Finite Group Databasebeta

← #14641897

Subgroups — #14641897

Order 2816.

440 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068759C211yesmaximal, characteristic
2#13068759C211yesmaximal, characteristic
3#13066439C214yesmaximal
4C4×C11×C4⋊Q8C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11—21no—
7C11×#391—21no—
8C11×#389—21no—
9C11×#389C2212yes—
10C11×#384C411yescharacteristic
11C4×C11×C4⋊C4—21no—
12C4×C11×C4⋊C4C412yes—
13C43×C11C2211yescharacteristic
14#10622162—21no—
15#10622162—21no—
16#10622162—21no—
17#10622162—21no—
18#10622162C2212yes—
19#10622162C2212yes—
20C22×Q8×C11—21no—
21C11×C4⋊Q8—22no—
22C11×C4⋊Q8C814yescomplemented
23C4×Q8×C11—44no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C42×C11—22no—
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—
42#7604—111nomaximal, Sylow
43C2×Q8×C11—24no—
44C2×Q8×C11—42no—
45C2×Q8×C11—42no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11C22⋊C411yescharacteristic
51C22×C4×C11C22⋊C411yescharacteristic
52C22×C4×C11C22×C411yescharacteristic
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C11×C4⋊C4—24no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—42no—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—44no—
61C11×C4⋊C4C2×C814yes—
62C42×C11—22no—
63C42×C11—22no—
64C42×C11—22no—
65C42×C11—41no—
66C42×C11—41no—
67C42×C11—41no—
68C42×C11—44no—
69C42×C11C2×C812yes—
70C42×C11M1612yes—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77C4×C4⋊Q8D1111yescharacteristic
78#1839—111no—
79#1839—111no—
80#1271—114no—
81C23×C11C2×C22⋊C411yescharacteristic
82Q8×C11—48no—
83C2×C4×C11—21no—
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—24no—
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×C11C22⋊C812yes—
105C2×C4×C11C22⋊C812yes—
106C2×C4×C11#10112yes—
107C2×C4×C11C22×C811yescharacteristic
108C2×C4×C11C2×M1611yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)12yes—
110C2×C4×C11#13712yes—
111C11⋊C8—82no—
112C11⋊C8—82no—
113C2×C4⋊Q8Dic1111yescharacteristic
114C2×C4×Q8—21no—
115#391—21no—
116#389—21no—
117#389C2×D1112yes—
118#384Dic1111yescharacteristic
119C4×C4⋊C4—21no—
120C4×C4⋊C4Dic1112yes—
121C43C2×D1111yescharacteristic
122#336—112no—
123#336—112no—
124#336—221no—
125#336—221no—
126#336—221no—
127#336—221no—
128C22×C11C2×C22⋊C811yescharacteristic
129C22×C11#41011yescharacteristic
130C22×C11C2×#10111yescharacteristic
131C22×C11#41811yescharacteristic
132C22×C11#41911yescharacteristic
133C22×C11#42111yescharacteristic
134C22×C11#42111yescharacteristic
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—41no—
143C4×C11—44no—
144C4×C11—82no—
145C22×Q8—21no—
146C22×C8—222no—
147C22×C8—222no—
148C4⋊Q8—22no—
149C4⋊Q8C11⋊C814yescomplemented
150C4×Q8—44no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C2×Dic1112yes—
156C2×C4⋊C4C2×Dic1112yes—
157C2×C42—22no—
158C2×C42C2×Dic1111yescharacteristic
159C2×C42C2×Dic1111yescharacteristic
160C2×C42C22⋊D1111yescharacteristic
161C2×C42C22⋊D1111yescharacteristic
162C2×C42C22⋊D1111yescharacteristic
163C2×C42C22⋊D1111yescharacteristic
164C2×C42C22×D1111yescharacteristic
165#95—22no—
166#95—22no—
167C2×C11#146111yescharacteristic
168C2×C11#147811yescharacteristic
169C2×C11#147911yescharacteristic
170C2×C11#151411yescharacteristic
171C2×C11#151511yescharacteristic
172C2×C11#153711yescharacteristic
173C2×C11#155611yescharacteristic
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic1111yescharacteristic
180C22×C4C22⋊Dic1111yescharacteristic
181C22×C4C22⋊Dic1111yescharacteristic
182C22×C4C22⋊Dic1111yescharacteristic
183C22×C4C22×Dic1111yescharacteristic
184C22×C4C2×C22⋊D1111yescharacteristic
185C22×C4C2×C22⋊D1111yescharacteristic
186C2×C8—442no—
187C2×C8—442no—
188C2×C8—442no—
189C2×C8—442no—
190C2×C8—442no—
191C2×C8—442no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4C2×C11⋊C814yes—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—41no—
203C42—41no—
204C42—41no—
205C42—44no—
206C42C2×C11⋊C812yes—
207C42#431812yes—
208C11#760411yescharacteristic, complemented, Sylow
209C23C2×C22⋊Dic1111yescharacteristic
210Q8—48no—
211C2×C4—21no—
212C2×C4—21no—
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—24no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4C22⋊(C11⋊C8)12yes—
233C2×C4C22⋊(C11⋊C8)12yes—
234C2×C4#6690012yes—
235C2×C4C22×C11⋊C811yescharacteristic
236C2×C4C2×#431811yescharacteristic
237C2×C4#6698512yes—
238C2×C4#6699512yes—
239C8—882no—
240C8—882no—
241C22C2×C22⋊(C11⋊C8)11yescharacteristic
242C22#1062282811yescharacteristic
243C22#1062283811yescharacteristic
244C22C2×#6690011yescharacteristic
245C22#1062284911yescharacteristic
246C22#1062284911yescharacteristic
247C22#1062285311yescharacteristic
248C4—22no—
249C4—22no—
250C4—22no—
251C4—22no—
252C4—21no—
253C4—21no—
254C4—22no—
255C4—41no—
256C4—44no—
257C4—82no—
258C2#1306694011yescharacteristic
259C2#1306700711yescharacteristic
260C2#1306701111yescharacteristic
261C2#1306716311yescharacteristic
262C2#1306716711yescharacteristic
263C2#1306725411yescharacteristic
264C2#1306733311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊Q8C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊Q8D11
hypocenterC11#7604
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
22. C11×C4⋊Q8C8semidirect
149. C4⋊Q8C11⋊C8semidirect
208. C11#7604semidirect

Maximal subgroups

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

subgroupindex
#130687592
#130664392
C4×C11×C4⋊Q82
#760411