Finite Group Databasebeta

← #14648285

Subgroups — #14648285

Order 2816.

356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077718C211yesmaximal, characteristic
2#13067407C211yesmaximal, characteristic
3#13067407C211yesmaximal, characteristic
4#13067281C211yesmaximal, characteristic
5#13066449C211yesmaximal, characteristic
6#13066449C211yesmaximal, characteristic
7C11×#1994C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C43×C11C2211yescharacteristic
11#10622637—21no—
12#10622637—21no—
13Q8×C11⋊C8—21no—
14Q8×C11⋊C8—21no—
15#10622613—22no—
16#10622538C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C11×#339—22no—
21#10622185C411yescharacteristic, complemented
22#10622185C411yescharacteristic, complemented
23#10622185C411yescharacteristic, complemented
24#10622185C411yescharacteristic, complemented
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×#125Q812yes—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C11×#117D412yes—
38C2×C42×C11—21no—
39C2×C42×C11—21no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C22⋊(C11⋊C8)—21no—
45C22⋊(C11⋊C8)—21no—
46C22⋊(C11⋊C8)—21no—
47C22⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)C2×C411yescharacteristic
51C4⋊(C11⋊C8)C2×C411yescharacteristic
52C4⋊(C11⋊C8)C2×C411yescharacteristic
53C4⋊(C11⋊C8)C2×C411yescharacteristic
54C4⋊(C11⋊C8)D411yescharacteristic
55C4⋊(C11⋊C8)D411yescharacteristic
56C4⋊(C11⋊C8)D411yescharacteristic
57C4⋊(C11⋊C8)D411yescharacteristic
58#66867—22no—
59C4×C11⋊C8—22no—
60C4×C11⋊C8—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#8936—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C11×M16—42no—
72C2×C8×C11—41no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4C4⋊C412yes—
78C11×C4⋊C4C4⋊C412yes—
79C11×C22⋊C4—22no—
80C42×C11—22no—
81C42×C11—22no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11C22×C411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×Q811yescharacteristic
91C2×C11⋊C8—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99#2986—111no—
100#1994D1111yescharacteristic
101#1574—111no—
102#1574—111no—
103#1544—111no—
104#1276—111no—
105#1276—111no—
106C23×C11#12311yescharacteristic
107Q8×C11—41no—
108Q8×C11—41no—
109Q8×C11—41no—
110Q8×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11C2×C4⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C8×C11—81no—
129C11⋊C8—41no—
130C11⋊C8—41no—
131C11⋊C8—41no—
132C11⋊C8—41no—
133C11⋊C8—41no—
134C11⋊C8—41no—
135C11⋊C8—41no—
136C11⋊C8—41no—
137#533C2×D1111yescharacteristic
138#446—221no—
139#446—221no—
140C8×Q8—221no—
141C8×Q8—221no—
142#433—222no—
143#431—111no—
144#431—111no—
145#431—111no—
146#431—111no—
147#423C2×D1111yescharacteristic
148C43C2×D1111yescharacteristic
149#339—22no—
150#335—221no—
151#335—221no—
152#334—221no—
153#334—221no—
154#332—111no—
155#332—111no—
156#332—111no—
157#332—111no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38511yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—44no—
166C4×C11—42no—
167C4×C11—42no—
168C4×C11#44311yescharacteristic
169C4×C11#44311yescharacteristic
170C4×C11#44411yescharacteristic
171C4×C11#44411yescharacteristic
172C4×C11#45411yescharacteristic
173C4×C11#45611yescharacteristic
174C2×M16—21no—
175C4⋊Q8C4×D1111yescharacteristic
176C4⋊Q8C4×D1111yescharacteristic
177#125Dic2212yes—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117C22⋊D1112yes—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—111no—
190C4⋊C8—111no—
191C4⋊C8—111no—
192C4⋊C8—111no—
193C4⋊C8—111no—
194C4⋊C8—111no—
195C4⋊C8—111no—
196C4⋊C8—111no—
197C4⋊C8—222no—
198C4⋊C8—222no—
199C22⋊C8—221no—
200C22⋊C8—221no—
201C22⋊C8—221no—
202C22⋊C8—221no—
203#97—222no—
204C4×C8—222no—
205C4×C8—221no—
206C4×C8—221no—
207C4×C8—221no—
208C4×C8—221no—
209C2×C11—41no—
210C2×C11#185711yescharacteristic
211C2×C11#186611yescharacteristic
212C2×C11#186611yescharacteristic
213C2×Q8—21no—
214C2×Q8—21no—
215C22×C4—41no—
216C22×C4#434111yescharacteristic
217C22×C4#434111yescharacteristic
218C22×C4C2×C22⋊D1111yescharacteristic
219M16—42no—
220C2×C8—41no—
221C2×C8—221no—
222C2×C8—221no—
223C2×C8—221no—
224C2×C8—221no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—221no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4Dic11⋊C412yes—
234C4⋊C4Dic11⋊C412yes—
235C22⋊C4—22no—
236C42—22no—
237C42—22no—
238C42—22no—
239C42—22no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42C2×Dic2211yescharacteristic
244C42C2×C4×D1111yescharacteristic
245C42D4×D1111yescharacteristic
246C42D4×D1111yescharacteristic
247C11#893611yescharacteristic, complemented, Sylow
248C23#6698811yescharacteristic
249Q8—41no—
250Q8—41no—
251Q8—41no—
252Q8—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4#6693111yescharacteristic
265C2×C4#6693111yescharacteristic
266C2×C4(C22⋊D11)⋊C411yescharacteristic
267C2×C4(C22⋊D11)⋊C411yescharacteristic
268C2×C4C2×Dic11⋊C411yescharacteristic
269C2×C4#6699011yescharacteristic
270C8—81no—
271C8—441no—
272C8—441no—
273C8—441no—
274C8—441no—
275C8—441no—
276C8—441no—
277C8—441no—
278C8—441no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22#1062255911yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—44no—
287C4—42no—
288C4—42no—
289C4#1062243611yescharacteristic
290C4#1062243611yescharacteristic
291C4#1062243711yescharacteristic
292C4#1062243711yescharacteristic
293C4#1062267511yescharacteristic
294C4#1062270811yescharacteristic
295C2—41no—
296C2#1306883011yescharacteristic
297C2#1306888911yescharacteristic
298C2#1306888911yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#385
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1994D11
hypocenterC11#8936
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
21. #10622185C4semidirect
22. #10622185C4semidirect
23. #10622185C4semidirect
24. #10622185C4semidirect
247. C11#8936semidirect

Maximal subgroups

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

subgroupindex
#130777182
#130674072
#130672812
#130664492
C11×#19942
#893611