Finite Group Databasebeta

← #14664950

Subgroups — #14664950

Order 2816.

318 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#13078963C211yesmaximal, characteristic
2D11×#347C212yesmaximal, complemented
3#13066651C211yesmaximal, characteristic, complemented
4#13066648C212yesmaximal, complemented
5C11×#1356C211yesmaximal, characteristic, complemented
6#10623256C411yescharacteristic
7#10623219C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C411yescharacteristic
10#10622680C411yescharacteristic
11D11×M32—22no—
12#10622417—22no—
13#10622408—22no—
14#10622326C2211yescharacteristic
15D11×#97C2211yescharacteristic
16C11×#347C2212yes—
17#10622150—22no—
18#10622104C2212yes—
19C2×#4343—21no—
20C11×C4⋊Q8C2×C411yescharacteristic
21C11×#125C2×C411yescharacteristic
22#67000—21no—
23C2×C8×D11D412yes—
24#66949—41no—
25#66948—41no—
26#66946—41no—
27#66945—21no—
28#66941—21no—
29#66940—41no—
30#66927C2×C411yescharacteristic
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33C11×M32—22no—
34C11×#103—22no—
35C11×#97C2311yescharacteristic
36#66899—22no—
37#66885—22no—
38#66879D412yes—
39#66876—22no—
40#66873—22no—
41#66867C2×C411yescharacteristic
42#66862—24no—
43C16×D11—24no—
44#11911—111nomaximal, Sylow
45C2×Q8×C11—21no—
46#4343—42no—
47#4343—42no—
48C2×D44—21no—
49C2×D44—41no—
50C2×D44—41no—
51C2×C4×D11—21no—
52C2×C4×D11—41no—
53C2×C4×D11C22⋊C411yescharacteristic
54C2×Dic22—41no—
55C2×C8×C11C2×D412yes—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C42×C11C22×C411yescharacteristic
60(C2×D11)⋊C4—42no—
61(C2×D11)⋊C4—41no—
62C4⋊Dic11—21no—
63Dic11⋊C4—41no—
64Dic11⋊C4—41no—
65C4×Dic11—21no—
66C4×Dic11—41no—
67C4×Dic11C22⋊C411yescharacteristic
68C2×C11⋊C8C22⋊C412yes—
69C8×D11—22no—
70C8×D11—22no—
71C11×C16—24no—
72C11⋊C16—24no—
73#3135—111no—
74C2×#347—112no—
75#1356—111no—
76#1356D1111yescharacteristic, complemented
77#1355—112no—
78C22×D11—41no—
79C22×D11#10011yescharacteristic
80Q8×C11—42no—
81C2×C4×C11—21no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11C2×C22⋊C411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—41no—
87C2×Dic11#10011yescharacteristic
88D44—42no—
89D44—82no—
90D44—82no—
91C4×D11—81no—
92C4×D11—81no—
93C4×D11—81no—
94C4×D11#10412yes—
95C4×D11#10412yes—
96Dic22—82no—
97C8×C11—22no—
98C11⋊C8—22no—
99#533—111no—
100#532—111no—
101C2×M32—222no—
102#491—111no—
103#491C2×D1111yescharacteristic
104#490—111no—
105#490—111no—
106#489—222no—
107#416—222no—
108C2×#97—111no—
109#347—112no—
110#347—222no—
111#347C2×D1112yes—
112C22×C11C2×#10011yescharacteristic
113C2×D11—41no—
114C2×D11—82no—
115C2×D11—81no—
116C2×D11#32912yes—
117C4×C11—41no—
118C4×C11—81no—
119C4×C11—81no—
120C4×C11C2×#10412yes—
121Dic11—41no—
122Dic11—81no—
123Dic11#32911yescharacteristic
124Dic11#32911yescharacteristic
125C2×#41—221no—
126C22×C8—112no—
127C4⋊Q8—221no—
128C4⋊Q8C4×D1111yescharacteristic
129#127—111no—
130#125—111no—
131#125C4×D1111yescharacteristic
132#124—221no—
133C22⋊Q8—441no—
134#121—441no—
135C4×Q8—441no—
136C4×D4—441no—
137#117—221no—
138C2×C42—111no—
139M32—22no—
140M32—224no—
141M32—222no—
142C2×C16—224no—
143#103—22no—
144#103—222no—
145#102—222no—
146#102—222no—
147#97—112no—
148#97—111no—
149#97C22×D1111yescharacteristic
150C2×C11—21no—
151C2×C11C2×#32911yescharacteristic
152D11—22no—
153D11—161no—
154#41—442no—
155#41—442no—
156C2×Q8—21no—
157C2×Q8—441no—
158C2×D4—221no—
159C2×D4—441no—
160C2×D4—441no—
161C22×C4—111no—
162C22×C4—221no—
163C22×C4—441no—
164C2×C8—112no—
165C2×C8—222no—
166C2×C8—222no—
167C2×C8D4×D1112yes—
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—221no—
172C4⋊C4—441no—
173C4⋊C4—441no—
174C22⋊C4—442no—
175C22⋊C4—441no—
176C42—111no—
177C42—221no—
178C42—441no—
179C42C2×C4×D1111yescharacteristic
180C16—24no—
181C16—224no—
182C11#1191111yescharacteristic, complemented, Sylow
183C23—111no—
184C23—441no—
185Q8—42no—
186Q8—882no—
187D4—442no—
188D4—882no—
189D4—882no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—111no—
194C2×C4—112no—
195C2×C4—112no—
196C2×C4—221no—
197C2×C4—441no—
198C2×C4—881no—
199C2×C4—881no—
200C2×C4—881no—
201C2×C4C22⋊C4×D1111yescharacteristic
202C8—22no—
203C8—222no—
204C22—112no—
205C22—441no—
206C22—882no—
207C22—881no—
208C22D11×#10011yescharacteristic
209C4—41no—
210C4—81no—
211C4—81no—
212C4—111no—
213C4—111no—
214C4—441no—
215C4—881no—
216C4D11×#10412yes—
217C2—21no—
218C2—222no—
219C2—1761no—
220C2D11×#32911yescharacteristic
subgroupG/H
centerC2D11×#329
commutatorC42×C11C22×C4
Frattini#97C22×D11
FittingC11×#1356C2
socleC2×C11C2×#329
prime radical#10623256C4
cosocleC11×#97C23
hypercenter#1356D11
hypocenterC11#11911
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
2. D11×#347C2semidirect
3. #13066651C2semidirect
4. #13066648C2semidirect
5. C11×#1356C2semidirect
76. #1356D11semidirect
182. C11#11911semidirect

Maximal subgroups

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

subgroupindex
#130789632
D11×#3472
#130666512
#130666482
C11×#13562
#1191111