Finite Group Databasebeta

← #14664066

Subgroups — #14664066

Order 2816.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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#13068349C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066640C214yesmaximal
4C11×#2628C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66979—21no—
8C11×#400C412yescomplemented
9C11×#399C2212yes—
10C11×#395—21no—
11C11×#393—21no—
12C11×#389—21no—
13C11×#382C411yescharacteristic, complemented
14C11×#380—21no—
15#10622538—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×#117—41no—
25C11×#117—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—22no—
38#66979—24no—
39#66979—42no—
40C2×C4⋊Dic11—41no—
41C2×C4×Dic11—41no—
42C11×#95—22no—
43C11×#95—21no—
44C11×#95—22no—
45C11×#95C2×C412yes—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—41no—
48C4×C11⋊C8—41no—
49#11718—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C2×Q8×C11—42no—
52C2×Q8×C11—82no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11SD1612yes—
63C22×C4×C11Q1612yes—
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—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—82no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—82no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C22⋊Dic11—24no—
82C22⋊Dic11—42no—
83C4⋊Dic11—44no—
84C4×Dic11—44no—
85C2×C11⋊C8—42no—
86#2628D1111yescharacteristic
87#1740—111no—
88#1458—111no—
89#1352—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11C2×C22⋊C411yescharacteristic
95C23×C11C2×SD1611yescharacteristic
96C23×C11C2×Q1611yescharacteristic
97Q8×C11—84no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11#9911yescharacteristic
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#10312yes—
121C2×C4×C11#10312yes—
122C2×C4×C11#10412yes—
123C2×Dic11—44no—
124C2×Dic11—82no—
125C2×Dic11—82no—
126C11⋊C8—82no—
127C2×C4⋊Q8Dic1111yescharacteristic, complemented
128C2×#117—221no—
129C2×#117C2×D1111yescharacteristic
130#431—221no—
131#400Dic1112yescomplemented
132#399C2×D1112yes—
133#395—21no—
134#393—21no—
135#389—21no—
136#382Dic1111yescharacteristic, complemented
137#380—21no—
138#342—112no—
139#342—221no—
140#324—221no—
141#323—112no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—81no—
151C22×C11C2×#9911yescharacteristic
152C22×C11C2×#10311yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C4×C11—22no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—82no—
160C4×C11—82no—
161C4×C11#32812yes—
162C4×C11#32812yes—
163Dic11—84no—
164C22×Q8—21no—
165C23×C4C22⋊D1111yescharacteristic
166C4⋊Q8—41no—
167C4⋊Q8—41no—
168#117—41no—
169#117—41no—
170#117—224no—
171#117—442no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—441no—
176C2×C4⋊C4C2×Dic1112yes—
177C2×C4⋊C4C2×Dic1111yescharacteristic
178C2×C4⋊C4C22⋊D1111yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—222no—
181C2×C22⋊C4C22⋊D1111yescharacteristic
182C2×C22⋊C4C22×D1111yescharacteristic
183C2×C42—441no—
184C2×C42C2×Dic1111yescharacteristic
185C2×C42C22⋊D1111yescharacteristic
186C4⋊C8—441no—
187C22⋊C8—222no—
188C4×C8—441no—
189#95—22no—
190#95—21no—
191#95—22no—
192#95C2×Dic1112yes—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—41no—
196C2×C11—41no—
197C2×C11C2×#32811yescharacteristic
198C2×C11#212311yescharacteristic
199C2×C11#212811yescharacteristic
200C24C2×C22⋊D1111yescharacteristic
201C2×Q8—42no—
202C2×Q8—82no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—442no—
209C22×C4#432512yes—
210C22×C4#432612yes—
211C22×C4C22⋊Dic1111yescharacteristic
212C22×C4C22⋊Dic1111yescharacteristic
213C22×C4C22⋊Dic1111yescharacteristic
214C22×C4C22⋊Dic1111yescharacteristic
215C22×C4C22×Dic1111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217C2×C8—442no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C4⋊C4—444no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—82no—
229C22⋊C4—224no—
230C22⋊C4—442no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—444no—
236C11#1171811yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23C2×#432511yescharacteristic
242C23C2×#432611yescharacteristic
243C23C2×C22⋊Dic1111yescharacteristic
244Q8—84no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—444no—
266C2×C4—882no—
267C2×C4—882no—
268C2×C4#6689811yescharacteristic
269C2×C4#6689811yescharacteristic
270C2×C4#6689912yes—
271C2×C4#6689912yes—
272C2×C4#6690112yes—
273C8—882no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22C2×#6689811yescharacteristic
284C22C2×#6689911yescharacteristic
285C22C2×#6690111yescharacteristic
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4—884no—
294C4#1062217612yes—
295C4#1062217612yes—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2C2×#1062217611yescharacteristic
301C2#1307027011yescharacteristic
302C2#1307028811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2628C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2628D11
hypocenterC11#11718
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
8. C11×#400C4semidirect
13. C11×#382C4semidirect
127. C2×C4⋊Q8Dic11semidirect
131. #400Dic11semidirect
136. #382Dic11semidirect
236. C11#11718semidirect

Maximal subgroups

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

subgroupindex
#130683492
#130669302
#130666402
C11×#26282
#1171811