Finite Group Databasebeta

← #14652800

Subgroups — #14652800

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068469C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic
3C2×#10622181C214yesmaximal
4C11×#2859C211yesmaximal, characteristic
5C2×C11×#125C2212yes—
6C11×#389—21no—
7C11×#389—21no—
8C11×#389—21no—
9C11×#389—21no—
10C11×#384C411yescharacteristic
11C11×#384C411yescharacteristic
12C11×#382C412yes—
13C43×C11C2211yescharacteristic
14C2×C4⋊(C11⋊C8)—21no—
15C2×#66867C2212yes—
16C2×#66867C2212yes—
17#10622181—28no—
18#10622162—21no—
19#10622162—21no—
20#10622162—21no—
21C11×#125—24no—
22C11×#125—24no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—22no—
40C11×#95—22no—
41C11×#95—22no—
42C4⋊(C11⋊C8)—24no—
43#66867—22no—
44#66867—24no—
45#66867D414yes—
46#9690—111nomaximal, Sylow
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11C22⋊C411yescharacteristic
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22⋊C411yescharacteristic
53C22×C4×C11C22×C411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C11×C4⋊C4—24no—
57C11×C4⋊C4—24no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—44no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C42×C11—22no—
66C42×C11—22no—
67C42×C11—22no—
68C42×C11—41no—
69C42×C11—41no—
70C42×C11—41no—
71C42×C11C2×D412yes—
72C42×C11#4112yes—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79#2859D1111yescharacteristic
80#1767—111no—
81#1745—111no—
82C2×#330—114no—
83C23×C11C2×C22⋊C411yescharacteristic
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11#10112yes—
106C2×C4×C11#10112yes—
107C2×C4×C11#10412yes—
108C2×C4×C11C4×D412yes—
109C2×C4×C11#12112yes—
110C2×C4×C11#12411yescharacteristic
111C2×C4×C11#12711yescharacteristic
112C11⋊C8—44no—
113C11⋊C8—44no—
114C2×#125C2×D1112yes—
115C2×C4⋊C8—221no—
116C2×#97—112no—
117C2×#97—112no—
118#389—21no—
119#389—21no—
120#389—21no—
121#389—21no—
122#384Dic1111yescharacteristic
123#384Dic1111yescharacteristic
124#382Dic1112yes—
125C43C2×D1111yescharacteristic
126#336—221no—
127#336—221no—
128#336—221no—
129#330—228no—
130C22×C11#39011yescharacteristic
131C22×C11C2×#10111yescharacteristic
132C22×C11C2×#10111yescharacteristic
133C22×C11C2×#10411yescharacteristic
134C22×C11#42111yescharacteristic
135C22×C11#42111yescharacteristic
136C22×C11#42111yescharacteristic
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—22no—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—41no—
145C4×C11—82no—
146C4×C11—82no—
147C22×C8—222no—
148C22×C8—222no—
149#125—24no—
150#125—24no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4C2×Dic1112yes—
158C2×C4⋊C4C2×Dic1112yes—
159C2×C42C2×Dic1111yescharacteristic
160C2×C42C2×Dic1111yescharacteristic
161C2×C42C22⋊D1111yescharacteristic
162C2×C42C22⋊D1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C2×C42C22⋊D1111yescharacteristic
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—224no—
167#97—114no—
168#97—224no—
169#97—222no—
170#95—22no—
171#95—22no—
172C2×C11#152811yescharacteristic
173C2×C11#153111yescharacteristic
174C2×C11#153411yescharacteristic
175C2×C11#153711yescharacteristic
176C2×C11#196311yescharacteristic
177C2×C11#196611yescharacteristic
178C2×C11#198011yescharacteristic
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic1111yescharacteristic
182C22×C4C22⋊Dic1111yescharacteristic
183C22×C4C22⋊Dic1111yescharacteristic
184C22×C4C22⋊Dic1111yescharacteristic
185C22×C4C22×Dic1111yescharacteristic
186C22×C4C2×C22⋊D1111yescharacteristic
187C22×C4C2×C22⋊D1111yescharacteristic
188C2×C8—224no—
189C2×C8—224no—
190C2×C8—442no—
191C2×C8—442no—
192C2×C8—442no—
193C2×C8—442no—
194C4⋊C4—24no—
195C4⋊C4—24no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—42no—
203C42—22no—
204C42—22no—
205C42—22no—
206C42—41no—
207C42—41no—
208C42—41no—
209C42D4×D1112yes—
210C42#434112yes—
211C11#969011yescharacteristic, complemented, Sylow
212C23C2×C22⋊Dic1111yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4#6690012yes—
235C2×C4#6690012yes—
236C2×C4#6690112yes—
237C2×C4D4×Dic1112yes—
238C2×C4#6698911yescharacteristic
239C2×C4#6699112yes—
240C2×C4#6699311yescharacteristic
241C8—444no—
242C8—444no—
243C22#1062283411yescharacteristic
244C22C2×#6690011yescharacteristic
245C22C2×#6690011yescharacteristic
246C22C2×#6690111yescharacteristic
247C22#1062284911yescharacteristic
248C22#1062284911yescharacteristic
249C22#1062284911yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—22no—
254C4—21no—
255C4—21no—
256C4—22no—
257C4—41no—
258C4—82no—
259C4—82no—
260C2#1306721811yescharacteristic
261C2#1306723111yescharacteristic
262C2#1306724311yescharacteristic
263C2#1306725411yescharacteristic
264C2#1306944911yescharacteristic
265C2#1306946111yescharacteristic
266C2#1306953611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2859C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2859D11
hypocenterC11#9690
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2859

Complements

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

NH ≅ G/Ntype
211. C11#9690semidirect

Maximal subgroups

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

subgroupindex
#130684692
#130683652
C2×#106221812
C11×#28592
#969011