Finite Group Databasebeta

← D11×#1356 #14664945

Subgroups — D11×#1356 #14664945

Order 2816.

314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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
1D11×#491C211yesmaximal, characteristic
2D11×#347C212yesmaximal
3#13066651C211yesmaximal, characteristic, complemented
4#13066650C212yesmaximal, complemented
5C11×#1356C211yesmaximal, characteristic, complemented
6D11×C4⋊Q8C411yescharacteristic
7D11×#125C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C411yescharacteristic
10#10622682C411yescharacteristic
11D11×M32—22no—
12D11×#103—22no—
13#10622410—22no—
14D11×#97C2211yescharacteristic
15#10622316C2211yescharacteristic
16C11×#347C2212yes—
17#10622150—22no—
18#10622104C2212yes—
19C2×Q8×D11—21no—
20C11×C4⋊Q8C2×C411yescharacteristic
21C11×#125C2×C411yescharacteristic
22#66997—21no—
23C2×C8×D11D412yes—
24C4⋊C4×D11—21no—
25C4⋊C4×D11—41no—
26C4⋊C4×D11—41no—
27#66943—21no—
28#66942—41no—
29#66941—41no—
30C42×D11C2×C411yescharacteristic
31#66923C2×C411yescharacteristic
32#66922C2×C411yescharacteristic
33C11×M32—22no—
34C11×#103—22no—
35C11×#97C2311yescharacteristic
36#66899—22no—
37#66880—22no—
38#66879D412yes—
39#66876—22no—
40#66874—22no—
41#66867C2×C411yescharacteristic
42#66862—24no—
43C16×D11—24no—
44C2×#1356—111nomaximal, Sylow
45C2×Q8×C11—21no—
46Q8×D11—42no—
47Q8×D11—42no—
48C2×C4×D11—21no—
49C2×C4×D11—41no—
50C2×C4×D11—41no—
51C2×C4×D11C22⋊C411yescharacteristic
52C2×Dic22—21no—
53C2×Dic22—41no—
54C2×C8×C11C2×D412yes—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C42×C11C22×C411yescharacteristic
59C4⋊Dic11—21no—
60C4⋊Dic11—41no—
61C4⋊Dic11—41no—
62Dic11⋊C4—41no—
63Dic11⋊C4—42no—
64Dic11⋊C4—41no—
65Dic11⋊C4—41no—
66C4×Dic11—21no—
67C4×Dic11C22⋊C411yescharacteristic
68C2×C11⋊C8C22⋊C412yes—
69C8×D11—22no—
70C8×D11—22no—
71C11×C16—24no—
72C11⋊C16—24no—
73C2×#491—111no—
74C2×#347—112no—
75#1356—111no—
76#1356—112no—
77#1356D1111yescharacteristic, direct product factor
78C22×D11#10011yescharacteristic
79Q8×C11—42no—
80C2×C4×C11—21no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11C2×C22⋊C411yescharacteristic
84C2×Dic11—21no—
85C2×Dic11—41no—
86C2×Dic11—41no—
87C2×Dic11#10011yescharacteristic
88C4×D11—42no—
89C4×D11—82no—
90C4×D11—81no—
91C4×D11—81no—
92C4×D11#10412yes—
93C4×D11#10412yes—
94Dic22—42no—
95Dic22—82no—
96C8×C11—22no—
97C11⋊C8—22no—
98C2×C4⋊Q8—111no—
99C2×#125—111no—
100C2×M32—222no—
101#491—111no—
102#491—111no—
103#491—111no—
104#491—222no—
105#491C2×D1111yescharacteristic
106C2×#103—222no—
107C2×#97—111no—
108#347—112no—
109#347—222no—
110#347C2×D1112yes—
111C22×C11C2×#10011yescharacteristic
112C2×D11—22no—
113C2×D11#32911yescharacteristic
114C2×D11#32911yescharacteristic
115C4×C11—41no—
116C4×C11—81no—
117C4×C11—81no—
118C4×C11C2×#10412yes—
119Dic11—41no—
120Dic11—81no—
121Dic11—81no—
122Dic11#32912yes—
123C22×Q8—221no—
124C22×C8—112no—
125C4⋊Q8—111no—
126C4⋊Q8—221no—
127C4⋊Q8—441no—
128C4⋊Q8C4×D1111yescharacteristic
129#125—111no—
130#125—221no—
131#125—441no—
132#125C4×D1111yescharacteristic
133C2×C4⋊C4—221no—
134C2×C4⋊C4—441no—
135C2×C4⋊C4—441no—
136C2×C42—111no—
137M32—22no—
138M32—224no—
139M32—222no—
140C2×C16—224no—
141#103—22no—
142#103—222no—
143#103—222no—
144#103—222no—
145#97—112no—
146#97—111no—
147#97C22×D1111yescharacteristic
148C2×C11—21no—
149C2×C11C2×#32911yescharacteristic
150D11—21no—
151D11#135612yesdirect product factor
152C2×Q8—21no—
153C2×Q8—221no—
154C2×Q8—441no—
155C2×Q8—442no—
156C2×Q8—442no—
157C22×C4—111no—
158C22×C4—221no—
159C22×C4—441no—
160C22×C4—441no—
161C2×C8—112no—
162C2×C8—222no—
163C2×C8—222no—
164C2×C8D4×D1112yes—
165C4⋊C4—21no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—221no—
169C4⋊C4—441no—
170C4⋊C4—441no—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C4⋊C4—441no—
174C4⋊C4—442no—
175C42—111no—
176C42—221no—
177C42C2×C4×D1111yescharacteristic
178C16—24no—
179C16—224no—
180C11C2×#135611yescharacteristic, complemented, Sylow
181C23—111no—
182Q8—42no—
183Q8—442no—
184Q8—882no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—111no—
189C2×C4—112no—
190C2×C4—112no—
191C2×C4—221no—
192C2×C4—442no—
193C2×C4—441no—
194C2×C4—441no—
195C2×C4—881no—
196C2×C4—881no—
197C2×C4—882no—
198C2×C4C22⋊C4×D1111yescharacteristic
199C8—22no—
200C8—222no—
201C22—111no—
202C22—111no—
203C22—222no—
204C22D11×#10011yescharacteristic
205C4—41no—
206C4—81no—
207C4—81no—
208C4—112no—
209C4—441no—
210C4—881no—
211C4—881no—
212C4D11×#10412yes—
213C2—21no—
214C2—112no—
215C2—221no—
216C2D11×#32911yescharacteristic
subgroupG/H
centerC2D11×#329
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1356C2
socleC2×C11C2×#329
prime radicalC22×D11#100
cosocleC11×#97C23
hypercenter#1356D11
hypocenterC11C2×#1356
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #13066651C2semidirect
4. #13066650C2semidirect
5. C11×#1356C2semidirect
77. #1356D11direct (N × H)
151. D11#1356direct (N × H)
180. C11C2×#1356semidirect

Maximal subgroups

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

subgroupindex
D11×#4912
D11×#3472
#130666512
#130666502
C11×#13562
C2×#135611