8—41no—
32C4×Q8×C11—22no—
33C4×Q8×C11—41no—
34C11×#117—21no—
35C11×#117—41no—
36C2×C42×C11D411yescharacteristic
37C11×M32—22no—
38C11×#106—21no—
39C11×#106C2×C412yes—
40C11×#103—22no—
41C11×#103—22no—
42C11×#97C2×C411yescharacteristic
43C11×#97D411yescharacteristic
44C4×C8×C11C2×C411yescharacteristic
45C4×C8×C11D411yescharacteristic
46#11838C1111yesmaximal, characteristic, direct product factor, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—41no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C11×Q16—42no—
52C11×Q16—42no—
53C11×M16—41no—
54C11×M16—41no—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11—41no—
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22×C411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—22no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C22⋊C4—42no—
70C11×C22⋊C4—41no—
71C42×C11—21no—
72C42×C11—42no—
73C42×C11—41no—
74C42×C11C22⋊C411yescharacteristic
75C42×C11C22⋊C411yescharacteristic
76C11×C16—42no—
77#3185C2×C1111yescharacteristic
78#2165C2×C1111yescharacteristic
79#1841C2×C1111yescharacteristic
80#1342C2×C1112yes—
81#1340C2×C1112yes—
82C23×C11AGL(1,ℤ/8)11yescharacteristic
83Q8×C11—42no—
84Q8×C11—42no—
85Q8×C11—82no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—81no—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—81no—
101#533—21no—
102#498C4×C1111yescharacteristic, complemented
103#494C4×C1111yescharacteristic, complemented
104#487—21no—
105#470—21no—
106#470C22×C1112yes—
107#441—21no—
108#441C4×C1112yescomplemented
109C4×M16C22×C1111yescharacteristic
110#364—21no—
111#349C22×C1112yes—
112#347—21no—
113#344—21no—
114#339—21no—
115#338C22×C1111yescharacteristic
116H(3,ℤ/4)C22×C1111yescharacteristic
117C22×C11—21no—
118C22×C11—41no—
119C22×C11#41811yescharacteristic
120C4×C11—22no—
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—82no—
124C4×C11—82no—
125C4×C11—161no—
126C4×C11#41011yescharacteristic
127C4×C11#42111yescharacteristic
128C2×Q16—21no—
129C2×Q16C2×C4×C1112yes—
130C2×M16—21no—
131C2×M16D4×C1111yescharacteristic
132C2×M16C23×C1111yescharacteristic
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135#125—41no—
136C22⋊Q8—22no—
137C22⋊Q8—41no—
138C4×Q8—22no—
139C4×Q8—41no—
140#117—21no—
141#117—41no—
142C2×C42D4×C1111yescharacteristic
143M32—22no—
144#106—21no—
145#106C2×C4×C1112yes—
146#103—22no—
147#103—22no—
148#97C2×C4×C1111yescharacteristic
149#97D4×C1111yescharacteristic
150C4×C8C2×C4×C1111yescharacteristic
151C4×C8D4×C1111yescharacteristic
152C2×C11—21no—
153C2×C11—41no—
154C2×C11#151411yescharacteristic
155C2×Q8—22no—
156C2×Q8—41no—
157C22×C4—21no—
158C22×C4C2×D4×C1111yescharacteristic
159Q16—42no—
160Q16—42no—
161M16—41no—
162M16—41no—
163M16—41no—
164M16—41no—
165C2×C8—41no—
166C2×C8C11×C22⋊C411yescharacteristic
167C2×C8C11×C22⋊C411yescharacteristic
168C2×C8C22×C4×C1111yescharacteristic
169C2×C8C2×D4×C1111yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C22⋊C4—42no—
178C22⋊C4—41no—
179C42—21no—
180C42—42no—
181C42—41no—
182C42C11×C22⋊C411yescharacteristic
183C42C11×C22⋊C411yescharacteristic
184C16—42no—
185C11#1183811yescharacteristic, direct product factor, Sylow
186C23C11×AGL(1,ℤ/8)11yescharacteristic
187Q8—42no—
188Q8—42no—
189Q8—82no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—81no—
198C2×C4C2×C11×C22⋊C411yescharacteristic
199C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—81no—
205C22—21no—
206C22—41no—
207C22C11×#41811yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—82no—
212C4—82no—
213C4—161no—
214C4C11×#41011yescharacteristic
215C4C11×#42111yescharacteristic
216C2—21no—
217C2—41no—
218C2C11×#151411yescharacteristic
subgroupG/H
center, socleC2×C11#1514
commutatorC2×C8C22×C4×C11
Frattini, cosocleC2×M16C23×C11
prime radicalC23×C11AGL(1,ℤ/8)
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
7. C11×#498C4semidirect
8. C11×#494C4semidirect
13. C11×#441C4semidirect
46. #11838C11direct (N × H)
102. #498C4×C11semidirect
103. #494C4×C11semidirect
108. #441C4×C11semidirect
185. C11#11838direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31852
C11×#21652
C11×#18412
C11×#13422
C11×#13402
#1183811