Finite Group Databasebeta

← #14664451

Subgroups — #14664451

Order 2816.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068693C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic
3#13066616C214yesmaximal
4C11×#2621C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C11×#117C2211yescharacteristic
8C11×#398—21no—
9C11×#398C412yescomplemented
10C11×#397—21no—
11C11×#397C2212yes—
12C11×#391—21no—
13C11×#382C411yescharacteristic, complemented
14#10622824—21no—
15#10622539—21no—
16#10622166—21no—
17#10622164—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C11×C22⋊Q8—44no—
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—22no—
39C11×#95—21no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95C2×C412yes—
43C11⋊#95—41no—
44C11⋊#95—41no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—41no—
47#66867—41no—
48#11801—111nomaximal, Sylow
49C24×C11C2×D411yescharacteristic
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—44no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—44no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C22⋊Dic11—42no—
81C22⋊Dic11—42no—
82C2×C11⋊C8—42no—
83#2621D1111yescharacteristic
84#1820—111no—
85#1464—111no—
86#1344—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11AGL(1,ℤ/8)12yes—
93Q8×C11—82no—
94Q8×C11—82no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11#9911yescharacteristic
118C2×Dic11—82no—
119C2×Dic11—82no—
120C2×Dic11—82no—
121C11⋊C8—82no—
122C2×C4⋊Q8Dic1111yescharacteristic, complemented
123C2×C22⋊Q8—21no—
124C2×#117C2×D1111yescharacteristic
125#432—221no—
126#398—21no—
127#398Dic1112yescomplemented
128#397—21no—
129#397C2×D1112yes—
130#391—21no—
131#382Dic1111yescharacteristic, complemented
132#381—221no—
133#342—112no—
134#342—221no—
135#324—221no—
136#323—112no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—22no—
140C22×C11—42no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11—81no—
144C22×C11C2×#9911yescharacteristic
145C22×C11#41811yescharacteristic
146C22×C11#42111yescharacteristic
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—82no—
155C4×C11—82no—
156Dic11—162no—
157C22×Q8—21no—
158C23×C4C22⋊D1111yescharacteristic
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C22⋊Q8—44no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×Dic1112yes—
168C2×C4⋊C4C2×Dic1111yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C22⋊C4—22no—
171C2×C22⋊C4—222no—
172C2×C22⋊C4C22⋊D1111yescharacteristic
173C2×C22⋊C4C22×D1111yescharacteristic
174C2×C42C2×Dic1111yescharacteristic
175C2×C42C22⋊D1111yescharacteristic
176C4⋊C8—441no—
177C22⋊C8—222no—
178#97—441no—
179#95—21no—
180#95—22no—
181#95—22no—
182#95—441no—
183#95—441no—
184#95C2×Dic1112yes—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11—42no—
188C2×C11#151011yescharacteristic
189C2×C11#212311yescharacteristic
190C2×C11#212911yescharacteristic
191C24C2×C22⋊D1111yescharacteristic
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C2×Q8—41no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—41no—
202C22×C4—442no—
203C22×C4C22⋊Dic1111yescharacteristic
204C22×C4C22⋊Dic1111yescharacteristic
205C22×C4C22⋊Dic1111yescharacteristic
206C22×C4C22⋊Dic1111yescharacteristic
207C22×C4C22×Dic1111yescharacteristic
208C22×C4C2×C22⋊D1111yescharacteristic
209C2×C8—442no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C4⋊C4—42no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—44no—
219C22⋊C4—442no—
220C22⋊C4—442no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C11#1180111yescharacteristic, complemented, Sylow
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23#6698512yes—
231C23C2×C22⋊Dic1111yescharacteristic
232Q8—82no—
233Q8—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—882no—
256C2×C4—882no—
257C2×C4—882no—
258C2×C4#6689811yescharacteristic
259C2×C4#6689811yescharacteristic
260C8—882no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22#1062282811yescharacteristic
269C22C2×#6689811yescharacteristic
270C22#1062284911yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—82no—
279C4—82no—
280C4—1762no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1306714511yescharacteristic
285C2#1307027011yescharacteristic
286C2#1307029111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2621C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2621D11
hypocenterC11#11801
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
9. C11×#398C4semidirect
13. C11×#382C4semidirect
122. C2×C4⋊Q8Dic11semidirect
127. #398Dic11semidirect
131. #382Dic11semidirect
225. C11#11801semidirect

Maximal subgroups

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

subgroupindex
#130686932
#130669502
#130666162
C11×#26212
#1180111